Thread: Length Contraction of Space Between Objects

You continue to avoid dealing with the trap you have put yourself in, colonel! And for you, this post is lesson #101!

In post #58 I wrote uncontroversially:

If we now have two objects e.g. spaceships, at distance x from one another and traveling at the same speed relative to a third observer (say on earth), would the earth observer also consider the distance between the two spaceships to be x (as implied by your above discussion) or less than x (according to applying the LTs)?

From your reply on post #61.

Yes the spaceships contract for the third observer but the distance between them does not.

Aha! Thank you cinci - the answer I was looking for!

cinci: He will find the distance to be whatever he measures it to be. Look at it this way . The ships are at two points in the sky; the distance between these two points doesn't change because the spaceships are there.

& post #64

TFOLZO: If I measure this distance from another spaceship moving relative to earth & the two commoving spaceships this distance will remain the same - i.e. it exists objectively, independently of observer motion.

cinci: No, we already said that the distance between the ships when measured by observers on the ships is contracted. You cannot ascribe measurements made by one observer to a different observer if they have relative motion. Each observer must make his own measurements and he must believe them to be true.

That highlighted statement is NOT correct cinci… etc.

Now that everyone can see your inner inconsistency we have to decide what sort of colonel you are! This is because the two spaceships are mutually at rest - hence there can be NO length contraction that they can observe between them. Nor, as you state, does the 3rd (earth) observer see any length contraction between the spaceships! Hence:

Are you the Colonel of KFC fame i.e. Kinematically Fried Concepts like Minkowski Diagrams that freeze the future into a predetermined 3D outcome in 4D spacetime?

Or just the Colonel who merely denies that anyone has ever successfully escaped from Relativity-Stalag 13?

TFOLZO

PS: Or better still, develop your scenario with S1, S2 & O - but this time by moving some of them around!

Originally Posted by TFOLZO

I agree Jilan...
...but just this weekend I passed thru a place called Jilakin Rock - but I doubt that you have relatives living there merely because it has that name!

TFOLZO

Apparently there is a village in Afghanistan called Jilan, but I don't think I have any relatives there either.

Isn't EVERYTHING relative?

Originally Posted by Gerry Nightingale

In reply to SpeedFreek, re: your post #80.

Do you mean the "forum as whole" or just this thread? Or are you saying you just want "book-thumpers" on the entire site, people who never write anything except endless "quotes"

from "Wiki" (knowing full well there is zero chance of being refuted, and thus not risking their "internet phys. sites" credibility)

You're implying with this comment that there is something wrong with quoting a text or Wiki etc. when in fact there's no problem whatsoever. Physics is a very demanding and exact science. Look how long some of those Wiki entries are and keep in mind that people are often asking the same questions which means we have to give the same answers. It's very difficult to provide details and derivations to the answers that need to be given. Also it's better to quote something since people in forum don't trust other members as far as they can throw them whereas its difficult to claim that a noted physicist who's an expert in a field is spouting nonsense in his text. Also typing equations is difficult using Latext. And it should be noted that most physicists don't keep derivations in their minds. The learn them by following them to make sure they're right and then they know that they can always trust it. However different authors give different derivations. In this forum there is a rule where we must he intellectually honest and give the source of what we post here. So what's the point of not quoting? Just to make more work for ourselves to impress others with our ability to work off the top of our heads? I don't think so.

Originally Posted by SinceYouAsked

It is true that no one really knows what time is.

I do. Lots of people do.

Originally Posted by SinceYouAsked

Many great physicists today debate whether time is real, and/or what it is.

Many pop-science "celebrity physicists" peddle books talking at length about the mystery of time. Only there is no mystery. Open up a clock and you don't see some river of time flowing through it. A clock doesn't literally "measure the flow of time" like it's some kind of cosmic gas meter. It just features some kind of regular cyclical motion. It "clocks this up" and shows you some cumulative display that you call the time. If the little hand and the big hand is pointing straight up, you say it's noon. If they move full circle you say it's midnight. If they move full circle again you say it's noon again. Then you say "a day has passed". But it didn't actually pass. Buses pass. Footballers pass. The day didn't pass you by like it was something moving. But the Earth did turn, your heart did beat, blood moved round your body, your chest heaved as you breathed, electrochemical signals moved through your brain, the cogs in the clock's "movement" turned, the clock ticked. Things moved. And in the science fiction movies, when some guy has some gizmo that stops time, what it really stops is motion.

Originally Posted by SinceYouAsked

The relative nature of the measurement of time as a function of relative velocity, is a mathematical requirement given the 2 postulates of relativity true. While the relativistic effects seems bizarre in relation to our everyday experience...

They aren't bizarre at all. Not when you understand it. Make sure you read The Other Meaning of Special Relativity by Robert Close. No matter how fast you go, the speed of light always looks the same because of the wave nature of matter.

Dear Farsight & SYA,

You're getting off the point of the thread here. Please start another to debate the complicated issue of time.

TFOLZO

Originally Posted by SinceYouAsked

It is true that no one really knows what time is. Many great physicists today debate whether time is real, and/or what it is. That said, what we do know is that we quantify time very well. Add, without that which we call time, we could calculate nothing. Yet, great physicists continue working on it.

That doesn't mean that no one knows that time really is. What's debatable is the definition. But that's a world apart from not knowing what it is. See how my friend defined time at
http://users.wfu.edu/brehme/time.htm. He's a well-known relativist (retired). He's the one who defined the Brehme diagram

Some Applications of the Brehme Diagram
http://www.farmingdale.edu/faculty/p...ty/Ch06Rel.pdf

Hi Physicist,

TFOLZO is right, we should not discuss the definition of time, a philosophical question at present, in this thread. Yet, it seems strange to discuss length-contraction (which requires time) knowing that the great physicists of the world have many differing opinions as to what time really is, many saying we simply don't know yet. But until a better definition of time comes along, we will continue to accept it a dimension of its on on equal footing with space, defined in the way it is ... a dimension that allows for change, with a progression in the direction of higher entropy. BTW, I brushed through your friend's paper, and while he is a decent writer, I would have some issues with some of what he's written. But then, that happens everyday amongst the world's leading physicists, and regarding the definition of time, so. Just to mention one ...

your friend: "Why is the lapse of physical time at the coach greater than that at the runner? That is, why is Eq. (2) true? We don't know."

Relativity explains what "relative time" is, which when expressed in terms of Minkowski 4 dimensional spacetime "does answer the question above" more conveniently. However, that does not help in explaining what "proper time" is. When answering the question what is time, we are truly asking what is proper time?. But the critical questions are ... why does (proper) time pass us by at seemingly steady rate? The great physicists of today agree in that no one really knows the definitive answer to that question. There's a Nobel prize awaiting he who does answer it, to the consensus of the leading scientific community at large. Julian Barbour is one such candidate with his block universe theory (called Platonia), and he doesn't even believe time is a real dimension, but rather something man made by the human consciousness. He may be right,, he may be wrong. But anyways ...

Per SR, length-contraction may be explained in terms of "relative orientation differentials of spacetime systems within the 4d spacetime continuum". time in conjunction with the path lengths through fused 4D spacetime, even though we do not know precisely what time itself is and why it passes us by.

Length-contraction is the relative comparison of spatial separation between a pair of spacetime events, for each of 2 differing inertial POVs. If the 2 events are defined by simultaneous events located at points at rest in frame A, then frame B is length contracted relatively per A, but the events are not simultaneous per B. If the 2 events are defined by simultaneous events located at points at rest in frame B, then frame A is length contracted relatively per B, but the events are not simultaneous per A. Minkowski's geometric model explains the why of that much more clearly.

Thank You,
SinceYouAsked

Originally Posted by TFOLZO

Are S1 & S2 mutually at rest or are they approaching on a collision course? Since if the latter is the case they will have to do their distance measurement simultaneously in order to get comparable answers!

The two spaceships are on a collision course. That is why I asked cincirob what time the spaceships were supposed to measure the distance between themselves. At first he didn't want to answer, but then he said something about they should just measure it at t=0.000 or something. So I guess he forgot about ROS already.

Originally Posted by Farsight

I do. Lots of people do.

Many pop-science "celebrity physicists" peddle books talking at length about the mystery of time. Only there is no mystery. Open up a clock and you don't see some river of time flowing through it. A clock doesn't literally "measure the flow of time" like it's some kind of cosmic gas meter. It just features some kind of regular cyclical motion. It "clocks this up" and shows you some cumulative display that you call the time. If the little hand and the big hand is pointing straight up, you say it's noon. If they move full circle you say it's midnight. If they move full circle again you say it's noon again. Then you say "a day has passed". But it didn't actually pass. Buses pass. Footballers pass. The day didn't pass you by like it was something moving. But the Earth did turn, your heart did beat, blood moved round your body, your chest heaved as you breathed, electrochemical signals moved through your brain, the cogs in the clock's "movement" turned, the clock ticked. Things moved. And in the science fiction movies, when some guy has some gizmo that stops time, what it really stops is motion.

They aren't bizarre at all. Not when you understand it. Make sure you read The Other Meaning of Special Relativity by Robert Close. No matter how fast you go, the speed of light always looks the same because of the wave nature of matter.

Well, that's one view, anyway. But it is by no means cut-and-dried. It is not the consensus view.

There definitely IS a mystery about time. It is generally acknowledged that we do not have a "theory of time" yet, and anyone who claims the contrary is going all "Michio Kaku" on us. The above is, at best, speculation.

Originally Posted by SpeedFreek

Well, that's one view, anyway. But it is by no means cut-and-dried. It is not the consensus view.

There definitely IS a mystery about time. It is generally acknowledged that we do not have a "theory of time" yet, and anyone who claims the contrary is going all "Michio Kaku" on us. The above is, at best, speculation.

There's a book out called From Eternity to Here: The Quest for the Ultimate Theory of Time which I plan on buying soon. Is this the kind of thing you mean?

What do you mean regarding "Theory of time"? Since when do simple concepts have theories? To me that's like saying that we don't have a theory of momentum yet.

What is the theory of momentum? A theory is something that can be derived through postulates and logical reasoning leading to a conclusion. What are the postulates you start out with? What logical reasoning is used? What is the conclusion of that reasoning? If its that momentum is conserved then it's a law. I.e. have you ever heard of the law of conservation of momentum?

I mean we do not understand how time works, what it is, or whether it actually even exists. There are many different views on this, but no consensus.

Originally Posted by SpeedFreek

I mean we do not understand how time works, what it is, or whether it actually even exists. There are many different views on this, but no consensus.

This is getting off subject but I want to discuss this so I'm going to create a new thread on it .... after I put a load of laundry in.

Originally Posted by JTyesthatJT

The two spaceships are on a collision course. That is why I asked cincirob what time the spaceships were supposed to measure the distance between themselves. At first he didn't want to answer, but then he said something about they should just measure it at t=0.000 or something. So I guess he forgot about ROS already.

Seems Cinci once more proves he simply doesn't know what he is talking about, because he doesn't know anything about special relativity.
As with the rolling wheel was the case he is even incapable of communicating -or getting agreement on- the correct set-up of the exercise. Pathetic.

VeeDee: Seems Cinci once more proves he simply doesn't know what he is talking about, because he doesn't know anything about special relativity.
As with the rolling wheel was the case he is even incapable of communicating -or getting agreement on- the correct set-up of the exercise. Pathetic.

cinci: Let's see.........oh yes, you're the guy who doesn't know the difference between a measurement and a Lorentz transformation.

JT: The two spaceships are on a collision course. That is why I asked cincirob what time the spaceships were supposed to measure the distance between themselves. At first he didn't want to answer, but then he said something about they should just measure it at t=0.000 or something. So I guess he forgot about ROS already.

cinci: What time was it when you transformed the wheel to the road?

Originally Posted by cincirob

VeeDee: Seems Cinci once more proves he simply doesn't know what he is talking about, because he doesn't know anything about special relativity.
As with the rolling wheel was the case he is even incapable of communicating -or getting agreement on- the correct set-up of the exercise. Pathetic.

cinci: Let's see.........oh yes, you're the guy who doesn't know the difference between a measurement and a Lorentz transformation.

Very interesting comment from a guy who has proved over and over again he doesn't know how Lorentz Transformations work.
Tell us cinci: how about the two spaceships? Making up your mind? Or once more playing games? Boring, you know.

Hey cinci,

how about dealing with question #101...

Originally Posted by cincirob

JT: The two spaceships are on a collision course. That is why I asked cincirob what time the spaceships were supposed to measure the distance between themselves. At first he didn't want to answer, but then he said something about they should just measure it at t=0.000 or something. So I guess he forgot about ROS already.

cinci: What time was it when you transformed the wheel to the road?

...instead of being distracted by trivial sniping i.e. the piratical SYAAAAARRGH & his uncouth rolling-wheel band of cutthroat logicians!

TFOLZO

Originally Posted by cincirob

JT: The two spaceships are on a collision course. That is why I asked cincirob what time the spaceships were supposed to measure the distance between themselves. At first he didn't want to answer, but then he said something about they should just measure it at t=0.000 or something. So I guess he forgot about ROS already.

cinci: What time was it when you transformed the wheel to the road?

You have S1 and S2 on a collision course so that the distance between them varies with time. And you can't tell us what time you want them to measure the distance between themselves, so that they can compare that distance with X? Great work, cinci.

Originally Posted by VeeDee

Seems Cinci once more proves he simply doesn't know what he is talking about, because he doesn't know anything about special relativity.
As with the rolling wheel was the case he is even incapable of communicating -or getting agreement on- the correct set-up of the exercise. Pathetic.

Yep. And he even made some comment about, "or just use length contraction," even though he hasn't even told us yet what 'lengths' he is trying to measure.

Probably the easier scenario would be to have the point-like spaceships collide at x=0.0 at time t=0.0, as measured by the O frame. If we let spaceship S1 use primed variables, we can say S1's clock displayed time t'=0 at the moment of impact. Likewise, if we let spaceship S2 use double-primed variables, we can say S2's clock displayed time t''=0 at the moment of impact. Now we only have to choose some negative time, say t=-1.0 as measured by the O frame, when the spaceships were separated by some distance D.

Let's say the velocities are v1=+0.6c and v2=-0.6c as measured by the O frame. So, at time t=-1.0 the locations of the two spaceships are x=vt=-0.6 and x=vt=+0.6 respectively. That makes the distance between the two spaceships:
D = 0.6 - (-0.6) = 1.2
as measured by the O frame at time t=-1.0.

Now frame O can Lorentz transform those known coordinates of spaceship S1 to that spacehip's own frame, as follows:
t' = γ(t - (vx / c²)) = -0.8
x' = γ(x - vt) = 0.0
Where:
γ = 1 / √(1 - v²/c²) =1.25

And frame O can Lorentz transform those known coordinates of spaceship S2 to that spacehip's own frame, as follows:
t'' = γ(t + (vx / c²)) = -0.8
x'' = γ(x + vt) = 0.0
Where:
γ = 1 / √(1 - v²/c²) =1.25

According to S1, the velocity of S2 is the composed velocity:
u' = (v2 - v1) / (1 - (v2*v1 / c²)) = -0.882c
Thus, when S1's own clock displays t'=-0.8 it would say that spaceship S2 would be located at x'=u't'=0.705.
Therefore the distance between the spaceships would be:
D1 = 0.705 - 0.0 = 0.705.
as measured by the S1 frame at time t'=-0.8.

And according to S2, the velocity of S1 is the composed velocity:
u'' = (v1 - v2) / (1 - (v1*v2 / c²)) = 0.882c
Thus, when S1's own clock displays t''=-0.8 it would say that spaceship S1 would be located at x''=u''t''=-0.705.
Therefore the distance between the spaceships would be:
D2 = 0.0 - (-0.705) = 0.705.
as measured by the S2 frame at time t''=-0.8.

As you can see, this does not have anything to do with "the length contraction formula" which cincirob said could be used. When, oh when, will cincirob ever learn?

Off topic, but I think if any of you haven't read Markus' warning thread, you may want to leave personal jabs out of the posts. He is obviously tiring of it.

JT, Cinci will never accept your x' and t' values as being measured values because you used Lorentz transformations.

I bet Cinci will come up with a jazzy contraction formula scenario that will blow our socks off. And be prepared to reformulate your exercise set-up. And so on, and so on...

I give up, but thanks Jilan, I did try.

VeeDee: Very interesting comment from a guy who has proved over and over again he doesn't know how Lorentz Transformations work.
Tell us cinci: how about the two spaceships? Making up your mind? Or once more playing games? Boring, you know.

cinci: You have seen my analysis of the wheel so you know better. Find some other song to sing; you are what's boring.

I'll deal with the spaceships when I choose and it isn't for you anyway, it's for TFOLZO. And only an idiot would lay it out using the Lorentz transformation analysis for TFOLZO; he doesn't believe the theory or the transformations..

By the way, have you figured out the difference between measurements and the Lorentz transformations yet? Until you do, I'm pretty sure you won't understand the spaceships.

JT: Probably the easier scenario would be to have the point-like spaceships collide at x=0.0 at time t=0.0, as measured by the O frame.

cinci: Well I see you figured out what time it is. Want to admit now that it was a dumb question?

Originally Posted by cincirob

JT: Probably the easier scenario would be to have the point-like spaceships collide at x=0.0 at time t=0.0, as measured by the O frame.

cinci: Well I see you figured out what time it is.

So you want S1 to measure the distance to S2 at t=0.0 when they are colliding?!?!? Or course the distance would be 0.0 at that time!! Was that your intention?

Originally Posted by cincirob

cinci: Want to admit now that it was a dumb question?

No, it is not a dumb question. Your scenario asks S1 to measure the distance to S2, but it does not tell us WHAT TIME to make that measurement. Since S1 and S2 are in constant motion, it is rather important that you tell us what time S1 should make that measurement, don't you think?

If you read and understood my post, you would see that when the clock of O displays t=-1.0, the distance between S1 and S2 is D=1.2 according to O, and the time on S1's own clock displays t'=-0.80 at that time. Since S1 measures the velocity of S2 as the composed velocity u'=0.882c, that means S1 measures the distance between the spaceships as D1=0.705 at that time. Is that the time arrangement that you wanted me to use? Because that does not match the length contraction equation that you said could be used.

JT: No, it is not a dumb question. Your scenario asks S1 to measure the distance to S2, but it does not tell us WHAT TIME to make that measurement. Since S1 and S2 are in constant motion, it is rather important that you tell us what time S1 should make that measurement, don't you think?

cinci: My scenario didn't ask anything. I didn't define any numbers.

I haven't bothered to look at your analysis but I'll assume you did it right. So you apparently didn't need for me to tell you what time it is.

It was a dumb question.

Originally Posted by cincirob

JT: No, it is not a dumb question. Your scenario asks S1 to measure the distance to S2, but it does not tell us WHAT TIME to make that measurement. Since S1 and S2 are in constant motion, it is rather important that you tell us what time S1 should make that measurement, don't you think?

cinci: My scenario didn't ask anything. I didn't define any numbers.

I haven't bothered to look at your analysis but I'll assume you did it right. So you apparently didn't need for me to tell you what time it is.

It was a dumb question.

You refused to define the time when S1 was supposed to measure the distance to S2. So, I had to assume you meant for O to determine the time on S1's clock at the same time O made his own measurement, and then S1 measures the distance to S2 at that particular time. I have no idea if that is what you wanted to do, because you did not specify it at all.

Calling it a "dumb" question is probably bordering on a violation of the site's new rules. I hope you don't get banned, or anything, lol. J/K

Originally Posted by VeeDee

JT, Cinci will never accept your x' and t' values as being measured values because you used Lorentz transformations.

I don't see why that's funny.

One can certainly perform a measurement to verify a value in a coordinate system, but a transformation is not a measurement. It takes a value, which may have been produced from measurement, to another value. That's the great thing about relativity theory, it shows what is fixed in physics and allows us to determine the value of a coordinate in that system without having to perform a specific measurement of that coordinate in that system.

Originally Posted by PhysBang

I don't see why that's funny.

One can certainly perform a measurement to verify a value in a coordinate system, but a transformation is not a measurement. It takes a value, which may have been produced from measurement, to another value. That's the great thing about relativity theory, it shows what is fixed in physics and allows us to determine the value of a coordinate in that system without having to perform a specific measurement of that coordinate in that system.

In JT's spaceship exercise that 'other value' is what the 'other' frame (=spaceship frame) reads on his clock or ruler.
You can get picky now by saying that the spaceship passenger actually does not have to make a physical measurement to obtain those values, because he can calcultate them with LT. ... If that makes you happy, so be it.

PhysBang: I don't see why that's funny.

cinci: It isn't funny; it's pitiful. VeeDee has an irrational need to say I'm wrong about everything whether I am or not.

JT: You refused to define the time when S1 was supposed to measure the distance to S2. So, I had to assume you meant for O to determine the time on S1's clock at the same time O made his own measurement, and then S1 measures the distance to S2 at that particular time. I have no idea if that is what you wanted to do, because you did not specify it at all.

cinci: I didn't want anything at all. I didn't ask you anything.

JT: Calling it a "dumb" question is probably bordering on a violation of the site's new rules. I hope you don't get banned, or anything, lol.

cinci: You could have assumed time = 0 for any clock in the problem and it will all work out. You know, RELATIVELY.

If that comment would get me banned, you and VeeDee would have been gone a long time ago. After all, I didn't say you were dumb. But how about I retract the "dumb question" statement and just say you wouldn't have asked it if you understood relativity.

Originally Posted by cincirob

the distance between the ships when measured by observers on the ships is contracted.

Wat a big joke! As long as you write this kind of nonsense you will not convince me you understand anything about relativity.

Even Lorentz with his ether theory would not pretend something stupid like this.

All that can save you -but I wonder for how long- is telling me that it was a slip of the tongue.

I don't see why that's funny.

One can certainly perform a measurement to verify a value in a coordinate system, but a transformation is not a measurement. It takes a value, which may have been produced from measurement, to another value. That's the great thing about relativity theory, it shows what is fixed in physics and allows us to determine the value of a coordinate in that system without having to perform a specific measurement of that coordinate in that system.

VeeDee: In JT's spaceship exercise that 'other value' is what the 'other' frame (=spaceship frame) reads on his clock or ruler.
You can get picky now by saying that the spaceship passenger actually does not have to make a physical measurement to obtain those values, because he can calcultate them with LT. ... If that makes you happy, so be it.

cinci: Picky? You're the one who got picky. You jumped on a perfectly valid comment that I made. And now that several other people have agreed with me, why don't you just admit my comment was valid instead of all this weasel wording?

A measurement is a measurement and that is a very specific concept both in relativity and quantum mechanics.

Originally Posted by cincirob

cinci: You could have assumed time = 0 for any clock in the problem and it will all work out. You know, RELATIVELY.

Look, according to the frame of O, when O's own clock displays t=-1.000, the three clocks are simultaneously like this:
t = -1.000 (clock of O)
t' = -0.800 (clock of S1)
t'' = -0.800 (clock of S2)

So I chose to have O make his measurement at time t=-1.000 and I chose for S1 to make his measurement at time t'=-0.800.


But according to the frame of S1, when S1's own clock displays t=-0.800, the three clocks are simultaneously like this:
t = -0.640 (clock of O)
t' = -0.800 (clock of S1)
t'' = -0.376 (clock of S2)

So I could just as well have chosen to have O make his measurement at time t=-0.640 and S1 make his measurement at time t'=-0.800.


Considering that you refused to tell me which arrangement you thought was going to give a meaningful comparison between the measurements made in the three different frames, I just chose one arrangement randomly.

Originally Posted by cincirob

cinci: ...and it will all work out.

What do you mean it all works out? You said we could use the length contraction formula (LCF), but the measurements were:

D = 1.200 (distance measurement of 0)
D1 = 0.705 (distance measurement of S1)
D2 = 0.705 (distance measurement of S2)

For the case of v1=+0.600 and v2=-0.600. How do you figure this "all works out?"

Originally Posted by cincirob

cinci: But how about I retract the "dumb question" statement and just say you wouldn't have asked it if you understood relativity.

My question was designed to get you to think about relativity of simultaneity (ROS). The three different frames do not agree on simultaneity of events along the x axis, and you've got them all measuring the position of moving spaceships along the x axis. There are a number of different possible time arrangements, and you refuse to choose one that you think makes it all work out. Do you see the problems with this now?

JT: My question was designed to get you to think about relativity of simultaneity (ROS).

cinci: I'm not interested in what you want me to think about. I have my own things to think about.

JT: The three different frames do not agree on simultaneity of events along the x axis, and you've got them all measuring the position of moving spaceships along the x axis.

cinci: I haven't got them all doing anything. I described the situation from the perspective of O. I said nothing about the others except where they are relative to O and that they have some velocity relative to O.

JT: There are a number of different possible time arrangements, and you refuse to choose one that you think makes it all work out. Do you see the problems with this now?

cinci: I didn't suggest any particular time arrangement other than what is obvious from the simple description I posted. And no, I don't think there's a problem with it.

Originally Posted by cincirob

JT: The three different frames do not agree on simultaneity of events along the x axis, and you've got them all measuring the position of moving spaceships along the x axis.

cinci: I haven't got them all doing anything. I described the situation from the perspective of O. I said nothing about the others except where they are relative to O and that they have some velocity relative to O.

You said S1 can measure the distance between the spaceships as X1, and you said S2 can measure the distance between the spaceships as X2. That is fine, but since there is relative movement along the x axis, ROS says it is meaningless to compare those measurements to O's measurements. The three frames simply do not agree on simultaneity along the x axis.

Originally Posted by cincirob

JT: There are a number of different possible time arrangements, and you refuse to choose one that you think makes it all work out. Do you see the problems with this now?

cinci: I didn't suggest any particular time arrangement other than what is obvious from the simple description I posted. And no, I don't think there's a problem with it.

There is more than one possible time arrangement, and none of them are necessarily more obvious than the others, unless one does not think about ROS. In that case the most obvious time arrangement is probably the one I chose to use. When O makes his measurement, he notes the times on the clocks co-moving with S1 and S2. Then S1 and S2 are to make their measurements at the time their clocks display that time.

In the example I worked out with v1=0.6c and v2=-0.6c, the result is that O measures the distance as 1.200 but S1 and S2 both measure the distance as 0.705. If you are fine with that, then I am also. But the length contraction formula (LCF) won't give you that answer.

JT,
here is a Minkowski diagram of your exercise.

Originally Posted by JTyesthatJT

Probably the easier scenario would be to have the point-like spaceships collide at x=0.0 at time t=0.0, as measured by the O frame. If we let spaceship S1 use primed variables, we can say S1's clock displayed time t'=0 at the moment of impact. Likewise, if we let spaceship S2 use double-primed variables, we can say S2's clock displayed time t''=0 at the moment of impact. Now we only have to choose some negative time, say t=-1.0 as measured by the O frame, when the spaceships were separated by some distance D.

Let's say the velocities are v1=+0.6c and v2=-0.6c as measured by the O frame. So, at time t=-1.0 the locations of the two spaceships are x=vt=-0.6 and x=vt=+0.6 respectively. That makes the distance between the two spaceships:
D = 0.6 - (-0.6) = 1.2
as measured by the O frame at time t=-1.0.

Now frame O can Lorentz transform those known coordinates of spaceship S1 to that spacehip's own frame, as follows:
t' = γ(t - (vx / c²)) = -0.8
x' = γ(x - vt) = 0.0
Where:
γ = 1 / √(1 - v²/c²) =1.25

And frame O can Lorentz transform those known coordinates of spaceship S2 to that spacehip's own frame, as follows:
t'' = γ(t + (vx / c²)) = -0.8
x'' = γ(x + vt) = 0.0
Where:
γ = 1 / √(1 - v²/c²) =1.25

According to S1, the velocity of S2 is the composed velocity:
u' = (v2 - v1) / (1 - (v2*v1 / c²)) = -0.882c
Thus, when S1's own clock displays t'=-0.8 it would say that spaceship S2 would be located at x'=u't'=0.705.
Therefore the distance between the spaceships would be:
D1 = 0.705 - 0.0 = 0.705.
as measured by the S1 frame at time t'=-0.8.

And according to S2, the velocity of S1 is the composed velocity:
u'' = (v1 - v2) / (1 - (v1*v2 / c²)) = 0.882c
Thus, when S1's own clock displays t''=-0.8 it would say that spaceship S1 would be located at x''=u''t''=-0.705.
Therefore the distance between the spaceships would be:
D2 = 0.0 - (-0.705) = 0.705.
as measured by the S2 frame at time t''=-0.8.

As you can see, this does not have anything to do with "the length contraction formula" which cincirob said could be used. When, oh when, will cincirob ever learn?

Originally Posted by JTyesthatJT

Look, according to the frame of O, when O's own clock displays t=-1.000, the three clocks are simultaneously like this:
t = -1.000 (clock of O)
t' = -0.800 (clock of S1)
t'' = -0.800 (clock of S2)

So I chose to have O make his measurement at time t=-1.000 and I chose for S1 to make his measurement at time t'=-0.800.


But according to the frame of S1, when S1's own clock displays t=-0.800, the three clocks are simultaneously like this:
t = -0.640 (clock of O)
t' = -0.800 (clock of S1)
t'' = -0.376 (clock of S2)

So I could just as well have chosen to have O make his measurement at time t=-0.640 and S1 make his measurement at time t'=-0.800.


Considering that you refused to tell me which arrangement you thought was going to give a meaningful comparison between the measurements made in the three different frames, I just chose one arrangement randomly.

---

What do you mean it all works out? You said we could use the length contraction formula (LCF), but the measurements were:

D = 1.200 (distance measurement of 0)
D1 = 0.705 (distance measurement of S1)
D2 = 0.705 (distance measurement of S2)

JT: The three different frames do not agree on simultaneity of events along the x axis, and you've got them all measuring the position of moving spaceships along the x axis.

cinci: I haven't got them all doing anything. I described the situation from the perspective of O. I said nothing about the others except where they are relative to O and that they have some velocity relative to O.

JT: You said S1 can measure the distance between the spaceships as X1, and you said S2 can measure the distance between the spaceships as X2. That is fine, but since there is relative movement along the x axis, ROS says it is meaningless to compare those measurements to O's measurements. The three frames simply do not agree on simultaneity along the x axis.

cinci: OK, where did I disagree with any of what you say here?

JT: There are a number of different possible time arrangements, and you refuse to choose one that you think makes it all work out. Do you see the problems with this now?

cinci: I didn't suggest any particular time arrangement other than what is obvious from the simple description I posted. And no, I don't think there's a problem with it.

JT: There is more than one possible time arrangement, and none of them are necessarily more obvious than the others, unless one does not think about ROS.

cinci: There are other possible arrangements and you have to deal with ROS in all of them. ROS doesn't prevent you from selecting any arrangement of frames; it will work with all of them.

In that case the most obvious time arrangement is probably the one I chose to use. When O makes his measurement, he notes the times on the clocks co-moving with S1 and S2. Then S1 and S2 are to make their measurements at the time their clocks display that time.

cinci: And where did I disagree with any of this?

JT: In the example I worked out with v1=0.6c and v2=-0.6c, the result is that O measures the distance as 1.200 but S1 and S2 both measure the distance as 0.705. If you are fine with that, then I am also. But the length contraction formula (LCF) won't give you that answer.

Originally Posted by VeeDee

JT,
here is a Minkowski diagram of your exercise.

Thank you, VeeDee, that looks great!!

Originally Posted by cincirob

JT: You said S1 can measure the distance between the spaceships as X1, and you said S2 can measure the distance between the spaceships as X2. That is fine, but since there is relative movement along the x axis, ROS says it is meaningless to compare those measurements to O's measurements. The three frames simply do not agree on simultaneity along the x axis.

cinci: OK, where did I disagree with any of what you say here?

Well, I asked you a number of times what time S1 and S2 are supposed to measure their distance for either one to be a meaningful comparison to the distance X measured by observer O. At no time did you ever say what I say above, that it is meaningless to compare those measurements to O's measurements because the three frames simply do not agree on simultaneity along the x axis.

So even though you never disagreed, you never indicated that you realised the above.

Originally Posted by cincirob

JT: There is more than one possible time arrangement, and none of them are necessarily more obvious than the others, unless one does not think about ROS.

cinci: There are other possible arrangements and you have to deal with ROS in all of them. ROS doesn't prevent you from selecting any arrangement of frames; it will work with all of them.

That is true, but no matter which arrangement you choose, it is still meaningless to compare the resulting distance measurements. All they tell you is that the three frames disagree on the simultaneity of events along the x axis.

Originally Posted by cincirob

In that case the most obvious time arrangement is probably the one I chose to use. When O makes his measurement, he notes the times on the clocks co-moving with S1 and S2. Then S1 and S2 are to make their measurements at the time their clocks display that time.

cinci: And where did I disagree with any of this?

You haven't. Just like you haven't addressed my comment that the length contraction formula (LCF) won't give you the distances that S1 and S2 would measure in that arrangement.

JT: Well, I asked you a number of times what time S1 and S2 are supposed to measure their distance for either one to be a meaningful comparison to the distance X measured by observer O.

cinci: When did answering questions become important? You've left a lot of mine unanswered.

JT: At no time did you ever say what I say above, that it is meaningless to compare those measurements to O's measurements because the three frames simply do not agree on simultaneity along the x axis.

cinci: Observes in relative motion never agree on simultaneity. The sun comes up every morning too. Should I have mentioned that?

JT: So even though you never disagreed, you never indicated that you realised the above.

cinci: I don't feel constrained to "indicate" to you what I do or don't realize. I didn't specify v1, v2, or x. So if I specified t, what good would that do? And again, you just have to pick any time you wish and it should all work out. You chose a collision time. What would be different if you had chosen a different one?

Originally Posted by cincirob

the distance between the ships when measured by observers on the ships is contracted.

Can you give us calculations (you are free to set up your own exercise) to illustrate your quote?

VeeDee: Can you give us calculations (you are free to set up your own exercise) to illustrate your quote?

cinci: Could. Won't.

Originally Posted by cincirob

JT: JT: Okay, so what time is spaceship S1 supposed to measure distance X1 for it to be a meaningful comparison to distance X? Likewise, what time is spaceship S2 supposed to measure distance X2 for it to be a meaningful comparison to distance X?

cinci: Since I didn't put numbers on any of this, most people who understand relativity would pick an instant in time, a couple of sets of coordinates whose origins are coincident at
t = 0 and write the "meaningful" equations. Or simply use length contraction and time dilation equations to do the same.

Can you give us calculations to illustrate the 'simple' technique described in the underlined part of your quote?

cinci: I proved a dozen times over that I know how to and have done the Gron wheel analysis......years ago. And still you both claim I can't do that analysis. I'd be stupid to get into that merry-go-round again. Besides, I just asked you two questions and you didn't answer either one. So you can look at this as returning the favor.

Originally Posted by cincirob

cinci: I proved a dozen times over that I know how to and have done the Gron wheel analysis......years ago. And still you both claim I can't do that analysis. I'd be stupid to get into that merry-go-round again. Besides, I just asked you two questions and you didn't answer either one. So you can look at this as returning the favor.

Cinci, your case is even worse than I anticipated. I thought in that other thread you only had a problem understanding the rolling wheel, but now it's obvious you also are on non speaking terms as far as simple length contraction is concerned. Boring.

Originally Posted by cincirob

cinci: I didn't specify v1, v2, or x. So if I specified t, what good would that do?

I wasn't asking you to specify a numerical time.

You could have said, "Whatever time is on S1 at the time when O makes his measurement in his own frame, that is the time S1 should make his measurement."

Or you could have said, "Whatever time is on O at the time when S1 makes his measurement in his own frame, that is the time O should make his measurement."

Or you could have said, "No matter when they make their measurements, comparing O's to S1's is pretty meaningless, since they are doing their measurements at different times."

But instead you said something like, "People who understand relativity know that the measurements can be done at any chosen time, and everything works out just as the length contraction formula says it should."

Originally Posted by cincirob

cinci: And again, you just have to pick any time you wish and it should all work out. You chose a collision time. What would be different if you had chosen a different one?

That would not matter, but there is certainly a difference between saying, "Whatever time is on S1 at the time when O makes his measurement in his own frame, that is the time S1 should make his measurement," and saying, "Whatever time is on O at the time when S1 makes his measurement in his own frame, that is the time O should make his measurement." You never specified either one, but they are different. That is why I was asking which one you wanted to use.

The point is moot now, because you are now saying that they can all make their measurements any time they want, and everything works out just as the length contraction formula says it should.

VeeDee: Cinci, your case is even worse than I anticipated. I thought in that other thread you only had a problem understanding the rolling wheel, but now it's obvious you also are on non speaking terms as far as simple length contraction is concerned. Boring.

cinci: My case is that no matter what I say you'll be saying I don't understand relativity. Thanks for confirming that.

JT: The point is moot now,...............

cinci: It was always moot. I never constructed the thing for analysis.

JT: ...........because you are now saying that they can all make their measurements any time they want, and everything works out just as the length contraction formula says it should.

cinci: According to your message #146, I said "Or simply use length contraction and time dilation equations to do the same. " But you've already rewritten the history of me solving Gron's wheel problem so go ahead and rewrite this too.

Originally Posted by cincirob

VeeDee: Cinci, your case is even worse than I anticipated. I thought in that other thread you only had a problem understanding the rolling wheel, but now it's obvious you also are on non speaking terms as far as simple length contraction is concerned. Boring.

cinci: My case is that no matter what I say you'll be saying I don't understand relativity. Thanks for confirming that.

Well, you do nothing to prove you DO understand relativity. If you write <<the distance between the ships when measured by observers on the ships is contracted>> you shout to everybody in the world you don't understand relativity. Problem is you refuse to accept this. And we try to find out why, but you refuse to help us. Nice guy.
Your case is: the way you communicate, and what you communicate about relativity makes us believe you don't understand how relativity works.
You talk a lot, in bold type, but what you say makes no sense to people who do know how relativity works. People who can handle Lorentz Tranformations, RoS, spacetime diagrams etc. But you are obviously too clever to deal with all that. What you prefer doing is... talk a lot about nothing. And when a question doesn't suit you, you counter by asking us a question. It's a game you like playing page after page after page. This only proves you try to cover-up your ignorance. And it gets very boring after all those posts.

VeeDee: Well, you do nothing to prove you DO understand relativity.

cinci: I got Gron's solution without copying his analysis like you did.

VeeDee: If you write <<the distance between the ships when measured by observers on the ships is contracted>> you shout to everybody in the world you don't understand relativity.

cinci: So you don't think that the observers on the ships see the distance contracted relative to what the third observer measures? You have excerpted part of a sentence which was part of a paragraph. The statement is right in the context of the whole message. Only people interested in nonsense arguments do this kind of cherry picking.

VeeDee: Problem is you refuse to accept this. And we try to find out why, but you refuse to help us. Nice guy. Your case is: the way you communicate, and what you communicate about relativity makes us believe you don't understand how relativity works. You talk a lot, in bold type, but what you say makes no sense to people who do know how relativity works. People who can handle Lorentz Tranformations, RoS, spacetime diagrams etc.

cinci: You mean the people who know the difference between a measurement and a Lorentz transformation?

VeeDee: But you are obviously too clever to deal with all that.

cinci: I'm clever enough to know I got Gron's solution years ago, posted it for you, and you still say I don't understand it.

VeeDee: What you prefer doing is... talk a lot about nothing. And when a question doesn't suit you, you counter by asking us a question. It's a game you like playing page after page after page. This only proves you try to cover-up your ignorance. And it gets very boring after all those posts.

cinci: What I like to do is have conversation where people ask me questions and I ask then questions in return. You prefer to not answer questions. You stuck your nose into a discussion I was having with TFOLZO. I didn't ask you anything. If you're bored here, then go away.

Originally Posted by cincirob

JT: ...........because you are now saying that they can all make their measurements any time they want, and everything works out just as the length contraction formula says it should.

cinci: According to your message #146, I said "Or simply use length contraction and time dilation equations to do the same. " But you've already rewritten the history of me solving Gron's wheel problem so go ahead and rewrite this too.

Well, you have not shown how one can solve your distance measurements X1 and X2 by simply using the length contraction and time dilation equations.

I can think of a way using the time dilation and velocity composition equations, but I don't see how the length contraction equation enters into it at all. Why not show us and impress everyone?

Thanx JT, my accidental posting in this thread, the post has been moved (with your corrections) to the appropriate thread here ...

http://www.thephysicsforum.com/speci...html#post20340

Thank You,
SinceYouAsked

Originally Posted by SinceYouAsked

Cincirob argued ...

1) The LT solns are correct in Gron's analysis, yet cinci has long argued Gron's elliptical shape is wrong because he misapplied the LTs.
2) Gron's rotating disk has a radius of R'=1 per the axle frame observer (A), rolling on a ground moving at v=-0.866c.
3) Cinci introduced an inertial rod, to prove his point ...
4) A records a moving inertial length-contracted rod at height y'= 0.866 (above the disk's axle) to be unit length a L_A=1.
5) Per A, when a linear cord of (at y'=+0.866) Gron's rolling disk is momentarily superposed with the moving rod, both then are the length L_A=1.
6) The ground observer G moves at -0.866c wrt axle observer A, because the rolling disk's axle translates at 0.866c per the ground observer G.
7) G holds the moving rod at length L_G = (L_A*1/√(1-v²/c²))*√(1-u²/c²), where u = 2v/(1+v²/c²), so for v=0.866c then L_G = (1*2)/7 = 0.28571

OK, so we know that Gron's rolling wheel is only L_G = 0.5 long (wrt x at y=y'=0.866) per ground observer G, yet the inertial rod must be L_G = 0.28571 per G ... even though they are the same x' length per the axle observer A. Is this a problem, relativistically? No. Yet, cincirob has long argued it an error on Gron's behalf. So while cincirob says the LTs are correct, he also argues that Gron does not apply them correctly under the case of rotation, and thus Gron's theory is all wrong. Hmmm.

Cincirob then points out that the inertial rod must have a proper length of L_P*1/√(1-v²/c²) = 1*2 = 2. Given such, he presumes that the length of the disk-cord (of atoms) associated with y=y'=0.866 per A, should have the same proper length (2 units) per the rest length of those atoms per the noon-inertial disk POV itself. Yet, he never concedes that the linear string of disk atoms defined by the axle observer A (in his instant t') must be non-linear in either the non-inertial non-euclidean disk POV and/or the ground POV. Hmmm.

Then, cincirob says Gron never took the various differing motions of the disk atoms into account in his analysis, nor did Gron consider the composed velocity of each individual atom, as though that's a problem of sort. Did Gron ever need to do this in his analysis? Of course not. Did Gron ever care about the proper length of disk cords in the non-inertial disk POV? Of course not, as it was never required. Cincirob says the Gron analysis is wrong, and cannot be validated until all those calculations are done. Hmmm.

Thank You,
SinceYouAsked

I think you meant to post this in the thread about the relativistic rolling wheel. That is the thread where cincirob argues that the length contraction formula (LCF) can be used to determine the shape of a round rotating disk to be pear-shaped according to the road it rolls along.

In this thread, cincirob has two spaceships on a collision course, and cincirob is arguing that the length contraction formula (LCF) can somehow be used to calculate the distance between the spaceships.

I can see why you'd get the two threads confused though, as there are definitely some similarities there. ^

Originally Posted by cincirob

VeeDee: If you write <<the distance between the ships when measured by observers on the ships is contracted>> you shout to everybody in the world you don't understand relativity.

]cinci: So you don't think that the observers on the ships see the distance contracted relative to what the third observer measures?

The 'distance' you talk about is the distance between the spaceships, both spaceships moving at same velocity and same direction relative to 'third observer (the earth) I know for sure the observers on the ships DO NOT measure the distance between spaceships contracted relative to what the third observer(earth) measures.
The third observer (earth) measures the distance between the two moving spaceships shorter than the distance between the two spaceships measured by spaceship travellers. The spaceship observer measures his spaceship, and the other spaceship, and the distance between the spaceships, not contracted.
O.K.?

You have excerpted part of a sentence which was part of a paragraph. The statement is right in the context of the whole message.

"The-statement-is-right-in-the-context-of-the-whole-message." ... I really wonder whether YOU understood the context! That's one of the games you play. You never understand the context in SR terms. You like to play games with the context. In such a way you never have to answer questions or explain anything.
I even bet you can't specify a correct context for an exercise. We saw that for your wheel as well. After 1500 posts we still didn't know what your wheel in the axle frame looked like. And if we asked you, you tell us you know but won't give it. That kind of nonsense talk. You love making a mess of everything in such a way you (think you) can get away with your ridiculous relativity interpretations.

VeeDee: After 1500 posts we still didn't know what your wheel in the axle frame looked like.

cinci: Then you're blind.

Originally Posted by cincirob

VeeDee: After 1500 posts we still didn't know what your wheel in the axle frame looked like.

cinci: Then you're blind.

Corre ct me if I'm wrong but the first thread of the rolling wheel contains 506 posts, and in the second thread you digged up that sketch in post #1012. That makes a total of 1518 posts we had to wait.

And it seems you are going to wait another 1518 posts in this thread until you come up with some explanation why according to you the distance between the spaceships contracts for the spaceship travellers.

Originally Posted by VeeDee

Corre ct me if I'm wrong but the first thread of the rolling wheel contains 506 posts, and in the second thread you digged up that sketch in post #1012. That makes a total of 1518 posts we had to wait.

And it seems you are going to wait another 1518 posts in this thread until you come up with some explanation why according to you the distance between the spaceships contracts for the spaceship travellers.

Actually, that sketch is cincirob showing us that he can do Gron's analysis. So that sketch assumes a circular wheel according to the axle frame, but only because that is what Gron did.

We are still waiting for cinci to show or tell us the details of cinci's own pear wheel model, and its shape according to the axle frame.

Just as we are still waiting for him to show us how we can use the length contraction formula (LCF) to calculate the distance between spaceships S1 and S2, as he claimed he knew how to do.

VeeDee: Correct me if I'm wrong but the first thread of the rolling wheel contains 506 posts, and in the second thread you digged up that sketch in post #1012. That makes a total of 1518 posts we had to wait.

cinci: I just corrected you. I had already shown what the wheel looked like in the axle frame. So why don't you apologize? I also described that analysis several different ways to you before I posted that plot (it's not a sketch, it's calculated numbers) and you didn't get it. And you're still pretending I don't know how to do that analysis.

I also corrected you on your statement about measurements and transformations as did others and you're still sticking to that nonsense.

VeeDee: And it seems you are going to wait another 1518 posts in this thread until you come up with some explanation why according to you the distance between the spaceships contracts for the spaceship travellers.

cinci: You can wait to hell freezes over. I never had any intention of putting numbers on that problem and if I did it now you'd still say I don't understand relativity. My goal in life isn't to have you bless my knowledge of relativity.

Originally Posted by cincirob

I never had any intention of putting numbers on that problem

Correct. Your only intention on these forums is dropping stupid statements about relativity that are plain wrong. And if we ask you to prove why you consider them correct, you bail out. Over and over again. You really waste your time doing this. You better start learning what relativity is about and how it works.

JT: Actually, that sketch is cincirob showing us that he can do Gron's analysis. So that sketch assumes a circular wheel according to the axle frame, but only because that is what Gron did.

cinci: What does "but only because that is what Gron did" mean. That was the definition of the problem. You used it too and so did everybody else. Why the qualification when I use it. Why don't you just acknowledge straight out that I know how to do that problem. VeeDee whines about hundreds of messages when most of them are me trying to get him to understand that I did the problem and got the right answers. All this time you knew it and kept your mouth shut. Were you afraid that VeeDee and SYA would throw you out of their club?

JT: Correct. Your only intention on these forums is dropping stupid statements about relativity that are plain wrong.

cinci: Show one. And do it without taking something I said out of context.

JT: And if we ask you to prove why you consider them correct, you bail out. Over and over again. You really waste your time doing this. You better start learning what relativity is about and how it works.

cinci: Well dealing with you has certainly become a waste of time. If you had an ounce of honesty you would have admitted months ago that I worked out the Gron solution years ago at the same time you did. We even checked numbers to make sure because I did it a different way. I did the curved spokes then too. I also did a curved chord before you did. Why haven't you acknowledge this before today?

Originally Posted by cincirob

JT: Actually, that sketch is cincirob showing us that he can do Gron's analysis. So that sketch assumes a circular wheel according to the axle frame, but only because that is what Gron did.

cinci: What does "but only because that is what Gron did" mean. That was the definition of the problem. You used it too and so did everybody else. Why the qualification when I use it.

If everyone starts in the axle frame, and everyone assumes a uniformly rotating circular wheel there, then we are all on equal footing.

But for a long time you started in the road frame, and did not assume a circular wheel in the axle frame. There were years that you even "steadfastly refused" (your own words) to consider the axle frame at all. There were times when you said the wheel shape could be a pear in the axle frame, which you claimed could be explained by the roll-up forces of a wheel on a treadmill. Many times you claimed the wheel did not seem to be rotating at all. So, it is a bit much for you to claim now that you were always on the same page as everyone else, and started in the axle frame with a uniformly rotating circular wheel.

Originally Posted by cincirob

cinci: Why don't you just acknowledge straight out that I know how to do that problem. VeeDee whines about hundreds of messages when most of them are me trying to get him to understand that I did the problem and got the right answers. All this time you knew it and kept your mouth shut. Were you afraid that VeeDee and SYA would throw you out of their club?

I acknowledge that you replicated Gron's results. But you did it in a different way than most folks would do it. First you simply length-contracted the shape from circle to ellipse, which you claimed is wrong in the first place, because you said that means the wheel is not rotating. Next you used ROS to shift all the wheel points around the ellipse, and sure enought that did match the results obtained by Gron. But of course applying ROS cannot change a shape which you had already decided was incorrectly obtained in the first place. So I cannot agree that you "know how to do that problem."

The way Gron, SYA, VeeDee, and I do it is different than that. We apply the LT rather than the LCF, and we let the points transform to where ever they want to go. If it turns out that the shape is an ellipse, that is fine, but we don't force it. We let the LT's do their thing. You know, the thing they are designed to do.

Originally Posted by cincirob

VeeDee: Correct. Your only intention on these forums is dropping stupid statements about relativity that are plain wrong.

cinci: Show one. And do it without taking something I said out of context.

VeeDee: And if we ask you to prove why you consider them correct, you bail out. Over and over again. You really waste your time doing this. You better start learning what relativity is about and how it works.

cinci: Well dealing with you has certainly become a waste of time. If you had an ounce of honesty you would have admitted months ago that I worked out the Gron solution years ago at the same time you did. We even checked numbers to make sure because I did it a different way. I did the curved spokes then too. I also did a curved chord before you did. Why haven't you acknowledge this before today?

Those two quotes are from VeeDee, not me.

Just a general statement here ... If one has difficulty with events, then one may well have difficulty with 4d spacetime coordinates. Don't understand 4d spacetime coordinates, then one thinks in terms of 3-space and time independently envisioning space and time as unfused (as Newton did), but then at the same time announcing that LT solns must be a correct model of nature because it's an accepted theory and most everyone believes it. Given such, one doesn't really understand the meaning of relativistic effects, even though they accept the LT solns as "must be correct". Their arguments usually make no sense, because of the confusion. The wise thing to do, is agree to go thru one basic all inertial analysis, front to end ... until one understands the significance of 4 dimensional events in Relativity's fused spacetime. Then, there's a better chance of understanding the meaning of relativistic effects and the model in collective.

Thank you,
SinceYouAsked

SYA,
Actually we tried that with the firecracker popping event. Cinci finally agreed it happened at t=.866 x=1.0 y=.866 (That was a kind of an eureka moment because he was not interested at all in what happens at t=.866).
But he refused to admit the rim of the wheel was also at that point and time in the road frame.
This simply proves Cinci doesn't know what an event is. And if he tells you he does know he simply has an abstract 'point' in mind without any 'physical' content it refers to.

In the axle frame the firecracker (at the end of the pole) happens when it hits the rim of the wheel. The 'physical content' of that event will not change after coordinate transformation, which means that if we obtain the location and time in the road frame for the firecracker popping, then that spot HAS TO contain a rim atom as well, hence location of wheel shape. Cinci simply does not understand this, and does not WANT to understand this. Worse, for some obscure reasons he is unable to understand this...

Therefore there is little hope he will ever get this spaceship topic correct.

Originally Posted by VeeDee

SYA,

Actually we tried that with the firecracker popping event. Cinci finally agreed it happened at t=.866 x=1.0 y=.866 (That was a kind of an eureka moment because he was not interested at all in what happens at t=.866).

But he refused to admit the rim of the wheel was also at that point and time in the road frame. This simply proves Cinci doesn't know what an event is. And if he tells you he does know he simply has an abstract 'point' in mind without any 'physical' content it refers to.[/B]

I know. It's as though he's half way to first base, but then first base keeps getting further away as he continues to run. The specific rim atom that is momentarily co-located with an axle frame LT input coordinate x',y',t' is the very same rim atom momentarily co-located at the transformed LT soln x,y,t of the ground POV. Cinci's disbelief there is rather consistent with TFOLZO's belief that LT solns require parallel (daughter) universes, because that's what would be required

Thank You,
SinceYouAsked

JT: Actually, that sketch is cincirob showing us that he can do Gron's analysis. So that sketch assumes a circular wheel according to the axle frame, but only because that is what Gron did.

cinci: What does "but only because that is what Gron did" mean. That was the definition of the problem. You used it too and so did everybody else. Why the qualification when I use it.

If everyone starts in the axle frame, and everyone assumes a uniformly rotating circular wheel there, then we are all on equal footing.

But for a long time you started in the road frame, and did not assume a circular wheel in the axle frame.

cinci: Not true, the pear is based on a round wheel. But that wasn't Gron's analysis anyway.

JT: There were years that you even "steadfastly refused" (your own words) to consider the axle frame at all. There were times when you said the wheel shape could be a pear in the axle frame, which you claimed could be explained by the roll-up forces of a wheel on a treadmill. Many times you claimed the wheel did not seem to be rotating at all. So, it is a bit much for you to claim now that you were always on the same page as everyone else, and started in the axle frame with a uniformly rotating circular wheel.

cinci: None of that has anything to doing Gron's analysis. Yes, I looked for other solutions but I did Gron's correctly and you know it.

cinci: Why don't you just acknowledge straight out that I know how to do that problem. VeeDee whines about hundreds of messages when most of them are me trying to get him to understand that I did the problem and got the right answers. All this time you knew it and kept your mouth shut. Were you afraid that VeeDee and SYA would throw you out of their club?

JT: I acknowledge that you replicated Gron's results. But you did it in a different way than most folks would do it. First you simply length-contracted the shape from circle to ellipse, which you claimed is wrong in the first place, because you said that means the wheel is not rotating. Next you used ROS to shift all the wheel points around the ellipse, and sure enough that did match the results obtained by Gron. But of course applying ROS cannot change a shape which you had already decided was incorrectly obtained in the first place. So I cannot agree that you "know how to do that problem."

cinci: :-) Getting the correct answers doesn't count? You are a complete phony. My analysis isn't really any different than Gron's but if it were, most people would say wow, an alternative solution. Great!

JT: The way Gron, SYA, VeeDee, and I do it is different than that. We apply the LT rather than the LCF, and we let the points transform to where ever they want to go. If it turns out that the shape is an ellipse, that is fine, but we don't force it. We let the LT's do their thing. You know, the thing they are designed to do.

cinci: If you don't think Gron's analysis is using length contraction, then you don't understand relativity or Gron's analysis.

SYA: I know. It's as though he's half way to first base, but then first base keeps getting further away as he continues to run. The specific rim atom that is momentarily co-located with an axle frame LT input coordinate x',y',t' is the very same rim atom momentarily co-located at the transformed LT soln x,y,t of the ground POV. Cinci's disbelief there is rather consistent with TFOLZO's belief that LT solns require parallel (daughter) universes, because that's what would be required

cinci: Look at my diagram. I have arrows between the two positions of each rim atom. So it's you who are off base.

VeeDee: Actually we tried that with the firecracker popping event. Cinci finally agreed it happened at t=.866 x=1.0 y=.866 (That was a kind of an eureka moment because he was not interested at all in what happens at t=.866).
But he refused to admit the rim of the wheel was also at that point and time in the road frame.

cinci: I didn't refuse to admit anything; I even explained JT's calculations. What I did was ask why the point shouldn't be transformed according to the pole and barn method. And you don't have an answer.

Originally Posted by cincirob

cinci: What I did was ask why the point shouldn't be transformed according to the pole and barn method. And you don't have an answer.

Everything about the wheel has been explained in detail. If you still have unanswered questions about it, then you must not understand it fully.

If you would try using your length contraction method on the S1 and S2 spaceship measurements, you would find the LCF does not work there either. There is more to relativity than length contraction.

JT: Everything about the wheel has been explained in detail. If you still have unanswered questions about it, then you must not understand it fully.

If you would try using your length contraction method on the S1 and S2 spaceship measurements, you would find the LCF does not work there either. There is more to relativity than length contraction.

cinci: Usual non-answer.

Originally Posted by cincirob

JT: Everything about the wheel has been explained in detail. If you still have unanswered questions about it, then you must not understand it fully.

If you would try using your length contraction method on the S1 and S2 spaceship measurements, you would find the LCF does not work there either. There is more to relativity than length contraction.

cinci: Usual non-answer.

Why not just try JT's simple spaceship scenario, see what happens? Why the fear of doing that? Shouldn't take more than a few post exchanges between relativists, under any normal circumstance.

Thank You,
SinceYouAsked

Originally Posted by cincirob

SYA: I know. It's as though he's half way to first base, but then first base keeps getting further away as he continues to run. The specific rim atom that is momentarily co-located with an axle frame LT input coordinate x',y',t' is the very same rim atom momentarily co-located at the transformed LT soln x,y,t of the ground POV. Cinci's disbelief there is rather consistent with TFOLZO's belief that LT solns require parallel (daughter) universes, because that's what would be required

cinci: Look at my diagram. I have arrows between the two positions of each rim atom. So it's you who are off base.

I've looked at it. I see the arrows. Yet, you have long argued that Gron's analysis is flawed. Only problem, you have never successfully supported your belief.

If you understood the meaning of relativistic effects, you would understand what the Gron solns mean, and you would not be repeatedly asking the same old questions again and again that have been already answered so many times before. If you learn more about events, and thus 4 dimensional spacetime coordinates, you won't need to continue re-asking your questions. They all go away. The hard part, is getting you to admit you need to go thru some basic relativity scenarios, such as the one JT keeps asking you to try (2 spaceships). He's trying to help you to understand why all your questions have been long answered. What harm can it do to try?

Thank You,
SinceYouAsked

Originally Posted by cincirob

cinci: What I did was ask why the point shouldn't be transformed according to the pole and barn method. And you don't have an answer.

Maybe I don't understand your question, because the right edge of your pole had axle frame coordinates x'=0.500 y'=0.866 t'=0.000 at the only moment in time when it was co-located with the right edge of the wheel. That was an event which transformed to the road frame as x=1.000, y=0.866, t=0.866 according to the only method there is, the LT. That is an ellipse point, so your pole method agrees with the ellipse shape.

So what exactly is the "pole and barn method" that you want to use, instead of the above pole? And why do you want to use it, to second-guess the LT? The LT is the foundation of SR. All other equations such as the length contraction formula, the time dilation formula, and the velocity composition formula, are special cases which are derived from the LT. But those can only be used in the special cases they are designed for, nothing more. For example, the LCF can be used to find the length of the pole in the road frame, but the LCF does not tell you WHAT TIME the right edge of the pole will be co-located with the right edge of the wheel. The LT does tell you that though, and that time is t=0.866.

SYA: I've looked at it. I see the arrows. Yet, you have long argued that Gron's analysis is flawed. Only problem, you have never successfully supported your belief.

cinci: And you've long argued that I don't understand Gron's analysis and you can't support that belief. Just because I have a problem with the analysis doesn't mena I don't understand it.

SYA: If you understood the meaning of relativistic effects, you would understand what the Gron solns mean, and you would not be repeatedly asking the same old questions again and again that have been already answered so many times before. If you learn more about events, and thus 4 dimensional spacetime coordinates, you won't need to continue re-asking your questions. They all go away. The hard part, is getting you to admit you need to go thru some basic relativity scenarios, such as the one JT keeps asking you to try (2 spaceships). He's trying to help you to understand why all your questions have been long answered. What harm can it do to try?

[B]cinci: OK, the two spaceships. My stated problem was that an observer, O, measures the distance between two ships. And I said both spaceships will observe that distance (the distance measured by O) to be contracted. The three of you have told me that's wrong. The JT puts numbers on it and concludes that the spaceships will observe the distance between the ships to be .705 when O measured 1.2. Sounds contracted but what do I know?

He apparently did the problem by looking at the ships when they collide which he labels t = -1 (I'd have used t = 0 but no matter). This corresponds to t' and t" = -.8. Then he says the relative velocity of the ships is .882 and calculates that the ships would move .8*882 = .705 and says the ships are .705 apart.

Let's make the problem a little more concrete and put O on a planet with S1 and S2 barreling in from different directions at .6c and each is .6 away from the planet according to measurements made by O. As JT says, it takes a travel time of dt = 1 for both to reach the planet. The time dilation formula tells me that on the ships,

dt' = dt" = dt(1 - .6^2)^.5 = .8.

So, ala JT's method, each ship would measure his travel distance ad D1 = D2 = .6*.8 = .48; therefore, they measure O's 1.2 as .96.

Or, they could have said we're travelling at .6 relative to a measured distance of 1.2 and 1.2*(1 - .6^2)^.5 = .96.

Apparently the three of you don't realize that if you take dilated time and multiply it by velocity to get a distance in a relatively moving frame you get the same answer as if you take the distance and contract it using the relative velocity.

As far as the analysis that JT goes, it doesn't answer my question. What S1 sees as the distance to the planet is not affected by the fact that there's another ship, S2, somewhere on the other side of the planet nor does his relative velocity to that ship affect what he sees. So JT has the answer to some question, but, as usual, it doesn't happen to be the answer to my question.

Originally Posted by cincirob

cinci: OK, the two spaceships. My stated problem was that an observer, O, measures the distance between two ships. And I said both spaceships will observe that distance (the distance measured by O) to be contracted. The three of you have told me that's wrong. The JT puts numbers on it and concludes that the spaceships will observe the distance between the ships to be .705 when O measured 1.2. Sounds contracted but what do I know?

He apparently did the problem by looking at the ships when they collide which he labels t = -1 (I'd have used t = 0 but no matter). This corresponds to t' and t" = -.8. Then he says the relative velocity of the ships is .882 and calculates that the ships would move .8*882 = .705 and says the ships are .705 apart.

Pretty much correct. Except the ships collide at t=t'=t''=0.000, and the distance between the ships would be zero at that time, so I do not make any measurements at that time. I look at an earlier time, before the ships collide. I let O make his measurement when his own clock says t=-1.000, at which time the clocks of S1 and S2 display t'=-0.800 and t''=-0.800 respectively. So I let S1 make his measurement at t'=-0.800, and I let S2 make his measurement at t''=-0.800.

Originally Posted by cincirob

cinci: Let's make the problem a little more concrete and put O on a planet with S1 and S2 barreling in from different directions at .6c and each is .6 away from the planet according to measurements made by O. As JT says, it takes a travel time of dt = 1 for both to reach the planet. The time dilation formula tells me that on the ships,

dt' = dt" = dt(1 - .6^2)^.5 = .8.

So, ala JT's method, each ship would measure his travel distance ad D1 = D2 = .6*.8 = .48; therefore, they measure O's 1.2 as .96.

WHAT?!?!?!?!?! The composed velocity is 0.882c therefore when the clock of S1 displays t'=-0.800 the distance to S2 must be 0.800*0.882=0.705.

While it is true that the relative speed between S1 and O is 0.600c, that does not mean you can use that speed to calculate the distance to S2!!!!!!

You are assuming that O is always at the midpoint between S1 and S2. That is not true in the frame of S1 where O moves at 0.600c and S2 moves at 0.882c!!!!!

Think, man, think!!

Originally Posted by cincirob

cinci: Or, they could have said we're travelling at .6 relative to a measured distance of 1.2 and 1.2*(1 - .6^2)^.5 = .96.

Apparently the three of you don't realize that if you take dilated time and multiply it by velocity to get a distance in a relatively moving frame you get the same answer as if you take the distance and contract it using the relative velocity.

As far as the analysis that JT goes, it doesn't answer my question. What S1 sees as the distance to the planet is not affected by the fact that there's another ship, S2, somewhere on the other side of the planet nor does his relative velocity to that ship affect what he sees. So JT has the answer to some question, but, as usual, it doesn't happen to be the answer to my question.

You might want to go back and read your own post #82:

Originally Posted by cincirob

cinci: OK, back to basics. First, using the Earth is a poor choice because it isn't really inertial but it can be assumed to be inertial without introducing much error if the problem involves relativistic velocities and long distances. To eliminate confusion, I will discuss the three observer problem (two spaceships and a third observer) as being located in deep space (away from any significant gravitating source).

All three elements (the two spaceships and the third observer) will be considered to be dimensionless points; this also introduces ignorable errors for large separations of the elements.

First let's name the spaceships S1 and S2 and the observer is O. S! and S2 are on a straight line collision course; O is somewhere off that line.

The occupy three points in space at any given instant.

YOU chose an instant when O knows S1 and S2 are separated by a distance x.

That statement implies that O has the ability to determine distance x and that he determined it as a distance that is stationary relative to O. This requires some technology: he could have beacons in space that he placed stationary to himself and can observe when the ships pass them by some means. Note, he may not be able to determine this at a given instant and may only know it some time after the ships pass the beacons but he can, with suitable technology determine that at a particular time on his clock, the spaceships were separated by a known distance x.

Next, YOU chose to acknowledge that O could also determine the velocities of S1 and S2 when they were separated by the distance x. Also technologically possible.

So now, YOU have specified that O knows a distance x, V1, and V2 and I have shown that he could technologically collect this data.

Note, that none of this data is subject to relativistic effects as far as O is concerned. The First Postulate confirms this in that it says the laws of physics hold good in a frame where the mechanics hold and they hold in an inertial frame. So no contraction of x.

S1 is also inertial. He can also make measurements. Since he is inertial, he cannot determine his own motion, but he can measure velocities relative to himself. So here is what he measured.

He can measure the distance to S2 but he gets a value x1 which is different than x as measured by O.

S2 gets a value for the distance to S1, let's call it x2.

TFOLZO, let the question begin.

You said S1 measures the distance to S2, and you said S2 measures the distance to S1. At t'=t''=-0.800 with a composed velocity of 0.882c, those distances must be 0.800*0.882=0.705.

Now please consider that maybe, just maybe, there is more to relativity than length contraction.

Originally Posted by cincirob

SYA: I've looked at it. I see the arrows. Yet, you have long argued that Gron's analysis is flawed. Only problem, you have never successfully supported your belief.

cinci: And you've long argued that I don't understand Gron's analysis and you can't support that belief. Just because I have a problem with the analysis doesn't mena I don't understand it.

SYA: If you understood the meaning of relativistic effects, you would understand what the Gron solns mean, and you would not be repeatedly asking the same old questions again and again that have been already answered so many times before. If you learn more about events, and thus 4 dimensional spacetime coordinates, you won't need to continue re-asking your questions. They all go away. The hard part, is getting you to admit you need to go thru some basic relativity scenarios, such as the one JT keeps asking you to try (2 spaceships). He's trying to help you to understand why all your questions have been long answered. What harm can it do to try?

[B]cinci: OK, the two spaceships. My stated problem was that an observer, O, measures the distance between two ships. And I said both spaceships will observe that distance (the distance measured by O) to be contracted. The three of you have told me that's wrong. The JT puts numbers on it and concludes that the spaceships will observe the distance between the ships to be .705 when O measured 1.2. Sounds contracted but what do I know?

He apparently did the problem by looking at the ships when they collide which he labels t = -1 (I'd have used t = 0 but no matter). This corresponds to t' and t" = -.8. Then he says the relative velocity of the ships is .882 and calculates that the ships would move .8*882 = .705 and says the ships are .705 apart.

Let's make the problem a little more concrete and put O on a planet with S1 and S2 barreling in from different directions at .6c and each is .6 away from the planet according to measurements made by O. As JT says, it takes a travel time of dt = 1 for both to reach the planet. The time dilation formula tells me that on the ships,

dt' = dt" = dt(1 - .6^2)^.5 = .8.

So, ala JT's method, each ship would measure his travel distance ad D1 = D2 = .6*.8 = .48; therefore, they measure O's 1.2 as .96.

Or, they could have said we're travelling at .6 relative to a measured distance of 1.2 and 1.2*(1 - .6^2)^.5 = .96.

Apparently the three of you don't realize that if you take dilated time and multiply it by velocity to get a distance in a relatively moving frame you get the same answer as if you take the distance and contract it using the relative velocity.

As far as the analysis that JT goes, it doesn't answer my question. What S1 sees as the distance to the planet is not affected by the fact that there's another ship, S2, somewhere on the other side of the planet nor does his relative velocity to that ship affect what he sees. So JT has the answer to some question, but, as usual, it doesn't happen to be the answer to my question.

Here's a pair of space-time diagrams of this scenario. The left image is from the frame of O and the right image is from the frame of S1. The collision happens at T=0 in all frames. I've added time indexes to each world line to help with illustration. (I kept them to a minimum to cut down on clutter.)

The Dark Blue line is the world line of O, and the Red and Blue lines are the world lines of the points that O measures to be 0.6 units away in distance to either side. The Cyan line is the world line for S1 and the Green is for S2.



The left image is pretty straight forward: At t=-1 for O, S1 and S2 are 0.6 units to the left and right and read a time of t=-0.8. S1 and S2 arrive at O when all three times read O.

So what distance does S1 and S2 measure between them?
This is not so straight forward. It depends on what time we choose. Do we mean litterally "when t=-1 for O"( as in the left image), or do we mean "When the time for the ship making the measurement is the same at was in the O frame when t=0 for O"? (IOW, when the ship time reads -0.8).

In either case, we cannot just take the 1.2 distance measured by O and apply the LC formula to it, because while the distance between the world lines representing these point does contract by this factor. In the frame of either ship, the two ships are never at these points at the same time. In fact, at no time are S1 and S2 an equal distance from O according to either S1 or S2.

So if we use the first case (t=-1 at O), then, for S1, this happens at t=-1.25 for him and at t= -0.59 for S2 and the distance works out to ~1.1 ( less than 1.2, but greater than 0.96)

On the other hand, if we go with the second choice for time (when t=-0.8 for S1) this happens at t=-0.64 for O and at t= - 0.377 for S2, and the measured distance is ~0.706.

If we were to switch to the frame of S2, the we would get the same types of answers with the roles of S1 and S2 reversed. The S-T diagram would be a mirror image of the right one with the Cyan and Green lines swapped.

Originally Posted by Janus

So what distance does S1 and S2 measure between them?
This is not so straight forward. It depends on what time we choose. Do we mean litterally "when t=-1 for O"( as in the left image), or do we mean "When the time for the ship making the measurement is the same at was in the O frame when t=0 for O"? (IOW, when the ship time reads -0.8).

Yes, and that is why I asked cincirob what time he intended for O, S1 and S2 to make their measurements. He said something about I would not have to ask that question if I understood relativity, or something. LOL.

Anyway, I arbitrarily chose to let S1 make his measurement at t'=-0.800 so that the frame of O would agree that the clock of S1 would display t=-0.800 at the time when O made his measurement at t=-1.000 in his own frame. However, I knew that the frame of S1 would not agree that the clock of O would display t=-1.000 at the time S1 made his measurement in his own frame.

I could have arbitrarily chosen to let S1 make his measurement at t'=-1.250 so that the frame of S1 would agree that the clock of O would display t=-1.000 at the time S1 made his measurement, but I knew the frame of O would not agree that t'=-1.250 was the time on S1's clock at the time when O made his measurement in hios own frame.

That is why the given arrangement makes it pretty meaningless for the measurement of S1 to be compared to the measurement of O, because the chosen times of measurement are always somewhat arbitrary.

BOTTOM LINE:

In the spaceship scenario, cincirob correctly determined that S1 would measure the distance to O as 0.600*0.800=0.480 at the time when S1's own clock displays t'=-0.800. Then cincirob assumed he could double that measurement and concluded S1 would measure the distance to S2 as 2*0.480=0.960. But that was simply incorrect, because the length contraction formula did not account for other relativistic effects such as velocity composition. With a composed velocity of 0.882c, if clock S1 displays t'=-0.800 then S1 must measure the distance to S2 as 0.882*0.800=0.705.

This is very similar to what happened when cincirob applied the length contraction formula to the pole which was passing by the wheel. He correctly determined the length of the pole as measured by the road frame, but then he assumed that measurement should also apply to the width of the wheel. That was simply incorrect, because the length contraction formula did not account for the fact that the time when the right edge of the pole meets the right edge of the wheel is not road time t=0.000 but a later road time of t=0.866. Apply the composed velocity to the pole, find where its right edge is located at road time t=0.866, and you have a wheel rim point. But not so at road time t=0.000.

These are excellent examples of why it is not good practice to rely on the length contraction formula for everything. One can use it where it applies, but one must be very careful with any further assumptions. When in doubt, one should check assumptions against a calculation using the full Lorentz transformation equations. They are not very difficult to use if one practices with them.

cinci: OK, the two spaceships. My stated problem was that an observer, O, measures the distance between two ships. And I said both spaceships will observe that distance (the distance measured by O) to be contracted. The three of you have told me that's wrong. The JT puts numbers on it and concludes that the spaceships will observe the distance between the ships to be .705 when O measured 1.2. Sounds contracted but what do I know?

He apparently did the problem by looking at the ships when they collide which he labels t = -1 (I'd have used t = 0 but no matter). This corresponds to t' and t" = -.8. Then he says the relative velocity of the ships is .882 and calculates that the ships would move .8*882 = .705 and says the ships are .705 apart.

JT: Pretty much correct. Except the ships collide at t=t'=t''=0.000, and the distance between the ships would be zero at that time, so I do not make any measurements at that time. I look at an earlier time, before the ships collide. I let O make his measurement when his own clock says t=-1.000, at which time the clocks of S1 and S2 display t'=-0.800 and t''=-0.800 respectively. So I let S1 make his measurement at t'=-0.800, and I let S2 make his measurement at t''=-0.800.

cinci: Let's make the problem a little more concrete and put O on a planet with S1 and S2 barreling in from different directions at .6c and each is .6 away from the planet according to measurements made by O. As JT says, it takes a travel time of dt = 1 for both to reach the planet. The time dilation formula tells me that on the ships,

dt' = dt" = dt(1 - .6^2)^.5 = .8.

So, ala JT's method, each ship would measure his travel distance ad D1 = D2 = .6*.8 = .48; therefore, they measure O's 1.2 as .96.


JT: WHAT?!?!?!?!?! The composed velocity is 0.882c therefore when the clock of S1 displays t'=-0.800 the distance to S2 must be 0.800*0.882=0.705.

While it is true that the relative speed between S1 and O is 0.600c, that does not mean you can use that speed to calculate the distance to S2!!!!!!

You are assuming that O is always at the midpoint between S1 and S2. That is not true in the frame of S1 where O moves at 0.600c and S2 moves at 0.882c!!!!!

Think, man, think!!

cinci: As you noted, I asked the question you answered. That was not my original intention. I was trying to give TFOLZO a simple problem, the one I worked above. And I believe it is correct as stated above. My intention was not to ask the distance between the ships but that is what I did. My apologies for that mis-statment.

cinci: As far as the analysis that JT goes, it doesn't answer my question. What S1 sees as the distance to the planet is not affected by the fact that there's another ship, S2, somewhere on the other side of the planet nor does his relative velocity to that ship affect what he sees. So JT has the answer to some question, but, as usual, it doesn't happen to be the answer to my question.

JT: You might want to go back and read your own post #82:

cinci: Noted above. My mistake. I should have checked back.

Originally Posted by cincirob

cinci: As you noted, I asked the question you answered. That was not my original intention. I was trying to give TFOLZO a simple problem, the one I worked above. And I believe it is correct as stated above. My intention was not to ask the distance between the ships but that is what I did. My apologies for that mis-statment.

That is fine, you can simplify the scenario so that the length contraction formula can be applied simply. But that does not change the fact that one must be very careful when trying to apply the length contraction formula in more complex cases, like the distance between the spaceships, and the pole flying past the wheel. The pole is certainly length contracted according to the road frame, and it is easy enough to calculate its length. However, the length contraction formula (LCF) does not tell you that the right edge of the pole will not be coincident with the right edge of the wheel at t=0.000 because that does not happen until t=0.866. Thus, the LCF can be a little bit misleading. That is all I was trying to say. Thanks.

JT: That is fine, you can simplify the scenario so that the length contraction formula can be applied simply.

cinci: It doesn't require simplification. You chose to use the time LT to find that t = -0.8 for the spaceship. You could have noted that the ship would travel .6 in the O frame and because the ship has a relative velocity of .6 to that frame, it would measure the distance travelled as .6*(1 - .6^2)^.5 = .6*.8 = .48. Travelling at .6c, it would cover the distance in 0.8 seconds. Time dilation and length contraction are opposite sides of the same coin; when you get one, you also get the other.

You made a comment recently that I only assumed the ellipse in my version of Gron's solution. But that isn't correct either. If you transform a coordinate from one frame to another, the length of the coordinate in the second frame is always (1 - (v/c)^2)^.5 times the original coordinate; this is because the other endo f the coordinate is at
x = x' = 0.

JT: But that does not change the fact that one must be very careful when trying to apply the length contraction formula in more complex cases, like the distance between the spaceships, and the pole flying past the wheel. The pole is certainly length contracted according to the road frame, and it is easy enough to calculate its length. However, the length contraction formula (LCF) does not tell you that the right edge of the pole will not be coincident with the right edge of the wheel at t=0.000 because that does not happen until t=0.866. Thus, the LCF can be a little bit misleading. That is all I was trying to say. Thanks.

Originally Posted by cincirob

JT: That is fine, you can simplify the scenario so that the length contraction formula can be applied simply.

cinci: It doesn't require simplification. You chose to use the time LT to find that t = -0.8 for the spaceship. You could have noted that the ship would travel .6 in the O frame and because the ship has a relative velocity of .6 to that frame, it would measure the distance travelled as .6*(1 - .6^2)^.5 = .6*.8 = .48. Travelling at .6c, it would cover the distance in 0.8 seconds. Time dilation and length contraction are opposite sides of the same coin; when you get one, you also get the other.

Sorry but your scenario, as originally stated, asked for S1 to measure the distance to S2. When S1's clock displays t'=-0.8 it must measure the distance to S2 as 0.8*0.882=0.705. That is not the simple length contraction that you are now talking about.

You have simplified the scenario so that S1 no longer has to measure the distance to S2 (which has a composed velocity of 0.882c). Instead, you want S1 to measure the distance to O (which has the non-composed velocity of 0.600c).

Originally Posted by cincirob

You made a comment recently that I only assumed the ellipse in my version of Gron's solution. But that isn't correct either. If you transform a coordinate from one frame to another, the length of the coordinate in the second frame is always (1 - (v/c)^2)^.5 times the original coordinate; this is because the other endo f the coordinate is at
x = x' = 0.

It sounds like you are finally realising that a circle (axle frame) must transform to an ellipse (road frame). Congratulations, you are finally in agreement with what everyone else has been saying.

Originally Posted by JTyesthatJT to cinci

It sounds like you are finally realising that a circle (axle frame) must transform to an ellipse (road frame). Congratulations, you are finally in agreement with what everyone else has been saying.

I wouldn't hold your breath

Thank You,
SinceYouAsked

JT: That is fine, you can simplify the scenario so that the length contraction formula can be applied simply.

cinci: It doesn't require simplification. You chose to use the time LT to find that t = -0.8 for the spaceship. You could have noted that the ship would travel .6 in the O frame and because the ship has a relative velocity of .6 to that frame, it would measure the distance travelled as .6*(1 - .6^2)^.5 = .6*.8 = .48. Travelling at .6c, it would cover the distance in 0.8 seconds. Time dilation and length contraction are opposite sides of the same coin; when you get one, you also get the other.

JT: Sorry but your scenario, as originally stated, asked for S1 to measure the distance to S2. When S1's clock displays t'=-0.8 it must measure the distance to S2 as 0.8*0.882=0.705. That is not the simple length contraction that you are now talking about.

You have simplified the scenario so that S1 no longer has to measure the distance to S2 (which has a composed velocity of 0.882c). Instead, you want S1 to measure the distance to O (which has the non-composed velocity of 0.600c).

cinci: I didn't intend to ask the S1 to S2 distance as I said before. But what I just showed you is that the .8 seconds travel time for S1 (or S2) seconds that you used to get the distance between them could just as easily have been determined using length contraction. You've been asking me to do the problem using length contraction. That's how it can be done.

cinci: You made a comment recently that I only assumed the ellipse in my version of Gron's solution. But that isn't correct either. If you transform a coordinate from one frame to another, the length of the coordinate in the second frame is always (1 - (v/c)^2)^.5 times the original coordinate; this is because the other end of the coordinate is at
x = x' = 0.

JT: It sounds like you are finally realising that a circle (axle frame) must transform to an ellipse (road frame). Congratulations, you are finally in agreement with what everyone else has been saying.

cinci: I always knew that the approach Gron used would produce and ellipse. I posted that solution time and again. Don't pretend otherwise.

I'm glad I don't have to hold my breath until you and SYA realize that it length contraction. The rest of the planet already knows.

Moderator Observation: There is an odd bit of frustration and personal remarks creeping into some of the posts. Let us take care to keep it polite. Nothing major, just want to keep it that way. Thank you.

Originally Posted by cincirob

JT: Sorry but your scenario, as originally stated, asked for S1 to measure the distance to S2. When S1's clock displays t'=-0.8 it must measure the distance to S2 as 0.8*0.882=0.705. That is not the simple length contraction that you are now talking about.

You have simplified the scenario so that S1 no longer has to measure the distance to S2 (which has a composed velocity of 0.882c). Instead, you want S1 to measure the distance to O (which has the non-composed velocity of 0.600c).

cinci: I didn't intend to ask the S1 to S2 distance as I said before. But what I just showed you is that the .8 seconds travel time for S1 (or S2) seconds that you used to get the distance between them could just as easily have been determined using length contraction. You've been asking me to do the problem using length contraction. That's how it can be done.

Yes, I agree that the length contraction formula works for the case where S1's own clock measures t'=-0.800 at the time it measures its distance to O as 0.800*0.600=0.480. One can simply take the distance as measured by O and divide by the gamma factor for v=0.600c, like this: 0.600/1.250=0.480.

But that method does not work for more complex scenarios, such as when S1 is to measure his distance to S2, or when we want to know the location of where and when the right edge of a pole is coincident with the right edge of a wheel. Since your method works in some cases but not others, you have to be extremely careful, or else you run the risk of making errors.

Originally Posted by cincirob

JT: It sounds like you are finally realising that a circle (axle frame) must transform to an ellipse (road frame). Congratulations, you are finally in agreement with what everyone else has been saying.

cinci: I always knew that the approach Gron used would produce and ellipse. I posted that solution time and again. Don't pretend otherwise.

I'm glad I don't have to hold my breath until you and SYA realize that it length contraction. The rest of the planet already knows.

Everyone knows it is some form of length contraction. Even if the shape were a pear, it would still be due to length contraction of the various horizontal poles flying by. So how can we determine whether the correct answer is the length-contracted-pear, or the length-contracted-ellipse?

The way SYA, VeeDee, and I do it is that we use the full Lorentz transformation equations. Those equations can tell us the contracted length of the pole, but they can also tell us that the right edge of the pole will not be coincident with the right edge of the wheel at t=0.000, because that event does not happen until t=0.866, when the right edge of the pole is located at x=1.000. At that road-time, the axle is located at x=vt=0.750, thus the correct answer is that the shape must be an ellipse. We do not have to guess about whether to apply the length contraction formula to the poles or to the circle itself. We just use the LT's and let the correct answer be whatever the LT's say it should be.

Response to post #1:
Length contraction (lc) is a motion induced phenomena resulting in deformed em fields. Forms of matter; particles, atoms, and composite objects would be subject to this effect. Although space may have a structure, it is not of em fields, and thus does not experience lc as defined above. Since it is also invisible, there is no way to verify any dimensional change. Special Relativity (SR) requires reciprocal observations by two observers in relative motion.
In fig.1 A is moving at .6c in the U frame. A has a rod of .5 length, with a clock and mirror at the far end, aligned in opposite x directions. Light is emitted at E, reflects at R and R2, and is detected at D. R2 is added to show that the axis of simultaneity (R2-R) or (Ax) is a natural result of a constant light speed c, and the motion of A. A reflecting object is located at Ux = 1.00. U measures the distance from A to R as .40, as a result of lc. The geometric coordinate transform (the arc from Ut of D to the vertical at Ux of D) gives ct = 1.00. U concludes A will think event D occurred at A(t) = 1.00, as a result of time dilation.
In fig.2 events E, R, and D are scaled by 1/g, while retaining the same ct scale. Then events are assigned to the A timeline using the axis of simultaneity. A calculates a time for R' using the SR synch convention of dividing the round trip time in half (magenta).
Transforming pertinent information from fig.2 to fig.3, the A perspective is formed. A assumes being in a rest frame with the reflecting object passing by at .6c. In fig.1 A detects the signal while at Ux = .75, but his clock reads 1.00, which equates to .60 from the origin. The object arrives earlier than calculated. Since his perception of time has slowed to the same extent as his clock, he concludes the objects are closer in the direction of motion, as if the space has contracted. His perception of lc of the world outside his frame in the x direction results from his interpretation of his own td, as shown in fig.2. The object with a Ux = 1.00, would be perceived as being at .8. If the reflecting object at Ux = 1.00 were a clock, then from fig.3, A would measure it's rate as (1.67)/(2.08) = .80, the same as U's measure of the A clock.
A clock at R in fig.1 would read 1.00. Even though the light paths are not equal (blue), the synch convention assigns an earlier time (R') for forward events as shown in fig.3.
Scaling the time line for U, maintains the perception of a rest frame for A, and produces reciprocity of td.
Coordinate transformations.
U(x, t) = (1, 1)
x' = xg(x-vt) = 1.25(1-.6) = .50
t' = tg(t-vx) = 1.25(1-.6) = .50
U(x, t) = (1, 0)
x' = xg(x-vt) = 1.25(1) = 1.25
t' = tg(t-vx) = 1.25(0-.6) = -.75



https://app.box.com/s/pde5hthfw7ysuwwlhoot

OK then,

(1) Using the length contraction formula (LCF) alone to determine a body's length, results in a soln where the spatial endoints of the body are assumed as simultaneous measurements in time. But that assumption fails if the body moves in both systems ...

(2) If the body is moving, and the moving body's length is LCF'd to another frame in which it also moves (target frame), then the LCF soln cannot match the length of the moving body per the target frame. It's the motion of the body in the frame (used for LT input coordinates) that causes this failure, because the body is not at rest in that POV.

(3) While the LCF alone cannot be used to correctly determine a body's moving length per (2) above, any LT transformation of a point of the moving body "DOES produce a valid and correct soln in the other frame in which the body also moves". That's why GRON's analysis works using the LTs, and which also explains why he did not just use an LCF analysis.

Once all the LT solns are attained, one need only collect all the solns for a specific time in the LT output frame, and the length of the moving body is known in that POV. There are no assumptions necessary.

Gron's eqns had the motion of rotating disk atoms "built in" to his axle frame equations using ω and given the r and t' values. As such, the location of any (moving) rotating disk atom is related to a "momentary co-location of a stationary spatial point in axle space", which of course means the spatial point is considered at a specific time t' and thus is a 4 dimension LT input coordinate (ie an event, which does not move). The 4d spacetime axle frame coordinate (an event) is transformed to the ground system. The reason this may be done, is because if a point (or disk-atom, moving or not) exists at x',y',z',t' in the axle system, then it MUST exist at the LT transformed soln X,Y,Z,T per ground.

For any steady rate scenario, ω is constant. So Gron can select a rotating atom at a specific radius r and time t', then determine X,T per ground. Run the transformation again with t' a little larger than the t' used prior, and the y'=y coordinate has changed due to the rotation ω over the delta rotation time ∆t' at the atom's same radius r. One can play with all Gron's input variables, and obtain correct LT solns in the ground system. Consider points where rotating disk atoms exist per axle, then one knows where and when they exist per ground. Hence, determining the shape of the disk per ground requires nothing more than the consideration of all LT solns for a specific ground time T.

Just for reference, see page 38 of Gron's paper ... http://areeweb.polito.it/ricerca/rel...los/gron_d.pdf

Thank You,
SinceYouAskewd

Originally Posted by phyti

Length contraction (lc) is a motion induced phenomena resulting in deformed em fields. Forms of matter; particles, atoms, and composite objects would be subject to this effect. Although space may have a structure, it is not of em fields, and thus does not experience lc as defined above. Since it is also invisible, there is no way to verify any dimensional change. Special Relativity (SR) requires reciprocal observations by two observers in relative motion.

But the volume of an object is mostly empty space between its atoms. So, if we measure an object as length contracted by a factor of 1/gamma, we aren't just measuring the atoms themselves as length-contracted, but also the space between the atoms must be contracted by that same factor.

Also, earlier we were talking about the distance between two point-like spaceships. There was nothing but empty space between them, yet we calculated the distance between them to be contracted.

Phyti, you are thinking about this is the wrong way in my opinion. "Length contraction is a motion induced phenomena ( I think you meant phenomenon) resulting in deformed em fields" is not really getting what relativity is about. There is no deformation of the fields, or even of spacetime for that matter. All there is a a rotation of the spacetime axes. Deformation is really the wrong word in my opinion. Only when one frame is considered from the other are the axes between space and time different to what is measured in a rest frame.

JT: Yes, I agree that the length contraction formula works for the case where S1's own clock measures t'=-0.800 at the time it measures its distance to O as 0.800*0.600=0.480. One can simply take the distance as measured by O and divide by the gamma factor for v=0.600c, like this: 0.600/1.250=0.480.

But that method does not work for more complex scenarios, such as when S1 is to measure his distance to S2, or when we want to know the location of where and when the right edge of a pole is coincident with the right edge of a wheel. Since your method works in some cases but not others, you have to be extremely careful, or else you run the risk of making errors.

cinci: What? Your solution was to show that .8s passed while S1 moved to the collision. During that .8s S2 was travelling toward S1 at .882c. .8*.882c = .705 ls. That's how you got the answer and you could have used length contraction to get it.

JT: The way SYA, VeeDee, and I do it is that we use the full Lorentz transformation equations.

cinci: And the full LT will always transform a coordinate as (1 - (v/c)^1)^.5 * the original coordinate.

Originally Posted by cincirob

JT: Yes, I agree that the length contraction formula works for the case where S1's own clock measures t'=-0.800 at the time it measures its distance to O as 0.800*0.600=0.480. One can simply take the distance as measured by O and divide by the gamma factor for v=0.600c, like this: 0.600/1.250=0.480.

But that method does not work for more complex scenarios, such as when S1 is to measure his distance to S2, or when we want to know the location of where and when the right edge of a pole is coincident with the right edge of a wheel. Since your method works in some cases but not others, you have to be extremely careful, or else you run the risk of making errors.

cinci: What? Your solution was to show that .8s passed while S1 moved to the collision. During that .8s S2 was travelling toward S1 at .882c. .8*.882c = .705 ls. That's how you got the answer and you could have used length contraction to get it.

I'm sure it can be done, since S2's frame is just as valid a frame as any other frame. But I bet it will require more steps than just 0.800*0.882=0.705.

But you definitely will not be able to use the LCF to determine when the right edge of the pole will be co-located with the right edge of the wheel.

Originally Posted by cincirob

JT: The way SYA, VeeDee, and I do it is that we use the full Lorentz transformation equations.

cinci: And the full LT will always transform a coordinate as (1 - (v/c)^1)^.5 * the original coordinate.

Really? Here is the full LT:
x' = (x - vt) / √(1 - (v²/c²))

Please show me how to rearrange that to be what you claim:
x' = x * √(1 - (v²/c²))

Hint: You will need to get rid of the t variable completely. Good luck.

--------

Here, let's try an example. For v=0.866, at t=1.000 the 12:00 o'clock point on the wheel is located at x=vt=0.866
x' = (x - vt) / √(1 - (v²/c²)) = 0.000

Looks like your claim is all wet.

Originally Posted by JT to cinci

Really? Here is the full LT:
x' = (x - vt) / √(1 - (v²/c²))

Please show me how to rearrange that to be what you claim:
x' = x * √(1 - (v²/c²))

Hint: You will need to get rid of the t variable completely. Good luck.

--------

Pretty simple question there indeed. Yes, I too would like to see how cincirob answers this question. I eagerly await.

Thank You,
SinceYouAsked

JT: Yes, I agree that the length contraction formula works for the case where S1's own clock measures t'=-0.800 at the time it measures its distance to O as 0.800*0.600=0.480. One can simply take the distance as measured by O and divide by the gamma factor for v=0.600c, like this: 0.600/1.250=0.480.

But that method does not work for more complex scenarios, such as when S1 is to measure his distance to S2, or when we want to know the location of where and when the right edge of a pole is coincident with the right edge of a wheel. Since your method works in some cases but not others, you have to be extremely careful, or else you run the risk of making errors.

cinci: What? Your solution was to show that .8s passed while S1 moved to the collision. During that .8s S2 was travelling toward S1 at .882c. .8*.882c = .705 ls. That's how you got the answer and you could have used length contraction to get it.

JT: I'm sure it can be done, since S2's frame is just as valid a frame as any other frame. But I bet it will require more steps than just 0.800*0.882=0.705.

cinci: Well .882 = 2*.6/(1+.6^2) is a step. S2 traverses .6 distance in .6/.6 = 1 second in O's frame. I guess that's a step. Now you can go two ways. While O's clock passes 1 sec, S2's clock passes 1*(1 - .6^2)^.5 = .8 sec. .8*.882 = .705. Or, if S2 traverses .6 ls in O's frame he traverses .6*(1 - .6^2)^.5 = .48 ls in his own frame; Since his velocity is .6c, this talks .48/.6 = .8s. So again .8*/882 = .705. I already showed you all these calculations.

JT: But you definitely will not be able to use the LCF to determine when the right edge of the pole will be co-located with the right edge of the wheel.

cinci: What does that have to do with the spaceships? As for the pole, the time at its right edge is t = -vx/(1 - V^2)^.5 and you can get x from LCF.

JT: The way SYA, VeeDee, and I do it is that we use the full Lorentz transformation equations.

cinci: And the full LT will always transform a coordinate as (1 - (v/c)^1)^.5 * (the original coordinate).

Really? Here is the full LT:
x' = (x - vt) / √(1 - (v²/c²))

Please show me how to rearrange that to be what you claim:
x' = x * √(1 - (v²/c²))

Hint: You will need to get rid of the t variable completely. Good luck.

cinci: After all this time it becomes clear that you really don't understand Gron's analysis. His equation for x is

X = (1 - (v/c)^2)^.5*cos(wt' + Q). So his analysis does what you say can't be done. All of the coordinates of the ellipse are found by length contracting a coordinate in the axle frame.

I don't know what you intended for prime an unprimed variables so I'll spell it out. Using the inverse LT.

x[in the wheel frame] = (x[in the axle frame] - vt[axle frame])/(1 - (v/c)^2)^.5

at t = 0,

x[axle frame] = x[wheel frame](1 - (v/c)^2)^.5

The axle frame, like all frames has only one time and it can be zero. The LTs in the form we use them are derived for

x = x' = 0 and t = t' = 0.

But an observer in the wheel frame doesn't see all the t[axle] at zero, RoS tells us that at t[wheel] = 0 he will see

t[axle] = (t[wheel] - vx/c^2)/(1 - (v/c)^2)^.5

But we usually look at the thing at t[wheel] = 0 so

t[axle] = (0- vx/c^2)/(1 - (v/c)^2)^.5

JT: Here, let's try an example. For v=0.866, at t=1.000 the 12:00 o'clock point on the wheel is located at x=vt=0.866
x' = (x - vt) / √(1 - (v²/c²)) = 0.000

JT: Looks like your claim is all wet.

cinci: Actually it looks like you don't understand relativity. Gron doesn't do his analysis at t = 1.00, he does it at t = 0. If you do it at
t = 1.00, you are looking at the wheel after it has rolled down the road; at t = 1, the origin of the axle frame has moved to x = .866 and that's where the center of the wheel is also.

All your little analysis shows is that the coordinate of the 12:00 point in the axle frame is always zero. Most of us already knew that. Since the 12:00 coordinate was zero in the wheel frame, applying length contraction says x' = 0*(1 - (v/c)^2)^.5 = 0. You know, anything times zero is still zero. So length contraction still works even in this degenerative case. It will be the same if you roll the wheel to infinity.

SYA: Pretty simple question there indeed. Yes, I too would like to see how cincirob answers this question.

I eagerly await.

cinci: Now you don't have to wait any more.

So when you said this:

Originally Posted by cincirob

cinci: And the full LT will always transform a coordinate as (1 - (v/c)^1)^.5 * (the original coordinate).

You meant to say that it is true only for the special case where t=0.000, but it is not true in general. And you just forgot to mention those conditional statements.

And you want everyone to believe that I don't understand relativity, whereas you do. Got it.

cinci: And the full LT will always transform a coordinate as (1 - (v/c)^1)^.5 * (the original coordinate).

JT: You meant to say that it is true only for the special case where t=0.000, but it is not true in general. And you just forgot to mention those conditional statements.

And you want everyone to believe that I don't understand relativity, whereas you do. Got it.

cinci: This whole discussion is you trying to prove I don't know relativity. Now you get all sensitive when I shove it up your nose? Give me a break.

Originally Posted by cincirob

cinci: As for the pole, the time at its right edge is t = -vx/(1 - V^2)^.5

Actually the road time when the right edge of the pole coincides with the right edge of the wheel is this:
t = γ(t' + (vx' / c²)) = 0.866
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Do you agree that the correct velocity to use in that equation is the axle velocity v=0.866, because x' and t' are axle-frame coordinates? Or did you want to use the composed velocity of the pole?

Originally Posted by cincirob

cinci: ...and you can get x from LCF.

Or you can get x from this equation for x:
x = γ(x' + vt') = 1.000
Where:
γ = 2.000
v = 0.866
t' = 0.000
x' = 0.500

Is there some reason you don't use the LT's for this?