# Thread: Einstein's equation E=mc² Question? Possibly challenge.

1. I have most likely a simple question, I watch alot of documentries on physics and well everything really... my question is this, Einstein's equation E=mc² pops up on everything, meaning energy is equal to mass. This dictates that the more somethings energy increases, so will its mass right? But what about light it self.. light has zero mass, No? and has tons of energy eg: solar panels.. I thought maybe it was the source for example the sun energizing the oxygen but made no sense 1. theres no oxygen in space 2. Solar panels don't use oxygen. lol, foolish thought but kinda funny.. I'm no math geniuses clearly but I was hoping for some clarity thanks guys/girls... and sry if this was a foolish question..
Your field is amazing. Mind = blown
Peace n love.

2. That isn't the full equation. Try this
http://en.wikipedia.org/wiki/Energy–momentum_relation
Light has no rest mass but it does have momentum (p).

3. E=mc^2 is only a part of the whole picture. It is the formula you use when you want to find the energy equivalence of the rest mass of an object. Light has no rest mass, So you need to use the full form formula:

Where p is the relativistic momentum.

Ergo, for an object with a rest mass and at rest, it reduces to E=mc^2

For something with no rest mass like a Photon, it reduces to E=pc

And for a photon,

where h is Planck's constant, and lambda is the wavelength of the photon.

Thus the energy of a photon is

4. E^2=(pc)^2+(mc^2)^2 this is the full equation.
when m=0 (e.g. photons,gluons etc.), it minimizes to E=pc

5. Thanks Janus for the clarification.

6. danny1986 - The mass you're thinking of is called relativistic mass and is defined as the m in p = mv. Therefore anything that has momentum has mass. This is also called inertial mass. You can read all about this at
Relativistic mass

7. Originally Posted by Physicist
The mass you're thinking of is called relativistic mass and is defined as the m in p = mv. Therefore anything that has momentum has mass.
This is demonstrably false, photons have momentum , yet they are massless.

8. It isn't demonstrably false. A photon has no rest mass, but it has a non-zero active gravitational mass, and a non-zero inertial mass. Have a look at Einstein's E=mc² paper and note the last line:

"If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies".

Also have a read of Light is heavy by van der Mark and 't Hooft (not the Nobel 't Hooft):

"On the one hand, electromagnetic radiation must have zero rest mass in order to propagate at the speed of light, but on the other hand, since it definitely carries momentum and energy, it has non-zero inertial mass. Hence, by the principle of equivalence, it must have non-zero gravitational mass, and so, light must be heavy. In this paper, no new results will be derived, but a possibly surprising perspective on the above paradox is given".

Physicist: it's nice to see somebody who knows his stuff. Welcome. I'm John Duffield, an IT guy who developed a deeper interest in physics about ten years back when our teenage children gave up all their science subjects. This little article kind of sums me up.

9. Originally Posted by Farsight
It isn't demonstrably false. A photon has no rest mass, but it has a non-zero active gravitational mass, and a non-zero inertial mass.
Piling another falsity on top of a previous falsity, Duffield. Mainstream science teaches you that photons are massless. Use the "active gravitational mass" to derive the photon trajectories in the presence of a gravitating body. Let's see the derivation, John.

10. No. And it isn't a falsehood. A concentration of energy causes gravity.

11. Originally Posted by Duffield
No. And it isn't a falsehood. A concentration of energy causes gravity.
So, the photons have energy (and momentum). Contrary to your earlier claim, they have no mass, gravitational or otherwise. You need to stop trying to do physics by cherrypicking soundbites, Farsight. It isn't working. Never did.

12. Photons don't have rest mass, but they do have energy so are affected by gravitational fields.

13. Originally Posted by Jilan
Photons don't have rest mass, but they do have energy so are affected by gravitational fields
All correct. Does the above mean that you agree with Farsight once again? Do photons "have gravitational mass"?

14. I think a photon would need to confined for this to be the case.

15. I think that you are misinterpreting the t'Hooft paper the same way that Farsight does. The fact that the photon exerts pressure on the walls of the enclosure doesn't mean that it has "gravitational mass". It means that it exchanges impulse with the walls, thus exerting a force on the walls.

16. It is nothing new or conversial to say that confined photons exhibit the properties of inertial and gravitational mass.
http://arxiv.org/pdf/1307.2830v1.pdf
"The inertial and gravitational mass of electromagnetic radiation (i.e., a photon distribution) in a cavity with reflecting walls has been treated by many authors for over a century. After many contending discussions, a consensus has emerged that the mass of such a photon distribution is equal to its total energy divided by the square of the speed of light".

17. What does a predicate like "has gravitational mass" actually mean, operationally speaking? If you are asking whether light is deflected by gravitational fields, the answer is yes. If you are asking whether light can act as a source of gravitational fields, the answer is again yes (whether confined or not).

18. Originally Posted by btr
What does a predicate like "has gravitational mass" actually mean, operationally speaking? If you are asking whether light is deflected by gravitational fields, the answer is yes. If you are asking whether light can act as a source of gravitational fields, the answer is again yes (whether confined or not).
While your statements are correct, it doesn't mean that photons "have gravitational mass". Photons are massless. They have energy and it is the energy that gravitates. More precisely, the element of the stress energy tensor represents the contribution of energy to the gravitation, where and E is the energy density per unit mass. The fact that gives a lot of people (not only the garden varity cranks) the wrong impression that photons might "have gravitational mass".
The fact that both you and Jilan repeat the same nonsense as Farsight makes it rather disturbing.

19. Originally Posted by Jilan
It is nothing new or conversial to say that confined photons exhibit the properties of inertial and gravitational mass.
http://arxiv.org/pdf/1307.2830v1.pdf
An interesting paper. Photons are massless. They have energy and it is the energy that gravitates. More precisely, the element of the stress energy tensor represents the contribution of energy to the gravitation, where and E is the energy density. The fact that gives a lot of people (not only the garden varity cranks) the wrong impression that photons might "have gravitational mass".

20. Originally Posted by x0x
While your statements are correct, ...

Originally Posted by x0x
The fact that both you and Jilan repeat the same nonsense as Farsight makes it rather disturbing.
Oh, wait, you don't agree after all?

So what specifically do you disagree with that I actually said? Can you provide a quote? Or is it something you imagined I said?

22. Please don't be so hasty (I feel you were,) but try to make this forum a better place.

23. Originally Posted by x0x
I did that, and I see that you edited your previous post. Let's take a look at what we have now:

Originally Posted by x0x
While your statements are correct, it doesn't mean that photons "have gravitational mass". Photons are massless. They have energy and it is the energy that gravitates. More precisely, the element of the stress energy tensor represents the contribution of energy to the gravitation, where is the energy density. The fact that gives a lot of people (not only the garden varity cranks) the wrong impression that photons might "have gravitational mass".
The fact that both you and Jilan repeat the same nonsense as Farsight makes it rather disturbing.
Originally Posted by x0x
An interesting paper. Photons are massless. They have energy and it is the energy that gravitates. More precisely, the element of the stress energy tensor represents the contribution of energy to the gravitation, where is the energy density. The fact that gives a lot of people (not only the garden varity cranks) the wrong impression that photons might "have gravitational mass".
You wrote the formula twice above. Since is (as you also said twice) the energy density, that gives some strange dimensions, no?

OK, so now that I have tried reading, are you actually going to answer my questions in #20? Or do I simply have to guess what it is that I said that you disagreed with?

24. Originally Posted by x0x
The fact that both you and Jilan repeat the same nonsense as Farsight makes it rather disturbing.
I too am interested to hear which of my sentences on this post you regard as nonsense.

25. Originally Posted by Jilan
I too am interested to hear which of my sentences on this post you regard as nonsense
The claim that the photon has "gravitational mass". You, btr and Farsight share the same claim.

26. Originally Posted by x0x
The claim that the photon has "gravitational mass". You, btr and Farsight share the same claim.
I will now just sit back and watch while you fail to produce a quote in which I claimed that.

27. Originally Posted by btr
But which of my claims did you disagree with? Can you quote it for me?
The claim that "the photon has gravitational mass". You and Jilan share this claim with Farsight. You didn't phrase it as badly as the other two but it is just as wrong.

28. See #26 - I edited it while you were in the middle of composing your reply.

29. If a black hole absorbs a photon does the gravitational mass of the black hole increase?

30. Originally Posted by Jilan
If a black hole absorbs a photon does the gravitational mass of the black hole increase?
Mass is not additive , total energy is. So, what increases is the total energy of the black hole. I thought that I made a very clear argument explaining the structure of the stress-energy tensor.

31. Originally Posted by x0x
The claim that "the photon has gravitational mass". You and Jilan share this claim with Farsight. You didn't phrase it as badly as the other two but it is just as wrong.
Here's the post you just linked to:

Originally Posted by btr
What does a predicate like "has gravitational mass" actually mean, operationally speaking? If you are asking whether light is deflected by gravitational fields, the answer is yes. If you are asking whether light can act as a source of gravitational fields, the answer is again yes (whether confined or not).
Nowhere in there did I say that "the photon has gravitational mass". I suggest you

Originally Posted by x0x
The point I was actually making is this: while it may be fun for some people to have these little debates about whether a photon has "gravitational mass", unless you actually define what "gravitational mass" means in operational terms, the question is meaningless. In the interests of moving past that semantic issue, I suggested a couple of questions about what we can observe, like whether light rays curve in gravitational fields, or whether light rays can act as sources of gravitational fields (in both cases, the answer is yes). Jilan asked another good question about actual physics, namely if you fire a photon into a black hole, does the mass of the black hole increase? Again, the answer is yes. If someone wants to sum up those facts by saying "the photon has a gravitational mass", more power to them. As long as we all understand each other and agree on what we will observe, I really couldn't care less.

Just out of interest, how do you define "gravitational mass", or do you hold that the phrase has no meaning at all?

Originally Posted by x0x
Mass is not additive , total energy is. So, what increases is the total energy of the black hole. I thought that I made a very clear argument explaining the structure of the stress-energy tensor.
Yeah, about that... see post #23.

32. Originally Posted by btr
Jilan asked another good question about actual physics, namely if you fire a photon into a black hole, does the mass of the black hole increase? Again, the answer is yes.
Nope, the answer is "no". Mass is not additive, total energy is. What increases is the total energy of the black hole.

You wrote the formula twice above. Since is (as you also said twice) the energy density, that gives some strange dimensions, no?
Not at all. I told you that E is the energy density, therefore is unitless, just like the rest of the components of the tensor.

or whether light rays can act as sources of gravitational fields (in both cases, the answer is yes).
"Light rays as sources of gravitational fields" is total rubbish, sounds like something Farsight would post. According to basic GR the source of gravitational field is the stress-energy tensor.

33. Originally Posted by x0x
Nope, the answer is "no". Mass is not additive, total energy is. What increases is the total energy of the black hole.
So you are saying that when a black hole absorbs a photon, the black hole's energy increases but its mass does not? You must be using a non-standard definition of "black hole mass" to make such a bizarre-sounding statement.

34. Originally Posted by x0x
"Light rays as sources of gravitational fields" is total rubbish,
A pretty standard exercise in General Relativity text books is to show that two beams of light travelling antiparallel to one another attract each other gravitationally, while beams travelling parallel do not.

You've evidently never had to do any exercises like that, so I'm sure you'll find the following paper illuminating (geddit?):

On the Gravitational Field Produced by Light, Richard C. Tolman, Paul Ehrenfest, and Boris Podolsky, Phys. Rev. 37, 602 (1931).

Originally Posted by x0x
sounds like something Farsight would post.
Sounds like an association fallacy and an ad hominem.

Originally Posted by x0x
According to basic GR the source of gravitational field is the stress-energy tensor.
According to basic electromagnetism, if you actually bother to compute (or look up) the stress-energy tensor for a light wave, you will find that it is non-zero.

35. Originally Posted by btr
A pretty standard exercise in General Relativity text books is to show that two beams of light travelling antiparallel to one another attract each other gravitationally, while beams travelling parallel do not.
Doesn't support your claim that "Light rays as sources of gravitational fields". Basic GR teaches you that the source of the gravitational field is the stress-energy tensor. This is the RHS of the EFEs.

According to basic electromagnetism, if you actually bother to compute (or look up) the stress-energy tensor for a light wave, you will find that it is non-zero.
Because the photons have energy. Contrary to your claims, they do not have "gravitational mass".

So you are saying that when a black hole absorbs a photon, the black hole's energy increases but its mass does not?
Once again, it is the total energy that it is additive, the mass is not. As a matter of fact, the mass of the resulting system (black hole and photon) may be less than the original mass of the black hole. So, contrary to your claims, the mass of the black hole does not increase. The explanation is simple, do you think that you could derive it?

So you said that is the energy density
Typo, live with it.

More oddly still, even if you had said was an energy density, that still wouldn't make dimensionless; it would make it have the dimensions of an ordinary (mass) density.
E is energy density, as in energy per unit of mass. Therefore, contrary to your objection, is indeed dimensionless. You are grasping at straws now.

36. Originally Posted by x0x
I told you that E is the energy density, therefore is unitless, just like the rest of the components of the tensor.
You actually said:

Originally Posted by x0x
...More precisely, the element of the stress energy tensor represents the contribution of energy to the gravitation, where is the energy density. The fact that gives a lot of people (not only the garden varity cranks) the wrong impression that photons might "have gravitational mass".
So you said that is the energy density, not . You then introduced into the post with nothing more than the equation , giving units of energy density (so whatever your is, it is not dimensionless). So you are wrong about the units of this mysterious , and you still haven't told us what on Earth it is supposed to represent; it's clearly not an energy, nor is it an energy density, so what is it? It looks like a mistake to me.

(More oddly still, even if you had said was an energy density, that still wouldn't make dimensionless; it would make it have the dimensions of an ordinary (mass) density. So even your attempted correction is wrong.)

37. Originally Posted by x0x
Doesn't support your claim that "Light rays as sources of gravitational fields". Basic GR teaches you that the source of the gravitational field is the stress-energy tensor. This is the RHS of the EFEs.
The same goes for all types of matter. Every type of matter that we (that is, the rest of us) consider to be sources of gravitational fields, contributes to the stress-energy tensor in the GR field equation. If you are really going to say that light rays do not qualify as sources, then you are also saying that protons, neutrons, electrons, muons, etc. don't qualify either. Go for it, I say; it's a free world. Just know that you are going to struggle to communicate with anyone else by adhering to such idiosyncrasies. But, hey, at least we can agree that light rays are sources of gravitational fields in the same way that all other matter is!

Originally Posted by x0x
Because the photons have energy. Contrary to your claims, they do not have "gravitational mass".
You're still beating that straw man, eh?

Originally Posted by x0x
Once again, it is the total energy that it is additive, the mass is not.
Once again, the rest mass of the black hole is its rest energy divided by . If I pop a photon into the black hole and the rest energy of the hole goes up, then the rest mass must also go up.

Originally Posted by x0x
As a matter of fact, the mass of the resulting system (black hole and photon) may be less than the original mass of the black hole.
Wrong. I presume you're alluding to the Penrose process, but forget it; you won't ever get that with a single photon.

------

Originally Posted by x0x
Typo, live with it. ... E is energy density, as in energy per unit of mass.
Utterly unconvincing. I'm done with this back-pedalling style of argumentation you've adopted; goodbye.

38. Originally Posted by btr
Once again, the rest mass of the black hole is its rest energy divided by . If I pop a photon into the black hole and the rest energy of the hole goes up, then the rest mass must also go up.
Basic math says that you are wrong. Hint: if you put two photons together the equivalent mass of the resulting system depends on the orientation of their momenta. You surely remember that, don't you?

If you are really going to say that light rays do not qualify as sources,
Yep, for the n-th time , light rays don't qualify as sources, their energy does.

Did you get the part with the energy density and the fact that the tensor components are dimensionless?

39. Can I just reiterate that a photon has non-zero "active gravitational mass". This isn't the same thing as "rest mass". It's a measure of how much gravity something causes. Like "relativistic mass", it's best to think of it as a measure of energy.

40. Originally Posted by Farsight
Can I just reiterate that a photon has non-zero "active gravitational mass".
Reiterating the same misconception doesn't make it true.

41. I think that this argument has descended into an argument over semantics. Not particularly interesting, yawn!

42. [
Originally Posted by x0x
This is demonstrably false, photons have momentum , yet they are massless.
You are incorrect. You clearly did not read the reference in the Newsgroup Physics FAQ on mass that I referred to you and you ignored the definition that I just gave you, i.e. that what I said regarding the relativistic mass (which I’ll simply refer to as just mass) of a particle with momentum p is defined as the m in p = mv. That means that the relativistic mass of a photon is m = p/v. Since for a photon v = c we have m = p/c. Also for a photon p = E/c so when we plug this in we obtain m = (E/c)/c = E/c^2. The link I gave you above describes and explains this. Did you read it? If not, why?

What I’ve just explained is found in most SR textbooks and in some GR textbooks. A friend of mine uses it in the course that he teaches at MIT on the Early Universe: Here is a short list of examples

Relativity: Special, General and Cosmological, Rindler, Oxford Univ., Press, (2001), page 120
According to Einstein, a photon with frequency n has energy hn /c2, and thus (as he only came to realize several years later) a finite mass and a finite momentum hn/c.

From Introducing Einstein's Relativity, Ray D'Inverno, Oxford Univ. Press, (1992), page 50
Finally, using the energy-mass relationship E = mc2,, we find that the relativistic mass of a photon is non-zero and given by

m = p/c.

Combining these results with Planck's hypothesis, we obtain the following formulae for the energy E, relativistic mass m, and linear momentum p of the photons:
E = hf m = hf/c2 p = hf/c
Special Relativity, A. P. French, MIT Press, page 20
Let us now try to put together some of the results we have discussed. For photons we have

E = cp
and

m = E/c^2

(the first experimental, the second based on Einstein's box). Combining these, we have
m = p/c
Originally Posted by x0x
An interesting paper. Photons are massless. They have energy and it is the energy that gravitates.
That is a common misconception. Energy is not a physical quantity. It’s a mathematical tool, i.e. a “bookkeeping” system that is a constant for a closed system. On the other hand “mass” is a physical property and that’s the physical property that a photon has through its momentum. And it’s mass that is the source of energy

Originally Posted by x0x
More precisely, the element of the stress energy tensor represents the contribution of energy to the gravitation, where and E is the energy density.
This is all wrong. First off = c^2 x (mass density) = energy density. Since energy density is non-zero for radiation then so too is mass density. These definitions are found in Gravitation by Misner, Thorne and Wheeler and Cosmological Physics by John Peacock (1999)

Originally Posted by x0x
The fact that gives a lot of people (not only the garden varity cranks) the wrong impression that photons might "have gravitational mass".
That’s quite incorrect. People who know what I just said are the people who are the ones teaching GR in the universities and the ones writing textbooks.

Let me teach you what these terms mean since you don’t seem to understand them:

Inertial mass: the quantity that gives an object momentum
Passive gravitational mass: the quantity that reacts to gravity
Active gravitational mass: the quantity which generates a gravitational field

The last two are often lumped together into just “gravitational mass” and sometimes into just “mass.” A good example of this is The Feynman Lectures – Volume I page 7-11
In the Einstein relativity theory, anything which has energy has mass – mass in the sense that it is attracted gravitationally. Even light, which has energy has mass.
Einstein said something similar in his 1916 GR review paper
The special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete mathematical expression in the energy tensor.
(he refers to the stress-energy-momentum (SEM) tensor as simply “the energy tensor”). So when the SEM tensor doesn’t vanish there is mass. Since that’s true in the presence of electromagnetic radiation it also means that photons have mass, just like many relativists agree nowadays.

Originally Posted by x0x
The claim that the photon has "gravitational mass". You, btr and Farsight share the same claim.
As does Feynman, myself, Tolman & , Ehrenfest and Podolsky in the paper mentioned above and in Tolman’s text.

If you would like to be educated on this point then I recommend reading Relativity, Thermodynamics and Cosmology by Richard C. Tolman. See page 271 110. The gravitational mass of disordered radiation

Originally Posted by Jilan
If a black hole absorbs a photon does the gravitational mass of the black hole increase?
Yes.

Originally Posted by x0x
According to basic GR the source of gravitational field is the stress-energy tensor.
You’re wrong here, too. You’re consistently confusing the mathematical object which describes the source of gravity with the actual physical quantities which are the source of gravity. That’s like saying that charge and current are not the sources of an EM field, the 4-current is. In reality it’s the 4-current which describes the sources of the EM field. And since current is merely charge in motion (like momentum is mass in motion) then its really charge which is the physical source of the EM field. A similar argument holds solid for gravity.

If you have Gravitation by Misner, Thorne and Wheeler turn to page 404
Mass is the source of gravity.

43. Originally Posted by Physicist
You are incorrect. You clearly did not read the reference in the Newsgroup Physics FAQ on mass that I referred to you and you ignored the definition that I just gave you, i.e. that what I said regarding the relativistic mass (which I’ll simply refer to as just mass) of a particle with momentum p is defined as the m in p = mv. That means that the relativistic mass of a photon is m = p/v. Since for a photon v = c we have m = p/c. Also for a photon p = E/c so when we plug this in we obtain m = (E/c)/c = E/c^2.
The notion of "relativistic mass" is no longer being used in modern physics. You need to come up to speed.
You see, it is very simple, really. The antiquated notion of "relativistic mass" is .
What makes it even worse in the case of your misconceptions is that in the case of photons and .
Modern textbooks simply use , no such thing as "relativistic mass". When did you graduate? In the 60's?

That is a common misconception. Energy is not a physical quantity.
The misconception is clearly yours, along with all the others you have been posting. Energy is what we measure, just like force, mechanical work, etc. So, contrary to your misconceptions, energy IS a physical quantity.

This is all wrong. First off T00= c^2 x (mass density) = energy density.
Err, you have this one backwards, as well : .
E is energy density, i.e. energy per unit of mass ( a well known constant of motion), therefore it is expressed in units of . So, is unitless (like all the other components of the tensor).

As does Feynman, myself, Tolman & , Ehrenfest and Podolsky in the paper mentioned above and in Tolman’s text.
Did you co-author anything with Feynman, Tolman , Ehrenfest or Podolsky?

44. Originally Posted by x0x
The notion of "relativistic mass" is no longer being used in modern physics.
(sigh!) Gee. As if I didn’t see that coming a mile away. You’re very predictable. Anyway, so what? I was pointing out your mistake, i.e. when you completely ignored the fact that I was speaking about relativistic mass. By the way, you have the definition wrong. Rel-mass is not defined as m = gamma * m_0, it’s defined as m = p/v. Please learn the correct meaning.

And that is a very ignorant claim, anyway. You seem to thrive on claims that you're either unable or unwilling to justify. I just quoted a small sample from modern relativity textbooks that are all written by respected physicists that proves that I’m right and you’re wrong. You won’t be able to prove otherwise and I suspect that you’ll merely make claims to the contrary and make no attempt to justify your claim. And since physicists think the way that they teach students to think it goes to show that most of those authors use relativistic mass, either in their publications or in their thinking. As I said (and which you expectedly ignored) A friend of mine teaches cosmology at MIT. He teaches his students that its useful to think of photons as having mass and he demonstrates this mathematically the same way I did. Since the percentage of authors who use it in their textbooks are representative of the people who work in their field it follows that a larger percentage of relativists use it.

I know how you've been misled, too. You've think that since most users of SR are particle physicists then what they use is what’s current. That’s quite wrong. First off it’s wrong to assume that their definition of mass as m = sqrt(E^2 – p^2) (c = 1) can be applied to all cases, which it can’t. E.g. when the body is not a closed system and it either gains or looses matter then different parts will gain it at different times. Since time is relative it follows that a body can gain matter from two different sides at the same time in one frame but at different times in another frame, making that definition meaningless. Only physicists who are relativists can really be said to determine what is and isn’t true in SR/GR. The others merely use what is convenient.

And since not only is it being taught in courses in cosmology at places like MIT and Harvard but most relativity texts teach the subject, contrary to this totally misguided claim of yours. Dr. Gary Oas from Stanford University did an empirical study of over 300 textbooks on relativity and found that most of the texts in modern relativity, use rel-mass.

Anyway, from this response of yours I see that you didn’t read that FAQ again and as a result made this current mistake of yours. Since you appear to ignore everything that proves you wrong and pretend it doesn’t exist I can’t see the point in talking to you, so I won’t.

45. (sigh!) Gee. As if I didn’t see that coming a mile away. You’re very predictable. Anyway, so what? I was pointing out your mistake, i.e. when you completely ignored the fact that I was speaking about relativistic mass. By the way, you have the definition wrong. Rel-mass is not defined as m = gamma * m_0, it’s defined as m = p/v. Please learn the correct meaning.
Nope:

"Tolman in 1912 further elaborated on this concept, and stated: “the expression m0(1 - v2/c2)-1/2 is best suited for THE mass of a moving body.”[15][16][17]"

You've think that since most users of SR are particle physicists then what they use is what’s current. That’s quite wrong.
Yes, everyone is wrong, you are the only one who is right. So, what articles id you publish with Feynman, Tolman , Ehrenfest, etc?

First off it’s wrong to assume that their definition of mass as m = sqrt(E^2 – p^2) (c = 1) can be applied to all cases, which it can’t.
It is fascinating to watch you digging yourself deeper and deeper. What degree did you get? From what university? maybe you should write to them and ask to be reimbursed.

46. Note to those posting in this thread - It appears to me that the reason that you're all having a difficult time teaching x0x the right understanding of mass is due to his selectiveness of what we post. Those parts that he is unable to prove wrong (actually they all prove that he's wrong) he pretends wasn't posted. That's why he ignores most of what is posted.

Watch and I'll demonstrate this to be true. x0x claims that body uses relativistic mass. However at Harvard they teach their physics students how to measure relativistic mass in a lab. See http://ipl.physics.harvard.edu/wp-up...3/03/191b5.pdf

The lab is based on the paper

Relativistic mass increase at slow speed by Gerald Gabrielse, Am. J. Phys.,63(6), Jun. (1995)

Gerald Gabrielse is a physics professor/physicist at Harvard University. Does anybody wonder why this is taught at HAVARD if its not used and as "old fashioned" as x0x wants you all to believe?

47. Originally Posted by Physicist
That's why he ignores most of what is posted.
I don't "ignore" what you post, I debunk it <shrug>.

"Even though Einstein initially used the expressions "longitudinal" and "transverse" mass in two papers (see previous section), in his first paper on E=mc^2 (1905) he treated m as what would now be called the rest mass.[20] In later years Einstein expressed his dislike of the idea of "relativistic mass":[21]

It is not good to introduce the concept of the mass M = m/\sqrt{1 - v^2/c^2} of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the ’rest mass’ m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion.

— Albert Einstein in letter to Lincoln Barnett, 19 June 1948 (quote from L. B. Okun (1989), p. 42[1])"

So, once again, when did you graduate?

However at Harvard they teach their physics students how to measure relativistic mass in a lab. See http://ipl.physics.harvard.edu/wp-up...3/03/191b5.pdf
Did you even read the contents of the link? There is no measurement of "relativistic mass" in it.

INSTEAD of defining a "relativistic mass," we consider an electron of mass and charge moving perpendicular to a uniform magnetic field, The MOMENTUM of such an electron is
Measuring P AND V and independently, one can verify the relativistic expression

The lab is based on the paper

Relativistic mass increase at slow speed by Gerald Gabrielse, Am. J. Phys.,63(6), Jun. (1995)

Gerald Gabrielse is a physics professor/physicist at Harvard University. Does anybody wonder why this is taught at HAVARD if its not used and as "old fashioned" as x0x wants you all to believe?
I also found the Gabrielese paper. Predictably, he doesn't do anything with "relativistic mass", all his formulas are expressed in terms of rest mass and all his measurements are SPEED measurements.

48. To x0x,

It seems to me that you want to make a distinction between energy causing mass and, for want of a better word, substances that cause mass. I believe that you would agree that "substances" or let's say "tangible items" cause mass. Part of the problem here is that our language was built before we knew the things we know now. And taking the language we use in science too literally will sometimes lead to confusion.

On the website Proton - Wikipedia, the free encyclopedia, you will find the quote below:

"The rest masses of the quarks are thought to contribute only about 1% of the proton's mass. The remainder of the proton mass is due to the kinetic energy of the quarks and to the energy of the gluon fields that bind the quarks together."

So much of the mass of the proton isn't its substance particles, but energy. They call the energy kinetic energy in this article and if does cause gravitation as stars composed mainly or hydrogen attest. Another way scientists will describe this situation is to posit that the kinetic energy has a transfer medium called a gluon and all the kinetic energy in the proton is contained in these gluons. Gluons are the "sister" particles to photons, and are also massless.

It seems to me that much of the discussion here is about semantics. These descriptions of what happens at the subatomic or elementary particle level represent models that work with our mathematics. None of them necessarily describe reality. For instance treating light as a wave works in some experiments and treating it as a particle works in others. We don't know reality, we only know experimental results.

Hope this helps,

cinci

49. Originally Posted by x0x
Of course I read it. Duh! But I’m clearly the one who truly understands it as I'm sure that everyone who's reading this thread would agree if you were to ask them. Since it’s become clear to me that everyone here is quite familiar now with the nature of your constant stream of errors I no longer need to keep correcting you. I’m going to do it once more just to demonstrate one last time the nature of all the mistakes that you keep making.

First off, nobody accepts your silly assumption that, just because you created a post with math in it, in any way implies that you’re right. And you most certainly have not debunked anything I’ve ever posted. That exists purely in your mind. In this case the article by Gabrielse is about RELATIVISTIC MASS INCREASE and the author assumes that the reader understands what he’s reading and he therefore doesn’t have to hold the readers hand and walk them through it like you clearly have a need to have done. Relativistic mass measurement is implicit in the experiments and like in so many cases has to be derived from the data.

In the second place you’re using very poor logic when you use the selective sight that I’ve seen you use quite often and all over the place. E.g. you completely ignored the following facts about the purpose of the experiment – First off the entire lab is entitled RELATIVISTIC MASS (doh!!!) so how you can claim that it’s not about relativistic mass is purely wishful thinking? (don't bother answering that becaue I know it will be a silly response). In the second place the purpose of the lab is stated in the PDF I posted the link to as follows
* Measure the mass of electrons traveling at relativistic speeds
* Become familiar with vacuum techniques
* Work safely with high voltages
* Learn how a Geiger tube works and how to operate one
* Perform nonlinear curve fits
If they wanted to merely measure the rest mass then they certainly wouldn’t want to do it at relativistic speeds unless they wanted to demonstrate the functional relationship between m = p/v and v.

The third fact is the one you clearly ignored which once again proves that you clearly have SELECTIVE SIGHT. The lab note reads
In this experiment the momentum and velocity of high-energy electrons are measured to obtain the dependence of the mass-to-charge ratio on velocity, for electrons of energy from 600 keV to 900 keV. Assuming that the electron charge is independent of velocity, we wish to measure the mass of the electron, which appears to change with velocity.
So it is you who are clearly not paying attention to what you’re reading.

Regarding Einstein – So what? I'd wager to guess that in your past you've insulted what Einstein said when it disagreed with what you believed. And you don't seem to grasp that he's only talking about the velocity dependance of a particle with a real nonzero rest mass. In the case of electromagnetic radiation, such as a beam of light or photons, he assigned it a finite nonzero mass density equal to energy density over c^2.

In his paper The Principle of Conservation of the Center of Gravity and the Inertia of Energy by Albert Einstein, Annalen der Physik, 20 (1906): 626-633 Einstein wrote
If we assign the electromagnetic field too a mass density
which in modern day parlance that photons have mass according to Einstein's definition. You also forgot his definition of mass as being described by what he called the "energy tensor."

In Einstein's SR/GR text The Meaning of Relativistic, Einstein discusses inert mass for a moving particle on page 100 a writes the value derived on page 102. If = 0 and v << c we have

Einstein used a approximationfor this value. Mine is the exact value. Use caution when reading his text because although he talks about the mass he cancels out the proper mass from both sides of the equation he derived.

This is an example of relativistic mass. See Moller's text for the derivation.

Regarding the lab experiment - When they measure both p and v independently they get what they wanted to measure, i.e. the relativistic mass of the electron because that mass is defined as m = p/v.

Now look at the figure to the right of where it says Data acquisition, control and LabVIEW vi – It reads “Relativistic mass LabVIEW multichannel scaler.”

Now will you PLEASE stop posting all these error laden posts filled with invalid claims and erroneous and misguided attempts at math?

I'm now washing my hands of you and your silly erroneous claims.

50. Originally Posted by Physicist
Of course I read it. Duh! But I’m clearly the one who truly understands it as I'm sure that everyone who's reading this thread would agree if you were to ask them.

which in modern day parlance that photons have mass according to Einstein's definition.
Last I checked, the mainstream modern view is that photons are massless.

First off, nobody accepts your silly assumption that, just because you created a post with math in it, in any way implies that you’re right.
Beats your style of "physics", based on cherry picking quotes, just like your buddy, Farsight.

51. OK, I seriously don't have a leg to stand on here -my textbook threw me off so badly.

Bold mine: "'If you continue your study of physics beyond this book, you will see more refined discussions of the relation between mass and energy. You might even encounter disagreements about just what that relation is and means."

I was thinking of starting a new thread and ask questions. Also bewildered with gravity and wiki being inaccurate - if mass increased with velocity and not just the total energy, I think I'd be a lot fatter.

52. Originally Posted by Beer w/Straw
I was thinking of starting a new thread and ask questions. Also bewildered with gravity and wiki being inaccurate - if mass increased with velocity and not just the total energy, I think I'd be a lot fatter.

Let me give you some good advice to start off with. Ignore every single post created by x0x. I tried to keep up with all the mistakes that he keeps making but there are simply too many of them and he's either unable or unwilling to understand the corrections I post. Since he seems to be beyond help and he's rude to the people who point out his mistakes and doesn't appreciate the help he's getting he really doesn't deserve anymore help. He's also seems to be one of those people that if you don't post a correction to his latest error that he thinks he's right and I was unable to prove his last post was another mistake.

I mean you can try to reason with him but I won't correct any of the errors that he makes ever again so it he tells you something wrong and you end up accepting it or don't see the flaw in his argument I won't correct them anymore. My time is way to precious to keep correcting his many mistakes.

Besides, he neither appreciates nor is able to understand all of the help I and other people are giving him, so why bother?

53. Originally Posted by Beer w/Straw
I was thinking of starting a new thread and ask questions. Also bewildered with gravity and wiki being inaccurate - if mass increased with velocity and not just the total energy, I think I'd be a lot fatter.
Relax, mass does NOT increase with velocity. If anything, there was a (now deprecated) notion that "mass increased with speed". Modern physics has abandoned this notion. So, you are not getting any fatter. Do you feel any fatter?
On the other hand , energy-momentum DO increase (non-linearly) with the speed .

54. I don't believe that the concept is abandoned, it is just less fashionable than it used to be. As a concept it serves the same role as time dilation and length contraction. If you abandon one, by the same logic you should abandon all three. They all have their uses as concepts, but can also lead to thought frustration as Beer w/straw pointed out. Is it really heavier, is it really shorter,is the clock really running slower etc.

55. Originally Posted by Jilan
I don’t believe that the concept has been abandoned, it is just less fashionable than it used to be. As a concept it serves the same role as time dilation and length contraction. .. Is it really heavier, is it really shorter, is the clock really running slower etc.
That’s quite correct, Jilan. The concept is most definitely NOT abandoned like x0x claims. What he claimed is very sad. I mean, come on. I gave him a whole list of counter examples and he ignores them so he can pretend to be right. Now that's truly a sad little act of his. Shame on you x0x!

This is certainly nothing new, that’s for sure. The debate on relativistic mass vs rest mass has been going on now for over 40 years now. The role of proper mass (i.e. ”rest mass”) plays a more important role in particle physics because that’s what particle physics study and if they leave the subscript off the equations aren’t as crammed with so many darn subscripts so it makes it easier to follow.

However particle physicists are not relativists, they’re particle physicists. They don’t spend all day thinking about the general nature of applying relativity. They are concerned only with particles. That means that most of then don’t even know how to apply special relativity (SR) to general situations such as the inertia of stress. E.g. if you were to ask a particle physicist which has more inertia, an object which is not under stress or an object which is under stress. Most particle physicist wouldn’t know how to answer this question.

The inertia of stress by Rodrigo Medina, Am. J. Phys., 74(11), Nov. (2006)
The inertia of stress

But many physicists still refer to it as rest mass in particle physics too. The thing is that its much easier to simply say “mass” whenever you want to say “relativistic mass” or “proper mass” because the context tells you which is which, especially since it’s often made clear by the author of the text or journal article. And I don’t use it all the time myself. I think it’d be bad physics to use it all the time when the situation would be better off without it. Especially to get rid of a subscript and not have to keep saying the “rest/proper” when I refer to “rest/proper mass.”

I told x0x to read Relativistic mass but he simply won’t read it or he’s yet again ignoring the parts which prove him wrong. The page wasn’t quite right when I first read it so I contacted the people who maintain the website and they changed it. The person who changed it is Dr. Don Koks. He’s the author of the text Explorations in Mathematical Physics which is sold at Amazon at

Explorations in Mathematical Physics - Kindle edition by Don Koks. Professional & Technical Kindle eBooks @ Amazon.com.

It’s going to be changed again soon because he has the definition of relativistic mass wrong. Don is going to change it to be consistent with his use of relativistic mass on page 208 of his text.

But it’s clear that x0x is either refusing to read it or he won’t admit to reading it because he found out that it clearly proves he’s wrong.

x0x is doing this forum a disservice by constantly and wrongly claiming that its no longer used. I mean come on! Everyone here clearly saw all the examples that I gave. And they were just that, samples. There’s hundreds more just like them. And countless physicists who currently use the concept in their work and in their teaching. E.g. I have a friend who lives on the other side of the country who works at MIT who told me that they teach relativistic mass in their classrooms. We already saw it at Harvard. Cohen-Tannoudji’s text on quantum mechanics uses it in one place in their two volume bible of quantum mechanics and Cohen-Tannoudji is a Nobel Laureate.

The new quantity gamma*m is traditionally called the body's relativistic mass. While rest mass is routinely used in many areas of physics, relativistic mass is mainly restricted to the dynamics of special relativity. Because of this, a body's rest mass tends to be called simply its "mass".
One of the most serious errors that x0x keeps making is the way he thinks that counting how many people use an idea means that it’s a better way. Don explains the error in that kind of logic
Abandoning the use of relativistic mass is sometimes validated by quoting select physicists who are or were against the term, or by exhaustively tabulating which textbooks use the term. But real science isn't done this way.
which is exactly x0x’s tactic.

Come on folks. Enough with x0x’s nonsense. Who really buys his claim and why?

Here’s an example of when it’s not even possible to use the concept of rest mass of a moving body defined as the m in .

In the inertial frame S there is a long rod of length L (it’s proper length) in the shape of a cylinder made of a thermal insulator. The rod is lying at rest along the x-axis. This object is at rest in S. Call S the rest frame. On each end there is a spherical ball of steel. The rod does not allow any energy to flow (or at least enough so that we can ignore it). The energy density is uniform at t < 0. The temperature is very high at first. This “dumbbell” is in vacuum where there is only the 3K CMBR. The moving body lies along the x-axis. At first no energy leaves the body. Then at t = 0 in the rest frame of the body each sphere releases a small amount of radiant energy dE. Now we examine these events in an inertial frame S’ which is in standard configuration with S and moving parallel to the x-axis. As reckoned in frame S’ the ball on the left emits energy first. There is then a time delay and then the ball on the right emits energy. Therefore there are three different values of energy and momentum used in whereas in frame S there is only one value. This is due to the invalid attempt to add 4-vectors which are defined at events which are not the same event. To add 4-vectors you have to add them at the same event. Only in special circumstances, such as the way it’s done in particle accelerators, can you get away with it. So x0x’s attempt at a definition falls apart. He’ll make some sort of attempt to prove that there’s a flaw here but I know there is none. But since this proves he’s wrong he’ll write the words out like he usually do and we’ll have a nice word salad with no meaning to it

56. What is the Lorentz factor for the objects motion?

:EDIT:

I'm guessing it is simply this

57. Originally Posted by Physicist
...

Here’s an example of when it’s not even possible to use the concept of rest mass of a moving body defined as the m in .

...
A minor observation: I think your word processor or whatever you use to compose posts has put an en-dash or em-dash or some funny character in there instead of a normal minus sign (ASCII code 45), and the LaTeX processor has choked on it. Obviously, you intended .

58. Originally Posted by Physicist
Here’s an example of when it’s not even possible to use the concept of rest mass of a moving body defined as the m in .
Total rubbish. The correct expression is where is the PROPER MASS , there is no relativistic mass in the expression. The origin of the expression is the invariance of the energy-momentum four-vector, a basic concept that you are denying in the next paragraph (see below). Let's further debunk your nonsense:

In the inertial frame S there is a long rod of length L (it’s proper length) in the shape of a cylinder made of a thermal insulator. The rod is lying at rest along the x-axis. This object is at rest in S. Call S the rest frame. On each end there is a spherical ball of steel. The rod does not allow any energy to flow (or at least enough so that we can ignore it). The energy density is uniform at t < 0. The temperature is very high at first. This “dumbbell” is in vacuum where there is only the 3K CMBR. The moving body lies along the x-axis. At first no energy leaves the body. Then at t = 0 in the rest frame of the body each sphere releases a small amount of radiant energy dE. Now we examine these events in an inertial frame S’ which is in standard configuration with S and moving parallel to the x-axis. As reckoned in frame S’ the ball on the left emits energy first. There is then a time delay and then the ball on the right emits energy. Therefore there are three different values of energy and momentum used in whereas in frame S there is only one value. This is due to the invalid attempt to add 4-vectors which are defined at events which are not the same event. To add 4-vectors you have to add them at the same event. Only in special circumstances, such as the way it’s done in particle accelerators, can you get away with it.
...which is precisely what real physicists do, they use the frame of the lab (Duh!) to do their calculations. Trivial. Your contrived "counterexample" doesn't have anything to do with:

-relativistic mass vs. rest mass

You simply created a strawman and you are beating it to death.

So x0x’s attempt at a definition falls apart.
It is not "my" attempt, it is the basic mainstream definition. You can find the definition in ALL the physics books. You can stop beating your strawman now.

He’ll make some sort of attempt to prove that there’s a flaw here but I know there is none. But since this proves he’s wrong he’ll write the words out like he usually do and we’ll have a nice word salad with no meaning to it
The fact that you have been resorting to personal attacks demonstrates that you have no leg to stand on.

59. OK since I'm all over the place and have edited my post too many times, I'm just going to ask for validation that this is correct and since the Lorentz factor can be written up different ways.

What is the Lorentz factor for the objects motion?

:EDIT:

I'm guessing it is simply this
Lorentz factor - Wikipedia, the free encyclopedia

Also, it may appear to be a really dumb question but the bloody textbook gave me the equation but no explanation!

60. Yes, it is correct.

is the definition of total energy.
is the definition of momentum.

There is a long and complicated explanation why they are defined this way.

61. Are there any documents readily available on the net I can view about it?

It is intriguing, even if I don't have the time or experience to learn it right now.

Besides what the wiki article links http://pdg.lbl.gov/2005/reviews/kinemarpp.pdf

62. Try reading this. If you have trouble, LMK and I will explain. It has to do (amongst other things) with the covariance of Newton's second law. It also has a lot to do with particle physics. I do not know why the "Quote" button doesn't work.

63. Thanks.

Just glancing briefly I see an equation exactly the way my textbook prints it.

64. Yes, this is the standard textbook stuff.

65. Can you link articles like that for calculus, chemistry, and linear algebra?

Is there a site I can go to to view articles. I know MIT opencourseware has stuff, but I feel it can be incomplete.

66. MIT is not bad (at least, for physics). Caltech is even better. The best, in my opinion, is Feynman "Lectures on Physics". It is complete and it is beautifully done. Make sure that you do the exercises.

67. Originally Posted by Beer w/Straw
Can you link articles like that for calculus, chemistry, and linear algebra?

Is there a site I can go to to view articles. I know MIT opencourseware has stuff, but I feel it can be incomplete.
Yale and Stanford also provide plenty of videos of lectures. E.g. if you look on YouTube, you'll find Leonard Susskind giving an introduction to Special Relativity that doesn't look too bad.

------

Edited to add: if you're going to get books and you don't mind shelling out a bit, I'd second the recommendation for The Feynman Lectures on Physics.

68. You don't have to, they are available for free, if you follow the link. But it is nice to have the books, I bought them cheaply on ebay.

69. Originally Posted by Physicist
...Here’s an example of when it’s not even possible to use the concept of rest mass of a moving body defined as the m in ....
Originally Posted by x0x
Total rubbish. The correct expression is where is the PROPER MASS , there is no relativistic mass in the expression...
Aside from the minor typo in Physicist's LaTeX code presumably introduced by a word processing package (there is an en-dash "–" for the minus sign, and LaTeX will only accept ASCII 45 "-"), what exactly was "rubbish" in this part of Physicist's post which you singled out? "Rest mass" and "proper mass" to refer to the same thing in this context, i.e. what he/she denotes by and you denote by in the two equations above are in fact the very same thing.

70. Originally Posted by btr
Aside from the minor typo in Physicist's LaTeX code presumably introduced by a word processing package (there is an en-dash "–" for the minus sign, and LaTeX will only accept ASCII 42 "-"), what exactly was "rubbish" in this part of Physicist's post which you singled out? "
Originally Posted by Physicst
it’s not even possible to use the concept of rest mass of a moving body defined as the m in....
Huh?

Aside from the typo, the nonsense in the redlined sentence AND the rant about non-applicability of rest mass and 4-vectors ?
Do I need to explain it to you or can you read all by yourself?

71. Originally Posted by x0x
MIT is not bad (at least, for physics). Caltech is even better. The best, in my opinion, is Feynman "Lectures on Physics". It is complete and it is beautifully done. Make sure that you do the exercises.
Great link, thanks for this it looks like a real gem!

72. You are welcome!

73. Originally Posted by x0x
Yes, it is correct.

is the definition of total energy.
is the definition of momentum.

There is a long and complicated explanation why they are defined this way.
Not so long: the quantities as defined above form a Lorentz 4-vector ; that is, they undergo the same linear transformation as the coordinates when going from one inertial reference frame to another. E.g. for a pure boost along the axis with velocity ,

(with and working in units with ).

74. Originally Posted by btr
Not so long
You missed the point, the question was "why" are they defined that way. The (one) explanation is given in the link I provided.

75. Originally Posted by x0x
the nonsense in the redlined sentence AND the rant about non-applicability of rest mass and 4-vectors ?
No, I mean what was "total nonsense" about the formula you quoted? Was it just the fact that you didn't realise that it was a typo because you didn't read the LaTeX code, or didn't you realise that was being used to denote the same thing you denoted ?

76. Originally Posted by btr
No, I mean what was "total nonsense" about the formula you quoted? Was it just the fact that you didn't realise that it was a typo because you didn't read the LaTeX code, or didn't you realise that was being used to denote the same thing you denoted ?
Neither. It was easy to see the typo, the rubbish was the sentence itself. I even redlined it for you and you still have difficulty seeing what's wrong with it? You can stop trolling now.

77. Originally Posted by x0x
You missed the point, the question was "why" are they defined that way. The (one) explanation is given in the link I provided.
There are numerous reasons "why". I gave one, from which several others follow. What link are you referring to?

To give another reason "why": for particles, the (energy-)momentum 4-vector, so defined, is equal to the particle's (rest) mass multiplied by another important 4-vector, the particle's 4-velocity . The 4-velocity, in turn, is the unit tangent vector to the particle's world-line in Minkowski space, and so arguably the most geometrically "natural" way to define velocity.

Yet another reason "why" is that the momentum 4-vector is the conserved quantity which corresponds to time and space translation invariance in relativistic Lagrangian mechanics; in other words, for closed relativistic systems in SR it is the momentum 4-vector as defined above which is conserved, rather than the non-relativistic kinetic energy and momentum definitions.

78. Originally Posted by x0x
Neither. It was easy to see the typo, the rubbish was the sentence itself. I even redlined it for you and you still have difficulty seeing what's wrong with it? You can stop trolling now.
"Total rubbish" would normally imply that you thought that the whole lot you quoted was rubbish, including the formula. The tendency to make the inference that you had a problem with the formula, and had not appreciated that Physicist was aware of the correct expression and that denoted rest mass as opposed to relativistic mass, was somewhat strengthened by the fact that you explicitly wrote

Originally Posted by x0x
Total rubbish. The correct expression is <...> where is the PROPER MASS , there is no relativistic mass in the expression
But since you now accept that Physicist's formula was correct (LaTeX rendering issues aside), we can move on.

79. btr - May I ask you a question? I tried to do it in PM but you don't accept them so I have to ask it here. If not then please ignore this post.

If so then here’s my question; Why do you bother with x0x? He clearly doesn't understand most of the physics of what's going on here and he refuses to correct the many mistakes he makes and instead backpedals so that he doesn’t have to admit his errors. When he makes assertions he refuses to correctly support them (i.e. he makes an attempt to but absolutely refuses to correct the mistakes he makes in all of his proofs) and then merely makes a claim that he proved his point rejecting all counter proof and evidence of his attempts at a proof. Also he's very easily slipped up when someone does something simple like changes notation like I did when I said
Here’s an example of when it’s not even possible to use the concept of rest mass of a body defined as the m in .
Note: Thanks for pointing out the missing "-" sign. I put it in here. My computer is running very slow tonight but I'll try it again.

Then as expected was incapable of grasping the very simple example I gave of when the concept of rest mass for a moving body fails. All he did was insult me and claim the derivation was wrong, proving once again that he is either unable or unwilling to correct his mistakes.

Wouldn’t your life be easier if you just ignored all the erroneous claims that x0x makes? He claims that the entire GR community is wrong on a daily basis when he claims that the coordinate speed of light doesn't vary with the gravitational potential since they all know that its true. Merely pick up a GR text and look. It says and proves it in nearly all GR textbooks. How much proof does he need before he can see his mistakes?

80. Originally Posted by Physicist
Then as expected was incapable of grasping the very simple example I gave of when the concept of rest mass for a moving body fails.
I understood the example perfectly, I simply pointed out the fallacy in your reasoning.

All he did was insult me and claim the derivation was wrong, proving once again that he is either unable or unwilling to correct his mistakes.
There is no "derivation" in your post, there is just a fallacious assertion.

he claims that the coordinate speed of light doesn't vary with the gravitational potential
I have claimed no such thing, actually, I have shown in great detail, exactly the opposite of your false claim, now you are just making up stuff. See this post and this post. There are more. I suggest that you retract this false claim.
I know that SpeedFreek asked us not to call each other liars but this is what you are doing, making up stories about the users that prove you wrong.

81. I'd like it if you posted the PM you sent me and my response.

:EDIT:

ugh I was referring to Physicist.

82. Originally Posted by Physicist
btr - May I ask you a question? I tried to do it in PM but you don't accept them so I have to ask it here. If not then please ignore this post.

If so then here’s my question; Why do you bother with x0x? He clearly doesn't understand most of the physics of what's going on here and he refuses to correct the many mistakes he makes and instead backpedals so that he doesn’t have to admit his errors. When he makes assertions he refuses to correctly support them (i.e. he makes an attempt to but absolutely refuses to correct the mistakes he makes in all of his proofs) and then merely makes a claim that he proved his point rejecting all counter proof and evidence of his attempts at a proof. Also he's very easily slipped up when someone does something simple like changes notation like I did when I said

Note: Thanks for pointing out the missing "-" sign. I put it in here. My computer is running very slow tonight but I'll try it again.

Then as expected was incapable of grasping the very simple example I gave of when the concept of rest mass for a moving body fails. All he did was insult me and claim the derivation was wrong, proving once again that he is either unable or unwilling to correct his mistakes.

Wouldn’t your life be easier if you just ignored all the erroneous claims that x0x makes? He claims that the entire GR community is wrong on a daily basis when he claims that the coordinate speed of light doesn't vary with the gravitational potential since they all know that its true. Merely pick up a GR text and look. It says and proves it in nearly all GR textbooks. How much proof does he need before he can see his mistakes?
It's not so much an attempt to educate, as to ensure some sort of corrections are visible for other participants and lurkers, wanting to learn, that may be misled by his/her errors. Your point is well taken though.

83. Originally Posted by btr
It's not so much an attempt to educate, as to ensure some sort of corrections are visible for other participants and lurkers, wanting to learn, that may be misled by his/her errors. Your point is well taken though.
Are you talking about your errors again? I am still waiting for you to point out the "ludicrous errors" in my derivation of the relative clock frequency for orbiting clocks. At this point, you either come up with the goods or you retract the false claim.

84. Originally Posted by x0x
I am still waiting for you to point out the "ludicrous errors" in my derivation of the relative clock frequency for orbiting clocks.
If you want to discuss that, do so in the appropriate thread. Also, if you use quotation marks to imply a direct quote, don't alter the words used (it is impolite and could be construed as dishonest).

-----------------

85. Originally Posted by btr
If you want to discuss that, do so in the appropriate thread. Also, if you use quotation marks to imply a direct quote, don't alter the words used (it is impolite and could be construed as dishonest).
No , I want to discuss it here, prove it or admit that you were wrong.

86. ...which is precisely what real physicists do, they use the frame of the lab (Duh!) to do their calculations. Trivial. Your contrived "counterexample" doesn't have anything to do with:

-relativistic mass vs. rest mass

You simply created a strawman and you are beating it to death.
That post was meant for the people here who are able to understand it, not you. We already know that you’re unable to follow these things.

The purpose of the example I gave was clearly beyond your understanding, i.e. it was to show why the so-called “definition” of proper mass, denoted in this post as m, defined through the relation . Given your demonstrated poor understanding of Sr there was no expectation that you’d be able to understand it. If you did then you’d know why it can’t work in the most general of cases, such as the one I gave. You didn’t understand it because you don’t understand the fact that us “real physicists” are required to be able to define all possible quantities in all possible frames of reference. Thus your bogus claim that
us “real physicists” only use the lab frame to do their calculations is an incredible display of ignorance. Had that been the truth then all us physicists would have no use for invariant quantities such as Lorentz scalars. And “us physicists” do much more than merely make measurements, we define and formulize quantities in all frames of reference.

So please continue to waste your time like this. Maybe someday you’ll learn why you can’t add 4-vectors at different events and why the invariant mass must be able to be determined from ANY frame of reference to have any meaning. My friends are particle physicists. Would you like me to e-mail them and ask them to explain in great detail why your silly comment above
…, they use the frame of the lab (Duh!) to do their calculations…
is total garbage? You’ll know him since he’s on the verge of winning a Nobel Prize.

I enjoy seeing you spout out all sorts of nonsense that only you enjoy reading. The rest of us have better things to do with our time. But please, go ahead and post more nonsense and erroneous nonsense. I do find it quite humorous and we do enjoy a good laugh about it in e-mail.

So later young fella. I sure hope you're not trying to become a real physicist like myself because you'll never be able to get far with such poor reasoning skills. You might feel like you've fooled someone with your erroneous "derivations/counter proofs" but all us see through you like a pane of glass. You just won't be able to make it in the real world. I on the other hand, have already made it in the real world for many decades. Most of them studying/working in SR and GR. That indeed was my profession and I was very good at it, well respected by my peers. So if you ever thought that you could make me think like you then you are sadly mistaken young fella.

Try to be more open minded because if you keep acting like this you'll never become a physicist no matter how hard you try. Have you ever thought about being an electronics technician instead?

87. Originally Posted by Beer w/Straw
I’d like it if you posted the PM you sent me and my response.
Sorry but I prefer to keep PM in PM. If I wanted it to be said in open forum I would have posted it in open forum and never sent you a PM.

To me, posting a request like this is inappropriate. It violates a trust that one has when they PM someone and assume it will be held in confidence. Since you've demonstrated that you'll tell the forum that I sent you a PM I've decided that it'd be unwise for me to ever send you another one.

88. Um... I asked. The moderators can read PM's. But, you are right, I should have made the request over in PM.

You did post this though:

btr - May I ask you a question? I tried to do it in PM but you don't accept them so I have to ask it here. If not then please ignore this post.
And I wouldn't have asked if you hadn't said something like that.

89. Originally Posted by Physicist
That post was meant for the people here who are able to understand it, not you.
I fully understood your posts, this is how I was able to point out the fallacies in them.

I sure hope you're not trying to become a real physicist like myself
Definitely not "one like yourself", you have demonstrated way too many misconceptions and errors in your posts. I tried to correct them but to no avail, you just keep repeating them. Here is another example:

Originally Posted by Physicist
However particle physicists are not relativists, they’re particle physicists. They don’t spend all day thinking about the general nature of applying relativity. They are concerned only with particles. That means that most of then don’t even know how to apply special relativity (SR)to general situations such as the inertia of stress. E.g. if you were to ask a particle physicist which has more inertia, an object which is not under stress or an object which is under stress. Most particle physicist wouldn’t know how to answer this question.
This is totally false, particle physicists use accelerators in order to study the particles. The equations governing the functioning of the accelerators are fully relativistic. A simple counter-example is sufficient to disprove your false claim:

-since you claimed to be a physicist, please calculate the radius of the trajectory a particle of mas m, charge q, injected perpendicular to a magnetic field of induction B at speed . Please solve this simple exercise or admit the fallacy of your claims redlined above.

90. Originally Posted by x0x
...which is precisely what real physicists do, they use the frame of the lab (Duh!) to do their calculations. Trivial. Your contrived "counterexample" doesn't have anything to do with:
Just when I resolve to ignore your unending erroneous claims you go ahead and say something incredibly wrong like this. I find that to be quite humorous.

It’s claims like this which tells me quite clearly that you’re far from being a professional physicist since no real physicist such as myself would ever make such a blatantly wrong assertion such as this since it’s clearly erroneous. And there certainly nobody on this forum, physicist or not, who’d agree with you in any way, shape or form.

For some odd reason you think that in all conceivable situations in special relativity all physicists are doing calculations relative to some sort of “laboratory frame” when such a lab might not even exist. The appropriate term is “frame of reference” not laboratory. We real physicists are concerned, typically, with only two frames of reference in relative motion, neither of which is distinguished enough to be referred to the lab frame. Just because one frame might be the frame in which the total momentum is zero doesn’t help anything, especially when it has nothing to do with the subject at hand.

Example No.1; if the physicist is trying to find the length of a [u]moving[/I] object then using the rest frame is absolutely useless.

Example No. 2: when a linear accelerator such as the SLAC National Accelerator Laboratory (originally named Stanford Linear Accelerator Center (SLAC)) is used then the lab frame is not the same frame as the zero momentum frame of the particles which the physicist is concerned with. He’s interested in the zero momenutm frame, not the lab frame. However if The zero momentum frame is the one which is quite useful in doing calculations in high energy particle physics. However when the accelerator is the LHC, which is a cyclotron, then the zero momentum frame is the same frame as the lab frame. Then and only then does the physicist use the lab frame.

Example No. 3: if the physicist wishes to calculate the magnitude of a 4-vector in the observers rest frame then, in general, that frame is not the rest frame of the particle. In that frame the magnitude of the 4-momentum of the particle is proportional to the magnitude of the proper mass of the particle. Those physicists who define the rest mass of a MOVING body define it as the m in . When the object has a finite spatial extent and is not a closed system then this relation cannot be used since a 4-mometum for such an object cannot be defined. You demonstrated your lack of understanding why that’s true in your response and I’m too tired of trying to help someone who has no wish to learn.

If we did things your way then we couldn’t even talk about the length of a moving rod because the rod would be at rest in the lab frame. Don’t you understand how off you are on all of this?

Anyway, for the reasons I explained above, you’re quite wrong in your attempt at a response. I know this as a fact because I am what you keep referring to as a “real physicist” and I’ve discussed this (very simple) concept with other relativist friends of mine who are experts in their field. I’ve been studying and working in relativity for over thirty years now (I incorrectly said 20 recently and then realized how fast time is flying and why I was off by 15 years at first). Clearly, from all the kinds of mistakes that you keep making you certainly aren’t a physicist, “real” or otherwise. Especially due to the fact that your understanding of the nature of adding 4-vectors in a non-closed system is non-existent. What makes me certain of that is your insistence that you’re right and the entire relativity community is wrong about so many things we’ve discussed in this forum so far such as the slowing of light in a gravitational field. Every legitimate physicist knows this fact. It’s a well established fact, found in most GR texts and clearly stated as such by Irwin Shapiro. When you see that fact you pretend it doesn’t exist and then repeat that you’re right and the world is wrong and make ZERO attempt to justify it, prove that you’re right or anything. And this is clearly new to you. Otherwise you’d have tried to publish your claim and win a prize for proving that the entire GR community is wrong.

Originally Posted by x0x
calculate the radius of the trajectory a particle of mas m, charge q, injected perpendicular to a magnetic field of induction B at speed .
It's inappropriate for you to give me a test like this when it's clearly you who doesn't understand all the physics under the discussion. The reason being because on each occasion you make a mistake and claim that the world is wrong. It’s you who are right.

I’ll do this ONCE and only once. Not because you challenged me. I’m not a trained dog who does tricks for you. You don’t have the ability to understand these derivations either. EVERTHING you’ve claimed in this forum has been insulting so far like the act of putting that facts I taught you above in red when that fact is quite correct as any “real” physicist on Earth will tell you. You’re just not a physicist so you can’t understand these things.

In any case the derivation is trivial. It’s p= qBR where p = m_0/sqrt[1 – v^2/c^2], B is the strength of the magnetic field and R the radius of the circle the charge moves in.

Since the field is uniform and F = qvxB then the particle moves in a circle of radius R where F = ma = mv^ 2/R where m = m_0/sqrt(1- v^2/c^2) is the relativistic mass since the motion is all transverse and the transverse mass is identical to relativistic mass. Therefore

mv^2/R = qvB

Cancel one q on each side to obtain

mv/R = qB

Multiply by R to get

mv = qBR

Since momentum = relativistic mass x speed we have

p = qBR

91. I'll even derive if for you. Something you'd be unable to do.
Since the acceleration is perpendicular to the force we can use the transverse mass m which is the same as the relativistic mass, m = m_0/sqrt[1 – v^2/c^2]. Therefore, since motion is perpendicular to the field v*B = vB. Let R be the radius of the circle that the charge moves in. Then

F = qvB = ma = mv^2/R

cancel v and put R on left side and we have

qvB = mv = p

Here's a test for you. It's a hard one. What is 1 + 1? We have to start small.

92. Originally Posted by Physicist
cancel v and put R on left side and we have
F = qvB=ma

qvB = mv = p
Huh? The dimensions don't match: LHS has dimensions of force, RHS has dimension of momentum, Rookie mistake. Where did you say you worked as a "physicist"? Try again, your first attempt failed miserably.

I know because I am what you keep referring to as a “real physicist”. I’ve been studying and working in relativity for over thirty years now (I incorrectly said 20 recently and then realized how fast time is flying!).
Based on the gross mistakes you are making, I respectfully disagree.

93. Originally Posted by physicist
....ignorant....Grow up little boy.....childish....
Seriously, can we STOP THE PERSONAL ATTACKS, stop the sniping, stop the personal comments! I don't want to have to ban people, but if this bickering continues I will have no choice.

94. Originally Posted by x0x
No , I want to discuss it here, prove it or admit that you were wrong.
btr is correct in saying that if you want to discuss it, do so in the appropriate thread.

95. SpeedFreek - Sure. No problem. I went back and took those terms out. Since he's in my ignore list I can't see what he's posting anymore so I won't be correcting his errors anymore.

Please take steps to stop x0x from being rude and insulting too. E.g. I'll delete the "Duh" that I put in when I responded to yet another one of his unceasing mistakes if you first delete the one he put in when I taught him about the error he made in his response. Fair's fair, right?

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