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Thread: Relativistic effects and relative motion

  1. #1 Relativistic effects and relative motion 
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    Einstein made two claims in special relativity which seem to me to be incompatible. I'm sure that I am wrong but I don't understand why. I would be grateful if someone could explain it to me.
    SR says that when you start travelling at speeds which are a significant portion of the speed of light, time slows down for you. For example, if a rocket was sent out zooming into space and humans on Earth watched a video feed of the people inside the rocket, they would see everyone moving more slowly and the clocks ticking slower etc. If the people in the high speed rocket watched a video feed of the people on Earth, then it is my understanding that they would see the people on earth moving really fast and everything happening faster. This is because for everyone in this setup, time seems to be passing normally where they are.
    SR also says that all motion is relative. So in the rocket example lets say after hard acceleration the rocket is zooming away from Earth at 50% the speed of light: a constant speed. Isn't it at that point just as correct for the people in the rocket to claim that it is really the Earth zooming away from them at 50% the speed of light, and they are stationery? But as we have seen, this symmetry- that motion is relative- is broken by time passing at different speeds on the Earth and in the rocket.
    How can these to claims both be true? They are also both in the very same theory. I must be missing something.
    Another thing that breaks the symmetry of relative motion is E^2=(mc^2)^2 + (pc)^2 . This equation tells us that an objects energy comes from both its mass and its velocity (p). But this would mean, going back to the rocket example, that the rocket has more energy that a stationery rocket so is objectively moving (not moving only relative to the Earth).
    I hope this made sense and responses would be much appreciated.
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  2. #2  
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    The people on the earth would see time running slower in the rocket and the people in the rocket would see time running slower for the people on earth whilst they are moving away from each other. When the rocket returns the people on earth would see time speeding up for the people on the rocket and vice versa. So far so good. If the situation were totally symmetric (like two rockets moving away from each other at the same acceleration and then coming back together) the same amount of time would have passed in both rockets. However the earth /rocket scenario is not symmetric as the rocket is undergoing the acceleration. The consequence of this is that more time will have passed in the earth frame than in the rocket frame.

    Energy is a relative concept. In the rest frame of the mass the energy is just the rest mass.
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    Einstein made two claims in special relativity which seem to me to be incompatible. I'm sure that I am wrong but I don't understand why. I would be grateful if someone could explain it to me.
    SR says that when you start travelling at speeds which are a significant portion of the speed of light, time slows down for you. For example, if a rocket was sent out zooming into space and humans on Earth watched a video feed of the people inside the rocket, they would see everyone moving more slowly and the clocks ticking slower etc. If the people in the high speed rocket watched a video feed of the people on Earth, then it is my understanding that they would see the people on earth moving really fast and everything happening faster. This is because for everyone in this setup, time seems to be passing normally where they are.


    SR also says that all motion is relative. So in the rocket example lets say after hard acceleration the rocket is zooming away from Earth at 50% the speed of light: a constant speed. Isn't it at that point just as correct for the people in the rocket to claim that it is really the Earth zooming away from them at 50% the speed of light, and they are stationery? But as we have seen, this symmetry- that motion is relative- is broken by time passing at different speeds on the Earth and in the rocket.
    How can these to claims both be true? They are also both in the very same theory. I must be missing something.
    First off, it is important to distinguish between what what each person would see via a video feed and what each person would determine what is happening. While they are receding from each other both will see the video feed from the other as Doppler shifted to a slower speed. When they are approaching each other, the effect of the Doppler shift will be reversed and they will see the video feed as being sped up. Both of these observations are due to the finite speed at which the video signals travel and the changing distance between the two.

    Now, it is possible to correct for this effect and have each observer work out how time is actually progressing for the other observer when compared to his own clock. When they do this, each observer will determine that the other observer's time runs slower than his own, regardless of whether they are receding from or approaching each other. Inertial motion is relative, and each can say that he is motionless and the other moving. As long as they have a unchanging velocity between them, you will not get the situation where they both agree that one of their clocks is running faster than the others.

    Okay, so what about the claim that if an twin heads out into space at some high fraction of c and returns he will be younger than his twin when he returns? Up to now, we have only dealt with time dilation ( the perceived flow of time between inertial frames). But there is more to Relativity than this. There is also length contraction and the Relativity of Simultaneity, both of which have to be accounted for when dealing with our twins.

    Length contraction come into play like this:

    We'll assume that the one twin travels to a star 10 ly away and then returns. At 0.5 c this takes 40 yrs according to the Earth twin, so he will be 40 yrs older when his twin returns. Now the spaceship twin can claim than it is the Earth and star that are traveling past him at 0.5c while he stands still. But this means that the Earth, star and the distance between them undergoes length contraction. Thus for him, the distance between Earth and star is only 8.66 ly. So the total time that passes for him from the time the Earth leaves him and returns is 34.64 yrs, So he will be 34.64 yrs older when he meets back up with his twin.

    So we've now established how much each twin will have aged by his own reckoning, but how much does each reckon the other twin as aging?

    For the Earth twin this is easy to work out. According to his reckoning his twin aged slower than he did during both legs of the trip and thus will be younger when he returns. This is just pure time dilation.

    For the spaceship twin, its a bit different. He can claim that it is the Earth twin that aged less than he did during both legs. The difference is that while his twin on Earth stayed in the same inertial frame, he does not. When he is next to the star he has to undergo an acceleration in order to get back to the Earth. He is in one inertial frame when Earth is receding and in another when Earth is approaching.

    Now while this change of inertial frames has no effect on the time dilation or length contraction he see's in the Earth-Star frame, it does have an effect on the the third factor I mentioned above; the Relativity of Simultaneity. Without going into too much detail (if you want, check out the SR primer in this section for a fuller discussion), It basically means that inertial frames with relative motion to each other will not agree as to whether separated event are simultaneous or not. And this effect is direction dependent. The end result is that during the time the Spaceship and Earth are receding, the spaceship twin will determine that the Earth clock is constantly falling behind his. But at the moment he changes inertial frames so that the Earth is now approaching, the time on Earth "jumps ahead" of his clock. The earth clock will then continue to run slower than his until they meet up again, but this will never completely cancel out the amount of time it gained with the frame change, and the Earth twin will have aged more than he did when they join back up.

    You can also follow what each twin sees using the video feed you mentioned.

    First we consider things from the Earth twin:

    As the spaceship recedes he will get a slowed down video feed. It take twenty years for the ship to reach the Star. However, it takes another ten years for the video feed from this event to reach the Earth twin. Thus he sees 30 yrs of slowed down video feed at a rate of 0.5774. He sees the spaceship twin age 17.32 yrs during this time. For the next ten year, he sees a sped up video feed at a rate of 1.732 He sees his twin age another 17.32 year for a total of 34.64 upon reunion.

    The spaceship twin:

    While receding he sees the same 0.5774 slow down for the video feed from Earth. However, he only sees this for the 17.32 years it takes to reach the star. This is again due to the fact that he is the one that accelerates. Since he is the one changing frame, he sees the result immediately. It is happening in the "here and now" and he doesn't have to wait ten years to see the shift in the video feed rate. So he sees the Earth twin age 10 yrs during this leg of the trip. For the return trip he sees the 1.732 speed video rate for anther 17.32 yrs and watches the Earth twin age another 30 yrs for a total of 40 years.
    Another thing that breaks the symmetry of relative motion is E^2=(mc^2)^2 + (pc)^2 . This equation tells us that an objects energy comes from both its mass and its velocity (p). But this would mean, going back to the rocket example, that the rocket has more energy that a stationery rocket so is objectively moving (not moving only relative to the Earth).
    I hope this made sense and responses would be much appreciated.
    Kinetic energy is relative. Even with the Newtonian E= mv^2/2, you can say that energy depends on velocity. But since velocity is relative so is energy. A ball sitting in a car driving down the road has a good sum of kinetic energy with respect to the the road, but zero kinetic energy with respect to the car. IOW, energy is measured with respect to some reference frame and is not universal.
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    Jilan - You're assertion When the rocket returns the people on earth would see time speeding up for the people on the rocket and vice versa. is not quite right. If by "see" you're talking about what a person on earth would see when they looked into a telescope then the light coming from the ship would be blue shifted and in that sense they'd see clocks running faster. However since the clock is moving they'd reckon that the clock on the rocket ship is still running slow. That means that when they actually measured the rate at which the clock is ticking in their frame of reference it'd be measured to be running slower. At no time is the moving clock ever speeding up. And of course the passengers never notice any difference at how fast their clocks are running inside the spaceship, so long as they're all at the same location inside the ship.
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    Quote Originally Posted by MaxH
    Another thing that breaks the symmetry of relative motion is E^2=(mc^2)^2 + (pc)^2 . This equation tells us that an objects energy comes from both its mass and its velocity (p). But this would mean, going back to the rocket example, that the rocket has more energy that a stationery rocket so is objectively moving (not moving only relative to the Earth).
    The energy of an object is composed of several forms. Typcially a charged particle will have kinetic energy (K), rest energy (E_0) and potential energy (V). The total energy E is then given by the sum

    E = K + E_0 + V

    If the rocket is moving such that there are no external forces acting on it then its potential energy is zero. The the energy is

    E = K + V = mc^2

    where m = relativistic mass of the body.
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    Quote Originally Posted by Physicist View Post
    Jilan - You're assertion When the rocket returns the people on earth would see time speeding up for the people on the rocket and vice versa. is not quite right. If by "see" you're talking about what a person on earth would see when they looked into a telescope then the light coming from the ship would be blue shifted and in that sense they'd see clocks running faster. However since the clock is moving they'd reckon that the clock on the rocket ship is still running slow. That means that when they actually measured the rate at which the clock is ticking in their frame of reference it'd be measured to be running slower. At no time is the moving clock ever speeding up. And of course the passengers never notice any difference at how fast their clocks are running inside the spaceship, so long as they're all at the same location inside the ship.
    Physicist, you are correct that what you see is not what you calculate/reckon. I was just talking about what you actually see.
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    Thanks for noting that Jilan. I suspected that was the case but wanted to make sure that any reader knew that too.
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