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SR motion, GR motion

  1. May 19, 2008 #1
    Since SR physics has considered motion strictly as the separation of bodies,
    no longer can a body move through space except with reference to another body.
    Consider an infinite number of frames (A, B, C, ... A1, B1, C1,...An) with common x axis.
    All move near the speed of light relative to their adjacent frames.
    If we choose as a frame of reference, say frame A, we have an infinite number of frames
    confirming the motion of A. If we now remove all frames except A, A is at rest.
    Not because of any dynamic change applied to A, but because the motion of A was always
    and only with respect to another frame.
    It is useless to argue whether A or any other frame is actually in motion with respect to space.
    Although this seems awkward, it is understandable in the framework of special relativity.
    If we now consider a mass as the origin of A, and A is the only mass in the universe,
    is it still useless to consider the motion of A with respect to space-time?
    Would it not be possible to measure the gravitational time dilation on the x axis of A to differ with significant motion along x?
     
  2. jcsd
  3. May 19, 2008 #2
    If we now remove all frames except A, A is at rest.


    does that mean that A cannot accelerate? if it accelerates is it still at rest?
     
  4. May 19, 2008 #3
    How would you accelerate a system of coordinates?
    I know I could state a system to be accelerating with respect to another,
    but I have no idea how I would accelerate one.
     
  5. May 19, 2008 #4
    by replacing the word 'frame' in your op with the word 'object'.

    you said each frame had a velocity. why can it have a velocity but not be able to be accelerated? if it cant be accelerated then it cant have a velocity.
     
    Last edited: May 19, 2008
  6. May 20, 2008 #5
    Granpa, I assume you mean the origin of A is a massive body. If this is the case you will probably want to be the observer in the frame as well to take measurements. This gives you two masses to work with. So how do you measure the frame to be accelerating? Will you tell me it moves with respect to you? Are you not moving instead?
    Let's make the frame A a box, you are an observer inside with a number of test objects that will remain at rest with respect to A whether A is in constant linear motion or at rest with respect to any other frame. Now accelerate A by any means you can think of and test the laws of physics against the test objects. They all accelerate toward one side of the box, as do you. Is A accelerating or are you and the test objects in free fall?
    Put windows in the box so you can look for the source of your free fall. You see nothing. Do you now choose to take the laws of physics as false because you cannot see a gravitational field? The field is a black whole, or maybe A is accelerating. The laws as measured by any test, do not, cannot distinguish.
    That is my question.
    If I can measure the time dilation of a clock on the surface of the Earth with respect to another at 100km above, would a similar set of clocks on the opposite side of the Earth prove motion with respect to space-time if they did not agree with the first?
     
  7. May 20, 2008 #6

    Dale

    Staff: Mentor

    This is a common misunderstanding. A reference frame is a coordinate system. In SR it is common to say things like "the rocket's frame" which is shorthand for "a coordinate system where the rocket is at rest". Frames are not objects, they have no mass, they have infinite extent (in SR), they are mathematical abstractions.

    Chrisc is right that a reference frame is at rest wrt itself, but to me it seems a trivial point.
     
  8. May 20, 2008 #7
    everything is at rest with respect to itself.
     
  9. May 20, 2008 #8
    Crisc, look up Mach's principle.

    Space and time and motion do not exist except by virtue of the presence of mass-energy. If "A" is the only mass in the universe, then as you remember from geometry, a point is zero dimensions, so there is no spacetime and, a fortiori, no motion.

    Gravitational time dilation could have no meaning unless "A" had some kind of internal structure which was in motion, in which case "A" would not be the only mass in the universe, but would be a collection of masses that would be their own universe.
     
  10. May 20, 2008 #9
    Hello Chrisc

    Quote:-
    -----If we choose as a frame of reference, say frame A, we have an infinite number of frames confirming the motion of A.----

    A trivial point. I see what you are getting at but is the above statement strictly true. Why do they confirm the motion of A. Could we not say A is at rest relative to the others.
    When all the other bodies are removed A is doing whatever it was doing before, whatever that was. Tricky one. But i suppose that if there is nothing to move relative to you have every right to say it is at rest, but then again you always had that right in SR irrespective of what other things are doing. I think????

    I suppose it all comes down to the question is a unique body in the universe at rest or not. It is trivially at rest with respect to itself. Perhaps the question is meaningless.

    If this is irrelevant just ignore it. They are only thoughts..

    As for gravitational time dilation i have enough trouble grasping SR to yet begin GR.

    Matheinste.
     
  11. May 20, 2008 #10

    paw

    User Avatar

    Chrisc, I think you are asking 'if point A is alone in the universe can it be said to be somehow at rest or in motion?'. If that's the case then the following are true.

    1) A is at rest wrt itself. Trivial? Sure, but none the less true.

    2) We can define an infinite number of frames in which A is at rest.

    3) We can define an infinite number of frames in which A is in uniform motion.

    4) We can even define an infinite number of frames in which A is in accelerated motion.

    All of the above are true because a frame of reference is an abstract mathematical construct. A frame is a coordinate system endowed with certain properties that allow us to make sense of a physical system. We choose one frame over another to simplify our analysis of the system.

    Note that none of the above says anything about the absolute state of A. The absolute state of A is probably meaningless. At the very least any discussion of the absolute state of A is philosophical.
     
  12. May 20, 2008 #11
    Hello paw.

    Interesting answer.

    Referring to the uniqueness of A as in the scenario above would it be correct to say that there are an infinite number of frames of reference and that A could be at rest or moving in any of them or is that not quite the same as you are saying. I have used the words could be rather than is.

    Also if we can define an infinite number of frames in which A is at rest how do they differ from each other.

    Matheinste.
     
  13. May 20, 2008 #12
    Mach would say you can not accelerate in such a universe with no other mass. Einstien would disagree. Of course accelerating usually involves ejecting mass in the opposite direction and then we would have more than one mass with relative motion in our hypothetical universe which would spoil the argument. This can be circumvented by having a device that pojects photons photons in one direction. The photons would not give away your relative velocity because stationary or moving you velocity relative to the photons is always c. However with powerful enough laser you would be able to feel and measure your acceleration in this empty universe (if you do not count the energy of the emitted photons.) One thing you should bear in mind is that the vacuum is not empty. With sufficient acceleration you would see Unruh radiation emmited from the seemingly empty vacuum originating fron the normally unobservable zero point energy that the vacuum contains.
     
  14. May 20, 2008 #13

    paw

    User Avatar

    As long as I'm not misunderstanding you yes, there are an infinite number of frames we could define in which A is at rest or in motion (uniform or accelerated). I say this as an illustration to the OP that a frame is an abstract concept and doesn't say anything about the absolute state of A.

    Well the obvious frame is the [cartesian] one in which A is at the origin for all time t. Another would be one in which A is at (0, 100, 1000) for all time t. Then there are frames with polar coords. I think you can have non-Euclidian frames (that's reaching the limits of my math knowledge). They would differ from each other by some transformation but would all agree that A is at rest by definition.

    As for uniform motion you can define a frame where A is at the origin at t=0, (1,0,0) at t=1, (2,0,0) at t=2 etc. Clearly you can do the same for any starting point and velocity you wish to give to A in the frame. Again, they differ by some transform.

    I stress all this was to illustrate that frames are abstract concepts we define and don't say anything about the absolute state of A, something I believe is meaningless.

    [Edit]I should add that my comments also illustrate that analysing the 'motion' of an isolated point particle borders on the absurd. Your choice of reference frame determines the outcome of the analysis and the results don't say anything in absolute (or physical) terms. It's only when you add a second point particle that the analysis becomes meaningful.
     
    Last edited: May 20, 2008
  15. May 20, 2008 #14
    Hello paw.

    Thanks that's quite clear. So they differ by the coordinate systems used to map them.


    Matheinste.
     
  16. May 21, 2008 #15
    So we go from an infinite number of frames to one only to realize we never were dealing with anything more than a mathematical abstraction.
    There is an infinite set of coordinates that will define A in motion and an infinite set of coordinates that will define A at rest.
    But we also knew this is the limit of SR. It is a mathematical construct of space and time that accounts for the
    constancy of the speed of light by removing "absolute" from the language of physics.
    No absolute motion, rest, mass, speed, scale, frequency, energy etc.
    SR exchanges absolute for infinite by a simple mathematical construct - the Lorentz transformation which via 1-v/c guarantees
    the constancy of the speed of light and requires all motion is relative to this "infinite limit".
    Infinite limit sounds like a contradiction but it is not the numerically infinite that sets the limit, it is the physically infinite that is,
    while mathematically possible, physically impossible. I requires infinite mass to acquire infinite speed, infinite energy to acquire infinite mass,
    infinite scale to acquire infinite energy, etc.
    This is a brilliant concept, but it is completely linear. If we introduce a single mass at A it all falls apart.
    Whether Newtonian, Machian or Einsteinian, the introduction of a single mass A, results in a gradient of space and time that with A,
    "IS" the universe. This previous principle of relativity, the sustaining of the laws anywhere, anytime which via the Lorentz transformation
    amounts to "any motion", must now account for a non-linear transformation that exists or "extends from" every mass.
    So once again we look to the relationship of space and time as the index of motion or in this case acceleration.
    To sustain the laws the rate of time must once again change with relative motion or conversely with respect to the principle of relativity,
    relative motion is a measure of the rate of time. If time changes with the proximity to mass, then clearly motion is relative to the proximity to mass.
    If time is constant with constant proximity to mass and changes with proximity to mass, then as a measure of d/t we have acceleration.

    So my question is this, with A and the extension of A to infinity, would a discrepancy in the rate of clocks at equal and constant proximity to
    A on opposite sides of A, be (theoretically) substantial proof of the motion of A with respect to the space-time extending from A?
     
  17. May 21, 2008 #16

    paw

    User Avatar

    Chrisc, I'm not sure what to make of your post #15. You seem offended that a frame is an abstract mathematical construct. I think you are wishing for absolutes where there are none.

    Look at it this way. You throw a rock. The rock 'flies' through the air. It 'travels' a 'distance'. It 'falls' back to the ground and 'stops'. The highlighted words are abstractions. They are labels for processes we observe. A frame of reference is just a more rigorous way of looking at the same process. It's still an abstraction.

    The single body problem you introduced in the op is a special case of 'motion'. Without something like the distant stars or an ether you have nothing to compare the single body to in order to analyse its 'motion'. So words like 'fly', 'travel', 'distance', 'fall' and 'stop' have no meaning.

    As I said, there are an infinite number of frames you could define on A in order to perform some analysis. It's logical to define a frame that is convenient for your analysis. But, since A is alone in the universe you can choose any frame with equal logic. Thus you have a situation where all frames are equally valid for the analysis. That's why you can define a frame that has A at rest or in any 'motion' you wish. This is a characteristic of the single body problem.

    If we introduce a second point particle B the situation changes dramatically. In this case all frames are not equally valid (in the sense of usefulness). A frame where A is at rest is more convenient. A frame where A is at rest at the origin is even more convenient. Now you CAN describe B's motion in sensible terms, that is wrt A. However, you still cannot describe the 'motion' of A or B in any absolute way. That's because there is nothing you can use to define a frame that is at rest in any absolute sense.
     
  18. May 21, 2008 #17

    Dale

    Staff: Mentor

    It does not matter if the "otherwise empty" universe is "Machian" or not. You can still perform your analysis in any arbitrary coordinate system you choose. The point is that the coordinate system is a mathematical tool and not something physical.
     
    Last edited: May 21, 2008
  19. May 21, 2008 #18
    Without something like the distant stars or an ether you have nothing to compare the single body to in order to analyse its 'motion'. So words like 'fly', 'travel', 'distance', 'fall' and 'stop' have no meaning.

    correct.

    It does not matter if the "otherwise empty" universe is "Machian" or not. You can still perform your analysis in any arbitrary coordinate system.

    coordinate system? coordinates of what? without an aether space itself would not exist.
     
  20. May 21, 2008 #19
    What I was trying to get at is that Mach said the inertia of a body is a property that is he result of all the mass of the "distant fixed stars". In the otherwise empty universe body A would not have the property of inertia in a Machian universe while Einstein came to a different conclusion.

    For example lets say body A is not an infinitesimal point particle but a large ship. Now lets say when this ship launches a small projectile in a normal universe the projectile leaves at 1000m/s and the ship recoils at 1m/s. The speed of the projectile can be measured becasue it is fired from near the nose of the ship and its progress towards the rear can be monotored. Now in the empty Machian universe the inertia of the ship would only be proportional to the mass of the projectile so would the recoil of the ship be much greater? Would the relative velocity of the projectile moving from the nose of the ship to the rear be measured as much greater in the otherwise empty Machian universe without all the massive stars to confer the property of inertia?
     
  21. May 21, 2008 #20

    paw

    User Avatar

    After reading this several times I think I know what you are asking.

    'If A is a single, massive, particle alone in the universe can we deduce its absolute motion from its interaction with spacetime'?

    My own feeling is that you can't deduce absolute motion.

    Let's say spacetime does exist independantly of mass/energy. Your hypothetical particle would then cause a 'bending' of spacetime. An imaginary clock would then tick at different rates at different distances from the particle. A change of tick rate would indicate that A is in motion. But......

    you can only position the clock in relation to A. How would you place the clock so that IT is not in 'motion' relative to spacetime? There is no universal reference frame that you can use to guarantee the clock is at rest. So in my opinion your scenario will not work.
     
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