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Cascading reference frames

  1. Jan 7, 2010 #1
    Here's a question that's bothered me for a while.

    Suppose you are a person (P) at point A. You travel between point A and B at some fraction of c (speed of light). And so relativity kicks in. Now, that's the standard relativity model and we talk about P with regard to A and B.

    Now, what if we extend the model. Let's suppose that A is Earth and B is Mars. Now, let's say there's some A' which contains both A and B. Let's also suppose there's some B' which contains C and D. Extending further, let's say there's som A'' which contains A', and A''' which contains A''. Also, B'' which contains B' and B''' which contains B'':


    Several questions come to mind:

    1) The velocity of P between A and B can be seen differently depending on the frame of reference (A''' vs A'). However, as the velocity of P approaches c, it approaches c for all frames of reference, doesn't it?

    2) Assuming that A', A'', and A''' have their own "group" velocity, that velocity must be additive to the velocity of P. For example, a person on a train at 60 MPH throws a ball at 10 MPH, from outside the train the ball is at 70 MPH. Assuming that question #1 is true, then if any "container" approaches c, then from frames of reference outside that container, P must be traveling at near c. But also, if #1 is true, then P must be traveling at something close to c WITHIN the local frame of reference, shouldn't it?

    3) Since we can observe that P isn't traveling near c (because it doesn't have the appropriate characteristics), can we then infer that no container for P is traveling near c from any frame of reference?

    4) And isn't all of the above true even from B', B'', and B'''?
  2. jcsd
  3. Jan 7, 2010 #2


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    Hi underworld! :smile:
    No, relativity only comes in if there are different frames of reference, ie observers with different velocities.

    All your As and Bs etc are points, not velocities (and I assume they're all stationary).

    Relativity simply isn't relevant.

    And there are no "local frames of reference" … a frame of reference is a coordinate system valid for the whole of space.

    (Two different frames of reference both cover the whole of space.)
  4. Jan 7, 2010 #3


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    You need to make it much more clear what you mean. Are A and B point particles, points in space, or points in spacetime? I'm guessing point particles. What are the primed letters? Inertial frames? More "points"? I'm guessing inertial frames. In that case, it doesn't make much sense to say that e.g. A' "contains" A, or that A'' contains A'. Do you mean that A has velocity 0 in A'?

    I don't know what you mean yet, but I suspect that this is heading towards the relativistic formula for addition of velocities, which I like to write as

    [tex]u\oplus v=\frac{u+v}{1+uv}[/tex]

    This is in units such that c=1. If you want to include c explicitly, replace uv with uv/c2. The [itex]\oplus[/itex] isn't a standard notation. It's just what I like to use. u can e.g. be the velocity of a train relative to the ground, and v can be a walking passenger's velocity relative to the train. Then [itex]u\oplus v[/itex] is the passenger's velocity relative to the ground.
  5. Jan 7, 2010 #4
    Sorry if I'm not being clear. It's a bit difficult to articular... let me try again.

    Let's assume that P is person, that A is the dining car on a train, and B is the sleeper car on a train. If I'm on that train observing P move from A to B, I observe a particular velocity for him ... let's say 2 MPH. If I'm on the earth, I observe his velocity as 2 MPH plus the velocity of the train (60MPH), so 62 MPH. If I'm off the earth, I might observe him as 62 MPH plus the speed of the earth relative to my observation point.

    The point then, is that if I keep "broadening" my observational reference point ... is it possible to observe P moving at or near c?

    For example, P moves, the train moves, the earth moves, the solar system moves, the milky way moves, and so on.

    If, from ANY of those observational perspectives, P moves at c, then I'm postulating that at ALL of them P must move at c. And if that is true, and we do not observe P moving at c, then we can infer that there is NO observational perspective where P does move at c.

    Additionally, I'm speculating that even if P doesn't move at c, that it also doesn't move near c, otherwise:

    1) We would observe motion closer to c


    2) Our local frame of reference is so far removed the frame of reference where P moves close to c that the local observed velocity is effectively "diluted".
  6. Jan 7, 2010 #5


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    That would be correct: if P moves at speed c from any inertial observer's perspective, then P moves at speed c from all inertial observers' perspectives. Case in point: photons. Note that this would require P to have zero rest mass.

    It's also true that if P moves at a speed less than c from any one inertial observer's perspective, then all other inertial observers will also see P moving with speed less than c.

    Note that you don't really need to "zoom out" and achieve a broader perspective to notice these effects. An observer on another train passing by in the opposite direction at, say, 0.999c would observe P moving at nearly the speed of light.
    That's actually not true, if I understand you correctly. The laws of physics prevent P from moving at c (assuming P has a rest mass) from any inertial observer's perspective, but there is nothing in physics to stop P's velocity from getting as close to c as you like. It all depends on the observer.
    It just so happens that in our reference frame here on Earth, most nearby matter moves with velocities much less than c, at least at the macroscopic scale. However, there is no shortage of subatomic particles from cosmic rays and the like that we can observe moving at speeds very close to c. The LHC, for example, will accelerate protons to speeds of 0.99999999c. Many cosmic rays are even faster.
  7. Jan 7, 2010 #6


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    Not exactly. It's actually a bit less than 62. Use the formula I posted.

    Edit: Note that this formula ensures that the result is always <c, no matter how large the velocities are, and therefore also no matter how many times you take the output of one calculation and use it as input in the next.
    Last edited: Jan 7, 2010
  8. Jan 8, 2010 #7


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    Actually, this is wrong. If the velocity of P equals c in one reference frame then it equals c in all reference frames. However, if the velocity of P only approaches c (e.g. 0.999999999999999 c) in one reference frame then there are reference frames where its velocity is 0 or even negative.
  9. Jan 11, 2010 #8
    Ok - this is quite interesting as I've not heard it like that before. If the above is true, then that implies that there are fundamental differences between objects. There are P objects which can move at <c, and P' objects which can move at c perhaps.

    Now this sparks the next question which is that photons and electrons can move at c, but also can move slower than c, right? In that case, you could have a frame of reference where the photon or electron can be observed to have a velocity of 0 - right?

    This leads to another thought now - which is that at c, the concept of "frame of reference" breaks down. Is it therefore hypothesized that at c there exists something like a "temporal phase shift"? In the same way that matter undergoes phase shifts with temperature/pressure - can time undergo a phase shift with velocity? If so, then maybe the difference between P and P' is their temporal phase.
  10. Jan 11, 2010 #9


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    Hi underworld! :smile:
    Yes, that's exactly right … anything with speed < c in one frame has speed < c in any frame, and no amount of force can make its speed ≥ c … and anything with speed = c in one frame has speed = c in any frame, and no amount of force can make its speed ≠ c.

    (and, mathematically, anything with speed > c in one frame has speed > c in any frame, and no amount of force can make its speed ≤ c … these would be called tachyons, but there's no reson to believe they actually exist :wink:)

    ok, i agree that light can move < c in glass etc, but that, very loosely speaking, is because it's still going at c, but getting delayed …

    hmm … perhaps someone else can explain this point better than i can? :redface:

    No, wrong premise … electrons always < c, photons always = c.

    (you may have been misled by seeing somewhere that "virtual" electrons and photons don't obey this rule … ignore that, they're only a mathematical device used in calculating the values of Feynman diagrams … they don't, and can't, actually exist … the clue's in the name! :wink:)
    That's right. It just doesn't work at c. :smile:
    Not following you :redface: … the same matter can change from solid to liquid, but it can't change from P to P', so I don't see how that difference could be analogous to a phase shift.
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