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B Which frame of reference is the correct one?

  1. Apr 2, 2017 #1
    If everything is relative to something else, who's frame of reference is actually correct? For example an observer moving at 99.9%c will use the exact same laws of physics we use and determine without any doubt whatsoever that Earth is flat... flat as a pancake!

    So who's frame of reference is correct? Is the Earth actually flat or is it spherical? I don't quite understand this. If it's dependent on the observer then doesn't that ultimately mean both are 100% true...

    Secondly imagine some object of height h at rest and directly facing a slot of height h/2. Obviously at rest the object cannot fit through the slot but at 99.9%c the object can fit through the slot.

    So according to the physics of the observer moving at 99.9% it will fit, but clearly to the stationary observer it won't fit... who is right? Does it fit or does it not fit?
     
  2. jcsd
  3. Apr 2, 2017 #2

    Dale

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    Every frame is really actually truly correct. That is the whole point.
     
  4. Apr 2, 2017 #3

    Nugatory

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    They are all equally correct. Of course that answer leads to questions like
    If the object passes through the slit when we analyse the situation using one frame, it will pass through the slit when we analyse the situation using the other frame. If you get any other result, there's a mistake in one or the other analysis.

    To properly work through your example above, we would need a more precise specification of exactly how the object and slot are oriented and moving relative to one another; and depending on the details this could be easy or it could be a very tricky problem. But before you try working this one out, you will want to google for "pole-barn paradox"; this is basically your problem in its most pure form, and understanding it will get you a long ways towards understanding the more complicated problems.
     
  5. Apr 2, 2017 #4

    PeroK

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    The shape of the Earth isn't a law of physics. The Earth is a certain shape in its rest frame. But, in a reference frame where the Earth is moving it is a different shape. The rest frame of an object is an important frame for that object. You could say: every planet is approximately spherical in its rest frame. That might be a sort of "law of physics".

    Another example: the average life expectancy of a muon is defined in its rest frame. But, if the muon is moving relative to you, then you will measure a much longer life expectancy. If you want a "law" or just a statement about a muon's life expectancy, you would have to specify its rest frame. But, of course, the muon's rest frame only applies to that muon (or any any muon at rest in that frame). Any other frame has the same property that a muon at rest in that frame has a certain life expectancy in that frame. That's roughly what's meant by the law of physics being the same in all inertial reference frames.

    There is no special frame where muons at rest in that frame have the right life expectancy, but muons at rest in another reference frame have a different life expectancy. That would mean different laws of physics.

    In fact, you could extend this law to give the life expectancy of a muon given its velocity (in the frame in which it is measured). You would then have the same law for all reference frames. The life expectancy of a muon would depend on its observed velocity.
     
  6. Apr 2, 2017 #5
    Thanks for your replies.

    The point I'm making though is the laws of physics don't change with velocity right? So large gravitational bodies form spheres (or close to spherical) but according to an observer who is moving very fast, Earth would not be spherical, it would be flat.

    If the observe flew past Earth and was somehow able to take a photo, it would show Earth looking like a coin right? So how could he ever know that Earth is actually round? Is there any test he can perform?
     
  7. Apr 2, 2017 #6

    PeroK

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    The observer can stop and take a proper look at the object at rest.
     
  8. Apr 2, 2017 #7

    PeterDonis

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    Actually, no, because light travel time affects what the observer actually photographs. Google "Penrose-Terrell rotation". But the observer could calculate that the Earth was highly length contracted in his rest frame.

    Also, as someone else pointed out, the laws of physics don't say "gravitating bodies have to be round." The laws that govern the shape of the Earth can be formulated in a frame-independent way, but they will involve things like the Earth's stress-energy tensor and the curvature of spacetime and how they are related by the Einstein Field Equation. The changed "shape" of the Earth in a frame in which it is moving very fast will be a consequence of those laws, just as length contraction is a consequence of the laws of special relativity in cases where gravity is insignificant.
     
  9. Apr 2, 2017 #8

    DrGreg

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    Or the observer can measure the velocity of the Earth relative to himself and do a relativistic calculation to work out what the shape would be if they were at rest relative to each other.
     
  10. Apr 2, 2017 #9
    OK thanks :)
     
  11. Apr 2, 2017 #10

    Dale

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    That is correct, but you need to be careful to use the laws of physics and not low speed approximations.

    You are thinking of Newton's law of gravitation. But Newton's law of gravitation is a low speed approximation to general relativity. If you use the correct law (GR) then you find that indeed, large gravitating bodies form ellipsoids rather than spheres.
     
  12. Apr 3, 2017 #11
    That's fascinating. Is it possible to give a b-level explanation for that? What determines the axes of symmetry?
     
  13. Apr 3, 2017 #12

    Dale

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    In GR the source of gravity is not just mass, but what is called the "stress energy tensor". It includes energy but it also includes momentum, pressure, and stress. In "normal" situations the momentum is very small and the only large component is the energy which is mostly due to the mass, and Newton's law is recovered. However, in relativistic scenarios the momentum is also significant and the energy includes substantial KE. That momentum axis is what determines the axis of symmetry.
     
  14. Apr 3, 2017 #13
    Very interesting! Thank you.
     
  15. Apr 3, 2017 #14
    So is the Earth round or flat?

    The physics in the strict sense of the word don't change, however velocity does have an impact as you've seen changes the "physical" appearance. I find it best to think of it as a change in "comparative geometry" due to relative motion and c being invariant.

    So in this example, as Dale already said, both frames are physically correct and "true" with their observations. The comparative geometry changed (and in this case symmetrically) in such a way that length contracts in the direction of compared motion.

    note for one to see the Earth flat they must also see the universe this way, and in turn "play out" in such a fashion. i.e. very "fast" to your proper time...basically the universe becomes way too similar to a graph on paper lol.
     
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