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Invariance and relativity

  1. Jun 12, 2015 #1
    Is it a fact of invariance that a person moving in an enclosed object cannot tell if he/she is moving at constant velocity or standing still (for case when he/she is not being accelerated nor in a gravitational field)? If so, would it be possible to perform an experiment within the closed object whereby a person adds a known amount of energy to an object with a known mass (older definition would have called this intrinsic mass) and then measure the acceleration of said object? The idea that an object that is in motion will require more energy to accelerate than an object rest. This would of course negate the idea that a person would not be able to tell if they were at rest or if they were moving at some velocity.
     
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  3. Jun 12, 2015 #2

    Orodruin

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    No, this is not possible. Energy is not a Lorentz scalar and depending on the frame you will be adding different amounts of energy. Relativity is perfectly self-consistent in this and the usual thing that people forget about is to use the relativistic versions of addition of velocities and acceleration relations.
     
  4. Jun 12, 2015 #3
    OK, so energy is also dependant on relative motion? Thus is it expected that the person in the enclosed object would think they are adding x amount of energy when in fact they would be adding x amount of energy plus additional amount of energy?
     
  5. Jun 12, 2015 #4

    Orodruin

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    You cannot say that a person adds a specific amount of energy without specifying the frame. Therefore, there is no universal answer to "how much energy was added?". It all depends on the reference frame, just as velocity does. There will even be reference frames where energy is removed from the object.
     
  6. Jun 12, 2015 #5

    Nugatory

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    Yes. This is true even in classical physics. If I'm sitting in a train with a heavy object in my lap, I'll say that the speed and therefore the kinetic energy of the object is zero; someone not at rest relative to the train will say that the speed and therefore the kinetic energy of the object is non-zero.
     
  7. Jun 12, 2015 #6
    Would both have to agree on the total energy (kinetic and potential)?
     
  8. Jun 12, 2015 #7

    Orodruin

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    No. This is a common misconception. That energy is conserved (in every frame) does not mean that it is the same in every frame.
     
  9. Jun 12, 2015 #8
    That's interesting.I never understood that before.Thanks.
    Just to make sure I completely get it, conservation of energy (or mass, momentum, etc..), only occurs within each frame of reference?
     
  10. Jun 12, 2015 #9

    DrGreg

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    Yes.
     
  11. Jun 12, 2015 #10
    Awesome I love learning new ideas. One last question about this. What happens when 2 inertial frames coincide (a collision). Would both parties describe the same event with the same amount of energy colliding of would they disagree on the amount of energy in the collision (assuming the collision didn't kill them off course).
     
  12. Jun 12, 2015 #11
    This is interestingly how einstein proved e=mc^2.
     
  13. Jun 12, 2015 #12

    PeterDonis

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    Can you give a reference?
     
  14. Jun 13, 2015 #13

    Nugatory

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    Frames cannot collide - the idea makes no sense because a frame is just a rule for describing movement and where and when things happen. Suppose that I'm watching two objects, one coming from the left at 10 km/hr and one coming from right at 10 km/hr, and they collide. That's the description using a frame in which I am at rest. If you are moving at a speed of 10 km/hr relative to me, then using a frame in which you are at rest, one of the object is moving at 20 km/hr and the other is at not moving Or we could use some other frame in which one of the objects is moving at 50 km/hr and other one is chasing it from behind at 70 km/hr - an observer at rest in that frame would be moving at 60 km/hr relative to you.

    Each of these three observers calculates a different amount of kinetic energy, both before and after the collision. However, all three will agree about the energy released by the collision (and presumably spent crushing and crumpling the colliding objects); and all three will agree that energy is conserved: the kinetic energy before the collision is equal to the sum of the kinetic energy after the collision and the energy released by the collision.
     
  15. Jun 13, 2015 #14
    I assume that after the collision both objects are at rest with respect to a stationary observer (and buildings, trees, etc). If after the collision they have the same frame of reference, how can you say that frames cannot collide and that it makes no sense to claim that? If frames colliding makes no sense, maybe it is just a semantic issue. What about the frames collapse to become the same frame off reference? The idea still holds, if both objects can have a different evaluation of the total energy (in order to keep conservation of energy, momentum, mass) within their local frame, and then the end up at the same frame off reference, then something has to allow their new frame to agree with the total energy in their new frame that they share.
     
  16. Jun 13, 2015 #15

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    We can set things up so that after the collision the two objects are at rest with respect to the buildings and trees and other nearby stuff. This will happen if the objects have equal masses and approach each other from opposite directions with the same speed as measured in a frame in which the buildings and trees are at rest, and if the two objects stick together (or are crushed into one lump of twisted metal) in the collision.

    However, that does not mean that after the collision they're at rest relative to a stationary observer. They aren't.

    They're at rest relative to the buildings and trees - but those buildings and trees are attached to the earth, the earth is going around the sun, the sun is moving through interstellar space. An observer sitting leisurely at rest in his astronomical observatory on Mars, feet comfortably propped up on a table as he watches the collision on earth through his telescope, would consider the proposition that he's somehow less "stationary" than the buildings and trees on earth to be utterly absurd. Nonetheless, he can analyze the collision using the frame in which he is at rest (which of course is completely unaffected by the collision) and he will find that both energy and momentum are conserved. He will also agree with the all other observers anywhere in the universe and moving with any speed relative to him (including the very special case of an observer who happens to be at rest relative to buildings and trees on the surface of the earth near the collision site) about how much energy is released by the collision.
     
  17. Jun 13, 2015 #16

    Nugatory

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    It's not a semantic issue, it goes to the heart of the definition of what a frame is.

    You may be being misled by the very common but sloppy English language idiom in which we say that something is "in a frame". When someone says that something is "in a frame" or talks about "the frame of something", that's a convenient verbal shortcut for the more precise "Until I say otherwise, I will be doing all my calculations of speeds and positions and energies and momenta using a frame in which that something is at rest right now, no matter what it does later".
     
  18. Jun 13, 2015 #17
    I guess my thought this is that once 2 objects are at rest with redirect to reach other they would be considered at the same frame of reference. And once they are at same reference they should be able to agree on the amount of energy of said collision. That seems like a paradox if they can have a different idea as to how much energy was involved in the collision.
     
  19. Jun 13, 2015 #18

    Nugatory

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    That's just not correct. Everything is always in all reference frames all the time - there's no such thing as being in one frame but not another.

    The two objects are in the reference frame in which the Martian astronomer is at rest, and using that reference frame their speed after the collision is the same as the earth's speed relative to Mars. The two objects are also in the reference frame in which the buildings and trees near the site of the collision are at rest, and using that frame their speed after the collision is zero. In both frames the speed changes in the collision, but this speed change doesn't mean that either object is changing reference frames, or that before the collision when their speeds were different they were somehow in different frames.
     
    Last edited: Jun 13, 2015
  20. Jun 14, 2015 #19
    The way I envision it is that 2 object each have their own reference frame that is unique to their circumstance.
    Thus 2 objects that are in motion relative to each other would each have their perspective on energy conservation.
    While there can be an infinite amount of frames of reference (your Martian example being one), only one frame of reference would apply to a person at any given time (as measured by them). Thus, I expect that 2 people/objects in motion relative to each other would each have a unique frame of reference that the other does not share. Further, I expect that 2 objects that are not in relative motion with each other, should be able to agree on and share the same frame of reference (again, only looking at the frame of reference as measured by either of the 2 objects and not the potentially infinite other frames of reference). If either one of these 2 ideas is inaccurate, please help me to understand. If both of those 2 ideas are accurate, then there can be a case when 2 objects that started off with motion relative to each other and then came to rest with respect each other (after a collision), would have started off with unique frames of reference (as measured by each object), and then ended with a shared / agreed upon frame of reference after the collision. Thus I see a case where they wouldn't see the same conservation of energy prior to collision but then after the collision, they would have the same views of conservation of energy. How can they start of not agreeing on their perspective of conservation of energy but finally ending up agreeing on it.
     
  21. Jun 14, 2015 #20

    Nugatory

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    Everything that I have bolded above is wrong and makes me wonder if you're even bothering to read the earlier posts in this thread.

    The objects do not have a perspective on energy conservation, although observers watching them collide might. The objects do not have reference frames and they do not share reference frames. Observers do not have reference frames or share reference frames.

    Instead, observers use reference frames (not necessarily the one in which the observer might be at rest) to assign values at a particular moment to the velocities of the objects they are observing. They use these values to make calculations about energy and momentum conservation.

    Now, go back and try writing your description of the collision and energy and momentum conservation, as seen by two different observers who are moving relative to one another, without saying things like "in a reference frame" or "having a reference frame" or "sharing a reference frame" or "the reference frame of..." or "this object's reference frame" or "this observer's reference frame". Instead, allow the words "reference frame" to appear only in the phrase "calculated using a reference frame in which...."
     
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