## "at rest" in Einsteinian relativity

 Quote by DaleSpam Relative to anything. "At rest" simply means "v=0", since v is always defined as relative to something then rest is also defined as relative to the same something. Just as you can arbitrarily pick what you measure v wrt, you can also arbitrarily pick what you measure rest wrt.
Apologies, I'm repeating myself now, more for posterity than anything - feel free to skip over this if you've addressed it in another post.

If we take the example of two lone obervers in empty space, moving relative to each other - again, let's call them Albert and Henry. Albert's co-ordinate labeling system will label him as "at rest" with a zero velocity, despite the relative motion between him and Henry. Relative to what is Albert "at rest" and relative to what does he have a zero velocity.

In the context of the PoR, the often stated consequence is that an inertial observer cannot determine if they are "in motion" or "at rest"; how then can Albert label himself as "at rest"? Do they refer to different things?

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 Quote by mangaroosh In the context of the PoR, the often stated consequence is that an inertial observer cannot determine if they are "in motion" or "at rest"; how then can Albert label himself as "at rest"? Do they refer to different things?
It is possible to determine if something is at rest wrt to other objects. So Albert's head is pretty much at rest wrt his body. What is meant by the above principle is that there is no universal or absolute state of rest.
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 Quote by mangaroosh The GPS is a good example; I probably have one on my phone but I haven't used it yet. It makes the point though that you don't move relative to the reference grid, because the reference grid is not physical; you move relative to the earth. The GPS represents the earth as a grid and represents you as a dot. The disconnect, though, is that a GPS defines a common reference frame for all earth-bound observers.
My point in bringing up GPS is that it provides four co-ordinates just like Einsteinian relativity does in a Frame of Reference. Your original question is: what the concept "at rest" means in Einsteinian relativity. Now that you understand how a Frame of Reference is constructed, please go back and read my first post #3 and then read Michael C's post #13. They are saying the same thing and directly addressing your original question.

You are correct, the Frame of Reference is not physical but until you create a non-physical, purely "theoretical" Frame of Reference, you're not doing Einsteinian relativity. Remember, Einsteinian relativity is based on two postulates, the first of which is the Principle of Relativity. The Principle of Relativity addresses your disconnect. It addresses your second concern with regard to the physical nature of being at rest.
 Quote by mangaroosh In the Einsteinian thought experiment with Albert on the platform and Henry in the train, two different reference frames are defined. Each reference frame labels their respective observers as "at rest" and their counterpart as "in motion". We can relocate this to empty space with just Albert and Henry, for the sake of simplicity. In this case we again have two separate reference frames; Albert's labels him as "at rest" and Henry as "in motion"; it ascribes a zero velocity to Albert and 100% of the relative velocity to Henry. If we only consider relative velocities, how can Albert be labelled with a zero velocity, and labeled as at rest? Relative to what is he at rest, given that it isn't Henry. Also, a stated consequence of the principle of relativity is that an inertial observer cannot determine if they are "in motion" or "at rest"; is it possible that Albert's labeling himself as "at rest" is incorrect, given that he cannot determine if he actually is or not? Or does the "at rest" refer to different things?
Yes, "at rest" can refer, as you just stated as a consequence of the Principle of Relativity, that each observer can label himself "at rest" and the other observer as moving relative to him, without regard to any coordinates defined by a particular Frame of Reference OR it can refer to any defined Frame of Reference and then you look at the spatial coordinates to see if they are the same for an observer, in which case, he is "at rest" or if they are changing, in which case, he is moving.

One of the important concepts of Einsteinian Special Relativity is that you can pick any arbitrary Frame of Reference in which you define, describe, demonstrate and analyze what is happening with all observers and objects, moving or at rest, accelerating or inertial, doing whatever you. Don't make the mistake of thinking that one observer is at rest all by himself in his own Frame of Reference while the other observer is at rest all by himself in his own Frame of Reference and mixing the coordinates between these two frames. You need to put everything and everybody in one Frame of Reference and then if you want to switch everything and everybody over to a different Frame of Reference, you use the Lorentz Transformation to convert the coordinates for all significant events from the first Frame of Reference to the coordinates in any other Frame of Reference you choose moving with respect to the first Frame of Reference.

 Quote by mangaroosh That we cannot determine which one is actually moving is reflected by the fact that we can define reference frames in which either is moving; but that we cannot determine which one is moving doesn't mean we can't deduce that one of them, at least, has to actually be moving. If neither was actually moving, they would remain at rest relative to each other.
You keep using the phrase "actually moving". Asking if something is "actually" moving or not makes no sense: it's like asking if the North end of the Earth's axis is "actually" pointing up or down. In both cases there's no answer: there is no definition of absolute motion, any more than there is a definition of absolute up and down in the Universe.

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 Quote by mangaroosh If we take the example of two lone obervers in empty space, moving relative to each other - again, let's call them Albert and Henry. Albert's co-ordinate labeling system will label him as "at rest" with a zero velocity, despite the relative motion between him and Henry. Relative to what is Albert "at rest" and relative to what does he have a zero velocity.
Albert's coordinate system labels velocities wrt himself. Albert's velocity wrt himself is 0 therefore he is at rest wrt himself. Hopefully there is nothing surprising or confusing about that.

 Quote by Mentz114 It is possible to determine if something is at rest wrt to other objects. So Albert's head is pretty much at rest wrt his body. What is meant by the above principle is that there is no universal or absolute state of rest.
Indeed, it is possible to determine if something is at rest wrt to other objects, so presumably it isn't this form or relative rest and motion that is referenced in the PoR.

I don't, however, think it can be said that what the principle means is that there is no universal or absolute state of rest; the PoR is an extension of the galilean principle of invariance, which meant that it is not possible to distinguish a state of absolute rest from a state of absolute, inertial, motion. I don't think that the PoR changes this somehow, although the equivalence principle extends this to accelerating reference frames.

The PoR, as far as I can see, still implies that we cannot distinguish a state of absolute rest from a state of absolute motion.

Some might say that because we can't distinguish between the two that we can conclude that absolute rest doesn't exist, but I think this is incorrect, because, firstly it isn't justifiable, but secondly, it has a material effect on the conclusions we draw.

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 Quote by mangaroosh Indeed, it is possible to determine if something is at rest wrt to other objects, so presumably it isn't this form or relative rest and motion that is referenced in the PoR. I don't, however, think it can be said that what the principle means is that there is no universal or absolute state of rest; the PoR is an extension of the galilean principle of invariance, which meant that it is not possible to distinguish a state of absolute rest from a state of absolute, inertial, motion. I don't think that the PoR changes this somehow, although the equivalence principle extends this to accelerating reference frames. The PoR, as far as I can see, still implies that we cannot distinguish a state of absolute rest from a state of absolute motion. Some might say that because we can't distinguish between the two that we can conclude that absolute rest doesn't exist, but I think this is incorrect, because, firstly it isn't justifiable, but secondly, it has a material effect on the conclusions we draw.
You can believe in a state of absolute rest if you want to but don't you think in order to not be a hypocrite, you should transform every scenario and every situation into your absolute rest frame? And when you get ready to use the GPS in your phone, you better get someone to reprogram in all the coordinates to show what they are in your absolute rest frame instead of latitude, longitude and altitude. Otherwise, I think you're not sincere.

 Quote by Chestermiller In the context of Special Relativity, "at rest" means "not moving relative to a specified inertial frame of reference." A frame of reference can be tested to ascertain whether it is an inertial frame of reference, by examining the motion of objects moving relative to that frame, and confirming that those which are not acted upon by an external force are traveling in a straight line at constant relative speed.
A stated consequence of the principle of relativity is that an inertial observer cannot determine if they are "in motion" or "at rest"; the equivalence principle extends this to accelerating reference frames; however, an observer can easily determine if they are in motion, or at rest, relative to a speficied inertial frame of reference.

What does the "at rest" in that context mean?

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 Quote by mangaroosh A stated consequence of the principle of relativity is that an inertial observer cannot determine if they are "in motion" or "at rest"; the equivalence principle extends this to accelerating reference frames; however, an observer can easily determine if they are in motion, or at rest, relative to a speficied inertial frame of reference. What does the "at rest" in that context mean?
 Quote by ghwellsjr It simply means that the spatial coordinates are constant while the temporal coordinate varies.
 Quote by ghwellsjr If I see that the three spatial coordinates for an adjacent pair of events are the same, then during that one-second interval of time, I was at rest.
Instead of posting anymore, you should just go back and read all the posts on all the threads you have started. All the answers are there and they aren't going to change or get any better.

 Quote by ghwellsjr My point in bringing up GPS is that it provides four co-ordinates just like Einsteinian relativity does in a Frame of Reference. Your original question is: what the concept "at rest" means in Einsteinian relativity. Now that you understand how a Frame of Reference is constructed, please go back and read my first post #3 and then read Michael C's post #13. They are saying the same thing and directly addressing your original question.
I understand the idea of how two objects can be at rest relative to each other; what I am less clear about is how an object can be "at rest" when another object is moving relative to it, as well as what the "at rest" in the stated consequence of the PoR refers to, given that an observer can easily determine if they are at rest relative to a physical reference frame or an arbitrarily defined, mathematical reference frame.

 Quote by ghwellsjr You are correct, the Frame of Reference is not physical but until you create a non-physical, purely "theoretical" Frame of Reference, you're not doing Einsteinian relativity.
That's fair enough, but we still need to relate it to the physical world and see what conclusions we can draw about the physical world.

 Quote by ghwellsjr Remember, Einsteinian relativity is based on two postulates, the first of which is the Principle of Relativity. The Principle of Relativity addresses your disconnect. It addresses your second concern with regard to the physical nature of being at rest.
I'm not sure how the PoR addresses the issue of the disconnect between the GPS example and the thought experiments where there are more than one reference frames; if there was only one reference frame there would be no need for the Lorentz transform.

I'm also not sure how it addresses a concern about the physical nature of being at rest, bcos I didn't think I'd specified one, although the inability to determine motion or rest may have implications for the conclusions that we draw from the application of the PoR.

 Quote by ghwellsjr Yes, "at rest" can refer, as you just stated as a consequence of the Principle of Relativity, that each observer can label himself "at rest" and the other observer as moving relative to him, without regard to any coordinates defined by a particular Frame of Reference OR it can refer to any defined Frame of Reference and then you look at the spatial coordinates to see if they are the same for an observer, in which case, he is "at rest" or if they are changing, in which case, he is moving.
I'm not entirely sure that that is what we can deduce from the statement that inertial (or relatively moving) observers cannot determine if they are in motion or at rest. The PoR is an extension of the galilean PoI which suggested that we cannot distinguish absolute motion from absolute rest, implying that we are either in a state of one or the other. Which one it is has implications for the conclusions we draw.

 Quote by ghwellsjr One of the important concepts of Einsteinian Special Relativity is that you can pick any arbitrary Frame of Reference in which you define, describe, demonstrate and analyze what is happening with all observers and objects, moving or at rest, accelerating or inertial, doing whatever you. Don't make the mistake of thinking that one observer is at rest all by himself in his own Frame of Reference while the other observer is at rest all by himself in his own Frame of Reference and mixing the coordinates between these two frames. You need to put everything and everybody in one Frame of Reference and then if you want to switch everything and everybody over to a different Frame of Reference, you use the Lorentz Transformation to convert the coordinates for all significant events from the first Frame of Reference to the coordinates in any other Frame of Reference you choose moving with respect to the first Frame of Reference.
Is the emboldened not precisely what happens in Einsteinian relativity; it's what leads to the notion of reciprocal contractions, no?

Again, if we put myself and yourself instead of those observers then my co-ordinate labeling system labels me as at rest "all by myself in my own reference frame", while yours labels you as at rest "all by yourself in your own reference frame".

 Quote by Michael C You keep using the phrase "actually moving". Asking if something is "actually" moving or not makes no sense: it's like asking if the North end of the Earth's axis is "actually" pointing up or down. In both cases there's no answer: there is no definition of absolute motion, any more than there is a definition of absolute up and down in the Universe.
I think it is a somewhat different question to the one about north; I don't think it so much that there is no answer to the question, there is an answer, we just can't determine which answer is correct - as per the PoR.

Again, if we take the example of two observers, and only consider relative motion; let's say that the observers start off at rest relative to each other; then, for whatever reason, there is relative motion between them. We can deduce from this, that at least one of them has to be moving i.e. at least one of them has to actually be moving.

If neither of the two observers moved, then they would remain at rest relative to each other, and there would be no relative motion. In order for relative motion to occur then, at least, one of them has to actually move.

Neither can determine which one it is that is moving, and each may label the other as moving, but we can deduce that one of them, absolutely, must be moving.

Is that a fair deduction?

 Quote by DaleSpam Albert's coordinate system labels velocities wrt himself. Albert's velocity wrt himself is 0 therefore he is at rest wrt himself. Hopefully there is nothing surprising or confusing about that.
It's been mentioned in this thread though, that it should be possible to construct a reference frame in which Albert is ascribed a velocity greater than zero; how is this possible if he is always "at rest" relative to himself?

 Quote by ghwellsjr You can believe in a state of absolute rest if you want to but don't you think in order to not be a hypocrite, you should transform every scenario and every situation into your absolute rest frame? And when you get ready to use the GPS in your phone, you better get someone to reprogram in all the coordinates to show what they are in your absolute rest frame instead of latitude, longitude and altitude. Otherwise, I think you're not sincere.
I don't think it is necessary to believe in a state of absolute rest at all, but we can utilise the entirely theoretical concept to make a number of deductions about different theories, including Einsteinian relativity - despite the contention that it plays no role in the theory.

 Quote by ghwellsjr I already answered your question twice on this thread: Instead of posting anymore, you should just go back and read all the posts on all the threads you have started. All the answers are there and they aren't going to change or get any better.
The point about the spatial and temporal co-ordinates doesn't address the question with respect to the "at rest" in the consequence of the PoR; your reply to that was that observers can choose whichever they wish; this part remains a point of contention because it arguably refers to "absolute motion" and "absolute rest"; which one is chosen materially affects the conclusions that are drawn.

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 Quote by mangaroosh It's been mentioned in this thread though, that it should be possible to construct a reference frame in which Albert is ascribed a velocity greater than zero; how is this possible if he is always "at rest" relative to himself?
It is possible because in such a reference frame velocities are not measured wrt Albert, they are measured wrt something else. A single object may have a zero velocity wrt one object and a non-zero velocity wrt another object.

I have a hard time believing that you are really confused by this concept. I don't know what game you are playing at, but it seems absurd to think that you really didn't already know the answer to your above question.

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 Quote by mangaroosh Apologies, I'm repeating myself now, more for posterity than anything - feel free to skip over this if you've addressed it in another post.
 Quote by ghwellsjr Instead of posting anymore, you should just go back and read all the posts on all the threads you have started. All the answers are there and they aren't going to change or get any better.
Look at your post #10, for example. You have shown that you know the answers to all your questions.