At rest in Einsteinian relativity

[mangaroosh]

"at rest" in Einsteinian relativity

I'm just wondering what the concept "at rest" means in Einsteinian relativity.

The common thought experiment of an observer on a platform (Albert) and an observer on a train (Henry), moving relative to each other, is often used to explain relativity. If we consider things from Albert's perspective, then Albert's co-ordinate labeling system will label him and the platform as having a zero velocity, while attributing all of the relative velocity to Henry. Albert's co-ordinate labeling system will label Albert and the platform as "at rest" but label Henry as "in motion". The question is, what does "at rest" mean in that scenario? I don't think it can simply mean the platform and Albert are "at rest" relative to each other, because Henry is also included - plus Albert can conduct numerous experiments to determine if he is at rest relative to the platform (contrary to the stated consequence of the PoR).

We can divest the thought experiment of everything except for just the two observers - putting them in "empty space". In this case Albert's co-ordinate labeling system will label him as "at rest" with a zero velocity, this is despite the relative motion to Henry.


What does the "at rest" mean in Einsteinian relativity?

 

[Matterwave]

At rest means not moving...what else could it mean? It means that from your own frame of reference (what is this PoR I keep seeing? You mean FoR?), you're not moving, relative to yourself.

 

[ghwellsjr]

I'm just wondering what the concept "at rest" means in Einsteinian relativity.

The common thought experiment of an observer on a platform (Albert) and an observer on a train (Henry), moving relative to each other, is often used to explain relativity. If we consider things from Albert's perspective, then Albert's co-ordinate labeling system will label him and the platform as having a zero velocity, while attributing all of the relative velocity to Henry. Albert's co-ordinate labeling system will label Albert and the platform as "at rest" but label Henry as "in motion". The question is, what does "at rest" mean in that scenario? I don't think it can simply mean the platform and Albert are "at rest" relative to each other, because Henry is also included - plus Albert can conduct numerous experiments to determine if he is at rest relative to the platform (contrary to the stated consequence of the PoR).

We can divest the thought experiment of everything except for just the two observers - putting them in "empty space". In this case Albert's co-ordinate labeling system will label him as "at rest" with a zero velocity, this is despite the relative motion to Henry.


What does the "at rest" mean in Einsteinian relativity?

Einsteinian Special Relativity is all about defining a Frame of Reference based on the first postulate of the Principle of Relativity and the second postulate of light propagating at c in any inertial state. Then, and only then, does "at rest" have any meaning. It simply means that the spatial coordinates are constant while the temporal coordinate varies. Albert and Henry establish two different FoR's in which one of them is at rest and the other one is moving. It has nothing to do with any experiments. Once a FoR is defined for any given scenario, you can use the Lorentz Transformation to see what the coordinates are for all the significant events in any other arbitrarily moving FoR with respect to the first one. It is of no consequence that there are any observers in any FoR or if there are, they need not be at rest. We could select another FoR moving "half way" between the "relative" speed between Albert and Henry in which they are both moving in opposite directions at the same speed if we want. All FoRs are equally valid and none is preferred, even the one in which you are at rest.

 

[mangaroosh]

At rest means not moving...what else could it mean? It means that from your own frame of reference (what is this PoR I keep seeing? You mean FoR?), you're not moving, relative to yourself.

PoR stands for principle of relativity.

One of the oft stated consequences of that (and the galilean Principle of Invariance) is that inertial observers cannot determine, by experiment, if they are "in motion" or "at rest" - I think the PoR together with the equivalence principle extends this to accelerating reference frames also (I mistakenly left this out above).

Presumably, though, you could determine, by experiment, if you are in motion relative to yourself or not, with the null result demonstrating this.


If we take the example of an observer on a train (with a light clock) who is "at rest" relative to themselves and the train carriage; the train carriage could still be in motion relative to the Earth such that the observer themselves is not "at rest" relative to the earth, even in their own FoR. This would mean that, in their own FoR, their instruments would be contracted due to the relative motion, even if they couldn't determine it.

That isn't how such a scenario is treated under Einsteinian relativity, however, so there must be some nuance to the meaning of "at rest".

 

[mangaroosh]

Einsteinian Special Relativity is all about defining a Frame of Reference based on the first postulate of the Principle of Relativity and the second postulate of light propagating at c in any inertial state. Then, and only then, does "at rest" have any meaning. It simply means that the spatial coordinates are constant while the temporal coordinate varies. Albert and Henry establish two different FoR's in which one of them is at rest and the other one is moving. It has nothing to do with any experiments. Once a FoR is defined for any given scenario, you can use the Lorentz Transformation to see what the coordinates are for all the significant events in any other arbitrarily moving FoR with respect to the first one. It is of no consequence that there are any observers in any FoR or if there are, they need not be at rest. We could select another FoR moving "half way" between the "relative" speed between Albert and Henry in which they are both moving in opposite directions at the same speed if we want. All FoRs are equally valid and none is preferred, even the one in which you are at rest.

The reference to "experiments" was in relation to the often stated consequence of the principle of invariance, or the principle of relativity, that inertial observers cannot determine, by experiment, if they are "in motion" or "at rest"; it's the PoR plus the equivalence principle which extends this to accelerating reference frames isn't it? My apologies, I left the latter part out above.


You mention that there is no need for an observer to be in an FoR, but it doesn't affect things if there is, and I think it makes it more intuitive to discuss it as though there is. I also think it is somewhat helpful to consider the most basic example, when trying to understand it; that would be the example of two lone observers in empty space.


If we take the example of those two observers moving relative to each other (inertially); each observer will label themselves as being at rest, but relative to what are they at rest? It isn't relative to each other, for obvious reasons.

Mw mentions above that it is "relative to themselves", but this allows for the possibility that they are in motion relative to something else and so their instruments would be contracted, even in their own FoR.

 

[ghwellsjr]

I am only interested in helping you understand Special Relativity, it is so much simpler that General Relativity, so let's forget about the equivalence principle and gravity and GR until you understand SR, OK?

Now I need to ask you what Einstein's process is for constructing a Frame of Reference. Until I am sure that you know the process, then there is no point in discussing anything more about Einstein's Special Relativity. Can you describe his process, please?

 

[mangaroosh]

I am only interested in helping you understand Special Relativity, it is so much simpler that General Relativity, so let's forget about the equivalence principle and gravity and GR until you understand SR, OK?

Now I need to ask you what Einstein's process is for constructing a Frame of Reference. Until I am sure that you know the process, then there is no point in discussing anything more about Einstein's Special Relativity. Can you describe his process, please?

I'm not familiar with the process for constructing a reference frame; I've never actually come across it.

I've only encountered information where the reference frame was "already constructed".

 

[ghwellsjr]

I'm not familiar with the process for constructing a reference frame; I've never actually come across it.

I've only encountered information where the reference frame was "already constructed".

Einstein presented the process in section one of his 1905 paper introducing Special Relativity. Please study just this section and note especially the fourteen places where he uses the words "define", "defined", "defining" and "definition", including in the title. Then please summarize what he said and I'll see if you have it right. This is very important.

 

[Dale]

What does the "at rest" mean in Einsteinian relativity?

It means v=0.

 

[mangaroosh]

Einstein presented the process in section one of his 1905 paper introducing Special Relativity. Please study just this section and note especially the fourteen places where he uses the words "define", "defined", "defining" and "definition", including in the title. Then please summarize what he said and I'll see if you have it right. This is very important.

OK, I had read that before; I was presuming there was more too it that that.

I'm not sure if I understand the intricacies of it, but it sounds like an arbitrary set of co-ordinates are defined and then the motion of objects is described in relation to that set of co-ordinates, "as a function of time".

I'm not entirely sure what "as a function of time" actually means, but I think I understand the idea that an event has 4 co-ordinates, such that we can describe the location of an object/event using those 4 co-ordinates, and plot it's movement.


I'm not entirely sure how a material point can be at rest relative to an imaginary, mathematical set of co-ordinates, but I can understand how a physical object can be at rest relative to another physical object and that mathematical co-ordinates can be used to describe the location of those objects.



Lone observers
If we translate that into the thought experiment of two lone, inertial, observers in empty space, moving relative to each other. One observers co-ordinate labeling system will label him as "at rest" and his counterpart as "in motion; he will ascribe a zero velocity to himself and 100% of the relative velocity to his counterpart. His counterpart will do the same in reverse.

Relative to what are they "at rest"?


A consequence of the relativity principles (Galilean and Einsteinian), states that inertial observers cannot determine, by experiment, if they are "in motion" or "at rest". Given that the observers can determine, by experiment, whether or not they are "in motion" or "at rest" relative to each other, relative to what can they not determine their motion?


If Albert labels himself as "at rest", given that he cannot determine if he is "in motion", or "at rest", is it possible that, despite his label of "at rest", that he is actually in motion?

 

[mangaroosh]

It means v=0.

Relative to what?

 

[ghwellsjr]

Relative to what are they "at rest"?

Do you have a GPS? On mine, there is a display that I can invoke that shows me the latitude, longitude, altitude and time and it is updated once a second. So each set of the four co-ordinates constitutes and event. I can record these events and later look at a listing of them. 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. If they are not the same, then during that one-second interval, I was in motion and I can calculate the distance that I moved and that will be my speed. The record of my positions with respect to time is "a function of time". It could also be expressed as I traveled on the interstate between X and Y at 70 miles an hour starting at 5PM yesterday.

GPS provides an arbitrary frame of reference and we all use it because we want to take advantage of maps with locations of items of interest but if some other scheme had been devised, we could use that just as effectively. It's just an imaginary, mathematical set of co-ordinates. I don't see any grid lines painted on the ground corresponding to what the GPS says is my location.

Einstein gives us a means to build our own Frame of Reference any way we choose. It doesn't matter who is moving or at rest in our choice of frame. But once we have selected our origin, directions for the axes, units of distance and time, we can determine or specify the location of any object and describe its changing position as a function of time. So "actual" motion or "actual" rest is not a concern, it only matters what the coordinates tell you according to the Frame of Reference you have defined. That's an important part of relativity.

 

[Michael C]

If Albert labels himself as "at rest", given that he cannot determine if he is "in motion", or "at rest", is it possible that, despite his label of "at rest", that he is actually in motion?

It makes no sense to ask if something is actually in motion or not. If you take any object, you can define a frame of reference in which it is at rest. You can also define a frame of reference in which it is moving at 10 km/h, or 1000 km/h, in any direction you choose. All these frames are equally valid.

Taking your example, we could choose a frame in which A is at rest and H is moving. We could also choose a frame in which H is at rest and A is moving. We could also choose a frame in which both A and H are moving. All these frames would be equally valid: there isn't one that could be considered to be the "actual" or "right" one.

 

[Dale]

Relative to what?

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.

 

[mangaroosh]

Do you have a GPS? On mine, there is a display that I can invoke that shows me the latitude, longitude, altitude and time and it is updated once a second. So each set of the four co-ordinates constitutes and event. I can record these events and later look at a listing of them. 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. If they are not the same, then during that one-second interval, I was in motion and I can calculate the distance that I moved and that will be my speed. The record of my positions with respect to time is "a function of time". It could also be expressed as I traveled on the interstate between X and Y at 70 miles an hour starting at 5PM yesterday.

GPS provides an arbitrary frame of reference and we all use it because we want to take advantage of maps with locations of items of interest but if some other scheme had been devised, we could use that just as effectively. It's just an imaginary, mathematical set of co-ordinates. I don't see any grid lines painted on the ground corresponding to what the GPS says is my location.

Einstein gives us a means to build our own Frame of Reference any way we choose. It doesn't matter who is moving or at rest in our choice of frame. But once we have selected our origin, directions for the axes, units of distance and time, we can determine or specify the location of any object and describe its changing position as a function of time. So "actual" motion or "actual" rest is not a concern, it only matters what the coordinates tell you according to the Frame of Reference you have defined. That's an important part of relativity.

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. 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?

 

[mangaroosh]

It makes no sense to ask if something is actually in motion or not. If you take any object, you can define a frame of reference in which it is at rest. You can also define a frame of reference in which it is moving at 10 km/h, or 1000 km/h, in any direction you choose. All these frames are equally valid.

Taking your example, we could choose a frame in which A is at rest and H is moving. We could also choose a frame in which H is at rest and A is moving. We could also choose a frame in which both A and H are moving. All these frames would be equally valid: there isn't one that could be considered to be the "actual" or "right" one.

A stated consequence of the principle of relativity is that inertial observers cannot determine if they are "in motion" or "at rest"; the equivalence principle extends this to accelerating reference frames also, such that relatively moving observers cannot determine which one is moving.


If we consider two observers - again in empty space for simplicity sake - at rest relative to each other. If neither observer moves then they will remain at rest relative to each other. In order for relative motion to occur between them, one of them actually has to move; again, if neither of them actually moves, they will remain at rest relative to each other.

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.

 

[Dale]

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.

If you are measuring velocities relative to yourself then clearly you are at rest since your velocity relative to yourself is 0 by definition. You are always at rest relative to yourself.

 

[mangaroosh]

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?

 

[Mentz114]

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.

 

[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.

 

[ghwellsjr]

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.

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.

 

[Michael C]

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.

 

[Dale]

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.

 

[mangaroosh]

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.

 

[ghwellsjr]

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.

 

[mangaroosh]

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?

 

[ghwellsjr]

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?

I already answered your question twice on this thread:

It simply means that the spatial coordinates are constant while the temporal coordinate varies.

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.

 

[mangaroosh]

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.

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.

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.

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.

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".

 

[mangaroosh]

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?

 

[mangaroosh]

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?

 

[mangaroosh]

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.

 

[mangaroosh]

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.

 

[Dale]

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.

 

[ghwellsjr]

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.

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.

 

[Michael C]

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?

That would only be a fair deduction if we were to accept the idea that a state of "absolute rest" exists. There is no evidence for this idea. In the theory of Relativity there is no absolute rest frame.