At rest in Einsteinian relativity

[Mentz114]

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.

It's been pointed out to you already that you keep using the phrase 'actually moving'. There's no such thing. If two observers are in uniform relative motion, there's nothing more that can be said about their states of motion.

 

[ghwellsjr]

Look at your post #10, for example. You have shown that you know the answers to all your questions.

I was just re-reading your post #10 and I think maybe I was a little hasty in assuming you understood this as well as I previously thought so I'm going to make some comments:

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.

Instead of saying that an event has 4 co-ordinates you should say that the 4 co-ordinates are the event. If you change anyone or more of the 4 co-ordinates, you have a different event.

So then you would not say that "we can describe the location of an object/event using those 4 co-ordinates". Do you see why? As I just said, each set of 4 co-ordinates is an event. What you should say is that we can describe the motion of an object using a series of events. Remember, 1 of those 4 co-ordinates is time and the other three are location. So the series of events would have the time co-ordinate increasing in the series and the location co-ordinates would describe the object's location at each different co-ordinate of time.

For example, let's use the nomenclature of [t,x,y,z] for an event and let's say that at time=20s we have an object located at the co-ordinates of x=12m, y=43m and z=74m. This would be the event [20,12,43,74]. Then let's say that the next event that we use to describe this object is [30,22,53,84]. This means that the object has moved in 10 seconds from the first location to x=22m, y=53m and z=84m. If we assume that the object has moved with constant speed then we know what all the events in between those two events are. For example, here is a list showing all the events spaced one second apart:

[20,12,43,74]
[21,13,44,75]
[22,14,45,76]
[23,15,46,77]
[24,16,47,78]
[25,17,48,79]
[26,18,49,80]
[27,19,50,81]
[28,20,51,82]
[29,21,52,83]
[30,22,53,84]

And, of course, between each pair of events in the list, there are even more events. So between the first two events in the above list, we could show nine more:

[20,12,43,74]
[20.1,12.1,43.1,74.1]
[20.2,12.2,43.2,74.2]
[20.3,12.3,43.3,74.3]
[20.4,12.4,43.4,74.4]
[20.5,12.5,43.5,74.5]
[20.6,12.6,43.6,74.6]
[20.7,12.7,43.7,74.7]
[20.8,12.8,43.8,74.8]
[20.9,12.9,43.9,74.9]
[21,13,44,75]

And we could continue this process for more detail all along the way. This is one way to describe the "function of time".

But another way is to write a formula. We could say that between the time of 20 seconds and 30 seconds, each location co-ordinate is defined by these formulas:

x=t-8,
y=t+23,
z=t+54

Now let's say that the object stops moving for the next 10 seconds. Here are two events that describe this new function of time:

[30,22,53,84]
[40,22,53,84]

And if we know its "speed" (equal to zero) is constant during this time, we can fill in all the events spaced one second apart:

[30,22,53,84]
[31,22,53,84]
[32,22,53,84]
[33,22,53,84]
[34,22,53,84]
[35,22,53,84]
[36,22,53,84]
[37,22,53,84]
[38,22,53,84]
[39,22,53,84]
[40,22,53,84]

Now we can look at any pair of events, and assuming that speed is constant between them, we can see if the location co-ordinates are the same to tell if the object is at rest, and, of course, in this last list, the object is at rest.

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.

You correlate the co-ordinates to the material world by defining the origin where all four co-ordinates are zero. For example, you could say that t=0 is a 5PM local time yesterday wherever you live and that x=0 is at the middle of the threshold of your front door with the x-axis pointing north, y=0 is the same location with the y-axis pointing east, and z=0 is the same location with the z-axis pointing up.

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"?

Let's first continue the previous example and say you are the first observer standing "at rest" on the threshold of your front door. Assuming the second observer was a salesman who left your front door at 5PM yesterday and is traveling at 1 meter per second north, then we can define his motion as:
x=t,
y=0,
z=0

He will describe his motion in his own reference frame in which he is at rest as:
x=0,
y=0,
z=0

And he will describe your motion as:
x=-t,
y=0,
z=0

But now you want to do away with your front door and have nothing in the universe except you and the salesman. You do the same thing except you don't relate it to your front door and of course there's no such thing as north or up so you relate it in the frame that you are at rest in by saying something like the origin is where you are and the x-axis is going away directly in front of you, the y-axis is going off to your right and the z-axis is going away in the direction of your head. Then you would describe the other observer as moving based on those co-ordinates.

It would make sense for the other observer to be using the same units and axes directions that you are and to be sharing the same origin. Then he would arrive at the same descriptions that I gave for the salesman.

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?

Previously, I suggested that we use the same origin for both observers but that takes some collaboration. Let's say that they didn't collaborate. Then it is impossible for them to come up with a common origin or directions for their axes or a common time. There is nothing in the universe that provides a common or shared reference frame that all observers can identify.

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?

In many other reference frames, yes. But if there is any sense from a physical point of view that nature is operating on an actual rest frame, she/he won't tell us where it is. You might just as well be concerned about whether we should refer to "nature" as a "she" or a "he".

 

[salvestrom]

It's been pointed out to you already that you keep using the phrase 'actually moving'. There's no such thing. If two observers are in uniform relative motion, there's nothing more that can be said about their states of motion.

No such thing? At best it's impractically provable. By this I mean you could create an unconductable experiment that in theory would work, but is unlikely to be actualised without significant developments in spacetravel. Take two clocks. A and B. Place them anywhere in the universe, and attempt to adjust their trajectories so they have aslittle relative motion as can be deduced. After sometime bring them together and compare. If one has recorded more time than the other, let us say clock A, then return that clock to its location and place the other, B, somewhere new. If, on bring them together again, clock B has recorded more time, then return that to its location and move A somewhere new.

We are looking for a needle in a haystack, but I see no reason we might not ultimately discover a location and make corrections to the clock's motion such that it would be impossible to discover another location where a clock would record more time.

I realize the two clocks would need to be reunited in a precise manner, such that the journey they make is equal.

Putting aside my bizarre experiment, when did it stop being the case that the Earth goes around the sun? Is it not "actually" moving? Does the sun not go around the galaxy, and the galaxy not move toward the Virgo Cluster. I appreciate there could be hidden velocities - a shared velocity that we cannot determine, but have we really gone from; "the sun goes around the Earth to; the Earth goes around the sun to; dang it, Albert, now we can't tell!"

EDiT: I just saw George's last lines in the previous post. I'm comfortable with the idea that we can't find it, more than the idea it doesn't exist. Even if we did discover a universal "at rest" it would be of no practical use for operating our gps, et al. Which was never the point for me, anyway.

 

[DrGreg]

To be precise when we say "there's no such thing as 'actually moving'" we mean the concept is undefined within the theory of relativity. If you want to try and define the concept outside of relativity, then that's up to you, but relativity doesn't care whether you do or don't, because it makes no use of such a concept. It's irrelevant.

 

[mangaroosh]

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.

As such, I don't trouble with the idea of taking an object with respect to which velocity is measured; the trouble I have is with the application of it and the conclusions drawn from that application; this, together with the stated consequence of the PoR, that observers cannot determine if they are in motion or at rest, are areas I have trouble with.

I have an understanding that is at odds with Einsteinian relativity, but if Einsteinian relativity unquestionably correct, then I must misunderstand something, so hopefully by outlining my own understanding it will be possible to see where the issue lies.


Relative to what?
As mentioned, I don't have trouble with the idea of measuring velocity with respect to something but it seems to me that it is always possible to determine ones motion wrt another physical object, including oneself. This would be at odds with the stated consequence of the PoR, that observers cannot determine if they are in motion or at rest.

In the case of the PoR, what does the "at rest" refer to in that sense?


Application
I have a little trouble with the application of the notion of "at rest" you provide above; if we again take the thought experiment involving Albert and Henry moving relative to each other; if we just consider on reference frame, Albert's say, he ascribes a zero velocity to himself, because he is at rest relative to himself, and ascribes all of the relative velocity to Henry; but shouldn't Albert be able to define a reference frame in which he ascribes all the relative velocity to himself also? How can he do this if he is always at rest relative to himself?

Arbitrarily choosing to measure velocity relative to Henry doesn't seem like a reasonable answer, because even when he measures velocity relative to himself, he still has velocity relative to Henry, meaning that both are simultaneously true (in Albert's own frame of reference). However, these scenarios result in conflicting outcomes; if Albert considers himself as at rest then his instruments aren't contracted, if he considers himself as in motion then his instruments are contracted. The same is true for Henry.

How can both these possibilities simultaneously be true, as they must be, if we consider that both reference frames are simultaneously true?

 

[mangaroosh]

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.

It's been pointed out to you already that you keep using the phrase 'actually moving'. There's no such thing. If two observers are in uniform relative motion, there's nothing more that can be said about their states of motion.

The 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 such that we can say, relatively moving observers cannot determine if they are in motion or at rest.We don't need to assume that a state of "absolute rest" exists, we can deduce it by considering only the relative velocities. If we, again, take the example of two observers (or reference frames) at rest relative to each other (without assuming absolute rest); if neither observer moves then they will remain at rest relative to each other.

In order for relative motion to occur, one of the observers actually has to move, because if neither of them moves, they will remain at rest relative to each other.The PoR (plus the equivalence principle) suggests that they will not be able to determine which one has actually moved, but we can deduce that one of them actually has to move in order for there to be relative motion.

All of that without assuming absolute rest.

 

[mangaroosh]

I was just re-reading your post #10 and I think maybe I was a little hasty in assuming you understood this as well as I previously thought so I'm going to make some comments:

Instead of saying that an event has 4 co-ordinates you should say that the 4 co-ordinates are the event. If you change anyone or more of the 4 co-ordinates, you have a different event.

Apologies, this is more of a side-note, but it seemed like the natural place to put it; it would probably be better to consider it in the context of the rest of the post below - which you will no doubt do, but just in case it is taken as a stand-alone point.

I'm not actually sure if it does, but I would think that, the degree to which the language used is representative of the treatment of events could, possibly, give an insight to a potential issue. Saying that an event is the 4 co-ordinates has a certain tacit assumption in it, which could materially affect the conclusions drawn.

I would think it is more accurate to say that an event can be described using 4 co-orindates.

So then you would not say that "we can describe the location of an object/event using those 4 co-ordinates". Do you see why? As I just said, each set of 4 co-ordinates is an event. What you should say is that we can describe the motion of an object using a series of events. Remember, 1 of those 4 co-ordinates is time and the other three are location. So the series of events would have the time co-ordinate increasing in the series and the location co-ordinates would describe the object's location at each different co-ordinate of time.

For example, let's use the nomenclature of [t,x,y,z] for an event and let's say that at time=20s we have an object located at the co-ordinates of x=12m, y=43m and z=74m. This would be the event [20,12,43,74]. Then let's say that the next event that we use to describe this object is [30,22,53,84]. This means that the object has moved in 10 seconds from the first location to x=22m, y=53m and z=84m. If we assume that the object has moved with constant speed then we know what all the events in between those two events are. For example, here is a list showing all the events spaced one second apart:

[20,12,43,74]
[21,13,44,75]
[22,14,45,76]
[23,15,46,77]
[24,16,47,78]
[25,17,48,79]
[26,18,49,80]
[27,19,50,81]
[28,20,51,82]
[29,21,52,83]
[30,22,53,84]

And, of course, between each pair of events in the list, there are even more events. So between the first two events in the above list, we could show nine more:

[20,12,43,74]
[20.1,12.1,43.1,74.1]
[20.2,12.2,43.2,74.2]
[20.3,12.3,43.3,74.3]
[20.4,12.4,43.4,74.4]
[20.5,12.5,43.5,74.5]
[20.6,12.6,43.6,74.6]
[20.7,12.7,43.7,74.7]
[20.8,12.8,43.8,74.8]
[20.9,12.9,43.9,74.9]
[21,13,44,75]

And we could continue this process for more detail all along the way. This is one way to describe the "function of time".

But another way is to write a formula. We could say that between the time of 20 seconds and 30 seconds, each location co-ordinate is defined by these formulas:

x=t-8,
y=t+23,
z=t+54

Now let's say that the object stops moving for the next 10 seconds. Here are two events that describe this new function of time:

[30,22,53,84]
[40,22,53,84]

And if we know its "speed" (equal to zero) is constant during this time, we can fill in all the events spaced one second apart:

[30,22,53,84]
[31,22,53,84]
[32,22,53,84]
[33,22,53,84]
[34,22,53,84]
[35,22,53,84]
[36,22,53,84]
[37,22,53,84]
[38,22,53,84]
[39,22,53,84]
[40,22,53,84]

Now we can look at any pair of events, and assuming that speed is constant between them, we can see if the location co-ordinates are the same to tell if the object is at rest, and, of course, in this last list, the object is at rest.

Thanks, this is quite helpful for trying to clarify what I am getting at.

The PoR says that observers cannot determine if they are in motion or at rest; but, in both instances above, it is possible for the observer to determine their motion relative to any given object/event; relative to what though, can they not determine their motion, or rest?

You correlate the co-ordinates to the material world by defining the origin where all four co-ordinates are zero. For example, you could say that t=0 is a 5PM local time yesterday wherever you live and that x=0 is at the middle of the threshold of your front door with the x-axis pointing north, y=0 is the same location with the y-axis pointing east, and z=0 is the same location with the z-axis pointing up.

I would, pretty much, agree with that fully; but, and it's probably not an important distinction, I would add the qualification that an observer cannot move relative to the imaginary reference frame; they move relative to the physical threshold, and this relative motion can be represented using the mathematical geometry.

Let's first continue the previous example and say you are the first observer standing "at rest" on the threshold of your front door. Assuming the second observer was a salesman who left your front door at 5PM yesterday and is traveling at 1 meter per second north, then we can define his motion as:
x=t,
y=0,
z=0

He will describe his motion in his own reference frame in which he is at rest as:
x=0,
y=0,
z=0

And he will describe your motion as:
x=-t,
y=0,
z=0

But now you want to do away with your front door and have nothing in the universe except you and the salesman. You do the same thing except you don't relate it to your front door and of course there's no such thing as north or up so you relate it in the frame that you are at rest in by saying something like the origin is where you are and the x-axis is going away directly in front of you, the y-axis is going off to your right and the z-axis is going away in the direction of your head. Then you would describe the other observer as moving based on those co-ordinates.

It would make sense for the other observer to be using the same units and axes directions that you are and to be sharing the same origin. Then he would arrive at the same descriptions that I gave for the salesman.

Previously, I suggested that we use the same origin for both observers but that takes some collaboration. Let's say that they didn't collaborate. Then it is impossible for them to come up with a common origin or directions for their axes or a common time. There is nothing in the universe that provides a common or shared reference frame that all observers can identify.

This is again quite helpful, thanks.

If we take me and the salesman again (let's say you're the salesman for the sake of discussion); now, we can collaborate, but let's say that we fundamentally disagree with each other over where the origin should be; let's say that you believe it should be on you, and I say it should be on me. This would mean that there are two different reference frames, as per Einsteinian relativity. Using these two reference frames we would describe the relative motion as you outlines above.

As mentioned, we can determine our motion and rest relative to each other, but the PoR suggests that we wouldn't be able to determine if we are in motion or at rest; relative to what could we not determine our motion, or lack thereof?

Also, if we take the example of you and I alone in the universe - I know, I'm a hopeless romantic - and we are at rest relative to each other; is it fair to say that, in order for there to be relative motion between us, one of us actually has to move; because if we didn't, then we would remain at rest relative to each other?

In many other reference frames, yes. But if there is any sense from a physical point of view that nature is operating on an actual rest frame, she/he won't tell us where it is. You might just as well be concerned about whether we should refer to "nature" as a "she" or a "he".

I would agree with the contention that we can't determine whether or not nature has an actual rest frame, as per the PoR, but I wouldn't necessarily agree with the analogy, because I think that we can use the concept of the rest frame to deduce certain relevant information; unlike the sex of the universe (which might equally be a hermaphrodite!)

 

[mangaroosh]

Putting aside my bizarre experiment, when did it stop being the case that the Earth goes around the sun? Is it not "actually" moving? Does the sun not go around the galaxy, and the galaxy not move toward the Virgo Cluster. I appreciate there could be hidden velocities - a shared velocity that we cannot determine, but have we really gone from; "the sun goes around the Earth to; the Earth goes around the sun to; dang it, Albert, now we can't tell!"

EDiT: I just saw George's last lines in the previous post. I'm comfortable with the idea that we can't find it, more than the idea it doesn't exist. Even if we did discover a universal "at rest" it would be of no practical use for operating our gps, et al. Which was never the point for me, anyway.

That is pretty much how I would see it, but I don't even think it is necessary for an actual rest frame to exist; regardless of whether or not we could detect it, I think we can deduce that there must be actual motion from relative motion.

 

[mangaroosh]

To be precise when we say "there's no such thing as 'actually moving'" we mean the concept is undefined within the theory of relativity. If you want to try and define the concept outside of relativity, then that's up to you, but relativity doesn't care whether you do or don't, because it makes no use of such a concept. It's irrelevant.

In the stated consequence of the PoR, it says that observers cannot determine if they are in motion or at rest; what do the motion and rest refer to in that context, given that motion and rest relative to other objects and observers is determinable?

 

[Michael C]

We don't need to assume that a state of "absolute rest" exists, we can deduce it by considering only the relative velocities.

No we can't.

If we, again, take the example of two observers (or reference frames) at rest relative to each other (without assuming absolute rest); if neither observer moves then they will remain at rest relative to each other.

In order for relative motion to occur, one of the observers actually has to move, because if neither of them moves, they will remain at rest relative to each other.

We're going round in circles here. "Actually move" has no meaning.

The PoR (plus the equivalence principle) suggests that they will not be able to determine which one has actually moved, but we can deduce that one of them actually has to move in order for there to be relative motion.

All of that without assuming absolute rest.

If you talk about "actually moving", you are automatically defining an absolute rest frame. All that we can say is that "there exists relative motion". For our two observers, we can define (a) a frame in which Albert is at rest, (b) a frame in which Henry is at rest or (c) a frame in which both of them are moving. The only thing we can't do is define a frame in which both are at rest, but this doesn't prove the existence of an absolute rest frame. Any one of the frames we use is as valid as any other: there's no frame that we can call the "actual" one.

 

[mangaroosh]

No we can't.

Sorry, that point might not have been clear. I didn't mean that we can deduce "absolute rest", rather that we can deduce actual motion.

We're going round in circles here. "Actually move" has no meaning.

You're asserting here that it doesn't have meaning, but in the example provided it does have meaning; and the example is a real world example (or at least can be extrapolated to the real world).

To prevent us from going around in circles, it might be best to address the logic directly. I am familiar with the idea that "there is no such thing as 'actual motion'"; however, the point is, I think we can deduce that there must be.

If you talk about "actually moving", you are automatically defining an absolute rest frame. All that we can say is that "there exists relative motion". For our two observers, we can define (a) a frame in which Albert is at rest, (b) a frame in which Henry is at rest or (c) a frame in which both of them are moving. The only thing we can't do is define a frame in which both are at rest, but this doesn't prove the existence of an absolute rest frame. Any one of the frames we use is as valid as any other: there's no frame that we can call the "actual" one.

When we talk about actually moving, we don't necessarily have to define an absolute rest frame. The perceived need for an absolute rest frame comes from the notion of measuring absolute velocity, but we're not necessarily talking about absolute velocity, as opposed to absolute motion. Absolute motion would be a yes or no answer to the question, is something in motion.



Again, though, from the example of the two observers at rest relative to each other, where relative motion then occurs, we can deduce that one of them actually has to be moving; but because we are not looking to measure the absolute velocity - which might be a contradiction in terms - we don't need to define an absolute rest frame.

We can simply deduce that, if neither of them moves then they will remain at rest relative to each other; therefore, in order for relative motion to occur between them, at least one of them has to move i.e. one of them has to actually move.

That we can define reference frames in which one or both are moving just demonstrates that we cannot determine which one is moving, but again, we can deduce that, at least, one of them has to move.

 

[salvestrom]

We're going round in circles here. "Actually move" has no meaning.

If you talk about "actually moving", you are automatically defining an absolute rest frame. All that we can say is that "there exists relative motion".

Hmm. In a situation of two ships (A, B) moving directly away from each other at 100km/s such that the relative velocity they ascribe to each other is 200km/s, then there can be no other frame where the ships may appear at rest. As such all frames must assign the 200km/s relative velocity between the two ships, ranging from 0-200km/s for each ship with the total velocity being 200. I.e, a frame of reference at the origin, represented by a space station perhaps, will say both are moving at 100km/s. A third ship, already traveling at 50km/s wrt to that station, in the direction of ship A will say B is moving at 150km/s and A at 50km/s (with the station also ascribed a velocity of 50km/s). Additionally, the space station may have a relative velocity in space, shared by the three ships. For example, in our galaxy all objects have a relative velocity of 600km/s in the direction of the Virgo Cluster-ish.

Since the entire system has the relative velocity of the galaxy, it would be entirely ignored in any real calculations. I assume no spaceflight ever takes account of the sun's 220km/s path around our galaxy, since we also share that velocity.

Yet no one talks about the sun going around the earth, even though in SR that's a perfectly valid frame. What becomes of the observations that led Copernicus to assert the sun was at the center of the solar system. I've also read about the stars in our rotating frame and how they technically are exceeding the speed of light, but isn't the simpilest solution to this to accept that despite the frame being valid, noones honestly suggesting the star's in the night sky are in orbit about us. It just looks that way from our point of view.

And if it depends on our point of view shouldn't we perhaps be move cautious in proclaiming "actually moving" has no meaning? I'm pretty sure my fingers are moving as I'm typing, Or should I more accurately describe my finger tips as being at rest in their own frame of reference and it's really the keyboard moving around underneath them? My aching wrist would disagree with me.

 

[russ_watters]

As such, I don't trouble with the idea of taking an object with respect to which velocity is measured; the trouble I have is with the application of it and the conclusions drawn from that application; this, together with the stated consequence of the PoR, that observers cannot determine if they are in motion or at rest, are areas I have trouble with.

You've misunderstood or chosen to misstate that. The PoR does not have that consequence except in a specific example: It is often said that there is no experiment you can do inside a windowless spaceship to determine if it is moving in any relative or absolute sense. That does not imply that if you do an external experiment you can't measure your speed wrt an external observer.

You're making something of nothing here.

 

[Dale]

the stated consequence of the PoR, that observers cannot determine if they are in motion or at rest, are areas I have trouble with.

Can you provide a reference for this stated consequence? The reference probably explains in more detail what they mean by that.

However, the statement is correct. Basically it is saying that there is no meaning to the unqualified statement "I am traveling with velocity v". Velocity is a relative quantity so all expressions of velocity must be of the form "I am traveling with velocity v wrt reference frame F". The unqualified expression is indeterminate because v is a relative quantity and like all relative quantities requires a frame for definition.

This would be at odds with the stated consequence of the PoR, that observers cannot determine if they are in motion or at rest.

In the case of the PoR, what does the "at rest" refer to in that sense?

It would help if you could provide a reference, but I suspect that they would explicitly state that "at rest" in that sense refers to a non-relative measurement of velocity.

shouldn't Albert be able to define a reference frame in which he ascribes all the relative velocity to himself also? How can he do this if he is always at rest relative to himself?

In a coordinate system where he ascribes all of the velocity to himself both he and himself are moving at the same velocity, so he is still at rest wrt himself even in a coordinate system where neither he nor himself are at rest.

However, these scenarios result in conflicting outcomes;

No, it does not result in any conflicting outcomes. Even including all of the relativistic effects such as LC and TD and RoS.

 

[Mentz114]

I think there might be confusion over the meaning of 'frame' in this discussion. Technically this is a set of coordinates, which is an abstract thing. A frame is not a region of space or a collection of objects.

It's pretty depressing that after all the effort that's been put into explanations in this thread that the OP still thinks there are contradictions in the SR formalism.

 

[mananvpanchal]

We cannot say we are in motion if we are in inertial frame. "At rest" is default condition of inertial frame. The inertial frame can be in motion relative to other frame which is at rest relative to everything. Do you get the point here? The rest condition is primary and default condition for inertial frame. Moving frame can be described by rest frame.

If we want to find that we are at rest relative to what then we have to make motion as a primary condition of inertial frame. Now all inertial frame say that they are moving, but the other frame which is seen as moving is really at rest relative to the moving frame. So now we can derive "at rest" condition from "moving" condition, but we cannot derive "moving" condition now. Because how can we find what is our speed and relative to what. Because we see our different different speed relative to different different frame. In this case we are moving relative to everything. Same as we can say that we are at rest relative to everything if rest is our primary condition.

So moral of the story is we should have a primary condition from this we can derive secondary condition. We cannot derive primary condition from secondary condition.

 

[mangaroosh]

You've misunderstood or chosen to misstate that. The PoR does not have that consequence except in a specific example: It is often said that there is no experiment you can do inside a windowless spaceship to determine if it is moving in any relative or absolute sense. That does not imply that if you do an external experiment you can't measure your speed wrt an external observer.

You're making something of nothing here.

Any uniformly moving observer in an inertial frame cannot determine his "absolute" state of motion by a co-moving experimental arrangement.

wiki - tests of SR
This doesn't make any reference to internal or external experiments, rather, co-moving experimental arrangements.The specific example you're referring to is, I think, Galileo's observer on the ship, isn't it?

When we talk about determining an observers state of motion, we refer to the idea of determining whether they are "in motion" or "at rest". This allows us to restate the above test of SR as "any uniformly moving observer in an inertial frame cannot determine if he is "in motion" or "at rest" by a co-moving experimental arrangement".

Am I right in saying that the equivalence principle extends this to accelerating reference frames, because the observer cannot determine if they are at rest in a zero gravity field, or free-falling in a gravitational field?

 

[mangaroosh]

Can you provide a reference for this stated consequence? The reference probably explains in more detail what they mean by that.

It would help if you could provide a reference, but I suspect that they would explicitly state that "at rest" in that sense refers to a non-relative measurement of velocity.

The only link I can find is

Any uniformly moving observer in an inertial frame cannot determine his "absolute" state of motion by a co-moving experimental arrangement.

wiki - tests of SR

My understanding of it though extends beyond just this, and comes from discussions of the idea, elsewhere.

As mentioned to Russ, when talking about determining absolute motion we can refer, as Galileo did, to determining "motion" or "rest". Such that the test can be restated as "any uniformly moving observer in an inertial frame cannot determine if he is "in motion" or "at rest" by a co-moving experimental arrangement".

I have been lead to believe that the equivalence principle extends this to accelerating reference frames/observers.

However, the statement is correct. Basically it is saying that there is no meaning to the unqualified statement "I am traveling with velocity v". Velocity is a relative quantity so all expressions of velocity must be of the form "I am traveling with velocity v wrt reference frame F". The unqualified expression is indeterminate because v is a relative quantity and like all relative quantities requires a frame for definition.

I don't think it makes any reference to statements about velocity.

In a coordinate system where he ascribes all of the velocity to himself both he and himself are moving at the same velocity, so he is still at rest wrt himself even in a coordinate system where neither he nor himself are at rest.

Does this mean that he can only ever define a co-ordinate system in which he is "at rest"?

It was mentioned that he should be possible to define a reference frame where is traveling at, or close to the speed of light, for example; how is this possible if he measures velocity relative to himself, where the velocity will always be zero?

Relating back to the example of Albert & Henry; Albert should be able to define a reference frame in which he, not Henry, is traveling at 0.6c. How can he do this if he measures the velocity relative to himself?

Arbitrarily choosing to measure velocity relative to Henry doesn't seem like a reasonable answer, because even when he chooses to measure velocity relative to himself, he still has velocity relative to Henry, meaning that both are simultaneously true (in Albert's own frame of reference).

No, it does not result in any conflicting outcomes. Even including all of the relativistic effects such as LC and TD and RoS.

If Albert ascribes the velocity to himself, then he must assume that the photon in his light clock is imparted with the horizontal velocity that he ascribes to his train (or platform). This means that his instruments must contract for him to measure the speed of light to be c.

The opposite would be true if motion is ascribed to Henry.

 

[Mentz114]

It was mentioned that he should be possible to define a reference frame where is traveling at, or close to the speed of light, for example; how is this possible if he measures velocity relative to himself, where the velocity will always be zero?

Sadly, you're back. In spite of everything you've been told you still write the meaningless phrase "traveling at, or close to the speed of light". For the umpteenth time - velocities are relative. Do you understand the meaning of 'relative' ?

Suppose we have an observer, somewhere in the cosmos who experiences no proper acceleration ( i.e. is in uniform motion). All around there are other objects. Our observer has a relative velocity with respect to all of these objects. Relative velocity is a pair relationship. It is necessary to give a pair whenever you say "moving at this or that velocity". Another example of a pair relationship is distance. Distance is defined between objects and is meaningless unless two points are specified. The distance between an object and itself is always zero, as is the relative velocity between an object and itself, because this distance is not changing. Therefore you are always at rest wrt yourself.
Perhaps you believe in absolute velocity - which is a crackpot idea in my opinion.

 

[mangaroosh]

Sadly, you're back. In spite of everything you've been told you still write the meaningless phrase "traveling at, or close to the speed of light". For the umpteenth time - velocities are relative. Do you understand the meaning of 'relative' ?

Suppose we have an observer, somewhere in the cosmos who experiences no proper acceleration ( i.e. is in uniform motion). All around there are other objects. Our observer has a relative velocity with respect to all of these objects. Relative velocity is a pair relationship. It is necessary to give a pair whenever you say "moving at this or that velocity". Another example of a pair relationship is distance. Distance is defined between objects and is meaningless unless two points are specified. The distance between an object and itself is always zero, as is the relative velocity between an object and itself, because this distance is not changing. Therefore you are always at rest wrt yourself.



Perhaps you believe in absolute velocity - which is a crackpot idea in my opinion.

:facepalm:

are you familiar with the idea of implied meaning; saying that it is possible to define a reference frame in which you are traveling close to the speed of light implies that it is relatvie to something. I was going to try and dig out a reference from a discussion on here that made that exact point, and I'm pretty sure there was no mention of relative to anything, because the meaning was implied; but frankly, it isn't worth the effort.

We don't have to talk about traveling at the speed of light though, we can talk about Albert and Henry moving relative to each other, where the relative velocity is, say, 0.6c


Supposedly Albert should be able to define a reference frame where he is traveling at 0.6c; how is this possible if he measures the velocity relative to himself, where he will always measure the velocity to be 0?

Also, Albert can determine his motion relative to himself or anythign else, by means of a co-moving experiemtnal arrangement e.g. using a radar gun. This, however, is not the test of the PoR as referenced above, which states that he cannot determine his "absolute motion" by means of a co-moving experimental arrangement.

To say he cannot determine his absolute motion means he cannot determine if he is "in motion" or "at rest"; what does this "at rest" refer to, becauase he can determine his rest relative to himself and other objects.


Also, are you suggesting that two relatively moving observers can determine which one is actually moving i.e. that they can determine their absolute motion by means of an experiment?


As for absolute velocity, I'm not sure, but I would think that that might be a contradiction in terms, because velocity, by its very nature is relative, not absolute. I think we can deduce, however, that there must be absolute motion, because if there wasn't then there would be relative motion.

 

[Michael C]

Does this mean that he can only ever define a co-ordinate system in which he is "at rest"?

He can define any coordinate system he chooses. If I define a reference frame that is moving at speed s with respect to me, then I am moving at speed s in the opposite direction with respect to that reference frame.

 

[russ_watters]

http://en.wikipedia.org/wiki/Tests_of_special_relativity#Basic_experiments

Great, so do you acknowledge that that doesn't match your previous wording? The wiki quote is about "absolute motion". Your formulation of the PoR did not include the word "absolute". It makes a big difference. The PoR doesn't say you can't measure a velocity RELATIVE to another object/frame.

Learning science is not a word game and our patience is wearing thin. You need to choose - rapidly - if you really want to learn what people are trying to teach you or not.

 

[russ_watters]

:facepalm:

are you familiar with the idea of implied meaning; saying that it is possible to define a reference frame in which you are traveling close to the speed of light implies that it is relatvie to something. I was going to try and dig out a reference from a discussion on here that made that exact point, and I'm pretty sure there was no mention of relative to anything, because the meaning was implied; but frankly, it isn't worth the effort.

Even if the issue of absolute vs relative wasn't the key point of discussion in this thread, clarity is a necessary component of discussion: Be clear.

 

[Dale]

The only link I can find is

wiki - tests of SR

So that link specifically mentioned the idea of a co-moving experiment, meaning some physical measurement of velocity where the experimental apparatus to measure the observer's velocity is also moving at the same speed and in the same direction as the observer. In such a case, the experimental result will always be the same (0) regardless of if the observer and apparatus are considered "moving" or "at rest". Is that clear now?

I don't think it makes any reference to statements about velocity.

Huh? The terms "moving" and "co-moving" are clearly statements about velocity.

Does this mean that he can only ever define a co-ordinate system in which he is "at rest"?

No.

It was mentioned that he should be possible to define a reference frame where is traveling at, or close to the speed of light, for example; how is this possible if he measures velocity relative to himself, where the velocity will always be zero?

By measuring his velocity relative to something other than himself.

Relating back to the example of Albert & Henry; Albert should be able to define a reference frame in which he, not Henry, is traveling at 0.6c. How can he do this if he measures the velocity relative to himself?

Arbitrarily choosing to measure velocity relative to Henry doesn't seem like a reasonable answer,

Why not? Arbitrarily choosing to measure velocity relative to Henry is no more nor less reasonable than arbitrarily choosing to measure velocity relative to Albert.

If Albert ascribes the velocity to himself, then he must assume that the photon in his light clock is imparted with the horizontal velocity that he ascribes to his train (or platform). This means that his instruments must contract for him to measure the speed of light to be c.

The opposite would be true if motion is ascribed to Henry.

Yes. Lengths are relative, just like velocity.

 

[darkhorror]

A frame of reference where the object's v = 0.

You are trying to make this too complicated.

 

[russ_watters]

Let me be as simple and clear as possible and see if we can end this:

"At rest" is an arbitrary choice anyone can make by choosing a reference frame other than himself and choosing to define either himself or that other reference frame as the "at rest" frame, then measuring the speed between the two frames. A statement about being at rest must include a definition of the two frames. For example, there are two common methods the police use to catch speeders (hopefully the existence of three potential frames won't confuse the issue...):

1. The police officer stands at the side of the road with a radar gun. He is standing still so he can tell he is "at rest" relative to the Earth and he thus declares himself to be "at rest", with the cars on the road moving relative to him. Thus, when he sees the measurement of 60mph on his radar gun, he says: "That car was moving at 60mph"...relative to me, who I have arbitrarily declared to be "at rest" in this system.

2. The police officer is driving in his car, following you. With his eyes, he maneuvers himself behind you at a constant distance so you are "at rest" relative to each other. He then reads his speedometer and declares that both of you are "moving" at 60mp relative to the earth.

 

[yuiop]

1. The police officer stands at the side of the road with a radar gun. He is standing still so he can tell he is "at rest" relative to the Earth and he thus declares himself to be "at rest" relative to the the cars on the road. Thus, when he sees the measurement of 60mph on his radar gun, he says: "That car was moving at 60mph"...relative to me, who I have arbitrarily declared to be "at rest" in this system.

Sorry to be picky, but the police officer cannot be both "at rest" relative the Earth and at the same time "at rest" relative to the cars on the road, if the cars on the road are moving relative to the Earth and himself.

 

[russ_watters]

Oy, awful error. Fixed now, thanks.

 

[bahamagreen]

I think the OP is using a logical extension of some form of proof by induction (like mathematical induction)... something like this:

Assume there is a detectable absolute frame.
If two objects are in relative motion, then one must measure at least one of the two objects to be in relative motion with respect to the detectable absolute frame.
This relative distinct motion to the detectable frame would be "actual" motion.
The inference of "actual" motion holds when the absolute frame is detectable.

Now alter the assumption of the absolute frame and make it undetectable.
If two objects are in relative motion, then one must conclude at least one of the two objects to be in relative motion with respect to the undetectable absolute frame.
This relative indistinct motion to the undetectable frame would be "actual" motion.
The inference of "actual" motion holds when the absolute frame is undetectable.

Now alter the assumption of the absolute frame and make it nonexistent.
Notice that the nonexistent absolute frame and the undetectable absolute frame are indistinguishable from each other.

Therefore the inference of "actual" motion still holds when there is no absolute frame.

Maybe the OP can verify that this is the form of his thought line?

 

[Austin0]

I think the OP is using a logical extension of some form of proof by induction (like mathematical induction)... something like this:

Assume there is a detectable absolute frame.
If two objects are in relative motion, then one must measure at least one of the two objects to be in relative motion with respect to the detectable absolute frame.
This relative distinct motion to the detectable frame would be "actual" motion.
The inference of "actual" motion holds when the absolute frame is detectable.

Now alter the assumption of the absolute frame and make it undetectable.
If two objects are in relative motion, then one must conclude at least one of the two objects to be in relative motion with respect to the undetectable absolute frame.
This relative indistinct motion to the undetectable frame would be "actual" motion.
The inference of "actual" motion holds when the absolute frame is undetectable.

Now alter the assumption of the absolute frame and make it nonexistent.
Notice that the nonexistent absolute frame and the undetectable absolute frame are indistinguishable from each other.

Therefore the inference of "actual" motion still holds when there is no absolute frame.

Maybe the OP can verify that this is the form of his thought line?

Hi bahamagreen brilliant. I think you have have described the logic in a coherent form.
If not exactly the OP's thought process, it is still a clever exercise in logic whether valid or not.

A similar chain might be:
If Reality describes that which does actually exist.
And
Fantasy describes that which does not actually exist.
And
The state of actual existence, or not, is indeterminable
Then
Fantasy is indistinguishable from Reality.

 

[Dale]

Or the only fantasy which is consistent with experimental evidence is one which is indistinguishable from reality.

 

[bahamagreen]

Thanks, AustinO... The OP's language on some of these points is a little arcane and I was getting frustrated that the heavy lifters here were being thrown off his train of thought; hope I captured the foundation of his position.

I like your interpretive restatement and DaleSpam's corollary extension to it very well.

If the OP will confirm or clarify that it is this epistemological indistinguishably between the existence of an undetectable absolute frame and the non-existance of an absolute frame which underlies his basis for "rest", "actual movement", and "deeper meaning", then we will have something to work with. Looking forward to seeing his and others' thoughts on this.

 

[Mentz114]

I think the OP is using a logical extension of some form of proof by induction (like mathematical induction)... something like this:

Assume there is a detectable absolute frame.
If two objects are in relative motion, then one must measure at least one of the two objects to be in relative motion with respect to the detectable absolute frame.
This relative distinct motion to the detectable frame would be "actual" motion.
The inference of "actual" motion holds when the absolute frame is detectable.

Now alter the assumption of the absolute frame and make it undetectable.
If two objects are in relative motion, then one must conclude at least one of the two objects to be in relative motion with respect to the undetectable absolute frame.
This relative indistinct motion to the undetectable frame would be "actual" motion.
The inference of "actual" motion holds when the absolute frame is undetectable.

Now alter the assumption of the absolute frame and make it nonexistent.
Notice that the nonexistent absolute frame and the undetectable absolute frame are indistinguishable from each other.

Therefore the inference of "actual" motion still holds when there is no absolute frame.

Maybe the OP can verify that this is the form of his thought line?

This is sophistry. There is no detectable absolute frame, no absolute motion and any argument that deduces "Therefore the inference of "actual" motion still holds when there is no absolute frame." is wrong.

 

[bahamagreen]

I'm not making the argument, I'm just trying to identify and reveal the basis for the OP's argument for subsequent examination. Pending his reply, we don't know yet what aspect of his position may or may not be subject to error.

Just to be clear, the observation that there is no detectable absolute frame is satisfied by two existential conditions; the absolute frame exists but is undetectable, and the absolute frame does not exist and is thereby undetectable. Undetectability does not establish nor preclude its existence.

It is the indistinguishably of these two possibilities that needs to be examined to see if the inference of absolute motion may be obtained across both cases - if logically inferred in the first case, does that extend to the second?

Was not this very form of thinking the basis for much of modern physics? The atomic theory, quark model, string theory, and even Einstein's predictions of phenomena before experiments could confirm them for example seem to be very much in line with DaleSpam's corollary, "...the only fantasy which is consistent with experimental evidence..." - this phrase is almost a perfect definition of the theory and practice of science itself, isn't it?

 

[Mentz114]

Undetectability does not establish nor preclude its existence.

Granted, but coupled with the fact that absolute velocity cannot be detected and is not required, by Occam's razor it is simpler to forget about it and avoid nugatory discussions like this.

Was not this very form of thinking the basis for much of modern physics? The atomic theory, quark model, string theory, and even Einstein's predictions of phenomena before experiments could confirm them for example seem to be very much in line with DaleSpam's corollary, "...the only fantasy which is consistent with experimental evidence..." - this phrase is almost a perfect definition of the theory and practice of science itself, isn't it?

If you take this argument further you might as well say that life itself is just a dream.

I don't agree with your last rhetorical question but I don't see any benefit in arguing about it.