Definition of Frame of Reference

[Chestermiller]

In studying SR, I've been subscribing to a particular definition of a Frame of Reference that makes sense to me. Recently, I've been made aware by another PF member that there may be other, broader, definitions that are valid and that people use. I would like to know more about these broader definitions, and, if possible, what fraction of the PF population uses them. My PF friend's comments have even led me to question the validity of my own definition. So here goes: According to my understanding, a FoR is a collection of physical objects (and possibly 3D spatial coordinate systems) which are all at rest relative to one another. So far, this is the only definition that has worked for me.

Chet

 

[phinds]

In studying SR, I've been subscribing to a particular definition of a Frame of Reference that makes sense to me. Recently, I've been made aware by another PF member that there may be other, broader, definitions that are valid and that people use. I would like to know more about these broader definitions, and, if possible, what fraction of the PF population uses them. My PF friend's comments have even led me to question the validity of my own definition. So here goes: According to my understanding, a FoR is a collection of physical objects (and possibly 3D spatial coordinate systems) which are all at rest relative to one another. So far, this is the only definition that has worked for me.

Chet

That's my understanding as well, but I'm just a moderately well-read amateur, not a pro.

 

[ghwellsjr]

In studying SR, I've been subscribing to a particular definition of a Frame of Reference that makes sense to me. Recently, I've been made aware by another PF member that there may be other, broader, definitions that are valid and that people use. I would like to know more about these broader definitions, and, if possible, what fraction of the PF population uses them. My PF friend's comments have even led me to question the validity of my own definition. So here goes: According to my understanding, a FoR is a collection of physical objects (and possibly 3D spatial coordinate systems) which are all at rest relative to one another. So far, this is the only definition that has worked for me.

Chet

A Frame of Reference is, as you say, a 3D spatial coordinate system, along with a 1D temporal coordinate added. Einstein describes this in the first section of his 1905 paper. It's very important to recognize how the time coordinate is established to make the coordinate system 4D. Once you get the concept down, you don't even have to think of the coordinate system as having any physical objects at rest either with one another or with respect to the coordinate system. For example, you could consider a FoR in which one observer/clock is traveling at 0.6c in one direction and another observer/clock is traveling a 0.6c in the other direction.

The other aspect of a FoR is the ability to take any event (the 4 coordinates describing a location at some time) and transform it into a new FoR moving with respect to the first one and get a new set of coordinates. This is done with the Lorentz Transformation process.

 

[phinds]

A Frame of Reference is, as you say, a 3D spatial coordinate system, along with a 1D temporal coordinate added. Einstein describes this in the first section of his 1905 paper. It's very important to recognize how the time coordinate is established to make the coordinate system 4D. Once you get the concept down, you don't even have to think of the coordinate system as having any physical objects at rest either with one another or with respect to the coordinate system. For example, you could consider a FoR in which one observer/clock is traveling at 0.6c in one direction and another observer/clock is traveling a 0.6c in the other direction.

The other aspect of a FoR is the ability to take any event (the 4 coordinates describing a location at some time) and transform it into a new FoR moving with respect to the first one and get a new set of coordinates. This is done with the Lorentz Transformation process.

Excellent correction. Thank you.

 

[ghwellsjr]

I might add that a common expression you see when discussing Special Relativity is something like "an observer's frame". This is usually taken to mean a FoR in which the observer is at rest. This is fine as long as the observer never accelerates, in other words, if he remains at rest. But then if you have a bunch of observers/objects that remain at rest with respect to each other (and the FoR), then you have a rather boring scenario. Almost always, we want to discuss what happens when the different observer/objects are moving and/or accelerating (changing their speed and/or their direction of motion). Now we either have to force one of them to remain at rest so that we can define the FoR from his "point of view" or we have to revert to a non-inertial FoR. In either case, we have given up the advantage of using the Lorentz Transformation process to see what the scenario looks like in a different FoR. A non-inertial FoR is very difficult to understand and there is no standard definition of a non-inertial FoR so I stay away from them as they don't provide any additional insight into what is happening than any inertial FoR would provide.

 

[phinds]

I have a sort of follow-on question to this. I've tried in various ways to explain to others the difference between the "proper" speed of far-away galaxies relative to us, vs the recession speed due to expansion. One of the things I found myself saying once, and this is were my question comes in, is "if you can discount expansion and consider the other galaxy as being in the same frame of reference as us [and I was intending an inertial FoR], then there is a small motion relative to us (and TINY relative to the recession speed)."

So, my question is, is that a sloppy use of terminology or does it make sense?

 

[Nugatory]

So, my question is, is that a sloppy use of terminology or does it make sense?

IMO, both. The additional words that would make it precise would almost certainly be more confusing to your audience than the widely-accepted shortcut that you're taking.

If anyone ever calls you on this particular sloppiness, you can rejoice knowing that you've successfully gotten the point across and that they really understand :)

 

[phinds]

If anyone ever calls you on this particular sloppiness, you can rejoice knowing that you've successfully gotten the point across and that they really understand :)

 

[ghwellsjr]

I have a sort of follow-on question to this. I've tried in various ways to explain to others the difference between the "proper" speed of far-away galaxies relative to us, vs the recession speed due to expansion. One of the things I found myself saying once, and this is were my question comes in, is "if you can discount expansion and consider the other galaxy as being in the same frame of reference as us [and I was intending an inertial FoR], then there is a small motion relative to us (and TINY relative to the recession speed)."

So, my question is, is that a sloppy use of terminology or does it make sense?

The expression "in the same frame of reference as us" implies that each observer/object owns a separate FoR in which it is at rest, which is pointless. Every observer/object is in every FoR, otherwise, what's the point of having a coordinate system? Pick one FoR, anyone you want, describe everything in that FoR. Then if you want, you can transform to any other inertial FoR. But this only works in SR.

Your question is outside the scope of Special Relativity and involves the much more complicated aspects of General Relativity which I avoid just like I avoid non-inertial frames in SR. I don't think there is any point in taking a situation that involves gravity and the expansion of the universe which requires GR and recasting it in terms of SR, to find an easy explanation, it just won't work. I don't know why so many people want to tackle GR before they understand SR, which is so much simpler. I think the doubts and confusion that people have about relativity could be assuaged simply by understanding SR and then recognizing that GR can be left to the experts.

 

[phinds]

The expression "in the same frame of reference as us" implies that each observer/object owns a separate FoR in which it is at rest, which is pointless. Every observer/object is in every FoR, otherwise, what's the point of having a coordinate system? Pick one FoR, anyone you want, describe everything in that FoR. Then if you want, you can transform to any other inertial FoR. But this only works in SR.

Your question is outside the scope of Special Relativity and involves the much more complicated aspects of General Relativity which I avoid just like I avoid non-inertial frames in SR. I don't think there is any point in taking a situation that involves gravity and the expansion of the universe which requires GR and recasting it in terms of SR, to find an easy explanation, it just won't work. I don't know why so many people want to tackle GR before they understand SR, which is so much simpler. I think the doubts and confusion that people have about relativity could be assuaged simply by understanding SR and then recognizing that GR can be left to the experts.

So what would you suggest as a method to explain the fact that distant galaxies have a (relatively small) "proper" motion relative to us and a (HUGE) velocity of recession relative to us.

 

[ghwellsjr]

So what would you suggest as a method to explain the fact that distant galaxies have a (relatively small) "proper" motion relative to us and a (HUGE) velocity of recession relative to us.

I never heard of those terms. What matters in SR is velocity according to a FoR and there is only one for each FoR. Transform to a different FoR and everything can have a different velocity. I don't know what is done in GR. If you want to imagine an unrealistic scenario involving a distant object like a galaxy traveling in some way, then that can be handled by SR but you will have to explain what you mean by "proper" motion and velocity of recession.

 

[Mark M]

So what would you suggest as a method to explain the fact that distant galaxies have a (relatively small) "proper" motion relative to us and a (HUGE) velocity of recession relative to us.

It's because the recessional velocity of galaxies isn't *really* velocity. It's observed because the intermediate space is undergoing metric expansion. However, metric expansion doesn't get you anywhere - it doesn't let you transfer information FTL. So, it doesn't violate SR and is a purely general relativistic effect.

 

[phinds]

It's because the recessional velocity of galaxies isn't *really* velocity. It's observed because the intermediate space is undergoing metric expansion. However, metric expansion doesn't get you anywhere - it doesn't let you transfer information FTL. So, it doesn't violate SR and is a purely general relativistic effect.

Yes, I'm aware of that and agree. My question is how to explain it to someone who had no physics background.

 

[DrGreg]

I don't think there is a single definition of "frame of reference" that all people agree with. Here are some possibilities to consider.

1. Some people take the view that a frame of reference is just another name for "coordinate system". So, they would regard changing the spatial coords from Cartesian (x,y,z) to polar (r,θ,φ) as a change of frame. I don't feel too happy with that.
   
2. The suggestion in the original question of a lattice of observers who are deemed to be "at rest" seems quite a good one. The observers also need to have agreed a definition of simultaneity, i.e. how to synchronise their personal clocks to each other. So a change in synchronisation would be a change of frame.
   
3. Or, I suppose, you could take the definition (2) but do not regard synchronisation as part of the "frame", i.e. it depends only on the observers and not their clock sync.
   
4. "Frame" could be taken to mean "frame field", a.k.a. tetrad or vierbein, in which you have a set of four orthonormal vectors at each event in space time, one timelike, e₀, and three spacelike, e₁, e₂, e₃. In the inertial frames of special relativity, there's a one-one correspondence between frame fields and Minkowski coordinate systems, but that doesn't follow in the more general cases. Note that, in general relativity we make a distinction between coordinates, which represent an event on the manifold, and vectors, which arise from differentiating coordinates and which reside in a tangent space to the manifold. A frame field defines an orthonormal basis for the tangent space, not for the coordinates in the manifold.

 

[sadraj]

So . How can you define "being at rest with respect to each other"?
I'm so confused with the defenition of coordinate like you. it seems that we can reduce your question to this question: " How can you campare the length of two objects" if you can define a camparing tool on space then it would be isomorphic with real valued numbers field.( in each dimention)

 

[Chestermiller]

A Frame of Reference is, as you say, a 3D spatial coordinate system, along with a 1D temporal coordinate added. Einstein describes this in the first section of his 1905 paper. It's very important to recognize how the time coordinate is established to make the coordinate system 4D. Once you get the concept down, you don't even have to think of the coordinate system as having any physical objects at rest either with one another or with respect to the coordinate system. For example, you could consider a FoR in which one observer/clock is traveling at 0.6c in one direction and another observer/clock is traveling a 0.6c in the other direction.

The other aspect of a FoR is the ability to take any event (the 4 coordinates describing a location at some time) and transform it into a new FoR moving with respect to the first one and get a new set of coordinates. This is done with the Lorentz Transformation process.

I don't rule out the possibility of objects traveling at 0.6c relative to myself in one direction or another, and being observable and measurable (kinematically) from my frame of reference. Thus, interesting things can still be happening in space and time, and I could still be able to observe them without being blind to them. But according to the definition I gave in my OP, I would not consider these objects as denizens of my own frame of reference; they would be residents of other reference frames. I know that this is not as broad a definition as the one that you are comfortable with, but it is also simpler to understand, and should not lead to any errors in SR analyses. In your opinion, is that correct?

As far as how the time direction is established to make the coordinate system 4D, you're probably not going to like what I have to say. I like to imagine the time direction as an actual spatial direction, orthogonal to the 3 spatial directions of my coordinate system (in SR). I like to consider the dot product of the coordinate basis vector in the time direction with itself to be -1, so that the Minkowski metric is automatically established. (I realize that, in order for the time direction to truly be considered a bona fide spatial direction, the metric would have to be positive definite, but this small difference doesn't bother me too much). I also like to imagine that my frame of reference is moving with the speed of light into the time direction that is assigned to my specific frame of reference. In this way, my frame of reference sweeps out all of 4D space-time, at least the part into my future.

I realize that this description is, to say the least, not very acceptable to mainstream physicists. However, as an engineer who has studied this subject for the first time during the past few years, I feel that it has significant appeal, and should not lead to any trouble in solving problems related to SR.

Chet

 

[pervect]

I have a sort of follow-on question to this. I've tried in various ways to explain to others the difference between the "proper" speed of far-away galaxies relative to us, vs the recession speed due to expansion. One of the things I found myself saying once, and this is were my question comes in, is "if you can discount expansion and consider the other galaxy as being in the same frame of reference as us [and I was intending an inertial FoR], then there is a small motion relative to us (and TINY relative to the recession speed)."

So, my question is, is that a sloppy use of terminology or does it make sense?

Well, being precise leads to what appears on the surface to be an unhelpful comment something like the following, from Baez's paper on GR.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime.

Which is quite clear, quite correct, very true, and probably won't be believed. (At least that's my experience, your mileage may vary).

Adding the rest of the more detailed explanation of why this is true will probably also result in a lot of blank looks, due to the lack of necessary background to understand the explanation.

The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.

 

[Vandam]

I don't rule out the possibility of objects traveling at 0.6c relative to myself in one direction or another, and being observable and measurable (kinematically) from my frame of reference. Thus, interesting things can still be happening in space and time, and I could still be able to observe them without being blind to them. But according to the definition I gave in my OP, I would not consider these objects as denizens of my own frame of reference; they would be residents of other reference frames. I know that this is not as broad a definition as the one that you are comfortable with, but it is also simpler to understand, and should not lead to any errors in SR analyses. In your opinion, is that correct?

As far as how the time direction is established to make the coordinate system 4D, you're probably not going to like what I have to say. I like to imagine the time direction as an actual spatial direction, orthogonal to the 3 spatial directions of my coordinate system (in SR). I like to consider the dot product of the coordinate basis vector in the time direction with itself to be -1, so that the Minkowski metric is automatically established. (I realize that, in order for the time direction to truly be considered a bona fide spatial direction, the metric would have to be positive definite, but this small difference doesn't bother me too much). I also like to imagine that my frame of reference is moving with the speed of light into the time direction that is assigned to my specific frame of reference. In this way, my frame of reference sweeps out all of 4D space-time, at least the part into my future.

I like the way you see it. I find it the only correct way to understand/interpret SR. Relativity of simultaneity means 4D block universe. But a lot of physicists do not want to take that step. It's very risky asking on PF what a frame of reference really means. Most physicists are happy with only the mathematical calculations. And asking about the meannig of those calculations is considered part of philosophy, not physics...

I realize that this description is, to say the least, not very acceptable to mainstream physicists. However, as an engineer who has studied this subject for the first time during the past few years, I feel that it has significant appeal, and should not lead to any trouble in solving problems related to SR.

Chet

 

[PeterDonis]

But according to the definition I gave in my OP, I would not consider these objects as denizens of my own frame of reference; they would be residents of other reference frames. I know that this is not as broad a definition as the one that you are comfortable with, but it is also simpler to understand, and should not lead to any errors in SR analyses. In your opinion, is that correct?

What is your criterion for something being "in your frame of reference"? Is it only objects that are at rest relative to you? That seems like a very restrictive definition, which basically makes the concept of "frame of reference" useless, as ghwellsjr pointed out earlier. But alternatively, if objects that are moving relative to you can still be in your frame of reference, why can't *all* objects be in it?

As far as how the time direction is established to make the coordinate system 4D, you're probably not going to like what I have to say. I like to imagine the time direction as an actual spatial direction, orthogonal to the 3 spatial directions of my coordinate system (in SR). I like to consider the dot product of the coordinate basis vector in the time direction with itself to be -1, so that the Minkowski metric is automatically established.

Assuming that you also consider the dot products of spacelike basis vectors with themselves to be +1, this is all just standard SR; you don't need to "consider" it, you can just use it. The term "spatial direction" applied to the time direction might raise some eyebrows, but as soon as you clarify the dot products, you are admitting that the time direction is different from the space directions.

(I realize that, in order for the time direction to truly be considered a bona fide spatial direction, the metric would have to be positive definite, but this small difference doesn't bother me too much).

If the word "spatial" is just to help you imagine things more easily, there's no problem. The only problem would be if you tried to infer from the word "spatial" that the time direction had properties that it doesn't actually have (like a positive dot product with itself), or that it didn't have properties that it actually does have; but it doesn't appear that you've done that.

I also like to imagine that my frame of reference is moving with the speed of light into the time direction that is assigned to my specific frame of reference.

If "moving with the speed of light into the time direction" is just another way of saying that your 4-velocity has length c (or 1 in the "natural" units usually used in relativity, where c = 1), then this is OK. But see further comments below.

In this way, my frame of reference sweeps out all of 4D space-time, at least the part into my future.

Why just into your future? You can extend everything you've said into your past as easily as into your future.

I realize that this description is, to say the least, not very acceptable to mainstream physicists.

It's not the description itself that causes problems; it's that a lot of people who see this description can't resist the temptation to draw wrong inferences from it. For example, every time a Brian Greene special airs on TV, we get a spate of threads here asking about things like the reference frame of a photon, whether everything "moves at c through spacetime", including photons, whether time dilation means you're moving "more through space and less through time", etc., etc. Then we have to spend a lot of time clearing away all the misconceptions that have arisen from the type of description you're talking about.

Ultimately, the "descriptions" don't matter; what matters is the physics--the actual predictions we make and whether or not they match experimental results. My personal view is that many of these "descriptions" are no help (at least not to me) in actually making the predictions, so I don't think they're worth spending a lot of time on; I'd rather concentrate on ways of organizing the material that *do* help me in making predictions. But your mileage may vary.

I feel that it has significant appeal, and should not lead to any trouble in solving problems related to SR.

If it helps you in generating predictions, and the predictions are correct, then yes, it should not lead to any trouble.

 

[PeterDonis]

It's very risky asking on PF what a frame of reference really means.

It's risky if what you're asking for can't be tied to any experimental result.

Most physicists are happy with only the mathematical calculations.

No, this is not correct. Most physicists are *not* happy with *only* the mathematical calculations. They also want to see if the calculations match the experimental results.

And asking about the meannig of those calculations is considered part of philosophy, not physics...

No, asking about the "meaning" of the calculations over and above the fact (if it is a fact) that they lead to correct experimental predictions is considered part of philosophy, not physics.

Perhaps it's worth a bit of a "postscript" here. Our physical theories, the mathematical models that go with them, and the predictions they make, are *models*. They are supposed to correctly reflect reality by making correct predictions about what we will observe, but they are not reality itself.

Furthermore, the fact that our models have a particular structure is no guarantee that "reality" has the same structure. A "frame of reference" is a part of the structure of our models; but asking what it "really means" is implicitly assuming that there is something in reality itself that corresponds to it. But what if (as I would say in the case of a frame of reference) there isn't? Then asking what a frame of reference "really means" would be like seeing an arrow with an "N" next to it on a map and expecting to see an arrow with an "N" actually there on the ground pointing north, or seeing a line drawn on a map along a border and expecting to see an actual line drawn on the ground where the border is.

 

[pervect]

In studying SR, I've been subscribing to a particular definition of a Frame of Reference that makes sense to me. Recently, I've been made aware by another PF member that there may be other, broader, definitions that are valid and that people use. I would like to know more about these broader definitions, and, if possible, what fraction of the PF population uses them. My PF friend's comments have even led me to question the validity of my own definition. So here goes: According to my understanding, a FoR is a collection of physical objects (and possibly 3D spatial coordinate systems) which are all at rest relative to one another. So far, this is the only definition that has worked for me.

Chet

It seems to me you're missing a few very important things that a frame of reference, or even a generalized frame of reference needs.

Those things are: 1) A concept of distance, so you can determine the distance between any 2 objects in your collection

2) A concept of simultaneity, so you can determine if events in the frame of reference occur at the same time. This also allows you to possibly form a notion of time interval betwen two events.

If you're just concenrned with SR, you probably don't need to worry too much about curvature - at least not yet.

You might have to consider at this stage whether or not you want to include "rotating" frames of reference or not. If you do, there will be some issues with point 2, the concept of simultaneity, at least if you use the standard Einstein notations.

A strict definition might insist that you can synchrornize all clocks in your frame of reference transitively, so that A can be synched to B can be synched to C can be synched to A. This modest requirement will wind up eliminating the problems associated with rotating frames of reference, with some loss in generality - at least it will if you insist that your synchronization scheme be able to be carried out by the Einstein convention, not so much if you propose some other scheme.

 

[Vandam]

It's not the description itself that causes problems; it's that a lot of people who see this description can't resist the temptation to draw wrong inferences from it.

You might call them wrong from a positivist point of view. But I consider physics as a tool to describe the world as it exists independent of perception. I know you have big problems with this approach.

 

[ghwellsjr]

I don't rule out the possibility of objects traveling at 0.6c relative to myself in one direction or another, and being observable and measurable (kinematically) from my frame of reference. Thus, interesting things can still be happening in space and time, and I could still be able to observe them without being blind to them.

Can you please expound on this statement. How does "my frame of reference" provide any advantage in being able to observe anything over any other frame of reference?

 

[jtbell]

I consider physics as a tool to describe the world as it exists independent of perception.

How do we know we have found out how something "exists independent of perception"?

 

[Dale]

But I consider physics as a tool to describe the world as it exists independent of perception.

If by "perception" you mean "measurement" then physics fundamentally cannot do that, nor can any other branch of science. If you mean something else, then it would be helpful if you were to clarify.

 

[Dale]

I don't think there is a single definition of "frame of reference" that all people agree with. Here are some possibilities to consider.

1. Some people take the view that a frame of reference is just another name for "coordinate system". So, they would regard changing the spatial coords from Cartesian (x,y,z) to polar (r,θ,φ) as a change of frame. I don't feel too happy with that.
   
2. The suggestion in the original question of a lattice of observers who are deemed to be "at rest" seems quite a good one. The observers also need to have agreed a definition of simultaneity, i.e. how to synchronise their personal clocks to each other. So a change in synchronisation would be a change of frame.
   
3. Or, I suppose, you could take the definition (2) but do not regard synchronisation as part of the "frame", i.e. it depends only on the observers and not their clock sync.
   
4. "Frame" could be taken to mean "frame field", a.k.a. tetrad or vierbein, in which you have a set of four orthonormal vectors at each event in space time, one timelike, e₀, and three spacelike, e₁, e₂, e₃. In the inertial frames of special relativity, there's a one-one correspondence between frame fields and Minkowski coordinate systems, but that doesn't follow in the more general cases. Note that, in general relativity we make a distinction between coordinates, which represent an event on the manifold, and vectors, which arise from differentiating coordinates and which reside in a tangent space to the manifold. A frame field defines an orthonormal basis for the tangent space, not for the coordinates in the manifold.

This is a good summary. I have always taken the fourth as the "official" definition of a reference frame, but in practice I use the first most of the time. I know the first is sloppy usage, for exactly the reason you specify, but it works most of the time and as long as you are aware of it you can avoid or clarify in the cases where it makes a difference.

 

[Vandam]

How do we know we have found out how something "exists independent of perception"?

Look at your computer in front of you. Then close your eyes. Open your eyes again. The computer is still there. Was the computer there when your eyes were closed?

 

[PeterDonis]

You might call them wrong from a positivist point of view.

If by this you mean I am calling them wrong because they lead to incorrect predictions, then yes, that's what I mean. But I don't think it's "positivist" to say that someone is wrong because they make an *incorrect* prediction. Arguments about "positivism" come into play when someone says that a statement is "wrong' or "meaningless" because it makes *no* experimental prediction whatsoever. Making no prediction is not the same as making an incorrect prediction.

But I consider physics as a tool to describe the world as it exists independent of perception.

First of all, see my comments above. If a prediction is incorrect, it's incorrect. That is a different question from whether it's "independent of perception"--a prediction of an invariant, something that is observed to be the same by everybody, can still be incorrect.

Also, when you talk about "the world as it exists independent of perception", are you considering the fact that what you call "perception" is *part* of "the world as it exists"? Your perceptions, like mine and everybody else's, are physical processes, governed ultimately by the same laws that govern all other physical processes. And in order to perceive something at all, you have to interact with it, which means you're not completely "independent" of it. This is usually ignored in classical physics, where "classical" here means "non-quantum" and includes relativity; but that doesn't mean it isn't true. And of course in quantum mechanics you can't ignore it.

I know you have big problems with this approach.

I'm not sure you really understand my position. See comments above.

 

[Vandam]

If by this you mean I am calling them wrong because they lead to incorrect predictions, then yes, that's what I mean. But I don't think it's "positivist" to say that someone is wrong because they make an *incorrect* prediction. Arguments about "positivism" come into play when someone says that a statement is "wrong' or "meaningless" because it makes *no* experimental prediction whatsoever. Making no prediction is not the same as making an incorrect prediction.



First of all, see my comments above. If a prediction is incorrect, it's incorrect. That is a different question from whether it's "independent of perception"--a prediction of an invariant, something that is observed to be the same by everybody, can still be incorrect.

Also, when you talk about "the world as it exists independent of perception", are you considering the fact that what you call "perception" is *part* of "the world as it exists"? Your perceptions, like mine and everybody else's, are physical processes, governed ultimately by the same laws that govern all other physical processes. And in order to perceive something at all, you have to interact with it, which means you're not completely "independent" of it. This is usually ignored in classical physics, where "classical" here means "non-quantum" and includes relativity; but that doesn't mean it isn't true. And of course in quantum mechanics you can't ignore it.

I know you are a positivist. You apply your QM approach to SR. That's why we do not agree.

 

[PeterDonis]

I know you are a positivist. You apply your QM approach to SR.

Huh? What I said about your perceptions being physical processes is a fact about "the world as it is", as you call it; it's true regardless of which *theory* we are using to describe that world. I would have thought such facts about "the world as it is", independent of our theories, are exactly the sorts of things you were talking about when you talked about "the world as it is independent of our perceptions". And yet when I mention such a fact, you call me a "positivist". I'm afraid you are very confused; or else you are not really reading what I write, but just latching on to one particular thing that strikes you.

 

[PeterDonis]

Look at your computer in front of you. Then close your eyes. Open your eyes again. The computer is still there. Was the computer there when your eyes were closed?

If this is all you mean by "the world independent of our perceptions", then it's something quite different from a claim that can't be related to experimental results. The claim that the computer is still there when your eyes are closed has plenty of testable consequences.

 

[Vandam]

If this is all you mean by "the world independent of our perceptions", then it's something quite different from a claim that can't be related to experimental results. The claim that the computer is still there when your eyes are closed has plenty of testable consequences.

Peter, I will not debating these off topic issus on PF.
We even tried off-record and we couldn't get it sorted out. So I leave it that way. Thanks for your effort.

 

[PeterDonis]

Peter, I will not debating these off topic issues on PF.

Well, as you can see from other comments in this thread (and the previous one that led to our offline discussion), I'm not the only one that is questioning what you say. But if it's off topic I have no problem dropping it.

 

[harrylin]

[..] I would like to know more about these broader definitions, and, if possible, what fraction of the PF population uses them.
[..] my own definition [..]: a FoR is a collection of physical objects (and possibly 3D spatial coordinate systems) which are all at rest relative to one another. So far, this is the only definition that has worked for me.

Chet

That's already very general. Indeed it does not need to be a material "frame", it can be imaginary; it can refer to a collection of spatial coordinate systems in which no physical object is in rest - compare "ECI frame".
https://en.wikipedia.org/wiki/Earth-centered_inertial

Thus, what is essential is the "R" of "reference", and not physical objects. We only need such physical objects as rulers to define the spatial coordinates, and even so a ruler may be composed of a laser with a mirror and a clock.

However, next you write:

Thus, interesting things can still be happening in space and time, and I could still be able to observe them without being blind to them. But according to the definition I gave in my OP, I would not consider these objects as denizens of my own frame of reference; they would be residents of other reference frames.

That does not follow from your OP... A collection of coordinate systems is not generally limited in space; just as the ECI frame, they can be of infinite extension. As a matter of fact, standard "inertial frames" are defined like that, so that all objects "reside" in all inertial frames.

 

[Chestermiller]

Can you please expound on this statement. How does "my frame of reference" provide any advantage in being able to observe anything over any other frame of reference?

There's nothing particularly special about my own personal frame of reference. Taking as the definition of a frame of reference that given in my original posting just seems to conceptually simply things for me, and I thought it might also simplify things for others. Instead of saying that "an object is moving in my frame of reference," I would prefer to say that "an object is moving relative to my frame of reference." I suppose that it's not such a big deal, but it's more to my personal taste, and, as we said, it shouldn't lead to any errors in analyzing SR problems. Maybe I'm making a mountain out of a molehill.

Chet

 

[Chestermiller]

What is your criterion for something being "in your frame of reference"? Is it only objects that are at rest relative to you? That seems like a very restrictive definition, which basically makes the concept of "frame of reference" useless, as ghwellsjr pointed out earlier. But alternatively, if objects that are moving relative to you can still be in your frame of reference, why can't *all* objects be in it?

No. I tried to explain what I'm saying, but it looks like I didn't do a very good job. I realize that if I only paid attention to objects that are at rest relative to myself, spacetime would be a very boring place. What I'm saying is that objects may be flying all over the place in spacetime, and that I would be able to observe and track them, but I only count the objects and coordinate systems that are at rest with respect to myself as part of my frame of reference (and, of course, I am part of their frame of reference). All other objects and coordinate systems occupy other frames of reference that, of course, share spacetime (i.e., overlap) with my own.

 

[PeterDonis]

What I'm saying is that objects may be flying all over the place in spacetime, and that I would be able to observe and track them, but I only count the objects and coordinate systems that are at rest with respect to myself as part of my frame of reference (and, of course, I am part of their frame of reference). All other objects and coordinate systems occupy other frames of reference that, of course, share spacetime (i.e., overlap) with my own.

I'm afraid I still don't understand how this system of yours is supposed to work. Or, rather, I can't tell whether or not it's just the standard system described in non-standard terminology. When you say that all objects "share spacetime" with you, and that you can observe and track them regardless of their states of motion, how is that different from saying they are all in your frame of reference? You can certainly *describe* their motions using coordinates in which you are at rest; and you can therefore compute any physical result you like using those coordinates. What's left over that makes you say the objects are nevertheless not in your frame of reference? It seems to me like that's just a fancy way of saying they are moving relative to you, and nothing else.

 

[PeterDonis]

Instead of saying that "an object is moving in my frame of reference," I would prefer to say that "an object is moving relative to my frame of reference."

This makes me think that your system *is* the standard system, just described in non-standard terminology. To me, both of these statements say the same thing.

 

[Darwin123]

That's already very general. Indeed it does not need to be a material "frame", it can be imaginary; it can refer to a collection of spatial coordinate systems in which no physical object is in rest - compare "ECI frame".
https://en.wikipedia.org/wiki/Earth-centered_inertial

Thus, what is essential is the "R" of "reference", and not physical objects. We only need such physical objects as rulers to define the spatial coordinates, and even so a ruler may be composed of a laser with a mirror and a clock.

However, next you write:

That does not follow from your OP... A collection of coordinate systems is not generally limited in space; just as the ECI frame, they can be of infinite extension. As a matter of fact, standard "inertial frames" are defined like that, so that all objects "reside" in all inertial frames.

Not all objects "in a reference frame" are "part of a reference frame." A reference frame can be considered a set of bodies that are stationary relative to each other at all points of time. Now, a body that is moving relative to these objects can be said to be within the reference frame. However, it is not part of the reference frame.
I include as part of my reference frame a set of identical clocks and a set of identical rulers that are stationary relative to my left eye. I will confine my measurements to these measuring instruments and none other.
There may be similar clocks and rulers moving near the speed of light relative to my left eye. These rulers and clocks are not part of my reference frame. However, they are inside my reference frame in a geometric sense. If measurements are done with these instruments, one can't consider the measurements as having been done in my reference frame. No measuring instrument that moves at high velocity relative to my left eye can be considered part of my reference frame.
If there is no external force acting on my left eye, my reference frame is also an inertial frame. Special relativity is applicable to all measurements made with instruments that are part of the same inertial frame.
All bodies everywhere are "geometrically within" ever frame everywhere. However, a frame is defined in terms of a set of bodies that do not move relative to each other.
An inertial reference frame specifies measuring instruments with a very specific state of motion. None of the instruments are moving relative to each other. None of the instruments are accelerating in a dynamic sense.
There is more than one inertial frame. One inertial frame can be moving with respect to the other. However, every body that is part of the inertial frame is moving as though it is attached to a rigid frame with no force acting on it.
You can reside in a house without being part of it. The pieces of house are stationary relative to each other. If one can move from room to room, then one is not part of the house.

 

[ghwellsjr]

Can you please expound on this statement. How does "my frame of reference" provide any advantage in being able to observe anything over any other frame of reference?

There's nothing particularly special about my own personal frame of reference. Taking as the definition of a frame of reference that given in my original posting just seems to conceptually simply things for me, and I thought it might also simplify things for others. Instead of saying that "an object is moving in my frame of reference," I would prefer to say that "an object is moving relative to my frame of reference." I suppose that it's not such a big deal, but it's more to my personal taste, and, as we said, it shouldn't lead to any errors in analyzing SR problems. Maybe I'm making a mountain out of a molehill.

Chet

You keep changing your definition of a Frame of Reference.

In your first post, you made no mention of it being "your personal frame of reference". Rather, a collection of physical objects at rest with one another constituted a single FoR.

Then in post #16, you added that this single FoR was your own FoR implying that you were one of the physical objects in mutual rest.

Finally in post #36, you disclosed that each of the objects in mutual rest with you has their own FoR.

Added to that is your statement that all the objects that are not at rest with respect to you have their own FoR and your preferred wording in post #35 leads me to the conclusion that you are envisioning a whole bunch of mutually overlapping and (possibly) relatively moving Frames of Reference, one for each object, correct?

Here's what's wrong with your idea: it's too limiting. There are an infinite number of Frames of Reference, all mutually overlapping and possibly moving with respect to one another. Why do you limit the number of them to the number of physical objects? You can use the Lorentz Transformation process to create as many new Frames of Reference based on your own personal FoR as you want, each moving at a slightly different speed with respect to your own personal FoR. And each one of them is just as valid as any of the others. This is a fundamental point of relativity. I emphasize the word one, because you need to use just one FoR when describing a scenario and when analyzing what is happening in that scenario.

Please go back in read my post #3 where I explained all this and see if it makes more sense to you now.

 

[Vandam]

Not all objects "in a reference frame" are "part of a reference frame." A reference frame can be considered a set of bodies that are stationary relative to each other at all points of time. Now, a body that is moving relative to these objects can be said to be within the reference frame. However, it is not part of the reference frame.
I include as part of my reference frame a set of identical clocks and a set of identical rulers that are stationary relative to my left eye. I will confine my measurements to these measuring instruments and none other.
There may be similar clocks and rulers moving near the speed of light relative to my left eye. These rulers and clocks are not part of my reference frame. However, they are inside my reference frame in a geometric sense. If measurements are done with these instruments, one can't consider the measurements as having been done in my reference frame. No measuring instrument that moves at high velocity relative to my left eye can be considered part of my reference frame. ...

Good job, Darwin. I would like to elaborate on this.

It made me think more specifically about the layman's definition of a world (everything that happens simultaneously at a specific moment in time)...
What you call 'in' a reference frame, I would rather call this 'part' of a world.
Let me explain this.

When I first learned about SR I interpreted the reference frame as a 'the world of simultaneous events at a specific time', but strictly spoken that's not correct if one considers that a moving object 'in' that reference frame' is not 'part' of that reference frame. However, the event of the moving object that is 'in', but not 'part' of my reference frame is indeed part of my world of simultaneous events at that moment !

A diagram shows this better:

154271[/ATTACH]"]

Event 'e' (car clock physically on 0,7) is in a green reference frame, but is not part of that reference frame.
However, event 'e' is part of the green world B ! And event 'e' is also part of red world R.

The O,7 car is definitely part of my green world of sim events. And the car clock ticks slow in my world relative to my reference frame. But the car clock is not part of my reference frame. The O,7 car clock is not slower in the green reference frame, but rather relative to my green reference frame.

Of course the car driver will have a similar but different story to tell... ;)

V.

 

[Chestermiller]

I'm afraid I still don't understand how this system of yours is supposed to work. Or, rather, I can't tell whether or not it's just the standard system described in non-standard terminology. When you say that all objects "share spacetime" with you, and that you can observe and track them regardless of their states of motion, how is that different from saying they are all in your frame of reference? You can certainly *describe* their motions using coordinates in which you are at rest; and you can therefore compute any physical result you like using those coordinates. What's left over that makes you say the objects are nevertheless not in your frame of reference? It seems to me like that's just a fancy way of saying they are moving relative to you, and nothing else.

As I said, maybe I've been making a mountain out of a molehill, and all we're really talking about is semantics.

Chet

 

[Chestermiller]

You keep changing your definition of a Frame of Reference.

In your first post, you made no mention of it being "your personal frame of reference". Rather, a collection of physical objects at rest with one another constituted a single FoR.

Then in post #16, you added that this single FoR was your own FoR implying that you were one of the physical objects in mutual rest.

Finally in post #36, you disclosed that each of the objects in mutual rest with you has their own FoR.

My comments in posts #16 and #36 are just examples. My OP is what I really intend to stand by.

Added to that is your statement that all the objects that are not at rest with respect to you have their own FoR and your preferred wording in post #35 leads me to the conclusion that you are envisioning a whole bunch of mutually overlapping and (possibly) relatively moving Frames of Reference, one for each object, correct?

Yes, but not only physical objects; Coordinate systems (which may or may not include physical objects) as well.

Here's what's wrong with your idea: it's too limiting. There are an infinite number of Frames of Reference, all mutually overlapping and possibly moving with respect to one another. Why do you limit the number of them to the number of physical objects? You can use the Lorentz Transformation process to create as many new Frames of Reference based on your own personal FoR as you want, each moving at a slightly different speed with respect to your own personal FoR. And each one of them is just as valid as any of the others. This is a fundamental point of relativity. I emphasize the word one, because you need to use just one FoR when describing a scenario and when analyzing what is happening in that scenario.

I agree with all of this. In my original post, I did include coordinate systems as well as objects.

Please go back in read my post #3 where I explained all this and see if it makes more sense to you now.

In my original post, I guess I should have allowed for coordinate systems that do not contain any physical objects as valid candidates for frames of reference. Is that what you are driving at?

Chet

 

[ghwellsjr]

In my original post, I guess I should have allowed for coordinate systems that do not contain any physical objects as valid candidates for frames of reference. Is that what you are driving at?

Yes and also physical objects that are moving in the reference frame. Here's your original definition:

According to my understanding, a FoR is a collection of physical objects (and possibly 3D spatial coordinate systems) which are all at rest relative to one another.

Note how you said the frame of reference is the collection of physical objects and the 3D coordinate system is optional.

Here's my correction:

A Frame of Reference is, as you say, a 3D spatial coordinate system, along with a 1D temporal coordinate added. Einstein describes this in the first section of his 1905 paper. It's very important to recognize how the time coordinate is established to make the coordinate system 4D. Once you get the concept down, you don't even have to think of the coordinate system as having any physical objects at rest either with one another or with respect to the coordinate system. For example, you could consider a FoR in which one observer/clock is traveling at 0.6c in one direction and another observer/clock is traveling a 0.6c in the other direction.

Note how I said the frame of reference is a 4D coordinate system and the physical objects (moving or stationary) are optional.

I then added:

The other aspect of a FoR is the ability to take any event (the 4 coordinates describing a location at some time) and transform it into a new FoR moving with respect to the first one and get a new set of coordinates. This is done with the Lorentz Transformation process.

An event in SR is a particular set of the four coordinate values in a particular coordinate system. It doesn't matter if there is a physical object or anything happening at that place at that time and there are an infinite number of events along each of the coordinates.

Even when Einstein built the concept of a FoR using rigid rulers connecting synchronized clocks at various locations, he made it clear that these were imaginary (as harrylin pointed out in post #34). If you required physical objects (physical clocks connected by physical rigid rulers) filling the universe to define a FoR, there would be no room for any other physical objects to move around and what about an event that was at the middle of a rigid ruler where there was no clock or an event that was in the middle of a clock? How would you define those events? And think about what happens when you take the coordinates of an event in one FoR and convert them into the coordinates of the same event in a second FoR moving with respect to the first one, the calculation can result in an arbitrary location where there may not be a clock if you follow the physical idea of a FoR.

To restate: a Frame of Reference is defined by Einstein as a 4D coordinate system empty of any physical objects and then you add in whatever physical objects you want and describe their positions and motions in terms of events, precise and exact with infinite resolution. Not only do you not require any "observers" you don't require anything at the origin or anywhere else or at any particular time. You do what you want.

 

[Darwin123]

Yes and also physical objects that are moving in the reference frame. Here's your original definition:

Note how you said the frame of reference is the collection of physical objects and the 3D coordinate system is optional.

Here's my correction:

Note how I said the frame of reference is a 4D coordinate system and the physical objects (moving or stationary) are optional.

I then added:

An event in SR is a particular set of the four coordinate values in a particular coordinate system. It doesn't matter if there is a physical object or anything happening at that place at that time and there are an infinite number of events along each of the coordinates.

Even when Einstein built the concept of a FoR using rigid rulers connecting synchronized clocks at various locations, he made it clear that these were imaginary (as harrylin pointed out in post #34). If you required physical objects (physical clocks connected by physical rigid rulers) filling the universe to define a FoR, there would be no room for any other physical objects to move around and what about an event that was at the middle of a rigid ruler where there was no clock or an event that was in the middle of a clock? How would you define those events? And think about what happens when you take the coordinates of an event in one FoR and convert them into the coordinates of the same event in a second FoR moving with respect to the first one, the calculation can result in an arbitrary location where there may not be a clock if you follow the physical idea of a FoR.

To restate: a Frame of Reference is defined by Einstein as a 4D coordinate system empty of any physical objects and then you add in whatever physical objects you want and describe their positions and motions in terms of events, precise and exact with infinite resolution. Not only do you not require any "observers" you don't require anything at the origin or anywhere else or at any particular time. You do what you want.

At this point, I am starting to lose you. Perhaps I should point out what the experimenter who validates relativity is doing. We have been talking about what the theorist considers a reference frame. What does the experimenter consider a reference frame?
An experimenter working on relativity usually has an array of detectors that determine when certain events occur. Almost always, these detectors have a zero velocity relative to each other. These detectors do not have to been near each other. In fact, they are often far away from each other. However, they are usually stationary with respect to each other.
This set of detectors determines a reference frame. I will refer to this as the first reference frame.
Suppose the experimenter has a second set of detectors that are moving at a a single velocity relative to the first with respect to the detectors in the first reference frame. It is easy to prove that if all these detectors are moving at the same nonzero velocity relative to any detector in the first reference frame, then they are not moving with respect to each other. This second set of detectors determines a second reference frame.
The experimenter can have any number of detectors. Every set of detectors that are not moving relative to each other determines a reference frame. If there is a set of detectors which are stationary with respect to each other, then any detector moving at a nonzero velocity is not part of this reference frame.
Relativity produces theoretical results that are specific to a reference frame. The experimenter validating relativity does relativity calculations specific to each reference frame in his experiment. If he does calculation for one reference frame, then he examines the detectors that are stationary in that reference frame. He does not include measurements from detectors that are part of a different reference frame.
Sometimes, the experimenter tries to compare the difference between measurements of two detectors that are in different inertial frames. For example, suppose the experimenter wants to compare two clocks that are moving at different velocities.
Suppose the experimenter is comparing measurements of two similar detectors that are moving at high velocity relative to each other. Because of signal delay, the results will be ambiguous unless the two detectors happen to be located at the same place at the same time. Einstein presented the hypothesis that two events can only be proven simultaneous unless they are coincident in space.
The ambiguity in simultaneity is a practical and unavoidable problem in engineering. Therefore, experimenters don't compare detectors corresponding to different inertial frames unless the two detectors are very close together.
In experimental practice, the reference frame is really determined using the detectors. The difference between the experimenters reference frame and the theorists reference frame is in number. The experimenter always works with a finite number of detectors.
Einstein's hypothetical reference frame had an infinite number of detectors. However, infinity is just a limit. What this means is that the theory can work with any number of detectors. In practice, one works with a finite set of detectors that are close to stationary with respect to each other. As long as the detectors are sufficiently stationary with respect to each other, they are close enough to being a reference frame.
An inertial frame is a type of reference frame. An inertial reference frame is a reference frame where there is no force applied to any of the detectors. As long as the total force acting on any detector is zero, the reference frame is an inertial frame.
Thus, the state of the detectors unambiguously determines what the experimenter decides is the reference frame, and whether it is inertial. If there is any "art" involved in experimentation, it is in making sure that the detectors approximately satisfy these approximations. As in all physics, reality is always slightly different from the theory. However, the criteria for reference frames is logically unambiguous when one considers the detectors.

 

[Chestermiller]

To restate: a Frame of Reference is defined by Einstein as a 4D coordinate system empty of any physical objects and then you add in whatever physical objects you want and describe their positions and motions in terms of events, precise and exact with infinite resolution. Not only do you not require any "observers" you don't require anything at the origin or anywhere else or at any particular time. You do what you want.

Yes, I can see evolving to this definition, but along the way, the clocks, meter sticks, and train examples are very helpful to the learning process. I can also see that the Lorentz Transformation represents the geometric relationship between two 4D coordinate systems that are offset from one another.

 

[harrylin]

Not all objects "in a reference frame" are "part of a reference frame." [..]

Yes indeed. Why did you add that as comment to my post? The point that I and others brought up is that the OP seems to think that a standard reference frame such as used in SR is of limited extension, which is wrong.

By the way (and this has nothing to do with your post), the coordinate systems that Einstein describes in his 1905 paper are very standard, made up of 3 coordinate axes ("each of three rigid material lines"), and so he can place a watch at the origin of such a system. By means of rulers and clocks he defines standard reference systems with "co-ordinates and times". And while according to his definition the related reference clocks must be at rest in the coordinate system, this is not the case in the ECI frame, for purely practical reasons.

 

[ghwellsjr]

At this point, I am starting to lose you. Perhaps I should point out what the experimenter who validates relativity is doing. We have been talking about what the theorist considers a reference frame. What does the experimenter consider a reference frame?

You're right, this forum is to help people learn the theories of relativity (SR and GR). We assume they have already been validated. I doubt that any experimenters who are still trying to validate them are coming here to learn how to perform their experiments.

But since you have pointed out that you are talking about something different, I don't know why you are losing me. Just remember, I'm trying to help people who don't understand Special Relativity learn what the theory is, not how to do any experiments to validate (or invalidate) it.

For that reason, I don't have any comments on the rest of your post.

 

[ghwellsjr]

Yes, I can see evolving to this definition, but along the way, the clocks, meter sticks, and train examples are very helpful to the learning process.

I agree and would even go back to what scientists believed prior to Einstein (ether) so that the learner can understand what the problem was that SR solved. They believed in a single absolute ether rest state in which light propagated at c and since the Earth and all of us observers were moving in that "frame", we must be experiencing length contraction and time dilation, although by an unknown amount, since the stationary state of the ether was indeterminate. Einstein said you could pick any inertial state in which you presume that light propagates at c and in which you presume that stationary objects do not experience length contraction or time dilation and from this you can build a Frame of Reference.

I can also see that the Lorentz Transformation represents the geometric relationship between two 4D coordinate systems that are offset from one another.

The geometric relationship between two 4D coordinate systems (in the standard configuration) is simply a constant speed between the x-axes. The Lorentz Transformation is how you convert the specific coordinates of one frame into the corresponding coordinates of a second frame.

 

[Chestermiller]

I agree and would even go back to what scientists believed prior to Einstein (ether) so that the learner can understand what the problem was that SR solved. They believed in a single absolute ether rest state in which light propagated at c and since the Earth and all of us observers were moving in that "frame", we must be experiencing length contraction and time dilation, although by an unknown amount, since the stationary state of the ether was indeterminate. Einstein said you could pick any inertial state in which you presume that light propagates at c and in which you presume that stationary objects do not experience length contraction or time dilation and from this you can build a Frame of Reference.

The geometric relationship between two 4D coordinate systems (in the standard configuration) is simply a constant speed between the x-axes. The Lorentz Transformation is how you convert the specific coordinates of one frame into the corresponding coordinates of a second frame.

I never mentioned the Standard Configuration in any of my posts. I don't know where you guys got the idea that I was restricting my thinking to the Standard Configuration. Also, I might mention that, even in the Standard Configuration, the orientation of the x-axis in 4D spacetime is not the same as the orientation of the x' axis. I've been working with, and deriving, much more-advanced forms of the Lorentz Transformation than the simple form specific to Standard Configuration.

Chet