## Definition of Frame of Reference

 Quote by Chestermiller 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

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 Quote by Chestermiller 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?

 Quote by Chestermiller 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.

 Quote by Chestermiller (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.

 Quote by Chestermiller 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.

 Quote by Chestermiller 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.

 Quote by Chestermiller 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.

 Quote by Chestermiller 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.

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 Quote by Vandam 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.

 Quote by Vandam 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.

 Quote by Vandam 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.

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 Quote by 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
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.

 Quote by PeterDonis 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.

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 Quote by Chestermiller 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?

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 Quote by Vandam 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"?

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 Quote by Vandam 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.

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 Quote by 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. 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. 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. 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. "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.

 Quote by jtbell 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?

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 Quote by Vandam 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.

 Quote by Vandam 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.

 Quote by Vandam I know you have big problems with this approach.
I'm not sure you really understand my position. See comments above.

 Quote by PeterDonis 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.

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 Quote by Vandam 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.

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 Quote by Vandam 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.

 Quote by PeterDonis 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.

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 Quote by Vandam 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.

 Quote by Chestermiller [..] 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.