# Definition of Frame of Reference

1. Jul 28, 2012

### Staff: Mentor

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

2. Jul 28, 2012

### phinds

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

3. Jul 28, 2012

### ghwellsjr

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.

4. Jul 28, 2012

### phinds

Excellent correction. Thank you.

5. Jul 28, 2012

### 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 in to what is happening than any inertial FoR would provide.

6. Jul 28, 2012

### 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?

7. Jul 28, 2012

### Staff: Mentor

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 :)

8. Jul 28, 2012

### phinds

:rofl:

9. Jul 28, 2012

### ghwellsjr

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, any one 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.

10. Jul 28, 2012

### phinds

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.

11. Jul 28, 2012

### ghwellsjr

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.

12. Jul 28, 2012

### Mark M

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.

13. Jul 28, 2012

### phinds

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

14. Jul 28, 2012

### 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,Î¸,Ï†) 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.

15. Jul 28, 2012

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)

16. Jul 28, 2012

### Staff: Mentor

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

17. Jul 29, 2012

### pervect

Staff Emeritus
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.

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.

18. Jul 29, 2012

### Vandam

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...

19. Jul 29, 2012

### Staff: Mentor

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?

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.

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.

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.

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

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.

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

Last edited: Jul 30, 2012
20. Jul 29, 2012

### Staff: Mentor

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

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.

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.

Last edited: Jul 30, 2012
21. Jul 30, 2012

### pervect

Staff Emeritus
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.

22. Jul 30, 2012

### Vandam

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.

23. Jul 30, 2012

### 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?

24. Jul 30, 2012

### Staff: Mentor

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

25. Jul 30, 2012

### Staff: Mentor

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.