# Defining a rest frame in the real world

1. Apr 4, 2014

### analyst5

Hey guys, as we know the concept of the rest frame is one of the most famous concepts in any kind of relativity, because it must be known in which frame the body is at rest.

My question is how do we define a rest frame on a solid object that has atoms vibrating, the body clearly does not have motion as a whole, it remains in place in some kind of way, but its atoms are vibrating and it isn't at rest in a different way. So what is different between standard analogy in SR between frames that are mutually at rest, and in real life when bodies are much more complex? What are the criteria?

2. Apr 4, 2014

### phinds

A rest frame is a mathematical construct that does not exist in reality, so your problem isn't a problem. You can pick an XYZ system based however you like and that is your frame of reference. If atoms then jiggle in that frame of reference, then so be it. You could pick a frame of reference based on the the center of the nucleus of one atom and then that atom as a whole would be at rest in that frame of reference but its electrons would not.

For most issues in SR, you're getting too far down in the weeds. Just pick a frame of reference and then assume that the objects you are talking about (a ball, for example) act like a point vis a vie that frame of reference.

3. Apr 4, 2014

### Staff: Mentor

If the net external force on an object is zero, its center of mass moves inertially (constant velocity), regardless of the individual motions of its component atoms. The object's "rest frame" is the inertial reference frame in which the center of mass is at rest.

4. Apr 4, 2014

### phinds

How is that different than what I said?

5. Apr 4, 2014

### Staff: Mentor

As phinds mentioned, rest frames are not part of "the real world", they are part of an analysis. Now, if your analysis assumes that a given object is at rest in an inertial reference frame (e.g. because you have excluded external forces or because you have used an accelerometer to measure the acceleration and it is measured as 0) and in fact there is some residual undetected acceleration, then you can mathematically analyze how much of an impact that error will cause in your final results. If that error is less than the precision of your measuring instruments for your experimental setup then the deviations don't matter and the assumption is valid.

6. Apr 4, 2014

### WannabeNewton

It's only "famous" because bad SR textbooks make it seem way more important than it actually is

Anyways, I seem to recall this being explained to you multiple times in the past. You cannot define a rest frame for a non-rigid body, no matter its state of motion. A body must be rigid (rotating or non-rotating) in order for a rest frame for the entire body to even make sense.

7. Apr 4, 2014

### DrStupid

p=0 and maybe L=0

8. Apr 4, 2014

### Staff: Mentor

As an engineer, I'm not sure I agree - maybe it is just a different way of thinking or an issue of theory vs practice:

If an architect designs a house, they have a model that exists only mathematically, in a computer. But when it gets built, you can then point to the real point in space that corresponds to the points in the model. It is diffult for me to conceive of why a real object can't be said to have a real reference frame.

9. Apr 4, 2014

### jkl71

Suppose you have a meter stick and you are in its real rest frame, along with observers on each end of if. Now you accelerate in the direction along it. You’ll observe it to contract. The two ends get closer, from your perspective the observers on each end are in different rest frames, the observers on each end would both say they haven't changed frames and are still in the real rest frame.

To me the basic point is just that picking a reference frame in special relativity is analogous to picking a coordinate system in Newtonian mechanics, there’s nothing special or fundamental about it.

10. Apr 4, 2014

### Staff: Mentor

I see your point, this may be a personal prejudice of mine, but, as you know, a reference frame corresponds to a set of orthonormal basis vectors defined at each event in spacetime. At a whim, the researcher can use a different set of basis vectors and get all of the same physical results.

I do like the blueprint analogy. Many features of a blueprint, such as the size of a window, cannot be changed without changing the "real world" thing that is built. But a blueprint also has features, such as the font, which can be changed without changing the "real world" thing. I would put things like the invariant mass in the "window size" category and things like the reference frame in the "font" category. Whatever you might claim about the "real world" status of the windows in a blueprint, surely you would not claim the same for the font.

11. Apr 7, 2014

### analyst5

@Wannabe Newton, you're right that we've had a discussion regarding this and I apologize if I'm bringing old stuff up, but it's clear that I still have some work to do in understanding.

This was you original post from the last thread:

I've red everything you wrote here, and it's a great post to begin with, but it's clear as I understand, that the definition of rigidity in SR is different than in classical mechanics. So you wrote here that we can talk about rest frames of the whole object, except in the case when the object isn't undergoing Born rigid acceleration and accelerates in a different manner.

12. Apr 7, 2014

### WannabeNewton

Yes, it is very different indeed. At least within the confines of SR, Born rigid motion is in fact a much more restrictive notion of rigidity than the Newtonian one, particularly in the context of rotational motion. This is because of a rather deep theorem in SR which states that the world-lines of any rotational Born rigid motion are necessarily flow lines of flat space-time isometries (i.e. those transformations which leave invariant the Minkowski metric).

13. Apr 8, 2014

### pervect

Staff Emeritus
If I might suggest, as far as vibration goes, just cool everything down low enough so it stops, then it's not a "real world issue". Then you analyze everything relative to the cold, non-vibrating frame.

I seem to recall that vibration of the atoms affects the rates of atomic clocks, so the most accurate ones need to be cooled, so atomic vibration issue is actually an issue if you want the maximum achieveable accuracy in timekeeping.

14. Apr 8, 2014

### analyst5

I get that WBN, thanks. But during the non-accelerated period of motion of the object, the inertial one, it seems reasonable to define a rest frame for the whole object where there are no radial velocities between its components and all parts move with the same velocity, right? In a restricted sense of rigidity of course.

15. Apr 8, 2014

### analyst5

I mean, in all examples of SR there is a frame associated with the body as a whole, a global rest frame which brings up all the points that are at rest together when the body is undergoing inertial motion and no acceleration is measured. And it seems that a body maintains the distances between its points after each point has accelerated, so that we can define a rest frame. Even the terms proper length and proper time are associated with the rest frame of the object as a whole, but I understand why the object 'loses' its rigidity during acceleration if it's not done in a Born rigid manner. So what is the answer? Some discutants clearly assign a rest frame to the body as a whole, and we can then indeed measure the proper length of the object at least in some phases of its motion (except acceleration). Note that I'm coming to this question from more of a philosophical standpoint, than from a point of measurement, even though of course the measurements are priority and they are the basis of this topic and physics in global. And assigning things like rest frames also.

16. Apr 8, 2014

### WannabeNewton

What exactly is the question? As an aside, the answer to your question in post #14 is "yes".

17. Apr 8, 2014

### analyst5

That's enough then, I was confused with your first post on this thread. Thank you very much