# B Why aren't standard rods and clocks affected by LC and TD?

1. Jan 30, 2016

### loislane

Are measuring rods and clocks(the ones that are used as reference to ascertain LC and TD of the relatively moving rods and clocks) left out of the theory in principle?

2. Jan 30, 2016

### DrGreg

What makes you think they are "left out of the theory"?

3. Jan 30, 2016

### loislane

That's what I am asking. Are they? Maybe answer first the thread's title question, and if that is explained by the theory then there is no need to answer the question in post #1.

4. Jan 30, 2016

### Staff: Mentor

The question was how did you come to assume this, and it's a justified question. Being rude is not the way we want to talk to each other.

5. Jan 30, 2016

### Staff: Mentor

The answer to that question is "mu". Standard rods and clocks are affected by LC and TD.

6. Jan 30, 2016

### loislane

"mu"?? what is that?
Ok, how exactly. You mean for instance that measuring standard rods are contracted?

7. Jan 30, 2016

### Staff: Mentor

It means that there is no valid answer to the question, because the question itself is not well-posed. For a quick reference, see here:

Yes; a standard measuring rod appears to be shorter relative to a frame in which it is moving, compared to a frame in which it is at rest.

8. Jan 30, 2016

### Ibix

Allegedly, it's a Chinese word used to mean "your question contains unexamined assumptions". For example - "have you stopped beating your wife?" If you answer yes, you imply that you used to beat her. If you answer no you imply that you continue to beat her. If you answer mu you point out that the question is structured on the assumptions that you have a wife and that you did beat your wife at some point in the past, and these assumptions should be examined before asking the question.

I don't speak a word of Chinese, so can neither confirm nor deny the accuracy of that, but Peter seems to be using it in that sense to address your title question.

Anything with a length is length contracted when not observed in its rest frame..

9. Jan 30, 2016

### loislane

Ok, thanks for the chinese class.
Here's the thing. I wonder how can one determine that some rod is contracted if the ruler one is using(even if only conceptually or ideally) is also contracted.
Maybe you are familiar with a thought experiment by Poincare about all the scales in the universe changing overnight, including the measuring rulers of course. And how nobody would notice since measurements would remain unaltered so the change would not really be physical.
Now in SR surely there are physical consequences but if I understood your reply you are saying that length contraction can be measured with a contracted ruler?
I don't think so, I guess you mean that the contraction of a moving rod is always compared with a Standard ruler that is not contracted, otherwise no contraction can be measured even in principle.
Now my question was if SR accounts for the fact that ideal clocks and rods cannot undergo dilation and contraction even in principle if they are to serve as standards against wich to judge the LC and TD in the moving frames.

10. Jan 30, 2016

### strangerep

Consider the "paradox" of the pole and the barn. Let's suppose that, when both are stationary, they have been measured (using standard rods) and the pole is found to be slightly longer than the barn. Upon boosting the pole, one encounters the well known paradox (also known as the ladder paradox). It is resolved by careful examination of simultaneity issues. I suspect the same thing applies for your question -- one must consider carefully how one would "compare" the rods...

11. Jan 30, 2016

### Ibix

Length contraction and time dilation are always things that happen to other people. You will never be able to measure it happening to you because, as you say, your own rulers and clocks would rescale. This is kind of the point of relativity - you can always consider yourself to be at rest (as long as you aren't accelerating), so your rods are always their standard length. If they changed, this would imply that there was some absolute rest frame that you weren't in any more.

You can use your rods and clocks to observe length contraction and time dilation in moving rods and clocks. Simply deploy your rods, synchronise your clocks and, at some agreed time, record the positions of the ends of the moving rod. It'll come in short. Two photos of the same moving clock some time $\Delta t$ apart will show a smaller elapsed time. These effects are symmetric, of course. An observer at rest with respect to the moving rods would observe your rods to be length contracted and your clocks to be time dilated.

So there is no "standard" rod. There is only a rod that is at rest with respect to you. That one is not length contracted according to you; any rods in motion with respect to you are contracted.

12. Jan 30, 2016

### loislane

So you are confirming that measuring rods and clocks with wich I am always referring to the ones that measure in the moving frame(and I already mentioned that it is understood this measurement is ideal but this doesn't detract from its physicality or we wouldn't have a physical theory to begin with) do not contract and dilate by definition(to avoid the rescaling issue), and that this point is not addressed or explained in the theory,i.e. there is not a relativistic theory of matter that justifies it(or LC and TD themselves, the theory doesn't enter into this wich makes it more flexible too).

13. Jan 30, 2016

### Ibix

I'm really not sure what you think I'm saying.

Measuring rods that are moving with respect to me will be contracted if I measure their length using rods at rest with respect to me and clocks synchronised according to the Einstein convention. However, someone at rest with respect to the moving rods using clocks synchronised with the same procedure will define their rods to be non-contracted and use them to measure my rods to be contracted.

The relativistic theory of matter would be quantum field theory - you'll have to ask (e.g.) @PeterDonis about that. However, one can see length contraction and time dilation as merely being the consequence of choosing different coordinate systems. I don't really need a theory of matter to explain a square turning into a diamond and back into a square as I rotate it, and I'm doing something quite similar when I change my choice of frame.

14. Jan 30, 2016

### Staff: Mentor

LC and TD are not things that require a theory of matter; they only require a theory of spacetime and kinematics, which is what SR is. When you measure a ruler moving relative to you to be length contracted, using a ruler at rest relative to you, you are not measuring something that physically happened to the moving ruler; you are measuring something that arises from the way spacetime works. It's the spacetime analogue of looking at an object from a different angle in ordinary 3-dimensional geometry; it doesn't change anything about the object you're looking at.

15. Jan 30, 2016

### Staff: Mentor

Yes. If Alice and Bob are moving relative to each other then in Alice's frame Bob's rulers are contracted and in Bob's frame Alice's rulers are contracted.

16. Jan 31, 2016

### loislane

Yes, all that is of course right and I'm aware of it and agree about SR not needing a theory of matter, that being probably a strong point as it makes the theory adaptable to possible different theories of matter. But I want to refer here to a point where the analogy with euclidean 3-geometry as presented by PeterDonis and Ibix(in the example of the square rotation) no longer works because we don't have the same tools and therefore cannot justify certain stipulations or tacit assumptions in the same way in euclidean geometry as in Minkowski geometry.

If I may elaborate it to achieve a better understanding this point can be summarized in the words of Max Born ("Einstein's theory of relativity" 1965 pg 211) by "The principle of the physical identity of the units of measure", or in other words any object that can act as a rigid ruler in the rest frame S retains that role in its new rest frame S' when boosted and the same tacit assumption hold for ideal clocks. Or as Einstein put it("The consequences of the principle of relativity in modern physics" 1910):"It should be noted that we will always implicitly assume that the fact of a measuring rod or clock being set in motion or brought back to rest doesn't change the length of the rod or the rate of the clock".
This stipulation was further stressed by Born in the above mentioned reference that I paraphrased but I quote here literally:"...it is a ssumed as self-evident that a measuring rod wich is brought into one system of reference S and then into another S' under exactly the same physical conditions would represent the same length in each, and the same would be postulated for clocks...[...] This is the feature of Einstein theory by wich it raises above the standpoint of a mere convention and asserts definite properties of physical bodies."(Born 1965 pp. 251-252)
The relevance of this tacit assumption that must be added in an ad hoc form to the theory since it is not justified nor derived from the mathematical formalism of the Minkowskian geometry and in this sense to answer Dr. Greg's question, one could say raher than being left out of the theory it is more appropriate to say that the theory separates artificially the measuring tools from the rest of the theory. Maybe it is best to use again Einstein's own words("Autobiographical notes" 1949):
"One is struck [by the fact] that the theory [of special relativity] [...] introduces two kinds of physical things, i.e., (1) measuring rods and clocks, (2) all other things, e.g., the electromagnetic field, the material point, etc. This, in a certain sense, is inconsistent; strictly speaking measuring rods and clocks would have to be represented as solutions of the basic equations (objects consisting of moving atomic configurations), not, as it were, as theoretically self-sufficient entities. However, the procedure justifies itself because it was clear from the very beginning that the postulates of the theory are not strong enough to deduce from them sufficiently complete equations. If one did not wish to forego a physical interpretation of the co-ordinates in general (something which, in itself would be possible), it was better to permit such inconsistency, with the obligation, however, of eliminating it at a later stage of the theory. But one must not legalize the mentioned sin so far as to imagine that intervals are physical entities of a special type, intrinsically different from other physical variables (‘reducing physics to geometry’, etc.)".

Now to come back to where the analogy used by PeterDonis breaks, it is trivial to see that euclidean geometry as a metric geometry that has a clear concept of rigid bodies and rigid rulers and thus has no difficulty justifying that even though we may observe changed lengths from our perspective the object measured in its position always retains its length as measured by any rigid ruler. Now in SR there are no rigid bodies since they contradict the theory(it would be possible to transmit info faster than light) so we don't have the luxury of deriving from their existence, like it is done in euclidean geometryand the 3D geometric example given by PD, the universality of standard lengths of rulers and rate of clocks mentioned by Born and Einstein and necessary to give the theory any physical meaning(that is to avoid the view that everythig amounts to "optical effects" and perspectives without physical consequences, this view is obviously false since we can observe the physical consequences in particle physics experiments, and all tests of SR to date (Hafele and Keating etc....). Minkowski geometry is not even a metrical(in the euclidean sense of distance function) geometry, it is an affine geometry without a notion of rigid ruler transportable to distant or rotated objects, it only allows parallel transport.

17. Jan 31, 2016

### loislane

You must have missed my point, I mean what Einstein and Born say in the references mentioned above.

18. Jan 31, 2016

### Staff: Mentor

There are no rigid bodies, but there are bodies which move rigidly (Born rigid motion).

Furthermore, if the laws of physics are the same in inertial frames then identically constructed clocks will keep time the same, so you can simply build the clock to be initially at rest in different frames.

19. Jan 31, 2016

### loislane

True, but as you probably know Born rigid motions are limited to three degrees of freedom and six d.o.f. are needed to account for all possible rigid motions, so I don't think Born rigidity is relevant in this discussion.

Yes, this is the first postulate of SR, the implicit stipulation that Born and Einstein talk about above can be seen as part of it or as added third postulate making sure the equivalence of physical laws in all inertial frames is implemented. But again it remains artificial to have to make measuring rods and clocks special and having a special stipulation for them because unlike the case in classical mechanics the geometry doesn't allow rigid rulers so it is necesary to stipulate additionally a "principle of physical identity of the units of measurement".

Last edited: Jan 31, 2016
20. Jan 31, 2016

### Staff: Mentor

So what? You only need to be able to get enough motion to determine the Lorentz transform. As far as I can tell a single degree of freedom is more than sufficient.

Here I agree. I think that the whole topic of rigidity is irrelevant. However, insofar as rigidity is at all relevant it must be Born rigidity since that is the only rigidity compatible with SR.

Most modern approaches don't even bother. They come at it from a symmetry approach.

If you find yourself dissatisfied with the postulates, I would recommend looking into symmetry-based approaches rather than trying to patch up the postulates.