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loislane
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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?
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.DrGreg said:What makes you think they are "left out of the theory"?
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.loislane said: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.
loislane said:answer first the thread's title question
"mu"?? what is that?PeterDonis said:The answer to that question is "mu".
Ok, how exactly. You mean for instance that measuring standard rods are contracted?Standard rods and clocks are affected by LC and TD.
loislane said:"mu"?? what is that?
loislane said:You mean for instance that measuring standard rods are contracted?
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.loislane said:"mu"?? what is that?
Anything with a length is length contracted when not observed in its rest frame..loislane said:Ok, how exactly. You mean for instance that measuring standard rods are contracted?
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.
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.Ibix said:Anything with a length is length contracted when not observed in its rest frame..
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...loislane said: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.
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.loislane said: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 which to judge the LC and TD in the moving frames.
So you are confirming that measuring rods and clocks with which 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 which makes it more flexible too).Ibix said: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.
I'm really not sure what you think I'm saying.loislane said:So you are confirming that measuring rods and clocks with which 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 which makes it more flexible too).
loislane said:this point is not addressed or explained in the theory,i.e. there is not a relativistic theory of matter that justifies it
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.loislane said:you are saying that length contraction can be measured with a contracted ruler?
Ibix said: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.
PeterDonis said: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.
You must have missed my point, I mean what Einstein and Born say in the references mentioned above.Dale said: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.
There are no rigid bodies, but there are bodies which move rigidly (Born rigid motion).loislane said:Now in SR there are no rigid bodies
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.Dale said:There are no rigid bodies, but there are bodies which move rigidly (Born rigid motion).
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".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.
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.loislane said:six d.o.f. are needed to account for all possible rigid motions,
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.loislane said:so I don't think Born rigidity is relevant in this discussion.
Most modern approaches don't even bother. They come at it from a symmetry approach.loislane said: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".
loislane said:six d.o.f. are needed to account for all possible rigid motions
Dale said:I think that the whole topic of rigidity is irrelevant.
loislane said:in SR there are no rigid bodies
loislane said:Minkowski geometry is not even a metrical(in the euclidean sense of distance function) geometry
loislane said: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?
H-N theorem says what you write between parenthesis only.PeterDonis said:In Newtonian physics, yes. Not in relativity. That is what the Herglotz-Noether theorem says (it's the theorem that says that all possible Born rigid motions can be described with only three degrees of freedom). Motions that do not meet the conditions of the H-N theorem are not rigid when relativistic effects are taken into account, even though they might seem to be in the Newtonian approximation.
Nobody stated that, only that one has to stipulate it tacitly without justification within the theory,and the claim is made by Born and Einstein.PeterDonis said:Not if it's going to be used to justify the statement that it's impossible to have measuring rods and clocks in SR. Then it does need some discussion in order to refute that erroneous statement. See my next post.
This was already settled by Laue in 1911 when it showed that rigid bodies cannot exist in SR so it is not worth arguing. You can accesss the paper here googling:"On the discussion concerning rigid bodies in the theory or relativity" by von Laue.PeterDonis said:This is not correct.
Minkowski spacetime does have a metric tensor for sure, I used the word metric with the meaning it has for instance in "metric space". And of course Minkowski spacetime is defined as an affine space with a metric tensor.The lack of a positive definite metric does not mean Minkowski spacetime does not have a metric and is just an affine geometry.
The problem comes when defining in a non-tautological way what an ideal clock is. And also in guaranteeing that it is not altered when transported. You have to stipulate it in an ad hoc way unrelated to the Minkowskian geometry and the Lorentz symmetry.Ibix said:Isn't Einstein making a distinction without a difference with his talk of two classes of objects? Any old atom is a clock - kick it into an excited state and watch what it emits when it decays. Any array of atoms is a ruler. Diffract some x-rays off it and see what you get.
What am I missing?
Ibix said:Isn't Einstein making a distinction without a difference with his talk of two classes of objects? Any old atom is a clock - kick it into an excited state and watch what it emits when it decays. Any array of atoms is a ruler. Diffract some x-rays off it and see what you get.
What am I missing?
Well if you restrict to 2-dimensional Minkowski diagrams you are right. But not in the more realistic 4-dimensions.Dale said: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.
The problem is the symmetry in this case doesn't address the issue of the stability of measuring rods and clocks in the absence of rigid rulers, that is the sense of Einstein's lament.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.
loislane said: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?
loislane said:Well if you restrict to 2-dimensional Minkowski diagrams you are right. But not in the more realistic 4-dimensions.
The problem is the symmetry in this case doesn't address the issue of the stability of measuring rods and clocks in the absence of rigid rulers, that is the sense of Einstein's lament.
Not exactly. It is because the assumption about physical validity of ideal clocks and rods unaffected by LC/TD is undoubtedly confirmed empirically by the stability of atoms and their spectra that we can do that "reverse engineering".FieldTheorist said:Ah, but they are affected by relativistic effects (GR and SR). That's actually why they're useful. Standardized objects are objects that are forced to do something very precise by nature. Let's take the type-1A supernovas. They are forced to emit a certain spectrum of light. So if you know that when the light's wavelength was when it was emitted, e.g. ## \lambda ##, and you observe it with a wavelength of ## \lambda ' ##, you can figure out how much the wavelength has been stretched whilst it traveled across spacetime, e.g.
[itex] \frac{\lambda '}{\lambda} = a[/itex]
where a is a parameter that comes from GR. Thus, by knowing how much the light has been stretched due to GR, you can use GR to reverse engineer (reconstruct) the distance that the supernova is away from you.
Even in 4D spacetime 3 degrees of freedom for Born rigid motion are more than enough to investigate the LT.loislane said:Well if you restrict to 2-dimensional Minkowski diagrams you are right. But not in the more realistic 4-dimensions.
Again, so what? Why does that issue need to be addressed?loislane said:The problem is the symmetry in this case doesn't address the issue of the stability of measuring rods and clocks in the absence of rigid rulers
The concern is Einstein's actually. I'm trying to come to terms with it.stevendaryl said:Could you relate this concern with nonideal clocks and measuring rods back to your original post? You were asking why ideal clocks and measurement rods are assumed to be unaffected by Lorentz contraction and time dilation. But that's not true, so isn't the original question answered?
Not at all. Non inertial frames and accelerations hace not entered the discussion and they are anyway taken care by the clock postulate. SR tests are conclusive.I'm having trouble understanding your concern about nonideal clocks and rods. Is it that you are worried that the actual clocks and rods used in tests of SR might be affected by acceleration in such a way as to mimic the effects of SR? And so tests of SR might not be conclusive?
Not if you include rototranslations and those are motions found in physics.Dale said:Even in 4D spacetime 3 degrees of freedom for Born rigid motion are more than enough to investigate the LT.
Ok, that's great. How dou you interpret Einstein's concern in that quote.Again, so what? Why does that ah issue that needs to be addressed?
If we assume that the laws of physics have the appropriate symmetries then we get the Lorentz transform, regardless of whether or not those laws include rigid objects. This is the point of the symmetry approach, it does not depend on any specific laws, it comes directly from the symmetries.
I just don't see a problem here.