Length contraction and time dilation

[PeterDonis]

if that is indeed the case, then how was the LT applied to the M-M experiment in the first place, since the Earth does not move at a relativistic speed?

Because the M-M experiment was measuring interference fringes of light, which is a much more sensitive measurement than the one you proposed, and which can therefore distinguish much smaller effects. M-M had calculated the size of the effect they expected to see, and it was more than large enough to be distinguished by their apparatus. That's why its absence was so surprising: because the effect they expected to see wasn't just at the borderline of detection, it was something they expected to see loud and clear in their data.

 

[robphy]

As @PeterDonis notes, this is essentially the Michelson-Morley apparatus, as described in special relativity to explain the null result, which was unexpected from a pre-SpecialRelativistic viewpoint.
( https://en.wikipedia.org/wiki/Michelson–Morley_experiment ).
The apparatus was a clever way to measure the expected time-difference in the round trips since high-precision clocks weren't available then.

I bolded my earlier comment.

 

[Jim Fern]

And yet the original transform for length contraction was invented and applied, what was it, maybe two years after the 1887 experiment had been conducted, and thus about eight years after the first, since Fitzgerald had tried to get one of his pupils, W. Preston, to publish its earliest form in his 1890 book? Where were the prior observations, and what were they specifically, that proved the contraction? They had what they would consdier a hypothesis, but it really couldn't have been that since it was contrived without observation of any particular phenomenon...only an interpretation of experimental data. They should've at least tried to observe this even after the scientific method was not completely satisfied. Where are those observations recorded? I would really rather not have to hang my hat of research on a formula that was derived a priori. All I'm trying to do is find observations that led to it. I know I sound like a broken record, but I love science, and even more I love history. Thanks.

 

[PeterDonis]

the original transform for length contraction was invented and applied, what was it, maybe two years after the 1887 experiment had been conducted

Yes.

Where were the prior observations, and what were they specifically, that proved the contraction?

What? The M-M experiment itself, and the totally unexpected null result, doesn't count as a prior observation?

I don't think you have thought this through very well. When you have an observation that doesn't match the current theoretical models, what else can you do but come up with new models that could account for it? That's exactly what the contraction was: a new, hypothesized theoretical model to account for the unexpected null result of the M-M experiment. What's wrong with that? That's how science progresses.

They had what they would consdier a hypothesis, but it really couldn't have been that since it was contrived without observation of any particular phenomenon...only an interpretation of experimental data.

I don't know where you are getting this weird rule for what can count as a "hypothesis". Certainly not from "the scientific method" or the history of science.

They should've at least tried to observe this even after the scientific method was not completely satisfied.

Observe what? Length contraction? If the M-M result itself doesn't count as such an observation, how would they do that? You have already admitted that your proposed experiment with a steel rod and lasers is not practical, now, in 2021. How are you expecting scientists in the 1880s to directly observe length contraction?

All I'm trying to do is find observations that led to it.

And it seems to me that you have such an observation staring you in the face--the M-M experiment itself--but your weird rules about how you think science is supposed to be conducted, which have no valid basis that I can see, are preventing you from seeing it.

 

[PeroK]

And yet the original transform for length contraction was invented and applied, what was it, maybe two years after the 1887 experiment had been conducted, and thus about eight years after the first, since Fitzgerald had tried to get one of his pupils, W. Preston, to publish its earliest form in his 1890 book? Where were the prior observations, and what were they specifically, that proved the contraction? They had what they would consdier a hypothesis, but it really couldn't have been that since it was contrived without observation of any particular phenomenon...only an interpretation of experimental data. They should've at least tried to observe this even after the scientific method was not completely satisfied. Where are those observations recorded? I would really rather not have to hang my hat of research on a formula that was derived a priori. All I'm trying to do is find observations that led to it. I know I sound like a broken record, but I love science, and even more I love history. Thanks.

Well, of course, an important point about mathematics and physics is that the history of how theorems and theories came about is irrelevant to their validity. You can always start with a clean sheet of paper and develop the theory afresh.

In terms of space and time, for example, you can start with a few basic assumptions about homogeneity and isotrophy and show that there are only two possibilities:

1) Newtonian space and time, withe the Galilean transformation.

2) SR spacetime, with the Lorentz transformation.

To decide between the two you need an experiment: any experiment that distinguishes between the two options will do. One option is that you build a particle accelerator and give particles enough energy so that if 1) were the case they would be traveling at hundreds of times the speed of light; and, if 2) were the case they would only be getting close to the speed light.

In any case, 1) and 2) imply very different theories of energy and momentum. All of modern physics at high energies uses the SR theory of energy and momentum. It is of no practical relevance how the theory came about or whether length contraction is practically testable. The theory of SR rests on its wider predictions at the heart of particle physics, general relativity and quantum field theory.

 

[bhobba]

I guess the crux of it is this: according to the scientific method, if something can't be observed, then how can it be tested? (I do hope that yet another rule that I may not have noticed or yet committed to memory arises here.)

I think you may need to start to think of SR differently. In the 19th century, mathematicians discovered many different geometries, not just Euclidian Geometry, all equally as logically consistent. What applies to our world is an experimental matter. As they delved further into the issue, something called the 'Erlangen Program' emerged:
https://en.wikipedia.org/wiki/Erlangen_program

Now group theory is the mathematical language of symmetry. So scientists can look at geometries as what results if we have certain symmetries. A fundamental concept, not often emphasised in the physics literature (Landau - Mechanics is a notable exception), is a precise definition, in terms of symmetry, of what an inertial frame is. The definition is as far as the laws of physics is concerned; all points, directions and instants of time are equivalent. Note an inertial frame is a conceptualisation - they do not exist in nature. But do exist to very high accuracy in interstellar space. For many practical purposes, the Earth can be considered an inertial frame even though it is easily demonstrated it isn't. But it is useful for theoretical work. A law of physics (well, a meta law, to be precise), called The Principle of Relativity, states the laws of nature are the same in any inertial reference frame or frame moving as constant velocity to an inertial frame. This is a symmetry condition, and our knowledge of math should allow us to work out the geometry of an inertial frame.: http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf.

This determines the geometry up to a constant c. Both theoretical considerations and direct experiment show c is the speed of light. These are the Lorentz transformations. It predicts length contraction, time dilation and all the other strange stuff. It depends on the POR, of course, which has been tested in many experiments - in fact, it is really is Newton's first law in disguise - but that is another story. It is about as rock-solid as any theory in physics can be.

Thanks
Bill

 

[Jim Fern]

Thank you all for this information and answering my questions, regardless of how idiotic some of them seemed, to be sure. You've certainly given me a great deal of things to look into. :)