Exact historical explanation of deducing speed of light constancy

[PeterDonis]

Do you mean here "applies to anything massless ..."

Yes, that's what "anything traveling on null worldlines" means.

 

[Sooty]

As much as i search Google, in an effort to find out how exactly the constancy of speed of light was historically deduced before 1905, from Maxwell equations or by any other means, i am not able to find such an explanation. In all of the search results that i could find, it is just stated that it was deduced from Maxwell equations and does not detail exactly how.

By using the term 'constancy' i mean that the speed of light is not changed for any observer, no matter the relative speed of a light emitting object.

If there is a difference between the 'constancy' of the speed of light and the 'invariance' of the speed of light, please add this also to the explanation.

What i am trying to understand is the exact way in which the constancy (or/and the invariance) of the speed of light was deduced before 1905, not how the exact number of 299,792,458 m/s was deduced before 1905, but if possible, please also add an exact explanation to how this number itself was deduced before 1905.

'Never use one word if you can get away with ten!' seems to be central to most of the 'answers' to questions you didn't even ask! :D
OK - your question - 'The exact way in which the constancy (or/and the invariance) of the speed of light was deduced before 1905?'...
So, unless I've got it wrong too, maybe try - https://simple.wikipedia.org/wiki/Michelson–Morley_experiment

 

[PAllen]

'Never use one word if you can get away with ten!' seems to be central to most of the 'answers' to questions you didn't even ask! :D
OK - your question - 'The exact way in which the constancy (or/and the invariance) of the speed of light was deduced before 1905?'...
So, unless I've got it wrong too, maybe try - https://simple.wikipedia.org/wiki/Michelson–Morley_experiment

That's not a deduction. It is an experiment whose outcome was inconsistent with the deductions of the physicists who conceived of the experiment. Maxwell's equations interpreted in a way differently than physicists used at the time could have led to such a deduction but @PeterDonis explained why this did not occur.

A feature distinguishing Einstein's development of SR from Lorentz and Poincare (which had the same physical consequences and slightly preceded Einstein) was that Einstein's development was deductive from axioms, and was considered a new framework for all laws, not just electromagnetism. However Einstein assumed the invariance light speed and deduces other things. So far as I know, no one before 1905 deduced the invariance of lightspeed. (note, there is plenty of evidence that Einstein's choice to assume such invariance was not related to experiment, but instead to his understanding of EM waves going back many years; in particular, to a notion that that a frame in which an EM wave was a stationary field was logically absurd).

 

[roineust]

So far as I know, no one before 1905 deduced the invariance of lightspeed

I am no physicist, mathematician or logician, but i think that the invariance, perhaps not of the speed of light, but the invariance of the Lorentz frames of reference, as a logic entity, is one that can never be deduced i.e. does not have the logical properties that enable it to be deduced from anything, but can be falsified i.e. does have the logical properties that enable it to be falsified, even if it was not falsified.

This might be totally wrong or a whole lot of nonsense, but whatever.

Perhaps it might be nonsense, because there is no type of logic that connects physics experiments and mathematics in a logic's framework but only in a quantitative relation? Am i making any sense or using the correct words?

 

[PeterDonis]

the invariance of the Lorentz frames of reference, as a logic entity, is one that can never be deduced

As a matter of logic, it's not deduced from anything. It's assumed as an axiom. You have to assume some things as axioms in order to construct a mathematical model in physics at all.

but can be falsified

Indeed it could, but it hasn't; all our experimental evidence is that it's true. And that's why physicists are perfectly OK with assuming it as an axiom when they construct mathematical models.

 

[roineust]

Indeed it could, but it hasn't;

Yes but if it is a logical entity that can never be deduced, isn't that a problem?

What i mean to ask is if this non-deducible Lorentz type of science different from a type of science, that finds out proportionality in experiments and then deduces (correct term here?) the equations from proportionality? i.e. having an operation (logical? mathematical? no difference?) that switches the experimental proportion sign, with an equal sign in order to create a new equation?

I am in a need here to find some basic courses that describe the logic's (and historical? and philosophical?) frame of the scientific operation, if this wording is correct.

 

[PeterDonis]

if it is a logical entity that can never be deduced, isn't that a problem?

Read this again:

It's assumed as an axiom. You have to assume some things as axioms in order to construct a mathematical model in physics at all.

Do you understand what that means?

 

[PeterDonis]

f this non-deducible Lorentz type of science different from a type of science, that finds out proportionality in experiments and then deduces (correct term here?) the equations from proportionality?

You can't deduce equations from experimental data alone. The experimental data is always consistent with multiple different possible equations--in fact, strictly speaking, with an infinite number of them. You have to bring in other assumptions to narrow down the equations you are going to consider.

 

[roineust]

Read this again:
Do you understand what that means?

Therefore, i would ask you if possible, to give more examples of a physics theories besides SR and GR, that decided to add a new axiom that were not used before them, in order to create a new equation and what were these axioms.

 

[roineust]

You can't deduce equations from experimental data alone. The experimental data is always consistent with multiple different possible equations--in fact, strictly speaking, with an infinite number of them. You have to bring in other assumptions to narrow down the equations you are going to consider.

If this answers my previous question, then please ignore it.

 

[PeterDonis]

if there is not also other types of science, that do not need new axioms but only build upon known ones (the proportionality thing?)

There is only one type of science: the type that builds mathematical models and tests their predictions against the results of experiments. If the predictions match the results, the models are accepted (at least until further results come in, when they have to be evaluated again). If the predictions don't match the results, the models are falsified and scientists have to go back to the drawing board to try to build different ones.

As far as how you build the mathematical models, see below.

i would ask you if possible, to give more examples of a physics theories besides SR and GR, that decided to add a new axiom that were not used before them, in order to create a new equation.

Every single scientific theory that has ever existed has done this.

If you have all the same axioms as before, you have the same mathematical model as before. But if you are trying to build a new mathematical model, it must be because the old one made wrong predictions and was falsified. So obviously you can't use the same axioms as the old one did, because you would then just have the old model and it would make the same falsified predictions. You have to pick at least one different axiom to get a different model that makes different predictions.

 

[roineust]

There is only one type of science: the type that builds mathematical models and tests their predictions against the results of experiments. If the predictions match the results, the models are accepted (at least until further results come in, when they have to be evaluated again). If the predictions don't match the results, the models are falsified and scientists have to go back to the drawing board to try to build different ones.

As far as how you build the mathematical models, see below.
Every single scientific theory that has ever existed has done this.

If you have all the same axioms as before, you have the same mathematical model as before. But if you are trying to build a new mathematical model, it must be because the old one made wrong predictions and was falsified. So obviously you can't use the same axioms as the old one did, because you would then just have the old model and it would make the same falsified predictions. You have to pick at least one different axiom to get a different model that makes different predictions.

And did every scientific theory before that also say what i interpret SR 1st postulate to say: "And this axiom is true also for any other existing scientific theory (axiom?)"? Isn't that a different type of axiom than any other axiom used before?

As much as i understand, it is not only SR (Lorentz) that said this but also Galileo (with the difference of light invariance), but still the question holds the same, i.e. isn't using that kind of axiom in a scientific theory, logically different from using other kinds of axioms in a scientific theory?

 

[PeterDonis]

did every scientific theory before that also say what i interpret SR 1st postulate to say: "And this axiom is true also for any other existing scientific theory (axiom?)"?

That's not what the SR axiom says. The SR axiom only applies to SR. It doesn't apply to other scientific theories, like Newtonian physics.

The SR axiom says that laws of physics have to be Lorentz invariant; but by "laws of physics" it means "laws of physics according to SR". It certainly doesn't say that laws of physics according to some other theory, like Newtonian physics, are Lorentz invariant. That would be obviously false.

Isn't that a different type of axiom than any other axiom used before?

No.

 

[vanhees71]

I think in this thread everything is very confused. The original question was, how Maxwell came to the prediction of em. waves and why it let him to conjecture that light might be such an electromagnetic wave. Then it drifted away to a discussion about special relativity, because perhaps, the question has been posted in the relativity subforum.

Of course, Maxwell had no idea about relativity. He just used the collected empirical wisdom (particularly the very detailed experimental results and visionary qualitative theoretical ideas leading to the field description by Faraday) and also previous mathematical models about electricity and magnetism and wrote down a new dynamical model of these empirical facts, based on very complicated mechanical models involving a socalled "aether", i.e., a substance with very "exotic" properties.

The equations were in essence of course what we now call Maxwell's equations, but they were written down in this form only later by Heaviside, who also introduced modern vector calculus. The fascinating thing about Maxwell's theoretical prediction of em. waves is that it rested entirely on static empirical input and the most important addition to the previous models (Ampere, Neumann), i.e., the famous "displacement current". This lead, of course using the then used electrostatic and magnetostatic units, Maxwell to deduce the existence of electromagnetic waves with a phase velocity that was equal within the then established accuracy to the speed of light in vacuum (or rather air, which is not too different, particularly not in view of the then established precision of measurement). The numerical value of the speed was deduced from the comparison of the measures for electric charge in electrostatic and magnetostatic units. The most accurate experiment was by Weber and Kohlrausch (1855). In the language of the modern SI, what was established is the relation $c=1/\sqrt{\mu_0 \epsilon_0}$, where $\mu_0$ and $\epsilon_0$ were measured at this time!

Another question is about Einstein's arguments leading him to the two famous postulates of 1905 ("On electrodynamics of moving bodies"). Einstein was very clear about the motivation resting on symmetry arguments (which brought into physics a line of thought that was of utmost importance for the entire modern physics, including quantum theory, based on Noether's famous theorems, which were inspired by the complicated question about the energy of the gravitational field in connection with Einstein's General Theory of Relativity). The problem was the lack of Galilei invariance of Maxwell's equations. Now, Einstein's idea was that the special principle of relativity should still be valid. If you now look at Maxwell's equations in their more lucid form when writing them in Gaussian or Heaviside-Lorentz units (which was the usually used units around 1900), you see that then the speed of light, which occurs as a natural constant in Maxwell's equations, must be invariant, implying that the speed of light cannot depend on the speed of (at least uniformly) moving light sources. From these two postulates Einstein could deduce the Lorentz transformation between inertial reference frames. Einstein bluntly gave up the very foundation of (Newtonian) physics, namely the spacetime model of Galilei and Newton. There was necessarily no absolute time and space anymore to make the special principle of relativity compatible with the "constancy of the speed of light". This implied that all of physics, particularly mechanics, had to be changed rather than Maxwell's equations, which were known to be invariant under Lorentz transformations even before Einstein (it was found up to a detail already by Woldemar Voigt around 1900).