I Exact historical explanation of deducing speed of light constancy

[roineust]

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.

 

[Vanadium 50]

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.

Start with ∇×∇×E (or B, it works either way), plug i Maxwell's equations and out pops a wave equation.

 

[Vanadium 50]

Indeed, there's a nice history at https://en.wikipedia.org/wiki/Electromagnetic_wave_equation

Not sure why all that Google searching you say you did didn't turn up...Wikipedia.

 

[roineust]

I am looking for a simpler explanation, if you do not think that such a simpler explanation exist, it does not mean that so will anyone who has years of experience in advanced math.

 

[PeterDonis]

I am looking for a simpler explanation

A simpler explanation of what? Of how the constancy of the speed of light was actually deduced, historically? That's what your question in this thread is about, and there is no reason to expect the actual historical development of any concept to be simple.

 

[roineust]

I do not expect anything, i am looking for a simplification or a tutorial that explains this step by step using also other means such as visualization.

 

[roineust]

I understand what the 4 Maxwell equations say in a general and visual sense and in a very rudimentary mathematical sense, but not in any rigorous mathematical form.

 

[PeterDonis]

i am looking for a simplification or a tutorial that explains this

That explains the historical development of physicists' understanding of the constancy of the speed of light?

I understand what the 4 Maxwell equations say in a general and visual sense and in a very rudimentary mathematical sense, but not in any rigorous mathematical form.

"Maxwell's Equations" and "constancy of the speed of light" are not the same thing. The latter can be viewed as a consequence of the former, but they're not the same.

Also, "what Maxwell's Equations say" is a different question from the question of how, historically, physicists came to understand Maxwell's Equations (or the constancy of the speed of light). So you need to clarify exactly what you want to ask about before you can expect to get any useful answers.

 

[roineust]

Also, "what Maxwell's Equations say" is a different question from the question of how, historically, physicists came to understand Maxwell's Equations (or the constancy of the speed of light). So you need to clarify exactly what you want to ask about before you can expect to get any useful answers.

Do you mean that the current understanding and the way of explaining Maxwell equations, is extremely different form the understanding and explanation of these 4 equations, right after they were written and made known by Maxwell ?

 

[Nugatory]

I am looking for a simpler explanation...

Unfortunately, we may not be able to help you there. You can learn enough math to see it for yourself, or you can let someone who has learned the math and seen the result tell you what they saw... but there aren't a lot of other options.

 

[PeterDonis]

Do you mean that the current understanding and the way of explaining Maxwell equations, is extremely different form the understanding and explanation of these 4 equations, right after they were written and made known by Maxwell ?

Most definitely. Physicists have had a century and a half to refine our understanding of Maxwell's Equations since they were first published. They have not been idle during all that time.

 

[roineust]

Most definitely. Physicists have had a century and a half to refine our understanding of Maxwell's Equations since they were first published. They have not been idle during all that time.

I mean the way they are currently explained to beginners vs. used to be explained to beginners, not the way scientists currently work with these equations.

 

[jtbell]

Maxwell's equations and the speed of electromagnetic waves predicted from them, were originally understood to apply only in a reference frame in which the supposed "luminiferous ether" is at rest. The ether served as the medium for light waves in a similar way as air serves as the medium for sound waves.

In this picture, the speed of a light wave depends on the velocity of the wave with respect to the ether, and on the velocity of the observer with respect to the ether. This led to the Michelson-Morley experiment which attempted to detect the velocity of earth-bound observers with respect to the ether, by measuring differences in the speed of light in different directions.

Now we understand Maxwell's equations to apply in any (inertial) reference frame. Therefore the speed of light predicted from them also applies in any (inertial) reference frame.

 

[PeterDonis]

I mean the way they are currently explained to beginners vs. used to be explained to beginners, not the way scientists currently work with these equations.

Same answer. As a matter of fact, Maxwell's Equations as they were originally published weren't really explainable to beginners at all. You had to have a fairly advanced knowledge of the physics of the time to have any chance of understanding what the equations were saying. Physicists have done a lot in the century and a half since to find ways to explain electrodynamics to beginners.

 

[roineust]

Maxwell's equations and the speed of electromagnetic waves predicted from them, were originally understood to apply only in a reference frame in which the supposed "luminiferous ether" is at rest. The ether served as the medium for light waves in a similar way as air serves as the medium for sound waves.

In this picture, the speed of a light wave depends on the velocity of the wave with respect to the ether, and on the velocity of the observer with respect to the ether. This led to the Michelson-Morley experiment which attempted to detect the velocity of earth-bound observers with respect to the ether, by measuring differences in the speed of light in different directions.

Now we understand Maxwell's equations to apply in any (inertial) reference frame. Therefore the speed of light predicted from them also applies in any (inertial) reference frame.

I see here here several options, can you please tell me which ones are correct and which ones are wrong:

1. It was not possible to deduce the constancy of the speed of light from Maxwell's equations before 1905.
2. It was possible to deduce the constancy of the speed of light from Maxwell's equations before 1905.
3. It is also currently not possible to deduce the constancy of the speed of light from Maxwell's equations as they are understood today.
4. It is currently possible to deduce the constancy of the speed of light from Maxwell's equations as they are understood today.
5. The constancy of the speed of light was postulated only from Michelson Morley experiment before/in 1905 and was not deduced from any equations.

 

[sysprog]

I see here here several options, can you please tell me which ones are correct and which ones are wrong:

1. It was not possible to deduce the constancy of the speed of light from Maxwell's equations before 1905.
2. It was possible to deduce the constancy of the speed of light from Maxwell's equations before 1905.
3. It is also currently not possible to deduce the constancy of the speed of light from Maxwell's equations as they are understood today.
4. It is currently possible to deduce the constancy of the speed of light from Maxwell's equations as they are understood today.
5. The constancy of the speed of light was postulated only from Michelson Morley experiment before/in 1905 and was not deduced from any equations.

1N 2Y 3N 4Y 5N

 

[Vanadium 50]

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

I am looking for a simpler explanation,

You can't ask for a historical fact and then complain about it. "Who was the first President of the United States?" "George Washington." "No, that's not the person I want. Can it be George Clooney?"

 

[pervect]

Rather than focusing on the history of the speed of light, it might be useful to look at the history of the meter. This is relevant to your question, because nowadays the meter is defined as the unit of length that makes the speed of light have a specific numerical value.

The meter, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s-1, where the second is defined in terms of ΔνCs.

The history of the evolution of the definition of the meter is a long an interesting one, but I don't have any good detailed and reliable information on it, not being a historian. But you can get a reasonablly good overview from the wikipedia, looking up it's soures to get to more reliable ones. I'd start with https://en.wikipedia.org/wiki/History_of_the_metre

The modern history of the meter starts around the time of the french revolution, where problems in commerce were arising because people were using different length standards. The organization called the BIPM, a bureau of weight and measures, was created to sort out the competing standards, and decide on the best route.

Where this history wound up, fast-forwarding to modern times, is that the speed of light is no longer measured. Instead , it is used to define the meter. How we got there is indeed an interesting story.

I'll also take the opportunity to try and answer the question you originally asked. The short and easy to understand version would be that historically, the constancy of the speed of light was a mathematical fact, but it was assumed that this speed was relative to a physical medium, called the ether.

So alternatively you could look into the history of the ether, and how experiments like the Michelson-Morley (henceforth MM) experiment failed to find any evidence of its existence. Einstein initially claimed that the MM experiment didn't directly inspire his theory, as I recall, but later on admitted that it probably had influenced his thinking significantly. At least that's my understanding, I could be wrong about the details as I am not a student of history.

The point I like to stress doesn't involve the ether at all though. The point I like to stress is that if you buy a tape measure, if you want a good one you'll want one that is traceable to the national standards. The history of how the national standards was created relates to the history of the meter I mentioned previously. Before there were national standards, there was a fair amount of chaos, as different people would , as you might guess, have incompatible measurements.

And if you investigate how the national standard bureau defines their standards (also a matter of written record), you'll see that nowadays it's based on the constancy of the speed of light.

 

[roineust]

You can't ask for a historical fact and then complain about it. "Who was the first President of the United States?" "George Washington." "No, that's not the person I want. Can it be George Clooney?"

Correct, what i meant was historically and simplified.

 

[Vanadium 50]

OK, then the answer is, as you like, "George Clooney". Not sure how this will help you.

 

[russ_watters]

1N 2Y 3N 4Y 5N

Caution here, as I think the OP is misusing the term "constancy" (to mean frame invariant), so I think the questions you answered aren't what he wants to know.

 

[roineust]

Here are the 4 Maxwell equations in a spoken word format taken from the following source: https://www.fiberoptics4sale.com/bl...ics/a-plain-explanation-of-maxwells-equations:

1.

• Electric charge q produces an electric field E
• The electric field flux passing through any closed surface is proportional to the total charge contained within that surface

2.

• The total magnetic flux passing through any closed surface is 0.
• The assumption that there are no magnetic monopoles.
• There are no magnetic flow sources, and the magnetic flux lines always close upon themselves.
• Also called the law of conservation of magnetic flux

3.

• Changing magnetic flux through a surface induces an electromotive force (EMF) in any boundary path of that surface.
• A changing magnetic field induces a circulating electric field.
• The voltage accumulated around a closed circuit is proportional to the time rate of change of the magnetic flux it encloses.

4.

• An electric current I or a changing electric flux through a surface produces a circulating magnetic field around any path that bounds that surface.
• Electric currents and changes in electric fields are proportional to the magnetic fields circulating about the areas where they accumulate.

And now to my question:

Is the general agreement within the physicists teachers community akin to the following:

Although it is possible to get a good intuition of the Maxwell equations using the above wording, some rudimentary mathematics, some diagrams and some hand gesture mnemonics, it is absolutely not possible to understand how the constancy of the speed light is deduced from these equations using the same means, but rather to make the step from Maxwell equations to understanding the constancy of the speed of light, only rigorous university level mathematics can be used?

 

[PeterDonis]

Here are the 4 Maxwell equations

No, that's not what those are. Those are descriptions of the kinds of physics that Maxwell's Equations describe. They are not Maxwell's Equations themselves.

Why not? Because there are no numbers. The descriptions use phrases like "produces" and "proportional to". They don't tell you exactly how much of something is produced by something else.

it is absolutely not possible to understand how the constancy of the speed light is deduced from these equations

You can deduce it from the equations. (More precisely, from the equations plus the general assumption that we expect all laws of physics to be Lorentz invariant. That is assuming, btw, that by "constancy" you actually mean "frame invariant", as @russ_watters has posted.) But obviously you can't deduce it from the descriptions in words that you posted, because to deduce the constancy of the speed of light, you need to be able to deduce the numerical speed of electromagnetic waves that Maxwell's Equations predict, in order to verify that it's the same numerical speed that other independent measurements have shown light to travel at, and you need the actual numbers to do that.

 

[roineust]

No, that's not what those are. Those are descriptions of the kinds of physics that Maxwell's Equations describe. They are not Maxwell's Equations themselves.

Why not? Because there are no numbers. The descriptions use phrases like "produces" and "proportional to". They don't tell you exactly how much of something is produced by something else.
You can deduce it from the equations. (More precisely, from the equations plus the general assumption that we expect all laws of physics to be Lorentz invariant. That is assuming, btw, that by "constancy" you actually mean "frame invariant", as @russ_watters has posted.) But obviously you can't deduce it from the descriptions in words that you posted, because to deduce the constancy of the speed of light, you need to be able to deduce the numerical speed of electromagnetic waves that Maxwell's Equations predict, in order to verify that it's the same numerical speed that other independent measurements have shown light to travel at, and you need the actual numbers to do that.

So after deducing the numerical value of the speed of light from Maxwell's equations, the equations themselves have nothing directly anymore to do with deducing the constancy of the speed of light, but it is only the 'frame invariant' assumption?

 

[PeterDonis]

So after deducing the numerical value of the speed of light from Maxwell's equations, the equations themselves have nothing directly anymore to do with deducing the constancy of the speed of light, but it is only the 'frame invariant' assumption?

Not "frame invariant", "Lorentz invariant". In other words, the assumption is that all of the laws of physics do not change their form under Lorentz transformations. Maxwell's Equations are already Lorentz invariant, so they are consistent with the assumption; but the assumption is still required to ground the conclusion that Maxwell's Equations are actually exact laws of physics, not approximations, so that the deduction from Maxwell's Equations that all electromagnetic waves travel with the same speed in all frames is also a law of physics.

In the late 1800s many physicists thought that was not the case--that Maxwell's Equations were not actually exactly true in all frames, but were only exactly true in one frame (which was often called the "ether" frame). Those physicists believed that the exact laws of physics were Galilean invariant, not Lorentz invariant--i.e., that they would not change their form under Galilean transformations (not Lorentz transformations). So to them, "frame invariant" meant "Galilean invariant", not "Lorentz invariant". Maxwell's Equations are not Galilean invariant.

 

[roineust]

Not "frame invariant", "Lorentz invariant". In other words, the assumption is that all of the laws of physics do not change their form under Lorentz transformations. Maxwell's Equations are already Lorentz invariant, so they are consistent with the assumption; but the assumption is still required to ground the conclusion that Maxwell's Equations are actually exact laws of physics, not approximations, so that the deduction from Maxwell's Equations that all electromagnetic waves travel with the same speed in all frames is also a law of physics.

In the late 1800s many physicists thought that was not the case--that Maxwell's Equations were not actually exactly true in all frames, but were only exactly true in one frame (which was often called the "ether" frame). Those physicists believed that the exact laws of physics were Galilean invariant, not Lorentz invariant--i.e., that they would not change their form under Galilean transformations (not Lorentz transformations). So to them, "frame invariant" meant "Galilean invariant", not "Lorentz invariant". Maxwell's Equations are not Galilean invariant.

Would it therefore be correct to say that SR has actually only one postulate, namely the 'Lorentz invariant' postulate and that the SR so called second postulate (constancy of the speed of light) is not a postulate, but actually a deduction from the 1st postulate ('Lorentz invariant')?

 

[Dale]

there is no reason to expect the actual historical development of any concept to be simple

Yes, in fact the historical approach is almost always not the simplest. Usually the history is filled with many false starts, near misses, and setbacks. Life is complicated.

 

[PeterDonis]

Would it therefore be correct to say that SR has actually only one postulate, namely the 'Lorentz invariant' postulate and that the SR so called second postulate (constancy of the speed of light) is not a postulate, but actually a deduction from the 1st postulate ('Lorentz invariant')?

You can't deduce the constancy (frame invariance) of the speed of light (where "light" means electromagnetic radiation--see below) just from the "Lorentz invariant" postulate. You also need Maxwell's Equations.

Also, Maxwell's Equations only describe electromagnetic radiation, but the SR postulate applies to anything that travels on null worldlines, not just EM radiation. So the SR postulate is more general than the property of EM radiation that can be deduced from Maxwell's Equations.

 

[Nugatory]

Would it therefore be correct to say that SR has actually only one postulate, namely the 'Lorentz invariant' postulate and that the SR so called second postulate (constancy of the speed of light) is not a postulate, but actually a deduction from the 1st postulate ('Lorentz invariant')?

You will find some older threads here discussing that line of thought, and I’ve said (with tongue firmly in cheek) that the second postulate could be paraphrased as “...and I really mean that first postulate!” or even “We don’t need no steenkin’ aether!”.

However, there's more to it than that. When Einstein proposed the second postulate, his 1905 wording exactly captured the way that his theory differed from the previous half-century's thinking about how to reconcile Maxell's equations and classical mechanics; the "really mean the first postulate" argument was just a hint that the second postulate should be taken seriously. So from a historical perspective, it was needed at the time.

 

[zoki85]

Also, Maxwell's Equations only describe electromagnetic radiation, but the SR postulate applies to anything that travels on null worldlines, not just EM radiation.

Do you mean here "applies to anything massless ...", or I misunderstood you?
And what other massless entity except EM radiation could that possibly be?
Apology for being slighty off topic.

 

[pervect]

Here are the 4 Maxwell equations in a spoken word format taken from the following source: https://www.fiberoptics4sale.com/bl...ics/a-plain-explanation-of-maxwells-equations:

1.

• Electric charge q produces an electric field E
• The electric field flux passing through any closed surface is proportional to the total charge contained within that surface.

The proportionality constant needs a name and a numerical value. We'll call it $\epsilon_0$, the permitivity of the vacuum

4.

• An electric current I or a changing electric flux through a surface produces a circulating magnetic field around any path that bounds that surface.
• Electric currents and changes in electric fields are proportional to the magnetic fields circulating about the areas where they accumulate.

This proportionality constant also needs a name. We'll call it $\mu_0$.

And now to my question:

Is the general agreement within the physicists teachers community akin to the following:

Although it is possible to get a good intuition of the Maxwell equations using the above wording, some rudimentary mathematics, some diagrams and some hand gesture mnemonics, it is absolutely not possible to understand how the constancy of the speed light is deduced from these equations using the same means, but rather to make the step from Maxwell equations to understanding the constancy of the speed of light, only rigorous university level mathematics can be used?

I have no idea. But trying to do it without math is difficult and feels unnecessarily restrictive. Like "can you do this with both hands tied behind your back?". Maybe you could, maybe you couldn't, but the only reason to try is bragging rights as to how good you are.

So let's use some math. What we can say using these tools is that given the above, it's possible to show that the speed of electromagnetic radiation is $1/\sqrt{\mu_0 \epsilon_0}$

So, what it is necessary to do to show that the speed of light is frame invariant requires some additional postulates, namely that $\epsilon_0$ and $\mu_0$ are constants that are independent of the choice of frame of reference, which is an assumption you didn't make specifically. At least I don't think you made that assumption.

THat's where the principle of relativity comes in.

 

[Dale]

And what other massless entity except EM radiation could that possibly be?

Gluons and gravitational radiation.

 

[zoki85]

Gluons and gravitational radiation.

OMG, I forgot about gravity waves

 

[weirdoguy]

gravity waves

Gravitational waves. Gravity waves are something different: https://en.wikipedia.org/wiki/Gravity_wave

Fun fact: in polish both types of waves are called the same: "fale grawitacyjne", so we have to add explicitly that we mean "waves on a surface of fluid" when we talk about gravity waves.

 

[zoki85]

Gravitational waves. Gravity waves are something different: https://en.wikipedia.org/wiki/Gravity_wave

Fun fact: in polish both types of waves are called the same: "fale grawitacyjne", so we have to add explicitly that we mean "waves on a surface of fluid" when we talk about gravity waves.

OK, English is not my native language

 

[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).