calculate light speed method

[Logicandreason]

Mu naught and epsilon zero can be used to calculate the sped of light, which is a universal constant.

It requires that both Epsilon zero and mu naught are constants for light speed to be a constant.

But from 2019,  Mu Naught is no longer considered to be a constant.  It is now a measured value, and as all measurements are relative their own frame of reference, and its possible to now get different values of Mu Naught even in that one frame, then its now not possible to claim  that Maxwell's equations prove  that light speed is constant,  or that it is has the same value in all frames of reference.

So you can not call on Maxwell to support Einstein's Special Relativity claims.

 

 

[exchemist]

2 hours ago, Logicandreason said:

Mu naught and epsilon zero can be used to calculate the sped of light, which is a universal constant.

It requires that both Epsilon zero and mu naught are constants for light speed to be a constant.

But from 2019,  Mu Naught is no longer considered to be a constant.  It is now a measured value, and as all measurements are relative their own frame of reference, and its possible to now get different values of Mu Naught even in that one frame, then its now not possible to claim  that Maxwell's equations prove  that light speed is constant,  or that it is has the same value in all frames of reference.

So you can not call on Maxwell to support Einstein's Special Relativity claims.

 

 

You have misunderstood this. The magnetic constant is still regarded as, er, a constant.  The distinction is that it is now treated as measured rather than defined. But it is still a constant.

It makes little sense saying it is frame-dependent, as it is measured via a pair of parallel wires in the same frame as the observer, or alternatively derived from measuring the fine structure constant (via quantum phenomena, again measured in the same frame as the observer) and applying defined values of the electron charge and Planck’s constant.

Edited June 21, 2023 by exchemist

[Logicandreason]

58 minutes ago, exchemist said:

You have misunderstood this. The magnetic constant is still regarded as, er, a constant.  The distinction is that it is now treated as measured rather than defined. But it is still a constant.

It makes little sense saying it is frame-dependent, as it is measured via a pair of parallel wires in the same frame as the observer, or alternatively derived from measuring the fine structure constant (via quantum phenomena, again measured in the same frame as the observer) and applying defined values of the electron charge and Planck’s constant.

If its measured, then then is an opportunity to get another measurement. In the frame where its measured, it may always be a constant.  But if measured from another frame, then the relative motion between frames must be included, thus its necessary to calculate it as v + 0r minus the other frame velocity.  Mu * Epsilon = seconds ²

And the units end up as Meters per second.   But now that one of the two "constants" IS frame dependent, its only valid in that frame of measurement, the the end result must be that the speed of light cannot be frame independent. 

[exchemist]

28 minutes ago, Logicandreason said:

If its measured, then then is an opportunity to get another measurement. In the frame where its measured, it may always be a constant.  But if measured from another frame, then the relative motion between frames must be included, thus its necessary to calculate it as v + 0r minus the other frame velocity.  Mu * Epsilon = seconds ²

And the units end up as Meters per second.   But now that one of the two "constants" IS frame dependent, its only valid in that frame of measurement, the the end result must be that the speed of light cannot be frame independent. 

This is nonsense. So long as observer and the observed phenomenon are all in the same frame of reference, you don't need to concern yourself at all with the issue of reference frames.

There is no "relative motion between frames" when you measure μ₀,  or Sommerfeld's constant (the fine structure constant), α. Everything is in the same lab, including the observer, and the phenomena observed in the making of the measurements do not involve relativistic effects.

Nothing in physics says that  μ₀ is frame-dependent. You appear to be making this up, in a forlorn attempt to pick holes in relativity, without understanding what μ₀ is.   

[Logicandreason]

51 minutes ago, exchemist said:

This is nonsense. So long as observer and the observed phenomenon are all in the same frame of reference, you don't need to concern yourself at all with the issue of reference frames.

There is no "relative motion between frames" when you measure μ₀,  or Sommerfeld's constant (the fine structure constant), α. Everything is in the same lab, including the observer, and the phenomena observed in the making of the measurements do not involve relativistic effects.

Nothing in physics says that  μ₀ is frame-dependent. You appear to be making this up, in a forlorn attempt to pick holes in relativity, without understanding what μ₀ is.   

Of course "observer and the observed phenomenon are all in the same frame of reference"  but what is happening in the one frame of reference is NOT what Relativity is all about is it?

So in that one frame, or in any frame we will still measure Mu naught and get the same results. 

But c is all about light speed being universal, not frame dependant. 

However, if I should observe the experiment that's being conducted in frame K,  as it whizzes past me at some considerable velocity, then if I try to measure what's going on with that experiment being conducted in frame K  (as it has to do with acceleration (F=ma) and having a final result in meters per second)  then I need to adjust my measurements to account for the relative motion differences between frame K and my own frame.

Therefore light speed is relative to the frame.    You said, "Nothing in physics says that μ₀ is frame-dependent"   but if its a measure, then where does that measurement have its origin? It can only possibly be the frame where the experiment is occurring.  Every measurement has an starting point and a target. Are you really claiming that you can measure something but not have a starting point to make the measurement meaningful?

 

 

Edited June 21, 2023 by Logicandreason

[exchemist]

45 minutes ago, Logicandreason said:

Of course "observer and the observed phenomenon are all in the same frame of reference"  but what happening in the one frame of reference is NOT what Relativity is all about is it?

So in that one frame, or in any frame we will still measure Mu naught and get the same results. 

But c is all about light speed being universal, not frame dependant. 

However, if I should observe the experiment that's being conducted in frame K,  as it whizzes past me at some considerable velocity, then if I try to measure what's going on with that experiment being conducted in frame K  (as it has to do with acceleration (F=ma) and having a final result in meters per second)  then I need to adjust my measurements to account for the relative motion differences between frame K and my own frame.

Therefore light speed is relative to the frame.    You said, "Nothing in physics says that μ₀ is frame-dependent"   but if its a measure, then where does that measurement have its origin? It can only possibly be the frame where the experiment is occurring.  Every measurement has an starting point and a target. Are you really claiming that you can measure something but not have a starting point to make the measurement meaningful?

 

 

I've told you how μ₀ is measured, the most modern being via measuring α, the fine structure constant and then applying the values of the charge on the electron e, Planck's constant h, and the speed of light c, by mean of the relation   μ₀ = 2αh/e²c. This is all done in the lab and does not need to involve relativity. Acceleration does not come into it. The units of μ₀ are N/A², i.e. force/current squared, which falls out of the formula. α itself, i.e. the thing being measured, is dimensionless. 

You say "therefore light speed is relative to the frame" but this firstly does not follow and secondly it is contrary to observation, namely that the speed of light is not relative to the frame of reference.

You seem to me to be looking at this from the wrong end of the telescope. This being science, it starts from the observations and then derives theories consistent with them. c is found by observation to be invariant and not frame dependent. So that is what we start from, not where we end up by some derivation or other.

So it's pointless futzing around with formulae containing c and trying to show that it can't be constant, due to some claimed frame-dependence of one or more quantities in a formula, when experiment says otherwise. 

 

Edited June 21, 2023 by exchemist

[Logicandreason]

13 hours ago, exchemist said:

Acceleration does not come into it. The units of μ₀ are N/A², i.e. force/current squared,

You work entirely with circular logic.

You say that acceleration is not involved, then immediately give the equation that has FORCE directly used. "The units of μ₀ are N/A², i.e. force/current squared"

Force is mass * ACCETERATION.    and acceleration is frame dependant because it can only be calculated by observation of changes in position over time.  DO YOU UNDERSTAND that a POSITION is frame dependant? 

Also, 

13 hours ago, exchemist said:

  μ₀ = 2αh/e²c.

We were trying to figure out if Mu  naught was correct, because its used to calculate the speed of Light c,  and here you have a circular reference because c here needs to be written according to maxwell's equation that uses mu and epsilon.  Because this is the topic we are discussing.   What is c? its the value of 1 over the square root of the product of mu and epsilon.  So if I plug that into the equation , I see that mu is not equal to mu.

Also the fine structure "constant" is calculated using such dubious other constants, after making a measurement of something else.  Assumptions must be made. I've just shown that Mu is frame dependant, so is not a universal constant. So that was an assumption about a constant that modern Physics got wrong. And there will be others.

[Mordred]

An object at constant velocity can also deliver a force so your assumption isn't valid. F=ma is the amount of force needed to change the velocity aka acceleration

Edited June 21, 2023 by Mordred

[Logicandreason]

17 minutes ago, Mordred said:

An object at constant velocity can also deliver a force so your assumption isn't valid. F=ma is the amount of force needed to change the velocity aka acceleration

But an object with velocity or zero (is also inertial) can't deliver any force, so your assumption is invalid.    If your constants or variables for Mu naught involve any use of Force, then the constant is relative to the frame and thus not universal.

[Mordred]

excuse me a car moving at 70 km/hour certainly delivers a force when it hits a brick wall

[swansont]

22 minutes ago, Logicandreason said:

But an object with velocity or zero (is also inertial) can't deliver any force, so your assumption is invalid.    

No, this is patently untrue. A charge at rest will exert a force on any other charge, and with Newtonian gravity, the same holds true for a mass at rest exerting a force on other masses. Rope tension, normal forces, and static friction are other examples of forces that can be present at zero velocity.

[Logicandreason]

5 minutes ago, swansont said:

No, this is patently untrue. A charge at rest will exert a force on any other charge, and with Newtonian gravity, the same holds true for a mass at rest exerting a force on other masses. Rope tension, normal forces, and static friction are other examples of forces that can be present at zero velocity.

With the measurement of Mu, the force we are talking about involves MOTION.   Motion is the observation of change in location. and in this case, time is also a factor. So if you are taking note of POSITION, then that position only makes sense if it is relative to some origin, the origin of the Frame of reference.  So its still relative to the frame, not to all frames. 

[swansont]

10 minutes ago, Logicandreason said:

With the measurement of Mu, the force we are talking about involves MOTION.   Motion is the observation of change in location. and in this case, time is also a factor. So if you are taking note of POSITION, then that position only makes sense if it is relative to some origin, the origin of the Frame of reference.  So its still relative to the frame, not to all frames. 

Something that’s the same in all frames is invariant. Something that’s the same everywhere (and over time) in one frame is a constant.

A constant current (which could be from charges at constant velocity) can exert a force.

[Logicandreason]

38 minutes ago, swansont said:

Something that’s the same in all frames is invariant. Something that’s the same everywhere (and over time) in one frame is a constant.

A constant current (which could be from charges at constant velocity) can exert a force.

Mu naught is measured by noting the MOVEMENT of a metallic rod relative to the other metallic object. One of them is considered as the "reference object", the other is the "object in motion". So that "reference object", defines the frame origin for this measurement.

Repeat the same measurement on a bus that has constant motion, and you will get the same value. According to Newtonian Mechanics.

Because you have fixed the "reference object"  be coincident with the whole bus.

But if you put that "reference object" on the ground, and drive the bus with the "object in motion" then you will not get the same result at all. Therefore the measurement of "Mu" IS FRAME DEPENDENT. and can not be an identical result  between frames. 

[Logicandreason]

2 hours ago, Mordred said:

excuse me a car moving at 70 km/hour certainly delivers a force when it hits a brick wall

I said, a car moving at a constant velocity of ZERO, has no force to impart to the brick wall. 

[MigL]

I see where you are going with this ...

In the equation       E=mc²         Both E ( energy ) and m ( rest mass ) are frame dependent.
It is actually  defined for the mass as measured in the rest frame; so if we re-arrange to get     c²=E/m      then how can c be constant ?

I guess your logic and reason have never considered that E and m will both changeso as to keep c constant?

Instead of just makng claims again, why not show math showing how mu naught and epsilon zero change through a frame transform.
Maybe, as with E and m , they also change so as to keep c constant.

[Logicandreason]

18 minutes ago, MigL said:

I see where you are going with this ...

In the equation       E=mc²         Both E ( energy ) and m ( rest mass ) are frame dependent.
It is actually  defined for the mass as measured in the rest frame; so if we re-arrange to get     c²=E/m      then how can c be constant ?

I guess your logic and reason have never considered that E and m will both changeso as to keep c constant?

Instead of just makng claims again, why not show math showing how mu naught and epsilon zero change through a frame transform.
Maybe, as with E and m , they also change so as to keep c constant.

Was I not talking about Maxwell's equation revealing Light speed from two universal constants?  I never mentioned any theories that came later. All I'm saying is that from Maxwell's equations and Mu and Epsilon, you can not conclude that Light speed is a universal constant. Because Mu and Epsilon are not universal constants.

From Maxwell, you can't get a constant in all frames light speed.  In fact you get the opposite.   It was Einstein's Postulate that Light speed was a universal constant, but we can now see that that postulate can not be accepted UNLESS you discard Maxwell's Equations. (because they indicate the exact opposite)

Edited June 22, 2023 by Logicandreason

[Logicandreason]

2 hours ago, MigL said:

how mu naught and epsilon zero change through a frame transform.
Maybe, as with E and m , they also change so as to keep c constant.

I just realized you made another logical error. I was the one who said that Mu and Epsilon CHANGED,  You claim they do not, so your next sentence makes no sense- you said, " as with E and m , they also change so as to keep c constant".    Meaning that you now agree that perhaps Mu and Epsilon are NOT CONSTANTS, because like E and m, they also change values to "keep c constant". 

So pick a side here, whether you believe that Mu and Epsilon are constants or you don't.

Edited June 22, 2023 by Logicandreason

[Janus]

Newsflash: Relativity doesn't rely on the "speed of light". It relies on there being an invariant speed "c", which is built into the Universe. Even if it were to turn out that light in a vacuum does not travel exactly at c, this would change nothing about Relativity. 

Now, to the best of our knowledge the speed of light in a vacuum does equal c, but this is a convenience, not a requirement for Relativity.

[exchemist]

6 hours ago, Logicandreason said:

You work entirely with circular logic.

You say that acceleration is not involved, then immediately give the equation that has FORCE directly used. "The units of μ₀ are N/A², i.e. force/current squared"

Force is mass * ACCETERATION.    and acceleration is frame dependant because it can only be calculated by observation of changes in position over time.  DO YOU UNDERSTAND that a POSITION is frame dependant? 

Also, 

We were trying to figure out if Mu  naught was correct, because its used to calculate the speed of Light c,  and here you have a circular reference because c here needs to be written according to maxwell's equation that uses mu and epsilon.  Because this is the topic we are discussing.   What is c? its the value of 1 over the square root of the product of mu and epsilon.  So if I plug that into the equation , I see that mu is not equal to mu.

Also the fine structure "constant" is calculated using such dubious other constants, after making a measurement of something else.  Assumptions must be made. I've just shown that Mu is frame dependant, so is not a universal constant. So that was an assumption about a constant that modern Physics got wrong. And there will be others.

Others have pointed out your misunderstanding of the concept of force and of what F=ma means.

As for “circular logic”, I reiterate my basic point that c is observed to be invariant, so that is an input number to all these formulae, not an output.

You have not shown the magnetic constant is not a constant. And you have no basis for describing the charge on the electron or Planck’s constant as “dubious”, when your ignorance of the simplest physics is painfully apparent in this thread. You don’t even know how units work. I’m sure everyone here is enthusiastic about helping you learn, but for goodness sake don’t claim modern physics is “wrong”, given your current level of understanding. That is just farcical, frankly.

[Logicandreason]

18 minutes ago, Janus said:

Newsflash: Relativity doesn't rely on the "speed of light". It relies on there being an invariant speed "c", which is built into the Universe. Even if it were to turn out that light in a vacuum does not travel exactly at c, this would change nothing about Relativity. 

Now, to the best of our knowledge the speed of light in a vacuum does equal c, but this is a convenience, not a requirement for Relativity.

No this is false information. Relativity is 100% dependent on light speed of approx. 300 million meters per second, which for convince, we call "c".  In Einstein's written words, " light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body" ,  and in the second place where he repeats this second postulate he writes, " light moves in the “stationary” system of co-ordinates with the determined velocity c,"

Now if Einstein meant to say "constant velocity" he would simple say this, but no, he said, "definite, determined velocity c".

But also if he just meant that "light velocity was of consistent motion", as you claim, then he cannot develop his theory of relativity.  It depends on the actual measured velocity for his theory to be possible. Because the constancy of the motion of light is noticeable by anyone anywhere, but measurements require an origin.  Einstein's argument was that the light Source or the Aether medium was not the origin, so they only option was that every inertial frame would be suitable by virtue that the  Laws of physics are applicable in all initial frames.  And Light speed had already been measured and also calculated as a known value by Maxwell.  And that is the determined and definite velocity of light in Einstein's day.

 

 

 

11 minutes ago, exchemist said:

Others have pointed out your misunderstanding of the concept of force and of what F=ma means.

As for “circular logic”, I reiterate my basic point that c is observed to be invariant, so that is an input number to all these formulae, not an output.

You have not shown the magnetic constant is not a constant. And you have no basis for describing the charge on the electron or Planck’s constant as “dubious”, when your ignorance of the simplest physics is painfully apparent in this thread. You don’t even know how units work. I’m sure everyone here is enthusiastic about helping you learn, but for goodness sake don’t claim modern physics is “wrong”, given your current level of understanding. That is just farcical, frankly.

No one has "observed"  that light velocity is invariant between differently moving inertial frames of reference.   Its never been demonstrated for the same reason you can't measure light speed in a one way experiment.  However Light speed IS invariant when measured in the one frame of reference.

And that is all your have ever "observed". Its a measurement that is  demonstrably locally invariant, but according to the Laws of Physics, in the reference frames where "the equations of mechanics hold good", then according to those very same equations and laws, Light speed measurement must take into account the relative speed difference between reference frames.

The words, "reference frames where "the equations of mechanics hold good" are used by Einstein in his paper, so you know he agrees with them. He called on them to define what an inertial frame of reference was.

22 minutes ago, exchemist said:

You have not shown the magnetic constant is not a constant.

But you made the claim that the "magnetic constant is universal", but you have not shown that it actually is constant in all frames of reference.

[exchemist]

1 hour ago, Logicandreason said:

No this is false information. Relativity is 100% dependent on light speed of approx. 300 million meters per second, which for convince, we call "c".  In Einstein's written words, " light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body" ,  and in the second place where he repeats this second postulate he writes, " light moves in the “stationary” system of co-ordinates with the determined velocity c,"

Now if Einstein meant to say "constant velocity" he would simple say this, but no, he said, "definite, determined velocity c".

But also if he just meant that "light velocity was of consistent motion", as you claim, then he cannot develop his theory of relativity.  It depends on the actual measured velocity for his theory to be possible. Because the constancy of the motion of light is noticeable by anyone anywhere, but measurements require an origin.  Einstein's argument was that the light Source or the Aether medium was not the origin, so they only option was that every inertial frame would be suitable by virtue that the  Laws of physics are applicable in all initial frames.  And Light speed had already been measured and also calculated as a known value by Maxwell.  And that is the determined and definite velocity of light in Einstein's day.

 

 

 

No one has "observed"  that light velocity is invariant between differently moving inertial frames of reference.   Its never been demonstrated for the same reason you can't measure light speed in a one way experiment.  However Light speed IS invariant when measured in the one frame of reference.

And that is all your have ever "observed". Its a measurement that is  demonstrably locally invariant, but according to the Laws of Physics, in the reference frames where "the equations of mechanics hold good", then according to those very same equations and laws, Light speed measurement must take into account the relative speed difference between reference frames.

The words, "reference frames where "the equations of mechanics hold good" are used by Einstein in his paper, so you know he agrees with them. He called on them to define what an inertial frame of reference was.

But you made the claim that the "magnetic constant is universal", but you have not shown that it actually is constant in all frames of reference.

Universal? I'm not sure what that means and it's not what I said. I said μ₀ is a constant. @swansont has explained to you what that means. I also said that nothing in physics says  μ₀ is frame-dependent. 

Look, if μ₀ were frame-dependent, then relativistically moving particles in magnetic fields, e.g. in particle accelerators, would behave respond to the field differently from prediction as their velocities through it changed.  So far as I am aware (I'm open to correction from the real physicists here ) that is not a feature of particle physics. 

And indeed, as @MigL has observed, if it were to be frame-dependent, than ε₀ would also need to alter in the opposite sense such that the observed invariance of c is maintained. Because that is where we start from. 

I know you keep arguing that the invariance of c can't really be observed, but that's because you have steadfastly refused to consider the observational evidence for that, in spite of my attempts to get you to do so.  

 

Edited June 22, 2023 by exchemist

[Logicandreason]

49 minutes ago, exchemist said:

Universal? I'm not sure what that means and it's not what I said. I said μ₀ is a constant. @swansont has explained to you what that means. I also said that nothing in physics says  μ₀ is frame-dependent. 

Look, if μ₀ were frame-dependent, then relativistically moving particles in magnetic fields, e.g. in particle accelerators, would behave respond to the field differently from prediction as their velocities through it changed.  So far as I am aware (I'm open to correction from the real physicists here ) that is not a feature of particle physics. 

And indeed, as @MigL has observed, if it were to be frame-dependent, than ε₀ would also need to alter in the opposite sense such that the observed invariance of c is maintained. Because that is where we start from. 

I know you keep arguing that the invariance of c can't really be observed, but that's because you have steadfastly refused to consider the observational evidence for that, in spite of my attempts to get you to do so.  

 

There is no observed invariance of c. Its assumed.  and ε₀ will indeed  change its measured value if measured from different frames, which has also never been tested. And Physics says nothing at all about the frame of reference for measurement of μ₀.  Nothing.  So you are just guessing.

Swansont said: "Something that’s the same everywhere (and over time) in one frame is a constant".

And I fully agree, but that's not what Einstein is talking about when he says that c is "constant". Einstein says that light is both constant in the way Swansont had defined, BUT light is ALSO "constant", that is, it is possessing the exact same measured values are measured BETWEEN reference frames that have different velocities. So the two examples here unfortunately use the same word, "constant".  In this situation, Newton says that the measures speed of light will have to reflect the fact that the frames have a relative speed differential.

So μ₀ is indeed a constant, having the same measured value, anywhere in the universe, as long as the measurement was conducted in an inertial frame.  Every inertial frame will get  that same value, as Newton Mechanics confirms. But if you measure μ₀  BETWEEN two frames that have a relative speed difference, so that the equipment has its origin on one frame and the thig being measured in that other frame, then you will not get the same measurement value.  μ₀ value is referenced to the frame its being measured in. It can't be referenced to anything else.   Measurement of μ₀ uses two parallel wires carrying a charge.  One serves as the  origin of the frame of  reference for the other wire.  But if you move one wire to a differently moving frame, then you must get a different result, proving that μ₀ is a locally frame dependant constant.  Is this not true?

Edited June 22, 2023 by Logicandreason

[exchemist]

39 minutes ago, Logicandreason said:

There is no observed invariance of c. Its assumed.  and ε₀ will indeed  change its measured value if measured from different frames, which has also never been tested. And Physics says nothing at all about the frame of reference for measurement of μ₀.  Nothing.  So you are just guessing.

Swansont said: "Something that’s the same everywhere (and over time) in one frame is a constant".

And I fully agree, but that's not what Einstein is talking about when he says that c is "constant". Einstein says that light is both constant in the way Swansont had defined, BUT light is ALSO "constant", that is, it is possessing the exact same measured values are measured BETWEEN reference frames that have different velocities. So the two examples here unfortunately use the same word, "constant".  In this situation, Newton says that the measures speed of light will have to reflect the fact that the frames have a relative speed differential.

So μ₀ is indeed a constant, having the same measured value, anywhere in the universe, as long as the measurement was conducted in an inertial frame.  Every inertial frame will get  that same value, as Newton Mechanics confirms. But if you measure μ₀  BETWEEN two frames that have a relative speed difference, so that the equipment has its origin on one frame and the thig being measured in that other frame, then you will not get the same measurement value.  μ₀ value is referenced to the frame its being measured in. It can't be referenced to anything else.   Measurement of μ₀ uses two parallel wires carrying a charge.  One serves as the  origin of the frame of  reference for the other wire.  But if you move one wire to a differently moving frame, then you must get a different result, proving that μ₀ is a locally frame dependant constant.  Is this not true?

In your scenario of one wire moving relative to the other, the extra motion will alter the current flow as seen from the other reference frame and this will affect the magnetic field experienced in each frame. But this can be allowed for without altering the value of μ₀ in the calculation.

In fact, the joke is that the whole phenomenon of magnetism arises precisely due to relativity, i.e. how an electric field in one frame appears from the viewpoint of another that is moving relative to it.

Further reading here: https://en.wikipedia.org/wiki/Relativistic_electromagnetism    

Edited June 22, 2023 by exchemist

[Logicandreason]

4 minutes ago, exchemist said:

In your scenario of one wire moving relative to the other, then Lorenz contraction and time dilation will operate and this may affect what is observed, but it will do so by virtue of the length contraction and time dilation, i.e. without necessitating an additional change to μ₀.

You have not engaged with with my point about what is observed in particle accelerators, which I think (subject to what a physicist here may say) also demonstrates that μ₀ is not frame-dependent.   

In Maxwell's equations, which use Mu and Epsilon, there is no such thing as "length contraction".   

SR will not exist if Mu and Epsilon are reference frame dependant. If SR doesn't exist, then you cant apply Lorentz transformations to the length of anything. You can apply Lorentz to waves frequency, but not to solid objects length. The Lorentz transformation doesn't change the length of objects, only the rate at which a length passes a point.  Even thought Lorentz in a desperate attempt to keep his belief in an Aether, suggested that the M&M interferometer has shrunk one arm. But this could only be justified IF there really was an Aether.

So your argument involving length contraction is invalid.

I don't intend to engage you about the voodoo of Particle physics.  It not in Maxwell's equation to calculate the speed of light. Particle Physics and the Standard Model has enough of its own issues without me adding my concerns. Anyway, nothing about Particle Accelerators are in different frames. The whole machine is in the one frame.