I The Possibility of Faster-Than-Light Communication?

[TerranIV]

If we were to discover a way to lower the electric and magnetic constants of free space, would this allow faster than light communications? This would probably only be useful for some sort of hyper-fast computers in the future, but I don't see of a physical reason why this wouldn't be feasible someday.
So, setting aside for a moment that this technology doesn't exist, if we did theoretically lower u0 and e0 is there some reason why we couldn't send signals faster than light?

 

[Baluncore]

The System International defines the following in free space;
The speed of light, c ≡ 299792458 metre/second exactly.
The absolute permeability, Uo ≡ 4 ⋅ π ⋅ 10^-7 henry/metre
The absolute permittivity, Eo ≡ 1 / ( Uo ⋅ c ⋅ c ) farad/metre.

Relative Ur and Er have only been observed with values greater than or equal to 1.
You seem to be hypothesising that you can remove something from free space.

 

[TerranIV]

I know what permeability and permittivity are. c0 is defined by 1/[sqrt(u0*e0)] = 3E8m/s
My question is if there is something other than u0 and e0 that is stopping light from propagating faster than 3E8 m/s.

In other words, if there was an area of space with a lower value of u0 and e0 if this would automatically make light travel faster or if there is something else that confines light to only going c0?

 

[Baluncore]

c0 is defined by 1/[sqrt(u0*e0)] = 3E8m/s

No.
c0 is defined as an integer 299,792,458 m/s.
Light never propagates at 3E8 m/s. By definition, it only ever gets to 299,792,458 m/s.

The wavelength would need to be very short for an EM wave to propagate inside a hollow conductor. That would be modeled as a waveguide. The group velocity in waveguides filled with real materials will always be less than c, while the phase velocity will always be greater than c.

What could you do to further rarefy the perfect vacuum of free space?
Could you stretch it without making it longer?
Could you halve the number of neutrinos per unit volume?

 

[TerranIV]

Maybe a better way to ask this question would have been, " If you imagine that e0 and u0 were zero, would EM waves propagate with infinite speed or would something else stop this?"

Is if there is something other than u0 and e0 that is restricting the speed of light to 3E8 m/s?

(I realize 3E8 m/s is shorthand estimation of c0. This is not important to the question. The hollow wire is also not important to the question, it is just an example. It could be in deep inter-galactic space, inside a wormhole, magic, whatever. This just just to understand the relationship of EM wave propagation to e0 and u0)

It seems that many people are so sure of the speed of c0 that they seem to forget it is tied to an actual value of empty space - a value that could easily not be the same everywhere in the universe. Perhaps there is a "more empty" kind of space somewhere. (I'm not proposing a theory about this, just a thought experiment like thinking about motion without air resistance.)

 

[ohwilleke]

No.
c0 is defined as an integer 299,792,458 m/s.
Light never propagates at 3E8 m/s. By definition, it only ever gets to 299,792,458 m/s.

The wavelength would need to be very short for an EM wave to propagate inside a hollow conductor. That would be modeled as a waveguide. The group velocity in waveguides filled with real materials will always be less than c, while the phase velocity will always be greater than c.

What could you do to further rarefy the perfect vacuum of free space?
Could you stretch it without making it longer?
Could you halve the number of neutrinos per unit volume?

In all fairness, 3E8 m/s in this rather informal context can be read, I think as intending to be a mere approximation which holds to three significant digits which is sufficient for many physics applications.

 

[ohwilleke]

No.

The permeability and permittivity of the vacuum are legacy terms that came into common use in classical electrodynamics in 1885 by Oliver Heaviside (a fascinating guy in the history of physics for what it is worth) two decades before Einstein's theory of special relativity was published in 1905, and the terminology struck by that point, before anyone knew that the speed of light is a fundamental constant of Nature. The prevailing assumption at the time was that the vacuum was just one more medium in which electromagnetic waves propagated by analogy to sound waves.

If these terms were named from scratch today, they would probably not have been given those names.

Put another way, we now understand the permeability and permittivity of the vacuum in Maxwell's equations to be derived physical constants that are functions of the speed of light in a vacuum, Planck's constant, the coupling constant of the electromagnetic force, and the fundamental unit charge of a single electron.

The more fundamental theories are special relativity and quantum electrodynamics (which obeys special relativity). We now know, as a consequence of special relativity, that no object with rest mass (e.g. an electron) can travel at the speed of light, because the closer you get to this asymptotic speed, the more energy it takes, so it is theoretically impossible for an object with rest mass (at least one that has ever had a speed of less than the speed of light) to travel at the speed of light. Special relativity was formulated without any medium dependence. So, it is theoretically impossible to modify the permeability and permittivity of any medium such that the speed of light would be faster than the speed of light in a vacuum. (Fun fact, Maxwell's equations, even though they are classical, are consistent with special relativity.)

If that was possible, all of the core theories of physics (general relativity, special relativity, and the Standard Model of Particle Physics) which rely on obedience to special relativity would unravel.

Violations of special relativity are also not permitted in BSM theories such as all varieties of supersymmetry, supergravity, and String theory (in case of String theory, at least with respect to the string theory vacuum in which we live for multiverse adherents).

It also follows that if we discover a force that propagates at a speed less than the speed of light via a carrier boson (the way all other forces are and the way that the graviton hypothetically does for a quantum gravity theory) that the carrier boson must have a non-zero rest mass. There is also new evidence from gravitational wave detector and telescope based observations of a black hole eating up a neutron star, that the speed of gravity has to be extremely close to the speed of light and is not inconsistent with being identical to the speed of light as predicted in general relativity and most, but not all, modifications and extensions of general relativity (the exceptions being named, aptly enough, massive gravity theories).

In quantum gravity theories such as loop quantum gravity that seek to quantize space-time itself, rather than a carrier boson for a gravitational force, the speed of light might merely be an average speed limit honored statistically for any distance significantly greater than the Planck length (which is more than a dozen orders of magnitude smaller than the size of an atom), although how this could be possible without having accumulating Lorentz invariance violations (i.e. special relativity violations) over long distances, is a subject of ongoing research in that area of quantum gravity theory. There are strict limits on the extent to which there can be violations of Lorentz invariance based upon observations of neutrinos emitted from supernovas at the same time as light is emitted whose arrival times are compared.

There is not a shred of positive credible evidence that the speed limit of special relativity is every violated and it has been robustly tested in many different kinds of experiments. We can't absolutely rule out slight violations of this speed limit experimentally (and quantum electrodynamics considers faster than speed of light paths of virtual probability amplitudes as part of an overall calculation that never actually violates the speed of light in the end result in its propagator path integral that tells you the probability of a particle moving from point A to point B), but that is purely a function of the limits of our extremely precise, but not infinitely precise measurement tools.

There is a theoretical possibility that there are some particles called tachyons that always travel at greater than the speed of light, but there is no positive evidence for that either and beyond the Standard Model theories that allow that are usually considered defective because it creates the possibility of causality paradoxes even at the theoretical level.

 

[Baluncore]

Maybe a better way to ask this question would have been, " If you imagine that e0 and u0 were zero, would EM waves propagate with infinite speed or would something else stop this?"

Is if there is something other than u0 and e0 that is restricting the speed of light to 3E8 m/s?

Since the metre is defined by the speed of light, if c0 changed in a region of space, then since c0 in that space would remain at 299,792,458 m/s, the metre would stretch to compensate. That would distort space and/or time.

 

[TerranIV]

The permeability and permittivity of the vacuum are legacy terms [...] we now understand the permeability and permittivity of the vacuum in Maxwell's equations to be derived physical constants that are functions of the speed of light in a vacuum, Planck's constant, the coupling constant of the electromagnetic force, and the fundamental unit charge of a single electron.

Not sure what you are trying to say here. The permeability and permittivity of the vacuum are not just "terms" but actual fundamental properties of free space that effect the propagation of electromagnetic waves through space.

Special relativity was formulated without any medium dependence. So, it is theoretically impossible to modify the permeability and permittivity of any medium such that the speed of light would be faster than the speed of light in a vacuum.

Right, because it is based on the constant speed of light in a vacuum and takes it as a constant. My question is about the fundamental reason this is a constant - which is based on the fine structure of space-time itself. The properties of space-time that dictate the speed that light propagates are the electric and magnetic constants

If that was possible, all of the core theories of physics (general relativity, special relativity, and the Standard Model of Particle Physics) which rely on obedience to special relativity would unravel.

This is more what I was looking for. Exactly what would unravel if c0 was slightly faster than 3E8? (3E9 for instance.)

It also follows that if we discover a force that propagates at a speed less than the speed of light via a carrier boson (the way all other forces are and the way that the graviton hypothetically does for a quantum gravity theory) that the carrier boson must have a non-zero rest mass.

Not sure what you are referring to again here as light propagates slower than c0 all the time when it is traveling through a portion of space with a higher permeability and permittivity - such as through water or glass.

There is not a shred of positive credible evidence that the speed limit of special relativity is every violated and it has been robustly tested in many different kinds of experiments.

I'm sure you are aware of the apparent faster than light speed communication between entangled particles. While there are many explanations for this "spooky action at a distance" I think it more than counts as evidence for the possibility of faster than light propagation, even considering the inability of such a system to transmit information faster than light.

There is a theoretical possibility that there are some particles called tachyons that always travel at greater than the speed of light, but there is no positive evidence for that either and beyond the Standard Model theories that allow that are usually considered defective because it creates the possibility of causality paradoxes even at the theoretical level.

Tachyons are fundamentally different particles than luxons or bradyons and cause severe Lorentz violations. I don't think we need to go to that extreme. However, if we are going there then I would point out that wormholes allow extreme violations of the speed of light in propagating information, not only across space, but also possibly through time. I am not aware of wormholes unraveling all of relativity and quantum dynamics.

Light travels slower than c0 all the time in mediums with higher permeability and permittivity values without destroying relativity. If c0 simply was 6E8 all of the equations would be the same, the values would just be slightly different.

I appreciate your thoughtful response, however, I don't think you actually explained WHY a lower value of the permeability and permittivity values wouldn't make light propagate faster.

 

[ohwilleke]

Not sure what you are trying to say here. The permeability and permittivity of the vacuum are not just "terms" but actual fundamental properties of free space that effect the propagation of electromagnetic waves through space.

The words used to describe these electromagnetic properties are words that imply that the medium matters when it actually doesn't at the fundamental level. Free space isn't actually a thing that has properties of permeability and permittivity as we describe them in Heavisde's terminology from 1885. Free space is nothing.

The reason that these properties are displayed is because if you take the more fundamental theory QED, and you calculate what the value of that observable property should be, the result that you get is e (i.e. the fundamental charge of an electron) divided by the product of cO (i.e. the speed of light), h (i.e. Planck's constant), α (the electromagnetic coupling constant), and the number 2. Flip the numerator and denominator and tweak by a factor of c0 and you get the other.

None of the physical constants that go into setting those two observable properties have anything to do with the medium through which photons are passing, because at a fundamental level, there is no such thing as a medium in QED.

Now, it is true that α (the electromagnetic coupling constant) isn't truly a constant. It is actually a function of momentum transfer in an interaction also known as energy scale. At higher energies, α is bigger. At lower energies, α is smaller. But, as used in the formula to determine the values of permeability and permittivity of the vacuum in Maxwell's equations from first principals using QED, the value in the infrared limit is the proper value to use.

My question is about the fundamental reason this is a constant - which is based on the fine structure of space-time itself. The properties of space-time that dictate the speed that light propagates are the electric and magnetic constants

This is the fundamental flaw in your analysis and it is very forgivable because terms like permeability and permittivity of the vacuum, and speed of light in a vacuum, give the false impression that the value of c0 is based on the fine structure of space-time itself, or that space-time has properties.

You are following linguistic clues that were put there by people who thought, pre-1905, that this was the way that it actually worked and described their physical constants accordingly and now we're stuck with that language.

But, they were wrong. The permeability and permittivity of the vacuum, and speed of light in a vacuum, are not actually properties of "something" that makes up space-time which is a medium called a vacuum. There is no medium that has properties.

c0 is really better thought of as the special relativity speed limit that causes light to travel at a certain speed.

The permeability and permittivity of the vacuum are really just stylized formats for describing the fundamentally dimensionless coupling constant of the electromagnetic force in dimensionful terminology. Both of them are just functions of the likelihood of an electron with one fundamental electric charge emitting or absorbing a photon in the limit of zero momentum transfer interactions (or transactions so close to zero that they work out to be indistinguishable. The momentum transfer is two particles at which the coupling constants has run from 1/137 in the zero momentum transfer limit to 1/125 is about 90 GeV. So, if the momentum transfer between just two particles in your interaction is much less than 90 GeV then the coupling constant of electromagnetism is indistinguishable from 1/137.

The concept of the running of the coupling constant of electromagnetism with momentum transfer is a quantum phenomena in QED that is inconsistent with Maxwell's equations and classical electromagnetism. One of the reasons it took so long to come up with QED is that physicists had trouble believing that the strength of the electromagnetic force was a function of momentum transfer scale.

c0 however, is not a quantum mechanical constant that runs with energy scale. c0 is the same in every reference frame. This isn't just a coincidental or observed similarity, the fact that c0 is the same everywhere and everytime in every reference frame is the first and most fundamental assumption of special relativity and is the key stone from which special relativity and general relativity arise. That assumption is all you need to work out the Lorentz transform.

This is more what I was looking for. Exactly what would unravel if c0 was slightly faster than 3E8? (3E9 for instance.)

If the speed of light (i.e. photons) were faster than c0, then all sorts of things would unravel. Time would start flowing backwards and there would be causality violations, you'd get infinite energies all over the place, the predicted probability of a photon going from point A to all possible other points would not equal 100%, light would escape from small black holes, the relative effective strengths of the electromagnetic force and strong force would change making free neutrons decay faster, and turning some stable isotypes into unstable ones, conservation of mass-energy would break down because you could create energy from nothing using photons, the calculation of the magnetic moments of the electron and muon would no longer converge and instead would blow up into infinities, all of the inferences we made from red shift data would be nonsense, light wouldn't travel along goedesics in general relativity and instead would take a different path that particles with rest mass and gravitons and gluons. All of the equations of the SM and special relativity and GR that involved photons in any direct or indirect way would become inconsistent or indeterminate. You wouldn't be able to calculate anything and the universe would cease to obey the laws of mathematics. All of your computer programs for physics calculations would start spitting out error messages.

If c0 was slightly more than we thought it was when we used it to define the length of the meter, the officially defined length of a meter would be a teensy bit longer than the physical meter stick whose length was used to define the meter (and why they didn't do just that and define c0 as equal to exactly 3E8 meters, I'll never fathom).

I'm sure you are aware of the apparent faster than light speed communication between entangled particles. While there are many explanations for this "spooky action at a distance" I think it more than counts as evidence for the possibility of faster than light propagation, even considering the inability of such a system to transmit information faster than light.

Entanglement does not make it possible to transmit information faster than the speed of light. The discussion of why that is the case is rather involved and has been addressed in other threads. This leads too far afield.

The simplest way to understand it at a heuristic level, while grossly oversimplifying is that any two entangled particles must always be in the same light cone and that photons don't experience time in their own reference frame.

Another inexact and heuristic way to describe it is that mere correlation does not imply an ability to transfer information.

But, the bottom line is that entanglement is not the loophole around the special relativity speed limit that it naively appears to be. Explaining it more precisely is a task for another day.

Tachyons are fundamentally different particles than luxons or bradyons and cause severe Lorentz violations. I don't think we need to go to that extreme. However, if we are going there then I would point out that wormholes allow extreme violations of the speed of light in propagating information, not only across space, but also possibly through time. I am not aware of wormholes unraveling all of relativity and quantum dynamics.

Wormholes would require a topology very different from what we see in the universe and there are papers out there established how very far you need to get from relativity and quantum mechanics to have a traversible wormhole.

At any rate, a wormhole, in a world where they exist, does not do its magic by changing the speed of light or being made out of a special medium, it does its magic by finding a path with a shorter distance from point A to point B than we were previously aware existed made possible by a topology of space-time different from what we seem to see. The explanation from Madeline L'Engle's book "A Wrinkle In Time" in a beautiful and accurate description of the meaning of a wormhole.

Not sure what you are referring to again here as light propagates slower than c0 all the time when it is traveling through a portion of space with a higher permeability and permittivity - such as through water or glass. . . . Light travels slower than c0 all the time in mediums with higher permeability and permittivity values without destroying relativity. If c0 simply was 6E8 all of the equations would be the same, the values would just be slightly different.

While we call it that, calling c0 the "speed of light" or the "speed of light in a vacuum" is conceptually unhelpful and misleading.

It is more useful to think about c0 as the constant of a Lorentz transformation that applies without regard to medium to any particle whether it is massive or massless. Special relativity forces all particles with zero rest mass (e.g. photons, gluons and hypothetical gravitons) to travel at the speed of light (no more and no less) and to not experience time in their own reference frames.

Logically, the speed limit of special relativity is prior to the speed of light in a true vacuum which is just an observational consequence of a particle with zero rest mass existing in a world where special relativity applies.

The apparent slowing of light in certain mediums with higher permeability and permittivity are classical approximations of photons either taking a non-straight path and/or the original photon being absorbed by an electron (or other charged particle) and then a new identical photon being emitted again. All photons are always moving at speed c0 all the time, while they exist, along whatever paths they take.

At the quantum level, there is no such thing as a medium. It is all just particles flying around and interacting with each other.

I appreciate your thoughtful response, however, I don't think you actually explained WHY a lower value of the permeability and permittivity values wouldn't make light propagate faster.

You are right.

What I actually did was explain to you why that is impossible, even in principle or hypothetically, to do with any medium whatsoever. The medium involved has nothing to do with the rate at which light propagates in the real world and under all of the very well tested laws of physics.

What I understood your question to ask was not "What would happen if all of the laws of physics were different?", but "If something physical (a special medium with particular values of permeability and permittivity) could change the speed of light through that medium, in a world with the same basic laws of physics that we have today, what would happen?"

But, unless you change special relativity, you can't do that. It isn't just practically impossible, it can't be done at all under any circumstances in any way. None of the equations of GR, special relativity or the Standard Model would be consistent if the speed of light were greater than c0 for all other purposes. The question is basically a category error.

 

[ohwilleke]

Since the metre is defined by the speed of light, if c0 changed in a region of space, then since c0 in that space would remain at 299,792,458 m/s, the metre would stretch to compensate. That would distort space and/or time.

No. it would just mean that the definition of the metre was a length slightly longer than the metre stick from which the defined value was determined. This would just be a tweak in units.

 

[Dr.AbeNikIanEdL]

Just to mention there was an insights article once on why it is not particularly meaningful to ask about the numerical value of c (and also a corresponding discussion afterwards):

https://www.physicsforums.com/insights/why-does-c-have-a-particular-value-and-can-it-change/

In short: It does not make much sense to ask what the value of constant with units is, as this just depends on what units you chose. It is more sensible to ask for dimensionless constants, in the context of the speed of light you are often actually asking about the electromagnetic fine structure constant.

 

[PhilDSP]

However, if you do not limit yourself to using scalar values for $\epsilon_0$ and $\rho_0$ then there is very much that can be accomplished with materials. For example, you can generate a negative index of refraction.

https://www.sciencedirect.com/science/article/pii/S1369702106715735
It seems to have been demonstrated that group velocities can be greater than c within certain special materials, though this does not imply that energy flows at such speeds.

https://phys.org/news/2007-01-mach-scientists-faster.html

 

[TerranIV]

Just to mention there was an insights article once on why it is not particularly meaningful to ask about the numerical value of c (and also a corresponding discussion afterwards):

https://www.physicsforums.com/insights/why-does-c-have-a-particular-value-and-can-it-change/

In short: It does not make much sense to ask what the value of constant with units is, as this just depends on what units you chose. It is more sensible to ask for dimensionless constants, in the context of the speed of light you are often actually asking about the electromagnetic fine structure constant.

While the number we use is for c is arbitrary, the value is not. You can use meters or kilometers or feet or miles - they all give you different numbers - however the value of c_0 is a very precise and constant speed (as measured by another mass).
As far as I know the speed we measure light to be traveling is DIRECTLY related to the permittivity of the space it moves through. (Just as c_0 is approx 3E8 m/s, c_water is 2.5E8 m/s, and c_glass is 2E8 m/s.)
My question again is, IF there was a way to artificially lower the permittivity of free space to LESS than that of a vacuum is there any reason the speed of light in that volume of space would not be more than 3E8 m/s?
I cannot think of any reason why this could not theoretically be possible (putting aside for the moment whether or not there is actually a way to lower permittivity below E_0).

 

[Dr.AbeNikIanEdL]

While the number we use is for c is arbitrary, the value is not.

I do not understand what the distinction you are trying to make.

lower the permittivity of free space to LESS than that of a vacuum

Again, what do you think is the difference between “free space” and “vacuum” in this context?

putting aside for the moment whether or not there is actually a way to lower permittivity below E_0

If I could make a ton have a mass of 1kg, could I lift it?

 

[Dale]

The permeability and permittivity of the vacuum are not just "terms" but actual fundamental properties of free space that effect the propagation of electromagnetic waves through space.

Not really. The permeability and permittivity of vacuum are simply constants that define your system of units. Changing them only amounts to a change in your units and does not change anything physical. In fact, in some unit systems they do not even exist.

If you want to talk about fundamental physical constants then you need to talk about dimensionless constants. In this case the relevant one is the fine structure constant

 

[TerranIV]

Not really. The permeability and permittivity of vacuum are simply constants that define your system of units. Changing them only amounts to a change in your units and does not change anything physical. In fact, in some unit systems they do not even exist.

If you want to talk about fundamental physical constants then you need to talk about dimensionless constants. In this case the relevant one is the fine structure constant

What are you getting at here? Are you trying to argue that permittivity is not real?

This thread is asking if there is some specific reason if the permittivity and permeability of space was lower that the speed of light would also be faster.

I don't understand why everyone keeps trying to change the subject.

 

[Dale]

What are you getting at here? Are you trying to argue that permittivity is not real?

I never said that. The vacuum permittivity and vacuum permeability are an artifact of your choice of units. They tell you nothing about the physics. Only dimensionless constants tell you about physics.

Here is an article explaining this:
http://math.ucr.edu/home/baez/constants.html

This thread is asking if there is some specific reason if the permittivity and permeability of space was lower that the speed of light would also be faster.

I don't understand why everyone keeps trying to change the subject

The question is based on some mistaken premises. When a question is based on a mistaken premise the best thing to do is to fix the mistaken premises. What you are seeing as changing the subject is addressing the underlying mistake

 

[TerranIV]

The question is based on some mistaken premises. When a question is based on a mistaken premise the best thing to do is to fix the mistaken premises. What you are seeing as changing the subject is addressing the underlying mistake

What "mistaken premises" are you referring to?

You agree that light travels at different speeds through volumes with different permittivity or refractive indexes, correct? I.e. c_0 is approx 3E8 m/s, c_water is 2.5E8 m/s, and c_glass is 2E8 m/s.

 

[Dale]

What "mistaken premises" are you referring to?

The main one is the mistaken premise that changing the permittivity of free space would have any physical consequences. It would not. All it would do is change your units. That is your biggest mistaken premise. Changing the dimensionless fine structure constant would change the physics, but changing the permittivity of vacuum would not.

You agree that light travels at different speeds through volumes with different permittivity or refractive indexes, correct? I.e. c_0 is approx 3E8 m/s, c_water is 2.5E8 m/s, and c_glass is 2E8 m/s.

Yes, but what is important here in terms of physics is the dimensionless relative permittivity, not the absolute permittivity.

 

[jackwhirl]

it is theoretically impossible for an object with rest mass (at least one that has ever had a speed of less than the speed of light) to travel at the speed of light.

This is completely aside, but I'd never heard this fun little caveat before. Thank you, @ohwilleke.

 

[TerranIV]

The main one is the mistaken premise that changing the permittivity of free space would have any physical consequences. It would not. All it would do is change your units. That is your biggest mistaken premise. Changing the dimensionless fine structure constant would change the physics, but changing the permittivity of vacuum would not.

Why would you think this? The speed of light does not depend on the fine structure constant. It is based on permittivity and permeability values.

Permittivity and permeability have different values depending on the electromagnetic field in the volume of space you are measuring. Free space has a non-zero electromagnetic field which gives rise to the values of e_0 and u_0. While it might take some extreme physics to lower this in free space, if you could theoretically lower the field you would increase the speed of light.

This would not change the value of u_0, it postulates a NEW VALUE, something like u_-1. There is no need to change anything about the fine structure constant. Of course the u_-1 would be related to the fine structure but with a unique equation.

Yes, but what is important here in terms of physics is the dimensionless relative permittivity, not the absolute permittivity.

The fine structure constant is a real measured value, not some vague ethereal thing. Theoretically lowering the permittivity or permeability less than e_0 and u_0 wouldn't change the measured values of e_0 and u_0 anymore than the higher values of e_glass and u_glass do.

 

[Dale]

Why would you think this?

Did you not read the link I sent? It explains why in quite a bit of detail. In addition, I have actually worked through the math on this topic myself and can confirm: changes in the dimensionful constants have no impact on physics, only changes in dimensionless constants.

The speed of light does not depend on the fine structure constant.

The speed of light is also a dimensionful constant. Read the link.

While it might take some extreme physics to lower this in free space, if you could theoretically lower the field you would increase the speed of light

It wouldn’t take any extreme physics. It would just take a vote of the CIPM. They could change the permittivity of free space and the speed of light any time they feel like doing so. Those constants only define the units, they do not change the physics.

The fine structure constant is a real measured value, not some vague ethereal thing.

I know. I have been trying to teach you its importance to your question. It is the most important physical quantity related to this discussion

There is no need to change anything about the fine structure constant.

Then there is no physical change.

 

[Nugatory]

Why would you think this? The speed of light does not depend on the fine structure constant. It is based on permittivity and permeability values.

You may want to try some of our many many threads about what would happen if $c$ had some other value.

The speed of light is determined by the permittivity and permeability values in the sense that given any two you can calculate the third, but that doesn’t mean what you think it does. I could just as reasonably argue that the permittivity is determined from the speed of light and the permeability, for example.

In fact, the value of all three depends only on our choice of units and the value of the fine structure constant, which being dimensionless has the same value (about 1/137) no matter what units we choose. Any physically meaningful change in the propagation of electromagnetic waves in a vacuum must imply a change in the fine structure constant; if that constant does not change the physics doesn’t change.

 

[Vanadium 50]

Let's start with permeability. Do you think the 4π is a) an artifact of the definition of units or b) a physical constant that just accidentally happens to be 4π?

 

[TerranIV]

Let's start with permeability. Do you think the 4π is a) an artifact of the definition of units or b) a physical constant that just accidentally happens to be 4π?

Do you think that something having a larger or smaller value than something else is dependent on units?
Do you think permeability of a volume is only determined by e_0?
Do you think that e_water = e_0?

 

[TerranIV]

You may want to try some of our many many threads about what would happen if $c$ had some other value.

The speed of light is determined by the permittivity and permeability values in the sense that given any two you can calculate the third, but that doesn’t mean what you think it does. I could just as reasonably argue that the permittivity is determined from the speed of light and the permeability, for example.

In fact, the value of all three depends only on our choice of units and the value of the fine structure constant, which being dimensionless has the same value (about 1/137) no matter what units we choose. Any physically meaningful change in the propagation of electromagnetic waves in a vacuum must imply a change in the fine structure constant; if that constant does not change the physics doesn’t change.

$c$ DOES have many values. $c0$ has a specific value. It doesn't matter what units you use to describe it. The units used determine the number of them when indicating the value.

The change of propagation of the electromagnetic waves in THE vacuum don't change, however if you make a change to the volume of space (fill it with water, fill it with glass, etc) this DOES change the speed EM waves propagate. If we changed the value of permittivity and permeability in the vacuum it would obviously no longer be THE vacuum.

I realize I am postulating a non-real volume to discuss how EM waves would propagate but I assumed most people in a physics forum would be familiar with the concept of a thought experiment. I guess I wasn't clear enough in my question.

 

[Vanadium 50]

I notice you didn't answer my question. I think you're not here to learn, you're here to pitch your own iconoclastic beliefs.

 

[Nugatory]

$c$ does have many values. $c0$ has a specific value

$c$ is the invariant speed in the special theory of relativity. It has multiple values only in the trivial sense that we can give it any value we please by appropriate choice of units (1 lightyear per year, 2999792458 meters/sec, 186000 miles per second, ...).

It so happens (as a consequence of the Lorentz invariance of Maxwell’s equations) that light propagates at that speed in a perfect vacuum. It also so happens (because of the historical accident that the speed of light was measured long before the discovery of Maxwell’s equations and then special relativity) that we casually refer to $c$ as “the speed of light” but that’s thinking about it backwards. It’s the invariant velocity, and light in a vacuum is one of the things that must propagate at that speed.

 

[Nugatory]

Do you think that something having a larger or smaller value than something else is dependent on units?

As long as we’re using the same units consistently (obviously the numerical value of the speed of light in water is greater than the numerical value of the speed of light in vacuum if we measure the first in miles per hour and the second in light years per years, but that’s just inconsistent units) then the answer is “of course not”. But now you’ve hit on why all the meaningful physics is in the dimensionless ratios. The ratio of the the speed of light in water to the speed of light in vacuum is the dimensionless quantity .75, and that’s a real comparison with real physical significance. Likewise, the ratio of the speed of light in vacuum to the invariant velocity of special relativity is 1.0.

Are you familiar with the modern definition of $\mu_0$ and $e_0$? Both have a fixed relationship to the fine-structure constant, so any “measurement” of either can serve only to refine our best known value for that quantity.

 

[Vanadium 50]

Are you familiar with the modern definition of μ0\mu_0 and e0e_0? Both have a fixed relationship to the fine-structure constant

I don't think they do, since the fine structure constant is quantum mechanical, and c is purely classical:

μ₀ is just the definition of the ampere. If one measures space and time in the same units (just as one measures northness and eastness in the same units), then ε₀ = 1/μ₀.

 

[Dale]

c0 has a specific value. It doesn't matter what units you use to describe it.

Actually, if you dig down into this concept you will find that what you actually mean is not related to the speed of light but to the fine structure constant. Think, what do you mean by the specific value of the speed of light if you don’t use units to describe it.

 

[ohwilleke]

I don't think they do, since the fine structure constant is quantum mechanical, and c is purely classical

The fine structure constant is quantum mechanical. c is just as much a part of quantum physics as it is a part of classical physics. Special relativity is observed in both Maxwell's equations and in QED.

 

[Nugatory]

Are you familiar with the modern definition of $\mu_0$ and $\epsilon_0$? Both have a fixed relationship to the fine-structure constant, so any “measurement” of either can serve only to refine our best known value for that quantity.

I don't think they do, since the fine structure constant is quantum mechanical, and c is purely classical:

I'm using (or misunderstanding?) the 2019 definitions. We have $\alpha=\frac{\mu_0}{2}\frac{e^2c}{h}$ with $e$, $c$, and $h$ all fixed, and we have $\epsilon_0=\frac{1}{\mu_0c^2}$. That leaves $\mu_0$ and $\alpha$ proportional to one another with a fixed constant of proportionality, and $\epsilon_0$ in a fixed relationship with $\mu_0$. Thus there is no freedom to vary them independently.

 

[Vanadium 50]

Sorry this took so long. By the time I thought it through, I couldn't find the message any more.

I think we can agree that the equation alone is a necessary but not sufficient condition for a physical relationship in it. In the case of alpha, we don't want to imply that there is a relationship between c and the number 2 for instance. So we need to understand where each term comes from.

The h comes in because there is no classical way to measure alpha: it is purely quantum-mechanical.

The first complication is that one can "hide" the h. In units where h is 1, one can replace the h with a plain old one. In other units, you can absorb it in the definition of μ₀. So one can write down what looks like a purely classical α, even though it is really quantum mechanical.

Are there any parts that can't be hidden? Yes, the e². Not only is it present no matter what units you are using, every measurement of α on objects of charge q₁ and q₂ has a q₁ and q₂ in it. So that's real. And, to jump to A-level for one line, if you are discussing different fundamental forces, they have different coupling constants (α is the coupling constant for electromagnetism) because they have different elementary charges. So α is essentially the electric charge of the electron (squared).

Let me slightly rewrite what you wrote: \alpha \sim \frac{e^2}{\epsilon_0}. This is a force times a distance squared. You can sort of see where this is going to cause you trouble relativistically, because distance is not an invariant, and α, being just a number, must be. So the reason the c is there comes into the fact that by convention we measure space and time in different units. (To jump to an I.5 level for one line, this is actually wrapped up in the definition of ε₀; it comes from Coloumb's Law, where you have a Force (which has a time derivative) on one side of the equation and something purely spatial on the other)

Had we worked in conventional units for airplane flight, where horizontal distances are measured in nautical miles and vertical distances in 100's of feet, we'd see the constant 60.76 appearing in these definitions as well.

So that's why I don't consider α a measure of c.

 

[Dale]

So that's why I don't consider α a measure of c.

I agree that $\alpha$ is not a measure of c, but when people actually express what they mean by statements like “c has a specific value regardless of the units used to describe it” what they are looking at is in fact the fine structure constant.

 

[Vanadium 50]

when people actually express what they mean by statements like “c has a specific value regardless of the units used to describe it” what they are looking at is in fact the fine structure constant.

I think that when people write that, they either don't believe in relativity, or they are completely confused.

Historically we measured time in seconds and length in meters. Also, for airplanes, we measure horizontal distances in nautical miles and vertical distances in 100-feet increments. In one case, you need c's and in the other you need 60.76's. They serve exactly the same function.

 

[Meir Achuz]

Let's start with permeability. Do you think the 4π is a) an artifact of the definition of units or b) a physical constant that just accidentally happens to be 4π?

Muzero is just a change of units like the fundamental constant 5280.
muzero/4pi=10^-7 to change the units from the original emu system to SI.
10^-5 comes from changing from cgs to MKS units. The 10^-2 comes from the change (in 1880 something) from the Absolute Ampere (defined by the force between two wires) to the SI Ampere. I think that was done because the telegraphers defined the ohm for their convenience.
If you changed 5280, an American could run faster.

 

[NBrown]

Somehow I stumbled across this question, that was posted 3 years ago. It is a brilliant, clear and simple question in search of an equally straightforward answer. Most of the answers show that there are many people around that have some level of grasp of modern physics, and that are willing to talk at length around it, but I found no good, direct, clear, simple and plausible answer. I do not believe that there is in principle no simple and elegant answer. I also don’t have it - and I don’t know whether science has it (yet). @TerranIV, if you have in the meantime received a satisfying answer, I would be intrigued to know what it is.

 

[PeroK]

Somehow I stumbled across this question, that was posted 3 years ago. It is a brilliant, clear and simple question in search of an equally straightforward answer. Most of the answers show that there are many people around that have some level of grasp of modern physics, and that are willing to talk at length around it, but I found no good, direct, clear, simple and plausible answer. I do not believe that there is in principle no simple and elegant answer. I also don’t have it - and I don’t know whether science has it (yet). @TerranIV, if you have in the meantime received a satisfying answer, I would be intrigued to know what it is.

I think @TerranIV was last seen looking for the company that built Nigel Tufnell's amplifier.

 

[Dale]

It is a brilliant, clear and simple question in search of an equally straightforward answer.

The straightforward answer is “no”.

 

[NBrown]

The straightforward answer is “no”.

Thanks, Dale, I already know your thoughts on the topic, but I was asking TerranIV if he had received a satisfying answer (meaning satisfying to him). I don’t expect this to be answered by anyone other than TerranIV.

 

[Dale]

Then I recommend you PM them. The public forums are for public commentary, not for a one on one discussion.

 

[Vanadium 50]

but I was asking TerranIV if he had received a satisfying answer

Then a PM would possibly be appropriate, but he hasn't been here in 3-1/2 years. But it sounds like you dislike the answers so far. As they say "Two plus two continue to make four, despite the whine of the amateur for three or the cry for the critic for five."

 

[gmax137]

I think @TerranIV was last seen looking for the company that built Nigel Tufnell's amplifier.

OMG I had to google that.