What Medium Does Light Travel Through in Space?

[Matterwave]

Whoop.. beat me to it..

 

[GRQFT]

What do you mean by "specific value" here?

Okay, let me try again.

Let's image two different universes each with just a star like our sun and a planet like Earth. And let's assume that in both universes (A and B) both the stars and planets are identical.

Thus, by "specific" I mean imagine that for a fixed definition of the unit of time in both universe A and B that the time it takes for one particular photon to get from the star's surface to the Earth's surface in universe A is one unit of time whereas in universe B, the same measurement produces an experimental result of two units of time.

 

[GRQFT]

Maxwell literally wrote the encyclopedia article on Ether: https://en.wikisource.org/wiki/Encyclopædia_Britannica,_Ninth_Edition/Ether_(2.)?hl=en-US

Yes, he was a firm believer in the Ether.

Hmm, Maxwell didn't understand Maxwell's equations? That's rather surprising!

 

[Sagittarius A-Star]

Hmm, Maxwell didn't understand Maxwell's equations? That's rather surprising!

He regarded them to be strictly valid only in the ether frame.

 

[A.T.]

Hmm, Maxwell didn't understand Maxwell's equations?

He just underestimated their applicability.

That's rather surprising!

Not really. It's not uncommon for one scientist to develop something, that is extended in applicability by others.

 

[collinsmark]

Again, I'm not asking this question, I'm just bringing up the issue that I think exists, the issue of talking past each other between 'the knowledgable' and people who ask this question.

I think I agree with @weirdoguy here that people might be talking past each other. Maybe.

(Personally, I think the real questions the OP has relates to the mathematical degrees of freedom our universe allows, rather than specific measured or chosen values, but I'm getting ahead of myself.)

Let me take a step back. There is a fun video game, free to download and play for anyone, called, "A Slower Speed of Light." It's from MIT. Here's the link. https://gamelab.mit.edu/games/a-slower-speed-of-light/



So hypothetically, if the speed of light were slower, what else would break? Is it merely something minor such as inconsistencies with measured or chosen values? Or is it something major like having to throw out our entire understanding of physics (even hypothetically)? Something in between?

I hear some essentially claiming that in order to hypothetically slow the speed of light in "A Slower Speed of Light," the game developers are effectively varying the fine structure constant. Is that true? Because it sounds like that's what some people on this thread are saying.

I think it's safe to say that given the physical constants $\alpha, c, \varepsilon_0, \mu_0$, it might look like they're independent, but they're not: there are fewer degrees of freedom then 4. But how much fewer? I think the OP (and others asking similar questions to the OP) are essentially asking this question. If we were to vary c, even in a hypothetical universe such as "A Slower Speed of Light," what other constants would we necessarily have to vary, even hypothetically?

Or is the speed c so intertwined with physical laws that "A Slower Speed of Light" is useless as an educational tool since we'd have to throw out all of known physics for such hypothetical shenanigans?

 

[A.T.]

Let's image two different universes each with just a star like our sun and a planet like Earth. And let's assume that in both universes (A and B) both the stars and planets are identical.

What do you mean by "identical"? How do you compare universes?

Thus, by "specific" I mean imagine that for a fixed definition of the unit of time in both universe A and B

What does "fixed definition of the unit of time in both universes" mean exactly? How do you compare definitions between universes?

 

[A.T.]

I hear some essentially claiming that in order to hypothetically slow the speed of light in "A Slower Speed of Light," the game developers are effectively varying the fine structure constant. Is that true?

You can interpret it in various valid ways. You could for example say: They kept speed of light as it is, but scaled up the level, so that village is multiple light seconds large.

 

[GRQFT]

How do you compare universes?

I assumed the constituents of the two universes (stars, planets, photons, etc.) are the same.

What does "fixed definition of the unit of time in both universes" mean exactly? How do you compare definitions between universes?

I'm not sure what's unclear here. Is this a question about ontological commitment? Metrology?

Let me add another assumption. The way I measure time in both universes is via an hourglass filled with sand. One unit of time in both universes corresponds to all the sand falling from the top compartment/chamber to the bottom.

Does that help?

 

[Sagittarius A-Star]

So, you think that Maxwell himself (who clearly was aware of Faraday's law and Maxwell's displacement [the curl of B equation]) thought that too?

In his ether paper, Maxwell proposed to repeat Ole Roemer's measurement of the speed of light two times with an interval of 6 months. Goal was to determine the relative velocity of the ether with respect to the solar system.
This experiment was not carried-out, but the same goal had the MM experiment, which was carried out later (with a negative result).

The only practicable method of determining directly the relative velocity of the aether with respect to the solar system is to compare the values of the velocity of light deduced from the observation of the eclipses of Jupiter's satellites when Jupiter is seen from the earth at nearly opposite points of the ecliptic.

Source:
https://en.wikisource.org/wiki/Encyclopædia_Britannica,_Ninth_Edition/Ether_(2.)?hl=en-US

 

[Dale]

I hear some essentially claiming that in order to hypothetically slow the speed of light in "A Slower Speed of Light," the game developers are effectively varying the fine structure constant. Is that true?

Yes. Anyone who wishes to can go through the exercise I linked to earlier to see that.

 

[A.T.]

I assumed the constituents of the two universes (stars, planets, photons, etc.) are the same.

Replacing "identical" with "the same" doesn't explain anything. Let's say the inhabitants of the two universes could exchange information (strings of bits). How could they compare their universes, without any common physical reference objects to base common units on? The only thing that would be comparable are unitless ratios, pure numbers.

If they measure numerically different photon travel times between the planet and sun, how would they know if this is because:
- the light propagation speed is different in the two universes?
- the universes have different spatial sizes?
- time runs at different rates in the two universes?

 

[GRQFT]

Replacing "identical" with "the same" doesn't explain anything. Let's say the inhabitants of the two universes could exchange information (strings of bits). How could they compare their universes, without any common physical reference objects to base common units on? The only thing that would be comparable are unitless ratios, pure numbers.

If they measure numerically different photon travel times between the planet and sun, how would they know if this is because:
- the light propagation speed is different in the two universes?
- the universes have different spatial sizes?
- time runs at different rates in the two universes?

Okay, let's just stick with our universe.

Are you saying that it is *hypothetically* inconceivable that the time it takes for a photon to travel from the surface of our sun to the surface of our planet could not be different? That's all I'm really asking.

And to be clear, I'm *not* asking about whether we can or can't measure the time, but simply that, ceteris paribus, the time *could* be different.

And yes, I realize this may seem like a strange question.

 

[A.T.]

And to be clear, I'm *not* asking about whether we can or can't measure the time, ...

Then it's off topic on PF, because physics is about what can be measured. Not about some unobservable difference.

 

[GRQFT]

Then it's off topic on PF, because physics is about what can be measured. Not about some unobservable difference.

Well, you alluded to the fact that c could be differnent in what you wrote below (my emphasis). I did try to use a scenario involving a measurement, but you took issue with that. No problem. So that's when I switched to a scenario sans any measurement.

If they measure numerically different photon travel times between the planet and sun, how would they know if this is because:
- the light propagation speed is different in the two universes?

Anyway, all of this was merely an answer to your question about what I meant by c having a specific value. I simply meant what you wrote above, namely that our value of c is what it is as opposed to it being something different. That's it. Nothing else.

It seems as though the physics of the propagation of EM waves has been subverted by the theoretical reinterpretation of c in SR and the practical demands of metrology.

Or maybe people (possibly me) think about c as a coin with two sides: 1) the EM side where you interpret it as how fast E and B fields propagate through space, and 2) the SR side where c is the conversion factor between time and space.

 

[Dale]

Okay, let me try again.

Let's image two different universes each with just a star like our sun and a planet like Earth. And let's assume that in both universes (A and B) both the stars and planets are identical.

Thus, by "specific" I mean imagine that for a fixed definition of the unit of time in both universe A and B that the time it takes for one particular photon to get from the star's surface to the Earth's surface in universe A is one unit of time whereas in universe B, the same measurement produces an experimental result of two units of time.

This is a much better question, and is getting close to the type of thing that you have to do in order to understand how important the values of the dimensionless constants are.

So the main thing that you have to do is decide what is different in the two universes, and what is the same.

Usually we are going to assume that the laws of physics are the same, but the constants that appear in those laws are different. So the question is which constants? For example, in SI units (with universe-specific values for the defining constants), we have $$\alpha=\frac{e^2}{4\pi \epsilon_0 \hbar c}$$ So you cannot only change $c$, you must also change at least one other constant.

Now, suppose that you set up the same experiment in both universes, under which conditions do we get different experimental outcomes in the two universes? For example, lay a fixed number of copper atoms in a line and count the number of cesium hyperfine transitions it takes for light to cross, reflect, and cross back.

If only $c$ and $\epsilon_0$ change, then the measurement will be the same. If only $c$ and $\hbar$ change the measurement will be the same. But if $c$ and $\alpha$ change then the measurement will be different. The measurement will be different only in universes with different $\alpha$. Any or all of the dimensionful constants may change without changing the measured outcome.

More specifically, the value of $c$ can be anything whatsoever without changing the experimental result, while changing the value of $\alpha$ always results in a different measurement outcome. The physics is in $\alpha$, not $c$.

 

[Sagittarius A-Star]

Or maybe people (possibly me) think about c as a coin with two sides: 1) the EM side where you interpret it as how fast E and B fields propagate through space, and 2) the SR side where c is the conversion factor between time and space.

That 1) and 2) are equivalent can be seen in Gaussian CGS units. Maxwells equations contain partial derivatives for $ct$ of the fields.

$\nabla \cdot \mathbf{E} = 4\pi\rho$
$\nabla \cdot \mathbf{B} = 0$
$\nabla \times \mathbf{E} = -\frac{1}{c}\frac{\partial \mathbf{B}}{\partial t}$
$\nabla \times \mathbf{B} = \frac{4\pi}{c}\mathbf{J} + \frac{1}{c}\frac{\partial \mathbf{E}}{\partial t}$
In vacuum:
$\nabla^2 \mathbf{E} - \frac{1}{c^2}\frac{\partial^2 \mathbf{E}}{\partial t^2} = 0$

 

[GRQFT]

That 1) and 2) are equivalent can be seen in CGS units.

$\nabla \cdot \mathbf{E} = 4\pi\rho$
$\nabla \cdot \mathbf{B} = 0$
$\nabla \times \mathbf{E} = -\frac{1}{c}\frac{\partial \mathbf{B}}{\partial t}$
$\nabla \times \mathbf{B} = \frac{4\pi}{c}\mathbf{J} + \frac{1}{c}\frac{\partial \mathbf{E}}{\partial t}$
In vacuum:
$\nabla^2 \mathbf{E} - \frac{1}{c^2}\frac{\partial^2 \mathbf{E}}{\partial t^2} = 0$

When I look at Maxwell's equations, the EM side is immediately obvious.

However, until now, the SR side was not. Are you seeing it in the last equation where you have something spatial (the Laplacian of E) on the LHS and something temporal (a time derivative of E) on the RHS with 1/c^2 acting as the conversion factor?

Edit: After reading my response I realized that all wave equations have that structure, but the one above specifically contains 1/c^2 making this, at least to me, something EM-related. So, I guess I don't really see SR in it after all.

 

[GRQFT]

This is a much better question, and is getting close to the type of thing that you have to do in order to understand how important the values of the dimensionless constants are.

Thanks. Your 2008 post on that subject is very useful in making these abstract concepts concrete. Cheers...

 

[Sagittarius A-Star]

When I look at Maxwell's equations, the EM side is immediately obvious.

However, until now, the SR side was not. Are you seeing it in the last equation where you have something spatial (the Laplacian of E) on the LHS and something temporal (a time derivative of E) on the RHS with 1/c^2 acting as the conversion factor?

In 4D-spacetime $(ct, x, y, z)$, the EM field is a bivector. It has 6 components (3 electric + 3 magnetic), which are projections on the 6 planes (xt, yt, zt, yz, zx, xy) of the 4D-coordinate system.

Usually, an antisymmetric 4-tensor of grade 2 is used as notation for the EM field:
http://www.scholarpedia.org/article/Special_relativity:_electromagnetism

The speed $c$ comes into the wave equation from the spacetime geometry (see posting #36).

 

[GRQFT]

For those of you who still have questions about the issues discussed in this thread, you should watch this (AI generated) video of Feynman. It's very informative!

 

[Matterwave]

For those of you who still have questions about the issues discussed in this thread, you should watch this YT video of Feynman. It's very informative!

It's an AI generated video of Feynman. Maybe his voice helps elucidate concepts.

 

[GRQFT]

It's an AI generated video of Feynman. Maybe his voice helps elucidate concepts.

Are you sure this isn't a recording of one of his lectures or an interview?

 

[Matterwave]

Are you sure this isn't a recording of one of his lectures or an interview?

If you open the video description it disclaimers that this is AI generated Feynman.

 

[flippiefanus]

The value of the invariant speed is just 1 (in natural units). So the equation is $c=1$.

The important thing that you get from spacetime is not the value of the invariant speed. The important thing is the fact that it is finite.

Even if a dimension parameter such as the speed of light is numerically equal to 1 in a specific set of units one should strictly speaking still provide the units. So the statement $c=1$ would imply that $c$ is dimensionless, which is not correct. The strictly correct expression should be something like $c=1 [units]$.

 

[flippiefanus]

They understood that some constants (like ϵ0) appear or disappear depending on the units.

Strictly speaking, the reason why such quantities "disappear" is because they are absorbed into other quantities. A change in units does not allow one to remove a quantity from an equation.

 

[flippiefanus]

So you cannot only change c, you must also change at least one other constant.

Perhaps, to clarify one should add that if one quantity is changed by a given factor, then another quantity must be change by the inverse of that factor (if they are on the same level above or below the line) to ensure that dimensionless quantity remains the same. By changing two quantities by different unrelated factors, one would end up with a different value for the dimensionless quantity.

 

[renormalize]

Even if a dimension parameter such as the speed of light is numerically equal to 1 in a specific set of units one should strictly speaking still provide the units. So the statement $c=1$ would imply that $c$ is dimensionless, which is not correct. The strictly correct expression should be something like $c=1 [units]$.

But the constant speed-of-light $c$ is "dimensional" only because we humans have traditionally chosen to measure length and time in different units. Knowing as we do now about the unification of space and time into Minkowski spacetime, we might all simply agree to redefine the "speed" of an object to be the dimensionless ratio $\beta=v/c\,$, which ranges from $0$ to $1$. So we would say that Maxwell's equations require that electromagnetic waves propagate at a speed of $1$ "beta" in vacuum. (Although for the speed of most everyday objects, using micro- or nano-betas would doubtless be more practical!)

 

[Sagittarius A-Star]

However, until now, the SR side was not. Are you seeing it in the last equation where you have something spatial (the Laplacian of E) on the LHS and something temporal (a time derivative of E) on the RHS with 1/c^2 acting as the conversion factor?

Yes. The RHS of the wave function contains a 2nd derivative for $ct$. In SR, $t$ is multiplied with $c$ as conversion factor.

Edit: After reading my response I realized that all wave equations have that structure, but the one above specifically contains 1/c^2 making this, at least to me, something EM-related. So, I guess I don't really see SR in it after all.

You will see SR in Maxwells equations, if you write them in 4-tensor notation.

Greek indices 1...4 stand for the spacetime coordinates:
$x^\mu = (x^1, x^2, x^3, x^4) = (x, y, z, ct)$

The EM field in Gaussian CGS units and convention (+++-):
$F^{\mu\nu} = \begin{pmatrix} 0 & B_z & -B_y & -E_x \\ -B_z & 0 & B_x & -E_y \\ B_y & -B_x & 0 & -E_z \\ E_x & E_y & E_z & 0 \end{pmatrix}$
The dual field tensor:
$\tilde{F}^{\mu\nu} = \begin{pmatrix} 0 & -E_z & E_y & -B_x \\ E_z & 0 & -E_x & -B_y \\ -E_y & E_x & 0 & -B_z \\ B_x & B_y & B_z & 0 \end{pmatrix}$
The 4-current:
$J^\mu = (J_x, J_y, J_z, c\rho)$

Maxwells 4 inhomogeneous equations (you get each by setting $\mu = 1...4$):
$\partial_\nu F^{\mu\nu} = \frac{4\pi}{c} J^\mu$

Maxwells 4 homogeneous equations by using the dual field tensor (you get each by setting $\mu = 1...4$):
$\partial_\nu \tilde{F}^{\mu\nu} = 0$ (no magnetic monopole current)

The EM-wave function follows from Maxwells equations.

 

[Matterwave]

propagate at a speed of $1$ "beta" in vacuum.

I vote for "lights"... $\frac{light\cdot \cancel{second}}{\cancel{second}}=light$