What Medium Does Light Travel Through in Space?

[GRQFT]

I just visited the NIST website and found the diagram below.

This is how they describe c:

And this is their list of the seven "base SI units"

Perhaps they were being sloppy with their choice of words, but in the figure caption they describe these seven base SI units as "fundamental constants" and provide dimensions for each. They give c in terms of m/s.

To be fair I also noticed that the date at the bottom of the webpage was Oct 12, 2018 (the year before the 2019 update went into effect), but next to that it also said that the page was updated May 7, 2026 (which was just a few months ago).

So, it's a little disconcerting (and confusing!) that the 'measurement people' have this information on their site.

 

[Dale]

So, presumably we can obtain a value for c from GR. Do you happen to know the relevant equation?

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.

 

[GRQFT]

In SR the invariant speed is finite.

The value of $c$ is defined by the SI definition of "1 meter".
https://en.wikipedia.org/wiki/Metre

And how does that relate to the geometry of spacetime?

$0={E \over c^2} \sqrt{1 - v^2/c^2} \Rightarrow v=c$

Which requires a measurement of the E (hv) of a photon.

 

[renormalize]

So, presumably we can obtain a value for c from GR. Do you happen to know the relevant equation?

You don't need curved spacetime (GR), only the flat Minkowski spacetime of SR. The relevant equation is simply $c=1$ in natural units. For example, think of astronomy: the distance to even nearby stars is huge by human standards, so astronomers (naturally!) measure distance in light-years. Their natural units are thus time in years, distance in light-years $\Rightarrow c=1$ light-year per year $=1\,$. Any other value just originates from the human historical tendency to measure space and time in different units.
(Oops, Dale beat me to it!)

 

[GRQFT]

You don't need curved spacetime (GR), only flat Minkowski spacetime of SR. The relevant equation is simply $c=1$ in natural units.

My understanding of natural units is that these "...systems simplify the form of each equation, [though] it is still necessary to keep track of the non-collapsed dimensions of each quantity or expression in order to reinsert physical constants (such dimensions uniquely determine the full formula)." Source: Natural units

Is this incorrect?

 

[Sagittarius A-Star]

And how does that relate to the geometry of spacetime?

In spacetime geometry, the following interval is invariant:
$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2$
This can be derived from the two SR postulates or from the first postulate and group properties of the coordinate transformation plus an experiment, which excludes the Galilei tramsformation as physically relevant.
https://arxiv.org/abs/physics/0302045

Which requires a measurement of the E (hv) of a photon.

Why? I don't think so.

 

[GRQFT]

In spacetime geometry, the following interval is invariant:
$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2$
This can be derived from the two SR postulates or from the first postulate and group properties of the coordinate transformation plus an experiment, which excludes the Galilei tramsformation as physically relevant.
https://arxiv.org/abs/physics/0302045

And so if I wanted to calculate the value of c using the spacetime interval (above), I would have to make three spatial measurements and one temporal measurement?

Why? I don't think so.

Again, if I want to obtain a numerical value for c using the equation you supplied (which contains the variables E and v), I would have to know them in order to obtain c. Without them the equation is mathematically undetermined (and, as such, has an infinite number of solutions).

 

[Sagittarius A-Star]

And so if I wanted to calculate the value of c using the spacetime interval (above), I would have to make three spatial measurements and one temporal measurement?

No, $c$ is defined by the SI unit system. No measurements are needed.

Again, if I want to obtain a numerical value for c using the equation you supplied (which contains the variables E and v), I would have to know them in order to obtain c. Without them the equation is mathematically undetermined (and, as such, has an infinite number of solutions).

No. If the square-root in posting #30 becomes zero, the energy $E>0$ of the photon is irrelevant to determine $c$.

 

[GRQFT]

This can be derived from the two SR postulates or from the first postulate and group properties of the coordinate transformation plus an experiment, which excludes the Galilei tramsformation as physically relevant.
https://arxiv.org/abs/physics/0302045

Okay, I very quickly skimmed the article you referenced, so maybe I missed the point relevant to the current discussion, but are you saying that we can drop Einstein's postulate that c will always have the same measured value and still arrive at SR, and that, in turn, means that c is somehow less fundamental then the way we've been thinking about it since 1905?

 

[PeroK]

This thread seems to over-complicating things. The speed of light is invariant. That is determined by experiment. At least to the point where we are confident enough to assume it's true.

The speed of light and the definition of the second are used to define the metre. So, we no longer measure the speed of light by experiment. We measure the metre by experiment. The speed of light in metre per second is postulated.

In the past, the metre was otherwise defined and the speed of light measured by experiment.

 

[Roberto Pavani]

Maxwell wave equation

 

[GRQFT]

No, $c$ is defined by the SI unit system. No measurements are needed.

Is it not tied to a measurement of the time it takes to travel a meter?

Source: Speed of light

 

[Sagittarius A-Star]

Okay, I very quickly skimmed the article you referenced, so maybe I missed the point relevant to the current discussion, but are you saying that we can drop Einstein's postulate that c will always have the same measured value and still arrive at SR, and that, in turn, means that c is somehow less fundamental then the way we've been thinking about it since 1905?

Transformartion equation (27) in the article can be derived without the 2nd postulate.

• K<0 : can be excluded (causality would be not invariant)
• K=0 : makes it the Galilean transformation
• K>0 : makes it the Lorentz transformation

An experiment is needed to decide between Galilean- or Lorentz-transformation.

 

[GRQFT]

Maxwell wave equation

?

 

[GRQFT]

Transformartion equation (27) in the article can be derived without the 2nd postulate.

• K<0 : can be excluded (causality would be not invariant)
• K=0 : makes it the Galilean transformation
• K>0 : makes it the Lorentz transformation

An experiment is needed to decide between Galilean- or Lorentz-transformation.

And what type of experiment would we do to make that determination?

 

[Sagittarius A-Star]

And what type of experiment would we do to make that determination?

For example a twin-paradox experiment (Bailey et al. 1977).
https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation#Twin_paradox_and_moving_clocks

 

[GRQFT]

For example a twin-paradox experiment (Bailey et al. 1977).
https://en.wikipedia.org/wiki/Experimental_testing_of_time_dilation#Twin_paradox_and_moving_clocks

Sorry, I don't see the relevance

 

[weirdoguy]

Sorry, I don't see the relevance

There is no time dilation and twin paradox when using Galilean transformation.

 

[GRQFT]

Sorry, I don't see the relevance

Sorry, I hit the return key before I finished typing.

 

[GRQFT]

There is no time dilation and twin paradox when using Galilean transformation.

Agreed.

 

[GRQFT]

Okay, I think this is a good point for me to stop and say thank you to all who have contributed to this discussion.

Cheers...

 

[PeroK]

And what type of experiment would we do to make that determination?

Accelerate a charged particle to high energy. If its speed goes up according to $E = \frac 1 2 m v^2$, and eventually exceeds the speed of light, then we have a Galilean universe. If the speed of light cannot be reached and the energy obeys $E = \gamma mc^2$, then we have a relativistic universe.

 

[Roberto Pavani]

Since the speed of light $c$ follows directly from Maxwell’s wave equations and is invariant across reference frames, Einstein was among the first to recognize the apparent paradox and resolve it through Special Relativity (SR).

 

[Sagittarius A-Star]

Is it not tied to a measurement of the time it takes to travel a meter?

This would be the measurement of a distance.

 

[Dale]

“in order to reinsert physical constants” … Is this incorrect?

I am not sure why you would want to reinsert physical constants. But if you wished to do so then yes that is correct. It is not necessary to do so in order to do physics, neither theoretically nor even experimentally.

Is it not tied to a measurement of the time it takes to travel a meter?

No, the meter is tied to a measurement of the distance light travels in a second.

c is somehow less fundamental then the way we've been thinking about it since 1905?

I think that the change between now and 1905 is more an over reliance on SI units. In Einstein’s day students understood Heaviside units, Gaussian units, and the SI units, and other conventional units. They understood that some constants (like $\epsilon_0$) appear or disappear depending on the units. They may not have understood that $c$ was also such a constant. But the idea that such constants exist would have been more generally understood than it is today.

Today students are so immersed in the SI units that they mistakenly believe that the only form of physical equations is the SI form, and that the SI dimensions and constants are part of nature rather than a convention. Scientists that had worked in both Gaussian and SI units would know otherwise from direct experience.

 

[bhobba]

so I'm not sure if I fully understand your point.

The point was simply that it's not a medium like, say, water is in water waves seen in the everyday world.

What is it (advanced undergrad, not HS level):
https://digitalcommons.usu.edu/cgi/viewcontent.cgi?article=3211&context=physics_facpub

Thanks
Bill

 

[bhobba]

Okay, I'll read what you referred to, but what about the Casimir effect, the Lamb shift, spontaneous emission, etc.? Surely these are real, yes?

The Casimir Effect is related to Van der Waals forces:
http://thphys.irb.hr/wiki/main/images/2/2c/Casimir.pdf

Thanks
Bill

 

[bhobba]

And so how would we calculate c by this approach?

In the classical limit, you get Maxwell's equations that imply c is the invariant speed of light.

Thanks
Bill

 

[GRQFT]

The Casimir Effect is related to Van der Waals forces:
https://www.nature.com/nature-index...van-der-waals-interactions-in-quantum-systems

Thanks
Bill

In the paper you reference, it says:

Casimir effect: Force between macroscopic bodies due to alteration of vacuum fluctuations by boundary conditions.

I'm confused why you would cite that one to support your claim that "The whole issue of virtual particles and vacuum fluctuations being real is complicated, with many experts (including me, not that I am an expert) thinking they are mathematical fictions."

 

[bhobba]

Why is it not 5% faster or 20% slower?

Many constants in physics are known to exist, but their values must be determined experimentally. The constant c in the Lorentz Transformations is one of them. To see why, you need to study a derivation of the Lorentz transformations from the Principle of Relativity (POR) alone:

https://physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

There are many ways of determining that value, but my favourite is that you can actually derive Maxwell's equations from Coulomb's law and the Lorentz Transformations:

https://www.amazon.com.au/Understanding-Special-Relativity-Maxwells-Equations/dp/1516864743

This leads to many ways of experimentally establishing the value of c in the Lorentz Transformations as the speed of light.

Also, you start to see a glimpse of the power of symmetry in physics.

Thanks
Bill