Undergrad How to rule out that the speed of light was different in the past?

[vanhees71]

E.g., we can just use the old SI. There we had $\Delta \nu_{\text{CS}}$ and $c$ as in the new SI, but the kg was still defined by the prototype in Paris, and the A was defined via setting $\mu_0=4 \pi \cdot 10^{-7} \text{N} \cdot \text{A}^{-2}$. Thus also $\epsilon_0=1/(\mu_0 c^2)$ was defined. So using the old SI units a measured change of $\alpha$ would imply a change of $h$ or $e$ (or both).

 

[Vanadium 50]

So using the old SI units a measured change of would imply a change of ħ orc (or both).

Or π! (Of course, under the new definitions, π is a measured quantity.)

 

[Vanadium 50]

Let’s say that we measured a change in α, would defining the fundamental constants still be the preferred method to define units?

Let's say that we defined the kilogram by an artifact, and noticed the mass of this artifact were changing over time. Would that be a good reason to redefine units?

Oh wait...that actually happened.

 

[member 728827]

Where are you getting that understanding from? Please give a reference.

For example, in this Wikipedia article (I'm not about VSL theories!) you can read:

Accepted classical theories of physics, and in particular general relativity, predict a constant speed of light in any local frame of reference and in some situations these predict apparent variations of the speed of light depending on frame of reference, but this article does not refer to this as a variable speed of light.

You can only define and measure the "speed of light in vacuum" locally. Let's say that I measure locally the speed of light to be 299 792 458 m/s, or that I fix that value and the way I measure that value locally. If I measure then the speed of a photon that comes from a distant Galaxy or Quasar, then locally I would measure that speed... but I can't tell what was the "local" speed then and there where the photon was produced.

 

[Sagittarius A-Star]

Let's say that I measure locally the speed of light to be 299 792 458 m/s

That's no measurement of the speed of light. That's a measurement, if the scale on your ruler is accurate.

 

[PeterDonis]

You can only define and measure the "speed of light in vacuum" locally.

No, you can only directly measure the fine structure constant and things that might depend on it (like the speed of light in vacuum locally, if you are using units where that is a measured quantity instead of a defined one--note that in SI units it s defined, not measured). But that in no way means you cannot indirectly measure the fine structure constant and things that might depend on it at distant locations or in the past.

 

[PeterDonis]

in this Wikipedia article (I'm not about VSL theories!) you can read:

This article has nothing to do with the thread topic or the concern you raised.

 

[vanhees71]

No, you can only directly measure the fine structure constant and things that might depend on it (like the speed of light in vacuum locally, if you are using units where that is a measured quantity instead of a defined one--note that in SI units it s defined, not measured). But that in no way means you cannot indirectly measure the fine structure constant and things that might depend on it at distant locations or in the past.

Of course for each of the definition you need also the "mises en pratique" for the units. E.g., to realize the definition of the kg via the defined values Planck action $h$ (and also of the definitions of the s, the, m, and the A) with the Kibble balance what's accurately measured are quantities like the magnetic-flux quantum in superconductors (Josephson constant).

You find the corresponding brochures in English here:

https://www.bipm.org/en/publications/mises-en-pratique

 

[member 728827]

No, you can only directly measure the fine structure constant and things that might depend on it (like the speed of light in vacuum locally, if you are using units where that is a measured quantity instead of a defined one--note that in SI units it s defined, not measured). But that in no way means you cannot indirectly measure the fine structure constant and things that might depend on it at distant locations or in the past.

But in the fine structure, there're other "constants" playing other than π and c.

For example, the Universe is expanding and seems the expansion is accelerating. Locally, lets say at every eventpoint of the worldline of a photon that comes from a distant Galaxy, its locally measured speed is c. But as space is expanding, then for a non-local observer the speed exceeds c if computed globally, but not measured locally.

What I don't understand (among other billion of things) is that my measuring 1 meter rod is not expanding itself, is the space outside the rod that's expanding - or I could not measure the expansion!

 

[vanhees71]

Your meter rod is held together by the electromagnetic force. How much stronger is the electromagnetic interaction compared to the gravitational one? How much do you think does thus "Hubble expansion" affect your meter stick used for the purpose of local (in time and space!) measurements?

 

[PeterDonis]

But in the fine structure, there're other "constants" playing other than π and c.

You're looking at it backwards. As has already been pointed out in this thread, the actual physically meaningful constant is the fine structure constant, since it's dimensionless. The "constants" that appear in the formula for the fine structure constant are dependent on your choice of units.

For example, the Universe is expanding and seems the expansion is accelerating.

This has nothing to do with the fine structure constant.

as space is expanding, then for a non-local observer the speed exceeds c if computed globally, but not measured locally.

The "speed" you are talking about is coordinate dependent and has no physical meaning.

What I don't understand (among other billion of things) is that my measuring 1 meter rod is not expanding itself

Correct, because its length is determined by the electromagnetic interactions between its atoms, i.e., by the fine structure constant.

is the space outside the rod that's expanding

This is a common pop science "explanation", but it's coordinate dependent.

or I could not measure the expansion!

If you mean expansion of the 1 meter rod, there is no such expansion to measure.

 

[Dale]

Of course for each of the definition you need also the "mises en pratique" for the units. E.g., to realize the definition of the kg via the defined values Planck action $h$ (and also of the definitions of the s, the, m, and the A) with the Kibble balance what's accurately measured are quantities like the magnetic-flux quantum in superconductors (Josephson constant).

You find the corresponding brochures in English here:

https://www.bipm.org/en/publications/mises-en-pratique

The mises en pratique is, IMO, a rather under appreciated part of the new SI. It is great that they have gotten away from the “artifact in a vault” definitions and are entirely based on physical constants. But without the mises en pratique it would be unclear how to actually measure the units. They provide a very important link between the SI as a theoretical construct and the SI as a practical thing.

 

[vanhees71]

The good thing of the "new SI" is that you can adapt the mises en pratique easily, if better technology becomes available. I guess "soon" (~some years) we'll see a change in how the second is realized since the $\Delta \nu_{\text{Cs}}$ is not so accurately realizable as the intrinsic accuracy of several optical atomic clocks (if I remember right it's an order of magnitude better) or probably soon the optical nuclear Th clock. The problem is of course that you have to get an accurate measurement of $\Delta \nu_{\text{Cs}}$ not to change the definition of the second by more than you can realize the unit right now. For details, see the "mise en pratique" for the second:

https://www.bipm.org/documents/2012...48?version=1.12&t=1643724477633&download=true

and the standard values for various optical atomic-clock frequencies

https://www.bipm.org/en/publication...ies?version=1.4&t=1637238077933&download=true

 

[Nugatory]

What I don't understand (among other billion of things) is that my measuring 1 meter rod is not expanding itself, is the space outside the rod that's expanding - or I could not measure the expansion!

The effect of expansion is that if the two ends of your meter stick were completely isolated, separate from one another and subject to no external forces at all, their worldlines would very slightly diverge as they follow their freefall paths through spacetime. (Exercise: calculate the amount of separation per year under these completely unrealistic hypothetical conditions).

In practice the two ends of the meter stick are not isolated. They are solidly attached to one another, and even if they weren't they would be bound together by the gravity of the earth, by the sun, the galaxy. Even gravity across our entire galactic cluster does more to hold them together than expansion does to separate them.

However, all of this is a digression in this thread. The speed of light in vacuum is 299792458 meters per second for the same reason that is also one light-second per per second and one light-year per year - if we were to measure some other value we would only know that one or both of our clock and our meter stick are out of calibration. However, any change in the physical behavior of propagating electromagnetic radiation would show up as a change in the fine structure constant, which is why you are being told to stop talking about the speed of light and instead focus on the fine structure constant (or other equivalent dimensionless quantities).

 

[hutchphd]

What I don't understand (among other billion of things) is that my measuring 1 meter rod is not expanding itself, is the space outside the rod that's expanding - or I could not measure the expansion!

In order to"measure" your meter rod, you necessarilly must compare it to another meter rod either real or created from a compounded measurement of length
If you find that comparison (ratio) changes in time then something in the chain of inference is not constant.
If the ratio is static then most probably all elements of the measurement are constant:but two or more could be changing in collusion
This argumant holds also for any nondimensional constant in any system

 

[Sagittarius A-Star]

but I can't tell what was the "local" speed then and there where the photon was produced.

GR spacetime is locally flat. That means, locally on earth and locally on the quasar SR is valid. The invariant speed of SR can be defined via a unit system to be $c=1$.

A photon must move with this invariant speed $v=c=1$ in every (local) inertial reference frame because it is massless.
$0=E \sqrt{1 - v^2}$

 

[member 728827]

This has nothing to do with the fine structure constant.

I have no other access to this article, but the "poor's man" first page :), but seems very interesting. As is from 2004, perhaps is outdated nowadays.

In this first page it talks about why you could not detect a change in c, because all you could say is that there's a change in α.

Nevertheless, seems that the expansion of the Universe could have something to do with the fine constant.