Is the value for the speed of light in vacuum irrelevant?

Question

Does it matter that the speed of light, $c$, is 299,792,458 meters per second in a vacuum? Would the universe be different if $c$ were, for example, 1 meter per second? Or should things be the same, whatever $c$'s value is?

The energy that we get from nuclear reactors is influenced by the value of the speed of light through the mass-energy formula. $E=\Delta m c^2$. If the speed of light had been slower, we wouldn't have had such a high speed communication. Also relativistic effects would have been more important at every day speeds. — AWanderingMind, Jul 13 '19 at 09:20
Yes, the actual value of $c$ is meaningless, which is why for instance in high energy physics many work in so-called natural units, in which $c=\hbar=1$. — , Jul 13 '19 at 09:36
@AWanderingMind actually by changing value of light, Lorentz transformations will change such that it becomes harder for us to come closer to this new value, so relativistic effects still would be far from everyday life. — Paradoxy, Jul 13 '19 at 09:39
@marmot although we indeed do that, but scale of constants are not meaningless. For example, see this question (https://physics.stackexchange.com/q/490700/) where actual value of $\hbar$ matters. — Paradoxy, Jul 13 '19 at 09:41
@Paradoxy This is a matter of perspective. You can achieve a full description of nature in natural units, do you agree? — , Jul 13 '19 at 09:49
@marmot well of course you are free to choose whatever coordinate system you want to describe nature, that's that, but if we choose one standard system, and then keep all parameters constant, then by changing one parameter such as cosmological constant we would expect a different universe. However, if other parameters change such that the change of cosmological constant becomes meaningless, well nothing will change. — Paradoxy, Jul 13 '19 at 09:58
@Paradoxy I do not agree with this as it is written but it might be that you want to say the correct things. First of all, this is about units, not coordinate systems. Then what we really measure are dimensionless quantities, but we often divide them by some standard lengths and so on to attach dimensions to them. So our main disagreement may be that the question is not very precise. — , Jul 13 '19 at 10:01
Possible duplicates: https://physics.stackexchange.com/q/144262/2451 and links therein. — Qmechanic, Jul 13 '19 at 10:06

score 1 · Answer 1 · answered Jul 13 '19 at 09:53

There are a few things to clarify:

the speed of light is c in vacuum when measured locally
the speed of light can be different if you measure it from far away (from a different gravitational field), this is the Shapiro effect

https://en.wikipedia.org/wiki/Shapiro_time_delay

You are asking basically, if the speed of light would be different, let's say half the current one, c/2:

locally, nothing would change. As per SR, and GR, we are in the same gravitational field, and if the speed of light would be c/2, we would not really recognize the difference, to us, this would be the normal speed.
measured from far away, it is very possible to measure a speed for light slower then c, as per the Shapiro effect, let's say you try to measure the speed of light ass it passes next to a black hole. What would this world next to the BH look like from here (Earth)? Every clock next to the BH would seem to tick slower (GR time dilation) relative to our clocks here on Earth. So basically, if you set the speed of light to be c/2, our world would look (from a far away observer's view) much slower.

Now you might be asking about something different. If your question is, whether if the speed of light (locally) would just change to a arbitrarily slow speed, and this change would be relative to everything else (meaning all other fundamental constants of physics would stay the same), then the answer is I believe it is not possible.

All the fundamental constants we know about are somehow connected to the speed of light (propagation of information). All matter that builds up our world, is built up by quarks, and gluons. Gluons are massless too, and propagate at the same speed c.

If you change c, you change the propagation of gluons, thus change all the binding energy that builds up matter. If that changes, then the change of speed of light (and thus gluons) will relatively cancel out (mass and energy equality), and our world will become again the same (or seem to be the same) as it is now.

Adam Latosiński · Answer 2 · 2019-07-13T10:20:01.033

The speed of light affect many quantum phenomena. For example, the fine-structure constant that is given by $$ \alpha = \frac{e^2}{4\pi\varepsilon_0\hbar c} $$ Among other things, the fine-structure constant is related to the ration of binding energy of an electron to its rest energy, for example in hydrogen atom the energy levels are given by $$ E_n = \frac{\alpha^2 }{2n^2} m_ec^2$$ Smaller c and greater $\alpha$ would mean that the enrgy scale of chemical reactions (defined by the binding energies of monecules) are closer to the energy scale of nuclear reactions (defined by the rest energies of the sub-atomic particles). We'd also see the relativistic effects easier, as the energy we can obtain in reactions is closer to what we need to propel masses to velocities close to the velocity of light.

That would change the chemical balance of many reactions, both chemical and nuclear, and the world would look significantly different.

If you had change not only the speed of light, but also other physical constants in a way that would keep various dimensionless constants (like fine-structure constant, but there are other) the same, the universe would behave exactly the same, and no experiment performed in it could show a difference.

score 0 · Answer 3 · answered Jul 13 '19 at 10:14

The speed of light is 186.000 miles per sec, not per hour. Yes, it would make a lot of difference if light travelled at 1 mile per hour An approaching car might seem to e a long distance away when in fact it is almost upon you. The light from the first galaxies wouldn't have had time to reach us, so we would know almost nothing about the universe. There are some small variations in the speed of light, because space is not a perfect vacuum. Even in the most transparent regions there is a proton every 50 metres or so. and this slows the light down very slightly. It is suspected there are other factors which slow down light from far distant sources, and some astronomers talk of "tired light". The situation will become clearer as science advances, but small variations in the speed of light from very distant galaxies might help explain puzzles such as dark energy, the mysterious force which is apparently speeding up the expansion of the universe

Is the value for the speed of light in vacuum irrelevant?

3 Answers3