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First of all, I've read almost all of the similar questions and duplicates given under them. And the question is never answered properly in any of them so please don't just share duplicates and leave it at that. The question is, is there a theoretical mechanism that explains why $c$ has the value it has? Is there a mechanism (even a proposed one) to explain this?

Before anyones says it, yes I would still ask this if $c$ was $1\frac{lightseconds}{second}$ ie. described in natural units. Regardless of the numbers and units we assign to it, speed of light has some intrinsic value. Whatever we define it to be, it takes 4 full rotations of Earth around the Sun for a beam we send to reach Proxima Centauri, which is about 4 lightyears away.

Yes, I know that speed of light isn't something unique about light or photons and that any massless particle in our universe travels in this speed. This doesn't answer anything about the question, just a fancy way of saying "it just is". I don't even know why some users gave this as an answer in other threads.

$c^2 = \frac{1}{\mu_0*\epsilon_0}$ is not a proper explanation because

  1. any massless particle has a speed of $c$, not just photons.

  2. this relation is just a consequence of special relativity in its core, which has no mechanism explaining the origin of $c$.

This is just one of its assumptions which is validated empirically.

It seems to me that this is just an observation at this point with no known mechanisms behind it to explain it. If so, what are some likely and popular proposals for such mechanisms?

edit: People are once again trying to explain why the value of 310^8 m/s is an arbitrary one similar to 1 mile = 1.609344 kilometers. Once again, these numbers and units are of course arbitrary and are just tools to convey the idea. I am not questioning the value of 310^8 m/s. It could have been 42 sticks/mississippis or 1 ls/s.

Yet the amount of time it takes for a photon to travel from the Sun to Earth isn't arbitrary is it?

Qmechanic
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GUNDOGAN
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    Natural units do solve the problem, if $c=1$, you can rewrite all physics without ever needing to use $c$ in the equations. The fact that it pops up everywhere is that we use nonnatural units. Think it this way, why is $k_B$ the value that it has? $k_B$ is just a contant, in natural units we can set $k_B=1$ and it never appears again, it is just telling us that temperature is a weird concept and we should be working in energies from the get-go. Same with $c$, we want to make the difference between mass and energy, but in fact they are the same kind of thing due to $E=m$. – Mauricio Jul 07 '22 at 11:57
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    This feels to me like asking "why is 1 mile = 1.609344 kilometers? Is there a deep theoretical reason for the factor of 1.609344?" -- it's not really plausible to answer the question, since the answer is history. – Allure Jul 07 '22 at 12:02
  • @Mauricio this is not the case at all. E != m because they have different dimensions, what you say is similar to claiming 42 m/s = 42 m because s = 1. In natural units c = 1 lightseconds/second. And then you have to explain "why is a light second as long as it is" without using the definition of light seconds (the distance light takes in a second) so as to not cause a circular argument – GUNDOGAN Jul 07 '22 at 12:18
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    @GUNDOGAN, in natural units $c=1$ and both $E$ and $m$ have the same unit, typically eV or some prefix thereof, like MeV or GeV. – Marius Ladegård Meyer Jul 07 '22 at 12:21
  • @MariusLadegårdMeyer even though I admit that I'm certainly not used to using natural units, a quick wikipedia search tells me that in natural units c's unit is light-second per second even though it is usually omitted. And until now I've thought that using eV as a unit of mass was a convention and that it was to be understood as "it would yield this amount of energy if all of its mass was to be converted to energy" – GUNDOGAN Jul 07 '22 at 12:35
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    @GUNDOGAN In natural units, $E$, $m$, $\frac{1}{L}$ and $\frac{1}{T}$ ALL have the exact same unit. The "convention" is that for historical reasons, we like to measure things in non-natural units. The type of question that would make sense is regarding the specific value of a dimensionless constant. For instance, "Why is the value of the fine structure constant 0.00729735256...?" – Prahar Jul 07 '22 at 12:43
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    I think the honest answer to this question is "we do not really know". – Martino Jul 07 '22 at 12:55
  • FYI: Your question is equivalent to asking why the permittivity and the permeability of free space are what they are. https://en.wikipedia.org/wiki/Maxwell%27s_equations – Solomon Slow Jul 07 '22 at 13:25
  • @SolomonSlow do you mean to say that it has the value that it has, because this is the value that satisfies the wave equation? If so, I don't believe this is satisfactory because all the massless particles move with this same speed even though they don't have anything to do with electromagnetic interactions. It seems to me that c is the "cause" that these values are the way they are, not the other way around. – GUNDOGAN Jul 07 '22 at 13:40
  • @Martino I honestly feel the same way but I'm ok with hypotheses too as long as they are scientifically sound. – GUNDOGAN Jul 07 '22 at 13:42
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    Does this answer your question? Why is the speed of light defined as 299792458 m/s? – Dale Jul 07 '22 at 14:58
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    Other duplicates: https://physics.stackexchange.com/q/9314/ https://physics.stackexchange.com/q/210389/ https://physics.stackexchange.com/q/567342/ https://physics.stackexchange.com/q/56973/ https://physics.stackexchange.com/q/3644/ – Dale Jul 07 '22 at 15:01
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    If you want the question reopened, please link to these duplicates (and any others you find) and explain SPECIFICALLY how your question differs from those and what you are looking for that is not already provided in those answers. Just saying that you have read them and that they do not properly answer your question does not help. We need specifics about what is different from those questions and what is missing from those answers. – Dale Jul 07 '22 at 15:03
  • Physics hypothetically could only explain scenario of why some constant $c=C$, if and only if $c=c(\dots)$, i.e. constant is actually a function, (changes in a timescale of universe evolution for example). This also assumes that changes in a "constant" is also a well-defined law. Whether or not a constant can change - is a different question. – Agnius Vasiliauskas Jul 07 '22 at 15:52

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The answer is that we don't yet know why the speed of light is what it is (leaving aside the question of the units in which you might choose to express it). The same can be said of many of the other building blocks of physics. For example, we cannot yet explain why an electron has a specific mass and charge. In physics we can explain complicated objects and phenomena in terms of their simpler components, but there is a point beyond which we cannot provide explanations about why things are as they are.

Marco Ocram
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  • I am not sure if this is frowned upon in this forum but do you know of any unproven hypotheses that try to explain this which was written by respectable people? I'm a physics undergrad so I'm not in the pursuit of some pop-sci crackpot thing and wouldn't be put-off by a couple numbers on the page. – GUNDOGAN Jul 07 '22 at 14:13
  • Hi, no I'm not aware of anything like that, but I am the wrong person to ask! Google 'Why is the speed of light the speed of light', or something similar, and see what you get. – Marco Ocram Jul 07 '22 at 14:18
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I think that @JohnDoty's answer may be closer to the mark than you expect. The missing concept is that time and space are much more alike than you think. They are so much alike that they are treated as different directions in a single $4$-D spacetime. So asking why $1$ lightsecond is the same as $1$ second is much like asking why $1$ lightsecond east is the same as $1$ lightsecond north.

The deep relationship between time and space is more than light travels $1$ lightsecond of distance in $1$ second of time. I have tried to explain the relationship in my answer to Euclidean space to Minkowski spacetime

That explains why there is a relationship between distance light travels in a time interval and that time interval. But you are asking if there is a mechanism to explain why it has a particular value. Perhaps another way to get at it would be to ask what would break if the speed of light had a different value.

The answer, as @MarcoOcram said, is we don't know. People have looked at how physics would change if various values were different. Perhaps life would be impossible, but we don't see any reason that physics wouldn't be self consistent. It just wouldn't explain the universe we see.

Here is a link to a rather speculative idea that the laws of physics could be different if you go far enough, beyond what we can see. The Multiverse, Science or Science Fiction? | Sean Carroll

Perhaps the problem is that you are asking why the universe is as it is. Physics doesn't answer "why" questions, except that more complicated answer are the results of simpler answers. It cannot explain why the simplest answers are as they are.

mmesser314
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  • In my opinion anthropological arguments only make sense if there actually is a multiverse, which is something I'm personally skeptical about. And a one little nitpick about physics not answering "why" questions: It sure does. We go further and further down in the "causal chain". Feynman had an example of ice being slippery. Today we can follow the causes of this down to the subatomic level yet there are still "why" questions we can ask at that level. Whether we will reach an end in this process is beyond me but is there anything else to physics besides following this causal trail? – GUNDOGAN Jul 07 '22 at 15:29
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Why did mariners historically use different units (fathoms and nautical miles) for depth and distance? It's because they were using different instruments to measure them, and also because the concerns (running aground versus crossing oceans) involved very different scales.

Similarly, we have historically used different instruments for measuring distance and time in physics. But we now have a well-tested principle that the speed of light in a vacuum is fixed. That opens up the possibility of using a clock as the basis for distance measurement, and for the past half century that has been the most reproducible way to measure distance. Thus, the speed of light is now an arbitrary defined constant.

But why is it so big? That relates to our human concerns about space and time. Meters and seconds are units that match the scale of our experiences: 1 m/s is a comfortable walking pace. Generally, the velocity dispersion of matter in the universe is well below the speed of light, and the velocity dispersion of macroscopic objects on Earth is extremely low. Biology as we know it would be impossible if this wasn't true.

John Doty
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    Am I that bad of a communicator, why does everybody keeps repeating the same things to me? The values and units we use to convey this particular speed is unrelated. It is as if I've asked why gravity has a $\frac{1}{r^2}$ term in it and not any other power of r. And people kept telling me this is the way universe is. I need someone to come and tell me "it is because area increases proportionally to r^2". – GUNDOGAN Jul 07 '22 at 14:10
  • @GUNDOGAN You apparently want mathematics, not physics. Mathematically, it's simply the geometry of Minkowski space, but of course that doesn't answer the question of why we choose that particular abstraction to model the physical world. – John Doty Jul 07 '22 at 14:17