Why is the speed of light a constant?

[Mohika]

TL;DR

Why is the speed of light in a vacuum exactly what we measure?

The question is of what does it depend on? We take it for a constant still how do we know that its the exactly the same as in a vacuum in a center or closer to the center of our galaxy for example. Why is the number what it is?

 

[phyzguy]

There is no answer to questions like these. Why is the universe the way it is? All we know is that this is the universe we live in and this is how it behaves. As far as what does it depend on, it depends on the permittivity of the vacuum (epsilon_0) and the permeability of the vacuum (mu_0).But then your question is, "why do these constants have the values that they do?" Again, no answer. They just do. How do we know if is the same everywhere? We don't know for sure, but when we assume that it is the same everywhere, we make calculations which are in very good agreement with observations.

 

[Mohika]

I was just watching too many YouTube videos, thinking what if there is no such thing as the Dark Matter but something we don't understand about gravity and spacetime. In that case speed of light probably would depend on where in a Galaxy you are. Closer to the center it wouldn't be the same also gravity force would change too. That would explain also why the galaxy rotates the way it does. .. Fullish of me. I just don't know enough about it.

 

[Nugatory]

We take it for a constant still how do we know that its the exactly the same as in a vacuum in a center or closer to the center of our galaxy for example.

We don't know that it is. We do know that every observation that we've done, including some of galaxies very far away from us, are consistent with the idea that the speed of light is constant. Furthermore, we can calculate the speed of light from the known laws of electrodynamics, so the only way that the speed of light is not constant everywhere would be if the laws of electrodynamics were not the same everywhere. Could be... but all the observations we have say that no matter how far out we look, everything we see follows the same laws of E&M as hold on earth. That's enough reason to say that the speed of light is constant unless and until some evidence shows up to suggest otherwise.

Why is the number what it is?

That's a different question. The number depends on how we define our units. The meter is defined to be the distance that light travels in 1/299792458 seconds so the speed of light has to 299792458 meters per second. The only way I could measure the speed of light and get any other answer would be if my clock was broken or my meter stick was wrong.

 

[Mohika]

Well E&M is also what we measure here. It has constants as well. Measurement wouldn't be the same here and closer to the center of the galaxy if there is something we don't understand about spacetime that causes the galaxy to rotate the way it does and if there is no dark matter.

 

[Dale]

Summary:: Why is the speed of light in a vacuum exactly what we measure?

The question is of what does it depend on? We take it for a constant still how do we know that its the exactly the same as in a vacuum in a center or closer to the center of our galaxy for example. Why is the number what it is?

Actually, these aren’t the important questions. As others mentioned the number is just an artifact of the units we use. And any spatial variation would simply mean that we had adopted units that vary spatially.

The important question is why is c invariant.

(Those other questions would be important questions about the fine structure constant)

 

[Mohika]

Actually, these aren’t the important questions. As others mentioned the number is just an artifact of the units we use. And any spatial variation would simply mean that we had adopted units that vary spatially.

The important question is why is c invariant.

(Those other questions would be important questions about the fine structure constant)

Well not exactly. Maybe measurement depends on something we still don't understand. What if there is something that determines the speed of the massless particles. And what if that is a different value across the galaxy for example (also across the vastness of space of course). IDK, for me, it would be best to think of it as a different density of space-time. Or different excitation of the field that gives mass to the particles. I am trying not to talk crazy or sound like it. I just don't know enough about it.

 

[FactChecker]

Just to be clear, even time changes near massive bodies, so the speed of light in a vacuum is only constant when the distortions due to gravity are taken into account appropriately. When the large-scale questions that you ask are considered, General Relativity must be applied.

 

[Dale]

Well not exactly. Maybe measurement depends on something we still don't understand.

The speed of light is just a choice of units. What could we not understand? We are free to choose any units we like. It is just a decision to make, not a fact of the universe to measure.

Again, I think you are actually interested in the fine structure constant.

 

[Mohika]

The speed of light is just a choice of units. What could we not understand? We are free to choose any units we like. It is just a decision to make, not a fact of the universe to measure.

Again, I think you are actually interested in the fine structure constant.

Yes, the number is the choice of units but you haven't understood me. I am not asking why is the choice of units what it is, but why the value is. Why the value is not 5% more or less for example. Could it be that it's not the constant and that it does depend on some other property?

 

[dlgoff]

I think you are actually interested in the fine structure constant.

Yes. And Wikipedia has a good explanation of this fine structure constant:
https://en.wikipedia.org/wiki/Fine-structure_constant

 

[Dale]

Yes, the number is the choice of units but you haven't understood me. I am not asking why is the choice of units what it is, but why the value is. Why the value is not 5% more or less for example. Could it be that it's not the constant and that it does depend on some other property?

I have understood you clearly, and you are refusing to believe what I am saying: that is simply not a meaningful question regarding the speed of light (and repeating it won’t make it meaningful). For the speed of light itself there are only two meaningful things: first it is invariant and second it is finite. All else is a question of units and nothing more.

I really recommend that you read about the fine structure constant. The questions you are asking are meaningful for it, and not the speed of light.

 

[Mohika]

Yes exactly my question was is it invariant, sorry.

 

[dlgoff]

Yes. And Wikipedia has a good explanation of this fine structure constant:
https://en.wikipedia.org/wiki/Fine-structure_constant

This then leads to the hyperfine structure. Aren't atoms cool?

 

[Dale]

Yes exactly my question was is it invariant, sorry.

Yes, it is invariant. It cannot be more or less invariant in the center of the galaxy.

 

[Mohika]

Yes, it is invariant. It cannot be more or less invariant in the center of the galaxy.

Please correct me if I am wrong fine-structure constant can be 1/137 even if c has a different value it only means that e would also need a different value and so on.. which is my point exactly :D (π can stay the same I guess)

 

[valenumr]

There is no answer to questions like these. Why is the universe the way it is? All we know is that this is the universe we live in and this is how it behaves. As far as what does it depend on, it depends on the permittivity of the vacuum (epsilon_0) and the permeability of the vacuum (mu_0).But then your question is, "why do these constants have the values that they do?" Again, no answer. They just do. How do we know if is the same everywhere? We don't know for sure, but when we assume that it is the same everywhere, we make calculations which are in very good agreement with observations.

But why is epsilon_0 * mu_0 even constant. They could vary proportionally and end up with the same value of c. I don't think it's unusual to ask such a question. It's a pretty weird property of reality.

 

[Orodruin]

The only way I could measure the speed of light and get any other answer would be if my clock was broken or my meter stick was wrong.

Or, as I told the professor teaching my subatomic particle physics lab when he asked what we had just done (clearly expecting the answer ”measured the speed of light”): We have checked the calibration of your ruler.

 

[Ibix]

Please correct me if I am wrong fine-structure constant can be 1/137 even if c has a different value it only means that e would also need a different value and so on.. which is my point exactly :D (π can stay the same I guess)

Dale's point is that the value of the fine structure constant, $\alpha$, is the thing that needs explaining. $c$ is a defined quantity and you are free to change the definition any way you like, as long as you change other constants so that $\alpha$ does not change - this is just a unit change and has no consequences beyond you having to recalibrate all your measuring devices. So the answer to "why does $c$ have the value it does" is totally uninteresting: it's because the SI committee chose that value. A consequence of that is that it doesn't change from one location to another because we have defined it as not doing so.

So there are two interesting physics questions here. The first is why there is an invariant speed at all. This can be rephrased as "why does the universe obey pseudo Riemannian geometry?" The answer is that we don't know. A working theory of quantum gravity might provide some insight, but might not too. We'll find out when we have one.

The other question is why $\alpha$ has the value it does, and does it change from place to place or time to time. Because it's a dimensionless quantity, you can't change it just by changing definitions the way you can with dimensionfull quantities like $c$. Again, we don't know the answers and future theories may provide some insight. Whether it varies, though, is an active research area, and people do look for evidence that it changes. As far as I'm aware, they've found no evidence of any variation in time or space.

 

[Melbourne Guy]

I note ten other 'Related Threads' below with almost exactly the same title. 60% are locked and the average number of posts is 25.9 (which I'm happy to round up to 26 because I can't see how to create .9 of a post on PF). So, this thread is currently under the average on responses but slightly more likely than not to be locked at some point soon.

And all the threads I skimmed meandered around before finally settling on the simple, unsatisfying outcome of, "We just don't know."

 

[Ibix]

And all the threads I skimmed meandered around before finally settling on the simple, unsatisfying outcome of, "We just don't know."

Unfortunately, it's fairly common because the forums on fundamental science frequently bump up against the limits of what we actually know. All of scientific theory is justified by saying "if we assume x and y then we predict z, and z is what we see in experiments", and not because we understand why x and y are true (yet, anyway). So questions about why x and y are true always eventually get met with a shrug (or, more formally, a statement that this is an ongoing area of research).

We can help to refine and restate questions like this in terms of our modern understanding, and we can discuss published hypotheses about what might lie beyond that, but ultimately we only know the things we know.

 

[Dale]

Please correct me if I am wrong fine-structure constant can be 1/137 even if c has a different value it only means that e would also need a different value and so on.. which is my point exactly :D (π can stay the same I guess)

Yes, exactly. So since e and h and the other dimensionful constants are also similarly fixed by their units we can always change c to any non-negative finite value, and change e or h to compensate such that the fine structure constant is unchanged.

The physics is determined by the fine structure constant. So changing c without changing the fine structure constant doesn’t change the outcome of any physical experiment. Only changes in the fine structure constant can affect the outcome of experiments

 

[Mohika]

So changing c without changing the fine structure constant doesn’t change the outcome of any physical experiment.

Is it so? If we lower the speed of light then recalculate all so fine structure constant doesn’t change and then calculate the Earth's (or any same number of atoms) gravity and mass?

 

[Ibix]

Is it so? If we lower the speed of light then recalculate all so fine structure constant doesn’t change and then calculate the Earth's (or any same number of atoms) gravity and mass?

You'll get a different number, because you've changed your unit definitions. But nothing has changed any more than anything changes if you decide to measure the mass in grams instead of kilograms.

 

[Mohika]

You'll get a different number, because you've changed your unit definitions. But nothing has changed any more than anything changes if you decide to measure the mass in grams instead of kilograms.

Quite contrary .. I would still get that the same mass still has the same force of gravity I guess... but the same number of particles would have different mass and gravity. So the star of the same size would be with different gravity.

What I am trying to ask is is there a possibility that closer to the center of the galaxy mass and gravity of the same size objects differ from the mass and gravity in outer regions due to the different "density" of spacetime.

 

[PeroK]

What I am trying to ask is is there a possibility that closer to the center of the galaxy mass and gravity of the same size objects differ from the mass and gravity in outer regions due to the different "density" of spacetime.

I switched on the television one day and caught an episode of the original Star Trek series. Mr Spock said "the spacetime in this region is particularly tenuous" (or words to that effect). But, sadly, that makes little sense in terms of modern cosmology.

There are ideas around, like MOND (google that, if you want) that try to explain things in a different way from general relativity. These ideas are grounded in mathematical models that try to explain the motion of galaxies.

 

[Ibix]

Quite contrary .. I would still get that the same mass still has the same force of gravity I guess... but the same number of particles would have different mass and gravity. So the star of the same size would be with different gravity.

You guess wrong. Nothing physical has changed because you specified $\alpha$ not to have changed. All you have done is changed your units.

What I am trying to ask is is there a possibility that closer to the center of the galaxy mass and gravity of the same size objects differ from the mass and gravity in outer regions

This has nothing to do with the speed of light. People have produced various modified gravity models, some of which have been quite successful on the galactic scale. However, none has come close to predicting any cosmological measurement, as far as I'm aware, so they remain less well thought of than dark matter.

"density" of spacetime.

Gravity is modeled as spacetime curvature, not density. I'm not aware of any formal mathematical model that uses "density of spacetime".

 

[Dale]

Is it so? If we lower the speed of light then recalculate all so fine structure constant doesn’t change and then calculate the Earth's (or any same number of atoms) gravity and mass?

It is so, it is a worthwhile exercise to calculate. I analyzed two simple experiments: one was to measure the length of a physical bar using a radar experiment and the other was to measure the duration of a pendulum tick using an atomic clock.

For your experiment you, for example, could analyze a measurement of the duration of a year using an atomic clock.

What I am trying to ask is is there a possibility that closer to the center of the galaxy mass and gravity of the same size objects differ from the mass and gravity in outer regions due to the different "density" of spacetime.

Well, I don't know of any theory that describes gravity in terms of a density of spacetime.

However, in keeping with the rest of the thread, there is of course the possibility that the fine structure constant is different in different regions of the galaxy. We have done astronomical measurements to detect such changes and have not been able to detect any.

 

[Vanadium 50]

I am not asking why is the choice of units what it is, but why the value is.

Why are there exactly 12 inches in a foot?

Could this number be different in the center of the galaxy?

 

[Sagittarius A-Star]

Why are there exactly 12 inches in a foot?

Could this number be different in the center of the galaxy?

Yes. Here in the center of the galaxy, we use the metric foot, but not the metric inch:

A metric foot[1][2] is a nickname for the preferred number length of 3 basic modules (3 M), or 300 millimetres (11.811 in).

Source:
https://en.wikipedia.org/wiki/ISO_2848#Metric_foot