# B Why does light move at the speed it does

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1. May 10, 2017

### RobC

Why does light move at the speed it does, why not half the speed or double?

2. May 10, 2017

### Mister T

There's nothing special about the value. A change of units will change its value so that tells you its value depends on whatever (arbitrary) choice was made for the sizes of those units.

3. May 10, 2017

### RobC

What I am saying is that why does it not travel at 150000 m/sec or 600000 m/sec ? Why 300000 m/sec ?
Sorry, should have added 000 to all the speeds.

4. May 10, 2017

### Staff: Mentor

Because we define the meter and the second the way we define them. It's not really meaningful to ask this kind of question about a number with units, since you can always change the number by changing the units.

A question that's more about an actual physical constant is a question about a dimensionless number, such as the fine structure constant--that's the one that is most closely related to the speed at which we observe light to move. But if you ask why the fine structure constant has the value it has, the answer is that we don't know: we don't have a theory that predicts that it should have a particular value, we just measure the value it actually has. (This measurement does not depend on our choice of units, since the fine structure constant is dimensionless.) So that's probably the best answer to the underlying question you are asking.

5. May 10, 2017

### RobC

I have a feeling that there is something that we are missing and discovering why light travels at the speed it does has some fundamental significance,

6. May 10, 2017

### Ibix

Another way to look at it is that relativity models space and time as part of a four-dimensional entity called spacetime. In this picture, the speed of light turns out to be the natural conversion factor between time and distance units. Just as it would be silly to use meters for left and right, feet for forwards and backwards, and fathoms for up and down, you can make a case that we should use the same unit for time and distance (e.g. seconds and light-seconds), which makes the speed of light "naturally" be 1.

Then your question is back to front. The question is - why do we use one second as a time unit and silly things like 3.3×10-9 of a light second as a unit of distance? The answer, of course, is because we happen to be built on a scale where 3.3 light nano seconds is about as far as our monkey arms can reach and one second is about as fast as our monkey hearts happen to tick. So they are convenient units.

7. May 10, 2017

### Staff: Mentor

It has as much significance as the conversion between miles and kilometers. In some places in everday life (mainly the US) you use miles, elsewhere you use kilometers, and if you want to convert between the two you need this conversion factor. The conversion factor is completely arbitrary and based on the definition of kilometers and miles.

In some places in everday life you use seconds, in others you use meters, and if you want to convert between the two you need this conversion factor. The conversion factor is completely arbitrary and based on the definition of seconds and meters. We could use light seconds instead of meters. That would be less practical, but then the speed of light would be just 1.

8. May 10, 2017

### Staff: Mentor

Because the BIPM committee met and voted to define the meter that way. There is no physical reason, it was just an arbitrary decision by a committee.

As @PeterDonis mentioned, what you probably actually want to know is why the fine structure constant has the dimensionless value it does.

Last edited: May 11, 2017
9. May 10, 2017

### Mister T

It has no more significance than wondering why a meter stick has the length it has.

There are fundamentally important reasons why we need theories that explain the magnitudes of some quantities, and discovering those theories will indeed have fundamental significance. But the speed of light is not one of those quantities.

10. May 11, 2017

### pixel

I think the replies may not be addressing RobC's initial question. Sure, you could change the units used for the speed of light and the value would change. I think he is asking why, if we stick to one particular set of units, the speed of light is what it is and not a different value. In other words, why is light as fast as it is. Of course, there's no answer to that.

11. May 11, 2017

### Staff: Mentor

That is the question answered. If you stick to one particular set of units then the speed of light is what it is and not a different value because you have chosen those units and are sticking to them.

If you want a non unit based answer then you need to ask a non unit based question. That would be regarding the fine structure constant as pointed out previously.

12. May 11, 2017

### pixel

The OP can clarify for us what he is asking, but I don't think it's so much about the value of the speed of light as the property of speed that it has. In other words, what makes light as fast as it is and not faster or slower. If he were asking about sound waves in a medium, we could discuss the elastic properties of the medium etc. to try to explain why sound has the particular speed it does. So light is an electromagnetic wave. The speed of an em wave is given by 1 divided by the square root of (με) where μ is the permeability and ε is the permittivity of the medium. So the speed of light in vacuum is determined by these properties of vacuum. You could of course then ask why these properties are what they are, etc. and will reach a point where you just have to accept that that's the way the universe works and "why" questions can't always be answered.

13. May 11, 2017

### Staff: Mentor

Yes - and that point is reached when you get to the value of one the unitless constants that PeterDonis mentioned in post #4.

14. May 11, 2017

### Staff: Mentor

But "as fast as it is and not faster or slower" refers to the value that the speed has. The only property it has is that it is invariant. "Faster or slower" is not a property but a value, and hence is just a question of units.

Those are also artifacts of the SI system of units and are set arbitrarily by a vote of the BIPM committee. Those constants don't even exist under other unit systems.

Again, the real physical question is not about the speed of light but about the fine structure constant. For example, you might want to know why the speed of light is 27 million times faster than the airspeed velocity of an unladen swallow. That is a dimensionless ratio and if you dig down enough, that will depend on the dimensionless fine structure constant, not the dimensionful speed of light.

15. May 11, 2017

### pixel

Suppose I want to know why the speed of light is not, say, 30 million times faster than the airspeed velocity of an unladen swallow instead of 27?

16. May 11, 2017

### Staff: Mentor

Again, that is actually a question about the fine structure constant. The dimensionful constants, like c, factor out.

17. May 11, 2017

### pixel

A pitcher throws a ball and it takes a certain amount of time to reach the catcher. The next pitch arrives in less time. Is it not faster? Has anyone mentioned units?

18. May 11, 2017

### Ibix

Depends on the frame of reference.

I think @Dale's point is that c isn't just any old speed. It's the only natural speed standard, so is involved in the definition of the units. So asking "why isn't c 6×108m/s" is, in fact, asking why the metre isn't 50cm long. The only questions that we can't turn around like that are about dimensionless quantities such as α. And the only answer we can give to such questions is to take two grand unified theories and call us in the morning.

19. May 11, 2017

### Staff: Mentor

"certain amount of time"

Last edited: May 11, 2017
20. May 11, 2017

### pixel

Yes, and using any units for that time.

21. May 11, 2017

### Staff: Mentor

Using any units is not the same as not using units.

There are two ways to assign meaning to a phrase like "certain amount of time". One is to pick a system of units and express it as a dimensionful quantity "the amount of time is 34 s". The other is to pick some other physical reference and express it as a dimensionless ratio "the amount of time is 34 times the amount of time required for this watch to tick".

Questions of the first type (dimensionful->speed of light) wind up being about the unit definitions, not the physics. Questions of the second type (dimensionless->fine structure constant) are independent of units so they can probe the physics.

22. May 11, 2017

### Staff: Mentor

The ratio between those two speeds is dimensionless because the units cancel. As with the question about the ratio of the speed of light to the speed of an unladen swallow posed above, if you grind through the physics (this will involve some serious biomechanics and biochemistry because a pitcher's arm is a very complex system, unsuited for thought experiments) you will eventually find that that ratio is what it is because of the value of one or more of the fundamental unitless constants of nature.

Last edited: May 11, 2017
23. May 11, 2017

### Mister T

Because of the (arbitrary) choice that was made for the sizes of those units.

Exactly.

24. May 12, 2017

### nitsuj

Why must a mass-less particle travel at c....what about the relationship of momentum, mass and energy means a photon must "go" c?

Does anything about that relationship imply that light cannot go less than c, or faster?

25. May 12, 2017

### Ibix

Mass is the modulus of the energy-momentum four vector, which is tangent to the particle's worldline. If the mass is non-zero then the particle's worldline is timelike. If it is zero then the particle's worldline is null.

So "it has zero mass" is, in relativity, just another way of saying "it travels at the speed of light".