# B Why 186,282 miles per second?

1. Dec 17, 2015

### thetexan

Why would the speed of light happen to be 186282 mps? What is the property of light that settles on that speed. Why not 200000? Why not 154000? There must be some reason light doesn't travel any faster. And I don't mean relativity.

If it was 200000 then Einstein and the rest of us would be talking about how light is measured at 200000 mph (instead of 186282) regardless of our frame of reference.

It seems like an odd, arbitrary number. Of course we humans chose the distance called a mile and specified its length. If miles were 7438 feet per then we'd all be talking about how the speed of light was constant at 132235 mps! But that's not even what I'm driving at.

Whatever the speed works out to be...Why? What property of light or physics puts the brakes on at this speed and no other. What property of light or physics pushes it to that speed and no slower? For example, if we use an automobile analogy, why does a car only go 70 mph? With this car there are two reasons that two different people might point to. One, the speed limit is 70. Two, on this particular car the engine is only capable of pushing it to 70. So I'm interested as to what about the engine limits it's ABILITY to go faster. Or stated another way...is the speed limit of thought of as 70 because the car CAN'T go faster or can the car not go faster because the speed limit is 70. And if the later, why 70? Why 186282?

I hope this makes sense.

tex

2. Dec 17, 2015

### m4r35n357

You are so close to working it out for yourself! You are showing signs of feeling that the numbers have no physical significance, and you would be right to feel this way. To cut a long story short you can get any number you like for c just by choosing the units. Most physicists use the value 1 (light year per year, light second per second, approximately feet per nanosecond etc) as it makes the formulas and calculations simpler.

3. Dec 17, 2015

### thetexan

I understand about the units of measurement. So let's try to leave those out of it. What limits light to "that" speed whatever you call "that". For example, if I look at a train and someone says that's as fast as the train can go, I don't need to know the actual speed to wonder, "why can't it go faster than "that"". Why is "that" speed, whatever it is, that particular speed? How did the train settle on "that" speed and no other?

Speed, or our perception of it, is dependent on measurements or cues of relative comparison. I perceive the train as having a velocity but it's relative to me or to a background or something. This defines motion and our perception of it. So I perceive the train as going "that" fast but wonder why it couldn't be a faster relative motion. Why "that" relative motion.

All of this to ask, what about light limits it's relative speed to the relative velocity we have come to know and love as the speed of light. This is the beginnings of a little anthropomorphic headache.

tex

4. Dec 17, 2015

### nikkkom

Time and space are in fact similar: they are dimensions. The only difference is that space enters the formula for distance with + sign: S^2 = x^2 + y^2 + z^2, but time has the minus there: S^2 = x^2 + y^2 + z^2 - t^2.

Therefore time and space, "for real", should be measured in the same units. Say, meters. A meter of time is ~3 nanoseconds.

When we do that, speed of light really is 1 meter per meter: "light covers one unit of space per one unit of time". Since "meter per meter" cancels out, the speed is dimensionless, it is 1 regardless of what units you are using to measure spacetime distances (but you must use the same unit for space and time).

Now, 1 _is not_ a surprising number, is it? ;)

5. Dec 17, 2015

### georgert

I've seen this question asked many times and similarly the responders go on about the relativity of units of measure. That's doesn't answer the question, but in reality, no one really knows. The speed of light is a constant of nature, just like the value for the Planck constant. The best answer I've come across ties the value c to the values of the electric constant (vacuum permittivity) and the magnetic constant (vacuum permeability), which are also established physical constants. That light has a limit has and is not infinite is a requirement of general relativity so it has to settle somewhere, and without GR and QFT there would be no one around to speculate. Ultimately the establishment of values for all of nature's constants are most likely the result of symmetry breaking during the initial phases of the big bang. The question about the nature of the speed of light crops up much more often than the question of say "why is the electron mass the value that it has?" is, it seems to me, because what we measure as the speed of light is ultimately the rate or speed of reality, i.e. the speed at which the universe evolves in any given observer's frame of reference, which is kind of mind boggling if you think about it for a moment.

6. Dec 17, 2015

### Hornbein

There are many things in physics that are measured but not understood. The speed of light in a vacuum has to do with the permittivity and permeability of the vacuum, but these are just more measured constants so it doesn't explain much.

The "why?" question seldom gets below three or so levels.

7. Dec 17, 2015

### gleem

Maxwell's equations tell us that c is a constant and relates it to physically measurable constants the permittivity and permeability of free space. As noted above distance scales and time scales are arbitrary so the actual numerical value of the speed of light is arbitrary.

However it is not the general goal of Physics to explain why something is what it is but to determine how things change to relation to other things to establish relationships between elements of our universe under different conditions. So Maxwell says the speed of light is constant in a vacuum and so it has be determined. Einstein has established a relation between the velocity of light and different gravitational fields. I do not totally understand what fixes the speed of light in free space but free space is believed not truly empty in the sense of having no structure with which you can interact . For current quantum electrodynamics suggest that the vacuum of space is a primordial quantum field which has a dynamic character of creating and annihilating particles continually thus creating fluctuating electromagnetic fields. Some are trying to calculate c's value from a quantum field theoretical starting point. See https://aeon.co/essays/why-is-the-speed-of-light-the-speed-of-light.

8. Dec 17, 2015

### nikkkom

That's the point: they are not "constants of Nature" (more proper mathematical term being "free parameters of theory").

Our current physical theories quite concretely say that space and time are fundamentally related, and that energy and frequency are fundamentally related.

Therefore they ought to be measured in the same units. (This is not done in practice partly for historical, partly for practical reasons (measuring time in 3 nanosecond chunks would be inconvenient)). In these units, there are neither speed of light nor Planck constants, they simply disappear from all formulas (get replaced by 1).

9. Dec 17, 2015

### Erland

I know this is slightly off topic, but I can't resist pointing out that in metric units, the light speed is very close to, not 200 000, but 300 000 km/s. To be precise, it is exactly 299 792 458 m/s, by definition (the metre is defined to make this hold).

10. Dec 17, 2015

### Staff: Mentor

Yes. That is it exactly. There is no other reason besides the choice of units. The same is true of all dimensionful universal constants: they don't tell you about the physics, they tell you about your units. You set them to any value you like or you can get rid of them entirely by choosing appropriate units.

Probably what you are actually interested in is why the fine structure constant has the value it does. That is dimensionless so it doesn't depend on your units, and it does tell you about the physics.

11. Dec 17, 2015

### Fuinne

It's actually a pretty good question, to be honest, but in the end, 186,200 and 154,000 have no difference between them except numbers. If the speed of light was to actually be 154,000, then we would just ask why isn't it 186,200 miles per second? I guess in my opinion, there is no reason for that number to be specific. What I mean is that it just happens to be 186,200. It may not have even been on purpose. When we see how old the universe is, why do we say 13 billion years? That's just an estimation, which could turn out pretty accurate, but why? Out of all numbers why not 11 billion years, or 10 billion years. Sometimes, there is no reason for things. Things go at random because nature doesn't like to be neat and tidy. The leaves don't blow into a neat stack and the universe doesn't get created at exactly, on the second, 13 billion years.

12. Dec 17, 2015

### Staff: Mentor

This is not one of those. This is completely understood as being entirely due to the choice of units.

13. Dec 17, 2015

### Burnerjack

Barring the arbitrary aspects of the length of a mile or meter, isn't the real question related to the propagation delay between the magnetic field and the electric field components of the EM wave? The greater the delay, the faster the wave. Am I way off track here?

14. Dec 17, 2015

### Staff: Mentor

There is no delay. They are in phase.

If you want to bar the arbitrary aspects of the length of a mile or meter then you need to look at dimensionless constants, like the fine structure constant.

15. Dec 18, 2015

### Svein

16. Dec 21, 2015

### Whyndham_UCL

So to paraphrase the original poster. What theory do we have that PRODUCES a particular value of c (and other constants) as opposed to merely having them as axioms. Answers on a postcard, hopefully!

17. Dec 21, 2015

### Staff: Mentor

The value of c is PRODUCED by the choice of units. There is no theory about why different people choose different units, but it would be a psychology theory not a physics theory.

18. Dec 21, 2015

### Tony Hambro

How fast does the photon accelerate from a standing start to 300,000m/sec?

19. Dec 21, 2015

### Staff: Mentor

Light starts at c, it doesn't accelerate.

20. Dec 21, 2015

### Gary Howard

I have always wondered if the speed of light was constant from the Big Bang to present.

How do we know that it was or is it an assumption? If not, this must affect many formulae and hypotheses...

21. Dec 21, 2015

### Whyndham_UCL

I meant, independent of the units involved, how does theory predict c? If indeed it does. Fine structure constant has been mentioned. How does this relate to c? This constant isn't predicted by any mainstream current theory, am I right?

22. Dec 21, 2015

### rootone

The speed of light is not a prediction of any theory, it's a measurement.
The actual 'number' in terms of numerical symbols will of course be dependant on the units used to do the measuring, but it has been found without exception to always be the same speed.
It is constant and it is what it is, just like the value for Pi is what it is.
We could use something other than decimal (base 10), to express the value of Pi, and would get different number (in numerical symbols), but Pi would still be the ratio of a circle's circumference to its diameter.
Why is Pi the value it is? Does the question even make sense?, Pi is what it is measured to be, and 'Pi' is just a name we give to this observed constant.
Same with 'c', it is what it is as a matter of observation, there can be no theory of why it has a particular value since the value is self-evident and it cannot be any other value.
Well perhaps c = c, might work.

Last edited: Dec 21, 2015
23. Dec 21, 2015

### Whyndham_UCL

Sure, c is a fundamental constant. But that doesn't mean that physicists should be satisfied with it being a constant, and not a result of an improved theory. Remember that there were many apparently arbitrary constants on the books (in physical chemistry) that have since become results of quantum mechanics over the years. Here's Richard Feynman riffing in this general key (he's talking about alpha, not c, but it could be any fundamental constant).

There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly!

— Richard Feynman, Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter.

24. Dec 21, 2015

### Whyndham_UCL

so what I object to in rootone's reply is "there can be no theory of why it has a particular value".

This is like saying Physics has been done, shop closed, try something else.

25. Dec 21, 2015

### rootone

No, the fact there are observable constants existing doesn't imply that all of physics is done.
It only implies that observable constants exist.