What Determines the Constant Speed of Light?

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SUMMARY

The speed of light is a fundamental constant of nature, recognized as such since James Clerk Maxwell formulated the equations of electromagnetism. The speed of light is defined as 299,792,458 meters per second, a value that remains constant regardless of the units used for measurement. This constancy is not merely a result of human definitions but is an intrinsic property of the universe. The discussion highlights the philosophical implications of why the speed of light has its specific value and the relationship between physical constants like the speed of light, Planck's constant, and gravitational constant.

PREREQUISITES
  • Understanding of electromagnetic theory and Maxwell's equations
  • Familiarity with the concept of physical constants in physics
  • Basic knowledge of Special Relativity and its implications on measurement
  • Awareness of unit definitions and their impact on scientific measurements
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  • Explore the implications of Special Relativity on measurements of time and distance
  • Research the relationship between fundamental constants in physics, including c, h, and G
  • Study the historical context of how the speed of light was measured and defined
  • Investigate the anthropic principle and its relevance to physical constants
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Physicists, students of physics, and anyone interested in the fundamental principles of the universe and the nature of light.

picass
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Has anyone an idea why speed of light is constant ? Has this something to do with lack of mass of a photon because I cannnot imagine it to be possible to add speed to something that has no mass. As light emerges from energy fall of an electron, does speed of light have anything to do with rotation speed of an electron ?
 
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I believe it is simply because of the lack of mass, it has a momentum and energie but I don't believe it has a mass, this would indeed separate light from most laws attributed to speed/travel.
 
The speed of light was first recognized as a constant by Clerk Maxwell after he cast the fundamental equations of electromagnetism in the form of a wave equation. The term

\frac 1 { \sqrt {\epsilon_0 \mu_0}}

appeared as the propagation speed of electromagnetic waves. When he computed this constant the value was the same as the then experimental value for the speed of light.

Why is it that value?? That is not a question answered by physics.
 
Light must go either:
  • infinitely fast
  • finitely fast
If it went infinitely fast, it would cause all sorts of problems with causality -- we couldn't tell what happened before what, or what caused what. Since electromagnetism is the force at work in chemistry and biology, life would happen instantly -- you'd be born and die at the same instant. Stars would burn all their fuel instantaneously. The universe just wouldn't be very nice.

So, light has to travel at some finite velocity. Why does it travel at 300,000 km/sec? Because us humans just happened to define the kilometer and the second that way. Many people feel quite comfortable just declaring that the speed of light is 1, and work with light-seconds and seconds (or light-years and years) instead of kilometers and seconds.

- Warren
 
chroot said: "So, light has to travel at some finite velocity. Why does it travel at 300,000 km/sec? Because us humans just happened to define the kilometer and the second that way."

The speed of light depends on how humans define their units?
 
jdavel said:
The speed of light depends on how humans define their units?
The speed itself does not, but its numerical representation certainly does.

For example, light travels at 299 792.458 kilometers per second, or 4.70279985 * 1014 furlongs per decade, or 9.71560349 * 10-18 parsecs per nanosecond. Or, if you prefer, 1 light-year per year.

- Warren
 
chroot said: "The speed itself does not, but its numerical representation certainly does."

Right. But if you measure the distance (any units) that light travels in a given time (any units) the ratio of distance to time (in those units) always has the same value. This raises two questions:

1) Why do you always get the same value?

2) Why is this particular value the one you always get?

I think the first question is the one that started this thread. It can be answered much the same way you answered the question about why it's not infinite. Namely, if you didn't always get the same value, the world would be completely different, and we wouldn't be here asking about it.

Integral says the second question isn't one answered by physics. Well, it certainly hasn't been yet. And there are probably some serious philosophical reasons to believe it never will be. But I believe physicists still hold out the hope of someday understanding why the values of c, h & G (light, Planck & gravity) are RELATED the way they are. That is, if we can just accept one of them being what it is, we'll understand why the others have to be what they are. I think I saw that on Nova!
 
Well, the anthropic principle (the universe is the way it is, for if it were not, we wouldn't be here to talk about it) certainly is an answer, though not a particularly fulfilling one.

It is possible that one day the zoo of 26+ "free parameters" (numbers which must be estimated from experiment and cannot currently be predicted) will one day be whittled down to just a handful as theories progress. However, I feel it's very unlikely that the number of free parameters will ever be driven all the way to zero. We'll always have the question looming over us: why do those parameters have the values they do? No one may ever know, and perhaps the anthropic principle really will be the only answer we'll ever have, satisfying or not.

- Warren
 
jdavel said:
... if you measure the distance (any units) that light travels in a given time (any units) the ratio of distance to time (in those units) always has the same value.
This seems kind of trivial (misleading), though. If you want to say this is absolutely true, then you have to talk about proper time and displacement, which critically depends on the invariance of c. Otherwise, I don't think that you can say such a thing, since, the further you move away from the pole of your geodesic coordinates, the more distortion you will get, either in dl WRT dt, or dt WRT dl, or both.
 
  • #10
The speed of light in meters per second is constant because the meter is defined as the distance that light travels in 1/299,792,458 second.
 
  • #11
DrMatrix said:
The speed of light in meters per second is constant because the meter is defined as the distance that light travels in 1/299,792,458 second.

c was constant when the meter was defined as a fraction of the Earth's diameter, it was constant when lengths were measured in cubits, it was constant when man had no concept of measurement. The constancy of the speed of light is not an artifact of mans ability to measure it is a property of the universe.
 
  • #12
DrMatrix said:
The speed of light in meters per second is constant because the meter is defined as the distance that light travels in 1/299,792,458 second.

Circular reasoning. Sorry, but this isn't useful.

Speed is the magnitude of some displacement of an object with respect to a reference displacement. Given that all possible displacements are contained in the universe we must choose one of them to measure the one of interest.

Your question could be restated: Why is a light-like displacement constant with respect to a reference displacement (clock) for all inertial frames. A complete explanation is surprisingly involved. But here's the simple explanation...

Because all of existence includes all places, there are no other places for the universe to travel to. I.e., the sum of all displacement vectors of all existents must sum to the null vector. ( I got to learn Latex sometime...) And so, if you write:

v_{net}= \sum_{i=0}^\infty v_i = {null}

implying...

|v_{j}| = | \sum_{i=0}^n {v_i} |

where n=\infty - 1 and v_j \ni v_i (you get the idea)

Which means that:

\frac{|v_{j}|}{| \sum_{i=0}^n {v_i} |} = 1

(and I learned some Latex. Vector magnitude doesn't work?)

In english, single objects must travel at a constant speed with respect to all possible frames of reference.
 
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  • #13
Integral said:
c was constant when the meter was defined as a fraction of the Earth's diameter, it was constant when lengths were measured in cubits, it was constant when man had no concept of measurement. The constancy of the speed of light is not an artifact of mans ability to measure it is a property of the universe.
I agree that the speed was constant when the meter was defined as a fraction of the Earth's diameter. But I'm not sure the speed of light is constant if distance is measured in cubits. Isn't a cubit the length of the forearm? My forearm is probably not the same length as yours and even if we use one person's forearm as the standard, people grow. So I'd say the speed of light is not constant if distance is measured in cubits. Please tell me how can a measurement be constant when it is not defined? In order to even ask the question "Is the speed of light constant?", you must have defined units of time and distance. And the answer depends upon the definitions.

Units of length are matters of definition. According to Special Relativity, when distance is measured by rigid rods, light has a constant velocity. This allowed us to define length in terms of the speed of light. With the meter defined as the distance light travels in 1/299,792,458 second, the speed of light is constant by definition.
 
  • #14
DrMatrix said:
I agree that the speed was constant when the meter was defined as a fraction of the Earth's diameter. But I'm not sure the speed of light is constant if distance is measured in cubits. Isn't a cubit the length of the forearm? My forearm is probably not the same length as yours and even if we use one person's forearm as the standard, people grow. So I'd say the speed of light is not constant if distance is measured in cubits. Please tell me how can a measurement be constant when it is not defined? In order to even ask the question "Is the speed of light constant?", you must have defined units of time and distance. And the answer depends upon the definitions.

Units of length are matters of definition. According to Special Relativity, when distance is measured by rigid rods, light has a constant velocity. This allowed us to define length in terms of the speed of light. With the meter defined as the distance light travels in 1/299,792,458 second, the speed of light is constant by definition.
Our ability to measure or even comprehend the speed of light is immaterial. The speed of light is a basic property of the universe, it appears to be constant. Our perception of it may change, but the property remains constant. (Unless, of course, there are long term slow variations which we have not been able to measure.)

Of course you must have a consistent unit of measurement to accomplish anything, If Noah had changed his definition of a cubit midway through construction the ark would not have floated. Do you think that the speed of light is different because the number of miles/year it travels is different then the number of m/s?

Your argument would lend itself to a blind man claiming color does not exist because he cannot see it. I personally believe that the universe exists independent of our observations.
 
  • #15
Integral said:
Of course you must have a consistent unit of measurement to accomplish anything, ...
...
Do you think that the speed of light is different because the number of miles/year it travels is different then the number of m/s?
I think DrMatrix and I are trying to make the same point. You must get the definitions straight. And, in order to have definitions, you must agree upon your standards. The speed of light c, last time I checked, was a fundamental constant that is used to define the meter, not vice versa. In this sense, asking whether the speed of light is a constant has a rather trivial answer and reason: "yes, by definition." Then, if one agrees upon a certain number of hyperfine oscillations of the Cs atom as a unit of time, the meter is defined using this unit and c. Thus, it is the meter that is the derived unit, no the speed. The way the mile and the year are defined requires agreement on further standards, at the very least a standard of conversion. I don't know how the mile was originally defined, but just think about the year. There are two equally valid definitions, sidereal and I can't remember the other one. But this already is quite ambiguous.
 
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  • #16
turin said:
I don't know how the mile was originally defined

This is off subject, but you brought it up so...

At one time, an acre was the amount of land that a man could plow in one day.

Later an acre was then defined as 60 square chains. 1 chain is 66 feet. That's why an acre is 43,560 square feet. (isn't this system convenient?)

A mile is 80 chains, or 5,280 feet.(nice round number to work with)

So, that's why one square mile is 640 acres.(cool huh?)
 
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  • #17
I do not care what units are used, or what defines what. The speed of light is a constant. The only thing that the definition of the meter in terms of the wave length of light does is make the number used to represent the speed of light in meters a rational. This is merely a matter of convince and does not effect the speed of light in any way. While dinosaurs were walking the Earth the speed of light was constant, it is the same constant now, the numbers used to describe it are of no real significance.
 
  • #18
Suppose the speed of light were to double when its speed is measured by rigid rods. The meter is defined as the distance light travels in 1/299,792,458 second. What is the new speed of light in meters per second?
 
  • #19
The speed of light does not, and cannot double. Only your units have changed. That has not effect on the speed of light.
 
  • #20
DrMatrix,

Since E=mc^2, if the speed of light changed suddenly on the day we redefined the meter, then so did the temperature of the sun. But it didn't. Or are you saying that it did?
 
  • #21
The Speed of light is constant with respect to all frames of reference. -- No preferred frames, no preferred rulers.

A ruler measures a length because it is line-like. I.e., bound by two distinguishable endpoints. If we define two electrons as the endpoints of our ruler (just another length in the universe), is the speed of light constant?

How about if we choose two galaxies as the end-points of our reference length.
 
  • #22
If Special Relativity is correct, the speed of light (using rigid rods to measure distance) is constant. If Special Realtivity is not correct, and the speed of light is variable (using rigid rods to measure distance), the speed of light will still be constant in meters per second because the meter is defined in terms of the speed of light.

You cannot measure (or even define) speed until you have defined units of time and distance. Units are matters of definition. There are no absolute units.
Jack Martinelli said:
How about if we choose two galaxies as the end-points of our reference length.
Good example. Then we would have a variable speed of light, but space would not be expanding. It's all a matter of how we define our units.
 
  • #23
Special Relativity is NOT the source of a constant c. Special Relativity is an exploration of space and time IF c is constant.

If you want to find the source of a constant c you must look to Maxwell's equation and the expression

c = \frac 1 {\sqrt {\epsilon_0 \mu_0}}

It is this expression which set the world of physics on its ear in the last half of the 19th century.

If you recall Einstein POSTULATED a constant speed of light. His work cannot be used to prove a constant speed of light. It is assumed on the first page.
 
  • #24
picass said:
Has anyone an idea why speed of light is constant ? Has this something to do with lack of mass of a photon because I cannnot imagine it to be possible to add speed to something that has no mass...

Integral is absolutely correct, picass. Maxwell's crowning achievement is that he determined that the value of c in free space is determined exclusively by the magnetic and electric properties of the vacuum; namely u and e, the permeability and permittivity of the vacuum. c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}

Thus the constancy of that value of c is fundamentally due to the invariance of the value of these two parameters in free space, and doesn't depend on the mass or energy of photons. :biggrin:

Creator :biggrin:
 
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  • #25
Those are some right pretty equations y'all got there, but they are unnecessary. I can calculate the exact value for the speed of light in meters per second knowing only that the meter is the distance light travels in 1/299,792,458 second. Don't need permeability or permittivity or anything else.

Integral said:
If you recall Einstein POSTULATED a constant speed of light. His work cannot be used to prove a constant speed of light. It is assumed on the first page.
Yes Einstein postulated a constant speed of light in a vacuum. He also assumed distance be measured by using rigid rods. It is remarkable that the speed of light is constant when distance is measured by rigid rods. It is not remarkable that the speed of light is constant in meters per second when the meter is defined in terms of the speed of light.
 
  • #26
DrMatrix said:
... I can calculate the exact value for the speed of light in meters per second knowing only that the meter is the distance light travels in 1/299,792,458 second. .

HA. HA; wonderful reasoning there. DrM; that's about as circular as you can get! :rolleyes: Wonderful; so you can "calculate" the speed of light by "knowing" only ...the speed of light. Ha, HA, HA ...Someone get me off the floor! :biggrin:
 
  • #27
No. I'm not calculating the speed of light given the speed of light. I'm calculating the speed of light given the definition of the meter. It's not my definition. It is the standard definition.
 
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  • #28
Integral,
This is a lot more fun as a spectator sport. Enjoy,
-Mike
 
  • #29
Congratulations DrMatrix we are all very proud of you.

LOL.

Oh, by the way the use of rods in Einsteins paper had no meaning other then a illustraion. The rods play no part in the theory. Perhaps when you can get past the introduction you will begin to get a grasp on Relativity.
 
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  • #30
No need to get tacky. I did get past the intro. Rigid rods play an essential role in Einstein's Special Relativity. In order to even discuss relativity, it is necessary to define a coordinate system. Einstein uses rigid rods to establish a coordinate system. Without a coordinate system in place, you can't begin to discuss relativity.

Answer this: Given that the meter is defined as the distance light travels in 1/299,792,458 second, how would a change to \epsilon_0 or \mu_0 affect the speed of light in meters per second?

You should read The Philosophy of Space and Time by Hans Reichenbach. Then you might begin to get a grasp of the philosophy behind special relativity. Though it might be a tough read for anyone who can't understand why defining the meter in terms of c makes c constant in meters per second.
 

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