What Determines the Constant Speed of Light?

[picass]

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 ?

 

[gta-maloy]]

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.

 

[Integral]

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 propogation 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.

 

[chroot]

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

 

[jdavel]

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?

 

[chroot]

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

 

[jdavel]

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!

 

[chroot]

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

 

[turin]

... 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.

 

[DrMatrix]

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.

 

[Integral]

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.

 

[Jack Martinelli]

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.

 

[DrMatrix]

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.

 

[Integral]

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.

 

[turin]

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.

 

[Michael D. Sewell]

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?)

 

[Integral]

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.

 

[DrMatrix]

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?

 

[Integral]

The speed of light does not, and cannot double. Only your units have changed. That has not effect on the speed of light.

 

[jdavel]

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?

 

[Jack Martinelli]

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.

 

[DrMatrix]

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.

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.

 

[Integral]

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.

 

[Creator]

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.

Creator

 

[DrMatrix]

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.

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.

 

[Creator]

... 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! 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!

 

[DrMatrix]

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.

 

[Michael D. Sewell]

Integral,
This is a lot more fun as a spectator sport. Enjoy,
-Mike

 

[Integral]

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.

 

[DrMatrix]

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.

 

[Integral]

What is your fascination with the meter? And where does Einstein use any method to prove that the speed of light is constant? Once again, Einstein postulates a constant speed of light. He does not even mention why it might be constant, he just says it is. Nothing having to do with relativity, can be used in a proof of the constancy of the speed of light. It does not matter that the meter has been redefined in terms of wavelengths of light. c Was recognized as a constant long before that was done. The reason the meter could be redefined in this manner is because the speed of light is constant. It has already been pointed out, that it is circular reasoning to use the redefined meter as an argument in the constancy of c.

We are not talking about relativity by the way we are talking about the reason it was necessary to develop relativity.

Reading the philosophy of relativity will not revel why the speed of light is constant, you need to read about Maxwell's Equations to learn that. And yes if \epsilon_0 or \mu_0 were to change then the speed of light in m/s would change.
edit:
Why? Because the meter would have to be redefined to correspond to the new conditions. It would be that or change all the road signs that use meters, because if the old definition were kept the length of the meter would change.

 

[DrMatrix]

Why? Because the meter would have to be redefined to correspond to the new conditions. It would be that or change all the road signs that use meters, because if the old definition were kept the length of the meter would change.

The length of the meter would change compared to what? The standard of length is the meter. Rigid rods might change length, but the length of the meter would remain one meter.

 

[jdavel]

DrMatrix,

I think I finally udersatand what you're saying!

If you make two measurements of the speed of light and calibrate the lengths of your apparatus before each measurement using the light speed method, then you'll always measure the same speed. If that's all you mean, then I agree with you. But you'd never do that.

If you want to find out whether the speed of light depends on the direction its traveling, get a stick and measure the time it takes for light to get from one end to the other when the stick is pointing in different directions. You don't even have to measure the length of the stick!

 

[Jack Martinelli]

...Reading the philosophy of relativity will not revel why the speed of light is constant, you need to read about Maxwell's Equations to learn that. And yes if or were to change then the speed of light in m/s would change.

This is also circular reasoning. You can say that c is constant because \mu_0 and \epsilon_0 are constant. But then, to make it non-circular, you are left with explaining the constancy of \mu_0 and \epsilon_0.

(and what do you have to do to get rid of that annoying undescore?)
(and how come I haven't been attacked yet?)

 

[russ_watters]

DrMatrix, you are harping on the fact that the meter is defined by the speed of light and its been explained to you several times now that that is irrelevant to the question of if the speed of light is constant. Exploring this point by Integral a little more may be useful:

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.

The speed of light has been known (or at least expected) to be constant for a hundreds of years. The meter was defined in terms of the speed of light only 20 years ago. The meter is tied to the speed of light because the speed of light is a universal constant, not the other way around.

In fact, the reason that the meter is no longer defined as the distance between two scratch marks on a bar of metal in France is that since about 20 years ago, our abiliy to measure the speed of light accurately has exceeded our ability to measure the distance between those two scratch marks accurately. As well, due to environmental factors, the distance between those two scratch marks wasn't even constant. The meter had to be re-defined in terms of something more constant/precise or it would hinder scientific research. The speed of light quite literally makes a better meter-stick than the meter-stick does.

If you really want to argue arbitrary units, how about the definition of a second...?

 

[Jack Martinelli]

If you really want to argue arbitrary units, how about the definition of a second...?

Why do that? Why not define a ruler in the general sense so that it can be used to measure intervals that are space-like or time-like.

 

[Integral]

This is also circular reasoning. You can say that c is constant because \mu_0 and \epsilon_0 are constant. But then, to make it non-circular, you are left with explaining the constancy of \mu_0 and \epsilon_0.

(and what do you have to do to get rid of that annoying undescore?)
(and how come I haven't been attacked yet?)

I do not see the circularity here. Yes, the question has changed but unless a measurement of c is involved in the experiment to find \epsilon_0 it is not circular.

 

[turin]

quoting Integral:

I do not care ... 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.

It is not a matter of what, but how.




quoting Integral:

While dinosaurs were walking the Earth the speed of light was constant, it is the same constant now, ...

How do you know this? Compared to what?




quoting Integral:

The speed of light does not, and cannot double.

How do you know this? Compared to what?




quoting Creator:

...Someone get me off the floor!

Would that I could.




quoting Integral:

... the use of rods in Einsteins paper had no meaning other then a illustraion. The rods play no part in the theory.

Say WHAT?! How do you define a coordinate system? I admit there are other ways to define one, but there must be one. Or, in the words of DrMatrix:

... it is necessary to define a coordinate system.

quoting Integral:

It does not matter that the meter has been redefined in terms of wavelengths of light.

Of course it matters. It matters for the same reason that most of you seem to be saying it doesn't. If the speed of light is taken to be the standard, then it is a constant by definition, which answers the original post, unless, by "speed of light," the original poster meant something other than "c."




quoting jdavel:

If you make two measurements of the speed of light and calibrate the lengths of your apparatus before each measurement using the light speed method, ...
...
... you'd never do that.

What do you mean, "you'd never do that"? That is exactly what would be done. How else would you calibrate length?




quoting russ_watters:

... due to environmental factors, the distance between those two scratch marks wasn't even constant. The meter had to be re-defined in terms of something more constant/precise ...

That's the point. Except, I would replace "constant/precise" with "universal;" the length of a rod is almost as constant and just as precise as the consant in the wave equation before we impose a scale on it. There isn't a rod for calibrating the meter locked in a vault and held at strict environmental conditions on Mars, but it is believed that Maxwell's equations can be found on Mars. Thus, they give us the standard, but it is still just a standard. I'm not saying that the equations are merely a standard (they are physical law), but the numerical value that we infer from the wave equation is defined as a standard universal constant. It is a constant because we have defined it that way. We have defined it that way because it is believed to be universal, and therefore more convenient than using a bar.

 

[Integral]

The length of the meter would change compared to what? The standard of length is the meter. Rigid rods might change length, but the length of the meter would remain one meter.

Since the definition of the meter is tied to the speed of light, if the speed of light were to change, the length of the standard would change. This means that if I were to use the standard meter to measure a known distance, I would come up with a different distance after the change in c. It would now be 60km to London it was 50km before

Those are some right pretty equations y'all got there,

I find this comment very interesting. What "fancy" equations are we talking about? A square root? If you consider the square root to be a "fancy equation" then the relativity understand so well is full of "fancy equations". I am afraid that anyone who considers the square root to be a "fancy" equation simply cannot comprehend the even the simply math used in the development of Special Relativity. Let's not say anything of the very difficult math required to understand General Relativity. By the way, since you are so enamored with the definition of a specific coordinate system you should realize that on of the important features of GR is the ability to express the Physical relationships in a manner that is independent of the coordinate system. In the fundamental expressions look the same in ALL coordinate systems.

 

[turin]

Since the definition of the meter is tied to the speed of light, if the speed of light were to change, the length of the standard would change. This means that if I were to use the standard meter to measure a known distance, I would come up with a different distance after the change in c. It would now be 60km to London it was 50km before

And that would show what? What's the big deal? Do you believe that lengths should be invariant in themselves? In SR, using the speed of light as a standard causes lengths to change. Is that wrong, too?

 

[Integral]

And that would show what? What's the big deal? Do you believe that lengths should be invariant in themselves? In SR, using the speed of light as a standard causes lengths to change. Is that wrong, too?

The whole point of the standard coordinate system you carried on about in your previous post is so that the standard length does not change. Now you seem to be arguing the other side of the coin. Make up your mind. Perhaps I do not understand your point. Lengths in SR change with relative velocity, if there is no relative velocity there is no length change. What has SR to do with the current discussion? I have asked this question over and over, never get an answer.


Suppose I were to define a standard volume of water as the amount of water in a certain bucket. Then using that bucket I measure the volume of several other buckets to be 5 standard buckets. One day I see a new shiny bucket that I would rather use as my standard. When I use my new standard to measure the amount of water in one of the previously measured buckets I find that it now holds 6 standard buckets. Are you telling me I should ignore this discrepancy or should I assume that all buckets have somehow changed? Clearly, if it is indeed used, a change in a standard will be noticed.

If the meter were never used to measure anything but the speed of light we would indeed never notice the change. But as soon as we apply the standard to something else we will certainly notice if the standard changes. Suddenly all previous measurements will be wrong according to our standard.

 

[DrMatrix]

What is a "known distance"? A distance is known only when compared to the standard of length. The meter is the standard. If the distance to London was 50km and it is now 60km, then the distance to London changed. The meter is still one meter.

Yes I am well aware that GR allows aribtrary coordinates systems. I didn't want to get into that. You can't talk about a constant speed of light in GR.

I find this comment very interesting. What "fancy" equations are we talking about? A square root? If you consider the square root to be a "fancy equation" then the relativity understand so well is full of "fancy equations.

I was being sarcastic, I thought you'd get that. Sorry.

 

[Integral]

quoting Integral:
It is not a matter of what, but how.

Please explain further what you mean, I don't get it.

quoting Integral:
How do you know this? Compared to what?

It is believed that the oil we are burning today was living plant life in the era of the dinosaurs. It has an atomic structure that is compatible with our current chemistry. Therefore atomic structure has not changed since the era of the dinosaurs, therefore the speed of light has not changed (significantly).

quoting Integral:
How do you know this? Compared to what?

Simply citing the current state of Physics. It may be that c has changed over the life time of the universe, but that is not the current understanding.

quoting Integral:
Say WHAT?! How do you define a coordinate system? I admit there are other ways to define one, but there must be one. Or, in the words of DrMatrix:

Ok, we need to establish a coordinate system. Now what is the significance of that coordinate system? What part does the coordinate system play in the final work of relativity?
Precisely, none. General Relativity allows expression of physical laws independent of the coordinate system.

quoting Integral:
Of course it matters. It matters for the same reason that most of you seem to be saying it doesn't. If the speed of light is taken to be the standard, then it is a constant by definition, which answers the original post, unless, by "speed of light," the original poster meant something other than "c."

How does the fact that the meter has been tied to the speed of light effect the speed of light? The key point to this entire discussion is the difference between
"the speed of light is constant because the meter is defined in terms of the wavelength of light?

and

"The meter is expressed in terms of the wavelengths of light because the speed of light is constant"

quoting russ_watters:
That's the point. Except, I would replace "constant/precise" with "universal;" the length of a rod is almost as constant and just as precise as the consant in the wave equation before we impose a scale on it. There isn't a rod for calibrating the meter locked in a vault and held at strict environmental conditions on Mars, but it is believed that Maxwell's equations can be found on Mars. Thus, they give us the standard, but it is still just a standard. I'm not saying that the equations are merely a standard (they are physical law), but the numerical value that we infer from the wave equation is defined as a standard universal constant. It is a constant because we have defined it that way. We have defined it that way because it is believed to be universal, and therefore more convenient than using a bar.

I think you are stepping beyond the Physics into philosophy and semantics here. The speed of light is a universal constant. Please take debates about this issue to Theory Development.

 

[turin]

The whole point of the standard coordinate system you carried on about in your previous post ...

What standard coordinate system? I simply supported DrMatrix' position that there must be a coordinate system. I even alluded to the possibility of other ways to define a coordinate system indicating that I do not think a lattice of rigid rods is a standard.

What has SR to do with the current discussion?

It provides an example to show that there is no problem with the spatial distance between any two points in space, such as the distance between two cities, changing.

Suppose I were to define a standard volume of water as ...

But this is just like changing from yards to meters. There is no problem here; it is just a matter of a conversion factor. What would make your example more interesting is to say:

What if we measured the amount of some water in terms of the number of standard shiney buckets full, and found it to be six one say, and then, the next day, the the amount was only five. Well, then we'd have to discard our conservation of water law, right? No, because, just in the nick of time, a genius comes along with an incredible breakthrough. He (or she; there have been female geniuses, too) declares that the amount of water is not determined by the volume, but by the weight. Now, whenever the water is measured, on whatever day, the weight is always found to be 8.3 standard shiney buckets. Hooray for the inovative minds on the standardization committee!

 

[Integral]

It provides an example to show that there is no problem with the spatial distance between any two points in space, such as the distance between two cities, changing.

There certainly is a problem with distances changing if it is due to a change in the standard. Why to you think that the US mileage signs are mileage signs and not km signs? A change in a standard requires a lot of re calibration this costs money. Sorry to bring real world issues into the argument.

I feel that there is a issue with the distance changes between cities, if standards mean anything, when I measure a distance in meters it had better read the same today as it did yesterday or next year. That is the whole point of a standard.

When London is moving at .5c wrt to Paris then I would expect the distance to change. As long as they are stationary the distance must remain the same. The distance is a physical quantity it does not change with the units you measure it in.

 

[turin]

Please explain further what you mean, I don't get it.

Consider defining distance against a standard rod. What is the prescription for measurement? Do we place the rod at rest along side the distance to be measured? If this is the method, then all we can do is put the distance in three categories: shorter, longer, same length as standard. Of course, this simply won't do, so we can translate the rod along the distance. This is, of course, inconvenient. For instance, this is impractical to measure microscopic distances and interstellar distances with the same standard. Also, translating the rod takes time. Things can change in time. Nothing fundamentally guaruntees that the object being measured will not change significantly during the process of translation.

By what, I mean the trivial issue of the standard itself. By how, I mean the more significant issue of the method used to compare to the standard.

... atomic structure has not changed since the era of the dinosaurs, therefore the speed of light has not changed (significantly).

I don't understand how you jumped from atomic stucture to speed of light.

Simply citing the current state of Physics. It may be that c has changed over the life time of the universe, but that is not the current understanding.

But this still doesn't answer the question, "compared to what?"

... what is the significance of that coordinate system? What part does the coordinate system play in the final work of relativity?
Precisely, none. General Relativity allows expression of physical laws independent of the coordinate system.

Expression of physical laws is math. In order to do physics, there is no way around a coordinate system. Therefore, the coordinate system becomes significant, and in GR quite non-trivial.

The key point to this entire discussion is the difference between
"the speed of light is constant because the meter is defined in terms of the wavelength of light?

and

"The meter is expressed in terms of the wavelengths of light because the speed of light is constant"

I don't support the first justification, if "speed of light" is intended to mean "c."

I support the second statement, but it is not an answer to the original post.

The speed of light is a universal constant. Please take debates about this issue to Theory Development.

Did I ever once disagree with c as a universal constant? I don't visit the theory development thread for two reasons: 1) I'm not interested in other peoples attempts to disprove relativity and 2) if I actually thought I had a sound theory to develope, I wouldn't post it on the internet to invite someone else to steal it from me and take all the credit.

 

[Integral]

Turin,
I am failing to see the point of your posts or your arguments.

 

[Jack Martinelli]

I do not see the circularity here. Yes, the question has changed but unless a measurement of c is involved in the experiment to find \epsilon_0 it is not circular.

The circularity is: if \mu_0 and \epsilon_0 are constant it is because c is constant, which is constant because \mu_0 and \epsilon_0 are constant which is constant because...

 

[turin]

Sorry to bring real world issues into the argument.

Are you, really, or are you being sarcastic. It seems like you're being sarcastic. Well, shame on you.

I feel that there is a issue with the distance changes between cities, if standards mean anything, ...

So do I. It shows that, if the distance between New York and Miami changes by a significant percentage in the course of a day, I'd better run for the west coast. One of the last things I would personally do is blame a standard for changing. Oh ya, and, sarcastically, I'm sorry for bringing the good old U.S. of A. into the argument.

... when I measure a distance in meters it had better read the same today as it did yesterday or next year. That is the whole point of a standard.

That's the whole point of defining that particular distance as a standard distance. Standards have different points depending on the application. But I don't agree that the point of a standard of one unit is to make sure that some arbitrary property of some arbitrary object remains constant.

When London is moving at .5c wrt to Paris then I would expect the distance to change. As long as they are stationary the distance must remain the same.

But they are never stationary, even WRT each other. As far as I know, the distance between London and Paris is not a standard, nor is it even assumed to remain constant, in the physics that I've studied. It is a reasonable approximation, but not a constant standard value.

The distance is a physical quantity it does not change with the units you measure it in.

It does if you first measure it in units of length, and then subsequently measure it in units of time. It completely changes in meaning. If you say that the space-like separation of London and Paris is x km, that implies that they are causally disconnected in that context. But, if you say that Paris is y hrs from London, you are talking about how much time you would experience during the flight or train ride from London to Paris. These two measurements/units have completely different physical meanings, but they both measure the distance between London and Paris.

 

[Integral]

The circularity is: if \mu_0 and \epsilon_0 are constant it is because c is constant, which is constant because \mu_0 and \epsilon_0 are constant which is constant because...

The experimental methods used to measure a value for \epsilon_0 are significantly different from those used to measure c.
The fact is with modern technology I believe it is easier to get a precise measurement of c then \epsilon_0 so it may well be that it is now defined it terms of c then the other way round.

That does not change the fact that \epsilon_0 is a basic property of space time which is a factor in the propagation of EM waves.
Which is the "more" fundamental constant. I personally do not know.