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 seperate 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 electomagnetism 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 quesiton 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 quesiton 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 earths 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 earths 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 prefered frames, no prefered 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. :biggrin:

Creator :biggrin:

[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! :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:

[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 earths 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 beforeThose 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. Lets 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 beforeAnd 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.

[Integral]

Turin,
You are now arguing semantics, can we get this thread back on topic.

[turin]

Integral,
Can you please, then, reword this question (the appropriate topic of this thread, I'm assuming) to elliminate any semantic ambiguity:Has anyone an idea why speed of light is constant ?I don't have any problem dropping the issue, and I certainly agree that it is semantic.




Perhaps you mean we should now address this question?As light emerges from energy fall of an electron, does speed of light have anything to do with rotation speed of an electron ?Well, if picass is referring to spin, then I've heard that it is related to c, but I don't know the details; I have no good understanding of QFT, which is the arena in which I've heard this is a relevant relationship by virtue of spin as a consequence of the Dirac equation. I've also heard people say that this is crap, that the Dirac equation was motivated out of elegance more than anything else, and that the result was an artificial consequence of the intention to show a relationship between spin and relativistic considerations.

[russ_watters]

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. Wow. That is spectacularly wrong. Wow.

DrMatrix, don't you see that you're now saying that a kilometer and .62 miles are different lengths? The number changes, the distance is the same because the number (I thought we had already established this) is arbitrary. Can you please, then, reword this question (the appropriate topic of this thread, I'm assuming) to elliminate any semantic ambiguity:

"Has anyone an idea why speed of light is constant?" Turin, I see no ambiguity in that question, the problem is that there is no simple answer: its answer is both philosophical and scientific. It has already been answered and it has nothing at all to do with the definiton of a meter.

DrMatrix seems to be trying to argue that due to our current definition of a meter, there is no way to prove that C is constant. He is incorrect, but either way, this has nothing to do with that question.

[Jack Martinelli]

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

What do you mean by universal? And I don't think you understand the difference between a "standard reference length" and a "reference length" and a "proper length" or how these are related to the speed of light (an electromagnetic phenomenon which might not be universal BTW -- particularly when the wave function collapses. Or where matter may be exotic.)

I know that when I compare two lengths one of them may be longer than, shorter than or equal to the other one. I can choose one of them as a static reference length and use it to measure other lengths (including other reference lengths). It doesn't matter which one I use unless I want to discuss my measurements with other people. Furthermore, I can say that any length maybe used as a reference length. But some choices are impractical. Because some choices for a reference length make discussion impossible or their use impractical we need to choose a practical standard. If we agree on one as a standard and _everyone_ agrees on the given choice then it is universal by definition.

The speed of light, however, must be defined as:

c = \frac l { t }

where l is a proper unit of length and t is a proper unit of time.

It is a quotient! And it is a quotient! And it is a quotient!

IOW, c is constant iff this quotient is a constant. Standards do not make this any truer or falser. It doesn't matter _how long_ a unit of proper length or proper time are. The quotient is what matters. (I've read a paper where the authoer uses a quotient of metics (topological) as his measurement primitive.)

So, going back to my example of two electrons defining the end-points of a reference length... You _can_ choose these two distinguishable objects for your static reference length and from the above quotient choose some observable dynamic as the proper unit of time (the dynamic is impied by the quotient -- what is it?). As Einstein said, there are no prefered frames. But there are frames where EMR mignt not exist & so you really need to know how to work in those frames (electron frame?) in a general way?

Objections?

[Jack Martinelli]

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.

Standards are different than references.

[Jack Martinelli]

Wow. That is spectacularly wrong. Wow.

And that statement makes you spectacularly right? Wrong.

Set your system boundaries to one length. How long is it? With respect to what? Is it a static length? With respect to what? Any good physics theory must be scalable. First you start with something and then expand. Unless you just want us to believe whatever you say.

Length is an intrinsic property of space but magnitude isn't. To talk about magnitude you need a reference length.

All statments we can say about a distance require some reference object. Period endofstory.

[Integral]

Jack,
It is not clear to me, again as with Turin, I fail to see the significance of your words.

Is or is not c a constant of the universe?

BTW: I have read of Magueijo and his VSL theories. I find them very interesting. But any discussion of those concepts must be restricted to the Theory Development forums.

It seems to me that you may well simply be agreeing with me in an argumentative fashion, this goes for Turin also. Which is why I suspect that this is all about semantics. You seem to be telling me I am wrong but then in the end I really can't pin down how you disagree.

[turin]

Turin, I see no ambiguity in that question, ...The speed of light can be slowed down to 0.5c in a lab: true or false?




... its answer is both philosophical and scientific. It has already been answered ...I agree with all of this quote, but I think some of the answers are not correct.




... it has nothing at all to do with the definiton of a meter.I don't think it has anything to do with the definition of a meter in the strictest since. But, by the way the original post posed the question, I don't believe you can disregard the definition of the meter as a standard of length, if you define the speed of light in the same manner as Jack has done.

If you define the standard unit of length as the length of some standard rod, or a fraction of the distance from the north pole to the equator, or whatever standard you want, then the speed of light can change in general if that standard unit of length changes and the speed of light is defined in terms of the number of standard lengths that EM radiation can traverse after a certain number of hyperfine oscillations, or clock ticks, or whatever.




The speed of light, ... must be defined as:

c = \frac l { t }

where l is a proper unit of length and t is a proper unit of time.I disagree with this. I can define speed as a fundamental unit, as well as time, and then define a derived unit as length = speed.time. Then, I don't need a quotient to talk about c.




Standards are different than references.I agree with this.

[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.Wow. That is spectacularly wrong. Wow.

DrMatrix, don't you see that you're now saying that a kilometer and .62 miles are different lengths? The number changes, the distance is the same because the number (I thought we had already established this) is arbitrary.A kilometer and a mile are different standards. The fact that a change from one standard to another produces another value for the distance does not mean the distance has changed. If the distance changes according to one agreed upon standard then, by the agreed upon definition, the distance has changed. What is your standard of length, the meter or the distance to London? Suppose I measure the distance between two objects and get 10 meters. Later I measure and I get the value 9 meters. I would conclude that the two objects are one meter closer together. Would you throw out your meter?DrMatrix seems to be trying to argue that due to our current definition of a meter, there is no way to prove that C is constant. He is incorrect, but either way, this has nothing to do with that question.You are so close. I am saying you cannot ask a question about speed until you have defined units of time and distance. And our current definition of meter is defined in such a way that the speed of light is constant by defintion.

[turin]

Is or is not c a constant of the universe?I believe that there is no evidence against this statement, or that our little region of the universe has strongly suggested to us that it is so. In other words, I accept that c is a constant of the universe. I appologize if you thought that I was arguing to the contrary.




It seems to me that you may well simply be agreeing with me in an argumentative fashion, ...This is possible.

[Integral]

You are so close. I am saying you cannot ask a question about speed until you have defined units of time and distance. And our current definition of meter is defined in such a way that the speed of light is constant by definition.

The conclusion is then that it is not a constant in mph which used to be a different standard from the meter?

Do you still fail to see the circularity of your reasoning? You say the speed of light is constant because the meter is defined in terms of wavelengths of light.

But the meter was defined in terms of the wavelength of light because the speed of light is constant.

And again the speed of light is constant independent of our ability to measure it.

[Integral]

I believe that there is no evidence against this statement, or that our little region of the universe has strongly suggested to us that it is so. In other words, I accept that c is a constant of the universe. I appologize if you thought that I was arguing to the contrary.

I agree with every word of this.

No apologies necessary :)

[Jack Martinelli]

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.

1. I don't know that \epsilon_0 universal (e.g., bigbang)
2. I don't know that EM is universal. Particularly near charged particles (r<< 10E-15m)

[jdavel]

turin asked: What do you mean, "you'd never do that" (calibrate lengths between each measurement)? That is exactly what would be done. How else would you calibrate length?


There's no need to calibrate length if all you're trying to do is test whether c is constant. Just measure the time t that it takes for light to go from one end of a stick to the other. If you always use the same stick, and you always get the same t, then you can say c is constant.

You don't even have to know the length of the stick! Michelson & Morley didn't know the relative length of their interferometer arms to anywhere near the precision that they got for the relative difference in light speed along the arms.

[Integral]

Jack,
The same qualifers apply to \epsilon_0 that turin stated with c up thread.

Why do you introduce QM to the question. Are you simply looking for arguments.

It's a yes or no question.

Is c constant?

[jdavel]

DrMatirx said: "you cannot ask a question about speed until you have defined units of time and distance."

You can ask (and answer) this question without defining units of distance: If two light beams start at the same time and place, and arrive simultaneously at some other place, then was their speed the same?

[turin]

turin asked: What do you mean, "you'd never do that" (calibrate lengths between each measurement)? That is exactly what would be done. How else would you calibrate length?I'm sorry. You have misunderstood me. I meant that, if you were to calibrate, you would use light to do so.

[turin]

If two light beams start at the same time and place, and arrive simultaneously at some other place, then was their speed the same?There is not enough information to answer this question. I can start a trip from NY to Miami in my car, and stop at a gas station every hour, going 80 mph between stops to make up for lost time. My friend can get in his car with a really big gas tank and and start the trip at the same time, but going nonstop at 70 mph. If we both get to Miami at the same time, was our speed the same?

Or a more relevant example:
If I first drive to San Diego, and then to Miami, but we still both leave NY and arrive at Miami at the same time, was our speed the same?

[Jack Martinelli]

Jack,
It is not clear to me, again as with Turin, I fail to see the significance of your words.


Its not my words, its what my words refer to.

Is or is not c a constant of the universe?

Yes it is, but the reason it is is the question under discussion.


It seems to me that you may well simply be agreeing with me in an argumentative fashion, this goes for Turin also. Which is why I suspect that this is all about semantics. You seem to be telling me I am wrong but then in the end I really can't pin down how you disagree.

You are not "wrong". Your explanations are just not very good. Just my opinion. I find an explanation about the physical more enlightening when the language used refers other physical phenomena -- not other constants. If your language just refers to the physical (line-like intervals) there is no argument. That they exist is self evident. Maxwell's equation, for example, are not self evident. Each term I use (ruler or clock) is a word that has a semantic anchor (an observable space-like interval defined by two distinguishable objects). When you use language this way there is no semantic argument. You can't refute the way the universe works. You can't really refute that, in our universe there are line like observables & that they may be used to measure other line-like observables. That the maximum possible speed of an object in the universe is a constant is simply a consequence of our measurement proceedure. It has nothing to do with EMR. Bosons are just test particles that let us find this speed and express it in terms of meters and seconds.

[DrMatrix]

The conclusion is then that it is not a constant in mph which used to be a different standard from the meter?I don't understand what you mean here. Do you still fail to see the circularity of your reasoning? You say the speed of light is constant because the meter is defined in terms of wavelengths of light.

But the meter was defined in terms of the wavelength of light because the speed of light is constant.

And again the speed of light is constant independent of our ability to measure it.The fact that the speed of light is constant when the distance is measured by rigid rods allows us to use the speed of light (not the wavelength) to establish an equivalent definition based upon the speed of light.

Mach one is defined as the speed of sound. Is the speed of sound constant? It depends upon what units you are talking about. In mach units, yes -- the speed of sound is mach one by defintion. In meters per second, no -- the speed depends upon the temperature and the pressure.
There's no need to calibrate length if all you're trying to do is test whether c is constant. Just measure the time t that it takes for light to go from one end of a stick to the other. If you always use the same stick, and you always get the same t, then you can say c is constant.

You don't even have to know the length of the stick! Michelson & Morley didn't know the relative length of their interferometer arms to anywhere near the precision that they got for the relative difference in light speed along the arms.You are assuming that your stick has a constant length. The stick has become your unit of length. And that's fine, so long as you realize the stick is your unit of length.DrMatirx said: "you cannot ask a question about speed until you have defined units of time and distance."

You can ask (and answer) this question without defining units of distance: If two light beams start at the same time and place, and arrive simultaneously at some other place, then was their speed the same?OK. So long as the beam of light traveled the same path, then yes. Are two beams emitted at the same point that travel along the same path and arrive simultaneously at some other point two beams or one beam?

[Integral]

The conclusion is then that it is not a constant in mph which used to be a different standard from the meter?

If it is constant by the definition of the meter then perhaps it is not constant in different units which are not defined in terms of the speed of light.

If it is constant in units not defined in the terms of light then what do you mean by constant by definition of the meter?

[Jack Martinelli]

Jack,
The same qualifers apply to \epsilon_0 that turin stated with c up thread.

Why do you introduce QM to the question. Are you simply looking for arguments.

It's a yes or no question.

Is c constant?

Sorry. This thread is beginning to unravel & I may have misread something you (or someone else wrote).

BTW, I think I've said just about all I can about the speed of light. You're right, c is a constant. You'll get no more arguments from me. :wink:

[DrMatrix]

If it is constant by the definition of the meter then perhaps it is not constant in different units which are not defined in terms of the speed of light.

If it is constant in units not defined in the terms of light then what do you mean by constant by definition of the meter?Does this explain? The speed of light is constant in meters per second because the meter is defined in terms of the speed of light. The speed of light is constant when the distance is measured by rigid rods because that's just the way the universe works. The speed of light may or may not be constant in units not defined in terms of the speed of light. The speed of light is not constant in General Relativity. So if our unit of length is based upon the coordinates of a non-inertial reference frame, the speed of light would not be constant.

[Loren Booda]

Are \epsilon_0 and \mu_0 invarient regardless of reference frame as c is?

[turin]

Are \epsilon_0 and \mu_0 invarient regardless of reference frame as c is?It is believed to be so, in empty flat space.

[Integral]

The speed of light is not constant in General Relativity

This is incorrect. c is constant in the General Theory.

Looks like you have some pretty fundamental misunderstandings. It is to bad that you cannot use this site to clear up those misunderstanding rather then attempt to present your incorrect opinions as physical fact.

One more time.

c is constant in all coordinate systems. These coordinate systems can even have a constant velocity. All will agree (after unit conversions) on the speed of light.

Jack,
For all of your words, and even considering the meaning of your words you have not and cannot prove that the speed of light is constant using only sticks and clocks. At least here and in words. To accomplish this would require actual measurements, even then you have not proven the constancy of c. You have only a single value at a single location. It is impossible to generalize that single measurement to apply to all locations and times. Historically, the constancy of c was not established until the work of Maxwell. It was his work that laid the theoretical basis of the constancy of c. His work forced the world of physics to come to grips with an ugly fact. This fact, that the speed of light was determined by well known and understood fundamental constants and only those constants, had very deep implications which shook the world of physics to its very foundations. To attempt to prove the constancy of c without reference to E&M is, in my opinion, impossible.

[DrMatrix]

This is incorrect. c is constant in the General Theory.

Looks like you have some pretty fundamental misunderstandings. It is to bad that you cannot use this site to clear up those misunderstanding rather then attempt to present your incorrect opinions as physical fact.

One more time.

c is constant in all coordinate systems. These coordinate systems can even have a constant velocity. All will agree (after unit conversions) on the speed of light.A beam of light trying to escape a black hole will hover at the event horizon. There you have light that is motionless. If I attach a coordinate system to the rotating earth, pluto is traveling faster than c. The speed of light is not constant in a general coordinate system.

Inertial coordinate systems can hae a constant velocity, sure. And the speed of light is constant in inertial frames, but not in general reference frames.

[cookiemonster]

I don't think anybody was asserting otherwise.

cookiemonster

[Integral]

A beam of light trying to escape a black hole will hover at the event horizon. There you have light that is motionless.

No. light follows geodesics. Inside the event horizon of a black hole geodesics form closed paths. When light enters a black hole it essentially orbits the singularity. One must be very carefully when doing physics in the vicinity of the singularity. Let us stay in our everyday universe. If you must resort to black holes to support your argument you are lost.

The speed of light is constant in GR.

[Janitor]

A rocket is floating out in interstellar space. A laser is floating next to the rocket. On the outside of the rocket there is some device that measures the speed of light. If the laser is pointing at this device on the rocket, the astronaut in the rocket gets a reading of precisely c on his LCD readout.

The astronaut hits the button to fire the engine, and away he goes. The laser remains behind, in free fall. The laser continues to shine at the rocket. The astronaut takes readings of the speed of the laser light as calculated by the apparatus on the side of his rocket.

The rocket runs out of fuel, and coasts at some high speed. The astronaut sees that the light from the laser is redshifted, but (I think everyone in this thread will agree) he sees precisely c on his LCD readout.

So my question is, what does the readout show for the powered phase of the rocket? I thought I had read at least once somewhere that it would read less than c. Does anyone agree? Does anyone disagree?

Or is this little thought experiment not even relevant to what you are discussing? Certainly the rocket itself can be thought of as a reference frame, one that is inertial for a time, then non-inertial for a time, then inertial once again, and we agree to ignore gravitational fields from heavenly bodies, which by assumption are all very far away.

[DrMatrix]

The speed of light is constant in GR.Wrong!
From A Few Inferences from the General Theory of Relativity (http://www.bartleby.com/173/22.html) by Albert Einstein:
In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.

Janitor, so long as your reference frame is inertial, you can apply Special Relativity where the speed of light is constant. In a non-inertial reference frame, the velocity of light is not constant.

[Integral]

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position.

Velocity is a very critical word in this paragraph. Without appreciation for the precise meaning of this word, one might think that he is saying that the speed of light is changing. But he did not say speed, he said velocity, he is telling us that light does not travel in straight lines (or what we consider to be straight lines) but changes direction in a gravitational field, therefore the velocity of light must change.

This says nothing of the speed of light. The speed of light remains constant but its velocity {direction} changes in a gravitational field.

[jdavel]

Integral said: "The speed of light remains constant but its velocity {direction} changes in a gravitational field."

I'm going to have to be careful here, because I know virtually nothing about GR. If the g field and the direction the light travels are perpendicular, then what you said seems right, direction changes but speed stays the same. But if they're parallel, wouldn't it be the other way around?

The SR postulate of constant c is limited to measurements in inertial frames. I thought that in GR the postulate is limited to both inertial frames and zero gravity locations.

[turin]

quoting Integral
Quote:
The speed of light is not constant in General RelativityThis is incorrect. c is constant in the General Theory.The speed of light in a literal sense of meaning is different than c. I can say that c is a constant everywhere in the universe, and you have shown that we agree what I would fundamentally mean by that: the constant that shows up in the wave equation that has units of speed. I can also say that the literal speed of a beam of light is different than c, both in the context of refraction, as well as in a coordinate system that considers a beam of light to hover at a horizon.


quoting DrMatrix
A beam of light trying to escape a black hole will hover at the event horizon. There you have light that is motionless. If I attach a coordinate system to the rotating earth, pluto is traveling faster than c. The speed of light is not constant in a general coordinate system.I agree. c is a constant in that coordinate system, but it only replaces the literally speed of light locally in general, where an experiment can be done to examine Maxwell's equations.


quoting Integral
When light enters a black hole it essentially orbits the singularity.I don't know what you mean by "enters a BH," but once anything gets "closer" to the "singularity" than a certain critical radius (I believe it is the Schwarzschild radius), orbits do not exist. The path of a photon inside a BH is a spiral that terminates at the singularity within a finite time interval in a coordinate system outside the BH, if I'm not mistaken. I guess you could mean "orbit" in the loose context of "free particle trajectory," so, I don't want to disagree with you. Is that what you mean?


quoting Integral
Let us stay in our everyday universe. If you must resort to black holes to support your argument you are lost. The speed of light is constant in GR.Say what? Why has this arbitrary rule of not resorting to a 90 year old well established theory been introduced? And the speed of light is not necessarily constant in GR, but c is.


quoting Janitor
Thought experiment.
... there is some device that measures the speed of light.
...
So my question is, what does the readout show for the powered phase of the rocket? I thought I had read at least once somewhere that it would read less than c. Does anyone agree? Does anyone disagree?I will have to defer this to some investigation, but I would ask how the device measures the value. I believe that the thought experiment critically depends on this. I will assume for my investigation that it has two points of detection (or possible four in the shape of a pyramid) separated by a known distance, and that it compares the detection times on clocks at each detection point by translating the clocks under negligible acceleration to a midpoint, and then adjusting for any time difference that appear among the clocks.


quoting Janitor
... is this little thought experiment not even relevant to what you are discussing? Certainly the rocket itself can be thought of as a reference frame, one that ... non-inertial for a time, ...I think it's relevant. I'm with you.

[russ_watters]

Good luck, Integral - I'm out.

[DrMatrix]

When light enters a black hole it essentially orbits the singularity.
I don't know what you mean by "enters a BH," but once anything gets "closer" to the "singularity" than a certain critical radius (I believe it is the Schwarzschild radius), orbits do not exist. The path of a photon inside a BH is a spiral that terminates at the singularity within a finite time interval in a coordinate system outside the BH, if I'm not mistaken. I guess you could mean "orbit" in the loose context of "free particle trajectory," so, I don't want to disagree with you. Is that what you mean?I was wondering what Integral meant too. Perhaps he'll explain.

In The Universe in a Nutshell by Stephen Hawking on page 114 Figure 4.12 we see a diagram of a star with rays of light leaving the surface. The axes are chosen so that a velocity of c will have slope equal to 1 or -1. The caption reads:Spacetime around a non-collapsing star. Light rays can escape from the surface of the star (the red vertical lines). Far from the star, the light rays are at 45 degrees to the vertical, but near the star the warping of spacetime by the mass of the star causes the light rays to be at a smaller angle to the vertical.Is the speed of light constant here? I'd say no. What say you?

[Integral]

Is the speed of light constant here? I'd say no. What say you?

Sure, what evidence have you provided to show otherwise?

Going to work, I drive 60Mph west, on the way home I drive 60mph East. Same speed different velocity.

What! No response to my reply to your Einstein quote? going try and simply ignore it, perhaps?? Just trot out another quote from another book that you thought you understood. Nice tactics, how to keep the argument going and convince yourself you are ahead. Ignore your failures and move on to a new and different misunderstanding.

It appears to me your understanding of basic physics is not even at the Halliday and Resnick level. (ie not able to appreciate the difference between velocity and speed, consider a square root to be a "fancy equation" )It would do you well to move beyond the coffee table physics books and attempt to learn the real deal. Start with a calculus text. Move on to a college level Physics text. Open your mind a bit, currently you are blinded by preconceived notions and crippled by your lack of formal physics knowledge.

The event horizon separates the universe from the black hole, what is different inside the event horizon? According to your man Hawking, inside the event horizon geodesics form closed paths. Thus light that enters a black hole tangent to a interior geodesic follows that path endlessly.


Hey I thought these were Hawking's ideas. You did read Brief History of time ? Perhaps I got it out of the collection of lectures by Hawking and Penrose.

If this is going to turn into a discussion of GR I will move the thread to the appropriate forum where mentors, with better knowledge of the details then I, can answer your questions.

BTW it would be nice if you could learn to ask questions to clarify your understanding.

Edit: Grammar and punctuation.

[Integral]

Janitor,
Consider this. In reality the earth is a constantly accelerating reference frame, we measure the speed of light to be constant. We live deep in the suns "gravity well". this means that, according to GR, Space time is not flat in our vicinity. We still measure a constant speed of light. If you conduct your experiment deep in space away from the influence of stars and planets would not space/time be flatter there then here? We measure a constant speed of light, why would you expect anything different on your space ship?

This is not meant to be an end all answer to your question, just something to think about.

[DrMatrix]

Sure, what evidence have you provided to show otherwise?The caption I quoted. It's easier to understand with the figure in front of you, but I'll try to explain. The x-axis is space and the y-axis is time. A vertical line represents stationary and a line at a 45 degree angle represents c. Closer to the vertical than 45 degrees represents a speed slower than c. With that in mind, please consider: "near the star the warping of spacetime by the mass of the star causes the light rays to be at a smaller angle to the vertical."Going to work, I drive 60Mph west, on the way home I drive 60mph East. Same speed different velocity.

What! No response to my reply to your Einstein quote? going try and simply ignore it, perhaps?? Just trot out another quote from another book that you thought you understood. Nice tactics, how to keep the argument going and convince yourself you are ahead. Ignore your failures and move on to a new and different misunderstanding.OK. I'll grant you that constant speed does not mean constant velocity. My Einstein quote does not contradict what you said. Happy? Good.

It appears to me your understanding of basic physics is not even at the Halliday and Resnick level. (ie not able to appreciate the difference between velocity and speed, consider a square root to be a "fancy equation" )It would do you well to move beyond the coffee table physics books and attempt to learn the real deal. Start with a calculus text. Move on to a college level Physics text. Open your mind a bit, currently you are blinded by preconceived notions and crippled by your lack of formal physics knowledge.In college, I studied calculus, advanced calculus, topology, and physics (not advanced physics). I graded the homework for elementary differential equations. I always try to keep an open mind, and I look forward to learning new things. Everyone has their preconceived notions, I suppose.

When I said "fancy equations" that was a failed attempt at humor. I now wish I had not said that. I do not consider square root fancy.
The event horizon separates the universe from the black hole, what is different inside the event horizon? According to your man Hawking, inside the event horizon geodesics form closed paths. Thus light that enters a black hole tangent to a interior geodesic follows that path endlessly.


Hey I thought these were Hawking's ideas. You did read Brief History of time ? Perhaps I got it out of the collection of lectures by Hawking and Penrose. I don't know enought to say that you are definitely wrong, but that does not sound right to me. My copy of A Brief History of Time is packed away somewhere.

If this is going to turn into a discussion of GR I will move the thread to the appropriate forum where mentors, with better knowledge of the details then I, can answer your questions. Well, the question of whether the speed of light is constant in a general reference frame does fall under relativity. If you feel the mentors in another forum would be better suited, that is your decision.

[Integral]

If you wish to pursue the implications of a variable speed of light, read Faster then the Speed of Light by Joao Maguelijo. The first half of the book discusses the current understanding of GR. I found this to be an excellent presentation. He spends a significant amount of text complaining about the rigidity and short sightedness of the current technical journal system. For him to seriously address, or even discuss, the idea of a variable speed of light was careerer threating. He and a colleague (who was the senior researcher, chickened out at the last minute, refusing to present their initial work or attach his name to it.) developed the theory behind locked doors. The implications of a variable speed of light are far reaching and fascinating. Find a copy and give it a read. But meanwhile this is still very controversial physics and not an appropriate topic for this forum.

But as I said earlier any real discussion of VSP must take place in the Theory Development Forum.

[jdavel]

Integral said: "We live deep in the suns "gravity well". this means that, according to GR, Space time is not flat in our vicinity."

At the earth's surface, the gravitational force of the sun is nearly negligible to that of the earth. In fact it's even small compared to that of the moon, which is why tides are more dependent on the moon than the sun. So wouldn't any curvature of space time near the earth be caused almost totally by the earth?

[Integral]

Clearly the sun has some significant effects. After all we orbit it, this is the gravitational well I am speaking of. As you mention the earth has significant and noticeable gravitational effects, we walk the surface.

We still measure the speed of light as a constant.

Jdavel,
Are your comments addressing this issue or just to disagree with something I have posted?

[jdavel]

Integral,

No, I wasn't just trying to be contrary. Somebody else had suggested a thought experiment involving an accelerating rocket. I thought you had said that space time where we live is curved a lot more than it would be in a rocket because we live "deep in the sun's gravity well". But since the gravitational field at the earth's surface is almost totally caused by the earth itself, and since it only causes one g of acceleration, any effects predicted by GR would be greater in a rocket accelerating at more than one g, which is not unreasonable for a rocket. That's all I meant.

[Integral]

Ok,
I think even earths gravitational well should be sufficient for the argument. After all any acceleration of more then 1 g for any significant amount of time is not a reasonable expectation of a human. (please do not quibble with the phrase "signifiant amount of time". significant >= 1 year. or what ever.

I am becoming more and more convinced that the SPEED of light will be a constant even if the velocity is not.

[chroot]

The speed of light is, according to current theory, always constant. The speed of light, as measured by experiment, is always constant. The speed is 1 light-second per second. Feel free to convert to your favorite units ad infininitum.

If you'd like to advance a new theory as a replacement of existing mainstream theory, you are welcome to do so in the Theory Development subforum.

If you'd like to argue that existing experiments don't reflect reality, I suggest that you begin looking for a new universe in which the experimental results better suit you.

Case closed.

- Warren

[DrMatrix]

The illustration I refered to in my previous post from The Universe in a Nutshell is a spacetime diagram where the path of light rays' slopes vary from almost vertical near the surface of a star to 45 degrees further away. I was under the impression that the inverse of the (absolute value of the) slope in a spacetime diagram is proportional to speed. Yet this does not indicate a change in speed. I don't understand how that can be.
Case closed.Fine.

[chroot]

I was under the impression that the inverse of the (absolute value of the) slope in a spacetime diagram is proportional to speed. Yet this does not indicate a change in speed. I don't understand how that can be. Fine.
You're forgetting time dilation.

- Warren

[DrMatrix]

What time dialation? There is only one reference frame and only one time axis. In order to say there is time dialation, don't you need to say time dialation with respect to something?

[Janitor]

John Baez seems to be all over the map on this issue. I will quote a chunk from this page of his:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html


Since Einstein talks of velocity (a vector quantity) rather than speed it is not clear that he meant the speed will change but the reference to special relativity suggests he did mean so. This interpretation is perfectly valid but a more modern interpretation is that the speed of light is constant in general relativity.
The problem here comes from the fact that speed is a coordinate-dependent quantity, and is therefore somewhat ambiguous. To determine speed (distance/time) you must first choose some standards of distance and time, and different choices can give different answers. This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c.
In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalization is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.
If general relativity is correct then the constancy of the speed of light, in inertial frames is a tautology from the geometry of space-time. The causal structure of the universe is determined by the geometry of null vectors. Travelling at the speed c means following world-lines tangent to these null vectors. The use of c as a conversion between units of metres and seconds, as in the SI definition of the metre, is fully justified on theoretical grounds as well as practical terms because c is not merely the speed of light, it is a fundamental feature of the geometry of space-time.
Like special relativity, the predictions of general relativity have been confirmed in many different observations. The book by Clifford Will is an excellent reference for further details.
Finally we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.

How is that for waffling?

[Integral]

My guess, is that Einstein was referring to the fact that light in SR is not only assumed to be constant speed but also constant velocity. In SR light always moves along a single coordinate axis, the only direction change occurs at the surface of a mirror. This pure rectilinear motion of a beam of light is strictly constant velocity. While it is not said specifically it is certainly built into his derivations. A nit picker could claim that the curvilinear motion of light in GR is a contradiction of SR. Because SR is developed for constant velocity light only.

[Thomas2]

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 ?

The speed of light is constant because, unlike ordinary waves, light propagates without a carrier medium and you don't therefore have an absolute reference frame you could refer the speed to (at least not in a vacuum). The trick of nature is here that a light wave carries itself, or to be more precise, the electric wave carries the magnetic wave and vice versa (as given by Maxwell's equations). The irony is that even Maxwell apparently did not realize this and believed in the Ether Theory and a positive outcome of the Michelson-Morley experiment.
For related aspects see my webpage http://www.physicsmyths.org.uk/lightspeed.htm .

[Nereid]

John Baez seems to be all over the map on this issue. I will quote a chunk from this page of his:

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

How is that for waffling?Thanks Janitor, this is excellent! Let's take time to go through it slowly, because it deals with nearly all the questions raised on this thread.

[Integral]

Frankly I see no sign of waffling in his conclusive statement.
Finally we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.

[DrMatrix]

I see no waffling in this statement:This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c.But when you look at that quote next to Integral's quote, the man sounds like he's running for office.

[jdavel]

Integral said: "My guess, is that Einstein was referring to the fact that light in SR is not only assumed to be constant speed but also constant velocity."

Another possibility: Either Einstein or the German to English translator was a little sloppy with the German words for velocity and speed.

Anyway it's clear from the English translation of Einstein's own words, that what he was talking about is what we call "speed". From the 1905 paper: '....light is always propagated through empty space with a definite velocity c...." And from chapter 7, paragraph 1 of his book "Relativity The Special and General Theory": 'The assumption that this velocity of propagation is dependent on the "direction in space" is in itself improbable.' Neither of these is consistent with the term "velocity" being a vector.

By the way none of this has anything to do with whether, according to GR, the speed of light in a gravitational field is a constant. Surely the math of GR eliminates any ambiguity, just as the math of SR does.

But back on the topic to which this thread has drifted. It seems to me what you're saying implies that, according to GR, a photon's momentum can be altered by a G field perpendicular to its path but not by one parallel to it. That seems very strange to me, but maybe you're right, or maybe that's not what you're saying.

[turin]

It seems ... that, according to GR, a photon's momentum can be altered by a G field perpendicular to its path but not by one parallel to it.The proper momentum of a photon does not change in GR. One can infer, however, that the coordinate momentum of a photon changes by deflection in the first case and by red/blue shift in the latter case. Neither one of these indicates a change in velocity, since velocity and momentum aren't so intimitely related as they are in Newtonian mechanics.

I'm leaning towards the speed of the light attaining a value of c at the point of measurement regardless of the frame, but I haven't had time to get to the thought experiment proposed by Janitor.

[russ_watters]

I see no waffling in this statement: Neither do I, its quite explicit: it says SR doesn't apply in non-inertial frames of reference. Its a re-statement of the domain of SR. That's not a surprise, not a shortcoming of SR, and not a statement against the constancy of the speed of light.

Integral's quote is equally clear. I don't see a problem here.

[russ_watters]

But back on the topic to which this thread has drifted. It seems to me what you're saying implies that, according to GR, a photon's momentum can be altered by a G field perpendicular to its path but not by one parallel to it. That seems very strange to me, but maybe you're right, or maybe that's not what you're saying. A photon's momentum is altered by gravity in either direction. That does not, however, imply a change in speed because it is not a classical phenomenon.

[DrMatrix]

OK. Please reconcile the following with Integral's assertion that: "Consider this. In reality the earth is a constantly accelerating reference frame, we measure the speed of light to be constant."In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalization is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.I know how amused everyone was when I said it, so for your amusement I quote:At the 1983 Conference Generale des Poids et Mesures the following SI (Systeme International) definition of the metre was adopted:The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is c constant": Yes, c is constant by definition!

In post #97, chroot said that I forgot about time dialation. I am waiting for an answer to how can I account for time dialation when I have only one reference frame.

[chroot]

You don't have just one. You have many, at different depths in the gravity well. Ever heard of gravitational time dilation?

- Warren

[DrMatrix]

You don't have just one. You have many, at different depths in the gravity well. Ever heard of gravitational time dilation?Sure, I've heard of gravitational time dialation. Clocks deeper in a gravity well tick more slowly than a similar clock not so deep. Each clock has it's own reference frame with its own time axis. These we can compare. In the illustration, there is only one time axis. We have the path of a photon in a single reference frame. The slope of the photon changes. If the slope of the path in a space time diagram is not proportional to the speed (as I thought), what does the slope tell us?

[turin]

A rocket is floating out in interstellar space. A laser is floating next to the rocket. On the outside of the rocket there is some device that measures the speed of light.
...
The astronaut hits the button to fire the engine, and away he goes.
...
The laser continues to shine at the rocket. The astronaut takes readings of the speed of the laser light as calculated by the apparatus on the side of his rocket.I have examined this thought experiment in 1+1 D Kruskal space. For those of you who don't know, this space maps the rocket frame to a 90o wedge during the acceleration phase. The wedge border is a light cone that essentially designates an event horizon. Any light signal on the other side of the cone is causally disconnected from the 90o wedge accelerated frame. There is a subtle (and probably unexpected to most people) consequence of this space: acceleration is a function of proper distance from the event horizon. The acceleration, a, of the rocket corresponds to a particular proper distance, ds, from the horizon as: a = c2 / (-ds). For instance, assuming 10 g acceleration would put the rocket at ~0.1 ly from the horizon. I will assume a measurement device as I have described:


I will assume for my investigation that it has two points of detection (or possible four in the shape of a pyramid) separated by a known distance, and that it compares the detection times on clocks at each detection point by translating the clocks under negligible acceleration to a midpoint, and then adjusting for any time difference that appear among the clocks.
Assuming that the characteristic size of the measuring device is << the proper distance from the horizon, the measurement will be ~c, but just slightly less. This anomoly is, however, an artifact of the measurement process that I examined (specifically, the finite size of the detector), as the region surrounding any given point (event) in the accelerated frame can be transformed to an inertial region. I used a greatly exagerated detector size even for an extremely liberal acceleration (in other words, my detector size was 50% of the proper distance to the horizon), and I got c' ~ 0.8 c. Using reasonable numbers should result in c' = 0.999... c. Again, I want to emphasise that the difference in c' and c is strictly an artifact of the measurement process.

[DrMatrix]

from The Universe in a Nutshell by Stephen Hawking, p. 115When the star reaches a certain critical radius, the path will be vertical in the diagram, which means that the light will hover at a constant distance from the center of the star, never getting away.Now, I know Integral has said that resorting to a black hole means that the point is lost. But Black Holes are a well established consequence of the General Theory of Relativity -- We're not talking fringe science. And it's not like I'm asking anyone to take my word here.

I'll also note that the light at the event horizon is not orbiting. Light orbits further out -- If I'm not mistaken, at 1.5 times the critical radius.

[chroot]

Yes, light orbits a black hole at

r = \frac{3 G M}{c^2}

What's your point?

- Warren

[DrMatrix]

The point is that since light at the event horizon remains a constant distance from the star, it therefore has zero velocity, zero speed. Since zero does not equal c, the speed of light there is not c. Sorry if I wasn't clear. Does it make sense now?

[chroot]

The light is still moving at c -- just around in a circle. Do horses going around a racetrack also have zero velocity and zero speed?

- Warren

[Integral]

What has this got to do with the reasons behind a constant c?

[DrMatrix]

chroot,

Please re-read my post. I'm talking about light at the event horizon -- not light orbiting. The only reason I mentioned the radius where light orbited, was to avoid someone suggesting that the light at the horizon was going around in a circle. The light at the event horizon is not orbiting. It is not going around in a circle. You yourself pointed out that the radius where light orbits is further out.

The light is at a constant distance from the center and it is not going around in a circle. Zero velocity, zero speed.

To answer your question. No horses don't have zero velocity or zero speed, going around a race track.

Integral,

c is constant. The speed of light in GR is not necessarily c. You have insisted that the speed of light is constant in GR. It is not.

[chroot]

Right, to an outside observer, it takes anything an infinite time to cross the event horizon. Again, what's your point?

You're apparently worrying about what people see from a distance. The speed of light is c only locally.

- Warren

[DrMatrix]

If by locally, you mean in an inertial reference frame where one can apply SR, then you are correct. I'm sure we're all in agreement that the speed (and the velocity) of light is constant in SR and the speed equals c.

Gravity and acceleration can affect the speed and the velocity of light. Light in a non-inertial reference frame does not, in general, travel at c. For example, at an event horizon the speed is zero.

My point is that the speed of light is not necessarily c in general relativity.

[chroot]

Listen, DrMatrix. You've gone on and on for pages now, seemingly convinced that you're teaching us something. You're not. Many of us know a lot more about GR than you do. We all know that it takes an infinite time for anything (even light) to cross an event horizon, as seen by an outside observer. We all know that light orbits at 1.5 times the Schwarzschild radius. Duh.

Now, realize this: when someone says the speed of light is a constant, c they mean the speed of light, when passing through my measurement aparatus, is a constant, c. Physicists don't deal much with things they can't measure, and measurement is synonymous with reality for us.

You can't measure the speed of light at an event horizon. Why not? Because time stops there. You can take an apparatus down there to the event horizon, and measure light there. It doesn't even matter if the apparatus works or not, because you won't ever be able to communicate any results to anyone outside. Time has stopped for you. You are in a singular environment. If either you can't make the measurement, or you can't tell anyone else what the result of that measurement was, the measurement is moot. It doesn't matter to any of us.

No one cares about someone saying "well, from my perspective, over here, it looks like light over there is not going c!" because that is not how we define measurements, and that is not what "light always goes c" means.

You're arguing semantics. No one cares.

- Warren

[Integral]

Dr Matrix,

If that were the case then would we not observe the variance of c? We do not live in flat space. Space around us is curved as described by GR. The fact is we DO NOT LIVE in the idealized world of SR, yet we measure a constant c. If what you say was true, then there would be no such thing as a constant c. It would not be predicted theoretically nor observed experimentally.

While not every photon which enters a black hole ends up orbiting, it is a possible path. Most of the analysis I have seen has dealt with photons ENTERING a BH, I am not certain how we can meaningfully speak of photon which originate inside the BH? What physics do we have which allows this? Since I do not have your source in front of me (Nutshell has not made it to our pathetic library yet!) I really am uncomfortable drawing any conclusions.

I will say that I am uncomfortable with discontinuous geodesics. That is what you are describing,can a photon reach the end of a geodesic? Not at all clear to me. Consider that over time photons would accumulate at this point, what does this imply for conservation of energy?

Lots of questions, few meaningful answers.

Chroot, do you suppose I should take the time to sort some of these GR questions to a separate thread and move it to the GR forum, perhaps Nedrid can provide better answers.

[DrMatrix]

Physicists don't deal much with things they can't measure, and measurement is synonymous with reality for us.You can't measure the event horizon. You certainly can't measure the singularity. Are you trying to say they are not real to you? The question of the existence of non-observables is getting away from science and into philosophy though. And I'm not sure we want to go there.

The event horizon is just the extreme where gravity causes light to stop. Gravity (acceleration) affects the speed of light and this can be measured (Although not, as you pointed out, at the horizon). John Baez said: "[I]f you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c." There is your measurable.

Integral,

Of course, I understand your reluctance to draw conclusions based upon my quotes without the source to give you proper context. (You could ask the librarian about a inter-branch or inter-library loan. I've had to do that here. Don't get me started!)

I don't think photons accumulate at the horizon. Hovering is unstable (not sure about this though).

[DrMatrix]

If that were the case then would we not observe the variance of c? We do not live in flat space. Space around us is curved as described by GR. The fact is we DO NOT LIVE in the idealized world of SR, yet we measure a constant c. If what you say was true, then there would be no such thing as a constant c. It would not be predicted theoretically nor observed experimentally.I'm not ignoring this. You make an excellent point here. I don't have the answer. [wild guess] Perhaps the gravity's effect is within the margin for error. [/wild guess]

[Integral]

Einstein was able to predict and Eddingion was able to measure the angle of deflection of light passing near the sun, why do we not have any predictions for the variation of the speed of light under any circumstances?

Why is it that Joao Miguliao (sp) (The Oxford physicist who has proposed the VSL theories) had colleagues who did not want to be associated with the VSL theories in spite of hours of hard work? A Variable speed of light is simply not part of accepted modern physical theory. The people who have proposed the theories have had a very hard time getting their work published in refereed journals simply because such considerations are in the realm of crackpots and not considered serious physics.

There is an effort being made to explore the implications of a Variable speed of light. I referred you to a lay person presentation of this work up thread. If you search on the correct spelling of the Joao Migualio you should be able to find more information.

[David]

why do we not have any predictions for the variation of the speed of light under any circumstances?


Shapiro showed that the speed of light slows down when it passes through the strong gravity field near the sun.

The trick to the “speed of light” measurement thing is that the oscillation rates of atoms slow down where light speed slows down, so atomic clocks slow down where light speed slows down, so the clocks always “measure” the speed of light to be “c” at themselves. But the actual speed of light through space in general does change as it passes in and out of strong gravity fields. This is the basic principle explained in Einstein’s 1911 gravitational redshift theory, which eventually became part of the GR theory.

[Integral]

Shapiro showed that the speed of light slows down when it passes through the strong gravity field near the sun.

The trick to the “speed of light” measurement thing is that the oscillation rates of atoms slow down where light speed slows down, so atomic clocks slow down where light speed slows down, so the clocks always “measure” the speed of light to be “c” at themselves. But the actual speed of light through space in general does change as it passes in and out of strong gravity fields. This is the basic principle explained in Einstein’s 1911 gravitational redshift theory, which eventually became part of the GR theory.

We have been here already. Einstein says, and means Velocity, the direction of light changes in gravitiational fields. The speed does not.

[David]

The speed of light was first recognized as a constant by Clerk Maxwell after he cast the fundamental equations of electomagnetism 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.



Where were those electrodynamics experiments of the 19th Century conducted? On the surface of the earth. Thus, Maxwell’s equations tend to be a little geocentrically oriented.

[Integral]

There is other, more universal, evidence of the constancy of c.

[David]

Einstein says,


Shapiro measured it and said the return signals were delayed because they slowed down when they passed the sun. This is the 21st Century. It’s time to move ahead and not get stuck in the past. Anyway, in the 1911 theory, Einstein used c1 and c2 for the two different speeds of light passing near the sun, at different distances from the sun’s center.

[David]

There is other, more universal, evidence of the constancy of c.

The speed of light can’t be always “constant” everywhere relative to all systems. That’s impossible, just as the speed of sound can’t always be “constant” everywhere relative to all systems. You are just going to have to realize some day that the original 1905 constancy postulate was just flat out wrong.

Remember, it was proposed in the days when Einstein thought the fastest objects moving in the universe were the planets, he thought the stars were “fixed”, he didn’t know the universe was expanding, and that was before he realized that strong gravity fields slow down the speed of light. He didn’t figure that out until 1911.

When the earth is moving toward a star that is fixed relative to the sun, we see a blueshift in the star’s light, and we see a redshift in the light coming from stars that are in the opposite direction. That indicates that the speed of light is controlled in our solar system by something inside the space of our solar system, and it indicates that we are moving toward the blueshifted light at the additive velocity of c + v and the redshifted light is moving toward us at the subtractive velocity of c – v, with v being our speed around the sun.

If you study the Doppler Effects, you will find that Doppler predicted this redshift and blueshift in 1843, and you will also learn that there are two main causes for these kinds of redshifts and blueshifts. One is a physical lengthening and shortening of waves (wavelengths) in space, and the other is caused by a less rapid and more rapid encountering of the waves. Study the Doppler Effects regarding sound and you’ll see what I’m talking about.

The redshifts and blueshifts due to the earth’s motion around the sun are due to subtractive and additive light-speed effects. This is common Doppler theory, it was well thought-out, explained, and predicted more than 160 years ago. When spectroscopes were adapted to telescopes, they proved the classical Doppler theory to be correct.

[David]

There is other


Here, read Dr. Su’s paper, “Quantum Electromagnetics – A Local-Ether Wave Equation Unifying Quantum Mechanics, Electromagnetics, and Gravitation,” and he’ll explain the whole thing to you. His papers are all over the internet and have been published in several languages and in several mainstream physics journals in several countries. This is not called “relativity” anymore. It’s called “quantum mechanics” and “electromagnetics”. “Relativity” is sort of an old-fashioned term now.

http://qem.ee.nthu.edu.tw/outline.pdf

[chroot]

Enough psuedoscience and handwaving. The original question has been answered in sufficient detail. David, keep your personal ideas out of the General Physics forum.

- Warren