# The Speed of Light is Not Constant

tl;dr?

Everyone agrees that the coordinate speed of light varies. But the local/measured/proper speed of light is constant. And that is what most people mean when they say "the speed of light is constant".

No, you don't. There are no wormholes. There are no tachyons. It's just space and light, not a Christmas tree lights.

The way that you are using speed can be divided infinitely. That would be very hard to associate with any physics. To use physics you need to quantize distances, and light so that you can no longer divide it infinitely.

Amazingly Maxila, it doesn't work the way people think. If you're in your gedanken spaceship and you step on the gas, things in this universe don't change. You do. And then things in this universe then look shorter to you. Think about it.

Thank you however I don't need to think about it, I recognized that is likely the correct interpretation several years ago. Just understand however that for such an observer their contracted length to all things is the only way they can see, therefore measure and interpret length. For them it is as physically real as any relatively extended length may be to an observer from a different perspective. In other words as long as their relative time remains constant that is the true length relative to their time it would take to journey any distance they observe.

This would mean the distance at black hole event horizon goes infinite, and doesn't square with the coordinate speed of light going to zero.

I agree with you that the apparent speed of a light clock decreases as it goes slower down in a gravitational field (Schwarzschild geometry). But that's still as seen by a distant observer. It could well be that nothing happens to the spatial distance between the two mirrors, but simply that time slows down.

Maybe I need to dig up my old notes of general relativity, or pull out a textbook.

I was kinda hoping that one of our resident GR experts would chime in to offer some help. Clearly you have no mathematics to offer us, Farsight, so we're not likely to get to the bottom of things with you.

Sorry to be tardy, I've had some kind of bug and then had to dedicate myself to a piece of work.

James R said:
Sometimes it's like it's too simple to understand. Just keep looking at the gif.

James R said:
I agree with you that the apparent speed of a light clock decreases as it goes slower down in a gravitational field (Schwarzschild geometry).
Good. The next step is to appreciate that it isn't the apparent speed of light. Or the coordinate speed of light. It's just the speed of light.

James R said:
But that's still as seen by a distant observer. It could well be that nothing happens to the spatial distance between the two mirrors, but simply that time slows down.
Like I've said, the gif is exaggerated but not misleading. And the "distant" observer is you, looking at things in the room you're in.

James R said:
Maybe I need to dig up my old notes of general relativity, or pull out a textbook.
Maybe. But the thing is this: your textbook is wrong.

James R said:
I was kinda hoping that one of our resident GR experts would chime in to offer some help. Clearly you have no mathematics to offer us, Farsight, so we're not likely to get to the bottom of things with you.
There is no mathematics I can use to show you that light goes lower when it's slower. All I can show you is the patent evidence that it does. Hopefully then you may come to appreciate that when it comes to GR, the expert is now me.

Good. The next step is to appreciate that it isn't the apparent speed of light. Or the coordinate speed of light. It's just the speed of light.
Measured or proper speed of light is the speed of light that you measure in your own frame. This speed of light is a constant. It is the "C" referred to in equations, including equations you yourself have posted. This is what people are referring to when they say "the speed of light".

Coordinate speed of light is the speed you would measure in someone else's frame if you could see their light beam, which you can't. You've said before that you think the coordinate speed of light is "the speed of light", but that's not how the term is used. If you want to use it that way, you're just doing what Trapped does and purposely misusing the term. But we can still get around it by always referring to the proper or coordinate speed instead of just the speed.

Now, there are two problems with considering the coordinate speed of light to be the "the" speed of light:
1. You can't measure it directly, you can only calculate it.

2. It isn't singular: there are an infinite number of different coordinate speeds of light for every frame. So you can't say, for example, that 'the coordinate speed of light on the surface of the earth is x'. It could be x or it could be any other number depending on who is doing the calculating (from where).
There is no mathematics I can use to show you that light goes lower when it's slower. All I can show you is the patent evidence that it does.
Then you've got a problem, since there is no direct evidence because you can't see light that never reaches your eyes. Coordinate speed is by definition a calculated number, so it is arrived at with math. Also, I'm guessing you think your animation is "evidence". It would appear that you don't know what the word "evidence" means.

Measured or proper speed of light is the speed of light that you measure in your own frame. This speed of light is a constant. It is the "C" referred to in equations, including equations you yourself have posted. This is what people are referring to when they say "the speed of light".
Yes I know. And hopefully you now know that it's constant because of a tautology. The wave nature of matter is such that if light goes slower, you go slower too, along with all your measuring devices. Then you measure this slower light with your slower clock and declare that it's going at the same old speed. It's like we have a clockwork clock, and we throw it into an oil bath. It goes slower as a result. But you're the clockwork man, you jump in after it, and then you declare that it's not going slower at all.

Coordinate speed of light is the speed you would measure in someone else's frame if you could see their light beam, which you can't.
Pay attention Russ. Read the OP. You have two NIST optical clocks in front of you, in the room you're in. One's going slower than the other. You know the same applies for parallel-mirror light clocks. Focus on what's there, do not be distracted by abstract things. You cannot look up to the clear night sky and point out a reference frame.

You've said before that you think the coordinate speed of light is "the speed of light", but that's not how the term is used. If you want to use it that way, you're just doing what Trapped does and purposely misusing the term. But we can still get around it by always referring to the proper or coordinate speed instead of just the speed.
I'm not purposely misusing the forum. I'm explaining some physics here, and giving you the Einstein and the evidence to support my case. Stop being such a naysayer, look at what Einstein said, and look at the evidence.

Now, there are two problems with considering the coordinate speed of light to be the "the" speed of light:
1. You can't measure it directly, you can only calculate it.
2. It isn't singular: there are an infinite number of different coordinate speeds of light for every frame. So you can't say, for example, that 'the coordinate speed of light on the surface of the earth is x'. It could be x or it could be any other number depending on who is doing the calculating (from where).
You measure it directly using light clocks at various locations. You haven't read the OP of Gravity Works Like This have you?

Then you've got a problem, since there is no direct evidence because you can't see light that never reaches your eyes. Coordinate speed is by definition a calculated number, so it is arrived at with math. Also, I'm guessing you think your animation is "evidence". It would appear that you don't know what the word "evidence" means.
I haven't got a problem Russ, you have. You're like an indoctrinated some who cannot bear any challenge to what he's been spoonfed for years. I'm telling you what Einstein said here. Geddit?

Pay attention Russ. Read the OP. You have two NIST optical clocks in front of you, in the room you're in. One's going slower than the other. You know the same applies for parallel-mirror light clocks. Focus on what's there, do not be distracted by abstract things. You cannot look up to the clear night sky and point out a reference frame.

Farsight, you keep making this same comparrison, as if it were some proven reality. Parallel mirror light clocks are hypothetical. They don't exist as real clocks, and the optical clocks NIST uses, only incorporate light as part of their control mechanisms.., yes the do use lasers... But the "clocking" is a function of the rate or frequency of electron transitions. The only connection the timing those clocks involve, has to do with light, is the lasers and the fact that light also originates with electron transitions.

The NIST experiment or data you keep referring to, says nothing special about the speed of light. It does confirm that at least the change associated with the transition rate involved, is consistent with predictions made by GR.

The question it does not say anything about, is how location in a gravity well affects; molecular reaction rates, nuclear decay rates or even the tick rate of say, a spring wound clock.

None of this is a denial of what GR represents as a theory of gravitation. It is a comment on what appears to be your misinterpretation, or at least biased narrow interpretation, of the evidence you cite. The theory and how that theory is conceptually projected as or into/onto reality, are two different things.

Farsight, you keep making this same comparrison, as if it were some proven reality. Parallel mirror light clocks are hypothetical. They don't exist as real clocks, and the optical clocks NIST uses, only incorporate light as part of their control mechanisms.., yes the do use lasers... But the "clocking" is a function of the rate or frequency of electron transitions. The only connection the timing those clocks involve, has to do with light, is the lasers and the fact that light also originates with electron transitions.
We don't need a produce a mirror light clock; the theory is sufficient. The reason is that all accurate clocks must behave the same way under the same circumstances or else we could simply compare a mechanical clock to a mirror light clock in a local frame, declare a difference in certain situations (e.g. in a moving train but not a stationary train), and reject relativity. It isn't really about light at all; it's the local time rate that determines the clocking rate, and that of course applies to all clocks regardless of their specifics.

We don't need a produce a mirror light clock; the theory is sufficient. The reason is that all accurate clocks must behave the same way under the same circumstances or else we could simply compare a mechanical clock to a mirror light clock in a local frame, declare a difference in certain situations (e.g. in a moving train but not a stationary train), and reject relativity. It isn't really about light at all; it's the local time rate that determines the clocking rate, and that of course applies to all clocks regardless of their specifics.

As you say, "the theory is sufficient"... But it remains theoretical. The point is that the we clocks we use to confirm the predicted time dilation experimentally, are based on the same mechanisms of change.., electron transition rates. Note that time dilation was initially based on the speed of light, measured locally as constant (in vacuum and an an inertial FoR).., and that the optical clocks used currently to confirm time dilation experimentally are based on the same atomic mechanism that the emmission of light originates from.

The theory has been proven accurate only in specific and narrowly defined conditions. The real problem is that we cannot experimentally confirm the necessary associated length contraction or have yet to confirm the constancy of the speed of light anywhere but an essentially uniform inertial frame of reference here on earth.

My point is not that the theory is not correct. It is that it is still theoretical and Farsight's (and others) personal interpretations are presented as the only realality, possible. GR is a predictive geometric theoretical model. It is not a complete description of reality. Even among those who would be considered modern day experts on GR there are differences in conceptual interpretation.

I continue to attempt to interject a touch of reality into discussions which seems to suggest that what remains theoretical, represents an absolute description of reality.

And it really bugs me that Farsight, continues to use a comparrison he knows is unreal, as proof that his favored conceptual understanding, is the one and only accurate description of reality.

P.S. To add, your statement that the theory applies to all clocks reguardless of their specifics is inaccurate and has been proven false. The most obvious example is that the clock rate of pendulum clocks is affected differently by location in a gravitational field than are the NIST optical clocks. They don't even work in some conditions. And even though we have had a spacestation in orbit long enough for at least a rough statistical comparrison, we don't have any data on how spring wound clocks, being based on classical mechanics, would be affected.

Hopefully then you may come to appreciate that when it comes to GR, the expert is now me.
The mods of this site agree with you there farsight, and not just for now, that’s why they allow you here on ‘ Physics & MathSciForum’. Carry on the good work along with chuckle brother RJ.

Now, there are two problems with considering the coordinate speed of light to be the "the" speed of light:
1. You can't measure it directly, you can only calculate it.

This is the gaping fallacy in relativity/speed of light denialist's thinking patterns. In the first place they don't seem to have any sense of differential calculus (velocity is the derivative of displacement with respect to time not some weird second derivative or partial derivative needed to eke out what it means when c varies), but more importantly, as you say, they seem to be completely oblivious to what "calculated speed of light" means. Further they simply are determined to never comprehend that the Lorentz factor is a simple rotation (something they would have encountered in Linear Algebra, concerning projections, not at all rocket science . . . just one of the prerequisites).

It's fine to be illiterate, but to "blight the boards" with moronic nonsense out of some psychopathic need to tell the folks who studied the material that it's rendered invalid through ignorance is just pure bullshit. Indeed, I gave Farsight some number of months to retread his tires before putting him on ignore. I'd much rather read reasoned responses from intelligent people like yourself and the many other good folks posting here than to feed the troll.

But I think this comment really nails it. Very concisely stated. He's lost in world that thinks the coordinate speed of light is actually something when in fact it's a mere artifact of a calculation, and one that is made improperly, that is, without applying the Lorentz transformation to account for the distortions of relativity. The particularly stupid part is that this notion appears to be entirely predicated on the test which corroborated GR (Shapiro) by demonstrating that coordinate speed is exactly that, a false artifact of calculation, based on the wrong model, the wrong assumption, the one that doesn't properly apply the rotation. The nuts seem to think Shapiro is arguing on their side, which is ludicrous. This is why it's often said that a little information can be dangerous in the wrong hands. Of course we don't have to worry about the Farsights of the world ever being at the controls, since they failed the 1st year exams, if they even got that far. But it does speak to core fallacy at play, not that this will ever snap them out of the naive and narcissistic little delusion they've built such enormous sand castles around (he's been working at his for at least a decade).

Not that anything will ever appease a troll of this variety. They seem to get up every morning needing nothing more than to claw at science to sustain themselves. Breakfast of champions, my foot. Breakfast of crampons, or tampons, or some such nonsense. The only thing being championed by Farsight is willful ignorance. He need only write on the blackboard about 10,000 times what you just said, perhaps snap himself with a rubber band every time he has an urge to cross it out and paint mustaches on your - well you're not sporting an avatar at the moment, but you get my drift.

Of course I'm singing to the choir, but I did like the way you stated that. Not that simple elegant truths have any place to roost in the irrational mind . . . but that doesn't diminish you and you ability to clearly articulate this simple elegant truth in the slightest.

P.S. To add, your statement that the theory applies to all clocks reguardless of their specifics is inaccurate and has been proven false. The most obvious example is that the clock rate of pendulum clocks is affected differently by location in a gravitational field than are the NIST optical clocks. They don't even work in some conditions. And even though we have had a spacestation in orbit long enough for at least a rough statistical comparrison, we don't have any data on how spring wound clocks, being based on classical mechanics, would be affected.
This is a valid point, but note that I qualified my statement with "accurate clocks". A clock which depends directly on gravitational potential will not be accurate in the void of space. Clocks which depend only on internal mechanics and the local rate of flow of time will be indistinguishable from theoretical light clocks. I must also say that I agree with your sentiment to interject reality in to these discussions, though. I think it's easy to forget that our models are just that.

I agree with you that the apparent speed of a light clock decreases as it goes slower down in a gravitational field (Schwarzschild geometry). But that's still as seen by a distant observer. It could well be that nothing happens to the spatial distance between the two mirrors, but simply that time slows down.

Maybe I need to dig up my old notes of general relativity, or pull out a textbook.

I was kinda hoping that one of our resident GR experts would chime in to offer some help. Clearly you have no mathematics to offer us, Farsight, so we're not likely to get to the bottom of things with you.

The only analysis that farsight thinks exists is the analysis using remote Schwarzschild coordinates [he thinks it's a preferred frame of reference] the coordinate singularity is his boogeyman. GR predicts, from remote bookkeeper coordinates, that dTau, and dr/dt_bkkpr are 0 at r=2M [the coordinate singularity] and the distance dr is infinite. You can integrate the distance component of the metric and show the distance is finite for the bookkeeper coordinates. Or just transform the coordinate singularity away by switching to a local proper frame coordinate system such as the rain coordinates for analysis over the entire path from boundary to r=0. Or you can stonewall everything you don't understand like farsight is prone to do. I see he's announced himself the expert. LOL. This is what you're probably looking for.
From Kevin Brown 'Refections on Relativity'.
7.3 Falling Into and Hovering Near A Black Hole
http://www.mathpages.com/rr/s7-03/7-03.htm

I agree with you that the apparent speed of a light clock decreases as it goes slower down in a gravitational field (Schwarzschild geometry). But that's still as seen by a distant observer. It could well be that nothing happens to the spatial distance between the two mirrors, but simply that time slows down.

Maybe I need to dig up my old notes of general relativity, or pull out a textbook.

I was kinda hoping that one of our resident GR experts would chime in to offer some help. Clearly you have no mathematics to offer us, Farsight, so we're not likely to get to the bottom of things with you.

The only analysis that farsight thinks exists is the analysis using remote Schwarzschild coordinates [he thinks it's a preferred frame of reference] the coordinate singularity is his boogeyman. GR predicts, from remote bookkeeper coordinates, that dTau, and dr/dt_bkkpr are 0 at r=2M [the coordinate singularity] and the distance dr is infinite. You can integrate the distance component of the metric and show the distance is finite for the bookkeeper coordinates. Or just transform the coordinate singularity away by switching to a local proper frame coordinate system such as the rain coordinates for analysis over the entire path from boundary to r=0. Or you can stonewall everything you don't understand like farsight is prone to do. I see he's announced himself the expert. LOL. This is what you're probably looking for.
From Kevin Brown 'Refections on Relativity'.
7.3 Falling Into and Hovering Near A Black Hole
http://www.mathpages.com/rr/s7-03/7-03.htm

This is the gaping fallacy in relativity/speed of light denialist's thinking patterns. In the first place they don't seem to have any sense of differential calculus (velocity is the derivative of displacement with respect to time not some weird second derivative or partial derivative needed to eke out what it means when c varies), but more importantly, as you say, they seem to be completely oblivious to what "calculated speed of light" means. Further they simply are determined to never comprehend that the Lorentz factor is a simple rotation (something they would have encountered in Linear Algebra, concerning projections, not at all rocket science . . . just one of the prerequisites).

It's fine to be illiterate, but to "blight the boards" with moronic nonsense out of some psychopathic need to tell the folks who studied the material that it's rendered invalid through ignorance is just pure bullshit. Indeed, I gave Farsight some number of months to retread his tires before putting him on ignore. I'd much rather read reasoned responses from intelligent people like yourself and the many other good folks posting here than to feed the troll.

But I think this comment really nails it. Very concisely stated. He's lost in world that thinks the coordinate speed of light is actually something when in fact it's a mere artifact of a calculation, and one that is made improperly, that is, without applying the Lorentz transformation to account for the distortions of relativity. The particularly stupid part is that this notion appears to be entirely predicated on the test which corroborated GR (Shapiro) by demonstrating that coordinate speed is exactly that, a false artifact of calculation, based on the wrong model, the wrong assumption, the one that doesn't properly apply the rotation. The nuts seem to think Shapiro is arguing on their side, which is ludicrous. This is why it's often said that a little information can be dangerous in the wrong hands. Of course we don't have to worry about the Farsights of the world ever being at the controls, since they failed the 1st year exams, if they even got that far. But it does speak to core fallacy at play, not that this will ever snap them out of the naive and narcissistic little delusion they've built such enormous sand castles around (he's been working at his for at least a decade).

Not that anything will ever appease a troll of this variety. They seem to get up every morning needing nothing more than to claw at science to sustain themselves. Breakfast of champions, my foot. Breakfast of crampons, or tampons, or some such nonsense. The only thing being championed by Farsight is willful ignorance. He need only write on the blackboard about 10,000 times what you just said, perhaps snap himself with a rubber band every time he has an urge to cross it out and paint mustaches on your - well you're not sporting an avatar at the moment, but you get my drift.

Of course I'm singing to the choir, but I did like the way you stated that. Not that simple elegant truths have any place to roost in the irrational mind . . . but that doesn't diminish you and you ability to clearly articulate this simple elegant truth in the slightest.

Willful ignorance is the height and breadth of intellectual dishonesty.

Like I've said, the gif is exaggerated but not misleading. And the "distant" observer is you, looking at things in the room you're in.

Your GIF is misleading for two reasons: 1) it isn't grounded in how experiments comparing clocks are actually performed, and 2) it only depicts the special case of two clocks at fixed altitudes above the Earth.

Concerning point 1), instantaneous comparison of two clocks separated by any nonzero distance is, strictly speaking, meaningless in relativity, and that's not what any experiment has ever done. The NIST optical clock experiment is reported in a Science report. They don't give many details about how they compared the clock frequencies themselves, but they do say this about their setup:

The two Al[sup]+[/sup] optical clocks were located in separate laboratories and were compared by transmitting the stable clock signal through a 75-m length of phase-stabilized optical fiber.

So they didn't just dump two clocks next to each other and magically know that one of them was ticking slower than the other. It seems that what they actually did was transmit the signal from one clock through an optical fibre so that a local comparison could be made between the frequency of the second clock and the frequency at which it was receiving signals from the first clock. In other words, what they actually measured was more akin to a relative gravitational Doppler shift.

Now, I hadn't read that paper before today. And yet, apart from saying "telescope" instead of "optical fibre", it's more or less what I [POST=3164543]told you[/POST] a couple of weeks ago:

You are confusing gravitational time dilation (a coordinate-dependent quantity) with two different quantities that are actually observable:

1) The apparent slowing of one clock as seen by a distant observer looking at it through a telescope (this is the relative Doppler shift factor).
2) The accumulated times shown on two clocks when they're brought side-by-side together for comparison. Simultaneity is only well defined for two events at the same place and at the same time in relativity, and the times shown on two clocks at the same place is the only invariant comparison that can be made.

These are what are actually measured in experiments. As far as what the theory has to say about them, the metric in Schwarzschild coordinates has the nice feature that it's static. This makes it very convenient for working out the Doppler shifts and accumulated times between two clocks if they spend a substantial amount of time at fixed Schwarzschild radii. This doesn't generalise, though.

Concerning point 2), you conveniently ignore that, according to general relativity, gravitational time dilation effects are predicted to largely disappear under free-fall conditions. You certainly can't challenge this on experimental grounds, because that experiment has never been performed.

Hopefully then you may come to appreciate that when it comes to GR, the expert is now me.

You've already admitted you are unable to derive measurable predictions, such as the perihelion advance of Mercury's orbit, from the theory. That alone rules you out as an expert. It also means you've never subjected your "understanding" of general relativity to any sort of external verification.

General relativity has, as you well know, been tested in a number of experiments over the last century since it was originally proposed. The thing is, those experimental tests were only meaningful because, in each case, a theorist somewhere worked out what general relativity predicted about the situation so that a comparison could be made. Those theorists, able to make the predictions, are the real experts on general relativity, Farsight. Not you.

Concerning point 2), you conveniently ignore that, according to general relativity, gravitational time dilation effects are predicted to largely disappear under free-fall conditions. You certainly can't challenge this on experimental grounds, because that experiment has never been performed.

Przyk, didn't the initial GPS satellite at least confirm gravitational time dilation? And once in orbit the satellites are essentially in a free fall state.., no?

Przyk, didn't the initial GPS satellite at least confirm gravitational time dilation? And once in orbit the satellites are essentially in a free fall state.., no?

That's true but not really the sort of thing I was talking about: the usually quoted figure for GPS clocks is 38 microseconds per day from our perspective on Earth. While the GPS satellites are in free-fall, we and our clocks on Earth aren't.

The sort of situation I was thinking of would be more like doing the NIST optical clock experiment on the International Space Station or (if it could somehow be done accurately and quickly enough) on a reduced gravity aircraft, with both clocks approximately in free-fall and kept at some fixed distance from one another.

That's true but not really the sort of thing I was talking about: the usually quoted figure for GPS clocks is 38 microseconds per day from our perspective on Earth. While the GPS satellites are in free-fall, we and our clocks on Earth aren't.

The sort of situation I was thinking of would be more like doing the NIST optical clock experiment on the International Space Station or (if it could somehow be done accurately and quickly enough) on a reduced gravity aircraft, with both clocks approximately in free-fall and kept at some fixed distance from one another.

Got ya! There are a lot of seemingly everyday experiments I would like to see done on the space station.