Black holes

[tensordyne]

Nope. I specified that from the beginning.

If you say so.

It doesn't, because it's flat-out wrong. You cannot make it curved, it's flat.

Sorry, that is true, it is flat.

You cannot make it pseudo-Euclidean, it's Euclidean.

Incorrect, and I already did. u = x and v = (-1)^(1/4) y with x and y Cartesian.

If u and v are either complex or octonians, that's not a real metric and hence nonsense.

Yep, metrics should map to the reals.

 

[tensordyne]

Yep - again with the caveat that you need to specify any finite ranges, identifications, or boundary conditions you're imposing.

That is not the only thing you need to know, you need to know how the coordinates are determined in the first place.

 

[tensordyne]

Nonsense. That metric is again flat Euclidean locally, regardless of "how" the coordinates were determined.

[In the following u and v are coordinate variables that are not specified as to how they are determined.]

That is not the only aspect of geometry as given above. I give one of the metrics I gave before and ask you to calculate the area of u0 < u < u1 and v0 < v < v1. You can do it no problem. Can you tell me though what the shape is of that area, what it looks like? NO. Can you tell me where it is? NO, not really, u and v are abstract.

 

[sol invictus]

Incorrect, and I already did. u = x and v = (-1)^(1/4) y with x and y Cartesian.

Nope. With that choice, the metric is ds^2=dx^2+dy^2=du^2-idv^2, which isn't even real and not what you wrote. Probably you mean u = x and v = (-1)^(1/2) y. That gives ds^2=dx^2+dy^2=du^2-dv^2, which is indeed pseudo-Riemannian, but again, not the metric you wrote. The metric you wrote is the Euclidean plane (locally), with positive definite metric.

 

[sol invictus]

That is not the only thing you need to know, you need to know how the coordinates are determined in the first place.

You can keep repeating that as often as you like, but it's still wrong. You've tried several times to give examples, all of which contained basic errors. That should tell you something.

[In the following u and v are coordinate variables that are not specified as to how they are determined.]

That is not the only aspect of geometry as given above. I give one of the metrics I gave before and ask you to calculate the area of u0 < u < u1 and v0 < v < v1. You can do it no problem. Can you tell me though what the shape is of that area, what it looks like? NO. Can you tell me where it is? NO, not really, u and v are abstract.

I can tell you exactly what the shape is. As for "where" it is, I can tell you where it is in relation to any geometrical feature of the manifold (such as a singularity, point of maximum curvature, etc.). Of course as I said before, if you've marked some points in a non-geometric way then obviously the metric alone can't tell you that.

 

[tensordyne]

Nope. With that choice, the metric is ds^2=dx^2+dy^2=du^2-idv^2, which isn't even real and not what you wrote. Probably you mean u = x and v = (-1)^(1/2) y. That gives ds^2=dx^2+dy^2=du^2-dv^2, which is indeed pseudo-Riemannian, but again, not the metric you wrote.

The metric you wrote is the Euclidean plane (locally), with positive definite metric.

This hardly matters, but the metric I gave was

ds² = u² du² + v² dv²
u = x, v = (-1)^(1/4) y, substituting one gets

ds² = x² dx² - y² dy²
Check me if you want...

The metric you wrote is the Euclidean plane (locally), with positive definite metric.

Incorrect assumption: I never said how u and v originally were to be determined. Without that knowledge, one should not make any such claims as are made above (which by the way, is MY WHOLE FREAKING POINT!).

 

[Farsight]

Well, that's at least an honest answer. Thanks for admitting that.

My pleasure.

However, it leaves me at a loss as to how you can claim to have identified a mistake in all general relativity textbooks, while at the same time acknowledging that you cannot answer a simple question about a trivial metric (which in fact is nothing more than flat spacetime). Indeed, it's clear from your response that you do not know how to manipulate metrics or extract physical predictions from them.[/QUOTE]Obscure maths questions are no substitute for addressing the scientific evidence, sol. You won't fool anybody with that. I don't speak Latin either.

 

[tensordyne]

I can tell you exactly what the shape is. As for "where" it is, I can tell you where it is in relation to any geometrical feature of the manifold (such as a singularity, point of maximum curvature, etc.). Of course as I said before, if you've marked some points in a non-geometric way then obviously the metric alone can't tell you that.

You can tell me the shape of regions of abstract, undefined coordinates eh?
What does 1 < p < 2 and 3 < q < 5 look like (p and q are coordinate variables)? I am not defining yet how p and q are to be determined. Let's hear it, what is that shape like? And I do not want its topology, I want its shape.

Quite an extraordinary claim you are making sol.

 

[Farsight]

Then no reference frame exists, relativity is nonsense from top to bottom, and we may as well all go home.

No it isn't. The relativity you've been taught is mistaken in some respects. Go back to the original, and it all makes sense. Then the mysteries evaporate.

Nothing which transmits information can move faster than light. But no information was transmitted, so no problem exists.

I don't know of anything that moves faster than light. Now come on man, think. When you accelerate towards a star it can't in reality flatten into a discoid in no time flat. Hence you know it's just an observer effect.

That's wrong even in special relativity. Hell, that's wrong in Galilean relativity.

No it isn't. Einstein gave the equations of motion.

Yes, it's an abstraction. But it's an abstraction that we can use to predict the results of measurements. Unless the theory is wrong, then the abstraction will work. Whenever you claim that there's no such thing as a reference frame, you're really saying that general relativity is nonsense.

No I most certainly am not. Learn to look at what's there, then go back and read what Einstein actually said, then you'll see that the nonsense is elsewhere.

 

[Mashuna]

Obscure maths questions are no substitute for addressing the scientific evidence, sol. You won't fool anybody with that. I don't speak Latin either.

Don't worry, I'm sure you'll manage to find a fundamental flaw in Latin soon enough.

 

[Farsight]

Thanks for this.

My pleasure.

Ya know Farsight, having read many a post by MM, I'm getting déjà vu all over again, reading your post. To be sure, you don't make extensive use of "double quotes", nor CAPITALS, nor ...

Focus on the scientific evidence I give you, and think things through.

"To do that we count 9 192 631 770 microwaves into the detector and then say a second has elapsed" - ?!?!

That's rather different than what it says on the couple of country's time standard webpages. For example, NIST says this:

"This process is repeated many times while the microwave signal in the cavity is tuned to different frequencies. Eventually, a microwave frequency is found that alters the states of most of the cesium atoms and maximizes their fluorescence. This frequency is the natural resonance frequency of the cesium atom (9,192,631,770 Hz), or the frequency used to define the second".

How did you derive "we count 9 192 631 770 microwaves into the detector" from "the microwave signal in the cavity is tuned to ... 9,192,631,770 Hz"?

We're defining the second here, Dopa. Hertz is cycles per second. How can you say the frequency is 9,192,631,770 Hz when you're defining the second? Oh because you've already defined the second? Don't think so. The tuning is like you twiddling the dial on your radio until you hear a loud noise. Then you count nine billion of them electromagnetic waves coming at you, and then you've defined your second, and the frequency is nine billion Hertz by definition.

Sorry, I just cannot follow what you're trying to say here.

Electromagnetic waves propagate through space. They move from A to B at the speed that they do. We use that motion to define the second, and then the metre. The we say those waves move at 299,458,792 m/s.

So, when you have time, what - in your own words - is "the parallel-mirror light clock"? (Later I may ask about "that runs slower at the lower elevation").

Look it up, see wiki and elsewhere. Do your own research.

"there's no time flowing in it, just light moving"? Who cares? And why?

Physicists care. Because physicists want to understand the world we live in and make it a better place. If you don't, that's up to you.

 

[DeiRenDopa]

(continued)

This is why people say the speed of light is constant. What they really mean by this is the locally measured speed of light is constant. What you don't hear so much is that the coordinate speed of light varies in a non-inertial reference frame, like the room you're in. There's nothign wrong with this per se, but it misses the trick that the true speed of light varies in that room too. If it didn't, optical clocks at different elevations would stay synchronised.

that clocks clock up regular cyclic motion rather than "the flow of time", and by reading the original Einstein to understand that that gravitational time dilation is the result of a reduced rate of motion caused in turn by a concentration of energy "conditioning" the surrounding space.

I have no idea what this is supposed to mean; does anyone (even Farsight)?

Yes of course. Open up a clock. In a mechanical clock you see cogs whirring. In a quartz wristwatch you see a crystal vibrating. Pick any clock and it's the same story. You don't see time flowing through it. As for the Einstein thing, see his 1920 Leyden Address

"According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration".

He says matter here, but he refers to energy elsewhere, such as in the Foundation of the General Theory of Relativity where he said:

"the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy"

And what's the relevance of "the original Einstein"? I mean, he came up with GR, and published a paper or two on it. But he's not a god; his word is not inerrant.

No, but we're talking GR here, and that hard scientific evidence is backed up by what Einstein said, see this post of mine on a previous thread.

Thanks for that link; reading your posts in that thread - and the responses of others to them - was most informative.

It would seem that you have rather idiosyncratic notions of what GR is, perhaps because you don't quite understand how the math relates to material things like clocks, microwave cavities, and rooms? Or perhaps it's a misunderstanding of how objective, independently verifiable experimental and observational results can be - and are - related to theories in physics (like GR)?

For example, you seem to think that two clocks, separated by a foot or so in elevation are (must be?) in the same reference frame; i.e. that they can both measure 'local' time and that the 'local' is the same.

I agree this is quite important, so important that I'll spend some time on it, later (in a different post).

Is it just me (that does not understand what Farsight is trying to say), or has he displayed a rather gross misunderstanding of relativity?

No. GR as taught today is no longer in line with Einstein's GR.

Which is, of course, the same thing. If it's "no longer in line with", it's a different theory, operationally, and will lead to different predictions, and experiments and/or observations can be used to test whether the universe works according to one rather than the other.

If nothing else, Farsight seems to be trying to have his GR cake and eat it.

Relativity is the sleeping beauty of physics. I'm doing my bit to hack through the thicket. It's a save the planet thing.

gravitational time dilation" is an effect you can derive from GR, and it is unambiguous. You can do experiments to test this GR prediction, and as far as I know, every such test has produced results consistent with GR (to the experimental uncertainties).

Yep. GR is a really well-tested theory, see Clifford Will's paper. But you don't see time flowing, and you don't see time flowing slower. Have a look at A World Without Time: The Forgotten Legacy of Godel and Einstein. Then ask yourself what you can see going slower.

Kinda beside the point, isn't it? I mean, apart (possibly) to philosophers.

The question is, as W.D.Clinger said (and which you quoted; my bold) "Spacetime manifolds are mathematical objects. We can prove their mathematical existence follows from the laws of logic and the axioms of mathematics, but we cannot use mathematics alone to prove a spacetime manifold accurately describes the physical universe. Whether something exists in a physical sense is a question for science, not mathematics."

And in this case "science" is the objective, independently verifiable experimental and observational results (and the extent to which they match the unambiguous predictions of theory/model/hypothesis, GR in this case).

You can paint any word picture you like, to 'explain' GR and tests of it; however, the only thing which counts is the quantitative agreement between results and predictions.

To understand what GR predicts concerning the observed behavior of light near black holes, you need to first understand GR (duh!). While the answers may be somewhat tricky to work out, and there will certainly be some subtleties, not least because the mathematical framework that GR is expressed in is not intuitive), they will nonetheless be unambiguous.

Yep.

But Farsight seems to be introducing his own ideas - beyond GR - and mixing them in, without making any attempt to distinguish the two.

Nope. I'm not some "my theory" guy.

If so, then what are the objective, independently verifiable experimental and/or observational results which are inconsistent with GR?

What am I missing?

The hard scientific evidence.

And that "hard scientific evidence" is ... what, exactly?

So far all I've seen you present is "optical clocks at different elevations don't stay synchronized" (that's a shorthand).

You've also alluded to "the GPS clock adjustment and the Shapiro delay"; what else?

...And if nothing else, then where are the experimental and observational results showing inconsistency with GR?

They aren't coming from me. I'm rooting for GR.

Huh?

And please note that I've mentioned vacuum impedance before now.

What is Farsight referring to?

The impedance of free space, usually written as Z₀ = √(μ₀/ε₀). It's described as a constant, but it isn't actually constant. Remember those light beams? The speed of light c = √(1/ε₀μ₀). Do your own research. Think for yourself.

Right.

But my question was, and still is, what is it about vacuum impedance that "mentioned before now"? How is it relevant?

And what you write here doesn't help much. "It's described as a constant, but it isn't actually constant" - that's your claim, but you don't actually provide any evidence to support it, do you?

(to be continued)

 

[Farsight]

How do you know what happens with the Schwarzschild metric at r= r_s? Let see: The dt component vanishes and the dr component is undefined (1/0). We call that a coordinate singularity. You think that means that the coordinate speed of light goes to zero at this event horizon.

No I think it means the actual speed of light goes to zero. You can't magic that away with a "coordinate transformation". Just as you can't make the lower clock go faster than the upper clock. Capiche?

And in sol invictus's metric what happens? Let see: The dt component vanishes and the dr component is undefined (1/0). We call that a coordinate singularity. Why do you not also think that means that the coordinate speed of light goes to zero at this "event horizon"?

What event horizon is that? I said I didn't know what this expression described. Care to enlighten me or are we all going to ignore reality and get lost in maths?

And what about Kruskal–Szekeres coordinates?

What happens to the coordinate speed of light at this event horizon.

I've told you umpteen times already. KS coordinates do a hop skippety jump over the end of time. They employ a stopped observer to fool you into thinking a stopped clock carries on merrily tick-tocking away in cloud-cuckoo land.

If you cannot answer these questions then you have to rely on the answers of others. What the textbooks state is:

• In Schwarzschild coordinates the coordinate speed of light is zero at the event horizon.
• In Kruskal–Szekeres coordinates the coordinate speed of light is c at the event horizon.

In other words: The coordinate speed of light at the event horizon depends on the coordinates that you use !

Oh yeah? Have a try switching coordinates to make the lower light-clock tick faster than the upper:

|-----------------|
|-----------------|

Then try switiching coordinates to make the lower light-clock tick:

|-----------------|
|-----------------|

Don't believe everything in your good book, RC.

 

[sol invictus]

This hardly matters, but the metric I gave was

ds² = u² du² + v² dv²
u = x, v = (-1)^(1/4) y, substituting one gets

ds² = x² dx² - y² dy²
Check me if you want...

You stated "Incorrect, and I already did. u = x and v = (-1)^(1/4) y with x and y Cartesian." That's wrong, and I showed you why.

In this latest attempt, you've moved the goal posts. Now x and y are not Cartesian. In fact, they're not real. And despite appearances, the metric above in terms of x and y is not pseudo-Euclidean, it's Euclidean, because y is restricted to a particular line in the complex plane such that the distance element is positive definite.

How do I know this? Well, you earlier failed to specify the range of u and v (despite being told repeatedly that you needed to). With nothing stated to the contrary, the universal convention is that the coordinates in the metric are real (they cannot be simply complex, else the metric itself isn't real). This has nothing to do with how u and v were "originally" (whatever that means) determined. It simply has to do with their range, which as I've told you from the beginning is part of the metric.

You can tell me the shape of regions of abstract, undefined coordinates eh?
What does 1 < p < 2 and 3 < q < 5 look like (p and q are coordinate variables)? I am not defining yet how p and q are to be determined. Let's hear it, what is that shape like? And I do not want its topology, I want its shape.

Quite an extraordinary claim you are making sol.

Not at all. Again, you are moving the goalposts. Earlier, you asserted "I give one of the metrics I gave before and ask you to calculate the area of u0 < u < u1 and v0 < v < v1. You can do it no problem. Can you tell me though what the shape is of that area, what it looks like? NO." [my bold]

That was wrong. Now, you are giving me the range, but not the metric. Obviously I cannot tell you the shape without the metric.

 

[sol invictus]

My pleasure.

However, it leaves me at a loss as to how you can claim to have identified a mistake in all general relativity textbooks, while at the same time acknowledging that you cannot answer a simple question about a trivial metric (which in fact is nothing more than flat spacetime). Indeed, it's clear from your response that you do not know how to manipulate metrics or extract physical predictions from them.

Obscure maths questions are no substitute for addressing the scientific evidence, sol. You won't fool anybody with that. I don't speak Latin either.

The claim you are making is a mathematical claim about the Schwarzschild metric, and based on that, a physical claim about the behavior of light, time, etc. I've just given you a metric that is identical to the Schwarzschild metric near the horizon, and you've told me you don't understand it and can't answer any questions about it, physical or mathematical.

How can you make confident assertions about the mathematical and physical properties of the Schwarzschild metric, when you cannot answer equivalent questions about a simpler metric, one that happens to be identical to the Schwarzschild metric in the region of interest?

 

[DeiRenDopa]

"To do that we count 9 192 631 770 microwaves into the detector and then say a second has elapsed" - ?!?!

That's rather different than what it says on the couple of country's time standard webpages. For example, NIST says this:

"This process is repeated many times while the microwave signal in the cavity is tuned to different frequencies. Eventually, a microwave frequency is found that alters the states of most of the cesium atoms and maximizes their fluorescence. This frequency is the natural resonance frequency of the cesium atom (9,192,631,770 Hz), or the frequency used to define the second".

How did you derive "we count 9 192 631 770 microwaves into the detector" from "the microwave signal in the cavity is tuned to ... 9,192,631,770 Hz"?

We're defining the second here, Dopa. Hertz is cycles per second. How can you say the frequency is 9,192,631,770 Hz when you're defining the second? Oh because you've already defined the second? Don't think so. The tuning is like you twiddling the dial on your radio until you hear a loud noise. Then you count nine billion of them electromagnetic waves coming at you, and then you've defined your second, and the frequency is nine billion Hertz by definition.

Sorry, I just cannot follow what you're trying to say here.

Electromagnetic waves propagate through space. They move from A to B at the speed that they do. We use that motion to define the second, and then the metre. The we say those waves move at 299,458,792 m/s.

Thanks for this.

You confirmed pretty much what I suspected; it seems you don't really understand how the cesium fountain clock works, in terms of determining, as a standard, one second, do you?

I'll guess that you have no problem with "maximizes their [the cesium atoms'] fluorescence", but you do seem to have difficulty with "a microwave frequency is found", as in "the microwave signal in the cavity is tuned to different frequencies".

So let's start with this: what do you think a "microwave cavity" is? And how do you think you "tune" the microwave signal in such a cavity to different frequencies?

To quote you, "this one is hugely important".

So, when you have time, what - in your own words - is "the parallel-mirror light clock"? (Later I may ask about "that runs slower at the lower elevation").

Look it up, see wiki and elsewhere. Do your own research.

Um, you do realize, don't you, that the ideas you express, in your posts in the threads in this part of JREF (at least the ones I'm actively participating in, on GR) are at considerable variance to standard, textbook GR?

That being so, if you wish others to understand you - and that's why, or one important reason why, you post here, right? - then those who seek to understand you need to be confident your understanding of key terms you use is the same as their own, right?

From our exchanges so far I've learned that you have some very different understandings of key terms and concepts than what I find in standard textbooks. To be sure I do not misunderstand you, I will - often - ask you to define key terms, in your own words. If you reply by pointing to definitions that are standard (or nearly so as never mind), I can be confident of at least that commonality in our mutual understanding.

Now that I know - with some degree of certainty - what you mean by "the parallel-mirror light clock", I can proceed to try to understand other things you've posted.

"there's no time flowing in it, just light moving"? Who cares? And why?

Physicists care. Because physicists want to understand the world we live in and make it a better place. If you don't, that's up to you.

Well, on this we may have to agree to disagree.

Some philosophers may care, and to the extent to which a nice mental picture may help some physicists develop new tests, models, hypotheses, etc, they may too.

But if the word pictures all produce the same results - in terms of quantitative matches between theory and experiment - they're equivalent, right? And if they're equivalent, who cares?

 

[Farsight]

Let me see if I understand you correctly: the extent to which these "optical clocks" "lose synchronisation when separated by a vertical elevation of only a foot" is an effect predicted by GR, and the quantitative extent to which they (the clocks) do so (lose synchronization) is the same as predicted by GR (to within the experimental uncertainties). Is that an accurate summary?

Yes.

When what moves? The optical clocks? The electromagnetic phenomena? A UV frequency?

Electrons move by doing a spin-flip. This emits electromagnetic waves, which move away.

And what does "at a lower rate" mean?

It means when they move slower.

I kinda wondered if this gross misunderstanding was at the root of your assertion ("It's based on the hard scientific evidence that the speed of light varies with gravitational potential" - the "it" is not important here), now you've confirmed my suspicion, thanks.

It's no gross misunderstanding. The evidence for it is right there under your nose.

I think you need to go read a good textbook on relativity, Farsight. The only way you can tell if a 'clock runs slower' is by comparing it with another clock in the same reference frame!

Let's see now. I can see my clock, and I can see my other clock. One's lower than the other, and it's running slower, just like Einstein said. Then I can open up my clocks and see them in action. I can see the cogs whirring, or the crystals oscillating, or using my gedeanken microscope I can the electrons flipping or the electromagnetic waves propagating. And in the lower clock I can see all those things moving slower than the upper. But then you lean over my shoulder and say No Farsight, they're moving at the same speed, they're just in different reference frames. What reference frames? Two little rectangles, one around each clock? And then you say you need to read the good book, Farsight. The last time I heard stuff like that was when I was having a dingdong with the YECs.

A parallel-mirror light clock ('first clock') will keep time with an optical clock ('second clock') if the two are in the same reference frame. If the first and second clocks are in different reference frames, they will not, necessarily, 'keep the same time'.

They'll keep time at the same elevation.

The definition of the unit of time, the second, says nothing about "light [having] any particular frequency"; it is about the frequency at which a tunable microwave cavity produces a maximum fluorescence signal.

You quoted it. Don't you remember? Here you go:

"This process is repeated many times while the microwave signal in the cavity is tuned to different frequencies. Eventually, a microwave frequency is found that alters the states of most of the cesium atoms and maximizes their fluorescence. This frequency is the natural resonance frequency of the cesium atom (9,192,631,770 Hz), or the frequency used to define the second".

The "true speed of light", eh? "True".
What is this?

The rate at which light moves. It moves at the speed that it does. We use that to define the second and the metre and then we label that speed 299,792,458 m/s. Wherever we are. Regardless of whether the light at the lower elevation is moving slower than at the upper elevation. Do you understand this yet? The Earth was not created six thousand years ago. And the speed of light is not constant.

 

[Farsight]

Thanks for that link; reading your posts in that thread - and the responses of others to them - was most informative.

My pleasure. I hope you're enjoying this physics discussion.

It would seem that you have rather idiosyncratic notions of what GR is, perhaps because you don't quite understand how the math relates to material things like clocks, microwave cavities, and rooms? Or perhaps it's a misunderstanding of how objective, independently verifiable experimental and observational results can be - and are - related to theories in physics (like GR)?

Nope. I've read the original GR, and the scientific evidence squares with it. However it doesn't square with what people say GR says.

For example, you seem to think that two clocks, separated by a foot or so in elevation are (must be?) in the same reference frame; i.e. that they can both measure 'local' time and that the 'local' is the same.

No. They're just two clocks at different elevations. They're in this room. Or if you prefer, they're in space near a planet. The things we call reference frames are "artefacts of measurement" that have no physical existence. And those clocks don't actually measure time. There is no time flowing through those clocks. Can you see it whooshing through? No. What they actually do is clock up some form of regular motion, and display a cumulative total that you call the time.

I agree this is quite important, so important that I'll spend some time on it, later (in a different post).

OK noted

Which is, of course, the same thing. If it's "no longer in line with", it's a different theory, operationally, and will lead to different predictions, and experiments and/or observations can be used to test whether the universe works according to one rather than the other.

That's what we're talking about concerning the nature of black holes.

...And in this case "science" is the objective, independently verifiable experimental and observational results (and the extent to which they match the unambiguous predictions of theory/model/hypothesis, GR in this case).

Sure.

You can paint any word picture you like, to 'explain' GR and tests of it; however, the only thing which counts is the quantitative agreement between results and predictions.

Agreed.

If so, then what are the objective, independently verifiable experimental and/or observational results which are inconsistent with GR?

Hawking radiation.

And that "hard scientific evidence" is ... what, exactly?

Light moving slower when its lower.

So far all I've seen you present is "optical clocks at different elevations don't stay synchronized" (that's a shorthand).

You've also alluded to "the GPS clock adjustment and the Shapiro delay"; what else?

Gravitational lensing.

But my question was, and still is, what is it about vacuum impedance that "mentioned before now"? How is it relevant?

Impedance is an electrical property of say a cable, but it applies to space too, which electromagnetic waves propagate through. It applies to alternating current rather than direct current, these both being associated with conduction current, which is the motion of charged particles. You can create such charged particles via pair production, and get the electromagnetic waves back again via annihilation. Those electromagnetic waves are displacement current rather than conduction current, and they wave. They're alternating.

And what you write here doesn't help much. "It's described as a constant, but it isn't actually constant" - that's your claim, but you don't actually provide any evidence to support it, do you?

Yes I do. The speed of light c = √(1/ε₀μ₀) depends on the impedance of space. And it varies. We can see it varies in the Shapiro delay, and in those optical clocks which lose synchronisation, as would parallel-mirror light clocks:

|--------------|
|--------------|

In a gravitational field the speed of light demonstrably varies. So the impedance of space must be varying too. It isn't constant either. So when you hear people rabbiting on about the fine-tuned "fundamental constants" and the anthropic universe or the multiverse, be sceptical.

Gotta go.

 

[Ziggurat]

I don't know of anything that moves faster than light.

Really? Because there are lots of things which do. If I point a flashlight at the moon and pass my hand across it quickly, the shadow of my hand on the moon will travel across the moon faster than c. Pick the right medium, and you can also get a phase velocity for light which is faster than c. Plenty of things travel faster than c. But none of them carry information. That's all we need to preserve causality.

Now come on man, think. When you accelerate towards a star it can't in reality flatten into a discoid in no time flat. Hence you know it's just an observer effect.

That doesn't mean it's not real. The relativity of velocity is just an observer effect too, under this logic. Yet if I'm on a train and you're on the ground, you really are moving. It's not an illusion, unless all motion is an illusion.

 

[Ziggurat]

Oh yeah? Have a try switching coordinates to make the lower light-clock tick faster than the upper:

|-----------------|
|-----------------|

That's easy: accelerate towards the lower clock from above.