Black holes

[ben m]

Standard GR isn't the same thing as Einstein's GR.

I disagree with you on this statement.

I have yet to see ANYONE agree with you on this statement.

You cited of Einstein describing a "variable speed of light", but I really have no idea why you think this is inconsistent with standard GR. Yes, there are observers and calculations in which GR has similar effects to a speed-of-light variation. There are other observers and calculations for which it does not.

Anyway, don't call it FGR, call it relativity+. I'm an IT guy, the name was apt.

You spent this whole thread pretending that you were doing something called "GR", and that everyone else, from 1938 on forward, was doing something else. Now that you've dropped that facade, you want to switch to "relativity+"? Sorry, no: because you spend this whole thread trying to sow confusion about what theory you're talking about, I declare that you've forfeited the right to pick your own name.

 

[D'rok]

. Anyway, don't call it FGR, call it relativity+. I'm an IT guy, the name was apt.

I used to be an IT guy. To be apt, shouldn't it be "relativity++"?

 

[Ziggurat]

I used to be an IT guy. To be apt, shouldn't it be "relativity++"?

No, to be apt it should be called 'Bob'.

 

[Ziggurat]

You cited of Einstein describing a "variable speed of light", but I really have no idea why you think this is inconsistent with standard GR.

Because he doesn't believe in coordinate transformations. They're just mathematical nonsense to him. Everything begins and ends with the Schwarzchild coordinates.

 

[D'rok]

No, to be apt it should be called 'Bob'.

 

[W.D.Clinger]

General relativity postdates classical electromagnetism. What I'm talking about here is the route to unification.

You're late to the party. Einstein began that unification of general relativity with classical electromagnetism in section 20 of this paper:

Albert Einstein. Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik 49, 1916. Online at http://www.alberteinstein.info/gallery/gtext3.html​

That web site also contains an English translation, from which I will quote often.

I meant what I said about GR being the sleeping beauty. You go back to what Einstein actually said,

If I go back to what Einstein actually said, instead of relying on what Farsight tells me Einstein said, I find that Einstein's interpretation of general relativity is indistinguishable from the modern interpretation.

Everybody now talks about curved spacetime, but Einstein didn't. He talks about curvature, but I can't actually find him talking about curved spacetime.

Here's an example of Einstein talking about curved spacetime:

...is always real on account of the hyperbolic character of the space-time continuum.

It matters because people say "GR tells us" when it's very different to what Einstein actually said. I'm sorry, but that matters to me.

What Farsight says about what Einstein said is often very different from what Einstein actually said. That matters to me.

Here, for example, are some of the things Einstein actually said in the paper cited above:

The mathematical tools that are necessary for general relativity were readily available in the "absolute differential calculus," which is based upon the research on non-Euclidean manifolds by Gauss, Riemann, and Christoffel, and which has been systematized by Ricci and Levi-Civita and has already been applied to problems of theoretical physics.

The modern name for "absolute differential calculus" is differential geometry. Note well that, according to Einstein, the tools provided by differential geometry are "necessary for general relativity".

It will be seen...that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to "produce" a gravitational field merely by changing the system of coordinates.

...so there is nothing for it but to regard all imaginable systems of co-ordinates, on principle, as equally suitable for the description of nature.

 

[ben m]

Because he doesn't believe in coordinate transformations. They're just mathematical nonsense to him. Everything begins and ends with the Schwarzchild coordinates.

I mean, yeah, it's obvious that he says that when cornered, but --- well, he says that and goes right back to pretending to follow Einstein in the original form. Meanwhile, when I read Einstein I keep seeing sentences like

Die allgemeinen Naturgesetze sind durch Gleichungen aus-
zudrücken, die füralle Koordinatensysteme gelten, d. h. die
beliebigen Substitutionen gegenüberkovariant (allgemein ko-
variant) sind.

(trans: The general laws of nature are to be expressed by equations which hold good for all the systems of coordinates, that is, are covariant with respect to any substitutions whatever (generally covariant).)

In the 1916 paper that's italicized for emphasis.

 

[ctamblyn]

(Part 1/2)

Just as it's a "delay" if your train spent part of its journey travelling at 50mph rather than its usual 60mph. Just take the evidence at face value.

Or if the train took a longer route than expected. Or a combination of those possibilities.

Of course. If you followed the path of the Shapiro radar signal in your gedanken spaceship carrying a parallel-mirror light clock and your metre rod, at no point in your journey will you measure a reduced speed of light. Where the speed of light is reduced, it is also reduced in your parallel-mirror-light clock. It's similarly reduced in your optical clock, your microwave atomic clock, your UV optical clock, and so on.

But I shun such clocks, and elect to use a combination of weak and strong decay processes to measure time. Still, I get a result that agrees with the rest of humanity's primitive electromagnetic-interaction clocks. Coincidence?

I know. Let me give you a simple analogy that hopefully brings it home: you're a clockwork man, and you hold a clockwork clock. It ticks at a certain rate, and when you plunge it in an oil bath, it ticks slower. Now jump in after it.

It's not that I don't understand what you're driving at, it's that it doesn't work as an argument. We know about the Shapiro delay, and we know that local measurements of light speed always yield 299792458 m/s. The two facts are perfectly consistent with each other, and perfectly consistent with "MTW" GR. So, these facts cannot serve to show that your point of view is superior to the "MTW" one.

General relativity postdates classical electromagnetism. What I'm talking about here is the route to unification.

Classical electromagnetism - Maxwell's equations, written in terms of differential forms - are already consistent with "MTW" GR. "MTW" GR does not in any way require the constancy of c and Z₀ to be abandoned. So I still maintain that whatever you're talking about is not classical electromagnetism or classical GR.

If you assume that c and μ₀ are varying through space, then it is quite clearly possible that they could vary in such a way that Z₀ remains constant.

I disagree with that.

(Hilighting added.)

You disagree that it is possible for c and μ₀ to vary in a way that leaves Z₀ constant? If that's the case, you're demonstrably wrong. If c varies in inverse proportion to μ₀ at all points in space, the product of μ₀ and c is constant everywhere, even though both are changing. And as you know, the product of μ₀ and c is equal to Z₀, which is therefore constant. QED.

Electromagnetism is an example of unification, the field concerned is the electromagnetic field rather than distinct electric and magnetic fields. Just as the electric field is one "aspect" of the electromagnetic field whilst the magnetic field is another, ε₀ is one aspect of a quality of space whilst μ₀ is another. The best word I can find for this is the "strength" of space. You see hints of this from time to time. For example see Mordehai Milgrom's New Physics at Low Accelerations (MOND): an Alternative to Dark Matter at http://arxiv.org/abs/0912.2678 where you can read this on page 5:

"We see that the modification of GR entailed by MOND does not enter here by modifying the ‘elasticity’ of spacetime (except perhaps its strength), as is done in f(R) theories and the like."

I don't think MOND is quite right by the way, but I don't think dark matter is particulate in nature. That's one for another day.

Like I've just demonstrated, if you are unwilling to state how ε₀ and μ₀ vary, there is no way to evaluate the truth of your claims. Furthermore, now that you've said that both can vary, there is no alternative but to reject as inconsistent your claim that c varies as a result of Z₀ varying; if ε₀ and μ₀ can vary separately, then so can c and Z₀.

As above.

No, you have only glossed over the issue so far. If you don't quantify these variations, you are expecting us to take your word on faith.

I reiterate that all I need to do is show that some quality of space changes affecting the propagation speed of light.

It is well known that no such model (ETA) variable-speed-of-light, "refraction" models cannot reproduce all the features of GR. It's logically impossible.

It's not my model, GR started life with a variable speed of light, but it's been airbrushed out of history. Look at those Einstein quotes...(snip)...

With all due respect, it doesn't matter to me what Einstein believed almost 100 years ago during the development of GR. It has no bearing on the current discussion.

I never said that.

So you don't believe that the paper you brought up puts forward a viable variable-speed-of-light interpretation of GR? Good, because it doesn't, but in that case why did you even bring it up?

Don't forget that Einstein referred to...(snip)...

Again, the history of GR's development is irrelevant.

 

[ctamblyn]

(Part 2/2)

You should read this short page for more information on that general "refractive index" approach (and why it falls down): http://mathpages.com/rr/s8-04/8-04.htm

I skimmed it, it's unconvincing, a bit of a straw man I'd say. See this:

"It’s also worth noting that physical refraction is ordinarily dependent on the frequency of the light, whereas gravitational deflection is not, so even a formal match between the two relies on the physically implausible assumption of refractive index that is independent of frequency".

It's not a straw man, it's actually an extremely pertinent article as far as this thread goes. You "skimmed it" and have focussed on one sentence near the end of the page (which is discussing one particular issue) but seem to have skipped the meat of the article (which deals with variable-speed-of-light models in a much more general way). I recommend reading the entire thing very carefully; it's actually a good read and very enlightening.

Again, a model in which only a single (ETA: scalar) quantity (in their case, a refractive index they denote by "n") is varying from point to point cannot logically be equivalent to GR in all its gory detail.

But it's a start. (...snipped another historical reference...)

Not in the context of this thread. Remember, you're claiming that a variable-speed-of-light model can be equivalent to GR. There is no use appealing to models which are already known to be inequivalent.

It matters because people say "GR tells us" when it's very different to what Einstein actually said. I'm sorry, but that matters to me.

It might matter to you, and to historians of science, but it's irrelevant to the topic.

They aren't well understood at all. Honestly.

QED is probably the most successful physical theory ever to have been developed. What evidence do you have for your assertion?

But that's another one for another day. And I'd say one needs an understanding of everything to take things forward. Then you can see how to join the dots.

To understand "MTW" GR requires no particle physics at all. You seem to be saying that understanding FGR does require such an understanding. On that basis, there's every reason to believe that the two are not equivalent. And even if FGR made the same predictions as "MTW" GR, its dependency on particle physics makes it less useful. It comes with conceptual baggage that simply isn't required.

(...snipped Einstein reference...)
As to what I've been telling you, clocks are made of particles, and light is what it is.

Not my clocks. I've got clocks based on weak and strong decays, remember? And yet they still agree with each other and with the clock on the wall.

They don't go slower for nothing, or because of some mystical magic.

Who knows (or could even tell) whether "magic" is involved? All we have is a set of mathematical models that work extremely (extremely!) well. That's all we can ever have.

A massive body "conditions" the surrounding space like Einstein said. It changes it, the change diminishing with distance.

Just as with magic, who knows? All we know is that what we can actually observe agrees with the predictions of "MTW" GR, as far as we can tell; all the rest is human imagination. If a particular "interpretation" makes it easier to learn, teach and work with the model then I'm all for it. Otherwise, throw it in the bin.

Anyway, don't call it FGR, call it relativity+. I'm an IT guy, the name was apt.

FGR is easier to type, and the "+" symbol implies something which I don't think anyone here is convinced of (save you, naturally).

And let's not forget that we were talking about black holes. I hope some of the guys here are starting to understand the frozen-star interpretation a bit better now. It's not some my-theory woo, it's what Oppenheimer called them.

No-one here has ever fallen into a black hole, so all we have to go on is what GR, a mathematical model, says. GR says I reach the event horizon in finite proper time, and that I can pass through that horizon without even noticing (for sufficiently large black holes). It says that I can reach the singularity in finite proper time, too. These are valid consequences of the mathematics.

Now, you might argue that the mathematics are being misapplied, but there is no axiom of GR that enables us to conclude that. There is absolutely no basis for rejecting such solutions unless you supplement GR with additional axioms (perhaps as a result of experimentation with real black holes), in which case you really have a different theory.

The modern equivalent is the gravastar, and the "stuff" it's made of is weird primal stuff. Much more interesting than a give-up-and-go-home point singularity.

As I understand it, they're an additional type of object rather than a replacement for black holes, and the physical universe could contain both. Of course, gravastars (depending as they do on quantum effects) are outside classical GR.

I must go. Nice talking to you ct. Somebody please explain to Zig abut the difference between distance and displacement.

He knows the difference.

Bye for now.

 

[W.D.Clinger]

Gravity Probe B refutes Farsight

Standard GR isn't the same thing as Einstein's GR.

Gravity Probe B refutes that claim:

C. W. F. Everitt, D. B. DeBra, B. W. Parkinson, J. P. Turneaure, J. W. Conklin, M. I. Heifetz, G. M. Keiser, A. S. Silbergleit, T. Holmes, J. Kolodziejczak, M. Al-Meshari, J. C. Mester, B. Muhlfelder, V. G. Solomonik, K. Stahl, P. W. Worden, Jr., W. Bencze, S. Buchman, B. Clarke, A. Al-Jadaan, H. Al-Jibreen, J. Li, J. A. Lipa, J. M. Lockhart, B. Al-Suwaidan, M. Taber, and S. Wang. Gravity Probe B: Final Results of a Space Experiment to Test General Relativity. Physical Review Letters 106, 221101 (2011), pages 221101-1 to 221101-5.​

Introduction.—In 1960, Schiff [1] showed that an ideal gyroscope in orbit around Earth would undergo two relativistic precessions with respect to a distant inertial frame: (1) a geodetic drift in the orbit plane due to motion through the space-time curved by Earth’s mass and (2) a frame-dragging due to Earth’s rotation. The geodetic term matches the curvature precession of the Earth-Moon system around the Sun given by de Sitter in 1916 [2]. The Schiff frame dragging is related to the dragging of the orbit plane of a satellite around a rotating planet computed by Lense and Thirring in 1918 [3].

Those 1916 and 1918 papers used Einstein's GR. So do modern papers, such as this one:

Clifford M Will. Covariant calculation of general relativistic effects in an orbiting gyroscope experiment. Physical Review D 67, 062003 (2003), pages 062003-1 through 062003-7.​

Will's predictions used modern (MTW) notation, but the foundations of that standard theory of general relativity were laid out in Einstein's 1916 paper (cited above by ben m and myself).

OK. But note this: I'm supplying the evidence, and the rationale. It isn't moonshine, it's mundane, and it's robust experimental physics. You aren't countering it with contrary evidence or an alternative rationale. All you're doing is saying "Farsight you're wrong because you don't agree with my textbook and my friends". You retire that too.

The results of Gravity Probe B agree with standard GR. That vindicates Einstein, and it also vindicates the modern relativists and mathematicians who take advantage of modern notation and differential geometry in textbooks such as MTW and Wald.

Even though it is popular lore that Einstein was right (I even wrote a book on the subject), no such book is ever completely closed in science. As we have seen with the 1998 discovery that the universe is accelerating, measuring an effect contrary to established dogma can open the door to a whole new world of understanding, as well as of mystery. The precession of a gyroscope in the gravitation field of a rotating body had never been measured before GP-B. While the results support Einstein, this didn’t have to be the case. Physicists will never cease testing their basic theories, out of curiosity that new physics could exist beyond the “accepted” picture.

Clifford M Will. Finally, results from Gravity Probe B. Physics 4, 43 (2011).​

 

[DeiRenDopa]

Those 1916 and 1918 papers used Einstein's GR. So do modern papers, such as this one:

Clifford M Will. Covariant calculation of general relativistic effects in an orbiting gyroscope experiment. Physical Review D 67, 062003 (2003), pages 062003-1 through 062003-7.​

Will's predictions used modern (MTW) notation, but the foundations of that standard theory of general relativity were laid out in Einstein's 1916 paper (cited above by ben m and myself).

The results of Gravity Probe B agree with standard GR. That vindicates Einstein, and it also vindicates the modern relativists and mathematicians who take advantage of modern notation and differential geometry in textbooks such as MTW and Wald.

I'm pretty sure I know the answer to the first of these questions, but I think it's worth asking anyway. And I do not know the answer to the second (and third).

First question: in the relevant literature on GR, is there anything which suggests that the "modern notation and differential geometry in textbooks such as MTW and Wald" is inconsistent with the foundations of the standard theory of general relativity, as "laid out in Einstein's 1916 paper (cited above by ben m and" W.D. Clinger)?

Second question: does any reader know of any posts by Farsight, in this part of JREF, in which he claims that "modern notation and differential geometry in textbooks such as MTW and Wald" is, in fact, inconsistent with the foundations of the standard theory of general relativity, as "laid out in Einstein's 1916 paper" (cited above ...)? NOTE: I'm only asking about one particular paper, not the entire body of Einstein's collected works.

Third question: Farsight, do you consider the "modern notation and differential geometry in textbooks such as MTW and Wald" to be inconsistent with the foundations of the standard theory of general relativity, as "laid out in Einstein's 1916 paper" (cited above ...)?

 

[W.D.Clinger]

I'm pretty sure I know the answer to the first of these questions, but I think it's worth asking anyway. And I do not know the answer to the second (and third).

First question: in the relevant literature on GR, is there anything which suggests that the "modern notation and differential geometry in textbooks such as MTW and Wald" is inconsistent with the foundations of the standard theory of general relativity, as "laid out in Einstein's 1916 paper (cited above by ben m and" W.D. Clinger)?

No.

Second question: does any reader know of any posts by Farsight, in this part of JREF, in which he claims that "modern notation and differential geometry in textbooks such as MTW and Wald" is, in fact, inconsistent with the foundations of the standard theory of general relativity, as "laid out in Einstein's 1916 paper" (cited above ...)? NOTE: I'm only asking about one particular paper, not the entire body of Einstein's collected works.

Yes. I'll give some examples below.

Note, however, that you're quoting me, not Farsight. When Farsight says "MTW is wrong", he seldom mentions differential geometry. When Farsight talks about the "misapplication of differential geometry", he seldom mentions MTW. When Farsight complains about "neverneverland coordinates", he seldom mentions MTW or differential geometry. It takes some knowledge of coordinates and differential geometry, MTW, and Einstein's 1916 paper to recognize that much of Farsight's argument is based upon his rejection of the coordinate transformations that are justified by the differential geometry in both MTW and Einstein's 1916 paper.

Third question: Farsight, do you consider the "modern notation and differential geometry in textbooks such as MTW and Wald" to be inconsistent with the foundations of the standard theory of general relativity, as "laid out in Einstein's 1916 paper" (cited above ...)?

That's for Farsight to answer.

I can only quote some of Farsight's previous answers to that question:

And MTW is wrong. That's what this whole discussion is about. Your good book is wrong. Look at that lefthand chart and the chopped off infinity. A clock going infinitely slow along with an observer observing infinitely slow doesn't get you past the end of time. Hop skippity jump!

Forget what you've been taught at Sunday School, forget what MTW has been telling people for decades, think for yourself.

They're imagining a line beyond eternity, and employing a coordinate system that does a hop skip and a jump over the end of time. See how the top of the left-hand chart below is omitted? The curve on the right of this chart goes vertical, and has no upper bound. That's the end of time. The light cone hasn't gotten past it yet, and never ever will, so everything to the left of the vertical dashed line is in never-never land. Sadly some people who appear to know mathematics and physics will duck and squirm and say anything other than admitting this to you because they fear that fallibility will erode their status, and the status of people like Hawking and Susskind.

[qimg]http://www.jessemazer.com/images/realisticBHkruskalsmall.jpg[/qimg]

That image shows parts (a) and (b) of MTW Figure 32.1. Farsight has shown no sign of having seen part (c). Farsight's knowledge of MTW appears to be derived from what he's read about it on the World-Wide Web:

The general relativity you're employing is a corrupted version of the original. Think for yourself, don't let MTW do your thinking for you. And no, I don't have a copy.

It isn't basic GR. Einstein never said anything like that. It's a corrupted cargo-cult version of GR where an observer at the black hole is given forever to make an observation using light that has stopped.

The idea of a black hole had not been proposed in 1916, so it is of course true that Einstein didn't say anything about black holes in that 1916 paper. On the other hand, Einstein's 1916 paper does say his theory allows for a large class of coordinate transformations that includes the particular transformations Farsight ridicules as "a corrupted cargo-cult version of GR".

And that utterly routine aspect of every General Relativity course ever taught is wrong. Doing a hop skip and a jump over the end of time and pretending it doesn't matter is cargo-cult pseudoscience that is a travesty of general relativity and an insult to Einstein.

The misunderstanding involves the basic facts of what clocks do, and the misapplication of differential geometry to promote an unfounded mathematical abstraction wherein a stopped clock and a stopped observer cancel each other out.

 

[dafydd]

OK. But note this: I'm supplying the evidence, and the rationale. It isn't moonshine, it's mundane, and it's robust experimental physics. You aren't countering it with contrary evidence or an alternative rationale. All you're doing is saying "Farsight you're wrong because you don't agree with my textbook and my friends". You retire that too.

That must be a stundie.

 

[DeiRenDopa]

I haven't moved the goalposts. You have. You have introduced the word "local" in your post #449. When we follow your "This began" link back to post #381 the word "local" is not present.

The updated/revised Gedankenexperiment protocol, outlined in post #476, rectifies this.

In particular, it incorporates several aspects designed to ensure that the experimental data produced is both objective and independently verifiable (and verified). It also explicitly allows questions concerning differences between local measurements and non-local ones (of the same phenomena) to be explored (in an objective, independently verifiable way).

I look forward to reading any comments you may have on it, and to discussing (and addressing) any questions or concerns you may have on it.

 

[DeiRenDopa]

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.

This post, by Farsight, is back a page or three, but I realize that I didn't ask a couple of questions that it triggered.

Farsight, by "gravitational lensing" do you mean "gravitational deflection"*, of which the lensing is just a particular example? Or is there something special about the former?

Also, how do you regard gravitational redshift? Is that phenomenon also in the same class - from your perspective - as "optical clocks at different elevations don't stay synchronized", "the GPS clock adjustment and the Shapiro delay", and "gravitational lensing"?

* as in the first verified prediction of GR, the apparent shifts in the positions of background stars, near the limb of the Sun, observed during the 1919 total solar eclipse

 

[DeiRenDopa]

Here's the context:
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
me: 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.

you: 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.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Again, a reference frame is an abstract thing, not an actual thing in which clocks are located.

I think we're going to have to go deeper here, in order to make sure the terms each of us uses have the same meaning (to each of us). Let's take some, apparently simple, terms.

OK.

And glad, I am, that I asked, and that you answered!

From your answers I have - tentatively - concluded that, at some pretty fundamental level, your approach to physics is different from mine. I also suspect that my approach is pretty close to that of most of the JREF members who've posted in this thread (so far).

I think it would be well worth the time spent to do so to explore these differences in some detail. Doing so will - I contend - go a long way to explaining much of the apparent ambiguities and contradictions in many of your posts.

velocity: can you measure velocity? does it have physical existence? can you point up to the clear night sky and say Look, that's a star. It has a velocity of {x}?

I can say that the star has a velocity relative to me, or relative to something else. I can deduce this via measurement of redshift, though at larger scales this is complicated by the expansion of the universe. Velocity exists like motion exists: a bullet moving fast relative to you will kill you. A bullet at rest with respect to you will not.

gravitational potential: can you measure gravitational potential? does it have physical existence? can you point up to the clear night sky and say Look, that's a star. It has a gravitational potential of {x}?

It's a phrase we use to in conjunction with a gravitational field, which definitely exists. If it didn't, you wouldn't fall down. Note however that a gravitational field is a region where there is a gradient in gravitational potential. You could place two clocks within voids at the centre of two large but unequal masses. In these voids the clocks don't fall down, but they do tick at different rates because the conditions we label as gravitational potential are not the same. The clocks ticking at different rates tells us that gravitational potential does label something very real.

temperature: can you measure temperature? does it have physical existence? can you point up to the clear night sky and say Look, that's a star. It has a temperature of {x}?

You can measure the temperature of the surface of a star, but temperature is an emergent property of motion. It's a measure that gives, for example, a measure of the average kinetic energy of gas molecules. See temperature on wikipedia. Temperature exists like heat exists: grab hold of the wrong end of a red-hot poker, and it burns you.

wavelength: can you measure wavelength? does it have physical existence? can you point up to the clear night sky and say Look, that's a star. It has a wavelength of {x}?

Yes, you can measure it, and it has a real existence. All you need to do is look at the ocean to confirm that. A star doesn’t have a wavelength, but the light it emits does.

elevation: can you measure elevation? does it have physical existence? can you point up to the clear night sky and say Look, that's a star. It has an elevation of {x}?

Elevation is a name we use when describing distance from the ground or some other surface. That distance is real. The word does not apply to a star. Note that elevation is also used to describe an angle.

Let's see if I can sketch the context and briefly characterize the nature of certain concepts - such as elevation, temperature, and velocity - within this context.

In this thread our discussion is implicitly - sometimes explicitly - within the scope of physics. By physics, we all agree - at some level - that it's a field of study whose early workers include Galileo and Newton.

Not so obvious is that 'physics' is quantitative, but quantitative it is; indeed, it would be nigh on impossible to write/describe 'non-quantitative physics'*.

Given 'quantitative', mathematics (or at least a subset of it) follows. As this post of yours makes clear, you fully accept that mathematics plays a vital role in physics.

Where you and I disagree - well, one place where we disagree - concerns the nature of (some? many?) concepts/terms commonly used in physics.

Some bullets may indeed kill me; red-hot pokers burn me; if a tree limb I am standing on breaks, I will fall; and so on. But the velocity, temperature, gravitational potential, etc we both may use to describe why these unwelcome consequences happen are abstract things. And, as Ziggurat's post on temperature (in response to your comment, above) makes clear, the degree of abstraction may vary.

There are several ways forward. I have implicitly proposed one, in post #476; namely, that we agree that the answer to "what is pressure?" is "what a pressure gauge measures", qualified by such things as "but only within the specific experiments we perform", and "actually, what all the different kinds of pressure gauge that we use measure", and "but we must be able to tie the pressure scale on every pressure gauge to the SI definition of {whatever}".

One merit of this approach is, I contend, that there is little room for ambiguity or subjectivity. Further, it easily allows disagreements and misunderstandings to be teased out and investigated. For example, the disagreements and confusions we seem to be having concerning the nature of clocks, the speed of light, and vacuum impedance.

Comments welcome (from anyone, not just Farsight).

* a very, very narrow field within physics, perhaps; but not anything with serious explanatory power

 

[Farsight]

Wow guys, I've just read through to the end of the thread and frankly I'm amazed. You're showing the most awful groupthink here. You still can't see the obvious. Let's try it another way. Let's say we've got two trains on parallel tracks. They start off at the same time, and one reaches the end before the other. Like this:

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

Which train is going faster? Easy. The top one.

Now repeat this with two light beams in parallel-mirror clocks:

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

Which one's going faster?

It's that simple, it really is.

Right, I'll go back through the thread giving some responses. Again, try to think all this through for yourself rather than relying on what you've been taught.

 

[Farsight]

The hard scientific evidence you have posted so just states that GR is correct, e.g. that the coordinate speed of light varies according to the coordinates used. That is trivial.

See above. That's trivial too. It doesn't matter which coordinates you use, the light in the upper clock gets to the end first. There is nothing you can do to make it get to the end second!

You though deny this by asserting that the speed of light at an event horizon is zero. This is wrong because the speed of light (no "coordinate") is always c.

And at the event horizon c is zero! Hence the gravitational time dilation goes infinite at the event horizon. Take the lower clock down to the event horizon, and this is what you've got:

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If you mean the coordinate speed of light then you have to specifiy the coordinate system that you are using. For example in Schwarzschild coordinates the coordinate speed of light is zero at the event horizon (there is a coordinate singularity there).

And that reflects what we can see with our parallel-mirror light clocks losing synchronisation at different elevations, just like those super-accurate optical clocks.

In Kruskal–Szekeres coordinates the coordinate speed of light is the same everywhere (there is no coordinate singularity at the event horizon).

And that doesn't. It's science fiction, RC. It contradicts the patent evidence. Come on, you could devise an experiment with superhighspeed cameras and watch the two light beams making progress in a misted chamber:

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

You could see the top beam getting to the end first. But KS coordinates are telling you that the coordinate speed of light is the same everywhere? Come on RC, surely you can see the problem?

 

[Farsight]

He made no mention of carbon dating, which would be useless for day-to-day timekeeping. A radioisotope clock could be built by using a Geiger-counter or scintilloscope to detect particles emitted by a radioactive substance with a long half-life. The passage of time would be measured by keeping count of the number of particles detected.

There isn't any actual time passing, Brian. The "passage of time" is just a figure of speech.

And I think you completely missed his point, which I assume was intended to address your assertions about the nature of clocks. A radio-isotope clock would not be covered by your concept of all clocks being based on regular motion.

It still would. Particles like protons and neutrons have spin, an atomic nucleus is composed of a group of protons and neutrons bound by the residual strong force, only some configurations aren't stable. The radio-isotope clock is like you setting up a warehouse full of unbalanced machines that shake themselves apart. They don't all do it at the same instant. You gauge the time by looking at how many are still going.

Why not just use Z₀ =μ₀C₀ or Z₀ = 1/ε₀C₀ instead of making it complicated?

Because μ₀ and ε₀ are related, and because there's a parallel between the mechanics expression v = √(G/ρ) and c = √(1/ε₀μ₀).

ETA: And since you could use these formulae to calculate the speed of light by measuring the impedance of space, this brings us back to DeiRenDopa's question. How do you measure the impedance of space? If you're trying to find the speed of light by measuring the impedance of space, the response "measure the speed of light" is less than helpful.

Sorry Brian, but it's a "triangle", and μ₀ and ε₀ are two sides of the same coin. When you pin c to a constant value of 299,796,458 m/s you pin impedance to a constant value of 376.73031 ohms.

Why would this be relevant for measuring the second? If you were trying to directly determine the length of the metre, sure, but not for measuring time.

It's like the boat example. You can't say how fast the waves are coming at you, and you can't say what their wavelength is, because you haven't defined the second or the metre yet. You count some number of up-and-down bobs and declare that duration to be the second. Then you watch how far a wave moves in some fraction of that duration, and declare that distance to be the metre. Then you can say how fast the waves are moving and what their frequency is.

A wavelength is the distance a photon travels per cycle. We don't care about distance, only how many cycles.

Yes, that's right. We count the cycles to define the second, then we define the metre by watching how far the wave moves and then we can describe the waves as having a wavelength x and a frequency y.

To determine the duration of the second, we ignore the length of the cycles that are passing us, and simply count the number of cycles.

Exactly.

No, we defined our second using the frequency of light. The exact motion or velocity of the beam of light that passed us was irrelevant...

You don't use frequency. You count.

... unless you're suggesting that the frequency of the 21cm hydrogen line varies with the speed of light?

No. When a light wave is emitted it has a given energy. Conservation of energy tells you that it isn't going to change, so the frequency isn't going to change either.

But since this line is the result of photons with a specific energy level interacting with hydrogen, slower light would need a smaller wavelength to get the same level of energy.

That's what's said to happen in refraction. The energy and frequency remains constant, but the wavelength is reduced. But don't apply this to the hydrogen atom, because we're talking about a hyperfine transistion. It's an electromagnetic spin flip, and anything that changes the propagation of light changes this in equal measure.

I assume that if you halved the speed of light, the 21cm line would probably become a 10.5cm line, and there'd be no difference in the time it takes to count the same number of cycles. Can anyone else (except Farsight) tell me if this is correct?

It wouldn't. Work it through. Imagine you're in that bobbing boat, and you define your second and your metre. Then imagine I snap my gedanken fingers and halve the wave speed, also halving the speed of waves in your body and brain so you don't notice directly. You repeat your exercise, and then your second is now twice as big, not that you know it. But your metre is the same.

 

[ben m]

Wow guys, I've just read through to the end of the thread and frankly I'm amazed. You're showing the most awful groupthink here. You still can't see the obvious. Let's try it another way. Let's say we've got two trains on parallel tracks. They start off at the same time, and one reaches the end before the other. Like this:

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Which train is going faster? Easy. The top one.

That's true according to an observer who actually thinks the tracks are the same length, that the starts were simultaneous, and that the finishes happened in the order you specified. You may recall that relativity (even special relativity) allows observers to disagree about lengths (even relative lengths), simulteneity, and sequences of events. Different observers may disagree on all of these issues, and may therefore disagree about which train is faster.