Black holes

[Ziggurat]

How many times do I have to offer the evidence of the Shapiro delay and the optical clocks at different elevations losing synchronisation?

That depends. How many times do I need to inform you that this matches exactly with the predictions of standard textbook GR?

If your evidence agrees with the predictions of standard textbooks, how is it logically possible for this evidence to show that standard textbooks are wrong?

Because the patent evidence tells you that the speed of light isn't constant.

That depends very much on how you define "speed". Which, in turn, is something which depends on....

(wait for it)

... your choice of coordinates!

Forget it Zig. This is a black hole thread, they used to be called frozen stars, the issue is the reality of Kruskal-Szekeres coordinates,

You cannot situate a clock at the event horizon. The only testable predictions we have, if we're not willing to jump in ourselves (and we'd never have a way of reporting back the results if we did) are what a distant observer will see. And using Kruskal coordinates, we will conclude the exact same thing about what a distant observer will see. Zero difference. So how can you dismiss Kruskal coordinates as wrong and Schwarzchild coordinates as right when there is no possible experiment you can do which can distinguish between the two? It's a mathematical impossibility, Farsight. Math itself would have to be wrong.

Which, good luck trying to argue that one.

and you think negative carpets are real.

What's wrong with my "negative carpet"? I've given you a perfectly sensible physical interpretation of the math. It's consistent, it's easy to actually do... so where is your basis for complaint? You just don't like it, but there's nothing unphysical about it.

Meanwhile I'm in the situation I've been in when arguing with young-earth creationists. Show them a fossil and that's not evidence. Show them carbon dating, strata, glaciation, magnetic reversals, and that's not evidence either. And then they come out with cargo-cult science, and nobody has the honesty to put them straight. Wince. Time to call it a day.

Sure, Farsight, sure. That's the perfect description of what's going on: the entire field of general relativity has been taken over by your earth creationists, and you've got piles and piles of evidence which prove them all wrong.

Except that your "evidence" actually agrees with everything they say.

Pickle bugs are real! I swear it!

 

[edd]

How many times do I have to offer the evidence of the Shapiro delay and the optical clocks at different elevations losing synchronisation? How many times do I have to show you the parallel-mirror light clocks and say that the vertical light beam doesn't bend, doesn't slow down, and doesn't fall back. So it has to have a zero speed, that's the reality underlying infinite gravitational time dilation, ergo the Schwarzschild "coordinate singularity" should not be ignored. A stopped clock doesn't start ticking because you put a stopped observer in front of it.

I don't think we're talking about putting a stopped observer in front of it. If we tried to hold an observer stationary at the event horizon then we might be in agreement, but I thought we were arguing about the state of an infalling observer?

I could observe a clock moving at a speed tending toward c and not see it tick but that doesn't mean my wristwatch has stopped, and similarly just because an 'outbound' lightray at a black hole doesn't tick doesn't mean my wristwatch has stopped as I fall in freely.

Neither does the fact you don't see my wristwatch tick mean that it's taking a long time to actually do so, any more than if I start travelling from here (not so far from you at all) to Australia (by some appropriately slow land-and-sea transport) and send daily postcards back to you in Poole and their arrival times change from daily to much longer mean that my days are getting longer in length as I travel across the globe.

 

[sol invictus]

I've described it in ample detail. It's two parallel-mirror light-clocks at different elevations, held flat. They don't stay synchronised. There's no time flowing between the mirrors, just light moving.

OK. Then I agree that a reasonable and consisten interpretation is that the speed of light is different. Another reasonable and consistent interpretation is that the speed of light is the same, but the lower mirror is accelerating up at a faster rate than the one above. Therefore, light has farther to travel between bounces. There are infinitely many more reasonable and consistent explanations.

And you still won't say what it represents. I've already said that if the spacetime is flat the speed of light is uniform. It isn't like the black hole situation.

I've already told you, three times now: flat, empty space. Nevertheless, you've asserted (correctly) that light clocks held close to r=r0 run slower than those at larger r. And yet, this is flat spacetime, and you've asserted that means the speed of light is uniform. So you have a problem. A big one.

You still won't say what [latex]$ds^2 = -(r-r_0) dt^2 + dr^2/(r-r_0) + dy^2 + dz^2$[/latex] represents. Again, what's the problem?

Flat, empty spacetime.

 

[ben m]

No. The evidence of optical clocks running at different rates at different heights tells you the speed of light isn't constant. They're optical clocks. Light moves in them. You can simplify them to parallel-mirror light clocks. Where the light moves slower the clock goes slower. There is no time flowing through those clocks.

Noooo. No. No? Farsight, I meant what I said. "Optical clocks run at different speeds at different heights" is a standard GR prediction. (Similarly, optical clocks run at different speeds if they are moving at different speeds.) Different observers will disagree on the separation of the mirrors, not on the local speed of light.

When I said "This is derived in section 38.5 of MTW", that's what I meant. Let me say it again. Gravitational redshift of, including optical clocks, is a standard prediction of standard general relativity. You thought otherwise? Too bad for you, you were wrong. It's right here in front of me.

ETA: If you had some actual complaint about it --- "Yes, I know that derivation, and it doesn't apply because X" --- but you don't even own a GR textbook. You've been guessing that the derivation doesn't exist, apparently because you don't want it to exist, because you're so certain you've found an error in GR.

The point of the derivation, by the way, is a recurring problem with your mythical "optical clock". If I see a distant pair-of-mirrors, and I see that it takes light 1.00 nanoseconds to complete one round-trip, I don't conclude "Hey, light is slow over there". I conclude "Those mirrors are 15cm apart". If I look somewhere else, and I see two other mirrors where light takes 10 nanoseconds roundtrip, I say "Those mirrors are 1.5 meters apart". Other observers, in other regions of space (or with motion relative to me and/or the mirrors) will disagree with me about these lengths, because they disagree with me about the time, which is (as perhaps you've heard) a common and uncontroversial aspect of relativity.

 

[Farsight]

You're inadvertently attributing the words of Ziggurat to sol invictus. I'm sure it's unintentional (given you refer to Zig in the last bit) but you might want to change it if it's not too late.

Sorry, my mistake. Too late, I can't edit it now.

 

[Farsight]

That depends. How many times do I need to inform you that this matches exactly with the predictions of standard textbook GR?

It doesn't match the description of a black hole provided by KS coordinates, or the associated advice that (given a suitably large black hole with negligible tidal force) that "the infalling observer notices nothing unusual". Or the waterfall analogy. That's what this whole discussion has been about.

If your evidence agrees with the predictions of standard textbooks, how is it logically possible for this evidence to show that standard textbooks are wrong?

It doesn't.

That depends very much on how you define "speed". Which, in turn, is something which depends on....

(wait for it)

... your choice of coordinates!

Speed is how fast something is moving. Even without choosing any coordinates or defining any units, one can point to the scientific evidence of optical clocks and parallel-mirror light clocks and say that one thing is moving faster than another. Your choice of coordinates does not alter this relationship, you cannot contrive gravitational time dilation to make the upper clock tick faster than the lower. Light does not curve away from a star, it curves towards it.

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You cannot situate a clock at the event horizon. The only testable predictions we have, if we're not willing to jump in ourselves (and we'd never have a way of reporting back the results if we did) are what a distant observer will see. And using Kruskal coordinates, we will conclude the exact same thing about what a distant observer will see. Zero difference. So how can you dismiss Kruskal coordinates as wrong and Schwarzchild coordinates as right when there is no possible experiment you can do which can distinguish between the two? It's a mathematical impossibility, Farsight. Math itself would have to be wrong.

Kruskal-Szekeres coordinates contradict the scientific evidence. Hence they're a fallacy. The maths isn't wrong as such, but it offers a non-real solution, like the negative carpet.

What's wrong with my "negative carpet"? I've given you a perfectly sensible physical interpretation of the math. It's consistent, it's easy to actually do... so where is your basis for complaint? You just don't like it, but there's nothing unphysical about it.

A square carpet can measure 4m by 4m. That 4m is a length, there is no such thing as a negative length. A length of -4m isn't something that exists in the real world. You can start with a 4m x 4m carpet and reduce the length of each side just as you can reduce the speed of light with gravitational potential, but when you get to zero, you can't reduce it any further. That's the end. KS coordinates ignore this limit.

Sure, Farsight, sure. That's the perfect description of what's going on: the entire field of general relativity has been taken over by your earth creationists, and you've got piles and piles of evidence which prove them all wrong.

Not the entire field, just the current "mainstream" who insist that the speed of light is absolutely constant. It directly contradicts Einstein, and the scientific evidence. See arXiv for some papers and to appreciate that what's called "VSL" is gaining ground.

Except that your "evidence" actually agrees with everything they say. Pickle bugs are real! I swear it!

Let's wrap it up, Zig.

 

[Farsight]

I don't think we're talking about putting a stopped observer in front of it. If we tried to hold an observer stationary at the event horizon then we might be in agreement, but I thought we were arguing about the state of an infalling observer?

We need to establish the situation for light at the event horizon first, and establish why a vertical outward beam, which doesn't slow down or bend round or fall back, can't get out. If you agree it's because the speed of light at that location is zero, you then understand that it can't go that any lower, so there's no further gradient in gravitational potential. And since light can't propagate at that location, and since the infalling observer can't go faster than light, he's stopped falling. Sadly we haven't got past step one with this the original "frozen star" black hole interpretation.

I could observe a clock moving at a speed tending toward c and not see it tick but that doesn't mean my wristwatch has stopped, and similarly just because an 'outbound' lightray at a black hole doesn't tick doesn't mean my wristwatch has stopped as I fall in freely.

If you were moving at a speed tending toward c with respect to say the CMB frame, all observers in the universe at large will agree that your wristwatch has tended to stopped. The principle of equivalence then relates this to the black hole situation. You might like to claim that your wristwatch hasn't stopped, but you can't, you're sitting there frozen whilst everybody talks about you.

Neither does the fact you don't see my wristwatch tick mean that it's taking a long time to actually do so, any more than if I start travelling from here (not so far from you at all) to Australia (by some appropriately slow land-and-sea transport) and send daily postcards back to you in Poole and their arrival times change from daily to much longer mean that my days are getting longer in length as I travel across the globe.

Imagine your wristwatch is a parallel-mirror light clock. If you were moving at c, it never ticks. It can't tick, because for it to do so light would have to be moving faster than c. Ergo time dilation is infinite. You're a blind frozen popsicle sweeping through the universe. At the event horizon, gravitational time dilation is similarly infinite. Your clock just doesn't tick. It's stopped. So have you. Kruskal-Szekeres coordinates sweep this under the carpet, and suggest that for you everything carries on as normal. It's a "mathematical sleight of hand" that leads to the wrong picture of what a black hole really is.

Sorry, I have to go, and like I've said, I don't think there's much more mileage in this thread. I hope nevertheless that some of you have gained some benefit from this discussion. Sadly IMHO there aren't enough hard physics conversations on a site like JREF. Such is life.

 

[ctamblyn]

I said in one reply that the permittivity and permeability of space are two aspects of the nature of space, where the best word I could find was "strength". Maybe an analogy will help. Imagine you're holding a spring steel bar. Think of permittivity a "how easy it is to bend it". Think of permeability as "how hard it springs back". Space is the way that it is, it sustains waves and fields. I can't alter the nature of it by changing only one side of the coin. If, say, I replaced your steel bar with a lead bar, it doesn't spring back. That means waves won't propagate through it. So by throwing away the permeability I've lost c too.

I'm pushed for time, but please don't hesitate to point out any post that you feel I haven't addressed.

OK, I won't hesitate. Let's start with the very post you replied to here.

My first question was:

First, it is a fact (that anyone can verify) that "MTW"-style black holes are valid solutions of the mathematical model we've been calling "MTW" GR. On the other hand, you assert (without details) that this is incompatible with FGR, which advocates a frozen star picture. I'm going to anticipate the answer to ben m's question above, and say that there is no available evidence which favours FGR over "MTW" GR on this issue. In fact I will go further and bet that there is no empirical evidence whatsoever that favours FGR over "MTW" GR (feel free to prove me wrong). Given that, on what rational basis are you actually rejecting the one and embracing the other?

(Emphasis added.)

Your response was:

I keep showing you how the speed of light really does vary with position, like Einstein said. And I've given lots of details. Pay careful attention to my conversation with Brian about the NIST clock and how we define the second.

That I can see that the speed of light varies with gravitational potential:

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These two light beams are not going at the same speed.

As you requested, I won't hesitate to point out that you have completely evaded my first question. You did not provide any evidence which favours FGR over "MTW" GR, and you did not explain what the rational reasons for your preference are.

My second question was:

Second, the "details" issue. You claim that FGR can be understood in terms of vacuum permittivity and permeability varying through space. You further claim that the predictions of FGR are in accord with the predictions of "MTW" GR when it comes to the classical tests of general relativity, but disagree in some other areas (e.g. black hole interiors and Hawking radiation). However, you have not given us any details; you have not shown us any quantitative laws. You are just asking us to take your word for it.
Indeed, in light of the demonstrated inequivalence of certain other similar-sounding models to GR there is every reason for a good skeptic to assign a very low prior probability to the truth of your claims. Given the lack of detail you have provided there is no way to know if they are even self-consistent.

(Emphasis added.)

To which you replied:

I'm asking you to look at the evidence and think for yourself.

Whoa. I'm the skeptic here. Not you.

So, I explain my reasons for disbelieving you - namely, that you have still not provided sufficient evidence to favour your model over standard, modern GR, and you have not even provided sufficient detail to determine whether your model is self-consistent - and you say that somehow that makes me non-skeptical. I ask you for details that would help me evaluate your model correctly, and you decline.

You did not provide the quantitative laws that determine how the permittivity and permeability are affected by the distribution of matter and energy, and likewise how matter and energy move in response to variations in permittivity and permeability. You did not give us the field equations of FGR, or the equations of motion. You did not provide a proof that FGR reproduces the results of "MTW" GR as far as the classical tests are concerned. Nor did you did provide any details whatsoever.

Please, put your mathematical model where your mouth is, and stop expecting us to be so gullible as to simply take your word for it.

 

[ctamblyn]

Yep. Farsight isn't just making the claim "I've thought of something and convinced myself I'm right". He's making the claim "I've thought about something. It's something which other people have also thought about, and their thoughts (backed up by detailed math) explicitly contradict mine, and I can't explain why, but you should believe me."

Imagine someone walking into a casino with such a claim.

• F: "I've got a betting system that will beat the roulette wheel."
• G: "What, is this the Martingale again? It doesn't work."
• F: "No, it's not what *you* think of as Martingale. It's the original uncorrupted Martingale."
• G: "Whatever it is, there's a generic problem with all such betting systems. One can prove that the game is a Markov process with <etc>."
• F: "That proof doesn't apply to my system. Next."
• G: "Why not? An error in the proof, or the premises?"
• F: "Either one. My system is that you double your bet on losses."
• G: "Yep, that's a Martingale. Here is the particular proof that Martingale loses. Here is the general proof in which Martingale is a special case."
• F: "Nope, it's not a Martingale. If none of you have any intelligent responses I will leave."
• G: "If it were not a Martingale, it would fail the general proof anyway."
• F: "It doesn't. Look here: I double the bet on losses. When you win it adds up to cover."
• G: "You're like the 1000th person to have convinced himself that Martingale can beat roulette. Your infinite-series of doublings ignores the finite bank. If you do something different, show your analysis."
• F: "Argument from authority. Ignored."
• G: "I said: what did you compute differently? Can you show your actual statistical analysis?"
• F: "Anyone have an argument? No? Anyone intelligent here?"
• G: "Analysis?"
• F: "I'm not a mathematician. I've thought about it logically and it works out. "

• F: "Don't try and hide behind obscure mathematics and fancy-sounding words. I'm showing you the physical evidence here!"
• G: "So, where are all your winnings?"
• *crickets*

 

[sol invictus]

Sadly we haven't got past step one with this the original "frozen star" black hole interpretation.

That's because, for one thing, exactly the same "logic" you are applying to black hole horizons applies equally well to Rindler horizons - but we know for certain that nothing out of the ordinary can happen at a Rindler horizon.

Imagine your wristwatch is a parallel-mirror light clock. If you were moving at c, it never ticks. It can't tick, because for it to do so light would have to be moving faster than c. Ergo time dilation is infinite. You're a blind frozen popsicle sweeping through the universe. At the event horizon, gravitational time dilation is similarly infinite. Your clock just doesn't tick. It's stopped. So have you.

And yet, all of that holds true at Rindler horizons.

Kruskal-Szekeres coordinates sweep this under the carpet, and suggest that for you everything carries on as normal. It's a "mathematical sleight of hand" that leads to the wrong picture of what a black hole really is.

And yet, the precise analogue of Kruskal coordinates for the Rindler horizon are simply the standard Minkowski coordinates.

Sorry, I have to go, and like I've said, I don't think there's much more mileage in this thread. I hope nevertheless that some of you have gained some benefit from this discussion. Sadly IMHO there aren't enough hard physics conversations on a site like JREF. Such is life.

In other words, you're "doing a runner".

 

[Reality Check]

It doesn't match the description of a black hole provided by KS coordinates, or the associated advice that (given a suitably large black hole with negligible tidal force) that "the infalling observer notices nothing unusual". Or the waterfall analogy. That's what this whole discussion has been about.

That is a bit dumb because the Shapiro delay and the optical clocks at different elevations losing synchronisation do not involve a black hole.
They are effects predicted from standard GR (not whatever your fantasy of GR is) and observed to match those predictions.

The "descriptions" of a black hole provided by KS coordinates and the description of a black hole provided by S coordinates are different baccarat the KS and S coordinates are different.
As Einstein stated: "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)."
That is not a specific solution of GR in an arbitary set of coordinates. The KS an S solutions are not "laws of nature". They are what is measured in those coordinated.

The actual description of a black hole is derived from the equations of GR.

 

[ctamblyn]

Sorry, I have to go, and like I've said, I don't think there's much more mileage in this thread. I hope nevertheless that some of you have gained some benefit from this discussion.
(...snip...)

There's no more mileage in this particular sub-topic of the thread.

What I have learned from this is that your position on "details" has apparently not changed since about two years ago. I have learned that you have no mathematical model (and therefore no quantitative predictions), but are somehow able to believe that FGR is superior to "MTW" GR (which makes excellent quantitative predictions). And let's not forget the most important thing I learned - I'm a hopeless non-skeptic for doubting you!

 

[ben m]

What I have learned from this is that your position on "details" has apparently not changed since about two years ago.

Two years ago? That's nothing, Farsight's view hasn't changed since at least 2008.

The funny thing about 2008? It's about 4 years ago. An 18-year-old high school graduate could have entered college in 2008, learned vector calculus, learned mechanics, learned differential equations, learned special relativity, learned differential geometry, learned general relativity, and (preparing to graduate in a few months) actually become a physicist. (And, simultaneously: learned a language, learned critical theory, played Ultimate, worked nights and weekends, took summers off, etc..)

I wonder how many times, over those same four years, Farsight said "don't demand that I do the math, I'm not a physicist"? If he had spent those four years becoming a physicist he'd be sitting here *calculating* whether or not GR predicts altitude-based clock disagreements, not guessing wildly that it doesn't.

 

[Ziggurat]

It doesn't match the description of a black hole provided by KS coordinates

Yes it does. You are simply wrong to claim that it doesn't. In fact, it's rather trivial to see on a plot that a distant observer staying at a fixed radius in Scharzchild coordinates, when transformed into Kruskal coordinates, will still see exactly the same redshifted signal from an infalling object. It's trivial to prove this mathematically as well: not only do the coordinates transform reversibly from one reference frame to the other, but the metrics will give the same distances for all curves. So we're guaranteed to calculate the exact same properties for EVERYTHING except where quantities are not defined in one coordinate or the other. But since that only happens at the event horizon in Schwarzchild coordinates, and since even by your own admission we can't see what happens there, it is literally impossible for there to be any disagreement for what a distant observer will observe, whether we calculate that with Kruskal coordinates or Schwarzchild coordinates.

Kruskal-Szekeres coordinates contradict the scientific evidence.

No, they don't. You have made an assertion about Kruskal coordinates which is simply wrong. Your understanding of Kruskal coordinates is therefore wrong as well (assuming that you're not just a liar).

A square carpet can measure 4m by 4m. That 4m is a length

No, Farsight. It's a displacement. That's how you know it's a square: there are two orthogonal displacements. If all you had was two lengths, well, two lengths don't make a square.

Let's wrap it up, Zig.

There's nothing to wrap up except your own misconceptions.

 

[sol invictus]

Kruskal-Szekeres coordinates contradict the scientific evidence. Hence they're a fallacy.

I missed that until Zig quoted it. That's flat-out totally wrong.

There is absolutely no scientific evidence that "contradicts" Kruskal coordinates. Kruskal coordinates make precisely the same predictions for every physical experiment that Schwarzschild coordinates do, including the fact that light clocks near the horizon run slow compared to those far from it.

 

[ctamblyn]

Two years ago? That's nothing, Farsight's view hasn't changed since at least 2008.

The funny thing about 2008? It's about 4 years ago. An 18-year-old high school graduate could have entered college in 2008, learned vector calculus, learned mechanics, learned differential equations, learned special relativity, learned differential geometry, learned general relativity, and (preparing to graduate in a few months) actually become a physicist. (And, simultaneously: learned a language, learned critical theory, played Ultimate, worked nights and weekends, took summers off, etc..)

I wonder how many times, over those same four years, Farsight said "don't demand that I do the math, I'm not a physicist"? If he had spent those four years becoming a physicist he'd be sitting here *calculating* whether or not GR predicts altitude-based clock disagreements, not guessing wildly that it doesn't.

Perhaps he had different priorities, such as writing and promoting his book.

But you are right, and he could have been writing and publishing papers in credible journals instead.

---

(ETA: It seems this goes back to at least 2006. Note the last sentence of the opening post .)

 

[W.D.Clinger]

There is absolutely no scientific evidence that "contradicts" Kruskal coordinates. Kruskal coordinates make precisely the same predictions for every physical experiment that Schwarzschild coordinates do, including the fact that light clocks near the horizon run slow compared to those far from it.

Yes, and the proof of that is a straightforward calculation, similar to the proofs of exercise 20 and exercise 25.

The funny thing about 2008? It's about 4 years ago. An 18-year-old high school graduate could have entered college in 2008, learned vector calculus, learned mechanics, learned differential equations, learned special relativity, learned differential geometry, learned general relativity, and (preparing to graduate in a few months) actually become a physicist.

That would have involved homework exercises.

In fairness to Farsight, he may have been supporting a family during those years, and not had enough free time to learn all that math or physics. Anti-physics is a less demanding hobby than physics.

Following up on one of DeiRenDopa's questions:

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)?

Yesterday, in a bookstore, I stumbled across this book:

Antoni A Kosinski. Differential Manifolds. Dover, 2007.​

It's basically a reprint of Kosinski's 1993 book, with a new appendix that discusses Perelman's proof of the Poincaré conjecture. Although the book covers only Riemannian (and not pseudo-Riemannian) manifolds, the "Historical Remarks" at the end of chapter 2 shed light on DeiRenDopa's question above.

Up to the time of B. Riemann manifolds thus appear only as curves or surfaces in R³. While Riemann is generally credited with the idea of an abstract n-dimensional manifold, what actually appears in [R] is what we would call one chart with a metric given by a linear element ds²....

The "modern" definition of a differentiable manifold appears for the first time in the 1895 paper of H. Poincaré [P1]. Manifolds are still submanifolds of Rⁿ, but all necessary elements are present: The definition is by overlapping charts and the condition on the rank of the Jacobian is stated explicitly...

By 1916, Einstein's "absolute differential calculus" had advanced 20 years beyond Poincaré's "modern" definition of a differentiable manifold.

Kosinski continues:

....The first intrinsic definition of a manifold---that is, not as a submanifold of anything else---appeared, in a rather awkward form as a set of axioms, in the work of O. Veblen and J.H.C. Whitehead ([VW]) in 1931.

In my opinion, that's giving Einstein too little credit. In Einstein's 1916 paper, it looks to me as though the spacetime manifold is already intrinsic.

Einstein does appear to be working within the domain of a single chart, but I can't tell whether he's doing that because he's writing a tutorial introduction to general relativity, or because he thinks all physically plausible spacetime manifolds can be covered by a single chart, or because he doesn't know any better.

Note well that assuming all of spacetime can be covered by a single chart is not at all the same as assuming a single chart. Sections 5 and 6 of Einstein's paper are all about coordinate transformations (from one chart to another, which are implicitly assumed to share the same domain), and the rest of part B is related to coordinate transformations.

When Farsight denies the validity of coordinate transformations (as he did above, and has been doing for years), he's arguing with The Foundation of the General Theory of Relativity by Albert Einstein.

 

[DeiRenDopa]

That is the first post in which I proposed some Gedankenexperiments.

Here's an updated proposal.

A small team of JREF members is going diving. Into a carefully constructed tank. Actually, a whole lot of identical tanks.

Each tank has a ruler on the inside of one of its vertical sides, with the surface marked as zero. Each tank is filled with pure water, held at a constant temperature.

Each diving team carries a suite of pressure gauges, each of which operates via physical processes that differ in at least one respect from all the other gauges. For example, one such gauge works by detecting phase changes in chemically pure substances, another by the deflection of a membrane (vacuum one side, water the other). Each team also has a chem lab and a thermometer, to check the composition and temperature of the medium (water).

Accompanying each JREF team is two teams of observers. One - the Observer A team (OAT, for short) - is equipped with appropriate recording devices, so there is an objective, independently verifiable, record of the experimental results. OAT also broadcasts their records, in real time, to the whole universe; their broadcast is a 'multi-messenger' one: the signal is encoded onto streams of photons (of several different wavelengths), also onto streams of neutrinos, OAT sends out little USB-key-like packets, etc.

The B Observer team (BOT, for short) is also equipped with appropriate recording devices and 'multi-messenger telescopes'. You see, BOT observes all the other JREF diving teams! I.e. they look, very closely, at how the experiments are carried out, sorta like taking a video of what's happening, from afar. BOT also detects the outputs from the OATs (other than their own team's OAT). The purpose is, as you might guess, to be able to compare and contrast the records of the experiments - their conduct and their outputs - as perceived by the locals (the OATs) and the remotes (the BOTs).

The diving teams set up their tanks in many locations: at various places on the solid surface of the Earth, deep in mines dug into that solid surface, on tall towers built above it; ditto on the surfaces of other solar system bodies, etc. (We are all living in the far future! )

For the next series of experiments, the teams travel the world each with a gravimeter, an altimeter, and our usual cast of observer teams. Again, this being the far future, we are able to conduct our experiments on, and above, the surfaces of many solar system bodies.

At the end of the experiments, everyone gathers together in a nice, comfortable resort. We all pitch in to analyze the data (which includes all the OATs' and BOTs' records). Our aim is to produce a succinct set of rules, which we call "laws" (and which all members of all teams agree on), which compactly summarize all the experimental results. These laws might, for example, include a formula relating depth to pressure, temperature, altitude, and g. The laws will also, explicitly, contain statements concerning any differences in laws derived by analyzing data obtained locally with those derived by analyzing data obtained by observing remotely.

With me so far? Any questions or comments?

For the next set of experiments each JREF team carries with it a standard clock, a standard ruler (i.e. devices which measure time and length, per the SI definitions), and a parallel-mirror light clock. They also have pressure gauges, thermometers, gravimeters, ... This time each team has some friends along, each of whom has their own clock, and each clock is of a different kind; one has a grandfather clock, another a quartz crystal clock, a third an optical clock, a fourth a radioisotope clock, a fifth a SAW (Surface Acoustic Wave) clock, a sixth a tuning fork clock, a ... Oh, and our usual retinue of OATs and BOTs.

A critically important set of members of each experimental team are friends of Farsight (FoF). They are thoroughly conversant with the Farsight method of measuring the (local) speed of light using distant pulsars, and with the Farsight method of measuring the (local) impedance of space*. Of course, the OATs record the work of the FoF, and the BOTs record that work too, remotely, as well as recording what they receive from the OATs.

The teams visit all the places previously visited in 'gravimeter experiments'. This being the very far future, there are teams which go to environments considerably more extreme than any visited previously, like near the photosphere of the Sun, in deep space, just above the surface of a white dwarf star, ditto of a neutron star.

As before, everyone gets together afterwards, at a (different) comfortable resort, analyzes the data, and agrees on a set of laws which succinctly describe/account for all that data.

With me so far? Any questions or comments?

* Note: we do not - yet - know what these methods are

In the last two days, Farsight has posted some 26 posts to this thread.

None of them directly quote any of mine.

Over the weekend, however, he did post a couple which are at least somewhat relevant to my posts, and which no one has yet addressed in a way that I would.

Anyway, I thought I'd start with this post, and propose a couple of things I'm pretty sure Farsight is in full agreement with.

When everyone gets together, they discover that the BOTs' records of the experiments matches exactly the OATs', in that the readings on the dials and printouts are the same, whether observed up-close-and-personal or remotely.

This has huge implications!

It means, for example, that if we can - somehow - be confident that we are seeing a local 'instrument' from afar, then the readings on that instrument's 'dial' are accurate (etc) records of the local pressure, temperature, etc. More on this later.

At this stage, I don't think we can be very confident that the various teams will agree, unanimously, that 'the local laws of physics' are the same, everywhere (and everywhen) they went. But here the good news is that I cannot see even a hint - from the contents of his posts - that Farsight would object to this conclusion.

Next: a closer look at Farsight's 'pulsar clock'.

 

[Brian-M]

I know it's futile to continue arguing, it's hard to resist...

But we don't. What we say is that the second is "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom". Cycles aren't used in the definition. You don't use cycles per second to define the second.

From Wikipedia:

The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency.
​

So period is synonymous with cycle, and is equal to 1/frequency.

But you're right, we don't use cycles per second to define the second. We just use cycles (or periods). However, if one second is defined as X cycles of radiation Y, then radiation Y must, by definition, have a frequency of X cycles per second.

No, you're defining the second, then after you've defined the second, you can ascribe a frequency to the radiation.

By your logic we can say:

S = XY​

But we can't say:

1/Y = X/S​

Until we know S?

(Where X is an arbitrary number, Y is the period of the reference signal, and S is our definition of seconds.)

Are you seriously arguing that we can't take S=XY and conclude that 1/Y=X/S until after we determine the value of S?

Frequency is 1/Y.

You and I will. But the people on spaceship A will see clocks on spaceship B going slower than their own, and the people on spaceship B will see clocks on spaceship A going slower than their own. That's a bit like two distant observers each seeing the other as smaller than themself.

No. That's a result of a different scenario, one where distance is accumulating between the ships. A commonly presented scenario, but not the scenario I described.

The people on each spaceship get a single glimpse of each-other's clocks each time they pass each-other, always from the same distance apart (just as people looking at each-other's clocks at different elevations on earth would always be the same distance apart).

The people on the slow ship will see that less time has elapsed on the fast ship than their own since they last passed, while the people on the fast ship will see that more time has elapsed on the slow ship than their own since the last time they passed each-other.

Clock rate is a function of gravitational potential. The "force" of gravity is a function of the local slope in gravitational potential. There's no force of gravity in a gedanken void at the centre of the earth, but that's where gravitational potential is lowest and clocks go slowest.

Firstly, gravitational potential is a negative value, so gravitational potential will be higher in the center of the earth than on the surface.

Secondly, there may be no gravitational potential, but there's lots of gravity in the center of the earth (pulling in opposing directions, so there's no net force). Wouldn't it make more sense to say that where gravity is strongest, clocks go slowest?

Thirdly, an object infinitely distant from the earth would have a gravitational potential of zero, the same potential you say the clock in the center of the earth would have. Assuming that the earth and the clocks were the only masses in the universe, would you argue that a clock in the center of the earth would tick at the same speed as a clock infinitely distant from the earth?

I'm afraid it isn't, not really. It's only "locally constant" in an infinitesimal region, which is a region of zero size. If there was some place in the room you're in where the speed of light was constant, light would go in a perfectly straight line and things wouldn't fall down.

Let's assume that the gravitational field is constant with height.

Maybe because the difference is infinitesimal (because we're doing our experiments on a planet with the density of a sack of ping-pong balls, but big enough that it's surface gravity much higher than that of Earth).

But if you want it perfectly constant, then we're doing our experiments in a spaceship undergoing constant acceleration. Or are you claiming the equivalence principle (which states that the gravitational force experienced while standing on a planet is exactly the same force experienced while accelerating) is also false?

 

[Brian-M]

Yep. Farsight isn't just making the claim "I've thought of something and convinced myself I'm right". He's making the claim "I've thought about something. It's something which other people have also thought about, and their thoughts (backed up by detailed math) explicitly contradict mine, and I can't explain why, but you should believe me."

Imagine someone walking into a casino with such a claim.

• F: "I've got a betting system that will beat the roulette wheel."
• G: "What, is this the Martingale again? It doesn't work."
• F: "No, it's not what *you* think of as Martingale. It's the original uncorrupted Martingale."
• G: "Whatever it is, there's a generic problem with all such betting systems. One can prove that the game is a Markov process with <etc>."
• F: "That proof doesn't apply to my system. Next."
• G: "Why not? An error in the proof, or the premises?"
• F: "Either one. My system is that you double your bet on losses."
• G: "Yep, that's a Martingale. Here is the particular proof that Martingale loses. Here is the general proof in which Martingale is a special case."
• F: "Nope, it's not a Martingale. If none of you have any intelligent responses I will leave."
• G: "If it were not a Martingale, it would fail the general proof anyway."
• F: "It doesn't. Look here: I double the bet on losses. When you win it adds up to cover."
• G: "You're like the 1000th person to have convinced himself that Martingale can beat roulette. Your infinite-series of doublings ignores the finite bank. If you do something different, show your analysis."
• F: "Argument from authority. Ignored."
• G: "I said: what did you compute differently? Can you show your actual statistical analysis?"
• F: "Anyone have an argument? No? Anyone intelligent here?"
• G: "Analysis?"
• F: "I'm not a mathematician. I've thought about it logically and it works out. "

• F: "Don't try and hide behind obscure mathematics and fancy-sounding words. I'm showing you the physical evidence here!"
• G: "So, where are all your winnings?"

• Gambling isn't allowed in my state, and it's not practical for me to travel right now. But I'm sure my system works. There's no way it could be flawed.