Black holes

[ctamblyn]

Indeed, if there were a reason for strong, weak, and E&M physics to respond differently to gravity, it would imply a violation of the weak equivalence principle. Experimentally speaking, the weak equivalence principle is by far the most-precisely-tested aspect of gravitational physics, and I'm personally acquainted with many of the people who have tested it.

I wonder, what are the current experimental limits on hypothetical violations of the WEP? If you know off-hand of a good article I'd be very grateful for a link .

 

[W.D.Clinger]

Indeed, if there were a reason for strong, weak, and E&M physics to respond differently to gravity, it would imply a violation of the weak equivalence principle. Experimentally speaking, the weak equivalence principle is by far the most-precisely-tested aspect of gravitational physics, and I'm personally acquainted with many of the people who have tested it.

I wonder, what are the current experimental limits on hypothetical violations of the WEP? If you know off-hand of a good article I'd be very grateful for a link .

Here's an article that Farsight's been citing (but apparently hasn't read):

Clifford M. Will. The confrontation between general relativity and experiment. Living Rev. Relativity, 9, (2006), 3. http://www.livingreviews.org/lrr-2006-3 (retrieved today).​

From section 2.1.1:

Many high-precision Eötvös-type experiments have been performed, from the pendulum experiments of Newton, Bessel, and Potter to the classic torsion-balance measurements of Eötvö̈s's [100], Dicke [94], Braginsky [43], and their collaborators....The “Eöt-Wash” experiments carried out at the University of Washington...have reached levels of 3 × 10⁻¹³ [2]. The resulting upper limits on η are summarized in Figure 1...

 

[ctamblyn]

I spotted it immediately. That's why I put it up. I'm good at proofreading. It's to do with the way I'm now very ontological. In the past I'd do some proofreading, and miss something glaringly obvious, like a spelling error or a missing word. When somebody pointed it out to me, I'd say something like How did I miss that!? With training you get better at seeing what's there.

I have no idea what you mean by "ontological" in this context.

Ontological (adj):
1. Of or relating to ontology.
2. Of or relating to essence or the nature of being.
3. Of or relating to the argument for the existence of God holding that the existence of the concept of God entails the existence of God.

(...snip...)

You can imagine what I'm going to say here: the constancy is an artefact of our system of units. I'm not kidding about that. The speed of light is the obvious one of course, but it isn't the only one.

Whether you could look at it that way, or not, we still have a perfectly good model of what goes on in which those quantities are constant. I see no utility in constructing a model in which they vary when there is no need to do so - consider it an application of Occam's Razor if you like.

(Worse still for your position, I have not yet seen you put forward enough detail for us to ascertain whether your model is even equivalent to the existing ones as far as observed phenomena go. However, you made it quite clear that you don't want to provide those details.)

I know. It's a unification thing.

So are you now agreeing that "FGR" (or relativity+, or whatever you want to call it) is not actually equivalent to GR?

OK. But I don't like the thought that it's some kind of mysterious black box.

Agreed.

OK, good.

I'd rather say incomplete myself. Or restricted. It doesn't cover everything. And a principle is a principle rather than a hard and fast rule.

This particular principle (the Einstein equivalence principle) is more than a mere guideline; it is fundamental to GR. If the EEP doesn't hold (if the clocks lose sync) then GR is wrong.

As ever it isn't my model, and look again at what I said - I'm just chucking in a bit of wave nature of matter and a bit of SR parallel-mirror-light-clock to say something that GR doesn't care about.

We'll have to agree to differ on that.

I refer to it as "your" model since I have not seen it anywhere else. Perhaps parts of it here and parts of it there, but not this exact collection of ideas.

And I'm afraid I can't agree to differ, whether you disagree with my premise or the structure of my argument. My premise was just an observation of fact: "GR says that strong-interaction and weak-interaction clocks keep sync with optical ones". The structure of my argument was simply "if X implies Y, then not-Y implies not-X".

I didn't want to make a big deal of it, just give you a hint as to why I'm interested in nuclear clocks v electromagnetic clocks. Again it's a unification thing, beyond GR.

Without, AFAIAA, any experimental support?

Again, it comes back to you being able to see that the speed of light isn't constant. Then you get into the fine structure constant. It's the ratio of the strength of electromagnetic force as compared to the strong force. In addition it's the ratio of the energy required to push two electrons together from infinity to some given distance, as compared to the energy of a photon with a wavelength 2π times that distance. It's often given as α = e²/2ε0hc, where e is the charge of the electron, ε0 is the permittivity of space, h is Planck's constant, and c is the speed of light. And it's a "running" constant. But let's talk about that another time.

This is wrong: the fine structure constant is not the ratio of the e/m force as compared to the strong force. It simply governs the strength of the e/m interaction. The strong force has its own coupling. But this is indeed a topic for another thread - perhaps you could pick up where you left off on your Relativity+ thread? That would be the most suitable place.

Agreed. I was never impressed with the hullabaloo around the OPERA thing.

I'm actually disappointed in some ways, as it would have been exciting had the results been validated. Maybe next time.

Don't kid yourself, ct.

(...snip...)

Regardless, that paper (interesting though it was) certainly didn't support your position. In fact, every paper I have seen so far involving a model similar to the one you suggest in this thread (with the vacuum permittivity and permeability varying through space, as a means of producing gravity) has been inequivalent to GR in some way.

You keep asking this wife-beater question, give it a rest. It's Einstein's GR, you've had the quotes where he was telling you again and again that the speed of light isn't constant. I've told you about the Shapiro delay and the optical clocks losing synchronisation when separated by a vertical foot. And you know that all clock will do this, including parallel-mirror light clocks, like below. The speed of light isn't constant, just like Einstien said, and you can see it. Now stop being cute and get on board 21st Century physics. And if you want to talk about electromagnetism, start a thread - I'm sure Vorpal will appreciate it.

(My highlight - perhaps your proofreading isn't as good as you thought? )

Let's go over what you have offered in this paragraph:

• Einstein quotes - these are not empirical evidence, so don't answer my question.
• Shapiro delay - this is predicted by "MTW" GR, so doesn't answer my question.
• Clocks losing synchronisation - this is predicted by "MTW" GR, so doesn't answer my question.

Again: what do you have that proves "MTW" GR is wrong (while not contradicting FGR)? You still haven't provided anything.

 

[DeiRenDopa]

It's Einstein's GR, you've had the quotes where he was telling you again and again that the speed of light isn't constant.

And we've all read W.D.Clinger's, Vorpal's, sol's, Zig's, ... posts referring to coordinate systems, transforms, etc, all tied back to Einstein's words.

Yet you've said - repeatedly - that that's not "Einstein's GR".

Some of us (I can't speak for every reader) have thought for ourselves, and done our own research (as you never tire of advising all readers to do), and have discovered that where there's a disagreement between what you claim "Einstein says" and what W.D.Clinger, Vorpal, ben m, ... have said, you've been the one who has misunderstood. And some of those misunderstandings of yours have been real howlers.

How to succinctly describe this idiosyncratic, inconsistent, subjective understanding that you have, Farsight, of "Einstein's GR"? An understanding that no one (as far as I know) has ever said they agree with by the way. FGR is good; perhaps FFGR (Farsight's Fantasy GR) might be better.

I've told you about the Shapiro delay and the optical clocks losing synchronisation when separated by a vertical foot. And you know that all clock will do this, including parallel-mirror light clocks, like below.

Care to put some hard numbers on your clocks, Farsight? Here are a few, basic, aspects that I think you should start with:

What is the physical distance between the pairs of mirrors?

By what factor have you slowed time down by?

What is the speed of light in each clock?

What is the vertical separation (physical distance) of the two clocks?

Are the clocks in free-fall? If not, what is their physical environment?

The speed of light isn't constant, just like Einstien said, and you can see it.

You can, no doubt.

But then you can see by farlight.

Care to explain how everyone else in the world can see that "the speed of light isn't constant"?

Oh, and by the way, who is (or was) "Einstien"?

Here's that parallel-mirror clock again:

 

[DeiRenDopa]

My thanks to ben, sol, ctamblyn, and edd: I hadn't realized that there was such an extensive set of objective, independently verifiable material showing how profound Farsight's misunderstanding of physics is.

In all your previous exchanges with him, have you ever come across posts (by him) which clearly show that he understands the quantitative nature of physics?

 

[Hellbound]

In all your previous exchanges with him, have you ever come across posts (by him) which clearly show that he understands the quantitative nature of physics?

I think he has to. How else could he avoid it so rigorously?

 

[ctamblyn]

Here's an article that Farsight's been citing (but apparently hasn't read):

Clifford M. Will. The confrontation between general relativity and experiment. Living Rev. Relativity, 9, (2006), 3. http://www.livingreviews.org/lrr-2006-3 (retrieved today).​

From section 2.1.1:

Thank you, I appreciate that.

----

This reminds me, I never got a reply from Farsight to the following question:

Imagine we do a careful and rigorous series of experiments to test the synchronisation of nuclear and electromagnetic clocks at various altitudes. Now imagine these two possible outcomes: In the first, nuclear clocks are found to consistently lose synchronisation with electromagnetic ones. In the second, nuclear clocks are not found to go out-of-synch with electromagnetic ones.

In one possible future, your confidence in your position is strengthened. In the other, it is weakened.

Which is which?

...Farsight?

 

[ctamblyn]

My thanks to ben, sol, ctamblyn, and edd: I hadn't realized that there was such an extensive set of objective, independently verifiable material showing how profound Farsight's misunderstanding of physics is.

In all your previous exchanges with him, have you ever come across posts (by him) which clearly show that he understands the quantitative nature of physics?

The other discussions were much like this one.

 

[DeiRenDopa]

This reminds me, I never got a reply from Farsight to the following question:

Imagine we do a careful and rigorous series of experiments to test the synchronisation of nuclear and electromagnetic clocks at various altitudes. Now imagine these two possible outcomes: In the first, nuclear clocks are found to consistently lose synchronisation with electromagnetic ones. In the second, nuclear clocks are not found to go out-of-synch with electromagnetic ones.

In one possible future, your confidence in your position is strengthened. In the other, it is weakened.

Which is which?

...Farsight?

Excellent question!

Excellent in many ways, but particularly in that it does not ask Farsight to do any quantitative analysis, and any reply* Farsight gives can be checked, for consistency, against a considerable corpus of his own posts.

* other than a non-reply reply of course. Regular readers will be familiar with this sort of thing; for example, MM often "replied" (or *REPLIED*) in this way ...

 

[Reality Check]

No I wasn't. RealityCheck's "correction" was a false assertion. See for example hyperphysics. You can find this elsewhere, such as here. Its coupling strength relative to the strong force is 1/137.

Yes you were wrong.
My correction on 5th April 2010 (exactly 2 years ago !) was in reply to your obviously wrong "fact"

Originally Posted by Farsight
The fine structure constant tells you the relative strength of the electromagnetic force as compared to the strong force. That's a fact.

The fine structure constant does not tell you the relative strength of the electromagnetic force as compared to the strong force. That's a fact.

The fine structure constant is a coupling constant indicating strength of the electromagnetic field by itself. That's a fact.

It is one of the coupling constants defined for the 4 fources that we know about. That's a fact.

Comparing the fine structure constant to the

• gravitational coupling constant gives an indication of the relative strength of the electromagnetic force as compared to the gravitational force.
• weak coupling constant gives an indication of the relative strength of the electromagnetic force as compared to the weak force.
• strong coupling constant gives an indication of the relative strength of the electromagnetic force as compared to the strong force.

That's a fact.

It is the fine structure constant and the strong coupling constant that "tells you the relative strength of the electromagnetic force as compared to the strong force".

That is what hyperphysics says, Farsight.

But the strong force coupling constant is not actually constant !
It is approximately 1 for energies that we typically see in electromagnetic phenomena. So it is common to state that the relative strengths of the strong and electromagnetic forces is 1/137. This is not the fine structure constant as you asserted 2 years ago.

You do have something right though: Divide 1/137 by 1 and you get 1/137!

 

[ben m]

In fact, every paper I have seen so far involving a model similar to the one you suggest in this thread (with the vacuum permittivity and permeability varying through space, as a means of producing gravity) has been inequivalent to GR in some way.

Yep. In fact, the frame-dragging effect, which Farsight links to approvingly a few posts back, is particularly hard to reconcile with Farsight's sort of scalar-potential speculation.

• Shapiro delay - this is predicted by "MTW" GR, so doesn't answer my question.
• Clocks losing synchronisation - this is predicted by "MTW" GR, so doesn't answer my question.

Again: what do you have that proves "MTW" GR is wrong (while not contradicting FGR)? You still haven't provided anything.

I predict that Farsight will ignore these questions, wait a few pages, and casually cite "clocks lose synchronization" as "experimental confirmation" of FGR. I predict someone will repeat ctamblyn's objection (because it's true) and the same thing will happen again.

 

[sol invictus]

My thanks to ben, sol, ctamblyn, and edd: I hadn't realized that there was such an extensive set of objective, independently verifiable material showing how profound Farsight's misunderstanding of physics is.

In all your previous exchanges with him, have you ever come across posts (by him) which clearly show that he understands the quantitative nature of physics?

Nope.

 

[Farsight]

No it's not. First of all, both alpha and alpha_s are mere *definitions*---when you write down a new field theory, you get to decide how to organize (and name) the constants of that theory. Alpha was introduced, defined, and measured by people who had never heard of the strong force. They defined and measured it purely with reference to E&M quantities---the electron charge, Planck's constant, and the Coulomb constant.

Secondly, you're utterly wrong to say alpha_s = 1.000 000 000 +/- 1, which is what it would need to be to make it "just happen" to fit into a ratio-definition of alpha. Alpha_s is often said to be "of order 1", which basically means only that it's large enough that you can't use it as a perturbation-theory "small parameter". It's been measured to about 1% precision at the Z-pole (alpha_s(MZ) = 0.1184 +/- 0.0007) or 3% at the tau (alpha_s(MT) = 0.330 +/- 0.014) and that extrapolates to "around 1-ish" at "nuclear-ish energies". http://arxiv.org/abs/0908.1135

It's true that because alpha is "around 1", you can divide *anything* by it and get around the same thing. Let's try it!

"c is the ratio of the speed of light to the strength of the strong force."

"Newton's Constant is the ratio of the strength of gravity and the strong force"

"The euro-dollar exchange rate is the strength of European currency, in units of dollars, relative to the strength of the strong force."

Try it, it works for anything.

Don't talk rot, c is the conversion factor between our measure of distance and our measure of time. And look again at that hyperphysics page See where it says 10^-39 for gravity? Gravity is a weak force compared to electromagnetic force, hence you can pick up a paperclip with a little magnet that overcomes the gravity of the entire earth. Honestly ben, your physics knowledge is so scant it's scary.

 

[Farsight]

I have no idea what you mean by "ontological" in this context.

Ontological (adj):
1. Of or relating to ontology.
2. Of or relating to essence or the nature of being.
3. Of or relating to the argument for the existence of God holding that the existence of the concept of God entails the existence of God.

Go read up on it on wikipedia.

"Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology deals with questions concerning what entities exist or can be said to exist, and how such entities can be grouped, related within a hierarchy, and subdivided according to similarities and differences..."

You'll hear me say things like space exists, light exists, and motion exists, but that things like reference frames and light cones are mathematical artefacts.

Whether you could look at it that way, or not, we still have a perfectly good model of what goes on in which those quantities are constant. I see no utility in constructing a model in which they vary when there is no need to do so - consider it an application of Occam's Razor if you like.

Your "perfectly good model" has led you astray when it comes to black holes, and in other respects. Yes, this is an application of Occam's Razor. You can see that the speed of light isn't constant.

(Worse still for your position, I have not yet seen you put forward enough detail for us to ascertain whether your model is even equivalent to the existing ones as far as observed phenomena go. However, you made it quite clear that you don't want to provide those details.)

Here you go avoiding the scientific evidence and what Einstein said again, and pretending that I'm being evasive!

So are you now agreeing that "FGR" (or relativity+, or whatever you want to call it) is not actually equivalent to GR?

Yes, because relativity+ includes elements that GR doesn't cover. Hence the plus sign.

This particular principle (the Einstein equivalence principle) is more than a mere guideline; it is fundamental to GR. If the EEP doesn't hold (if the clocks lose sync) then GR is wrong.

No, it's a principle. The principle of equivalence isn't exact. You can tell the difference between being in an accelerating spaceship and being on a planet. There's a 1/r versus a 1/r² factor that distinguishes the two.

I refer to it as "your" model since I have not seen it anywhere else. Perhaps parts of it here and parts of it there, but not this exact collection of ideas.

OK, but it isn't my model.

And I'm afraid I can't agree to differ, whether you disagree with my premise or the structure of my argument. My premise was just an observation of fact: "GR says that strong-interaction and weak-interaction clocks keep sync with optical ones". The structure of my argument was simply "if X implies Y, then not-Y implies not-X".

GR doesn't say anything about strong interaction. You're reading too much into it.

I didn't want to make a big deal of it, just give you a hint as to why I'm interested in nuclear clocks v electromagnetic clocks. Again it's a unification thing, beyond GR.

Without, AFAIAA, any experimental support?

That's right. That's why I'm interested in the experiment.

This is wrong: the fine structure constant is not the ratio of the e/m force as compared to the strong force. It simply governs the strength of the e/m interaction. The strong force has its own coupling. But this is indeed a topic for another thread - perhaps you could pick up where you left off on your Relativity+ thread? That would be the most suitable place.

No. Let's get this nailed down, and why the strong force is called the strong force, and why the coupling constant is given as 1 whilst for electromagnetism it's given as 1/137 and for gravity it's given as 10^-39.

I'm actually disappointed in some ways, as it would have been exciting had the results been validated. Maybe next time.

I feel sorry for the guys who've resigned, and irritated that the media people who hyped it don't come clean about their part in it.

Regardless, that paper (interesting though it was) certainly didn't support your position. In fact, every paper I have seen so far involving a model similar to the one you suggest in this thread (with the vacuum permittivity and permeability varying through space, as a means of producing gravity) has been inequivalent to GR in some way.

I didn't say it supported my position. I just pointed out a couple of interesting bits to it, that's all.

(My highlight - perhaps your proofreading isn't as good as you thought? )

I missed an s off clocks too. You missed that didn't you? I'm sometimes pushed for time here, and don't subject posts to the same degree of quality control as I might.

Let's go over what you have offered in this paragraph:

• Einstein quotes - these are not empirical evidence, so don't answer my question.
• Shapiro delay - this is predicted by "MTW" GR, so doesn't answer my question.
• Clocks losing synchronisation - this is predicted by "MTW" GR, so doesn't answer my question.

Again: what do you have that proves "MTW" GR is wrong (while not contradicting FGR)? You still haven't provided anything.

You can see that the speed of light isn't constant. Like Einstein said. That's it.

 

[Farsight]

...This reminds me, I never got a reply from Farsight to the following question:

Imagine we do a careful and rigorous series of experiments to test the synchronisation of nuclear and electromagnetic clocks at various altitudes. Now imagine these two possible outcomes: In the first, nuclear clocks are found to consistently lose synchronisation with electromagnetic ones. In the second, nuclear clocks are not found to go out-of-synch with electromagnetic ones. In one possible future, your confidence in your position is strengthened. In the other, it is weakened.

Which is which?

I don't have a position on this, that's why I'm so interested in the experiment. If we find that nuclear clocks aren't in line with electromagnetic clocks, we might assert that "the properties of space" are already altered down in the nucleus, and that changing altitude has less affect there than it does out amongst the electrons. If we find that nuclear clocks are exactly in line with electromagnetic clocks, then when we look at low-energy proton-antiproton annihilation to gamma photons as well, we might assert that the strong interaction is just an "aspect of electromagnetism". You know how electricity and magnetism are sometimes portrayed as being orthogonal? If you have two things that are orthogonal to each another, you can have a third thing that's orthogonal to them both.

I think the right thing to do is to do the experiment and see what happens. Gravitational changes are however very slight, so I wouldn't get too excited about it. IMHO it would be more interesting if we had a black hole handy and could throw something straight in and see if we can detect electron stripping and 511KeV gamma photons etc.

 

[DeiRenDopa]

This may be my last post, concerning FFGR, and in this thread.

This post is aimed at the general lurker, some of whom have posted occasionally here. In this post I'm going to try to explain why it is essentially impossible to have a meaningful dialog with Farsight, on any topic directly related to any aspect of contemporary physics*.

And I'm going to start with a post by Zig:

In fact, any time a poster has to start resorting to "math isn't real", well, that's pretty much a guarantee that the poster is a crank. We see it time and time again, and it usually arises from people who can't even do the math. It's also not what real scientists say when debating a theory. They'll say that the math is wrong (if it is) or the theory is wrong. Or they might say that the theory is untested under some conditions, and its accuracy under those conditions is unknown. That's even defensible in regards to black holes: we haven't actually seen any up close, so we haven't actually tested GR under such strong fields.

But "math isn't real"? That's an argument for losers.

But why is this so?

Why is it impossible - as I claim - to have a meaningful dialog with someone, like Farsight, who does not (and, very likely, cannot) base their ideas on "math"?

For several centuries now - since the time of Newton, perhaps Galileo - physics has been quantitative, and its application (astrophysics, geophysics, etc) built on consistency ... internally, and with all relevant observational and experimental results - I wrote that, some time ago, in another thread, about another topic.

It takes some hard thinking to realize just how profound the quantitative revolution Galileo and Newton ushered in was. It's not just that so many of the things which make our daily lives comfortable and safe would be impossible (to design, build, maintain) without this quantitative revolution, but also that none of the words we use when discussing physics have meaning without it!

We are so used to talking about "electrons", "energy", "gravity", "mass", and so on that we forget that, without the quantitative revolution, these would be just empty words. You don't believe me? OK, try to explain what an "electron" is, without using any of the physics of the last ~500 years.

A corollary: an alternative which purports to be physics-based but lacks a quantitative basis and/or consistency is pseudo-science at best. - from the same post of long ago.

But where does Farsight stand, with regard to the quantitative revolution Galileo and Newton ushered in? W.D.Clinger already read his posts, and provided a very revealing compendium of what Farsight says about math.

Now Farsight has said, many times, that the ideas he's been posting are just Einstein's, and are backed by hard, scientific evidence.

Yes, he's said that, many times. But where's the quantitative meat on these bare bones of his? Well, in the consistency department, several active members have shown that the Einstein words Farsight loves to quote are fully consistent with other words he wrote, especially the paper in which he presented GR. In the quantitative department, even Farsight admits that the experimental and observational results, to date, are fully consistent with GR.

So where's the Farsight beef? I contend that the only place there's any beef is in the non-quantitative, inconsistent parts: only if you ignore "quantitative" is anything Farsight claims consistent; if you accept "inconsistent" then the quantitative parts are OK (sorta like saying, yes, 1+1 does equal 2, but 2+1 equals 99).

Am I being too harsh? After all, Farsight has said "I'm on record as saying mathematics is a vital tool for physics", and "I understand the mathematics, I've given the numbers, and I've supplied rock-solid scientific evidence", hasn't he? Why yes he has said that. He might even believe it. But is it true? If you take his repeated advice - to think for yourself and do your own research - can you find the numbers? find any evidence that Farsight understands the math? explain in your own words how the "rock-solid scientific evidence" Farsight has supplied is consistent - quantitatively - with his claims? I don't think you can.

Myself, I realized that meaningful discussion with Farsight was impossible when I tried to make the lower train explode first, but couldn't. Slowly it dawned on me that Farsight hasn't got a quantitative clue about his belovéd pair of parallel-mirror light clocks.

And if he hasn't got a quantitative clue about that, then there's no basis for having a meaningful, physics-based, discussion with him.

But I'm open minded; if Farsight can show that he does have a quantitative clue, I will gladly eat my hat.

* it may be possible to have such a dialog on peripheral topics, such as philosophy or the history of physics

 

[Farsight]

...Slowly it dawned on me that Farsight hasn't got a quantitative clue about his belovéd pair of parallel-mirror light clocks.

And if he hasn't got a quantitative clue about that, then there's no basis for having a meaningful, physics-based, discussion with him.

But I'm open minded; if Farsight can show that he does have a quantitative clue, I will gladly eat my hat.

Are you for real? Do you really think you can get away with ad-hominems like that when I've already been through this? It's kid's stuff. The expression for a spacetime interval in flat Minkowski spacetime is this:

[latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]

It's related to Pythagoras' theorem, used in the Simple inference of time dilation due to relative velocity. We've got two parallel-mirror light clocks, one in front of us, the other which we've sent on an out-and -back trip. We observe the light moving like this ǁ in the local clock and like this /\ in the moving clock. Treat one side of the angled path as a right-angled triangle and the hypotenuse is the lightpath where c=1 in natural units, the base is the speed v as a fraction of c, and the height gives the Lorentz factor γ = 1/√(1-v²/c²), where we apply a reciprocal to distinguish length contraction from time dilation. So if the moving mirror os going at .99c the Lorentz factor is 1/√(1-0.99²/1²) = 1/√(1-0.98) = 1/√0.2 = 1/0.142 = 7. So there's a sevenfold time dilation. And as I've said previously there's no literal time flowing in these clocks, merely light moving at a uniform rate through the space of the universe, from which we plot straight worldlines through the abstract mathematical space we call Minkowski spacetime. And the underlying reality behind the invariant spacetime interval between the start and end events of our little experiment is that the two light-path lengths are the same. Macroscopic motion comes at the cost of a reduced local rate of motion. Hence the minus in front of the t.

But I'm open minded; if Farsight can show that he does have a quantitative clue, I will gladly eat my hat.

No you won't, you'll just change tack and throw out some other vacuous thread-spoiler ad-hominems, and everybody will see through you. They'll be reminded again that there's no basis for having a meaningful, physics-based, discussion with you.

 

[Farsight]

Here's another post I'm replying to here to avoid hijacking Perpetual Student's thread. Could be that both this thread and that are dead anyway, but nevermind.

First, homogeneity and isotropy of space requires constant curvature, not zero curvature. So this still gives less-than-completely-trival geometry.

There's a huge issue with this. If you have absolutely homogeneous isotropic space, you've thrown away the baby with the bathwater, and you no longer have anything that causes a ray of light to curve. Yes, I've read The Meaning of Relativity. And no, I don't know what happened to Einstein after 1920.

A completely homogeneous gravitational force field just describes normal flat spacetime, since such a field would have no tidal forces, i.e., zero curvature. It's flat spacetime...

And therefore there is no gravitational force. Shine a light beam, it goes straight as a die, and you don't fall down.

Einstein calls g_μν as the gravitational potentials, as he does elsewhere. If that's the potential, what's the force? The Christoffel symbols.

The gradient in the potential. The Christoffel symbols denote the curvature of the gradient, which is a necessary component of a gravitational field. If you didn't have it, the force of gravity wouldn't reduce with distance.

In fact it's almost eerie the extent to which the relationship between
(1) gravitational potential g_μν, Christoffel symbols, geodesic equation
is just like the relationship between
(2) electromagnetic potential A_μ, electromagnetic field F_μν, electromagnetic (Lorentz) force equation.
If one compares them without context, it's almost like someone decided to slap on an extra index and symmetrize.

It's not eerie at all if you know how to look at it. Draw a grid with a bulge at the bottom to represent a photon, the horizontals getting flatter higher up. A_μ is the pressure in the bulge, E is the curvature, B is the is the rate of change of curvature. Take a derivative for D and the sinusoidal electromagnetic waveform, and think of electromagnetism as "curved space".

Now draw another grid, but imagine a zillion overlapping photons spread out along the bottom of it. You end up drawing all-flat horizontals which are further apart at the bottom and closer at the top. You've still got pressure at the bottom, but now you call it g_μν. If a photon moves horizontally across the middle of this grid it veers downwards, and you can plot its path with a curved line and think of gravity as "curved spacetime".

 

[Ziggurat]

Are you for real? Do you really think you can get away with ad-hominems like that when I've already been through this? It's kid's stuff. The expression for a spacetime interval in flat Minkowski spacetime is this:

[latex]$ds^2 = -dt^2 + dx^2 + dy^2 + dz^2$[/latex]

That's one expression for the metric of flat spacetime. Sol gave you another one, which you couldn't handle.

No you won't, you'll just change tack and throw out some other vacuous thread-spoiler ad-hominems, and everybody will see through you. They'll be reminded again that there's no basis for having a meaningful, physics-based, discussion with you.

Who is this "everybody" you keep referring to? Because pretty much all the actual people posting here are on DRD's side, not yours. Unless you did some sort of psychic survey of all the lurkers here, in which case you could qualify for a million dollars.

 

[Dancing David]

Don't talk rot, c is the conversion factor between our measure of distance and our measure of time. And look again at that hyperphysics page See where it says 10^-39 for gravity? Gravity is a weak force compared to electromagnetic force, hence you can pick up a paperclip with a little magnet that overcomes the gravity of the entire earth. Honestly ben, your physics knowledge is so scant it's scary.

And you still don't understand the fire structure constant.