At Rest with our Hubble view

[Cheezle]

Farsight, I did not feel the need to further address it because przyk, brucep and others have offered explanations that I like. My time here on sciforums has given me some personal insight into which users have informed opinions and which do not. I am not very educated in the subject and so I defer to these other people. Your ideas conflict with (a guesstimate) virtually all experts in the field. That tells me everything I really need to know. And before you retort with the old saw about 'appeal to authority being a logical fallacy.' It is all I really have to form an opinion with at this time. I know the standard line you alternative types use, about how for science to progress it has to accept new ideas. But your ideas don't seem to be cutting the muster. Just an observation.

Perhaps in a year or so I will have learned enough to form my own informed explanation. Who knows, maybe I will agree with your ideas at that time. But I actually hope that will not happen. I have seen cranks take their ideas too seriously and waste their lives on an unproductive pursuit. I used to watch videos on youtube by a guy who had a TOE. A unification of all the stuff that needs to be unified. He struggled with acceptance for a longtime. Finally he discovered his error and retracted his ideas. I thought that was very admirable of him. Maybe you should try more critical examination of your ideas. And by critical I mean critical, to actually try and find fault with them.

 

[Farsight]

What does the quote you pulled from Wikipedia have to do with the coordinate speed of light? How do your Einstein quotes or the Baez article address the fact that the coordinate speed of light is just as variable in SR as it is in GR, and for the same reasons?

The wiki quote indicates that GR was altered in the sixties, and underwent a change in interpretation, which is backed up by the Einstein VSL quotes and the Baez article. They don't address the SR coordinate speed of light. Instead they make it clear that the GR interpretation changed, and is no longer in line with Einstein. The NIST optical clocks simplified to the parallel-mirror gif make it clear that Einstein was right.

The distance between me and the star would shrink very literally according to any standard definition of distance you would care to use. I don't know what it is supposed to mean for "space" to contract.

It didn't shrink. A whole rack of observers watching you will assure you that the distance between you and that star didn't contract like some concertina merely because you stepped on the gas. And you are outvoted.

"Exist" as in "can be constructed/defined". In SR (flat spacetime) it is always possible to map the whole of spacetime with a globally inertial reference frame. In GR, it is not possible to map the whole of spacetime with a globally inertial reference frame if the Riemann curvature tensor is nonzero. This is essentially the only "postulate" of SR that is abandoned by GR.

Yes, you cannot transform away a real gravitational field. It's there. Your frame isn't. It's just an abstract thing that you have defined. And regardless of the definition you use, that lower clock goes slower. And it is a light clock.

This is flat out wrong.

No it isn't wrong. I derived my gif by simplifying the empirical observations of the NIST optical clocks. The lower clock runs slower, it's an empirical observation.

Gravitational time dilation was derived by Einstein on purely theoretical grounds as early as 1907. You yourself have frequently cited a 1911 paper in which Einstein gives the coordinate speed of light formula as $$c' \,\approx\, c(1 \,+\, \Phi/c'^{2})$$. This was long before the first experimental confirmation of gravitational time dilation. Again: do you know how these were derived?

Yes. And again, the gif represents an empirical observation, not the derivation of GR.

This is also wrong. A free-fall observer won't necessarily agree for instance.

He will on his next orbital pass. You're clutching at straws with that przyk.

It also holds, to a good approximation, over larger distances where the spacetime curvature is small. Like near the Earth's surface, for instance.

No it doesn't. There is no detectable spacetime curvature in the room you're in. But you can detect the difference in the NIST clock rates. You cannot transform away a gravitational field.

Speaking of empirical evidence, can you cite an experiment where two clocks at different altitudes were compared by a free-falling observer?

No, and it isn't relevant, because we all know that gravitational time dilation is not symmetrical. SR time dilation is, GR time dilation isn't. Again, you're clutching at straws.

Since when?

Since 1915. Read those Synge and Ray quotes.

 

[Aqueous Id]

Rather than perpetuate the disdain,

Meaning: here come the insults . . .

I'll respond to you by saying that he [me] created a straw man about my dissing mainstream,

That isn't even an alternative view. There's 'physics' and 'clueless'. Within 'physics' there is 'mainstream' and minority theory but they are generally regarded (meaning mainstream: majority view) as actual theory, not just bald claims. There is a huge difference.

put on a false defense,

My reply to your statement 'I have a clue' is properly categorized as rebuttal, not defense. It's not clear to me what you were defending.

and then got all holy on us, lol.

Apparently running a thread conveys bragging rights to sanctimony.

If he wants to break his off topic nonsense out into another thread somewhere I'll consider responding point by point.

Apparently running a thread incurs a belief that this is no longer a public, but a by-invitation/private, forum.

This is all about letting it all hang out, nothing to be embarrassed about.

I for one found this statement ironically amusing.

I think I know you, and I have only a vague inkling of who you are, but my instincts tell me you are an aether proponent. Is that it?

Many have been given 'little holidays', or even permabans, for doing that.

The rules are posted. It's not my site, so I respect the owners' rights to do what they want with their property. But the rules are fine with me anyway, there's nothing unusual about them.

What makes you "brave" enough to do it may have something to do with your reputation as "mainstream",

Way to patronize me. Hate to bust your bubble, but if you want to wear Big Boy britches, you have get a handle on that incontinence.

and hence consider yourself "invulnerable" to the same standards applying to "others"

Sounds like you have a gripe with management. Let me refer you to them. As you know, I'm not running this thread.

who may also (in a perfect forum-world) wish to "let it all hang out"

In a perfect forum world, there would be a way to confirm that members are at least reasonably qualified to post in the science and math forums.

while trying to discuss the status quo without fear or favor from a different perspective,

By 'status quo' we mean 'laws of nature', no?

and so "hopefully safely" question that "mainstream" (as required by the scientific method)?

Ah so now the scientific method is available as a tool for those who did not read science to jimmy the hinge on the door and vandalize the lab.

There are "political safety" benefits to be had by "running with the orthodoxy herd".

Herd = school. Orthodoxy = the theorems of Geometry. What a herd, those Geometers. They are so obsessed with congruence.

Some people are not part of a herd,

Meaning some people never went to school.

so may be subject to more "double standard" attacks

IOW: crackpots can expect critiques from folks who actualy bothered to read science.

than you seem to think that you are,

Here we go with the patronizing again. How are those britches working out anyway. Ooops. Down the hall, first door on the left.

based on your above-quoted "brave" attitude about letting it all hang out

You're sure giving us a case study, big fella.

----if you are "mainstream" no doubt you assume it is "safe" for you to do that;

Even Macchiavelli would call that a Gordian Knot.

however, not so much for questioners of mainstream,

The folks who never read science . . .

as oft-proven by case history here and elsewhere, hey?).

Case history . . . case history . . . oh, you mean you were banned. Go figure.

Although I have to say that the situation has improved immensely since the days of "testing the fairness".

Glory days, were they. Did you get the Purple Heart, and they still left you out in the rain in your wheelchair? Those dirty dogs.

Much better for all now, including the scientific method

Really. Are you planning to employ it?

and scientific leading-edge probing/alternative discussion/advance.

Meaning anything that just magically pops into your head.

Let's just try to 'bury the baggage' and no hard feelings, everyone!

IOW, may the cranks go about their business as usual without feedback from the folks who read science.

Good luck to you both, q-w, aq-id.

It's not a joust, just a question of fact. Is q_w (or you and the other usual suspects) 'clueless' ? Yes. Therefore my claim, stating that he can get to the truth of his self-appraisement rests on whether he has access to any clues (has read science). That pretty well pares it down, without all the digressions into emotional issues, politics and all of those Gordian knots.

 

[Cheezle]

I haven't made any mistakes. You're clutching at straws to avoid facing up to the empirical fact that the lower clock goes slower. And when a clock goes slower, it's because the regular cyclic motion within that clock is going slower. Again, do not try to use abstraction to avoid facing up to the empirical evidence. And by the way, bruce is not being honest when he said yours is a good post. He knows full well that the SR expression for the invariant Lorentz interval does not apply to GR.

Undefined: your posts noted. Good stuff.

Actually my only points I view as worthwhile are about the hyperbolic nature of the equation you posted ($${s^2} = {c^2}{t^2} - {x^2} - {y^2} - {z^2}$$) and the ideas about not being able to use the Pythagorean theorem on it. I think the hyperbolic nature is obviously true. But I would listen to any reasonable argument against it. On the pythagorean theorem point I will concede on the grounds that it is generally viewed as being acceptable to mush around the theorem into other forms. Pythagorus would certainly have had a problem with the $$a = \sqrt {{c^2} - {b^2}} $$ form. Pythagorus would not have wanted to his name attached to that! And from what I understand Euclid would have had a problem with it too. $${a^2} = {c^2} - {b^2}$$ is also not really a statement of the theorem, though I am sure Pythagorus and everybody since understood it. If you allow that to be a statement of the theorem then most any mathematical principle could be claimed as a version of the Pythagorean Theorem because so much of mathematics relies on it. But as I said I will concede the point in the mathematical parlance of our times, these are popularly acceptable forms.

I am also going to back off on the non-euclidean nature of hyperbolic functions until I study the subject more.

 

[Farsight]

The massless photon fits a set of theories, but the theories that it fits require it to be massless or the greater theory falls apart. Photons having mass in my so called model also accommodates the wave nature of photons that we observe for the reason that it has a standing wave nature; standing waves have an inflowing component and an out flowing component; the out flowing component is the emitted spherical wave.

I'm sorry quantum_wave, but that is totally at odds with everything I know about electromagnetism and relativity. The photon isn't a standing wave, it goes linearly at c. It's only a standing wave when it doesn't go linearly at c but instead goes round and round at c. But then we don't call it a photon any more. We call it an electron.

Check Cheezle's video on the quantum nature of
http://www.sciforums.com/showthread...-Hubble-view&p=3085968&viewfull=1#post3085968
My response to that video described the nature of the photon particle in my so called model. It is consistent with the quantum concept of a specific number of quanta emitted by an electron and with the decreasing mass of the electron after emitting a photon. It is consistent with my hypothesis about the explanation of how a single photon can go through either slit, causing the interference patten. My disclaimer about my so called model being a hobby is common knowledge, and my hypotheses are not presented in any scientific way; simply ideas for discussion.

It's good to think for yourself, and it's good to have ideas. But whatever you come up with has to fit in with empirical evidence along with relativity, particle physics, classical electromagnetism, and so on. For example, see what I said above? Check out atomic orbitals. See where it says The electrons do not orbit the nucleus in the sense of a planet orbiting the sun, but instead exist as standing waves. Electrons exist as standing waves in an atomic orbital. Everybody will agree with that. So if an electron is kicked out of an atomic orbital, what does it exist as? We can diffract an electron. It exists as a wave. What sort of wave? A wave propagating linearly at c? No. So it still exists as a standing wave. You need to work on your model to make it more difficult for people like przyk to find fault with it.

 

[PhysBang]

The wiki quote indicates that GR was altered in the sixties, and underwent a change in interpretation, which is backed up by the Einstein VSL quotes and the Baez article. They don't address the SR coordinate speed of light. Instead they make it clear that the GR interpretation changed, and is no longer in line with Einstein. The NIST optical clocks simplified to the parallel-mirror gif make it clear that Einstein was right.

If I were charitable, I would suggest that you should take the time to actually learn GR because then you would realize that you are wrong. However, at this point you should already know that you know that you are wrong.

It didn't shrink. A whole rack of observers watching you will assure you that the distance between you and that star didn't contract like some concertina merely because you stepped on the gas. And you are outvoted.

You are simply presenting a straw man. You seem not to know how to answer the question, "What is the distance between two points?" This is because you have never, ever done a problem in physics, let alone in relativity theory.

No it isn't wrong. I derived my gif by simplifying the empirical observations of the NIST optical clocks. The lower clock runs slower, it's an empirical observation.

If you have actually done this, please provide the mathematical details.

 

[Cheezle]

I'm sorry quantum_wave, but that is totally at odds with everything I know about electromagnetism and relativity. The photon isn't a standing wave, it goes linearly at c. It's only a standing wave when it doesn't go linearly at c but instead goes round and round at c. But then we don't call it a photon any more. We call it an electron.

I have a question about this circulating photon is an electron idea. An electron can emit a photon. I think this is indisputable. If that photon could then become an electron then the electron would have given birth (as it were) to another electron. This would seem to violate the conservation of charge. You must have thought about this point before and I was wondering what your view of it is.

 

[Farsight]

I guess it offends a number of people for me to say that the mainstream does not answer all the questions I have.

It doesn't offend me at all.

I familiarize myself with physics and theoretical physics, mainstream and alternative, and seek answers for myself when the scientific community has no answer or has inconsistent answers.

I wish more people would do that.

I have not missed that point.

Good.

It has wave-particle duality.

Trust me: it's a wave. When we talk of photons we say E=hf and E=hc/λ where f is for frequency and λ is wavelength. Radio waves can be 1500m long. They aren't made up of billiard-ball photons. The photons that make up those radio waves are themselves waves, and they have a wavelength of 1500m too.

Not in mainstream models, but I explained why I have a "so called" model; the mainstream models don't answer all of my questions, and when you build a so-called model you have to hypothesize about ways to answer those questions. If you include hypothetical answers to as yet unanswered or undiscovered physics, they quickly tend to diverge from the mainstream.

Try to diverge less.

That works to account for the type of gravity waves that mainstream theory needs to explain observations and events that otherwise are contrary to the mainstream. Theory is that such a "transient field-variation" produces spherical waves that then traverse the medium of space at the speed of light, thus on a time delay. That accounts for the mainstream recognition of a time delay for such "transient" events, which would also include collisions in space that interrupt normal motion.

You seem to be too anti-mainstream, so much so that you're coming up with things that don't fit with experimental evidence, which people will use to shoot down everything you say.

Otherwise the motion of objects, according to theory, respond instantly across distances of space to the curvature of spacetime. I'm just asking how the emission of such waves is not a normal characteristic of objects, and if all objects emit spherical gravitational waves that traverse the medium of space, then there is a huge amount of energy in space that is unaccounted for by the mainstream view.

A photon is a wave, it is an object. It doesn't emit waves, it is a wave.

That is one of my hypotheses, and not in agreement with the particular theories that you foster. It is a simple answer to how objects transmit information through space to which distant objects respond on a time delay basis, and is the reason why I discuss the time delay of gravity. See my earlier response to Aqueous Id, which included a brief exchange between Markus Hanke and me.

I'll take a look.

 

[Tach]

This is why I naively observe that:


-And if, as you imply, the space (not 'space-time', but space only) SR/GR defined "locally infinitesimal distance' reference frame 'd' value is invariant between all given "local frames" at all "local" altitude positions above the Earth's surface;

This is , of course , false. Length contracts in GR, see here. It is a function of the gravitational potential , exactly the way clock rate is a function of gravitational potential (the two functions are not the same). You need to make an attempt to learn, making up stuff and trying to pass it as science would not work. It is very simple , really, one starts with the general form of the Schwarschild metric:

$$ds^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)-(rd\theta)^2$$

In the absence of rotation:

$$ds^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)$$

If we try to compare stationary clocks, then:

$$dr=0$$

$$ds^2=(1-r_s/r)(cdt)^2$$

$$ds=c d\tau$$

so:

$$d\tau=dt \sqrt{1-r_s/r}$$

If we try to measure length, then we need to fix the endpoints of a line segment simultaneously ($$dt=0$$, so:

$$ds^2=-dr^2/(1-r_s/r)$$

meaning that

$$dL^2=-ds^2=dr^2/(1-r_s/r)$$

so:

$$dL=\frac{dr}{\sqrt{1-r_s/r}}$$

Very simple, you only need to be willing to learn.

-Then the 'actual' (not theoretically assumed) speed of light values must be affected in order to compensate for the varying 't' used in your same equation for each different local frame 'calculated 'c' to come out as 'invariant c'.

No, this is false as well, you are promoting the same crackpot idea as Farsight, the speed of light is NOT "affected", the speed of light is an invariant.

If not, then the calcuated c would not always be equal to '1' or remain 'unitary' as assumed for your mathematical treatment using 'variable t' values for each local conditioned space environment affecting the local clock tick count values 'absolutely and Empirically' and not just theoretically assumed to be 'the same t' values' as you seem to do in your analytical construct above. Yes?

Nope. See above, you are repeating Farsight's crackpot ideas.

 

[quantum_wave]

That will be my pleasure, quantum_wave.

I'm afraid I can easily resist responding to your posts if they're in an "alternative theories" section. That carries a stigma by association. *

OK.

Noted and agreed.

Perhaps those who are prone to flaming will have your attitude and will stop posting their off topic nonsense after the moderators hopefully grant the many requests to move this thread to Alternative Theories. It is full of alternative theories, and even those who suppose they are posting mainstream views can't agree it seems.

Apologies for the unpleasantness we've seen on this thread.

Not a problem.

 

[Farsight]

I have a question about this circulating photon is an electron idea. An electron can emit a photon. I think this is indisputable. If that photon could then become an electron then the electron would have given birth (as it were) to another electron. This would seem to violate the conservation of charge. You must have thought about this point before and I was wondering what your view of it is.

Pretty much the standard view. An electron is created in pair production along with a positron. Pair production might be gamma-gamma pair production, or it might involve the interaction of a photon with a nucleon. You can view this as a situation where one photon is "split" and then gamma-gamma pair production occurs.

See two-photon physics on Wikipedia for gamma-gamma pair production, but note that the given explanation is somewhat misleading. A photon does not spend its life spontaneously fluctuating into an electron-positron pair which then combine back into a single photon. Pair production does not occur because pair production occurs.

Re your post #741, I would urge you to think for yourself. If somebody offers an explanation that you find less than satisfactory, say so, and ask for more.

 

[Farsight]

This is , of course , false. Length contracts in GR, see here...

Which is headed Length contraction in a gravitational field and says rulers "shrink" in a gravitational field. So Tach, how come you said the distance between the two mirrors increases?

...Nope. See above, you are repeating Farsight's crackpot ideas.

And I reiterate, the idea that the speed of light is lower at a lower elevation is Einstein's idea, not mine.

 

[Tach]

Which is headed Length contraction in a gravitational field and says rulers "shrink" in a gravitational field. So Tach, how come you said the distance between the two mirrors increases?

Very simple, Duffield, you need to be able to use the basic info that I explained to your sidekick in the post above:


If we try to compare stationary clocks, then:

$$dr=0$$

$$ds^2=(1-r_s/r)(cdt)^2$$

$$ds=c d\tau$$

so:

$$d\tau=dt \sqrt{1-r_s/r}$$

If we try to measure length, then we need to fix the endpoints of a line segment simultaneously ($$dt=0$$, so:

$$ds^2=-dr^2/(1-r_s/r)$$

meaning that

$$dL^2=-ds^2=dr^2/(1-r_s/r)$$

so:

$$dL=\frac{dr}{\sqrt{1-r_s/r}}$$

Since $$ds$$ is invariant:

-for two stationary clocks, situated at radial coordinates $$r_1,r_2$$ it follows that:

$$dt_1 \sqrt{1-r_s/r_1}=dt_2 \sqrt{1-r_s/r_2}$$

The above shows that $$r_1<r_2 => dt_1>dt_2$$

-for two rulers, situated at radial coordinates $$r_1,r_2$$ it follows that:

$$\frac{dl_1}{\sqrt{1-r_s/r_1}}=\frac{dl_2}{\sqrt{1-r_s/r_2}}$$

The above shows that $$r_1<r_2 => dl_1>dl_2$$, exactly as I was (hopelessly) trying to teach you.

And I reiterate, the idea that the speed of light is lower at a lower elevation is Einstein's idea, not mine.

And to reiterate to you, Einstein realized he had made a mistake on the subject and corrected himself. You , on the other hand....

 

[quantum_wave]

Re Post #672

...

I take issue with the idea of an infinite universe, whether it's your model or the standard model of cosmology. This indicates that the universe started small, WMAP suggests it's flat, Planck corroborated this, as far as we know it's been expanding for 13.8 billion years. In addition we know the universe didn't collapse when it was small and dense. The GR stress-energy-momentum tensor features pressure, and dark energy was described as pressure by Phil Plait. If that "pressure" is counterbalanced at all locations because the universe is infinite, it cannot result in expansion.

True, but if you will give me one small point of clarification, I intend for this thread to distinguish between our Hubble view, and the greater universe. What you just said applies to our observable universe and the parts beyond that are causally connected to our Big Bang. I mentioned to you above that my so called model address questions that the mainstream theories don't address, and preconditions to the Big Bang is a good example.

I also mentioned that when I hypothesize about preconditions, I am considering various precondtions and choosing the hypothesis that I personally feel is most likely.

I also acknowledge that when I simply hypothesize some set of preconditions I am not pretending to do science, another straw man often used by some.

Now the straw man that was invoked by Aqueous Id is that I am dissing mainstream views by questioning things like "the beginning", preconditions, and unknowns and unknowables. That is an opinion that you appear to share, perhaps. In my defense, a complete cosmology should address the issue of a beginning. We must at least recognize that there are differences in the standard cosmology, and alternatives, when the alternatives address the question of a beginning. There is no mention of a beginning in BBT. That is automatically a difference, and it is insincere to say that I am dissing mainstream by discussing the issue of a "beginning" vs. "always existed". There must be thousands of reputable mainstream science professionals that contemplate the nature of the universe and whether it all began with the Big Bang.

Often I get the response that, 1) We can't know the answer, 2) BBT is the best we can do, and 3) if GR says there is no "before" the Big Bang, problem solved. Where do you stand?

 

[Tach]

Often I get the response that, 1) We can't know the answer, 2) BBT is the best we can do, and 3) if GR says there is no "before" the Big Bang, problem solved. Where do you stand?

Mainstream cosmology clearly says option 3. Cranks, on the other hand....

 

[PhysBang]

See two-photon physics on Wikipedia for gamma-gamma pair production, but note that the given explanation is somewhat misleading. A photon does not spend its life spontaneously fluctuating into an electron-positron pair which then combine back into a single photon. Pair production does not occur because pair production occurs.

Do you have a better theory that explains quantum phenomena with more accuracy than the current, tested theories of particle physics that you are here directly disagreeing with?

Re your post #741, I would urge you to think for yourself. If somebody offers an explanation that you find less than satisfactory, say so, and ask for more.

Yet you tell everyone to simply believe you and to believe cherry-picked quotations from Einstein rather than read the mathematics that Einstein provided for explanation.

 

[brucep]

I'm sorry I have nothing to add too or advance, only intuition says that when something intuitivle feels right, it is worth acknowledging. Wish I had the mathematics to follow specifics. Not understanding the mathematics or a lot of the mainstream physics, I have to rely on my intuitive feelings from what I have read as reference to the bits and pieces of math and physics that so many of cosmos lovers have piece-mealed together along the years of study and exploration.

Thx to brucep for the physics parts that just seem on the mark to me. If only we had some who can bring the math and concepts into more simple format for us less educated--- in the math and physics --to really appreciated and validate or not with some confidence.

r6

The first two chapters of the book, I keep touting, are pretty good reading even if you don't understand the math. On page 2-35 of chapter 2 Curving, figure 9, the Schwarzschild map is visually revealing about the path of light falling to the black hole observed from remote coordinates. The path of light over flat spacetime could be represented by a straight line, the shortest distance between where the light is emitted and where it falls past the event horizon. Over this path the local coordinate speed of light is measured to be c at every point on the manifold. These are direct measurements and invariant. So you can draw a straight line to represent the local path of the light falling to the event horizon. So as you know

dr/dt = 1 the local coordinate speed of light. c=1 in geometric units.

You can build your own Schwarzschild map using the remote coordinate speed of light since you're familiar with that formula.

dr/dt = 1-2M/r

For example in geometric units

for r=2M

dr/dt = 1-2M/2M = 1-1 = 0

for r=100,000M

dr/dt = 1-2M/100,000M = .99998

for r=4M

dr/dt = 1-2M/4M = .5

etc.

The path measured/reckoned from remote coordinates is longer than the path over flat spacetime. The invariant path is the local path. The frame dependent path is the remote path. Those are easy formulas to play with. Both paths are equally valid. Let me know if you do it and what your intuition tells you about your results.

BTW M is the mass in geometric units. Everything is expressed in unit L for geometric units. For this project we'll say the value of M is one solar mass = 1477m.

http://www.eftaylor.com/pub/chapter2.pdf

 

[Undefined]

This is , of course , false. Length contracts in GR, see here. It is a function of the gravitational potential , exactly the way clock rate is a function of gravitational potential (the two functions are not the same). You need to make an attempt to learn, making up stuff and trying to pass it as science would not work. It is very simple , really, one starts with the general form of the Schwarschild metric:

$$ds^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)-(rd\theta)^2$$

In the absence of rotation:

$$ds^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)$$

If we try to compare stationary clocks, then:

$$dr=0$$

$$ds^2=(1-r_s/r)(cdt)^2$$

$$ds=c d\tau$$

so:

$$d\tau=dt \sqrt{1-r_s/r}$$

If we try to measure length, then we need to fix the endpoints of a line segment simultaneously ($$dt=0$$, so:

$$ds^2=-dr^2/(1-r_s/r)$$

meaning that

$$dL^2=-ds^2=dr^2/(1-r_s/r)$$

so:

$$dL=\frac{dr}{\sqrt{1-r_s/r}}$$

Very simple, you only need to be willing to learn.






No, this is false as well, you are promoting the same crackpot idea as Farsight, the speed of light is NOT "affected", the speed of light is an invariant.




Nope. See above, you are repeating Farsight's crackpot ideas.

Thanks, Tach, for your response in answer to my questions to brucep.

Since the light clocks as made remain intact at/in all times/frames, there is no need for abstract theoretical/mathematical exercise to "fix the end-points simultaneously", especially as it is not "a line" but an actual empirically measurable distance within the clock physical construct of two parallel mirrors in fixed relation to each other in any given GR frame where it is located.

Which leads to the obvious question indicated by your 'take' on this: why does the light clock tick slower when lower in the gravity well, if, as you claim theoretically/mathematically that "the distance/length shrinks lower down"? Shouldn't the tick rate speed up if the distance between reflections is supposedly "shrunk" as you claim?

So far all you have done is present a math treatment based on inconsistent/contradictory assumptions and theoretical 'ad hoc values/terms input to your equations which do not in any real way reflect/address the actual empirical values/phenomena you purport to analyze abstractly based on the preconclusionary assumptions input from the get-go in your apparently circuitous-logics infested analytical construct.

Thanks anyway, Tach, for your (less insulting than usual) response to my questions to brucep. Much appreciated even if I do not agree on the validity of your assertions on the matters involved.

 

[Tach]

Thanks, Tach, for your response in answer to my questions to brucep.

Since the light clocks as made remain intact at/in all times/frames, there is no need for abstract theoretical/mathematical exercise to "fix the end-points simultaneously", especially as it is not "a line" but an actual empirically measurable distance within the clock physical construct.

Which leads to the question: why does the light clock tick slower when lower in the gravity well, if, as you claim theoretically/mathematically that "the distance/length shrinks lower down"?

You managed to get it exactly backwards, the clock lower in the gravity well is elongated, not shortened. I told you specifically, twice that your claim "the distance/length shrinks lower down" is FALSE. I even demonstrated it with math, obviously you weren't able to follow the simple proof. Try again:

$$\frac{dl_1}{\sqrt{1-r_s/r_1}}=\frac{dl_2}{\sqrt{1-r_s/r_2}}$$

So: $$r_1<r_2 => dl_1>dl_2$$, the clock lower in the gravity well is longer.

So far all you have done is present a math treatment based on inconsistent/contradictory assumptions and theoretical 'ad hoc values/terms input to your equations which do not in any real way address the actual empirical situation you purport to analyze so.

Nope, so far I presented textbook stuff that you are unable to comprehend.

 

[Undefined]

You managed to get it exactly backwards, the clock lower in the gravity well is elongated, not shortened. I told you specifically, twice that your claim "the distance/length shrinks lower down" is FALSE. I even demonstrated it with math, obviously you weren't able to follow the simple proof. Try again:

$$\frac{dl_1}{\sqrt{1-r_s/r_1}}=\frac{dl_2}{\sqrt{1-r_s/r_2}}$$

So: $$r_1<r_2 => dl_1>dl_2$$, the clock lower in the gravity well is longer.



Nope, so far I presented textbook stuff that you are unable to comprehend.

Thank you for that clarification, Tach. Understood. How does your abstract mathematical "result" agree with the actual fixed distance between the mirrors? Can you demonstrate empirically rather than theoretically that the distance between the mirrors has changed between upper and lower frame positions?

Unless you can demonstrate empirically that the already empirically determined and fixed relation distance between the mirrors has changed as you assume for your equations, then the rest of your mathematical treatment/assertions/results remains abstraction and conjecture and interpretation on the part of the math analysis construct, yes?