Is time universal? NO (and its proof)

[Pete]

Using SR only, it is not possible to use the frame of reference in which one of the twins is at rest throughout. Only non-accelerating frames can be used.

I stand corrected. Apparently such frames can be analysed with SRT, using something called "curvilinear coordinates", which I haven't a clue about.

It also seems that my view that using GR to analyse such frames is an Interesting Thing could be somewhat dated. See What is General Relativity in the Twin paradox section of the UseNet Relativity FAQ:

So modern usage demotes the uniform "gravitational" field back to its old status as a pseudo-field, with all the pejorative connotations of the prefix "pseudo". And the hallmark of a truly GR problem (i.e., not SR) is that spacetime is not flat. By contrast, the free choice of charts --- the modern form of the General Principle of Relativity --- doesn't pack much of a punch. You can use curvilinear coordinates in flat spacetime.

 

[Billy T]

Billy T, You are not taking into consideration that the Earth could be dragging the aether around with it. Even Einstein believed that the Earth is dragging spacetime around (frame-dragging). ....

Einstein's prediction that the rotation of the Earth causes a very very slight "twist" to near by space is entirely unrelated to "dragging aether" - This is the last of his predictions to be subjeted to an experimental test and a sattelite of incredable sophistication is planned to test it, but many believe the effect is too small be measured.

Now to your main point, a little history:

Because it was hard for most physicists to understand how Maxwell’s electromagnetic waves could propagate in the absence of any medium of propagation, most supported the aether concept.
When M&M demonstrated that the speed of light did not vary as the Earth moved thru the aether, many adopted the idea that the Earth was dragging the aether with it, so at the surface of the Earth, where M&M did their experiment, no change in c should be expected.
Some did not accept this escape from M&M's negative results, because there should be turbulence in the boundary layer between the universal aether and the aether moving with the Earth and this turbulence would greatly distort the our view of the stars, but many postulated the boundary could be very laminar flow, without significant distortion, and continued to support the aether theory with some drug thru space by the Earth.
This view was abandoned by all (except you?) when the stellar aberration experiments were done. Even laminar flow shifts the rays passing thru it slightly and thus if aether were real, the apparent position of the stars should shift with the season, which of course they do not.

 

[Billy T]

Here is the root of your problem. You {Billy T} seem to believe the mathematical nonsense of SRT is the only answer and you are not considering any other alternatives as to why the speed of light "appears" invariant.

Math is never "nonsense." Either it is correct or has an error. In the latter case, one should be able to point out where the error occurs. In this thread, I have used math to derive and numerically illustrate things you dispute, even numbering my paragraphs so you could easily refer to the point where I made an error. You have chosen to respond only with words, assertions, etc, based only on your opinons, never any math or citation of errors in mine.

Now you are asserting, contrary to the M&M experiments and the many that have repeated them later, that the speed of light is not really constant, again without any proof other than your opinion.

I will be kind and assume that, like Prosoothus, you think that Earth is dragging the eather with it to explain the negative results of M&M type experiments. Thus I refer you to my reply to him below. If you have some other explaination as to why M&M type experiments support the "false idea" that the speed of light is constant, (other than you opinion), I would like to hear them.

I've said it before and I will repeat it.

I know, and repeating your opinion 1000 times more will not persuade me!

The speed of light may "appear" invariant if you are not looking at the same photon when you have different velocities relative to the source.

I don't know how to take this "looking at the same photon." Perhaps it is just your ignorance of fact that any "look" destroys it - Looking converts it into energy in the instrument or eye that "looked." (You can measure its momentum by reflecting it on a small, light weight, mirror**; but you can not know exactly when you did so - i.e. where it was at a particular time better than the uncertainty principle will allow.)
Do you mean (trying to say): Measure the speed of photon A (one that unobserved passed thru a briefly open shutter) from a stationary source and traveled a long distance (for accuracy in speed measurement) before being distroyed in an instrument that measured how long after the shutted closed that it arrived and them repeat for photon B with the source rapidly moving away? In this case what is your "looking at the same photon" all about? (Two different photons, A & B, are inherent if two "looks" are required.) You really are not making any sense anymore and I am trying hard to understand you.

A very sound theory of that principle has been put forth by Dr Dowdye, a NASA, Phd, Physicist, which he supports mathematically. Have you actually looked at such possiblity and understand the consequences are that you have the same observations and emperical test results but without any relativity at all? You should.

I never have been much for the "appeal to authority" type of argument (I much prefer logical argument, preferable supported by math and examples like I give), but give me a reference to his published work and I will try to read.

You can continue to post your opinions (no way I can stop you) but unless there is some hint of logic or math, I will no longer read them, at least not carefully. You are clearly intelligent but it appers that you not capable of persuasive argument - only opinionated assertions. I hope you will prove this conclusion of mine wrong.

** In actual pratice, your "mirror" could be a "cold atom" and you measure the recoil velocity given to the atom by a time of flight measurement, but even in this case the photon is changed to another with lower energy.

 

[Prosoothus]

Billy T,

Some did not accept this escape from M&M's negative results, because there should be turbulence in the boundary layer between the universal aether and the aether moving with the Earth and this turbulence would greatly distort the our view of the stars, but many postulated the boundary could be very laminar flow, without significant distortion, and continued to support the aether theory with some drug thru space by the Earth.

This view was abandoned by all (except you?) when the stellar aberration experiments were done. Even laminar flow shifts the rays passing thru it slightly and thus if aether were real, the apparent position of the stars should shift with the season, which of course they do not.

You, like other physicists, assume that "aether" must be both a "medium of travel" AND a "medium of propulsion" of light. It's possible that spacetime is the photon's "medium of travel", while gravitational fields are the photon's "medium of propulsion". In other words, this means that a photon can travel anywhere in spacetime, but is only pushed, or pulled, when it's in a gravitational field. If this was the case, then as light enters a moving gravitational field, its speed would change so that its speed is equal to c relative to the field, but its path WOULD NOT change because spacetime itself is not moving.

To understand this concept a little better, imagine the photon as a gravitational dipole in a uniform positive gravitational field. If the photon is travelling at a speed of lower than c, the external gravitational field in front of the photon will pull the positive pole of the photon, and the external gravitational field in the back of the photon will push the negative pole of the photon. This will create a force on the photon causing it to speed up. As the photon's speeding up, the force is decreasing. Once the photon reaches the speed of c in the field, the force becomes zero because the speed of the photon is equal to the speed of the gravitational interaction. If you can invision this model, then you can understand that a uniform gravitational field can speed up or slow down a photon by interacting with the photon's poles, but it CANNOT drag a photon in any specific direction. Only in a non-uniform gravitational field, can the field actually change a photon's path by rotating it towards the stronger section of the field.

In conclusion, it's possible that as light from a distant star enters the Earth's gravitational field, its speed changes so that its speed is equal to c relative to the field, but it's path does not change so an observer on the surface of the Earth will not see a change in the star's location.

 

[Billy T]

.....Extremely briefly (too briefly.. really, find and read it!):
In the curved spacetime paradigm of GR, Perfect clocks and Perfect rulers accurately measure spacetime, which is curved by mass-energy.
In the flat spacetime paradigm of GR, spacetime is flat, but Perfect clocks and Perfect rulers are rubbery, their shapes and readings altered by gravitational fields. ...

Thanks for posting your drawings a few post back. If one studies them, one can understand that the twins are not twins anymore and why the modified twin paradox that I and Neddy Bate concocked is only a paradox, not a disproof of SRT.

Now more to this post: It seems that even within GR there are two different but equivalent ways to look at things. Gr is above me, so I will rely on the logic that SR is sub set of GR and conclude that I may have understated the number of choices available to one. there are two ways in SR to view the sun's bending of the photon plus the old fassion way that gives it relativistic mass (m =E/c^2) and lets sun's gravity force atract it while passing.

 

[Billy T]

...To understand this concept a little better, imagine the photon as a gravitational dipole in a uniform positive gravitational field. If the photon is travelling at a speed of lower than c, the external gravitational field in front of the photon will pull the positive pole of the photon, and the external gravitational field in the back of the photon will push the negative pole of the photon. This will create a force on the photon causing it to speed up. As the photon's speeding up, the force is decreasing. Once the photon reaches the speed of c in the field, the force becomes zero because the speed of the photon is equal to the speed of the gravitational interaction. If you can invision this model, then you can understand that a uniform gravitational field can speed up or slow down a photon by interacting with the photon's poles, but it CANNOT drag a photon in any specific direction. Only in a non-uniform gravitational field, can the field actually change a photon's path by rotating it towards the stronger section of the field.
In conclusion, it's possible that as light from a distant star enters the Earth's gravitational field, its speed changes so that its speed is equal to c relative to the field, but it's path does not change so an observer on the surface of the Earth will not see a change in the star's location.

I don't doubt your ability to dream up new theories or mechanism. I only doubt that you can explain all the experiments that have supported the standard view with your new ideas and that you have any bases for believing the new theories, except "armchair speculation."

 

[Prosoothus]

Billy T,

I don't doubt your ability to dream up new theories or mechanism. I only doubt that you can explain all the experiments that have supported the standard view with your new ideas and that you have any bases for believing the new theories, except "armchair speculation."

My "gravitational dipole" model not only explains why and how photons travel at c, why the omnidirectional speed of light on the surface of the Earth is constant, but it also explains why and how reactions slow down in an object that is moving through a gravitational field. In other words, my model not only explains all of the experimental evidence that SR uses as proof of its validity, but then some. And I did all this by only linking the speed of photons with gravitational fields. I didn't even have to introduce any whacky paranormal and paraphysical phenomena like length contraction and time dilation.

And the funny thing is that all that has to be done to prove my theory, and all other aether theories, wrong is to measure the speed of light in an object that is moving through a gravitational field. And yet, in the last one hundred years, since the creation of SR, the scientific community couldn't do this simple experiment and prove all of us crackpots wrong. Maybe they are afraid of the results. Maybe it would turn out that we weren't the crackpots.

 

[Billy T]

Billy T, My "gravitational dipole" model not only explains why and how photons travel at c, why the omnidirectional speed of light on the surface of the Earth is constant, but it also explains why and how reactions slow down in an object that is moving through a gravitational field. ....

No it doesn't. It is not even consistent with simple physics concept like "work" BEING "force" times distance thru which that force acts. To show this, I need to quote from your prior post:

imagine the photon as a gravitational dipole in a uniform positive gravitational field. If the photon is travelling at a speed of lower than c, the external gravitational field in front of the photon will pull the positive pole of the photon, and the external gravitational field in the back of the photon will push the negative pole of the photon. This will create a force on the photon causing it to speed up.

and teach you the simple concept of "virtual displacement work calculations" if you do not already know how they permit force to be evaluated when it is easy to evaluate the energy change as object is moved.

You state that the gravitational field you are considering is uniform. For example, consider a photon passing far from the sun and parallel to a line which is tangent to the sun's surface at the closest point on the sun to the photon. For a brief time (or photon motion) this approximates your "uniform gravitational field" does it not? If one were to consider another photon, moving parrallel with this one, it could be closer to the sun and the period of photon travel reduced corresponding to still preserve a good approximation of your "uniform gravitational field." In the limit of a "virtual displacement" the photon could just graze the solar surface and still be approximately in a "uniform gravitational field"

Now to the extent that these photons are in a "uniform gravitational field" and moving transversely to it, no work is done in a virtual displacement. Hence transverse to the local graviatational field, there would be no force applied to the photon to either speed it up or slow it down, as you assert. M&M's experiments were done tranvsely to the local gravational field (Their entire interferometer was floating on a shallow pool of mercury so they could easily turn it relative to the Earth's motion without introducing any forces that might change the separation of the mirrors in the interferometer and produce a shift in the interference pattern.)

Even if the photon were traveling in the direction of the gravitational field, there is no reason to think that:
"the external gravitational field in front of the photon will pull the positive pole of the photon, and the external gravitational field in the back of the photon will push the negative pole of the photon."
Why not just the opposite? I. e. why not:
the external gravitational field in back of the photon will pull the positive pole of the photon, and the external gravitational field in the front of the photon will push the negative pole of the photon.

You did say the gravitational field was "uniform" thus its "front" and "back" should be interchangeable. Also what if the photon diapole is flipped 180 degrees fron the direction you assumed? or turned at 90 degrees to it? Your whole idea is add hoch non sense and does not explain anything. It is not even internally consistent or clearly defined (what orientates the photon as you assume, Is it the same for both polarizations, and why? etc..) It does however, clearly claim that the speed of light will depend upon the trajectory of the photon relative to that of the gravitational field lines - more non sense by experimental observation.

 

[Pete]

It seems that even within GR there are two different but equivalent ways to look at things.

At least two...

Gr is above me, ...

Yeah, me too, but I'm taking baby steps when I can.

...so I will rely on the logic that SR is sub set of GR and conclude that I may have understated the number of choices available to one. there are two ways in SR to view the sun's bending of the photon plus the old fassion way that gives it relativistic mass (m =E/c^2) and lets sun's gravity force atract it while passing.

Do you think that's useful?
Isn't it enough to acknowledge that an SR + Newtonian gravity model is a good but not perfect approximation to reality?
Ie there are things that don't happen in the model that do happen in reality (such as bent light paths, cosmological expansion, gravitational doppler)... and that's OK.

I think that trying to "bend" a model to meet observations that don't fit is a bit dangerous... you'd have to really know what you're doing. I have the feeling that there's a pretty fine line between real science and pseudoscience when it comes to modifying models to match observations.

Witness Prosoothus and the dynamic ether... such a line of enquiry was (is?) serious science (Here's a good page), but the paradigms presented didn't gain wide acceptance... not, it seems, because they gave incorrect predictions, but because they were inelegant or ad hoc. In fact, the Lorentz transform was developed as an end result of modifying ether theories to match observations! That's why its the Lorentz transform, not the Einstein transform.


But then again, I think that at our level it comes down to whether we're constructing a reasonable surface understanding... and who am I to criticize the way you construct your own understanding? Again with Prosoothus... if he wishes to use an ether-based paradigm that gives exactly the same predictions as special relativity... so what? Perhaps it could be useful in some situations? (His gravity stuff is something else... :bugeye: )

 

[Billy T]

....Isn't it enough to acknowledge that an SR + Newtonian gravity model is a good but not perfect approximation to reality?
Ie there are things that don't happen in the model that do happen in reality (such as bent light paths, cosmological expansion, gravitational doppler)... and that's OK.
I think that trying to "bend" a model to meet observations that don't fit is a bit dangerous... you'd have to really know what you're doing. ....

I am not trying to bend the SR model and or Newton's gravity - I am not enough of an expert in it to know where to grab hold and twist I think they my even give the wrong results numerically when the observed bending of light passing near the sun is modeled as the photon's relativistic mass being attracted by the sun's gravity, but the direction of the bend and the order of magnitude are correct. I am not sure there is any error, but recall reading that there is with this non GR approach.

 

[Aer]

Aer,
I'm not sure if we have a real difference of opinion or not.
My position is:

• Using SR only, it is not possible to use the frame of reference in which one of the twins is at rest throughout. Only non-accelerating frames can be used.
• Using GR, it is possible to use the frame of reference in which one of the twins is at rest throughout.
• Both models give the same prediction for this situation - the proper time between birth and photo is thirty years for each twin.

You agree with all that, right?

The problem with your stance is you are claiming the acceleration phase is significant when in fact it is not. The acceleration is almost simultaneous. However, if one of the twins was in constant acceleration... then you may have a valid argument.

I disagree with nothing you've said about GR in this thread except your first comment:

It is clear that GR does say particular things about accelerating frames in flat space-time.

And we can get the same information using special relativity, what is the point?

Yes, SR gives the same conclusions. So what? The reasoning leading to the conclusions is different - and that is interesting.

What is the different reasoning? Would you like to provide the analysis?

I think you've misread me. I don't think I ever said that.

Perhaps I don't understand you, you just stated above "Yes, SR gives the same conclusions. So what? The reasoning leading to the conclusions is different - and that is interesting."

"anything more" would include a different explanation which you claim GR will provide.

 

[Aer]

When using a curved-spacetime paradigm, it's not a matter of choice... but that's not the only paradigm available!

Very well, but these paradigms are not mainstream and people who adhere to these non-mainstream paradigms are labeled crackpots

In the curved spacetime paradigm of GR, Perfect clocks and Perfect rulers accurately measure spacetime, which is curved by mass-energy.
In the flat spacetime paradigm of GR, spacetime is flat, but Perfect clocks and Perfect rulers are rubbery, their shapes and readings altered by gravitational fields. They don't always accurately measure spacetime.

Like I said, this is definately heading non-mainstream, but if you wish to discuss it, feel free to start a new thread on it.

"That is why physicists were not content with Einstein's cured spacetime paradigm, and have developed the flat spacetime paradigm as a supplement to it."

Exactly how many physicists does this include? I don't really know of any..

 

[Aer]

My "gravitational dipole" model not only explains why and how photons travel at c, why the omnidirectional speed of light on the surface of the Earth is constant, but it also explains why and how reactions slow down in an object that is moving through a gravitational field.

Sounds a lot like the "local ether" model of wave propogation. When did you come up with your so-called theory?

 

[Neddy Bate]

</em>They both accelerated synetrically, starting at noon of their 15th birthday and were in one common frame, but very far apart. Each after the start of acceleration is moving thru a series of frames, but the accleration is intenst (and still symetric) and lasts 1 second on the identicl clocks they both carry.
Then after the brief period (not necessarily 1 second in the original "birth frame", but by symetry it is the same amount of time in the birth frame) they drift for years in inertaila frames towards each other. They aged one second during the period of acceleration by their local clocks, but 15 years during the inertail drift. The starting birth frame separation was very great and just such that on ech of their 30th birthday they pass each other and the flashbulb fixed in the birth frame mid way between their launch sites. I need some help to see your answer, more than simple assertion of the standard SRT claim. I think the problem Neddy and I have joinly built is the toughest I have ever read for SRT and frankly I am at al loss to explain how the photos can have only 25 candles on the cake as time dialtion predicts if each is passing the flash on his 30th birthday. The exterme symetry combined with the long period of drift in inertial frames is what makes this tought to understand.

The above "modified twin paradox" is exactly the kind of thought experiment that has been keeping me perplexed about 'reciprocal' time dilation. If it had BillyT (who is one smart guy in physics) puzzled for awhile, then it must be a tough problem. But then a solution was reached here:

</em>May seem strange to reply to myself, but I did not "know symetry" when I see it.

In the birthframe of the two twins, they are twins, but the sign of their accelerations for the second of acceleration (on their own clocks) is opposite. Thus, the equations that mix their great birthframe separation into time-like separations are different.

Because some of the purely space-like separation in the original birth frame is transformed in to time-like separation, DIFFERENTLY in their new different frames, they are no longer twins in their new frames. (Being "twins" is not something like being fat that you can take with you to a new frame. It is a relationship to the birthday of some one else.) That is, the day, which in the original birthframe that is simultaneous with twin A's birthday in the new A frame is not the day which is simultaneoous with twin B' birthday in his new frame. (Frame A has always existed before twin A enter it. So twin A has a birthday in new frame A. It is simultaneous with someday, but not the birthday in the birthframe. Likewise for twin in frame B, he has a day in the birthframe which is simultaneous with his date of birth in frame B.)

No problem with making a single pair of events simultaneous between two frames - just set t=0 ON CO-LOCATED clocks in both frames, but note that a second event, later, will not have the same date/time accumulated on clocks that are keeping "proper time" correctly.

I.e. B's new birthday in frame of birth is not the same day as either the original birthday in birth frame or the day which was simultaneous with A's birthday in the birthframe. Being twins is a relationship between two birthdays in the same frame (their birthframe in this case) but as they were born on different days which are simultaneous with the day of their birth in their new frames (A and B). I.e. they are no longer twins in frames A & B.

I know it is very intutive to think that "once twins," "always twins" but it ain't so. (Unlike being fat, they can't take their "twinness" with them to the new frames.) Their great space-like separtion in their birthframe was transformed differently into time-like spepartaion as they moved to frames A & B.

I thank Pete for helping me see my way thru this modified twin paradox. I hope he will post the drawings he made that show (in each of the three frames separately) exactly what is happening - the time they drift inertially back towards each other to have their photo taken with common flash is clearly seen to be different in these drawings. Each "inertial drift time" is time dilated wrt the proper time and simultaneity of the other, just as SR states.

This is starting to make sense, if their birthdays lose simultanaety then we might be able to reach a solution acceptable to everyone. I am going to have to look into the math in Pete's XLS file to make sure I follow everything.

</em>At BillyT's request...
Modified Twin Paradox - Excel Spreadsheet

Graphs from the spreadsheet
Short explanation - in all frames, the twins meet after 30 years proper time for each twin (ie 30 candles on each cake).

For example, in Twin-One's after-acceleration rest frame:
Twin one moved at v=0.447c (gamma=1.118) for 16.771 years, which makes for a proper time of 15 years. Twin one then accelerated to rest, and stayed at rest for 15 years.
Twin two also moved at v=-0.447c (gamma=1.118) for 16.771 years, which makes for a proper time of 15 years. Twin two then accelerated, and moved at v=-0.745 (gamma=1.5) for 22.5 years, making another 15 years proper time.

Pete, I am very grateful for the graphs, the XLS file, and the summary explanation. I omitted the graphs from this reply to save bandwidth, but they can be found just about one page back in this thread, if some new reader is looking for them.

I will be studying the XLS file later, but at first glance, this solution seems to imply that while TwinA is accelerating, they see TwinB shift in age (a shift in birthday, due to simultanaety issues). From TwinA's frame of reference, I would imagine TwinB would need to shift to become older since TwinB's clock is going to be ticking relatively slow for the rest of the journey. I am not sure why the two twin's graphs do not both show the 'other' twin as jumping 7.5 years ahead (one seems to jump back?) but I admit I have not looked deeply into this yet.

It will be interesting for me to try to see if any paradox remains in this latest solution. Thank you, Pete, BillyT, and everyone else for a very interesting and helpful thread so far.

 

[Pete]

Very well, but these paradigms are not mainstream and people who adhere to these non-mainstream paradigms are labeled crackpots

Like I said, this is definately heading non-mainstream, but if you wish to discuss it, feel free to start a new thread on it.

Exactly how many physicists does this include? I don't really know of any..

Kip Thorne is as mainstream as they come. He cowrote *the* textbook on Relativity: Gravitation

 

[Aer]

Kip Thorne is as mainstream as they come. He cowrote *the* textbook on Relativity: Gravitation

I didn't say anything about him personally, I just don't think "the flat spacetime paradigm of GR" is mainstream. How many physicist have any knowledge of it? And how many of the physicist that qualified above have extensive (beyond just "hearing") knowledge of it? Furthermore, how many of those with extensive knowledge accept it?

 

[Pete]

"anything more" would include a different explanation which you claim GR will provide...

...The problem with your stance is you are claiming the acceleration phase is significant when in fact it is not...

...What is the different reasoning? Would you like to provide the analysis?

Ah, OK... I thought you meant something more regarding end results.
I will now point you to the UseNet Relativity Faq - Twin Paradox "General Relativity" explanation
(Note that "General Relativity is in quotes for a reason, as I conceded in [post=856313]my last but two post[/post].)

Using ideas from that site, (which I think are in accord with Relativity, BUT I now realise that I've relied on it too heavily in formulating my understanding of GR), here is the alternative reasoning to which I alluded:

Be careful of the figures in this story - they're not supposed to be a proof. I didn't derive them using GR, or using curvilinear coordinates in SR, I cheated by assuming that this explanation was equivalent to the SR explanation. This is just an arm-waving explanation, not a rigorous analysis.

Consider the frame of reference in which Twin One is at rest the whole time. When he ignites his thrusters for the acceleration, a pseudogravitational field permeates the universe in Twin One's rest frame.

Reality check! We know that in reality, it is the frame that is accelerating rather than the universe... but the point of relativity is that it doesn't matter - we get the same results.​

The field exactly cancels the force of his thrusters, so he stays motionless.

This pseudogravitational field lasts for only a second, but has incredible strength. One result of this field is gravitational time dilation. Twin Two is much higher (15 light years!) than Twin One in a very strong field, thus Twin Two's clocks run much faster during that time. By the time Twin One stops accelerating and the field disappears, Twin two has aged by 5 years, and is 3.82 light-years closer.

Reality check! In Twin one's frame, Twin two has moved 3.82 light years in one second!
This is true, and is not a violation of relativity. Globally, Twin-two is moving FTL, but locally they are not. Just as something falling across the event horizon is moving at light speed globally, but not locally.​

So now, Twin-one is 15 years old, and Twin two is 20 years old. What happens next? Twin-two approaches at v=-.745c (gamma=1.5), and ages another 10 years in the 15 years it takes to reach Twin-one. Both twins are 30 years old when they pass.​

 

[Pete]

I didn't say anything about him personally, I just don't think "the flat spacetime paradigm of GR" is mainstream. How many physicist have any knowledge of it? And how many of the physicist that qualified above have extensive (beyond just "hearing") knowledge of it? Furthermore, how many of those with extensive knowledge accept it?

I'm sorry Aer, but I can't satisfy you on this one - I can only appeal to the authority of Kip Thorne, who I assume knows many physicists and how they work.

Just out of curiosity, why do you think the flat spacetime paradigm isn't mainstream? Is it just an impression you have, or is there something more?

 

[Aer]

I will now point you to the UseNet Relativity Faq - Twin Paradox "General Relativity" explanation
(Note that "General Relativity is in quotes for a reason, as I conceded in [post=856313]my last but two post[/post].)

Using ideas from that site, (which I think are in accord with Relativity, BUT I now realise that I've relied on it too heavily in formulating my understanding of GR), here is the alternative reasoning to which I alluded:

Be careful of the figures in this story - they're not supposed to be a proof. I didn't derive them using GR, or using curvilinear coordinates in SR, I cheated by assuming that this explanation was equivalent to the SR explanation. This is just an arm-waving explanation, not a rigorous analysis.

I think you are refering to what Einstein thought of Relativity in 1907 in making your analysis? Because the link you provided clearly makes the point that the analysis you provided is not accepted in "modern relativity"

</em>
Here's the modern physicist's list (again, not sweating the fine points):

Spacetime Structure
Spacetime is a 4-dimensional Riemannian manifold. If you want to study it with coordinates, you may use any smooth set of charts (aka local coordinate systems). (This free choice is what has become of the General Principle of Relativity.)
Principle of Equivalence
The metric of spacetime induces a Minkowski metric on the tangent spaces. In other words, to a first-order approximation, a small patch of spacetime looks like a small patch of Minkowski spacetime. Freely falling bodies follow geodesics.
Gravitation = Curvature
A gravitational field due to matter exhibits itself as curvature in spacetime. In other words, once we subtract off the first-order effects by using a free-falling frame of reference, the remaining second-order effects betray the presence of a (true) gravitational field.

Note the lacking of:

</em>
General Principle of Relativity
All motion is relative, not just uniform motion. You will have to include so-called pseudo-forces, however (like centrifugal force or Coriolis force).

Which was an Einstein thought.

I'll admit, I do not know all the views of relativity. The only view I have any knowledge of is the modern view, which I think we should agree is the only view we should be considering when talking about what GR says.

I'll point you to the numbnuts on physicsforums if you want to only consider the view of relativity that Einstein held!

 

[Aer]

Just out of curiosity, why do you think the flat spacetime paradigm isn't mainstream? Is it just an impression you have, or is there something more?

Because I am the center of my universe and have not heard of it