A Refutation of General Relativity

[Guest Zanket]

And I'm telling you the schwarzschild r coordinate can not be easily interpreted as a linear radius! It is defined by the area of spherical shells. Thats why you don't see the result you are expecting. You need a space coordinate that applies to linear distances in the rest frame of the particle. This is why you are mistaken.

 

It is not me who is interpreting that. It is not my math. You say that I’m misapplying the math, but the reason you give relates to how the math is derived, and that is not my doing. The only way I can be misapplying the math is to be misusing the derived equation. You have not shown how I am misusing it. I used the derived equation in an example in my original post (the one about the star whose escape velocity at its surface is almost c) to show a glaring inconsistency between SR and GR. If you are right that I’m misapplying the math, then it should be a simple matter to explain away this inconsistency. Please do that.

 

The only interpretation of the GR derivation that I made is, since the derived equation is also valid in Newtonian mechanics, length contraction that is consistent with SR could not have been incorporated into the derivation. An equation that returns the proper time it takes a test particle to traverse between r-coordinates, that is valid in Newtonian mechanics, cannot be compatible with SR for the muon experiment, in which SR’s prediction of the muon’s proper time to traverse between r-coordinates is less than that predicted by Newtonian mechanics. Although I understand the definition of the r-coordinate, and how it differs from a directly-measured radius, that understanding is not required to reach this conclusion.

[Erasmus00]

The only interpretation of the GR derivation that I made is, since the derived equation is also valid in Newtonian mechanics, length contraction that is consistent with SR could not have been incorporated into the derivation. An equation that returns the proper time it takes a test particle to traverse between r-coordinates, that is valid in Newtonian mechanics, cannot be compatible with SR for the muon experiment, in which SR’s prediction of the muon’s proper time to traverse between r-coordinates is less than that predicted by Newtonian mechanics. Although I understand the definition of the r-coordinate, and how it differs from a directly-measured radius, that understanding is not required to reach this conclusion.

 

And thats where your misinterpretation. You are using an equation for the proper time a 0 energy freely falling particle takes to travel between two different schwarzschild radii and trying to use this equation to show that there is no length contraction in GR.

 

Your mistake with the radii is this: your equation looks superficially like an equation valid in Newtonian mechanics, its not, because in Newtonian mechanics, the r is the actual radius measured in a flat space. That is not actually what r is. How much general relativity do you understand?

 

Finally, do you really think that a whole generation of physicists wouldn't notice such an obvious "contradiction" where it to actually exist?

-Will

[Guest Zanket]

Your mistake with the radii is this: your equation looks superficially like an equation valid in Newtonian mechanics, its not, because in Newtonian mechanics, the r is the actual radius measured in a flat space. That is not actually what r is. How much general relativity do you understand?

 

You don’t seem to be addressing my points, so I will reiterate and emphasize the most pertinent parts: I understand the difference between the r-coordinate and the directly-measured radius. But all that matters about GR’s math I cited is that GR’s prediction matches the prediction of Newtonian mechanics. Then I know—as I showed by example in my original post—that GR contradicts SR, for SR’s prediction diverges from the prediction of Newtonian mechanics. Compare those two boldfaced points; my conclusion requires only basic logic. That the interpretation of the math in the derivation differs between GR and Newtonian mechanics is irrelevant. The discrepancy between the two boldfaced points, and because SR diverges from Newtonian mechanics because of length-contraction in the particle’s frame, tells me that there is no length-contraction in the particle’s frame in GR that is consistent with SR.

 

Finally, do you really think that a whole generation of physicists wouldn't notice such an obvious "contradiction" where it to actually exist?

 

What they have noticed or not is irrelevant here, of course. The only question here is, can you or anyone on this forum resolve the inconsistency of GR that I showed by example in my original post? You have not done that. The inconsistency is not subtle; the example shows that GR differs from SR by a factor up to infinity. If you are right that I have misapplied the GR equation, then it should be a simple matter for you to point out something like “SR does not predict that the star is contracted to almost zero length, because…”, or “GR’s prediction for the proper time elapsed for the particle is not based on the star’s mass, because…”.

 

So long as GR’s equation (the final product of the derivation) is valid in Newtonian mechanics, the derivation of the equation is irrelevant. Other than showing that the same equation does not work in Newtonian mechanics, no discussion of its derivation will resolve the inconsistency.

[Erasmus00]

You don’t seem to be addressing my points, so I will reiterate and emphasize the most pertinent parts: I understand the difference between the r-coordinate and the directly-measured radius. But all that matters about GR’s math I cited is that GR’s prediction matches the prediction of Newtonian mechanics. Then I know—as I showed by example in my original post—that GR contradicts SR, for SR’s prediction diverges from the prediction of Newtonian mechanics. Compare those two boldfaced points; my conclusion requires only basic logic. That the interpretation of the math in the derivation differs between GR and Newtonian mechanics is irrelevant. The discrepancy between the two boldfaced points, and because SR diverges from Newtonian mechanics because of length-contraction in the particle’s frame, tells me that there is no length-contraction in the particle’s frame in GR that is consistent with SR.

 

I am addressing your point. The fact that the escape velocity formula works out the same in Newtonian physics as GR is a happy coincidence. It does not mean that there is no length contraction in GR. I suggest the following calculations to convince yourself: first, coordinate transform into a system of space/time coords from the particles reference frame. Directly look at different lengths. Also, try the same calculations with a particle that doesn't start with 0 energy (i.e. at rest at infinity). You'll see the length contraction. You don't have to believe me, just do the calculations and you'll see.

 

What they have noticed or not is irrelevant here, of course. The only question here is, can you or anyone on this forum resolve the inconsistency of GR that I showed by example in my original post? You have not done that. The inconsistency is not subtle; the example shows that GR differs from SR by a factor up to infinity. If you are right that I have misapplied the GR equation, then it should be a simple matter for you to point out something like “SR does not predict that the star is contracted to almost zero length, because…”, or “GR’s prediction for the proper time elapsed for the particle is not based on the star’s mass, because…”.

 

I have repeated myself about half a dozen times. I'm trying to show you why your logic is flawed. Do the calculations I suggest above, and you'll resolve this with ease. I must ask, how much GR do you actually know? Forgive me if I'm wrong, but it seems like you've picked up one formula from a book and are trying to rewrite physics.

 

Now, SRs length contraction formula obviously does not depend on the mass of the gravitating object, as it ignores gravity. It should be obvious to you that SR and GR should only completely agree in the low mass limit. This is why the fact that GRs prediction depends on the star's mass shouldn't be a surprise.

 

So long as GR’s equation (the final product of the derivation) is valid in Newtonian mechanics, the derivation of the equation is irrelevant. Other than showing that the same equation does not work in Newtonian mechanics, no discussion of its derivation will resolve the inconsistency.

 

At the surface of the star, the classical idea of radius and the schwarzchild radius happily coincide. That is why your formula is valid at the surface of a planet (hence valid for escape velocity) HOWEVER, you at other radii, GR formula is not the same as the Newtonian one, because of the forementioned difference in Radii. Try the calculations above, you'll see the contraction you are looking for.

-Will

[Guest Zanket]

The fact that the escape velocity formula works out the same in Newtonian physics as GR is a happy coincidence. It does not mean that there is no length contraction in GR.

 

When the GR equation I cited (that incorporates that escape velocity formula) is identical to that used in Newtonian physics, it does mean that there is no length contraction in GR that is consistent with SR, as I showed by example by using the equation.

 

You don't have to believe me, just do the calculations and you'll see.

 

Regardless, the inconsistency between GR and SR would remain, so it would be a wild goose chase. It doesn’t matter to me if GR has length contraction. It matters to me only if it has length contraction that is consistent with SR. I drew the star uncontracted in drawing C (GR’s prediction) because a theory in which a free-falling test particle’s predicted proper time between r-coordinates is not reduced by length contraction (and I know that it’s not reduced if only because Newtonian mechanics predicts the same) is a theory in which there is effectively no length contraction. That is, whatever length contraction GR does have, has no effect.

 

I must ask, how much GR do you actually know? Forgive me if I'm wrong, but it seems like you've picked up one formula from a book and are trying to rewrite physics.

 

How much I know or not is irrelevant. How few formulas I use to show an inconsistency is irrelevant.

 

Now, SRs length contraction formula obviously does not depend on the mass of the gravitating object, as it ignores gravity.

 

Agreed. (And now we’re making progress.)

 

It should be obvious to you that SR and GR should only completely agree in the low mass limit.

 

Agreed, they completely agree only in flat spacetime. However, in the example about the star, GR is consistent with SR only if GR’s prediction is less than SR’s prediction. SR’s prediction is based on the particle’s velocity at the star’s surface, but the particle’s velocity reaches a maximum at the center of the star, so the particle traverses the star in less proper time than SR predicts. But I showed that GR’s prediction can exceed SR’s prediction.

 

This is why the fact that GRs prediction depends on the star's mass shouldn't be a surprise.

 

It isn’t GR’s dependency on the star’s mass per se that points to an inconsistency. It is that GR’s prediction exceeds SR’s prediction. GR’s dependency on the star’s mass serves only to show that there is no upper limit to GR’s prediction. But SR always predicts “almost instantly”, and the accurate prediction (the one that GR must predict to be consistent with SR) must be less than that.

 

Think of it intuitively: Does it makes sense to you that it could take the particle millions of proper years (for a sufficiently massive star) to traverse a star that is length-contracted in the particle’s frame to almost zero length, even though it moves relative to the star at almost c?

 

At the surface of the star, the classical idea of radius and the schwarzchild radius happily coincide. That is why your formula is valid at the surface of a planet (hence valid for escape velocity) HOWEVER, you at other radii, GR formula is not the same as the Newtonian one, because of the forementioned difference in Radii.

 

The GR equation is valid in Newtonian mechanics for any two radii at or above the surface (the equation I cited from the PDF file allows any two radii to be input). The GR equation uses the r-coordinate, just as the Newtonian derivation would. The interpretations of the derivations may differ, but the derivations (starting with eq. 51 in the PDF file) would look identical.

[Erasmus00]

It appears as if I will not convince you. I can only suggest you carry out the calculations I recommended and take the low mass limits to see the two theories agree. You'll find the two theories are indeed in agreement.

-Will

[Guest Zanket]

It appears as if I will not convince you. I can only suggest you carry out the calculations I recommended and take the low mass limits to see the two theories agree. You'll find the two theories are indeed in agreement.

 

I already agreed that the theories agree in flat spacetime. And I’ve shown that regardless of any length contraction incorporated into GR, it is inconsistent with SR. Can’t you even answer the intuitive question I gave? I’m not being obstinate here. I’ve given logical replies to all of your points. For example, I did not flippantly say that it would be a wild goose chase to do the calculations you propose; rather, I gave a good reason why it would be. You can convince me if you can counter my replies to the point where I cannot counter yours—a standard, fair argument. And I am very interested in whether you can accomplish that.

[Erasmus00]

Fine. I fail to see why you think the calculations are a wild goose chase. The way you attempt to calculate makes the agreement of SR and GR very difficult to see. The way I suggest makes it much more obvious. GR is not an intuitive science. Your (and my) intuition is not equipped to handle 4d curved geometries. Differential geometry is. Hence, calculations are the easiest way to go.

 

Think of it intuitively: Does it makes sense to you that it could take the particle millions of proper years (for a sufficiently massive star) to traverse a star that is length-contracted in the particle’s frame to almost zero length, even though it moves relative to the star at almost c?

 

Thinking about intuitively is bound to fail. I can't claim to intuit 4d curved spaces. I'd like to point out that as the particle gets very close to a very dense object (since you are using a formula for falling from the s. radius to the center of a black hole, only very dense objects and STRONG gravitational fields apply), spacetime becomes very warped. This warping adds to an increased linear distance that the particle must travel.

 

Finally, you seem to think that the only way GR can be consistant with SR is for the proper time interval to decrease from SR to GR. I don't understand why you think this must be?

-Will

[Guest Zanket]

After this post, Erasmus00 has opted to take our discussion offline.

 

I fail to see why you think the calculations are a wild goose chase.

 

I’ll put it as simply as I can:

 

In my original post I cite a GR equation (that returns the proper time it takes a test particle, having free-fallen from rest at infinity, to fall between two r-coordinates above the surface of a massive object). Then I use this equation to show an inconsistency between GR and SR.

 

To show the inconsistency, I need not have mentioned the derivation of this equation. I did so only to make an additional point that validates drawing C. In SR, the prediction of proper time between r-coordinates is reduced (from the prediction of Newtonian mechanics) by length contraction, as it is in the muon experiment. Since GR matches Newtonian mechanics for this prediction, GR effectively has no length contraction. That is why the star in drawing C is not drawn as length-contracted.

 

Now, you say that if I did the math differently, I would see that GR does indeed have length contraction. But the calculation you propose is not going to change the fact that the GR equation predicts the same as does Newtonian mechanics, leading to the inconsistency and the validation of drawing C. Then doing the calculation you propose is a wild goose chase.

 

When I next post this refutation somewhere, the derivation will not be mentioned. Had I done that this time, you could not have focused on it.

 

Your (and my) intuition is not equipped to handle 4d curved geometries. Differential geometry is. Hence, calculations are the easiest way to go.

 

Here we’re talking about a simple case of a free-falling object moving radially. I gave the way to calculations in my original post. But now I see that I must do better than that.

 

Let a test particle free-fall from rest at infinity (or a great distance) to a star whose escape velocity at its surface is infinitesimally less than c. The particle reaches the surface at infinitesimally less than c.

 

Now both SR and GR are used to make a prediction of the proper time it takes the particle to pass through the star, assuming it were able to pass through it unimpeded.

 

SR applies to a directly measured velocity. The velocity at the star’s surface is used. At the surface, SR predicts that the star is length-contracted in the particle’s frame to a percentage = sqrt(1 – (infinitesimally less than c, as a fraction of c)^2) = infinitesimal length. (This is supported by the muon experiment.) At a velocity infinitesimally less than c, the particle takes an infinitesimal time in its frame (by its clock) to pass through the star. SR’s prediction is higher than the accurate prediction, because the velocity input was that at the star’s surface, but the particle’s maximum velocity while traversing the star is at the star’s center. Then the exact prediction is less proper time than SR predicts, yet still infinitesimal.

 

SR’s prediction = “lower than an infinitesimal proper time”, regardless of the star’s mass. In other words, always infinitesimal.

 

Now GR is used to make the same prediction. The GR equation cited in my original post (in the PDF file) works for any two r-coordinates above the surface of a massive object. The equation shows that the proper time for the particle to pass between any two r-coordinates is dependent on the object’s mass. The more mass, the more time required, with no upper time limit. Unlike the crude SR equation used above, the GR equation factors in the particle’s velocity at each increment of r-coordinate; that is, the GR equation handles the particle’s gravitational acceleration. What the GR equation does not handle is a particle falling below the surface of the mass. However, the prediction of the GR equation, for a particle to fall between r-coordinates above a surface, is guaranteed to be less than the prediction for a particle to fall between the same r-coordinates below the surface of an object having the same mass, since the strength of gravity is more in the former case. Then the exact prediction is more proper time than GR predicts, and is dependent on the star’s mass, with no upper time limit.

 

GR’s prediction = higher than a proper time that depends on the star’s mass, with no upper time limit.

 

Now compare the boldfaced statements. GR’s prediction is incompatible with SR’s prediction.

 

Thinking about intuitively is bound to fail.

 

I say the opposite. Einstein succeeded by fitting his math to his intuition. He said, “The only real valuable thing is intuition.”

 

I'd like to point out that as the particle gets very close to a very dense object (since you are using a formula for falling from the s. radius to the center of a black hole, only very dense objects and STRONG gravitational fields apply), spacetime becomes very warped. This warping adds to an increased linear distance that the particle must travel.

 

Yes, but 0% of any distance is zero, and an infinitesimal portion of any distance is infinitesimal. That’s why my example uses a star whose escape velocity at its surface is infinitesimally less than c. Then SR predicts that the star is contracted to infinitesimal length in the particle’s frame, regardless of the star’s directly-measured radius (= regardless of its mass).

 

I cited two compatible formulas. The one in the book is the one you mention. The other, the one in the online PDF file, is more versatile, allowing any two r-coordinates to be input. (If I could find that one in a book, I would cite it alone.)

 

Finally, you seem to think that the only way GR can be consistant with SR is for the proper time interval to decrease from SR to GR. I don't understand why you think this must be?

 

I tried to make that more clear above, in the example in this post. SR can be used to make accurate predictions within a range. (Such is done in the muon experiment.) SR is used above to make an accurate prediction of “lower than an infinitesimal proper time”, where “infinitesimal proper time” is SR’s prediction. GR, taking gravity into account, gives the exact prediction. That exact prediction must fit within the range that is based on SR’s prediction. In this case, GR’s prediction must be lower than SR’s to fit within the range.

[andrewgray]

Zanket,

 

Are you still monitoring scienceforums?

 

 

Andrew Gray

[Guest Zanket]

Are you still monitoring scienceforums?

Hi Andrew,

 

Your PM mailbox is full. PM is a little awkward. How about in a few days to a week I'll post a thread here about GR's self-inconsistency, with my latest improvements.

 

I need a little break from physics right now anyway. :friday:

 

Regards.

[andrewgray]

Zanket,

 

Sounds good. I will look for your "updated" post.

 

Andrew A. Gray

 

P.S.

 

It seems newbies are allowed only 1 message, including the one in "sent items". I deleted this one, so I have one left now. However, I did get a legitimate email notification to my real email box, so it did work. So send me another message when you post, and even if my SF box is full, I will be notified.

[Tormod]

It seems newbies are allowed only 1 message, including the one in "sent items". I deleted this one, so I have one left now. However, I did get a legitimate email notification to my real email box, so it did work. So send me another message when you post, and even if my SF box is full, I will be notified.

 

Now that you have reached 10 posts, your PM limit is higher. :phones:

 

We had some problems with people signing up only to start spamming via PM - it's just a safety precaution.

[Farsight]

Hi Zanket and Andrewgray. I'm Farsight. I go by the name of Popular here for historical reasons.

 

All: For the record, I concur with some of Zanket's points. I think he's right to challenge a modern and arguably corrupted interpretation of General Relativity. However I don't share his view that General Relativity is rendered invalid. A theory might be wrong in some respect, but it can be fixed, improved, enhanced. A theory can surely evolve. Look at String Theory. If Zanket's refutation was a valid assertion, String Theory should have been dead and buried ten times over by now.

 

Zanket: I'll take another look at your point in case there's something new that we haven't discussed already.

[snoopy]

Dear Zanket,

 

This is quite a silly post but I will play anyway.

 

In the beginning you say all drawings are from the particles perspective so you have chosen the particle as your frame of reference.

 

Then you go and and create situations A, B, and C I think you only included A to either confuse yourself or others.

 

You then go onto say that B and C are the same at impact but you changed your frame of reference in B and "because of your inconsistency" you then blame it on GR you cant go chopping and changing your frames of reference then complain about it doesnt make sense.

 

In the strictest terms B and C are not identical its A and C that are identical.

 

You also go on about length contractions why ? Length contractions only happen at high speeds you have chosen an arbitrary speed so if I choose it to be 5 miles per hour there are no length contractions involved. Why do you even mention it ?

 

You then go onto say that drawing B is confirmed by muon experiments.

 

No muon experiment I have ever heard of involves hurling a star at a muon.

 

You then go onto confuse others and yourself even more when you state that drawing C is confirmed by a book on Black Holes ? First its in free fall around a star now the star has turned into a black hole, please make your mind up. You then go onto say that its distance from the weird Black Hole/Star is "infinite" or a very great distance well if its at an "infinite" distance it would take an infinite amount of time to get their or in other words it would never get there. There is a difference between a large distance and an infinite one please try to be more exact with your refutation of the whole of classical physics please.

 

 

You then ramble that SR predicts that fast moving objects can somehow cause stars they are on a collision course with to be length contracted to almost zero.

 

This is absolutely false SR claims that rulers and timeclocks are affected when measuring fast moving objects by Lorentz contractions that is it.

 

From the particles perspective the distance between it and the star is shorter than from our outside perspective so its the distance between it and the star that undergoes a Lorentz contraction not the actual star.

 

You then go onto discuss about the particle passing through the star without giving any of us the slightest idea what kind of particle it is ? Is it a neutrino, a pi-meson, a photon ? God himself apparently only knows.

 

You would have to give more details about the particle its velocity what type of star it is, and where the heck the black hole comes in ?

 

SR in the strictest terms has nothing to say about particles passing through stars. This is maybe where you are getting confused its a misrepresntation of the theory to use it in this way.

 

Any situation where gravity played such a big role as this you would be forced to use GR.

 

So in fact you have failed to produce any inconsistencies in GR you just have inconsistencies in your application of the theory.

 

GR is not a superset of SR.

 

SR was called special because it applies only to inertial frames and it does not have anything to say about gravity.

 

GR is obviously more general and applies to any frame and includes gravity.

 

So thanks for playing and goodbye. :)

[Guest Zanket]

However I don't share his view that General Relativity is rendered invalid. A theory might be wrong in some respect, but it can be fixed, improved, enhanced.

A theory that is wrong in some respect is invalid. Any modified theory is a new theory, even if it retains its name.

 

If Zanket's refutation was a valid assertion, String Theory should have been dead and buried ten times over by now.

I think not. Even if my refutation was valid, string theory would go on without me.

[Guest Zanket]

This is quite a silly post but I will play anyway.

Had I anticipated that anyone would try to refute this circa-2005 thread now, I would have waved them off in advance. Please see my new argument here.