Zanket

Arguing with you is pointless because you disagree with SR, except when you contradict yourself.

No. I am using well established theories backed up by observed facts. Objects cannot exceed the speed of light; none has been observed to do so.

The equations always return v < c. I showed that your method of measuring velocity is invalid.

Your paper has one thing right: The velocity of an object relative to some other object asymptotes to c. You yourself disprove your own theory.

It disproves nothing in my paper. It’s a key point of it.

You are mixing frames again.

Nope. The Usenet Physics FAQ did not mix frames without anybody noticing for years.

The rocket can get to Andromeda in 28 years because, to the crew, the apparent distance to Andromeda has shrunk from 2 million light years to a bit less than 28 light years.

Irrelevant.

Andromeda can traverse the rocket in 28 years ...

You contradicted yourself yet again. Before you said it would take > h/c for an object to traverse the rocket in the crew's frame. Now you agree it can take < h/c, agreeing with me.

Of course there isn't any jerk in a uniform field. The field generated by a massive body is not uniform. The acceleration in such a field is not uniform. Your treasured equations do not apply in such a field.

Nor are they applied to such a field. You could not quote anything from my paper that does that.

What value of a do you propose to use in these equations when the test particle changes its acceleration every step of the way on falling toward the star?

Section 3 implicitly increases the value of a as the particle falls.

No we aren't. It takes a beam of light 0.3336 microseconds to traverse a spacecraft that is 100 meters long (your example). 0.3336 microseconds is quite measurable with modern instruments. I guarantee you that a ball (assuming it has some mass) takes longer than this to traverse the spacecraft in the frame of the crew.

You’re using circular logic there. You’re basically saying “since I’m right that it takes time h/c for light to traverse, which is not an arbitrarily short time, then you’re wrong that the acceleration is unsurvivable”. But you’re wrong that it takes h/c. If you input an unsurvivable acceleration into eq. 19 then you would see that. Or you can input an acceleration as little as 1g into the equations for a super-long rocket; more on that below.

Believe it or not, this is not the best source in the world. It is a Classics Illustrated version of physics. It is correct, but there is little explanatory background.

All that matters here is that it is correct. My paper is not intended to be a tutorial on SR.

It is mostly a compendium of equations that can be easily be applied incorrectly.

The equations are simple, the descriptions of the variables are clear, and I walked you through how to use them. The site also uses them to report that my finding is correct, and you can double-check its results with the equations to verify that you are applying them correctly.

For example, the site reports that a crew can get from Earth to the Andromeda galaxy in 28 years on their clock. The proper distance between the Earth and Andromeda is 2 million light years. Let the ship have a proper length of 2 million light years. Let it be initially at rest with respect to Andromeda, with Andromeda near the tip of it. Then Andromeda can traverse the rocket in 28 years on the crew’s clock (upon which the tail of the ship reaches Andromeda), and in a shorter time if they accelerate at a higher rate. (This is not a “standard-sized rocket”, so you still have to measure velocity using a “known distance apart” that is zero in the limit.)

Equations 12-21 in your paper only apply to a constant acceleration. They do not apply when jerk is present.

There is no jerk present in a uniform gravitational field, by definition. An object falling in a uniform gravitational field accelerates at a constant rate. Hence the qualifier “uniform” = “constant”.

You left out a rather critical line:

For a standard-sized rocket with a survivable acceleration, this difference in how fast things age within its cabin is very small.

Here we’re talking about an arbitrarily short time elapsed in the crew’s frame, so we’re talking about an unsurvivable acceleration.

The effect is challenging to measure on a spaceship the size of the Earth: It is small.

The effect can be arbitrarily large on any spaceship undergoing extreme acceleration.

I asked you to show me the math. You did not. You showed a theoretical result, and no math.

It's not my job to tutor you on SR, a theory. You are arguing against the link I gave you from the Usenet Physics FAQ.

What other clocks? I said "I only need one clock."

When clocks along the length of the “known distance apart” run at various rates, what one clock will you use? You’d be mixing frames in that case.

What gravitational time dilation are you talking about? You had better show this, mathemetically.

From The Relativistic Rocket:

... a clock attached to the rocket's ceiling (i.e. furthest from the motor) ages faster than a clock attached to its floor.

This is standard SR, so you can look up the math yourself.

Only one clock is needed.

As long as it runs at the same rate as all of the other clocks along the "known distance apart", which it will only when that distance is zero in the limit.

One way to measure the velocity is to note how much time passes when some object passes between two points that are a known distance apart. For example, the time of passage between (1) the ball crossing the tip of the rocket and (2) the ball crossing the tail of the rocket. If it takes an arbitrarily short time for this to occur, the ball's velocity can be arbitrarily high.

 

Forget the star, forget the rod, make the ball a single point. You are making this overly complex and thereby not seeing your mistakes.

OK, make the ball a test particle. Measure the velocity using the method in your example. How can you tell how much time passes, when clocks all along the length of the rocket run at different rates due to gravitational time dilation? A clock at the tip of the rocket runs faster than a clock at the tail of the rocket. Measuring your way is mixing frames, which leads to invalid results.

You can’t accurately tell how much time passes unless the clocks at both ends of the “known distance apart” run at the same rate. The only such distance is zero in the limit. When velocity is measured that way, it will always be less than c. While moving between two points zero distance apart in the limit, the test particle does not length-contract further. Then the increasing length contraction (increasing because the rocket is accelerating) that lets the particle traverse the rocket in an arbitrarily short time in the crew's frame does not affect the velocity measurement.

The rocket does not move with respect to the crew. The rocket remains a constant length in the eyes of the crew. That’s even more basic SR. And it is the key piece of information that you are ignoring.

This was not ignored above.

The tip of the rocket can get to the ball and star in an arbitrarily short period of time because the distance to the star can be made arbitrarily small in the crew's frame by making the relative velocity approach that of light. Suppose the ball is even with the tip of the rocket. The key question, and the one you refuse to answer, is how much longer does it take for the ball to traverse the length of the rocket as observed in the crew's frame? Certainly it is more than h/c, no? Remember, the length of the rocket is not subject to length contraction.

If you think the star can get to the tip of the rocket in an arbitrarily short period of time in the crew’s frame, why would you think the star cannot get to the crew in such time? After all, the star has traversed almost 100% of the distance by that point.

If you read closely, I covered this above. But I’ll elaborate. In the initial condition where the rocket is at rest with respect to the rod, let the ball, which is attached to the rod, be even with the tip of the rocket. Let the crew be even with the tip of the rod opposite from the star. Let the proper height of the rocket (h) be 100 meters. Now let the rocket accelerate such that the entire rod (which has a proper length of one hundred thousand light years) length-contracts to a length of one meter in the crew’s frame (i.e. as they measure) in a negligible amount of time elapsed on the crew’s clock. At that moment the crew is beyond the tip of the rod and has moved partway along it. Then at that moment the distance in the crew’s frame between the crew and the star is less than one meter. The star has traversed over 99% of the rocket (> 99 meters / 100 meters). Meanwhile the ball, which is between the crew and the star, has traversed almost the entire rocket. Yet when the crew passes the ball, they will measure its velocity to be less than c. Same thing for the star. In the crew’s frame, even as the rod length-contracts from a length of one hundred thousand light years to a length of one meter in a neglible amount of time elapsed, decreasing the distance they measure to the star from one hundred thousand light years to less than one meter, they will always measure their velocity relative to any part of the rod passing directly by to be less than c. Any decent book on SR covers this. The equations in the Usenet Physics FAQ (section 8 of my paper) support this.

The answer to your question is that it can take an arbitrarily short time for the ball to finish traversing the length of the rocket, as observed in the crew's frame.

You can even take the limit as [math]v\to c[/math].

That's what Farsight did when he said "You can reduce the velocity of the rocket by as little as you like".

You can reduce the velocity of the rocket by as little as you like, and the stationary ball takes as little time as you like to traverse the interior of the rocket as far as the crew are concerned.

Correct.

Nowhere have we contradicted Special Relativity.

Correct.

English isn't his first language ...

Incorrect!

The ball still has some location as perceived by the crew. This location is some fixed point on the ball.

The location of an object is not just one of many points on the object. Even if you choose one point arbitrarily and deem it the ball’s sole location, it only obfuscates the issue.

How can some object (e.g., the ball) be observed to exceed the speed of light by the crew?

I’ve shown you in multiple ways that the ball need not exceed c while traversing the rocket in an arbitrarily short time in the crew’s frame, including showing you the relevant equations from the Usenet Physics FAQ (in section 8 of my paper). You’re arguing against not just me, but also the Usenet Physics FAQ.

If you want to measure the velocity of some object as perceived by an observer in some frame, the distances must be measured with rulers fixed in the observer's frame and times must be measured with clocks fixed in the observer's frame. You are not doing this.

The equations implicitly do that.

Do you see the mixing of frames going on here?

Do you think the Usenet Physics FAQ mixed frames without anybody noticing for years?

I'm sorry for the poor wording here. Obviously the ball is moving in the crew frame. What I meant was that this vector is expressed in the crew frame. I used fixed here meaning not subject to length contraction.

Anything that moves relative to the crew is length-contracted in their frame. That’s basic SR. The relevant equation is eq. 23 in my paper, for the Lorentz factor. And you contradicted yourself again. Above you agreed that “The ball is subject to length contraction” in the crew’s frame. The ball cannot be simultaneously both length-contracted and not length-contracted in the crew’s frame.

Right back at ya, you are a pedant and a crackpot.

Despite your rudeness I will again help you to see that the Usenet Physics FAQ is correct.

Consider this initial situation:

[CXXXXXX]

RRRRRRRRBRRRRRRRRRRRRRRRRRRRRRRRRRRRRRS

[CXXXXXX] = rocket, initially at rest with respect to the rod

C = crew, who remain in a fixed position with respect to the rocket

X = empty space

R = rod with ball and star affixed

B = ball affixed to the rod

S = star affixed to the rod

As shown, the ball is initially near the top of the rocket. Let the rocket begin accelerating toward the star. Then the ball and the star move towards the crew. You agree that the crew can get to the star in an arbitrarily short time in their frame; the rod doesn’t change that. It should be ultra clear that the crew will always get to the ball before they get to the star. Then they must be able to get to the ball in an arbitrarily short time in their frame. In other words, the ball can traverse the rocket in an arbitrarily short time in their frame.

Nothing need move faster than c. The entire rod, including the ball and star affixed to it, length-contracts in the crew's frame. They traverse it at less than c relative to it. Let the rod have a proper length of one hundred thousand light years. Let it be length-contracted to a length of one meter in the crew's frame (i.e. as measured by them), in which case the crew’s velocity relative to the rod is nearly c. Then they need move less than one meter at a velocity of nearly c, both measured in their frame, to reach either the ball or the star. That shows how they can get to either the ball or the star in a fraction of the time h/c on their clock (where h is the proper height of the rocket) while moving slower than c relative to those objects. Any decent text on SR explains this.

If the ball can traverse the rocket in an arbitrarily short interval of time in the frame of the crew, the ball can exceed the speed of light in the frame of the crew.

No, you agreed that the star S need not exceed c to traverse the rocket in such time. Then the ball, which is in the frame of the star S, need not exceed c either.

They use non sequitur, rhetoric, false analogy, and argue till you are blue in the face.

A classic case of the pot calling the kettle black. More on that below.

There has been no reply from zanket after his "theory" was shown to be rubbish.

I haven’t replied after one day! I must be a crackpot!

Untangling the web of errors in a crackpot theory is a chore and leads to little of any use.

Let’s recap your “logic” displayed in this thread:

You think SR is not applicable in the presence of a gravitational source. No word from you on how it could then be experimentally confirmed.

You think the equivalence principle is limited to non-gravitational experiments only. And you think it applies to gravitational experiments.

You think a ball can simultaneously both move and not move relative to someone.

CXXXXXB is fixed in the frame of the crew and is not subject to length contraction.

No, the ball is not fixed in the frame of the crew. The ball remains at rest with respect to the galaxy. The crew moves with respect to the ball and the galaxy. The ball is subject to length contraction in the crew's frame. My drawing is the initial condition only; that was clear from the text.

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXS is in the frame of the star S and is subject to length contraction.

It is XXXXXXBXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXS that is subject to length contraction in the crew's frame. The ball is in the frame of the star S.

It is the length contraction that makes the crew able to traverse the length of the galaxy in an arbitrarily short period of time. The CXXXXXB length is not contracted.

No, it is [CXXXXXX] that is not length contracted in the crew’s frame. The ball moves relative to the crew.

Mods, please put this thread in Speculations.

You are illogical. Above you say “suppose the crew observes the ball to traverse the rocket in time [math]0.1 h/c[/math]”, yet you say that the ball does not move relative to the crew with “CXXXXXB is fixed in the frame of the crew”. The ball cannot both move and not move relative to the crew.

The rocket traverses the galaxy in an arbitrary period of time because the galaxy shrinks due to length contraction. The rocket itself does not shrink in the frame of the crew. You are mixing frames, a very bad thing to do, particularly when dealing with relativistic effects.

No, I am not mixing frames. For the sake of argument drop your insistence that the ball needs to move faster than c to traverse the rocket in an arbitrarily short time in the crew’s frame; otherwise you’ll never see it. Keep an open mind. Now consider this situation:

[CXXXXXB]XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXS

[CXXXXXB] = rocket, initially at rest with respect to the galaxy

C = crew, who remain in a fixed position with respect to the rocket

X = empty space

B = ball, which remains at rest with respect to the galaxy

S = star at far side of galaxy

As shown, the ball is initially at the top of the rocket. Let the rocket begin accelerating toward S. Then the ball, which remains at rest with respect to the galaxy, moves towards the crew. You agree that the crew can get to S in an arbitrarily short time in their frame. But the crew will get to the ball first. Then they can get to the ball in an arbitrarily short time in their frame too. Nothing need move faster than c.

Eq. 19 in my paper returns the time elapsed in the crew’s frame, for them to reach either the ball or S. Eq. 16 shows that the ball does not move faster than c. The ball, because it remains at rest with respect to the galaxy, can be treated as part of the galaxy. The ball shrinks due to length contraction along with the galaxy of which it is part.

That the rocket itself does not shrink in the frame of the crew is irrelevant. We’re discussing what happens to the ball in the crew’s frame, not what happens to the rocket in that frame.

This is the misapplication of the equivalence principle that gets you into trouble.

You are defying logic there. My statement follows logically from the definition of the EP you gave.

From http://relativity.livingreviews.org/Articles/lrr-2001-4/:

The outcome of any local non-gravitational experiment is independent of where and when in the universe it is performed.

 

You are not performing a non-gravitational experiment here. You are asking how a point mass accelerates a body with negligible mass.

The definition you give here is one of the many definitions of the strong EP.

Wikipedia says:

The strong equivalence principle states that the results of any local experiment, gravitational or not, in an inertial frame of reference are independent of where and when in the universe it is conducted.

Then my usage of the EP is fine. You don’t fully understand it.

You misapplied those equations.

No, the ball is treated the same as the star. If you want the crew’s elapsed time to reach the ball, then you put the height of the rocket into eq. 19 for d, which is the initial distance between the crew and the ball as measured in the galaxy’s frame (or the crew's frame; doesn't matter because they are initially at rest with respect to the galaxy). If you want the crew’s elapsed time to reach S (the star), then you put the initial distance between the crew and the star as measured in the galaxy’s frame.

The second postulate (the speed of light is the same to all observers) is very applicable. Think about what you are saying in your paper in light of this postulate. By saying the ball can traverse the spacecraft in an arbitrarily small amount of time, you are saying the ball can exceed the speed of light.

No, as shown by eq. 16. The velocity of the ball (v) is always less than c, just as it is for S.

Wrong. A sufficient velocity relative to the galaxy makes the galaxy shrink to the size of a pinhead in the crew's frame.

Yes, and the ball along with it. That’s how the ball (or any other object in the galaxy that is at rest with respect to the galaxy) traverses the rocket in an arbitrarily short time in the crew’s frame.

The rocket has zero velocity in the crew's frame.

Irrelevant. The ball moves independently of the rocket.

The equivalence principle talks about the inability to distinguish between uniform acceleration and a uniform gravitational field. You are applying the principle erroneously.

Nothing you boldfaced of mine violates the EP.

“The crew of a relativistic rocket experiences the equivalent of a uniform gravitational field” is implied by the EP. They must experience the equivalent of a uniform gravitational field, if they are unable to distinguish between what they experience and what someone in a uniform gravitational field experiences.

The second statement you boldfaced is not based on the EP. “A nonuniform gravitational field is everywhere uniform locally” is implied by the definition of “local”. From that it follows that the “particle always falls through a uniform gravitational field (a succession of them, each applying only locally)”. Deem the gravitational field between your head and feet as uniform. Then a particle that falls between your head and feet falls in a uniform gravitational field. If it fell from higher up, then it fell through a succession of uniform gravitational fields, each applying only locally.

The nonuniform gravitational field produced by a point mass is everywhere nonuniform.

Except locally, where by definition it is uniform.

People like you are dangerous. People who don't know math very well may see you spouting nonsense and not see that what you spout is nonsense. You showed us how to solve the problem incorrectly. I posted the link to show how the problem can be solved correctly.

It’s the other way around. People who see only what they want to see and favor a rush to judgment are dangerous. I gave you the equation for the ball, I showed you that it comes from the Usenet Physics FAQ, but still you ignore it in favor of your own viewpoint. You think SR is inapplicable despite its experimental confirmation. And basic logic says that you cannot refute a paper that purports to refute GR by simply referencing a paper on GR; that ignores my evidence to the contrary.

Try again. In the frame of the crew (fixed with respect to the rocket), the ball takes more than [math]h/c[/math] time to traverse the rocket, where [math]h[/math] is the height of the rocket.

No. See the equations for the rocket in section 8 in my paper. These equations come from the Usenet Physics FAQ that section 8 references. Let the ball remain at rest in the gantry’s frame, initially at the top of the rocket. The time required in the crew’s frame for the bottom of the rocket to reach the ball is given by eq. 19 in my paper, where d is the height of the rocket. The equation shows that the time elapsed in the crew’s frame can be arbitrarily short for any given d.

Any decent book on SR tells you that the crew can reach the far side of a galaxy in an arbitrarily short time on their clock. Then of course they can reach a ball on the far side of their rocket in an arbitrarily short time on their clock as well.

Your principal mistake is a misinterpretation of the equivalence principle:

According to general relativity’s equivalence principle, the crew experiences the equivalent of a uniform gravitational field.

This is not quite right; the equivalence principle holds no experiment performed in a closed system can distinguish between an accelerated reference frame or a reference frame in a uniform gravitational field.

You have given one of many compatible definitions of the EP. What you quoted of mine follows from it, and is not intended to be a definition of the EP.

You explicitly propagate this mistaken interpretation of the equivalence principle in section 1, where you equate the non-uniform gravitational field induced by a point mass to a uniform gravitational field.

I do not equate those anywhere in the paper. Quote me.

For a proper analysis of the problem of a particle of negligible mass falling from rest at [math]r=\infty[/math] toward a point mass, see Voracek, P., "Relativistic gravitational potential and its relation to mass-energy", Astrophysics and Space Science, vol. 65, no. 2, Oct. 1979, p. 397-413.

That’s like trying to refute GR by referencing a paper on Newtonian mechanics. It proves nothing.

The theory of relativity is 90+ years old. Don't you think that this blatant flaw, should it exist, would have been uncovered by now?

One could have said the same thing about Newtonian mechanics in 1915, except change “90+” to “200+”.

Section 2 has a related reader-author comment:

Reader: Do you really expect us to believe that an inconsistency has existed undetected in general relativity ever since it was published?

Author: It is known that general relativity predicts central singularities where its equations break down and where it is incompatible with quantum mechanics. Then it should not be a surprise that the theory is flawed in another way.

Eienstein did see the issue of Entropy and Thermal Eqilibrium. He never claimed his theory could explain this, he merely thought it an improvement to current theories of gravity. Once it was shown by Hubble the universe is indeed expanding, he had that problem fixed. Explain why these issues are irrelevant to your theory? These may prove it falsifiable, which every good theory should do.

Can you prove with references that this is an issue? Let's be clear that you say this is an issue with any universe that always exists. I've read extensively on cosmology, and the only issue with entropy that I've seen is for a universe that always oscillates between a big bang and a big crunch. Is that the one you're talking about? Harrison says this issue is highly speculative.

Now, if we use the same coordinates used to derive the almost infamous Eq. (17) we get that the infalling lightcones collapse at the Schwarzschild radius, i.e. the coordinate system and any equations resulting from the use of it breaks down at the Schwarzschild radius, including Eq. (17).

To avoid confusion I won’t refer to eq. 17 from my online reference; I’ll refer to eq. 4 in my paper, the same equation. Notice the circular logic in your statement. You’re using eq. 4 to show that eq. 4 doesn’t apply below the Schwarzschild radius. Really it’s by interpretation that eq. 4 shows that v (of section 2) cannot be measured at and below the Schwarzschild radius, because otherwise SR would be violated. In other words, someone looked at eq. 4 and said, “Holy crap, SR will be violated unless we assume that no object can be fixed at an altitude at and below the Schwarzschild radius, disallowing v from being measured”. And so it was assumed that all objects must fall there. Eq. 4 is still valid there; it just has no practical purpose.

Your claim is that Eq. (17) holds even here, whereas I've just shown, by means general relativity allows, that it doesn't.

No, that is not my claim. Section 2 shows that eq. 4 is invalid. That’s because it is inferable by means GR allows (and not by eq. 4) that v is less than c there, rather than v not applying there as eq. 4 indicates. Because GR makes contradicting predictions about the same situation, it is inconsistent.

It is thus quite clear that, by means general relativity allows, Eq. (17) only applies outside the Schwarzschild radius, and that different coordinates are required to cover more of the Schwarzschild space-time manifold. Your alleged inconsistency is thereby explained and accounted for, by means general relativity allows.

You are looking at only one side of the inconsistency, which is to say you’re ignoring the inconsistency. (That’s what everyone does.) Suppose a theory about birds contains these statements:

Most birds can fly.

No birds can fly.

If I pointed out that these statements contradict each other, using your reasoning one would say either “Zanket, you’re wrong because the theory clearly says that most birds can fly” or “Zanket, you’re wrong because the theory clearly says that no birds can fly”.

Section 2 already has two reader-author comments that address this:

Reader: The velocity v asymptotes to c only as low as the Schwarzschild radius, at the event horizon.

Author: The analysis above shows that v always asymptotes to c; i.e. as long as the particle falls. Since this was inferred by means general relativity allows, the theory cannot demand otherwise without being inconsistent.

Reader: At and below an event horizon no object can be fixed at an altitude, so your analysis fails.

Author: That puts the cart before the horse. When v always asymptotes to c then so does escape velocity, in which case escape velocity is always less than c and then there are no event horizons. Since this was inferred by means general relativity allows, the theory cannot demand otherwise without being inconsistent.

Finally I'd like to bring to your attention something I noticed in your article, the following statement:

 

Likewise, Taylor and Wheeler place no limit on the size of an inertial frame.

 

Here you're referring to pages GL-4 and 2-4, sect. 3 (your ref. #6). I then refer you to page 1-14, sect. 8 in that same book. The sections begins with the following sentence:

 

In practice there are limits on the space and time extent of the free-float (inertial) frame.

 

I just thought you should know if there's a typo or something.

The distinction is made by “in practice”. If you look more closely you’ll see that there is no contradiction between their statement and mine. First, look at their definition on pg. GL-4 for a free-float (inertial) frame, which I shorten to “a frame with respect to which the tidal force can be neglected for the purposes of a given experiment”. Notice that no limit on the size of the frame is placed. Next, see sample problem 2 on pg. 1-4, where they “assume that a single free-float frame can stretch all the way from Sun to Andromeda”, a distance of two million light years. Finally, read the text of section 8 starting on pg. 1-14. It should become clear that “in practice” means “for the purposes of a given experiment”. For one experiment, the inertial frame may be no larger than a breadbox before the tidal force becomes significant. For another experiment, the inertial frame may be a billion light years long, with a negligible tidal force throughout. In practice (for any given experiment), there is a limit on the size of the frame. But by definition (for experiments in general), there is no such limit.

He misapplies the equivalence principle ...

You have demonstrated that you don’t understand it. You think SR is inapplicable in the in the presence of a gravitational source, i.e. inapplicable period. How do you explain the experimental confirmation of SR then? The equivalence principle is what allows SR to be used in the presence of a gravitational source.

... and proceeds from this point to assume a uniform gravitational field everywhere.

According to the equivalence principle, the crew of a relativistic rocket experiences the equivalent of a uniform gravitational field.

That quote does not imply a uniform gravitational field everywhere. The quote is implied by any decent text on the equivalence principle.

The equivalence principal only applies at a point.

That’s no more an issue for me than it is for all the texts on the equivalence principle that show it applied to larger regions. The reader-author comment in my introduction addresses this issue and shows that Feynman, Taylor, Thorne, and Wheeler all apply the equivalence principle to larger regions.

I do not see a single tensor equation in the paper. The equations of motion in general relativity are tensor equations.

Can you prove logically or mathematically that tensor equations are required? I didn’t think so. A reader-author comment in section 5 addresses this:

Reader: Without new field equations, your theory is worthless.

Author: Field equations are not required. Using only the new metric and the principle of extremal aging, a principle of special relativity, one can make falsifiable predictions.

I do see a lot of hand-waving and misapplications of various equations.

You’re the one doing the handwaving. Your "I do not see a single tensor equation in the paper" is a prime example. You've not shown a misapplication of any equation.

The free-fall velocity will asymptote to c, but this occurs at the Schwarzschild radius, not at r = 0.

Section 2 shows that v always asymptotes to c even in the local region that straddles the Schwarzschild radius, or else the equivalence principle is invalidated. Then v is less than c at the Schwarzschild radius, and this was inferred by means GR allows. You haven’t refuted that; you've only insisted otherwise without a basis.

Zanket, sure even for Eienstein he believed in a static universe. But we are not dealing that. We are dealing with his theory, which DOES predict a non-static universe.

What is your point? My model allows for a non-static universe too. My point was that Einstein believed for years that the universe was likely static, yet he apparently saw no issue between that and the second law of thermodynamics. Then there probably was no issue.

This deserves to be put into "Speculations" because it is a crackpot conjecture.

I’m the crackpot, yet you cannot show one problem with my paper that I cannot refute. Hmm.

Yes, it does. You are using equation 17, which assumes the Minkowski metric over all space. This is an invalid assumption in the presence of a gravitational source.

There may have been some confusion above. Epsen referenced eq. 17 from my online reference #7 from Taylor and Wheeler; that’s GR’s equation for escape velocity, and GR’s equation for v in section 2. You are referring to eq. 17 in section 8 in my paper. The equivalence principle lets eq. 17 be used in the presence of a gravitational source, as long as it’s used only locally (as given by the definition of “local” in my paper).

Review Einstein’s equivalence principle from here:

The outcome of any local non-gravitational experiment in a laboratory moving in an inertial frame of reference is independent of the velocity of the laboratory, or its location in spacetime.

What is an inertial frame? It’s a local frame in free fall; i.e. one in the presence of a gravitational source. SR, including eq. 17 from my paper, can be used in an inertial frame. And that’s the only way section 2 uses it.

How else do you think SR can be experimentally confirmed, when every laboratory is in the presence of a gravitational source? According to your logic, SR cannot be experimentally confirmed, let alone applied at all.

All your paper does is show an inconsistency between special and general relativity.

No, it shows an inconsistency between two predictions of GR for the same situation. Section 2 shows, inferred by means GR allows, that v always asymptotes to c even in a local region that straddles the Schwarzschild radius. That disagrees with GR’s eq. 4 in my paper (the same as eq. 17 in my online reference).

Now, observe what happens when your infalling particle reaches the Schwarzschild radius, you get a division by zero.

That was a good attempt. A division-by-zero error leads to logical problems, such as the one that generates the absurdity that 2 = 1 here. The site says “In practice, division by a term in any algebraic argument requires an explicit assumption that the term is not zero or a justification that the term can never be zero”. GR satisfies that requirement for your example by preventing the particle from reaching the Schwarzschild radius in the frame measuring t. In that frame the particle moves ever closer to but never reaches the Schwarzschild radius, as any decent text on black holes will tell you. So there will never be a division by zero in that example.

So, I'm curious as to see how you'll deal with this division-by-zero error I've pointed to (which you yourself claims can be the end of any theory). Will you dismiss it as irrelevant again?

I meet all challenges head on. It is possible for something to be irrelevant you know.

From the paper,

Let a test particle fall radially from rest at infinity toward a large point mass ...

 

The Minkowski metric does not apply in such a case.

Section 2 doesn’t use SR for the particle’s whole fall, but rather only in each local region. The following conclusion ...:

Then v always asymptotes to c; i.e. as long as the particle falls.

... is based on the following logic ...:

The particle always falls through a uniform gravitational field (a succession of them, each applying only locally) since a nonuniform gravitational field is everywhere uniform locally.

... which is not a global usage of SR.

This thread belongs in "Speculations" with all of the other "I found a flaw in relativity" conjectures.

Good thing you’re not a mod then, or else there might be the same rush to judgment here as in other forums.

The Schwarzschild metric applies outside the Schwarzschild radius.

The Schwarzschild metric applies outside the Schwarzschild object, including at and below the Schwarzschild radius.

Equation 17 does not apply, from which your whole argument fails.

Eq. 17 applies only as low as the Schwarzschild radius, but that is irrelevant. What is relevant is that a prediction inferred by means GR allows contradicts eq. 17. The following conclusion in section 2 ...:

Then v always asymptotes to c; i.e. as long as the particle falls.

... is not dependent on eq. 17, and contradicts eq. 17. When v always asymptotes to c, it asymptotes to c even in the local region that straddles the Schwarzschild radius, hence it is less than c at the Schwarzschild radius, in contradiction with eq. 17. As I noted to Espen above, section 2 already covers this with this reader-author comment:

Reader: The velocity v asymptotes to c only as low as the Schwarzschild radius, at the event horizon.

Author: The analysis above shows that v always asymptotes to c; i.e. as long as the particle falls. Since this was inferred by means general relativity allows, the theory cannot demand otherwise without being inconsistent.

I have a feeling you’ll ignore that again though.

Natural Units are good for equations, but nothing more. In deriving equations Natural units are frowned upon by most, as it provides less understanding of the formulae. Only after derivation are natural units used, to simplify calculations and nothing else. A flaw may be found with much less effort if SI units were used.

I disagree. Since geometric units make simpler equations and hence simpler calculations, and are convertible to SI units with no ambiguity (and vice versa), there’s little reason to use SI units. No errors creep into derivations by the use of geometric units. Simpler equations and calculations make flaws easier to see. Geometric units are common in texts about relativity, as noted in the link in the Definitions section of my paper. (The link gives you the conversion factors.) For example, Taylor and Wheeler use geometric units throughout their book Exploring Black Holes, for which my paper includes an online reference. See page 2-13 for their take on this topic.

Now, I have not completely analysised your paper yet, which I will as soon as possible, but it seems you have a circular argument going on. You seemed to critcise Espens comment on assuming equation 17 is correct, which you said you have shown an inconsistancy in. However, in a seperable section you use your assumption that equation 17 is not correct to prove another flaw.

Section 2 shows that eq. 17 from the reference (GR's equation for escape velocity, equivalent to eq. 4 in my paper, so hereafter I reference eq. 4 to avoid confusion) contradicts a prediction that can be inferred by means GR allows. The equation is inconsistent with section 1, thereby shown to be incorrect. Section 4 shows that Einstein's eq. 8 is derivable from eq. 4, hence eq. 8 is incorrect as well. There's no circular argument there. Can you be more specific?

Would you please, using your theories equations, tell us to what extent [the universe] expands then contracts?

I decline. Keep in mind that cosmology models are based on incomplete observational information.

Not to mention, having existed for an infinite amount of time, shouldn't the second law of thermodynamics result in a heat death of the universe already, or the universe reached thermal eqilibrium? I can not remember the quote exa ctly, or by who it was from, but someone once said that "If your theory disagrees with observances, well even sometimes experimentalists get it wrong. But if your theory is incompatible with the Second law of thermodynamics, I can offer you no hope". Quite true I have to say.

If this was a problem for me, then it would have been a problem as well for Einstein, who for years thought the universe was likely static, having always existed. In my model, the universe can oscillate between arbitrarily dense (maximum contraction) and arbitrarily sparse (maximum expansion) states. So there’s no requirement that it reach thermal equilibrium or result in heat death.

Please do not dismiss my comments merely on the factor of my age, you will find I know just as much Relativity as you do.

I’ll treat you the same as anyone.

Indeed v of a massive particle always asymptotes c, locally.

Yes, locally, but locally everywhere, so v asymptotes to c as long as the particle falls, even in the local region that straddles the Schwarzschild radius, and local regions below that. This was inferred by means GR allows.

There is a uniform gravitational field that straddles the Schwarzschild radius. The equivalence principle demands that v always asymptotes to c within that local region.

Now, Eq. (17) was derived using the metric from Schwarzschild's exterior solution, a metric with a special set of coordinates that exhibit a coordinate singularity at the Schwarzschild radius. Furthermore, like I've said, below the Schwarzschild radius the proper time of the falling object will become imaginary, which means that the analysis breaks down, as well as Eq. (17).

This is all irrelevant. What is relevant is that eq. 17 contradicts something that can be inferred by means GR allows.

Section 2 already covers this with this reader-author comment:

Reader: The velocity v asymptotes to c only as low as the Schwarzschild radius, at the event horizon.

Author: The analysis above shows that v always asymptotes to c; i.e. as long as the particle falls. Since this was inferred by means general relativity allows, the theory cannot demand otherwise without being inconsistent.

Trust me, I know this is hard to grasp, but that doesn't make it any less real.

I’m aware of what GR says about the region at and below the Schwarzschild radius. The paper is concerned with GR’s inconsistency about that, which you are ignoring.

Perhaps a new theory under development, but in order to refute a well tested, well scrutinized and well established theory you need more than an incomplete understanding of it.

No, even the most venerable theory can be refuted by an arrow pointing to a division-by-zero error. Can you prove your viewpoint logically or mathematically? I didn’t think so.

You know, the more I discuss this with you, the more I begin to realize the futility of convincing you. I believe James "The Amazing" Randi said it the best: No amount of contrary evidence will ever un-convince the true believer.

This is a common tactic: If I disagree then call me stubborn. I am refuting your points with logic and reason. You will convince me only by incontrovertibly refuting me in the same manner.

Well, technically Eq. (17) only applies for radii greater than the Schwarzschild radius.

Section 2 shows that v always asymptotes to c, i.e. as long as the particle falls. That includes below the Schwarzschild radius. You agreed with that, saying "their velocities will always asymptote c". If eq. 17 agreed with section 2 and you, then it would apply both above and below the Schwarzschild radius, and always return v < c.

I'm afraid your paper is far too lacking in extent, depth and understanding of the subject to be taken even remotely serious, I'm sorry to say...

That's a common refrain, but neither you nor anyone else has proven a problem with it. Subjective impressions are scientifically meaningless. A theory can be refuted by as little as an arrow pointing to a division-by-zero error.