Is there any experimental or observational confirmation of curvature of spacetime?

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Your desperation tactics continue: The onus is on you to show that the incumbent model of GR, curved spacetime and all that goes with it is invalid.
You have failed to do that, and only offer one doubtful scientific paper, from a less than reputable publisher, as against the many experiments and observations pointing to the validity of GR and all that it entails.
And as you well know, and as you well avoid mentioning, if there was any substance in what you claim, you would not be here.
The desperation tactics obviously also extend to "twitching my nose"

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in a vain effort to side track from the enormity of the errors of judgement, and obfuscating mistakes that you continually make in near every post.

 

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You are resorting to bad argument. Period from my side.

 

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You are resorting to trolling.

 

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Thanks a lot . Can I also ask/pick up on ...?

* Is there any concept of “parallel lines” in spacetime geometry that has any meaning or definition?

** What other candidate properties are there that might determine or be affected by such a putative force?

*** Not quite sure what that phrase means.What are masses "composed of"?

As a generality might it be correct to say that any model of a particular n-dimensional reality requires a n+1 dimensional "standpoint" in order for the human mind to visualize it (but not to mathematically describe it) ?

 

I recently read an article which really confounded me.

The proposition was that when a circle gets bigger its curvature diminishes. Therefore a circle of infinite size would have no curvature at all, yet it would be connected to itself.

There is clearly something wrong here.[/QUOTE]

 

[/QUOTE]

Why? If you treat curvature as the rate of change of orientation with respect to distance, it makes perfect sense, surely?

 

[/QUOTE]A "circle of infinite size" is just a limit isn't it?

It doesn't actually exist except as an idea.

As the circle gets bigger it's curvature approaches zero but never reaches it.

If you physically draw the circle it is made up of small points but when we manipulate objects geometrically the lines are continuous.


Am I right?

 

A slightly off topic question perhaps:

Does simple acceleration cause curvature of spacetime as well as mass and energy?

In other words ,if we are in an accelerating frame of reference are all the lines of constant spacial or temporal distance that we would draw to describe the region wrt which we are accelerating curved?

 

No TG. You are making the claim, you have the burden of proof. That's how it works. No one has any obligation to prove you wrong.

I am pretty sure you know this, since you are no stranger to public forum discussion, and I find your attempt to call it a 'bad argument' disingenuous.

 

I think you have two possible generalizations of "parallel lines" from Euclidean geometry.

1) Initially parallel geodesics. Since geodesics are the straight lines of curved manifolds, they have constant tangent vector when computed with a geometrically-informed version of the derivative. Using the generalization of irrotational sliding called parallel transport, we may take a path to a point off the first geodesic and establish a second geodesic with the "same" (parallel-transported) tangent vector. At least we can do this in well-defined manner in the limit of short paths, for the result of parallel transport is path-dependent when the manifold is curved.

Example on a globe. The prime meridian and the line of 1° W longitude both run purely north-to-south at the Equator (and everywhere else), which because they have the "same" tangent vector (moving purely north at the rate of one meter per meter of arc length). You can parallel transport such a vector along the geodesic of the equator. But if you parallel transport the prime meridian 179° along the Equator, it will now be anti-parallel to the geodesic which is both 1° W longitude and 179° E longitude. Likewise if you parallel transport the tangent vector of the prime meridian via a geodesic which is not the Equator, the new geodesic will not be a line of longitude except in the limit of a short separation.

Example on a globe. If you don't use short geodesics, parallel transport can turn a "north" tangent vector of a line of longitude into the "east" vector of the Equator. (Hint: Use a big circle centered on Quito, Ecuador.)

2) Curves of fixed geodesic separation. Let A be a curve, and L be a length, and n be an arbirary tangent vector. Then along every point of A we have n' which is the parallel-transported tangent vector. Thus at every point of A we can start a new geodesic of length L and those endpoints form a curve B. If A is a geodesic, then B is not expected to be a geodesic.

Example on a globe. Let A be a circle of radius 500 km about New York City. Let n be "north" as defined at the south-east extremal point of the circle and L be 50 km. But n' is not "north" anywhere else. Then B is a smaller circle than A a smooth curve which superficially resembles a circle centered 50 km north of New York City.

Example on a globe. Let A be the Equator (a geodesic). Let n be "north" as defined in Quito. Then n' is always "north". Let L be 5000 km, then B is the line of 45° latitude, but is not a geodesic.

Only in flat geometry can you have Initially parallel geodesics that have fixed separation, thus never cross or diverge. Since all space-times are approximately flat in the limit of small regions, it follows that on a globe or in space-time we can work in the approximation of flat geometry. Thus most square buildings don't have corners that can be measured to be more than 90° and terrestrial gravity never enters into discussion of atomic phenomena lasting only tiny fractions of a second.

The sky's the limit. We have evidence of fundamental particles have such intrinsic properties as mass, electric charge, angular momentum, electroweak charge and chromodynamics charge. Recently, evidence that fundamental mass is really a measure of a type of charge which is coupling with the Higgs field was shown. But non-fundamental particles, like protons, have a mass which is not explained by the Higgs mechanism, but rather in the coupling of quarks together to form a colorless composite particle. Even though the types of mass are theoretically distinct, their behavior under gravity is identical which suggests that behavior in a gravity field is not a force but something more fundamental like the behavior of geometry.

Atoms. Each atom is composed of electrons, protons and neutrons, but the mass of each atom is less than the mass of free constituents and varies significantly between isotopes. But don't appear to care about composition to the limits of testing.

Space-time curvature does not imply that there is some higher dimensional reality that the space-time manifold is embedded in. While the math of curvature of manifolds was developed assuming the manifolds were embedded in some Euclidean space, nothing in the math requires or depends on such a superspace. Also, 5 dimensions do not suffice to embed all possible space-time manifolds in GR, so even if your meta-physics were correct in concept, it is wrong quantitatively.

// Edit, inserted "big" in hint for second example. Fixed third example

 

That holds true for any circle with a epicenter (occupying a cardinal point, situated on a center). But where is the epicenter of an infinite circle?

I realize this is just a theoretical question, but if we consider the equation of Pi, could this somehow explain the transcendental nature of Pi?

 

Thanks again rpenner. That looks interesting.

I will try to look into all that. It seems fairly advanced.

 

No.

 

They say this is true because light has no mass. If it had no mass, then it wouldn't follow a curved trajectory, because it wouldn't be pulled by the force of gravity. Although, light has not been proven to have exactly zero mass with 100% certainty, even though a lot of people already assume that it has exactly zero mass. If light was found to have a very small amount of mass that was less than our current experiments could detect, then it could bring the idea of spacetime actually being curved back into question. Then the resent gravitational wave experiments could be interpreted as it being proof that spacetime can ripple (then it would be incredibly more likely that it can curve as well).

 

I may be wrong, but is the mass, even of a zero-mass particle (at rest) not increased by its speed?
Perhaps *mass* may be substituted for *energy*, IOW a zero-mass particle increases its energy @ *c*. Particles of pure energy which travels as a wave function?
Would that also not solve the problem of the effects of gravity on massless particles traveling @ *c* ?

 

On this limited point is it possible to have access to Einstein's cogitations regarding this particular area.

I know he published some books for the layman. Did he include this area in his explanations? I know that the whole area has moved on since his time but I would still be excited at the prospect of ,as it were going on various legs of his own journey of discovery .

The area of manifolds is one that I find interesting and extremely difficult at the moment.

 

One of the main reasons why physicist believe that the photon has zero mass is because it would increase infinitely by traveling the speed of light, but infinity and zero doesn't make for good mathematical proofs. Another explanation could possibly be that the mass is so little that the limit of it being increased infinitely could still be a very small undetectable amount. There is no way to know for sure from what I have read about it, because of that possibility. Although, I am starting to think that there is a really good chance that the mass of the photon is exactly zero. It could mean that the true nature of mass or the fundamental mechanism that causes an object to have mass is independent of relativistic mass increase. Then an object with zero mass could still have zero mass, even though it is increased infinitely.

 

It is part of the problem of quantum mechanics not having a proven theory of quantum gravity and relativity not being compatible with quantum mechanics, so it is hard to say for sure. As far as I know, there is no real way to solve physics problems or show how or why a particle traveling the speed of light has no mass. It could be the case that GR tells us how gravity works on large scales due to spacetime curvature, but one single quantum of gravity could come from something else completely different. Since the photon has no detectable mass, even though it always travels the speed of light, it could mean that a relative velocity could not give a particle a quantum of mass. Then it could mean that there is a real need for something like Quantum Loop Gravity or Gravitons in order to more fully explain gravity in place of GR on the quantum scale. Then neither of those two quantum theories of gravity explain why there should be spacetime curvature, as far as I know...

 

I have not read all of the Posts to this Thread & apologize if remarks similar to the following have already been posted.

Curved space-time is a model, not a reality. It is merely a very useful model, which can be said of much (all?) of the mathematics used to describe the laws of physics.

It is interesting to note that using (x, y, z, t) as coordinates for the space time model describes a static 4D geometry, which allows the use of differential geometry (a formidable tool) to describe the laws of physics.

While it is very useful, there are those who do not like the notion that the model is a static one with no motion.