[PmbPhy (OP)]

This is a leading question of course since I know the answer. I'm merely curious as to who believes it.

I'm good on my word so when I said I'd post the original letter by Einstein o Lincoln Barnette I meant it so here it is. Please see attachment.

In essence Einstein stated in no uncertain terms that gravity should not be thought of as a curvature of spacetime. Spacetime curvature is just the relativistic term for tidal gradients. He also stated the relativity does not geometrize physics anymore that EM or the distance between two points.


Einstein_SR_GR.pdf (666.56 kB - downloaded 429 times)

[geordief]

So the geometrization can be seen as a geometric model bearing an  exceedingly close approximation to a deeper physicality ?(this being so on statistical grounds as the basis for this physicality is so  "deeply rooted" in the tiny interactions at possibly graviton levels.)

It is the model that is geometric according to   this letter?

A bit similar to the arguments as to why all physics can be reduced to maths and numbers....

EDIT:the geometric model has shown no signs of  becoming less accurate at "higher definition" levels ,though has it? (ie measuring gravity/curvature  at extremely small levels of mass/energy )

It is anticipated to break down at some point but that point seems not to have been reached or even "approached".

[opportunity]

The idea of gravity being a curvature of spacetime....is.... a fluid idea of bodies in motion undergoing relativistic effects dependent on underlying conditions. The first condition with these bodies is that they are massive and that there is a natural curvature in play with their relation to one another (orbits). The second condition is the play of light in those spatial regions.

I'm terrible at explaining this stuff, so hopefully it didn't offend.

I'd like to add more beyond this basic stuff......(?)

This is the physics section, not a new ideas symposium, so I look at the question and hesitate with an answer, such a good question.

[jeffreyH]

This is a leading question of course since I know the answer. I'm merely curious as to who believes it.

I'm good on my word so when I said I'd post the original letter by Einstein o Lincoln Barnette I meant it so here it is. Please see attachment.

In essence Einstein stated in no uncertain terms that gravity should not be thought of as a curvature of spacetime. Spacetime curvature is just the relativistic term for tidal gradients. He also stated the relativity does not geometrize physics anymore that EM or the distance between two points.


Einstein_SR_GR.pdf (666.56 kB - downloaded 429 times)

Somebody had to say it. Well done.

[opportunity]

And the answer goes to.....the dude playing the flute we are making poetry to.....?

< I should make that my call sign >

[geordief]

And the answer goes to.....the dude playing the flute we are making poetry to.....?

< I should make that my call sign >

Pan's People?
https://en.wikipedia.org/wiki/Pan%27s_People   

[opportunity]

I know.

Pan's pandemia.

I would like physics to have a few metaphors, but "math" seems to take centre stage, especially when billions of dollars and the investments of many are at stake......as a way to be serious about living. I love that. Couldn't love it less.

"Clearly" this response is in response to a question, yet please do not let this response, all members, detract you from the OP's question. Apologies if I answered outside of the OP's intent.


Who claimed gravity is a curvature of spacetime?

Einstein.

He didn't say spacetime is a curvature of gravity. Or did he, and is there a difference between saying gravity is a curvature of spacetime or spacetime is a curvature of gravity?

[PmbPhy (OP)]

Who claimed gravity is a curvature of spacetime?

Einstein.

Nope. It was Max von Laue. Did you read the PDF file I posted in the OP?

He didn't say spacetime is a curvature of gravity. Or did he, and is there a difference between saying gravity is a curvature of spacetime or spacetime is a curvature of gravity?

You can have spacetime with no curvature so no. They're not the same.

[saspinski]

If the Riemann tensor is zero in a region of spacetime, is it possible a gravity field there?
Or, is it possible a Riemann tensor different from zero in a region and no gravity field there?
If the answer is no for both questions, then spacetime curvature <=> gravity.

[PmbPhy (OP)]

If the Riemann tensor is zero in a region of spacetime, is it possible a gravity field there?

Yes. Without question. Its the affine connection that determines the presence of a gravitational field, no tidal forces.

Or, is it possible a Riemann tensor different from zero in a region and no gravity field there?

Yes. In fact if you have a gradiometer in free fall while in orbit of Earth then in that frame the gravitational field is zero but there are still tidal forces present.

If the answer is no for both questions, then spacetime curvature <=> gravity.

Wrong. And if I might add - Wow! You said all of that without reading the letter Einstein wrote. That's a problem in this thread and there's no excuse for it. In that letter Einstein wrote

... what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the components of the affine connection], not the vanishing of the [components of the Riemann tensor]. If one does not think in such intuitive (anschaulich) ways, one cannot grasp why
something like curvature should have anything at all to do with gravitation. In any case, no rational person would have hit upon anything otherwise. The key to the understanding of the equality of gravitational mass and inertial mass would have been missing.

Case closed.

Please folks. Before making a claim on a paper/letter first read the paper/letter. Otherwise you come off quite poorly. Okay?

I should note something very important here. It's not me that who discovered this point. It was Dr. John Stachel, someone whom I became friends with over the last 18 years. He wrote a paper which touched on this subject and gave me a copy. He's a great guy who had a lot of interesting friends and acquaintances such as Karl Popper and Wolfgang Rindler (may he rest in peace).

https://en.wikipedia.org/wiki/John_Stachel

[jeffreyH]

Just a note. To understand affine connections you need to study differential geometry. It is not an easy road. People say all sorts of things about relativity without actually putting in the effort to study the subject. That is a shame because it is so rewarding.

[opportunity]

PmbPhy, I applaud your archival work.

However the extract/letter you are referring to is central to "general" relativiity.

"Special" relativity has a differennt can of worms as Einstein would know.

Its is far easier to relate "special" relativity with geometry than "general" relatviity.......and I think this is the uniquue case of the letter you have provided.

Once again though, bravo for diigging this letter up.

[saspinski]

 
Yes. Without question. Its the affine connection that determines the presence of a gravitational field, no tidal forces.

Do you have an example? I can imagine a gravitational field generated by an infinite plane. In that case the field is uniform and there are no tidal forces. But infinite planes were not detected by astronomers until now.

Yes. In fact if you have a gradiometer in free fall while in orbit of Earth then in that frame the gravitational field is zero but there are still tidal forces present.

If there are tidal forces, and the Riemann tensor is not zero, some Christoffel symbols must be non zero. What according to the Einstein text (..non-vanishing of the components of the affine connection...) => gravitational field.

[PmbPhy (OP)]

Do you have an example? I can imagine a gravitational field generated by an infinite plane. In that case the field is uniform and there are no tidal forces. But infinite planes were not detected by astronomers until now.

If you looked in MTW you'd see their example. But, sure. See:
http://www.newenglandphysics.org/physics_world/gr/grav_cavity.htm

If there are tidal forces, and the Riemann tensor is not zero, some Christoffel symbols must be non zero.

Not true. In a locally inertial frame in a curved spacetime all of the affine connections vanish but the Riemann tensor doesn't. That's because the Riemann tensor is a function of both the Christoffel symbols as well as their derivatives. See "Coordinate expression" at
https://en.wikipedia.org/wiki/Riemann_curvature_tensor

What according to the Einstein text (..non-vanishing of the components of the affine connection...) => gravitational field.

You're making it about Einstein when in fact many others agree with him and its in all of his books. Its simple. How do you tell if there's a gravitational field in your living room? Simple; hold an apple in your hand while its stretched out and then let it go. If it drops to the floor at a rate independent of its mass (drop others with different masses to check this out) then there's a gravitational field in that room. How do you tell if there are tidal forces? Use sensitive equipment and measure the small changes in the field with height. If they exist then there are tidal forces present.

You could read Einstein's gravitational field by Peter M. Brown which is online at:
https://arxiv.org/abs/physics/0204044

Yes. I wrote it. It should answer your questions. If not then your comments would be invaluable to me.

[saspinski]

Not true. In a locally inertial frame in a curved spacetime all of the affine connections vanish but the Riemann tensor doesn't. That's because the Riemann tensor is a function of both the Christoffel symbols as well as their derivatives.

The Christoffel symbols are functions of position and time. If in a point and its neighborhood  they vanish, their derivatives also vanish at this point => Riemann tensor = 0.

About the example, it is too complicated to calculate the metric tensor and see if the Riemann tensor is zero. By the way, it is nomally said that if there are no tidal forces, the Riemann tensor is zero, but I don't know a proof from the tensor definition. 

[Bill S]

Could be worth a look by those who have time to read books.  "Lighthearted" doesn't always mean poor information.

Einstein Didn't Say That: Exposing the Common Sense in Relativity Theory.
 Don Griffin

"Einstein Didn't Say That" is a lighthearted but respectful exploration of the everyday logic behind special and general relativity. The first person to use the term 'curved space' was not Einstein, and not a physicist, but a reporter for the New York Times, who needed a catchy headline. What did Einstein really say, or not say, about curved space, time travel, wormholes, traveling twins, extra dimensions, multiple universes, dark matter and more? Have we been sold more sizzle than steak? With the help of dozens of quotes from well-known physicists, but mainly from Einstein himself, the author tries to separate Einstein's original ideas from some of the speculation that those ideas inspired in others. This is not a textbook or a history of physics, but rather the personal story of an ordinary guy's delight in discovering

[jeffreyH]

Scientific theories aren't written in stone. Einstein may have formulated relativity theory but others have studied and worked on it since. To understand all the implications is not easy. It requires a lot of work. I myself have merely started to scratch the surface. There is an awful lot that I don't know. I am most interested in the mathematics and theoretical aspects. I will not likely be in the position to experiment. But it's my idea of fun.

[PmbPhy (OP)]

The Christoffel symbols are functions of position and time. If in a point and its neighborhood  they vanish, their derivatives also vanish at this point => Riemann tensor = 0.

That' incorrect. It's only when both al the first derivatives a ad the Christoffel symbols and tthey all vanish is the spacetime flat. That doesn't mean there's no gravitational filed. In fact Einstein said that a gravitational field can be "produced" by a change in the frame of reference. This is not about a time varying thing like you're implying.

Since this thread was diverted from is purpose I'm brining it back on track. Einstein wrote

... what characterizes the existence of a gravitational field from the empirical standpoint is the non-vanishing of the components of the affine connection], not the vanishing of the [components of the Riemann tensor]. If one does not think in such intuitive (anschaulich) ways, one cannot grasp why
something like curvature should have anything at all to do with gravitation.In any case, no rational person would have hit upon anything otherwise. The key to the understanding of the equality of gravitational mass and inertial mass would have been missing.

Please focus on the subject at hand, i.e. What Einstein actually said, regardless of whether you think that he was right opr wrong. Okay?

About the example, it is too complicated to calculate the metric tensor and see if the Riemann tensor is zero.

It's rehire easy. See: http://www.newenglandphysics.org/physics_world/gr/uniform_force.htm

[PmbPhy (OP)]

[quote author=Bill S
"Einstein Didn't Say That" is a lighthearted but respectful exploration of the everyday logic behind special and general relativity. The first person to use the term 'curved space' was not Einstein, and not a physicist, but a reporter for the New York Times, who needed a catchy headline.
[/quote]
Awesome. Can you tell me what news paper it was in and how I can get a copy of it:?

I really appreciate this bill. I love you!   That ..doesn't mean we'll be taking warm showers in the wee hours of he morning - Clint Eastwood in "Heartbreak Ridge". I love that saying!

[saspinski]

Suppose a function f(x,y,z,t). f is zero in a region around (x0,y0,z0,t0). All derivatives of f are also zero. So, it is not possible all Christoffel symbols be zero while some of its derivatives escape this fate.
That is the reason for the Riemann tensor be zero in this case.