B How Does Gravity Affect Spring Stretching in Einstein's Theory?

[Sagittarius A-Star]

Einstein:
- Surface frame is non-inertial
- Downward acceleration in the surface frame is caused by an inertial force

Mentioning, which frame is inertial and which not, is very helpful!

But I think, speaking about an "inertial force" in context of this discussion about GR, although not wrong, creates irritation. The "inertial force" (="pseudo force") can be omitted in GR, according to my above discussion #71 with @pervect. It has no physical "added value". I prefer to use the arguments from my above posts
#86

Einstein: Free fall is the natural motion

and #87

The contact force at the "modest mass" must not to be canceled by another force, because it has a proper acceleration (=not following it's geodesic) and F = m * a.

see also:

In order to adjust that to general relativity you need to generalise the force-free motion to geodesics: A force is an external influence that compels a body out of the geodesic. Gravity doesn't do that in general relativity but it defines the geodesics.

 

[A.T.]

But I think, speaking about an "inertial force" in context of this discussion about GR, although not wrong, creates irritation. The "inertial force" (="pseudo force") can be omitted in GR, according to my above discussion #71 with @pervect. It has no physical "added value".

You can omit "inertial force" and model the non-inertial frame using curve-linear coordinates, like in the video:


But I think, if someone is already familiar with inertial vs- non-inertial frames in Newtonian mechanics, and thus also knows the difference between interaction and inertial forces, then this is a much simpler first step to take:

"Gravity is an inertial force now"

compared to:

"There is no force of gravity, and you have to understand differential geometry to explain why an apple falls."

 

[Sagittarius A-Star]

You can omit "inertial force" and model the non-inertial frame using curve-linear coordinates, like in the video:
...

Yes. But, as going to curve-linear coordinates does not change the reference frame, it must also be possible to calculate the (almost) parabolic trajectory in the normal coordinates in the accelerated frame without inertial forces. I described in my above posting #61 the approach by making use of the "principle of maximum proper time".

"Gravity is an inertial force now"

That would mean for example, that two forces pull at the Earth moving around the sun: One inertial force in the direction of the sun and another one (centrifugal force) in the opposite direction. That sounds too similar to the theory of Newton. I think it is easier to say, that the Earth follows with no force the ellipse in space, because this is locally a straight line in curved 4D-spacetime.

 

[A.T.]

That would mean for example, that two forces pull at the Earth moving around the sun: One inertial force in the direction of the sun and another one (centrifugal force) in the opposite direction.

The inertial force description only works locally, in approximately uniform fields. It's basically the Equivalence Principle, as a first step to transition from Newtonian mechanics.

I think it is easier to say, that the Earth follows with no force the ellipse in space, because this is locally a straight line in curved 4D-spacetime.

"Easier to say" is not always "easier to understand". At some point you have to go there, to explain the global picture, but the local Equivalence Principle is a good starting point.

 

[Dale]

it must also be possible to calculate the (almost) parabolic trajectory in the normal coordinates in the accelerated frame without inertial forces. I described in my above posting #61 the approach by making use of the "principle of maximum proper time".

This is just a question of semantics. When you do the calculations you will get a term that is proportional to the mass. You can derive it from GR and call it a Christoffel symbol. You can derive it from Newtonian gravity and call it a real force. You can derive it from the equivalence principle and call it an inertial force. You can derive it from a variational principle and not call it anything at all. Regardless of what you call it or how you derive it, the term is present in the equations of motion in those coordinates and not in other coordinates.

 

[sqljunkey]

Well I believe that because of gravitational waves, GR strips away the meaning of force. Newtonian gravity has 0 notions that waves exist. By saying there is a dynamic fabric that constantly interacts with mass and also with itself, (probably), GR is saying spacetime curvature is not a artifact of some external force field.

In theory , I don't know for sure, two waves can come and cancel each other out. Leaving zero force, from the way I understand it.

PeterDoris might be able to expand more on this though.

 

[A.T.]

...semantic discussions about what should be called a "force".

...strips away the meaning of force

There we go again...

 

[PeterDonis]

I believe that because of gravitational waves, GR strips away the meaning of force.

The fact that GR does not treat gravity as a force is not just due to gravitational waves. GR treats all aspects of gravity as due to spacetime geometry.

In theory , I don't know for sure, two waves can come and cancel each other out. Leaving zero force, from the way I understand it.

Your understanding is flawed.

Gravitational waves are not "waves of force". What Newtonian physics calls "gravitational force" is present in GR in cases where there are no gravitational waves present at all.

 

[Sagittarius A-Star]

When you do the calculations you will get a term that is proportional to the mass.

O.K. My understanding of this is: The OP described here only scenarios, which are corner-cases of GR (locally, weak gravitation, small velocities), in which alternatively GR, SR (in accelerated frame) or Newton's theory can be used. Therefore, you must get with all approches the same motion formula for free fall in the surface-reference frame, containing in vertical direction a term "m * a", with "a" being the coordinate-acceleration. In case of using SR, you may or may not call this term a pseudo-force.

 

[pervect]

Well I believe that because of gravitational waves, GR strips away the meaning of force. Newtonian gravity has 0 notions that waves exist. By saying there is a dynamic fabric that constantly interacts with mass and also with itself, (probably), GR is saying spacetime curvature is not a artifact of some external force field.

In theory , I don't know for sure, two waves can come and cancel each other out. Leaving zero force, from the way I understand it.

GR certainly says that an electric field exerts a force, so your statement that "GR strips away the meaning of force" isn't accurate. Perhaps you'd care to try again?

Going back to my general remarks about science making physical predictions, and philosophy being about things that can't be experimentally tested, let's look at a few experimental results.

1) When we measure "gravitational mass" and "inertial mass", they've always turned out the same. For instance, see wiki on "tests of the weak equivalence principle", https://en.wikipedia.org/w/index.ph...52193#Tests_of_the_weak_equivalence_principle, and note that current tests say that the two agree within a few parts in 10,000,000,000,000, i.e. a few parts in 10^13.

2) The Pound Rebka experiment, and other later experiments with atomic clocks, show that the rate of clocks on the Earth depends on their height in the Earth's gravity. This effect is so significant that it's taken into account when averaging the readings of atomic clocks to create our base time standards, including TAI which is the bases for Universal Coordinate Time.

These results are both predicted from GR, and I believe that the predictions were made before the experiments were done. Do you have any alternative explanation for these results? If so, what is it?

Lastly, but perhaps the most importantly: what experimental predictions, if any, does the notion that "gravity is a force" actually make? Follow up questions , applicable only if it does make predictions, are "what predictions are they" and "have they been tested".

I have a few additional comments about point 2, "gravitation's effects on time". There is no evidence that I'm aware of, that forces such as electric fields, would cause similar time dilation. Do you think there should be such an effect, if so, do you have some theoretical basis for it? Has anyone, before the existence of the effect was noticed, made such a prediction about electric fields? Note that GR predicted this result before the experiments were done.

If "gravity is just a force, like an electric field", shouldn't both forces cause similar effects on clocks?

As far as your wave ideas go, there is no precedent for colliding waves cancelling out. I suspect it's not possible, but I don't have a formal proof. It seems rather speculative, at least, to suggest that they should cancel and worse to then use that speculation as an argument against GR.

 

[sqljunkey]

well since I've been asked to try again, I'll try again. People in this thread have been saying that as soon as you have curvature in the spacetime you will see these test masses start free falling along these geodesics. Gravitational waves, are curves in spacetime. So I would assume that as soon as these waves hit test masses they will start free falling alongside those geodesics. And I extrapolated that since these waves move along one spacetime they will probably interact with one another. And there could be a hypothetical situation where these waves in spacetime cancel each other out and create a total flat space. Now there will probably be a geodesic this test mass free falls along. This could all be happening near a massive star.

In my opinion when they came with the idea of gravitational waves they were saying that GR was in fact the theory of gravity. It didn't matter anymore if there was no mass or no energy in the south, you can still be compelled to free fall in that direction.

 

[PeterDonis]

People in this thread have been saying that as soon as you have curvature in the spacetime you will see these test masses start free falling along these geodesics.

Test masses will free fall along geodesics whether spacetime is flat or curved. Curvature just changes the relationship between different geodesics.

Gravitational waves, are curves in spacetime. So I would assume that as soon as these waves hit test masses they will start free falling alongside those geodesics.

They won't "start" free falling--they'll be free falling the whole time. But as a result of the gravitational wave passing, the relationship between the different geodesics that nearby test masses are free-falling on will change. That is exactly what a gravitational wave detector like LIGO is detecting: the change in the relative motion of different test masses due to a gravitational wave passing.

I extrapolated that since these waves move along one spacetime they will probably interact with one another.

Since the Einstein Field Equation is nonlinear, yes, in principle gravitational waves can interact with one another. In practice, any gravitational waves we can detect here on Earth are so weak that the nonlinearities are negligible, and they can be treated like linear waves, which just superpose without any interaction between them--as, for example, EM waves do.

there could be a hypothetical situation where these waves in spacetime cancel each other out and create a total flat space

You should first ask yourself if this is possible with EM waves: can EM waves cancel each other out and create a region where there are zero EM fields whatsoever? And if so, how large can such a region be?

(Hint: the answer is that while EM waves can cancel each other out at particular points, they can't cancel each other out completely over an extended region.)

This could all be happening near a massive star.

Near a massive star, even at points where incoming gravitational waves do cancel each other out, that doesn't remove the static spacetime curvature due to the star. You can't cancel out that kind of spacetime curvature with gravitational waves at all.

In my opinion when they came with the idea of gravitational waves they were saying that GR was in fact the theory of gravity.

This is nonsense. GR was known to be a theory of gravity as soon as it was invented, and this had nothing to do with its prediction of gravitational waves. It had to do with all the predictions it made that matched Newtonian gravity, plus the additional predictions it made that accounted for phenomena that couldn't be explained by Newtonian gravity (like the precession of Mercury's perihelion), and also predicted new phenomena that had never been observed (like bending of light by the Sun and gravitational redshift).

It didn't matter anymore if there was no mass or no energy in the south, you can still be compelled to free fall in that direction.

I have no idea what you mean by this.

 

[pervect]

well since I've been asked to try again, I'll try again.

I noticed you didn't answer any of my questions, though. Did you think about them at all? They might help you understand a bit more about what GR does say and doesn't say.

People in this thread have been saying that as soon as you have curvature in the spacetime you will see these test masses start free falling along these geodesics.

Another poster has mentioned that test masses always free fall along geodesics, regardless of curvature, by definition, and has addressed some of the other thigns you have said fairly well.

 

[sqljunkey]

alright fine gravity is the curvature in spacetime.