I Why does a body at rest move if Gravity is not a force?

[Orodruin]

Indeed in flat spacetime the result of rockets attached to both Earth and object to push them together is basically the same as the effect of spacetime curvature.

It most certainly is not and it is not what Peter was saying.

 

[cianfa72]

It most certainly is not and it is not what Peter was saying.

Sorry, if we could magically turn off gravity then we would get a flat spacetime and locally the result of rockets pushing should be the same, I believe.

 

[Orodruin]

Sorry, if we could magically turn off gravity then we would get a flat spacetime and locally the result of rockets pushing should be the same, I believe.

Same as what? This statement is very very vague and it is unclear what you mean should be the same.

 

[cianfa72]

Same as what? This statement is very very vague and it is unclear what you mean should be the same.

I mean if the spacetime was flat then the rockets attached to both Earth and the object would push each other in the same way as in case of gravity -- i.e. spacetime curvature.

 

[Orodruin]

I mean if the spacetime was flat then the rockets attached to both Earth and the object would push each other in the same way as in case of gravity -- i.e. spacetime curvature.

Still vague.

 

[vanhees71]

I haven't read the entire thread, and I hope, I'm not repeating the obvious once more.

Before thinking in terms of relativity it helps to first look at the issue from a Newtonian point of view. In this context the question is of course related to Newton's 1st postulate. This postulate states that there exists a special class of reference frames, where the "principle of inertia" holds: A body, unaffected by any force, stays at rest or in uniform rectilinear motion (or shorter: moves with constant velocity within this frame of reference). It also follows that there is no way to distinguish any inertial reference frame from another, i.e., all motion can only be described relative to some inertial frame, but all the physical laws are the same in all inertial frames. So there is no distinguished inertial frame of reference.

Now there is special relativity, where also Newton's 1st postulate holds true, but as Einstein famously figured out in 1905, in order to make it valid to hold also for electromagnetic phenomena, one has to change the spacetime description to Minkowski spacetime, and the transformation between different inertial reference frames must be done with Poincare (Lorentz) transformations rather than Galilei transformations, including the change of the time "coordinate" such that the speed of light in vacuum is the same in all frames, independent of the velocity of the light source.

Finally, there's also Einstein's general theory of relativity, which he had to introduce in order to describe gravity within a relativistic framework. The upshot is that inertial frames exist only locally, i.e., you can always find a frame of reference in a small "space-time volume", where for all local phenomena the laws as described by special relativity and without gravity hold true. These are determined by (non-rotating) free-falling frames of reference. In a small enough region within such a free-falling frame of reference Newton's law of inertia holds true and there is (almost) no gravity acting on a body, i.e., it will move with constant velocity relative to this local inertial frame of reference.

Now I always emphasized that this holds only locally, i.e., for sufficiently small space-time volumes. That's because if there is a true gravitational field around, you can never get rid of this gravitational field simply by choosing any frame of reference. If you look only at long enough distances you'll always have an effect of the gravitational field, the socalled tidal forces, and that's described in general relativity by the fact that at presence of true gravitational fields the spacetime is described by a space with curvature.

So to answer the original question: In GR there are always local inertial frames of reference, and these are realized by free-falling non-rotating reference frames, and wrt. such a local inertial reference frame Newton's Law of Inertia still holds for not too large neighborhoods around the free falling "origin" of this reference frame.

 

[PeterDonis]

if the spacetime was flat then the rockets attached to both Earth and the object would push each other in the same way as in case of gravity -- i.e. spacetime curvature.

The only thing I said would be the same was the contact force between the Earth and the object (and the fact that each exerts an equal and opposite force on the other by Newton's Third Law). That has nothing to do with spacetime curvature or the lack of it. It has to do with non-gravitational forces. Spacetime curvature itself is not a force and does not exert a force on anything.

 

[cianfa72]

The only thing I said would be the same was the contact force between the Earth and the object (and the fact that each exerts an equal and opposite force on the other by Newton's Third Law). That has nothing to do with spacetime curvature or the lack of it.

ok, I do not understand how gravity is involved though. It seemed to me that gravity vs rockets strapped on both Earth and the object were actually alternative.

 

[PeterDonis]

It seemed to me that gravity vs rockets strapped on both Earth and the object were actually alternative.

For the particular (thought experiment only) case I was describing, they are.

My original post about this was not in response to you, it was in response to @sysprog. Please let @sysprog ask questions about it instead of confusing the issue further.

 

[zoltrix]

might acceleration of a body in a gravitational field be a matter of metric ?

a rocket is moving through equally spaced waypoints A-B-C in equally spaced time intervals Tab e Tbc, in deep space
AB = BC and Tab = Tbc
the rocket enters a gravitational field
space is streched , the flow of time slows down
BC > AB and Tbc < Tab
differences are infinitesimal but their ratio maybe not
rocket accelerates

 

[PeroK]

might acceleration of a body in a gravitational field be a matter of metric ?

a rocket is moving through equally spaced waypoints A-B-C in equally spaced time intervals Tab e Tbc, in deep space
AB = BC and Tab = Tbc
the rocket enters a gravitational field
space is streched , the flow of time slows down
BC > AB and Tbc < Tab
differences are infinitesimal but their ratio maybe not
rocket accelerates

If you want to learn about GR, then that there's nothing stopping you. But, physics is unlikely to be what you invent off the top of your head.

 

[Orodruin]

might acceleration of a body in a gravitational field be a matter of metric ?

a rocket is moving through equally spaced waypoints A-B-C in equally spaced time intervals Tab e Tbc, in deep space
AB = BC and Tab = Tbc
the rocket enters a gravitational field
space is streched , the flow of time slows down
BC > AB and Tbc < Tab
differences are infinitesimal but their ratio maybe not
rocket accelerates

No. The correct answer has already been givem several times in this thread. There is no need to start personal speculations.

 

[Nugatory]

might acceleration of a body in a gravitational field be a matter of metric ?

Not the way you’re thinking. Ask yourself (but don’t answer here!) how would you identify a “waypoint” in empty space? It can’t be done. What does “the flow of time slows down” mean? It is meaningless babble - time always flows at the rate of one second per second.

 

[zoltrix]

in what way, then ?
is acceleration related to the metric or not ?

 

[PeroK]

in what way, then ?
is acceleration related to the metric or not ?

Gravitational acceleration is related to the coordinates you choose. There's no "proper" acceleration free-falling under gravity. No force, no acceleration.

 

[zoltrix]

I gave for granted that gravital acceleration is related to the set of coordinates
take the following assumption

a) the closer to the Earth the slower the time
b) the closer to the Earth the tighter the spatial dimensions

of course a) and b) must be understood one observer with respect to the other observer

The only way to combine in a logical way a) and b) with the symmetry of the observers is to assume an accelerated motion

 

[Orodruin]

I gave for granted that gravital acceleration is related to the set of coordinates
take the following assumption

a) the closer to the Earth the slower the time
b) the closer to the Earth the tighter the spatial dimensions

of course a) and b) must be understood one observer with respect to the other observer

The only way to combine in a logical way a) and b) with the symmetry of the observers is to assume an accelerated motion

This is just more mumbo jumbo not really connected to how general relativity actually works. You cannot reach proper conclusions with mumbo jumbo arguments. Note that while popular science is often using descriptive language to convey the main points and ideas, it is ultimately based on the actual theory. You cannot go in the other direction and use descriptive language to make appropriate deductions.

 

[zoltrix]

well in my opinion its the direct oppposite
descriptive language is often used to explain a counter intuitive theory such as RG
it is a useless and ,even worse, a deceiving exercise , in my opinion
take for example the super famous analogy of the elastic net deformed by a mass
a ball far away from the mass should cover a straight path but it should fall into the hole when it gets close to the mass
Why ?
just in case a force is applied to ball !
is my explanation wrong ?
no problem but experts should try to explain the "acceleration in a gravitational field with no force applied" using the language of RG which, at the end of the day, is the language of math
intuitive analogies are misleading

 

[berkeman]

Thread closed temporarily for Moderation and cleanup...

 

[PeterDonis]

might acceleration of a body in a gravitational field be a matter of metric ?

The trajectory through spacetime of anybody that is not subjected to any non-gravitational forces is determined by the metric. Such a body will have zero proper acceleration. Its coordinate acceleration will depend on what coordinates you choose; but it is always possible to choose coordinates that make that particular body's coordinate acceleration zero.

The above is basically a summary of what has already been said in this thread. I suggest taking the time to read it again, carefully. The rest of your post #60, as well as your posts #66 and #68, are garbled misunderstandings, so it does not seem like you have a firm grasp of what has been said in this thread in response to your OP. It would be a good idea to also take some time studying the basics of GR from a textbook; Sean Carroll's online lecture notes on GR are free:

https://arxiv.org/abs/gr-qc/9712019

If you have further questions after taking the time to do those things, you can start a new thread. This thread will remain closed.

 

[PeterDonis]

experts should try to explain the "acceleration in a gravitational field with no force applied" using the language of RG which, at the end of the day, is the language of math
intuitive analogies are misleading

Some final words in response to the above: yes, intuitive analogies are misleading, that's why you shouldn't use them, you should use math. But everything you have said in this thread is intuitive analogies, all of them wrong. You need to take your own advice and stop doing that and learn the actual math. The reference I gave in my previous post would be a good start.

When you do learn the math, you will see why the phrase "acceleration in a gravitational field with no force applied" is just another intuitive analogy in vague ordinary language and should not be used.