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

[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.