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

[PeterDonis]

I think that in this instance calling something that is "negligibly small", "nothing", is occlusive of the reality that an object affected by gravity cannot be massless

Wrong. Light is massless but is affected by gravity.

(outside of black holes bending light

Any gravitating mass bends light, not just a black hole. (The Sun's bending of light has been experimentally measured.)

depending on whether light is regarded as massless).

It is. See above.

if it were 'massless', there would be no Third Law equal pressure holding it to the Earth.

Wrong. You can confine light in a box at the Earth's surface and it will stay there just fine. An unconfined light ray will of course not stay on the Earth's surface, but neither will anything else moving at greater than escape velocity; there is nothing special about light in that respect.

Again, the reason the trajectory of an object at rest on the Earth's surface, and the piece of the Earth's surface it is on, are stable, is due to the spacetime curvature of the Earth. It has nothing to do with the (hegligibly small) spacetime curvature due to the object.

I in this instance respectfully disagree that the mass of the smaller object should be neglected, even if it is quantitatively comparatively negligible, because I think that the qualitative fact of the non-zero-ness of the mass of the small object should be part of a full explanation.

Sorry, but it isn't, and your thinking it should be does not change that.

 

[sysprog]

The mass of a 100kg man compared to that of Earth is about $\frac 1 {5.972 \times 10^{22}}$, which $\neq 0$. it seems to me that you have good reason for treating such a comparitively small mass as zero in some situations. I think that perspicuity of explanation, in this discussion of why gravity impels if it is not a force, calls for acknowledgment of the fact of the massivity (discursionally, the non-non-massivity) of the lesser mass.

 

[PeterDonis]

when we are accounting for why the object remains attached to the Earth it's because the Earth and the object are pushing against each other; it's not only because the Earth is pushing against the object.

Perhaps an observation about the quote above will help: yes, the Earth and the object are pushing against each other, but neither of these pushes are due to gravity! The Earth's isn't, any more than the object's.

The reason the Earth and the object push on each other is the non-gravitational interactions between their atoms (mostly electromagnetic repulsion between the electron shells, plus some Pauli exclusion principle thrown in for seasoning). It has nothing to do with gravity. If you could magically turn off gravity, and then you strapped rockets to both the Earth and the object and used the rockets to push them together, they would push on each other the same way.

The thing that the Earth's (not the object's) gravity accounts for is why the Earth can exist as a stable sphere (actually an oblate spheroid, but we'll leave out the Earth's rotation for now) even though the parts below are pushing upward on the parts above. That is because of the spacetime curvature due to the Earth's mass. But the object's mass is much too small to make any contribution to that--not just because the mass is small in and of itself, but because it's so small that non-gravitational interactions between the parts of the object are many orders of magnitude stronger than gravitational ones, so the object's shape is determined by those non-gravitational interactions (that's why, for example, a table doesn't crush itself into a sphere). The opposite is true for the Earth: its gravity (spacetime curvature) is much stronger than the non-gravitational interactions between its parts, which is why its shape is determined by gravity (hydrostatic equilibrium) rather than non-gravitational interactions. The "shape is determined by gravity" part is why it's the Earth's spacetime curvature that determines the stable trajectories for objects on its surface.

 

[PeterDonis]

The mass of a man is about $\frac 1 {3.5 \times 10^6}$, which $\neq 0$. it seems to me that you have good reason for treating such a comparitively small mass as zero in some situations.

That's not what is being done. See my post #38 just now.

I think that perspicuity of explanation, in this discussion of why gravity impels if it is not a force, calls for acknowledgment of the fact of the massivity (discursionally, the non-non-massivity) of the lesser mass.

So far your thoughts on this matter in this thread have been wrong. That should indicate to you that you might want to reconsider them. Perhaps my post #38 just now will help.

 

[sysprog]

I agree that the other (non-pseudo) forces are stronger than gravity. I think that your post #38 is intriguing; in my view it illustrates why we might want to at least temporarily disregard a non-zero comparatively small quantity, in order to render something more important better elucidated, especially in an explanation.

 

[PeterDonis]

your post #18

I think you mean post #38?

 

[sysprog]

I think you mean post #38?

Yes (edited to correct)

 

[Orodruin]

Isn't the object's surface pushing its own 'up', however weakly, against the Earth, even though the object is of so much lesser mass?

We were discussing an object in free fall, so no. What gives the ground proper acceleration is the ground below it pressing up on it (ultimately due to electromagnetism).

 

[PeroK]

I agree that the other (non-pseudo) forces are stronger than gravity. I think that your post #38 is intriguing; in my view it illustrates why we might want to at least temporarily disregard a non-zero comparatively small quantity, in order to render something more important better elucidated, especially in an explanation.

There's elucidation and there are unnecessary tangents. In a few threads recently you have argued a contrary position - partly, IMO, because you focus on extraneous detail which detracts from your understanding of the main point.

It's like watching a tennis match and focusing on how the players have tied their shoelaces. Yes, it's important that a player's shoes don't fall off while he/she is running around; but, it hardly adds to an understanding of the game.

 

[zoltrix]

Hi all

After going through 45 plus posts I tend to believe that trying to explain the acceleration of a body in a gravitational field , with the use of "analogies" is of no use or even deceiving
the Einstein's elevator ideal experiment entails that electromagnetics waves move along a straight path in the deep space but along a curved path in presence of a mass
we must simply accept that
a mathematical model of the universe must embody such ideal "experiment" thus the space must be regarded as curved
Einstein put it together with the apparent paradoxes of special relativity, the results are the Einstein's equation of the gravitational field
getting back to the original question

why doesn't a body at rest remain at rest ?

simply (so to speak) because the equation of general relativity claim that a body in a gravitational field is accelerated without evoking the existence of a real force
all attempts to explain the reason of such acceleration using analogies taken from our daily experience lead only to confusions

I gave it up
same as the relativity of space and time , the "curved space" is something beyond our experience
we must accept it simply because the general relativity proved to be more accurate than the Newtonian mechanics

 

[jbriggs444]

why doesn't a body at rest remain at rest ?

If you accelerate your coordinate system past a body that is subject to no external forces then its coordinates will be seen to change in an accelerating fashion. Why would you expect otherwise?

 

[Orodruin]

If you accelerate your coordinate system past a body that is subject to no external forces then its coordinates will be seen to change in an accelerating fashion. Why would you expect otherwise?

Just to add to this, the above has no requirement of spacetime being curved so it can be understood already in flat spacetime.

 

[Ibix]

why doesn't a body at rest remain at rest ?

simply (so to speak) because the equation of general relativity claim that a body in a gravitational field is accelerated

You are looking at this backwards. General relativity does not claim that a body in a gravitational field is accelerated. It asks: why do you think a body under no force goes in a straight line through space? The answer is that you are assuming all sorts of things like the least action principle and Euclidean geometry. General relativity merely points out that Euclidean geometry is not the correct assumption - you need to use pseudo-Riemannian geometry with a metric determined by the field equations. And when you do that, it's the curvature of spacetime in the time direction (loosely speaking) that means that a test body will curve towards the Earth, just as naturally as you seem to be assuming it "should" carry straight on because you haven't checked your assumption of Euclidean geometry.

The picture of the rubber sheet is misleading.

 

[Orodruin]

And when you do that, it's the curvature of spacetime in the time direction (loosely speaking) that means that a test body will curve towards the Earth, just as naturally as you seem to be assuming it "should" carry straight on because you haven't checked your assumption of Euclidean geometry.

I disagree. That an object in free fall falls to the ground just means that the ground is accelerating towards the object. This does not require any curvature and is a local effect mostly due to using curvilinear coordinates in the local inertial frame. Spacetime curvature will however be necessary when one considers the global picture (including why the ground has proper acceleration and how the ground can remain stationary even though it has proper acceleration).

 

[cianfa72]

If you could magically turn off gravity, and then you strapped rockets to both the Earth and the object and used the rockets to push them together, they would push on each other the same way.

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.

 

[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.