# Force due to acceleration and time flowing differently

• I
• HansH
In summary, Special relativity predicts that a moving clock as measured against an array of "stationary" clocks all synchronized according to the standard of a chosen rest frame will appear to tick slowly by comparison. Meanwhile, a "stationary" clock as measuerd against an array of "moving" clocks all synchronized according to the standard of the chosen moving frame will also appear to tick slowly by comparison. It is not about the clocks. It is about the standard of comparison.f
I'm not sure, whether I understand what the question is.
Watch the video in post 132 at around 11:40. It seems like complete nonsense to me, and I have never read any professional scientific reference that says anything that I can remotely connect to this idea. Your recent posts are a little ambiguous, but seem to indicate that you recognize the concept.

The question is does it seem like nonsense to you, and if not then can you please cite some professional scientific literature that explains what you think the video is talking about?

vanhees71 and Motore
I thinkt I've to agree with your assessment that this is "complete nonsense". I thought the question was about the equations of motion of a medium, i.e., something like fluid dynamics or dynamics of an elastic body, i.e., a continuum mechanical model, and there if you have an exact solution of the Einstein field equation, you also have the solution of the equations of motion for the dynamical system. An example is the FLRW solution, where you automatically get an ideal fluid for the cosmological medium. The various types usually put in (massive particles, radiation, cosmological constant/dark energy) just vary in their equations of state.

For me these somewhat Machian idea in this video has never been convincingly demonstrated from GR. The message of GR concerning the "equivalence principle" is that both "inertia" as well as "source of gravitation" are not (only) mass but all kinds of energy, momentum, and stress.

Dale
I thought the question was about the equations of motion of a medium,
The question is about mass being accelerated by an external force such as a rocket engine. the question now is if it could be that the energy delivered by the force to acellerate the mass is stored in the distortion of the spacetime around the mass. so if due to the acelleration spacetime if deformed different at the front of the mass compared to the back of the mass in the direction of the aceleration and so giving as result a force that we recognze as F=m*dv/dt.

the question now is if it could be that the energy delivered by the force to acellerate the mass is stored in the distortion of the spacetime around the mass.
The answer to this is no for two reasons:

(1) The energy delivered by the force to accelerate the mass goes into the mass. If it didn't, it wouldn't be accelerating the mass, it would be doing something else.

(2) You can't store energy "in the distortion of spacetime" because there is no such thing; there is no tensor that describes "energy stored in the distortion of spacetime".

You can transport energy by gravitational waves, which can be thought of as changes in the curvature of spacetime that propagate. But there is no way to localize the energy that is being transported.

vanhees71
The answer to this is no for two reasons:

(1) The energy delivered by the force to accelerate the mass goes into the mass. If it didn't, it wouldn't be accelerating the mass, it would be doing something else.

(2) You can't store energy "in the distortion of spacetime" because there is no such thing; there is no tensor that describes "energy stored in the distortion of spacetime".

You can transport energy by gravitational waves, which can be thought of as changes in the curvature of spacetime that propagate. But there is no way to localize the energy that is being transported.
For the first point I would say that this sounds like a chicken and egg problem: you directly refer to the relation F=m*dv/dt and conclude that the energy should be stored in the mass. But the discussion is just about the question if it could be stored in something underlying different than directly the mass. So therefore I think you cannot use that argument that a different explanation cannot be true because the regular explanation must be true.

The second remark I cannot judge. however I could imagine that a mass curving the spacetime around it is a form of energy storage. Because if you would take away the mass instantly, the energy propagates away as gravitational waves. so then I would say that a moving mass can be interpretet as a a mass being taken away at one point and put back at another point and so then when spacetime curvature is a form of energy storage, then energy is taken away from spacetime around one point and stored into the spacetime around the next point similar to energy being stored in a magnetic inductor ad then converted to another inductor. If you do that slow, the energy stored in waves is very small so all energy is then transported. I think that is what is said in the movie I referred to in relation to mass and accelleration. and then the question was: how does this work if I have a mass following a geodesic and If I have a mass being accelerated by an external force. Unfortnately I do not have sufficient knowledge to write down the equations, so therefore I was hoping that a specialist would like to use these equations in relation to both situations to prove it or bust it.

Dale
For the first point I would say that this sounds like a chicken and egg problem: you directly refer to the relation F=m*dv/dt and conclude that the energy should be stored in the mass.
Yes, because that is what ##m \ dv/dt## means -- it means you stored what the force transmitted in the kinetic energy of the mass. There is no "chicken and egg problem". This is just basic physics: a force does work, and when the work it does is to accelerate a mass, the energy transmitted by the work done goes into the kinetic energy of the mass.

I could imagine that a mass curving the spacetime around it is a form of energy storage
You should not be trying to "imagine" things like this. You should be learning how the physics actually works. When you do, you will find exactly what I said: that there is no tensor that represents "energy stored in spacetime", and in GR, physical things are represented by tensors.

the movie
Is, as you have already been told, nonsense. It is not a valid basis for PF discussion.

there is no tensor that represents "energy stored in spacetime"
Then is it stil unclear to me how we can explain that gravitational waves occur (representing enrgy flow) when you would instantly take away a mass. so where is the energy of the gravitational wave then coming from?

Motore
Because if you would take away the mass instantly,
You can't, and attempting to describe doing this leads to a self-contradiction. This kind of thing (which seems a superficially reasonable idealisation, but actually invalidates all subsequent reasoning) is why generating plausible ideas in GR is hard.

Yes, because that is what ##m \ dv/dt## means -- it means you stored what the force transmitted in the kinetic energy of the mass. There is no "chicken and egg problem". This is just basic physics: a force does work, and when the work it does is to accelerate a mass, the energy transmitted by the work done goes into the kinetic energy of the mass.
I know that of course, but the fact that there is kinetic energy does on its own not say where this energy is actually stored I assume.

You can't, and attempting to describe doing this leads to a self-contradiction. This kind of thing (which seems a superficially reasonable idealisation, but actually invalidates all subsequent reasoning) is why generating plausible ideas in GR is hard.
bringing together 1 kg of matter and 1 kg of antimatter?

Then is it stil unclear to me how we can explain that gravitational waves occur (representing enrgy flow) when you would instantly take away a mass. so where is the energy of the gravitational wave then coming from?
Good question.

Note that in non-stationary spacetimes energy is not conserved, so the answer might just be "nowhere". If you want a better answer we first need to define what the quantity that is conserved is, and despite a lot of trying nobody has managed to come up with a solution that is satisfactory to most physicists. And that's why this kind of conversation stalls - we don't know how (or even if we can) write the terms we need to be able to have it.

bringing together 1 kg of matter and 1 kg of antimatter?
...gives you 2kg of EM radiation which radiates away in finite time. Probably spherically symmetrically, so it doesn't emit gravitational waves.

...gives you 2kg of EM radiation which radiates away in finite time. Probably spherically symmetrically, so it doesn't emit gravitational waves.
ok then probably this is not a good example. as you see I am trying to find ways to create a situation from which we can get better understanding.

Good question.

Note that in non-stationary spacetimes energy is not conserved, so the answer might just be "nowhere". If you want a better answer we first need to define what the quantity that is conserved is, and despite a lot of trying nobody has managed to come up with a solution that is satisfactory to most physicists. And that's why this kind of conversation stalls - we don't know how (or even if we can) write the terms we need to be able to have it.
ok, that sounds like we do not understand nature suffiiently to answer these kind of questions. but if we do no understand, how can we then conclude that my reasoning (what is said in the movie) is wrong? (of cource we also cannot prove then that it is right)

ok then probably this is not a good example. as you see I am trying to find ways to create a situation from which we can get better understanding.
thinking a bit further: a mass generates a gravitational field so in case of the sun this gives the orbit of the Earth around the sun. suppose we would let the sun disappear in the same way by assuming the matter, antimatter way, then (beside an anormous amount of readiation) it would lead to the the Earth stopping to follow its orbit (lets neglect the effct of the wave of readiation on the Earth orbit) so there shoud be an instant change in gravitational field I assume 10 minutes later, so gravitational waves passing the Earth at that moment?

ok, that sounds like we do not understand nature suffiiently to answer these kind of questions. but if we do no understand, how can we then conclude that my reasoning (what is said in the movie) is wrong? (of cource we also cannot prove then that it is right)
It's more that speculating wildly is a waste of time. If you can't tie your "energy stored in curved spacetime" to something mathematical that we can have quantitative discussions (and eventually measurements) about then it's the same as suggesting the energy is stored in invisible unicorn dung accumulating infront of the matter. You can't prove the unicorn dung idea is wrong, but until I can make quantitative predictions based off it, why would you take it seriously? Energy building up in curved spacetime merely sounds slightly less ridiculous than the unicorn dung, but without some maths to describe the behaviour it's just as useless.
so gravitational waves passing the Earth at that moment?
No, that's the EM radiation that used to be the Sun passing us. The radiation's stress-energy is a source of gravity until it's outside our orbit (when it doesn't affect us any more by the GR equivalent of the shell theorem). There may be no gravitational waves in this spacetime - it depends how you added the solar mass of antimatter.

Motore
No, that's the EM radiation that used to be the Sun passing us. The radiation's stress-energy is a source of gravity until it's outside our orbit (when it doesn't affect us any more by the GR equivalent of the shell theorem). There may be no gravitational waves in this spacetime - it depends how you added the solar mass of antimatter.
ok but at least gravity becomes different from that moment onwards. before it took energy to come from the sun surface to the Earth overcoming the gravitational field sand afterwards not anymore, so there should be a difference in energy stored somewhere. (or energy is lost ?)

It's more that speculating wildly is a waste of time. If you can't tie your "energy stored in curved spacetime" to something mathematical that we can have quantitative discussions (and eventually measurements) about then it's the same as suggesting the energy is stored in invisible unicorn dung accumulating infront of the matter. You can't prove the unicorn dung idea is wrong, but until I can make quantitative predictions based off it, why would you take it seriously? Energy building up in curved spacetime merely sounds slightly less ridiculous than the unicorn dung, but without some maths to describe the behaviour it's just as useless.
point is that I do not have the background to check the ideas, but I would assume it could be calculated or simulated as I assume we have the equations to calculate or simulate what happens with spacetime if you accelerate a mass. so the only thing I can do at the moment is share my ideas and hope that someone can do the math because the equations should be there so we can have quantitative discussions after doing that first.

Motore
I do not have the background to check the ideas, but I would assume it could be calculated or simulated
In order to calculate or simulate something it must be converted into math. Not every string of words can be translated into math. In particular, the words in the movie are not translatable into math. That is what I meant above by “nonsense” and “not even wrong”. It is just a string of words with no connection to actual physics.

At this point we are done discussing this unacceptable source. It is not a valid source as you have already been told, the concepts are not valid, and the more time you spend on them the less time you will have to actually learn something.

In order to calculate or simulate something it must be converted into math. Not every string of words can be translated into math. In particular, the words in the movie are not translatable into math. That is what I meant above by “nonsense” and “not even wrong”. It is just a string of words with no connection to actual physics.

At this point we are done discussing this unacceptable source. It is not a valid source as you have already been told, the concepts are not valid, and the more time you spend on them the less time you will have to actually learn something.
ok then one last remark: what I mean is the math of general relativity not the math directly describing the story in the movie. I assume there should be tools available to calculate or simulate the effect of an accelerating mass in such environment. (I assume same tools that are used to calculate for example black holes spinning around each other) I am not convinced until I see some results or calculations.

Convinced of what? What exactly do you want calculated? Since you are (correctly) not talking about the movie then what are you asking about instead?

Thelamon
Then is it stil unclear to me how we can explain that gravitational waves occur (representing enrgy flow) when you would instantly take away a mass.
As @Ibix says, you can't "instantly take away a mass". That violates local stress-energy conservation.

Gravitational waves are produced by quadrupole oscillations of mass distributions. Examples are mutually orbiting binary pulsars and mergers of neutron stars or black holes.

where is the energy of the gravitational wave then coming from?
Since the energy carried by gravitational waves can't be localized, there is no answer to this question the way I think you mean it.

The effect that emission of gravitational waves has on mass distributions is, heuristically, to make them more compact and reduce their quadrupole asymmetry. For example, binary pulsar systems have their orbits become smaller and less elliptical. This generally results in a decrease in the externally measured mass of the system, but the externally measured mass is not the sum of locally measured masses, so locally measured masses don't need to change at all for this to happen. (One heuristic way of thinking of this is gravitational binding energy.)

what happens with spacetime if you accelerate a mass
Unless the mass you are accelerating is large enough to have a significant effect on spacetime geometry--something like a planet or star--then, to a very good approximation, nothing happens to spacetime if you accelerate the mass. The fact of the mass accelerating, by itself, has no effect on spacetime; "accelerating mass" by itself is not a source of gravity and doesn't change the spacetime geometry.

If you had a big enough rocket to, say, impart some proper acceleration to the Earth, then the rocket itself, or more precisely its fuel and reaction mass, would have to be the size of a planet and would affect the spacetime geometry: and the process of firing the rocket and accelerating the Earth would redistribute stress-energy (the Earth would move and the rocket exhaust would move the other way), which would change the spacetime geometry. In general, for a scenario like this, we would not have an exact solution for the spacetime geometry and you would have to solve it numerically.

There is one known exact solution for accelerating a mass that is large enough to affect the spacetime geometry, by having the mass emit photons as "exhaust" in the direction opposite to its acceleration. This is the Kinnersley photon rocket:

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

The "mass" in this solution is treated as a point mass, not an actual planet or star, and the photon "rocket exhaust" is assumed to be perfectly collimated in a single direction, so it is highly idealized.

In general, for a scenario like this, we would not have an exact solution for the spacetime geometry and you would have to solve it numerically.

There is one known exact solution for accelerating a mass that is large enough to affect the spacetime geometry, by having the mass emit photons as "exhaust" in the direction opposite to its acceleration. This is the Kinnersley photon rocket:

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

The "mass" in this solution is treated as a point mass, not an actual planet or star, and the photon "rocket exhaust" is assumed to be perfectly collimated in a single direction, so it is highly idealized.
Thanks for checking this. For me an exact solution of something does not have more value than a numerical solution to get a good understanding. of course it is nice to have exact solutions but should not be a limitation.
unfortunately I cannot see the impact of the link between the Kinnersley photon rocket on the answer to my question, but that is most likely my own limitation of knowledge. so if you can draw a conclusion would be great.

Convinced of what? What exactly do you want calculated? Since you are (correctly) not talking about the movie then what are you asking about instead?
The movie triggered me to the idea that any mass even a small one curves spacetime and the assumption is that spacetime curvature represents an amount of energy similar to a spring being windup. so such a mass changing position would therefore mean a change in the spacetime curvature so therefore also a redistibution of the energy stored.
so what could be calculated is:
1) how much energy is stored in an infinite volume of spacetime due to for example a mass of 1kg.
2) if I give this mass an accelaration by applying an external force, then how does the stored energy be build off in the volume that the mass just passed and ho does it build up in the volume the mass is entering
3) is the difference between these 2 zero or not?
4) if it is zero then the conclusion is that an acceleration of a mass in situation of daily life (so no extreme curvature situations) requires a force but that force then doesn't have an underlying cause resulting from changing spacetime curvature.
5) if it is not zero then the energy needed to accelerate the mass is related to the changing curvature.
6) if 5 is true then can we derive an equation for the relation between the accelaration, the mass and the energy stored in the spacetime curvature and does that relation then explain the relation we measure being F=m x dv/dt ?

Motore
I cannot see the impact of the link between the Kinnersley photon rocket on the answer to my question
The Kinnersley photon rocket is an example of a mass being accelerated (by emitting photons in one direction, which accelerates the mass in the opposite direction) and the spacetime geometry that results (because the mass is significant enough to affect the spacetime geometry).

vanhees71
The movie triggered me to the idea
This is going to be very blunt: forget the movie. The movie is bogus. Do not use the movie to imagine anything or get any ideas. The movie is useless to you.

You have been told this before in this thread, but apparently you didn't get the point, so now I'm telling you more emphatically. If you post about the movie again you will receive a warning. The movie is not a valid source for PF discussion. Period.

1) how much energy is stored in an infinite volume of spacetime due to for example a mass of 1kg.
2) if I give this mass an accelaration by applying an external force, then how does the stored energy be build off in the volume that the mass just passed and ho does it build up in the volume the mass is entering
3) is the difference between these 2 zero or not?
4) if it is zero then the conclusion is that an acceleration of a mass in situation of daily life (so no extreme curvature situations) requires a force but that force then doesn't have an underlying cause resulting from changing spacetime curvature.
5) if it is not zero then the energy needed to accelerate the mass is related to the changing curvature.
6) if 5 is true then can we derive an equation for the relation between the accelaration, the mass and the energy stored in the spacetime curvature and does that relation then explain the relation we measure being F=m x dv/dt ?
All of these are nonsense. You have already been told why. There is no point in continuing to repeat the same responses.

Motore and vanhees71
The substantive questions posed in this thread have been answered, and the thread is now veering off into nonsensical speculation.