I Gravity: Force or Acceleration?

[PeroK]

.Being "accelerated" and being "stationary" is weird.

You have that in any accelerating reference frame. If you are on an aircraft taking off, then you feel the accelerating force, but inside the plane everything remains stationary relative to you.

In any case, one of the underlying principles of relativity is that there is no concept in nature of a state of absolute rest. "Stationary" is, therefore, always frame-dependent.

 

[valenumr]

You have that in any accelerating reference frame. If you are on an aircraft taking off, then you feel the accelerating force, but inside the plane everything remains stationary relative to you.

In any case, one of the underlying principles of relativity is that there is no concept in nature of a state of absolute rest. "Stationary" is, therefore, always frame-dependent.

Oh for sure. I just mean weird from an intuitive point of view. Sort of basic training 101 is that if you a

You have that in any accelerating reference frame. If you are on an aircraft taking off, then you feel the accelerating force, but inside the plane everything remains stationary relative to you.

In any case, one of the underlying principles of relativity is that there is no concept in nature of a state of absolute rest. "Stationary" is, therefore, always frame-dependent.

I don't mean to say it's weird mathematically, just intuitively. Think Newton's second law and how we think about the everyday world.

 

[PeroK]

Oh for sure. I just mean weird from an intuitive point of view. Sort of basic training 101 is that if you a

I don't mean to say it's weird mathematically, just intuitively. Think Newton's second law and how we think about the everyday world.

This is why we study physics. To free ourselves of these basic misconceptions.

For example, there's almost no evidence for Newton's first law. Almost all the evidence appears to be to the contrary. The pre-Newtonian laws were:

1) Any object will naturally slow down unless kept moving by some external agency.

2) The planets and stars are kept in their orbits around the stationary Earth by the hand of God.

That was all what appeared must be the case. Newton's first law was a revelation and an enormous insight that it's the other way round.

But, in our practical everyday world, we cannot rely on the first law. There are always resisting forces, so we do have to keep putting energy into a system to keep it moving.

 

[Nugatory]

I don't mean to say it's weird mathematically, just intuitively

Much of this weirdness is because you are confusing two different things: coordinate acceleration and proper acceleration. Get this distinction clear in your mind and you will find it easier to see how your intuition has been misleading you.

 

[valenumr]

Much of this weirdness is because you are confusing two different things: coordinate acceleration and proper acceleration. Get this distinction clear in your mind and you will find it easier to see how your intuition has been misleading you.

Right. Considering an object at rest on a massive body is non-inertial is my struggle. I can grasp GRa little bit conceptually, but I run into some mental challenges. The vast majority of my experience is with dynamics, and especially 6-dof mechanics simulation. My first assertion might be incorrect with a good explanation that I haven't grasped.

 

[PeterDonis]

Considering an object at rest on a massive body is non-inertial is my struggle.

"Non-inertial" = "feels weight".

Does that help?

 

[valenumr]

"Non-inertial" = "feels weight".

Does that help?

No problem with that, but I'm use to the idea that physics get broken in non-inertial frames. And I suppose that goes to my lack of understanding of coordinate choices, perhaps.

 

[PeterDonis]

I'm use to the idea that physics get broken in non-inertial frames.

Why would physics be "broken" in non-inertial frames? Where are you getting that idea from?

 

[valenumr]

Why would physics be "broken" in non-inertial frames? Where are you getting that idea from?

I mean that from my understanding you can't count on conservation of energy. I can give an (perhaps misguided example).

 

[valenumr]

Why would physics be "broken" in non-inertial frames? Where are you getting that idea from?

And sorry, I didn't mean broken. Obviously that isn't the case. Not my understanding is broken.

 

[PeterDonis]

I mean that from my understanding you can't count on conservation of energy. I can give an (perhaps misguided example).

Please do give an example, yes.

 

[Nugatory]

I mean that from my understanding you can't count on conservation of energy. I can give an (perhaps misguided example).

Energy conservation works in non-inertial frames, as long as we include the work done by the so-called fictitious forces. The math is exactly that used to demonstrate conservation of energy on the surface of the earth: throw an object upwards and it gains potential energy as it loses kinetic energy, and the total (KE+PE) is conserved.

We need to be more careful with energy conservation in curved spacetimes, but even there the differential form of the conservation law (total amount of energy within an infinitesimal volume changes only when energy enters or leaves that volume) works. It is the integral form (integrate across these infinitesimal volumes to define the total energy in the system at any given moment) that is problematic because "at any given moment" is not unambiguously defined in a curved spacetime.

 

[valenumr]

Please do give an example, yes.

That's going to take a minute.

 

[f todd baker]

Although I have not read every posting on this thread, I find it surprising that so many state that gravity IS curvature of spacetime. What I have learned is that general relativity is a field theory and therefore may be thought of as a force. Curvature is just one possible way to describe the field equations. If GR weren't a field theory then people wouldn't be trying to quantize it. An excellent, readable essay on this can be found at https://www.quantum-field-theory.net/space-time-curvature-relativity/. Note that Steven Weinberg advocates this view.
Here is one paragraph from that essay: "By stretching our minds, some of us can even form a vague mental image of what four-dimensional curvature would be like if it did exist. Nevertheless, saying that the gravitational field equations are equivalent to curvature is not the same as saying that there is curvature. In QFT, the gravitational field is just another force field, like the EM, strong and weak fields, albeit with a greater complexity that is reflected in its higher spin value of 2."

 

[PeroK]

Although I have not read every posting on this thread, I find it surprising that so many state that gravity IS curvature of spacetime. ... In QFT, the gravitational field is just another force field, like the EM, strong and weak fields, albeit with a greater complexity that is reflected in its higher spin value of 2."

There is no acceptable theory of quantum gravity yet. GR is the best we have; and in GR, whether you like it or not, gravity is spacetime curvature.

 

[cianfa72]

Energy conservation works in non-inertial frames, as long as we include the work done by the so-called fictitious forces. The math is exactly that used to demonstrate conservation of energy on the surface of the earth: throw an object upwards and it gains potential energy as it loses kinetic energy, and the total (KE+PE) is conserved.

I think we need carefully define which is the 'system' involved. Potential energy for an object alone (i.e. without any internal structure) actually makes no sense: it applies only to systems made of parts since it is related to their configuration within the 'system' itself.

Now to talk about Potential energy (PE) in the case at hand, we need to consider the 'Earth + rock' system in the non-inertial Earth's rest frame. Analyzed in this frame the Earth's kinetic energy (KE) is by definition zero.

When a rock is thrown the PE of the 'Earth + rock' system changes (since its configuration changes) and energy is transferred from the system PE to the system KE (i.e. to the KE of the rock alone).

 

[f todd baker]

There is no acceptable theory of quantum gravity yet. GR is the best we have; and in GR, whether you like it or not, gravity is spacetime curvature.

Of course I know there is no acceptable quantization. That does not have to mean that GR is not a field theory.

 

[Nugatory]

I think we need carefully define which is the 'system' involved.

Of course we do, but that doesn't change the point about energy conservation: the non-inertial frame is no impediment to conservation of energy if we do it right. A curved spacetime may be.

 

[PeterDonis]

What I have learned is that general relativity is a field theory and therefore may be thought of as a force.

If we consider GR as an "effective field theory", i.e., as a low energy approximation to some underlying quantum theory, then yes, we can consider gravity as an "interaction" on that view. That is the view that Weinberg, for example, is advocating in the article you linked to. But that view is off topic in this forum; discussion of it belongs either in the quantum physics forum, or more likely in the Beyond the Standard Model forum since that's where discussion of quantum gravity in general belongs. See my post #3 for further discussion of this point.

 

[cianfa72]

Of course we do, but that doesn't change the point about energy conservation: the non-inertial frame is no impediment to conservation of energy if we do it right.

Yes, definitely.

A curved spacetime may be.

Which is the problem curved spacetime bring in ?

 

[Nugatory]

Which is the problem curved spacetime bring in ?

The difficulty in applying the integral form of the conservation law, second paragraph of #42 above.

 

[cianfa72]

We need to be more careful with energy conservation in curved spacetimes, but even there the differential form of the conservation law (total amount of energy within an infinitesimal volume changes only when energy enters or leaves that volume) works.

Do you mean an infinitesimal volume of spacetime or just a infinitesimal volume of a "space" slice (i.e. a spacelike hypersurface) ?

 

[f todd baker]

If we consider GR as an "effective field theory", i.e., as a low energy approximation to some underlying quantum theory, then yes, we can consider gravity as an "interaction" on that view. That is the view that Weinberg, for example, is advocating in the article you linked to. But that view is off topic in this forum; discussion of it belongs either in the quantum physics forum, or more likely in the Beyond the Standard Model forum since that's where discussion of quantum gravity in general belongs. See my post #3 for further discussion of this point.

Sorry, I guess I don't see why a comment about force in GR is "off topic" for a question about whether gravity is a force. It sure isn't worth splitting hairs over, though.

 

[Robert Stenton]

Summary:: Conflicting opinions on videos I’ve watched

I’ve watched a few videos recently that explained that gravity is not a force rather it is caused by time dilation because clocks tick slower closer to mass. Objects will follow a geodesic through spacetime and require a force to move them away from a geodesic - so the surface of the Earth is accelerating everything on the surface. If you fall into a hole you don’t experience a gravitational force pulling you down rather you feel the removal of the force that was pushing you away from your geodesic. I then watched a video on quantum gravity that said gravity was a force (although almost infinitely weaker than the other known forces) and the theoretical particle is the graviton.
So which is true?

On the subject of gravity not being a force - if we are being constantly accelerated by standing on the surface of the Earth doesn’t that require some energy? If yes where does that energy come from?

There are four fundamental forces in nature: strong and weak nuclear, electromagnetic and gravity. They all share one thing in common and that is at a lower energy level time goes slower. If a large cloud condenses into a star,even though the atoms in the star are the same as the ones in the original cloud, the mass of star is reduced because the atoms go through time slower. Think of a butterfly on a scale that flies off and on but is only on the scale half the time, the scale weight of the butterfly would then be cut in half. It is from the missing mass that the energy comes from to create the gravitational field. The gravitational field would be the same as it was outside the boundary of the original cloud but much greater between that boundary and the surface of the star. Visualize it this way, the side of the moon facing the Earth is traveling slower than the side away from earth. Now I am sure that someone will tell me I am all wrong but this is a simple way for me to logically understand gravity. Hope it helps.
Robert Stenton

 

[PeterDonis]

I guess I don't see why a comment about force in GR is "off topic" for a question about whether gravity is a force

The point is that in classical GR, considered as an exact classical theory, without regard to whether it could be a low energy "effective theory" approximation to something else, gravity is simply not a force. Any view that considers gravity a force has to rely on some claim about GR being an "effective field theory" approximation to something else. Such claims are off topic in this particular forum because this particular forum is not about GR as a possible "effective field theory" approximation to something else; it's about classical GR, considered as an exact classical theory.

 

[PeterDonis]

There are four fundamental forces in nature: strong and weak nuclear, electromagnetic and gravity.

In classical GR, as has already been remarked several times now in this thread, gravity is not a force. It is not like the other "fundamental forces" you describe.

They all share one thing in common and that is at a lower energy level time goes slower.

This is not correct. There is no analogue of gravitational time dilation for the strong, weak, or electromagnetic interactions.

I am sure that someone will tell me I am all wrong

Indeed, yes, you are.

but this is a simple way for me to logically understand gravity.

Personal theories and personal speculations are not allowed here at PF. You would be much better advised to learn a proper understanding from a GR textbook.

 

[H_A_Landman]

This, unfortunately, is utter nonsense, since it is backwards. Gravitational time dilation is CAUSED by gravity, it is not a cause OF gravity.

It's really disheartening to see people still getting this exactly wrong and being loudly insistent that they are right. And other people upvoting them.

In the Newtonian (weak-field, low-speed) limit of GR, gravity is 100% caused by time dilation. That is, the reduced metric consists of flat Minkowski spacetime (which causes no gravity by definition) plus a time-curvature term, proportional to the Newtonian gravitational potential, that represents the time dilation field. And the geodesics of that metric are the arcs of Newtonian gravity. So there isn't any "gravity" left over to cause anything, let alone the time dilation which is already baked into the metric.

So, from the GR perspective, Newtonian gravity is a theory of curved time only (in flat space). The curved time is what bends paths. This isn't news. It's been known for over half a century. Even Feynman spent some time explaining it (Lectures II 42-8).

Around a perfectly spherical non-rotating Earth, this would be accurate to within 1 part per billion. Around real Earth, it's more like 1 part per million.

If you back out of taking the low-speed limit (so it's only weak-field), then there is a space curvature term that ranges from zero (at zero speed) to equal in size to the time-curvature term (at the speed of light). This is why the bending of light is double the Newtonian prediction. But the time curvature still causes at least 50% in all cases, even for light.

Please note that I am not making any claims about what happens in the strong-field regime, e.g. close to a black hole or neutron star. That's above my pay grade.

 

[PeterDonis]

It's really disheartening to see people still getting this exactly wrong and being loudly insistent that they are right. And other people upvoting them.

It's really disheartening to see someone talking about one particular solution of the Einstein Field Equation, described in one particular coordinate chart, as though it were "GR" and "gravity" without qualification.

In the Newtonian (weak-field, low-speed) limit of the Schwarzschild metric of GR

See the bolded addition I made above. It makes a huge difference. The Schwarzschild metric is just one solution of the Einstein Field Equation. There are many others. Most of them do not even have a simple concept of "gravity" as arising from a Newtonian potential.

the reduced metric in Schwarzschild coordinates

Again, see the bolded addition I made above. It makes a huge difference.

consists of flat Minkowski spacetime (which causes no gravity by definition)

Depends on how you define "gravity". By at least one fairly common definition (the one that underlies the equivalence principle), there is "gravity" in the non-inertial rest frame of a rocket accelerating in a straight line in flat spacetime.

plus a time-curvature term, proportional to the Newtonian gravitational potential, that represents the time dilation field.

The $- 2M / r$ term in the $g_{tt}$ metric coefficient in Schwarzschild coordinates, which is what you are referring to here, is not a "time curvature" term. Curvature is expressed by the Riemann curvature tensor, not the metric. This term can be thought of, in this particular solution, in these particular coordinates, in this particular approximation, as arising from the Newtonian gravitational potential. But that just means that spacetime curvature, in its manifestation in this particular solution, in these particular coordinates, in this particular approximation as Newtonian gravitational potential, causes both time dilation for stationary observers (note that qualifier, it also makes a big difference--"time dilation" is observer-dependent) and "gravity" (more precisely, the fact that radial geodesics converge towards the central mass). It does not mean that time dilation causes gravity.

If you back out of taking the low-speed limit (so it's only weak-field), then there is a space curvature term that ranges from zero (at zero speed) to equal in size to the time-curvature term (at the speed of light).

This claim, with appropriate caveats (just as for $g_{tt}$ above, the appearance of a term proportional to $2M / r$ in the spatial terms in the metric is not "space curvature", since that, as noted, is expressed by the Riemann curvature tensor, not the metric), is also only true for this particular solution, in these particular coordinates, in this particular approximation (weak field).

 

[H_A_Landman]

See the bolded addition I made above. It makes a huge difference. The Schwarzschild metric is just one solution of the Einstein Field Equation. There are many others.

Well, sure, it's easiest to see with the Schwarzschild metric, but that's a one-body metric. It also works with multiple bodies. You just add up the Newtonian potentials for each body and plug that in. You can do a whole galaxy (minus the strong-field parts) this way.

If you're more comfortable with the phrase "time-only term" than "time-curvature term", I don't have any great objection. But "flat" implies no force-like effects, and "curved" implies force-like effects, and this clearly has force-like effects (curved geodesics). The metric is not flat, but the Minkowski part is flat. So all the non-flatness comes from the time dilation.

 

[PeterDonis]

although what you say is certainly true for consensus mainstream physics

Which is what's on topic here; more precisely, mainstream physics regarding classical GR.

there are multiple physicists who think otherwise.

If you want to discuss these speculative theories, please do so in a new thread in the Beyond the Standard Model forum. They are off topic here.