I Gravity: Force or Acceleration?

[Schnellmann]

TL;DR 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?

 

[phinds]

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.

This, unfortunately, is utter nonsense, since it is backwards. Gravitational time dilation is CAUSED by gravity, it is not a cause OF gravity. Also, clocks do NOT tick slower in a gravity well, they tick at the same one second per second as all clocks. This all gets mildly complicated. I suggest you read some actual physics rather than pop-sci presentations which are misleading you badly.

Gravity is considered a force in Newtonian Physics, but our universe doesn't work on Newtonian physics, it works on General Relativity and gravity is not a force.

Newtonian Physics is a limited range of General Relativity so is used for day to day practical applications like building bridges.

 

[PeterDonis]

I’ve watched a few videos

Videos are generally not good sources if you want to actually learn physics. Textbooks or peer-reviewed papers are better.

gravity is not a force

In General Relativity, this is true; gravity is not a force. Instead it is due to spacetime curvature.

rather it is caused by time dilation because clocks tick slower closer to mass.

This is one aspect of "gravity", and ultimately the time dilation effect being referred to is due to spacetime curvature.

Objects will follow a geodesic through spacetime and require a force to move them away from a geodesic

Yes, this is one way of restating the fact that gravity is not a force--objects that, in pre-relativity physics, we would have said were moving "solely due to gravity", are in fact moving on geodesics; they are in free fall, and feel no force. In fact, the GR view that gravity is not a force is actually simpler than the Newtonian (pre-relativity) view that gravity is a force, because on the Newtonian view one has to explain why objects moving solely under the "force" of gravity, such as falling rocks or planets orbiting the Sun, do not feel any force. In GR, this is obvious: they feel no force because they are not being acted on by any force.

the surface of the Earth is accelerating everything on the surface.

Yes.

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.

Yes.

I then watched a video on quantum gravity that said gravity was a force (although almost infinitely weaker than the other known forces)

This is the relativity forum, not the quantum physics forum; and in any case we don't have a good theory of quantum gravity (though trying to find one is an active area of research). The basic quantum gravity idea being referred to here is better described by the term "interaction", not "force"; basically, the idea is that "gravity", aka spacetime curvature, should ultimately be due to the same kind of thing that underlies the three known interactions in the Standard Model of particle physics (strong, weak, electromagnetic).

the theoretical particle is the graviton.

At some level of theory, yes, most physicists expect that quantum aspects of gravity will manifest themselves as a massless, spin-2 gauge field, the particle aspect of which is called the graviton. However, it is extremely unlikely that we will be able to test such quantum aspects of gravity experimentally in the foreseeable future.

 

[Dale]

Summary:: Conflicting opinions on videos I’ve watched

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?

Currently there is no accepted and validated quantum theory of gravity. So any claims about gravitons are purely speculative at this time.

In contrast, the other concepts of gravity that you described are on firm theoretical and experimental ground.

 

[Schnellmann]

. I suggest you read some actual physics rather than pop-sci presentations which are misleading you badly.

Seems a little harsh. The videos I’ve been watching are by scientists working in the field eg Don Lincoln from Fermilab not just random bods posting fake science from their shed.

Learning from textbooks would be a challenge as I haven’t done any advanced maths in 35 years so would need to revise that intensively before I could tackle any physics textbooks (unless they were without the maths but then they wouldn’t really be more useful than videos).

 

[Orodruin]

Seems a little harsh. The videos I’ve been watching are by scientists working in the field eg Don Lincoln from Fermilab not just random bods posting fake science from their shed.

It really isn’t. Popular scientific presentations are not designed to teach you physics. They are designed to tell you about physics in an entertaining and light fashion without being too far out of bounds. This is true regardless of whether the presenter is a respectable physicist in their own right.

 

[PeroK]

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?

Acceleration does not, in general, require energy. Let's return to the Newtonian model of gravity for an example. The Moon is in an approximately circular orbit of the Earth, hence has continuous centripetal acceleration towards the Earth. No additional energy is needed to maintain this acceleration.

In GR, the situation for someone standing on the surface of the Earth is somewhat analagous: there is continuous upwards acceleration, but it requires no energy input to maintain this.

 

[pervect]

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?

In Newtonian theory, gravity is a force. When Einstein created the theory of special relativity, he observed that the concept of Newtonian gravity was not consistent with special relativity. Einstein was concerned by this - there is now plenty of evidence that his special theory of relativity was correct. Then and now, though, the issue of how the special theory could possibly incorporate gravity remains.

There were several possibilities, but eventually Einstein came up with what is now called General Relativity as a way to incorporate gravity into the framework of special relativity.

You've already given a good lay summary of how GR works, congratulations on doing your research. I'll address a few things you haven't mentioned, though.

In order to incorporate gravity into special relativity, Einstein considered what the reference frame of an accelerating rocket or elevator would act like according to the theory. This is commonly called "Einstein's elevator". The motivation for considering the two cases, the force one feels in an accelerating elevator, and the force one feels due to gravity, as being equivalent is usually called "The Principle of Equivalence". There are several flavors of how the principle of equivalence works, this is just a short and not very detailed summary.

One of the predictions that comes out of a detailed, formal, analysis of Einstein's elevator is that clocks on the floor of Einstein's elevator do not tick at the same rate as clocks on top of the elevator. This effect is not compatible with the idea of considering gravity as "just a force". Forces do not, by themselves, cause clocks to tick at different rates. Now, it is perhaps possible to view gravity as a force plus other effects that cannot be fit into the mold of a "force", effects that would cause clocks to tick at different rates. However, I'm not aware of any such approach that has been published, and in any event it is not how we currently view and use the theory of General Relativity in practice. Einstein thought for quite a long time on the matter, and he eventually came up with a full theory of how he thought gravity could work in a manner that was compatible with special relativity, a theory that we now call "General Relativity".

Experimental results, such as the Pound-Rebka experiment, illustrate that the predictions that General Relativity makes are consistent with experiment, while Newton's theories of gravity fall short. The differences are small, but measurable with sufficiently precise and careful experiments.

Unfortunately, while this is all well and good as far as it goes, it is difficult to proceed further with just popularizations. I don't think it is possible to get a really good understanding of all aspects of General Relativity from the popularizations you have mentioned, though they are good start. In particular, I'm not aware of any way to popularize the treatment of energy in General relativity. There are some advanced graduate level treatments, but reducing them to a popular level has not, as far as I know, been done. Of course, I don't know everything, but I haven't heard of such a treatment.

What I can say though is that it doesn't take any energy to keep an object stationary on the surface of the Earth. It turns out that General Relativity has many different notions of energy - I would reagard ADM, Bondi, and Komar energy as being the "big three", though there are others. All of the formulations of energy in GR that I've mentioned are consistent with the idea that it doesn't take any work to hold an object at rest on the Earth's surface.

 

[valenumr]

Acceleration does not, in general, require energy. Let's return to the Newtonian model of gravity for an example. The Moon is in an approximately circular orbit of the Earth, hence has continuous centripetal acceleration towards the Earth. No additional energy is needed to maintain this acceleration.

In GR, the situation for someone standing on the surface of the Earth is somewhat analagous: there is continuous upwards acceleration, but it requires no energy input to maintain this.

My brain always gets messed up by this case. For example, if I fall toward the Earth from a substantial height, very bad things will happen to me. Which seems to imply some type of work being done on my fragile body.

 

[PeroK]

My brain always gets messed up by this case. For example, if I fall toward the Earth from a substantial height, very bad things will happen to me. Which seems to imply some type of work being done on my fragile body.

In Newtonian physics, the gravitational force does work on you in that scenario. You have increasing KE in the Earth's frame of reference.

In GR, if we choose your local free falling frame, then the Earth's surface has a force on it and the part that hits you has increasing KE in your frame.

GR locally reduces to SR and to Newtonian mechanics. It's the global picture that you need curved spacetime to explain. E.g. bodies falling on opposite sides of the Earth.

 

[valenumr]

In Newtonian physics, the gravitational force does work on you in that scenario. You have increasing KE in the Earth's frame of reference.

In GR, if we choose your local free falling frame, then the Earth's surface has a force on it and the part that hits you has increasing KE in your frame.

GR locally reduces to SR and to Newtonian mechanics. It's the global picture that you need curved spacetime to explain. E.g. bodies falling on opposite sides of the Earth.

That mostly makes sense, especially the Earth having increasing KE in my frame (honestly, that seems workable even in Galilean relativity), but what do you mean by "the Earth has a force on it?"

 

[PeroK]

what do you mean by "the Earth has a force on it?"

I didn't say that!

 

[valenumr]

I didn't say that!

Sorry, I didn't mean to misquote you. You said the Earth's surface has a force on it, specifically if we chose the free falling frame.

 

[PeroK]

Sorry, I didn't mean to misquote you. You said the Earth's surface has a force on it, specifically if we chose the free falling frame.

If you land on a bit of ground, that bit of ground has a real upward force from below. That's why (looking at things locally) that bit of ground is accelerating upwards. And, even after you collide with it, it's still being forced upwards.

What doesn't work is if you try to follow those local mechanics down to the centre of the Earth. From the global perspective, things don't add up in purely Newtonian terms without gravity itself as a force.

 

[valenumr]

Sorry, I didn't mean to misquote you. You said the Earth's surface has a force on it, specifically if we chose the free falling frame.

In any case, maybe I could pose a better set of questions to describe my confusion. How is gravitational heating explained, or nuclear fusion in stars? What if I where to set down on a planet with something like 30x G(earth)? Would I just turn into a pool of organic sludge? Would it be fair to say that the small patch of Earth that I am resting on would experience some (very trivial amount) of gravitational heating?

I can grasp the fact that I am essentially I'm the same frame as the surface of the earth, but why do I have weight, suddenly when I come to rest with respect to the surface?

This is why I said earlier that this specific case (at rest on the surface of a massive body) breaks my brain.

 

[valenumr]

If you land on a bit of ground, that bit of ground has a real upward force from below. That's why (looking at things locally) that bit of ground is accelerating upwards. And, even after you collide with it, it's still being forced upwards.

What doesn't work is if you try to follow those local mechanics down to the centre of the Earth. From the global perspective, things don't add up in purely Newtonian terms without gravity itself as a force.

Ok, so I think you mean just the coulomb forces that make the Earth a solid mass. Is that correct?

 

[valenumr]

And let me please reframe it one other way. If I'm at rest on th

In any case, maybe I could pose a better set of questions to describe my confusion. How is gravitational heating explained, or nuclear fusion in stars? What if I where to set down on a planet with something like 30x G(earth)? Would I just turn into a pool of organic sludge? Would it be fair to say that the small patch of Earth that I am resting on would experience some (very trivial amount) of gravitational heating?

I can grasp the fact that I am essentially I'm the same frame as the surface of the earth, but why do I have weight, suddenly when I come to rest with respect to the surface?

This is why I said earlier that this specific case (at rest on the surface of a massive body) breaks my brain.

And one more example that probably mashes things up a little, but hopefully makes some sense. If I am at rest on the surface of the earth, there is no work. And if I am at rest hovering above the surface of the earth, there is no work. In the latter case I would have to expend energy to do so. Is that correct? At least classically?

 

[Dale]

In GR, the situation for someone standing on the surface of the Earth is somewhat analagous: there is continuous upwards acceleration, but it requires no energy input to maintain this.

However, even this statement requires some clarification. Energy is frame variant. So for the scenario of someone standing on the surface of the earth, in the Earth’s frame no energy is required, but in the local free-fall frame energy is required. Where that energy comes from cannot be answered locally, and requires transitioning from a local flat free-fall frame to a global curved frame. At that point there is no longer a nice easy to describe flat analogy, but you are stuck using the full tensor math of GR.

 

[PeroK]

Ok, so I think you mean just the coulomb forces that make the Earth a solid mass. Is that correct?

I don't care where the forces come from. Kinematically, the Earth's surface is accelerating.

You have two options:

1) Take gravity as a force and do Newtonian mechanics.

2) Use GR.

There are ways (as I have tried to show you) to explain local gravity without curved spacetime or gravity as a force. It's clear that you can't explain everything that way - otherwise, there would be no need for GR at all.

If you don't like that idea, then stick with 1) or 2).

 

[Dale]

if I am at rest hovering above the surface of the earth, there is no work. In the latter case I would have to expend energy to do so. Is that correct? At least classically?

No, that is not correct classically. For example, a piece of superconductor material can hover over a magnet without expending energy. The fact that a helicopter requires energy just means that it is inefficient, not that energy is always required to hover.

 

[valenumr]

I don't care where the forces come from. Kinematically, the Earth's surface is accelerating.

You have two options:

1) Take gravity as a force and do Newtonian mechanics.

2) Use GR.

There are ways (as I have tried to show you) to explain local gravity without curved spacetime or gravity as a force. It's clear that you can't explain everything that way - otherwise, there would be no need for GR at all.

If you don't like that idea, then stick with 1) or 2).

Just to rewind a bit... the part that boggles my mind is that from the GR point of view, an object at rest on a massive body experiences constant acceleration, with no transfer of energy. This is very weird to me. it's much easier for me to grasp an orbiting body (technically with Newtonian acceleration) not requiring energy to maintain orbit, as in GR it is in free fall.

 

[valenumr]

No, that is not correct classically. For example, a piece of superconductor material can hover over a magnet without expending energy. The fact that a helicopter requires energy just means that it is inefficient, not that energy is always required to hover.

Thanks, great counter example.

 

[PeroK]

Just to rewind a bit... the part that boggles my mind is that from the GR point of view, an object at rest on a massive body experiences constant acceleration, with no transfer of energy. This is very weird to me. it's much easier for me to grasp an orbiting body (technically with Newtonian acceleration) not requiring energy to maintain orbit, as in GR it is in free fall.

You can use valenumr's laws of motion if you like:

Newton: $\vec F = m \vec a$

valenumr: $E = m|\vec a|$

I know which one I'm sticking with.

 

[PeroK]

PS classically, for a body of velocity $\vec v$ under force $\vec F$: $$\frac{dE}{dt} = \vec F \cdot \vec v$$There is, therefore, no change in kinetic energy due to a force if:

1) $\vec F$ is perpendicular to $\vec v$

or

2) $|\vec v| = 0$

In GR, in the reference frame of the Earth, the curvature of spacetime counteracts the real force and results in $\vec v = 0$ for an object at rest in the Earth's frame of reference. Hence $\frac{dE}{dt} = 0$.

You can't explain this using classical mechanics, but given that curved spacetime does counteract the real force, it's not inconsistent with classical ideas about energy.

 

[valenumr]

You can use valenumr's laws of motion if you like:

Newton: $\vec F = m \vec a$

valenumr: $E = m|\vec a|$

I know which one I'm sticking with.

Well, that wasn't what I was trying to say at all. I certainly understand that energy is frame dependent. I have no problem with the fact that an object at rest in an inertial frame has zero (kinetic) energy in that frame.

 

[PeroK]

Well, that wasn't what I was trying to say at all. I certainly understand that energy is frame dependent. I have no problem with the fact that an object at rest in an inertial frame has zero (kinetic) energy in that frame.

I was only joking!

 

[valenumr]

I was only joking!

Well, after your previous post, and now that I typed that, things make a lot more sense. I think it's just the stubborn classical physics train of thought in my head making me stubborn.

 

[cianfa72]

PS classically, for a body of velocity $\vec v$ under force $\vec F$: $$\frac{dE}{dt} = \vec F \cdot \vec v$$
You can't explain this using classical mechanics, but given that curved spacetime does counteract the real force, it's not inconsistent with classical ideas about energy.

I take it as in classic mechanics gravity is a force that adds up vectorially to the 'real' force (interaction force) from the Earth's surface that acts on a body at rest on it. Hence in Earth's frame there is no change of the body's kinetic energy.

 

[valenumr]

Well, after your previous post, and now that I typed that, things make a lot more sense. I think it's just the stubborn classical physics train of thought in my head making me stubborn.

Just want to add, it's not that the math doesn't make sense, I just meant the case is less intuitive in my head. Being "accelerated" and being "stationary" is weird. Especially considering that things like energy and momentum are only conserved when calculated in non-accelerating frames, I think anyway. Maybe that's not exactly correct.

 

[pervect]

The sci.physics FAQ on energy in GR is probably the most helpful thing I can think of that talks about energy conservation in GR. The link is https://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

A short excerpt.

In special cases, yes. In general, it depends on what you mean by "energy", and what you mean by "conserved".

In flat spacetime (the backdrop for special relativity), you can phrase energy conservation in two ways: as a differential equation, or as an equation involving integrals (gory details below). The two formulations are mathematically equivalent. But when you try to generalize this to curved spacetimes (the arena for general relativity), this equivalence breaks down. The differential form extends with nary a hiccup; not so the integral form.

For an opposing view, which I would categorize as a popularization (though it's written by a respected author), I'll mention Sean Caroll, who argues in his blog that energy is not conserved in General Relativity.

https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/

The point is pretty simple: back when you thought energy was conserved, there was a reason why you thought that, namely time-translation invariance. A fancy way of saying “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity that’s simply no longer true. Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.

The two statements from these two sources are not really inconsistent, they simply focus on different aspects of energy in General relativity. Caroll focuses on one specific notion of energy, based on Noether's theorem, and that notion leads to a formulation which is not conserved, while Baez mentions correctly (though it may not seem helpful at first) that there are different ways of thinking about the problem.

My main focus at this point is to point out that it's not a simple topic, though there is a lot written about it, mostly at a fairly high level.

I would also say that while Noether's theorem is not necessarily the only way to think about energy in General relativity, it's a good way. Hilbert, Klein, and a few others noticed some of the complexities surrounding energy in General Relativity, and some of the historical discussion may be of some interest and not totally and overwhelmingly technical. I haven't read it in detail, but https://arxiv.org/abs/2103.17160 looks like it might be a place to get some idea of this one specific idea, Noether's theorem. [add] I've glanced at it more - unfortunately, it's quite technical - so it's not a good place to learn the basics of Noether's theorem. It's definitely A-level, but I found the bits I could follow without a serious study quite illuminating. It'd be better if I had a less demanding reference, but at the moment I don't.

Emmy Noether’s (1918) two theorems, on the correspondence between symmetries of the
action under infinitesimal transformations of a continuous group, and local conservation
laws, are better known for their applications in classical mechanics and gauge theories
than in general relativity. Yet Noether’s motivation to study this problem came chiefly
out of discussions between David Hilbert, Felix Klein, Albert Einstein, and herself about
the interpretation of general relativity, between 1915 and 1918: specifically, about the
nature of the conservation equations in GR.10

So if one is already familiar with the classical applications of Noether's theorem, the take-away here is that Noether's theorem actually arose to handle the issues of energy conservation in General Relativity. But I don't have a good I-level reference for Noether's theorem handy.

I [also] don't have any suggestions for non-technical papers for other approaches, but in contrast to the Noether approach, I would suggest looking at the notion of ADM energy. I suspect, though, that this will unavoidably become very technical.

If one gets to the point where those two concepts of energy are understood, one could then go on to read about still more alternatives that have been published in the literature.

 

[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 ?