Einstein theory on bending of space

[PeterDonis]

It seems, with the right coordinate system, we could basically eventually get rid of at least one separate fundamental force, that of gravity

If you're talking about "fundamental forces", as in strong, weak, EM, and gravity, that's really a quantum field theory concept, not a GR concept. "Interaction" is a better term in this context, since not all of the manifestations of these things, from a QFT perspective, look like "forces" in the usual layman's sense. In QFT terms, gravity is believed to be an interaction just like the others, with an exchange particle, the graviton, just like the others (gluon, W and Z bosons, and photon). The property of gravity that singles it out from a GR perspective (that an object moving solely under gravity feels zero proper acceleration) is, from a QFT perspective, just a consequence of the fact that the graviton is spin-2 while the other exchange particles are spin-1. None of this depends on your choice of coordinates.

If by "with the right coordinate system" you are just referring to the fact that you can always find a local inertial frame in which a freely falling object is at rest, that does not eliminate all of the aspects of gravity; it only eliminates the "Newtonian force" aspect. Tidal gravity is not eliminated by choosing a local inertial frame, and in GR, tidal gravity is spacetime curvature--and strictly speaking, the word "gravity" in GR should refer specifically to tidal gravity, since that's the aspect of gravity that is independent of coordinates.

 

[MattRob]

If I recall correctly, I think the Newtonian approximations are so precise that space agencies use them for interplanetary missions. Funny story; one big kicker that convinced me to switch my major from Mechanical Engineering (planning to go into astronautical) to Physics-Astronomy was when I learned that I wouldn't be formally studying General Relativity as an Engineering major.

 

[stevendaryl]

If I recall correctly, I think the Newtonian approximations are so precise that space agencies use them for interplanetary missions. Funny story; one big kicker that convinced me to switch my major from Mechanical Engineering (planning to go into astronautical) to Physics-Astronomy was when I learned that I wouldn't be formally studying General Relativity as an Engineering major.

I had an acquaintance who was a PhD in physics, which back then would almost guarantee you a high-paying job somewhere. He got a job for some company that was a contractor for NASA. So his job was calculating orbits. It was all Newtonian physics. He found it ironic that to get his degree, he studied General Relativity, quantum field theory, condensed matter physics, etc., and then he got a job using the science that he learned in high school.

Of course, it was really HARD Newtonian physics.

 

[Wes Tausend]

Wes Tausend said: ↑
"It seems, with the right coordinate system, we could basically eventually get rid of at least one separate fundamental force, that of gravity"

If you're talking about "fundamental forces", as in strong, weak, EM, and gravity, that's really a quantum field theory concept, not a GR concept. "Interaction" is a better term in this context, since not all of the manifestations of these things, from a QFT perspective, look like "forces" in the usual layman's sense. In QFT terms, gravity is believed to be an interaction just like the others, with an exchange particle, the graviton, just like the others (gluon, W and Z bosons, and photon). The property of gravity that singles it out from a GR perspective (that an object moving solely under gravity feels zero proper acceleration) is, from a QFT perspective, just a consequence of the fact that the graviton is spin-2 while the other exchange particles are spin-1. None of this depends on your choice of coordinates...

Thanks for the kind reply Peter.

I do now see that the Four Fundamental Forces are all elements of quantum theory, perhaps exclusively. It is my student layman's understanding that Einstein once sought to unify three of these quantum forces with GR (tidal?) gravity (aka Unified Field Theory) in the past. It was also my understanding that the strong, weak and EM have been more recently(?) associated (reconciled) in QM, but that gravity alone yet remained elusive to this united family. So now I see that gravitons have a spin-2. Does this directly affect GR vs QM?

It also seemed to me that Einstein's so-named United Field Theory is identical to the Theory of Everything that Steven Hawking still seeks. I had just assumed that the perfect resolution would someday be to combine GR/QM and reduce all four forces into one; one all-encompassing "fundamental force" only. And finally, I assumed it must all be accomplished without damaging thee hard-fought, valid but separate, foundations of GR vs QM that have been already built.

But from what you have just stated, all four fundamental forces appear already entirely reconciled by QM. So what is it that Hawking still wishes to resolve by his proposed Theory of Everything? Is it merely to simplify the interactive math to a single, concise general formula-- because we've already conceived how it all works? I must admit this does not readily make sense to me.

Any comment on interpretation of coordinate SR/GR systems are on hold of course.

Wes
...

 

[PeterDonis]

It is my student layman's understanding that Einstein once sought to unify three of these quantum forces with GR (tidal?) gravity (aka Unified Field Theory) in the past.

Einstein's attempt at Unified Field Theory only covered electromagnetism; the strong and weak forces were not well understood at that time and he didn't include them.

It was also my understanding that the strong, weak and EM have been more recently(?) associated (reconciled) in QM, but that gravity alone yet remained elusive to this united family.

Yes. The theory that unifies the strong, weak, and EM interactions is called the Standard Model of particle physics. It does not include gravity (see further comments below on why).

So now I see that gravitons have a spin-2. Does this directly affect GR vs QM?

Not really; it affects the difficulty of incorporating gravity into a quantum field theory, but GR is a classical theory, and at the classical level there is no problem with gravity being spin-2; as I think I said before, it's that which makes the GR model of gravity as spacetime curvature possible.

It also seemed to me that Einstein's so-named United Field Theory is identical to the Theory of Everything that Steven Hawking still seeks.

Not really; Einstein sort of intended it to be one, but, as above, he didn't include the strong and weak interactions, and he also didn't take quantum effects into account--during the latter part of his career he became very dissatisfied with quantum theory, even though he had helped to create the field.

from what you have just stated, all four fundamental forces appear already entirely reconciled by QM

"Entirely reconciled" is too strong, and I didn't mean to give that impression. There are several issues:

(1) Gravity, as an interaction, is so weak compared to the others that we have no way of experimentally detecting any quantum aspects that it might have. So we have no way of experimentally confirming that gravitons exist or investigating their properties. We basically believe they exist because all the other interactions have quantum aspects. But there are a number of physicists (Freeman Dyson, who was instrumental in the development of quantum field theory, is one of them) who question whether gravity really has to have quantum aspects the way the other interactions do. Without experimental input there is really no way of resolving this question.

(2) Constructing a quantum field theory of a spin-2 particle has issues that constructing a quantum field theory of particles with spin-1 or lower (which all of the particles in the Standard Model are) does not. The main one is that the QFT of a spin-2 particle is not renormalizable. For a detailed discussion of this we would really need to start a separate thread in the Quantum Physics forum, but the key point is that the Standard Model is entirely renormalizable, and that is an important feature. So there isn't a simple, obvious way to add gravitons to the Standard Model; doing that would break an important feature of the theory.

(3) Even if we assume that finding a quantum theory that includes gravity is the right way to go, it's not entirely clear that doing it by constructing a QFT including a spin-2 graviton along the same lines as the Standard Model is the way to do it. There are a number of different candidates for a quantum gravity theory being investigated, and we don't know at this point how that will play out. (The lack of experimental input is a big issue here.)

When Hawking talks about a Theory of Everything, he's talking about getting all these issues resolved. He's gone back and forth over the years about how close he thinks we are to actually doing it. I personally think we still have quite a way to go.

 

[Wes Tausend]

Einstein's attempt at Unified Field Theory only covered electromagnetism; the strong and weak forces were not well understood at that time and he didn't include them.

Yes. The theory that unifies the strong, weak, and EM interactions is called the Standard Model of particle physics. It does not include gravity (see further comments below on why).

Not really; it affects the difficulty of incorporating gravity into a quantum field theory, but GR is a classical theory, and at the classical level there is no problem with gravity being spin-2; as I think I said before, it's that which makes the GR model of gravity as spacetime curvature possible.

Not really; Einstein sort of intended it to be one, but, as above, he didn't include the strong and weak interactions, and he also didn't take quantum effects into account--during the latter part of his career he became very dissatisfied with quantum theory, even though he had helped to create the field.

"Entirely reconciled" is too strong, and I didn't mean to give that impression. There are several issues:

(1) Gravity, as an interaction, is so weak compared to the others that we have no way of experimentally detecting any quantum aspects that it might have. So we have no way of experimentally confirming that gravitons exist or investigating their properties. We basically believe they exist because all the other interactions have quantum aspects. But there are a number of physicists (Freeman Dyson, who was instrumental in the development of quantum field theory, is one of them) who question whether gravity really has to have quantum aspects the way the other interactions do. Without experimental input there is really no way of resolving this question.

(2) Constructing a quantum field theory of a spin-2 particle has issues that constructing a quantum field theory of particles with spin-1 or lower (which all of the particles in the Standard Model are) does not. The main one is that the QFT of a spin-2 particle is not renormalizable. For a detailed discussion of this we would really need to start a separate thread in the Quantum Physics forum, but the key point is that the Standard Model is entirely renormalizable, and that is an important feature. So there isn't a simple, obvious way to add gravitons to the Standard Model; doing that would break an important feature of the theory.

(3) Even if we assume that finding a quantum theory that includes gravity is the right way to go, it's not entirely clear that doing it by constructing a QFT including a spin-2 graviton along the same lines as the Standard Model is the way to do it. There are a number of different candidates for a quantum gravity theory being investigated, and we don't know at this point how that will play out. (The lack of experimental input is a big issue here.)

When Hawking talks about a Theory of Everything, he's talking about getting all these issues resolved. He's gone back and forth over the years about how close he thinks we are to actually doing it. I personally think we still have quite a way to go.

I really do appreciate the thorough explanation you have presented, Peter. It is exceptionally clear and informative.

The link to the Standard Model is a pleasant surprise. I've seen casual reference to the term before, but took it as a generic phrase for any early science. I had no idea it was a modern specific theory. I am incredibly naive sometimes.

Wes
...

 

[PeterDonis]

I really do appreciate the thorough explanation you have presented, Peter. It is exceptionally clear and informative.

Thanks! Glad it was helpful.