# Einstein theory on bending of space

• ronric
In summary, according to Einstein's theory, it is the bending (more precisely, curvature) of space-time, not just space, that is responsible for gravity. This is a more complex theory than Newton's, and is only accessible to a select few college-level students or higher.

#### ronric

According to Einstein's theory it is the bending of space that keeps the Earth moving on its orbit around the sun and not any invisible force. Why they still teach gravitational force in school ?

1. Einstein says it is the bending (more precisely, curvature) of space-time, not just space, that is responsible for gravity.
2. Einstein's theory of gravity is very complex, involving advanced mathematical concepts that would be inaccessible to a high school student or beginning college student. So unless you want to teach the students nothing about gravity until they are junior or senior undergraduate level physics students or higher, you are stuck teaching Newton's theory of gravity.
3. Newton's theory of gravity is an excellent approximation and works very well for almost all aspects of gravity that we encounter in every day life, including predicting all of the orbits of the planets to very high accuracy. The largest inaccuracy for predicting things in our solar system of Newton's theory is the perihelion precession of Mercury. Even then, the precession rate that is predicted by General Relativity over Newtonian theory is a mere 43 arc-seconds per century.
4. School is not about teaching the students the state-of-the-art in every science. If you wanted to do that, you better become a researcher in that area of science. It's about giving the student a database of working knowledge. As such, there is no reason to teach Einstein's general relativity unless you specialize to that area.

• Chestermiller
Gravitational force isn't exactly incorrect, it just depends on your point of view. From the point of view of bodies within space-time that can't "see" the curvature, there does seem to be a force attracting bodies together. This force is capable of accelerating masses and can be measured with F = ma like any other force. If you could adopt a "god's eye view" however and see space-time from the outside (somehow!), you'd be able to see that bodies are just following geodesics - the shortest possible paths they can take through space-time. General relativity doesn't replace gravitational force, it explains the origin of that force as curved space-time.

Besides, Newton's theory of gravitational force is a lot simpler than Einstein's. You may protest that Newton's theory of gravity is wrong, and therefore we should never teach it. But Einstein's theory of gravity is also wrong! That's because, as Isaac Asimov said, scientific theories are not so much wrong as incomplete. (I highly recommend this essay if you're struggling with this concept!)

Scientific theories are never the whole truth - only approximations to the truth. Einstein's theory is a better approximation to the truth than Newton's, but neither theories are the absolute truth. General relativity breaks down under super-extreme conditions anyway - like the earliest moments of the Big Bang, or the centre of a black hole - and it's incompatible with quantum mechanics, so we already know that Einstein isn't the last word and a better theory of gravity is needed! When we get that theory though it won't replace curved space-time - a phenomenon we know exists - it'll just provide a deeper explanation for why matter-energy curves space-time, and will presumably be compatible with quantum mechanics and its equations will work inside a black hole or close to the Big Bang. The equations of general relativity, and the phenomenon of curved space-time, will still of course be very useful, and when we aren't dealing with those super-extreme conditions, general relativity will still be used for other purposes.

In the same way curved space-time didn't replace the force of gravity - only provided a deeper and more satisfying explanation for why the force exists, and provided better answers to calculations for the extreme conditions Newton's theory breaks down in (e.g. high speeds, large distances and strong gravitational fields like the Sun's gravity near the orbit of Mercury). But Newton's equation for gravitational force is still useful for most purposes, and the phenomenon of gravitational force is still a very useful concept. General relativity does provide a deeper understanding of gravity than Newton's theory, but it's still not necessary for the vast majority of purposes, up to and including sending a space probe to Neptune.

I do agree with you it'd be interesting if we introduced the concept of curved space-time earlier on in education - it's cool, and while the detailed mathematics of general relativity is horrendously complicated, the general concept of curved space isn't too difficult for secondary school aged kids to wrap their minds around! But they'd need to know what gravity is first. Newton's a necessary stepping stone along the way to Einstein. Schools have to teach gravitational force first - then later let the students find out about the curved space-time that underlies it all - and later still, maybe one of them will help create that future, all-encompassing quantum theory of gravity that will do for Einstein what Einstein did for Newton - not replace his theory or render it obsolete, but explain why his theory works, fill in the gaps and patch up the problems, and set it in a broader and deeper physical context. Long live both Newton and Einstein!

(Electrons orbiting the nucleus inside an atom like planets orbiting a star... now there's something that's just plain wrong and shouldn't be taught in schools!)

• Constantine, Wes Tausend and gianeshwar
Amaterasu21 said:
General relativity doesn't replace gravitational force, it explains the origin of that force as curved space-time.

There is a sense in which this is true, if we interpret the word "force" in the Newtonian sense. However, it's important to understand that, in GR, the word "force" is given a different meaning than in Newtonian physics. That is primarily because, in GR, the word "acceleration" is given a different meaning than in Newtonian physics.

In Newtonian physics, the word "acceleration" means what, in GR, is called "coordinate acceleration" (with the intended implication that it is not "really" acceleration). This works in Newtonian physics because Newtonian physics has absolute space and absolute time, so there are "privileged" systems of coordinates in which acceleration "really is" acceleration. In such a system of coordinates, a rock freely falling towards Earth is "really" accelerating, and we attribute this to the action of a "force", namely gravity.

In GR, however, the word "acceleration" is properly used to denote "proper acceleration" (pun intended ;) ). Proper acceleration is a direct observable: you measure it with an accelerometer (your bathroom scale is an example of an accelerometer). A "force" in GR is then something which produces proper acceleration. Gravity does not do this: an object moving solely under the influence of gravity, like the rock falling, is in free fall, with zero proper acceleration, and therefore is not being subjected to any force. So in GR, gravity is not a force--period.

The fact that proper acceleration is directly measurable also means that geodesics are directly measurable: they're just the worldlines (paths through spacetime) of freely falling objects. So you don't have to look at spacetime "from the outside" to see that objects moving solely under gravity travel on geodesics; you can tell that just by attaching accelerometers to them and seeing that they read zero. Similarly, you don't have to look at spacetime "from the outside" to see that its geometry is curved; you can tell that by looking for tidal gravity, since tidal gravity, physically, is spacetime curvature.

Amaterasu21 said:
as Isaac Asimov said, scientific theories are not so much wrong as incomplete.

This is true, and it may well be that, when we have a still deeper theory than GR (such as a full theory of quantum gravity), we will see that GR concepts, perhaps including "spacetime" itself, are only approximations, just as the idea of gravity as a "force" is only an approximation.

• Constantine, martinbn, Amaterasu21 and 2 others
Correct me if I'm wrong.Since the force can't travel in vacuum like for instance the gap between the sun and the earth. Isn't it more practical if we just say gravity only instead of gravitational force?

ronric said:
Correct me if I'm wrong.Since the force can't travel in vacuum like for instance the gap between the sun and the earth. Isn't it more practical if we just say gravity only instead of gravitational force?
So, do you think that if you place two magnets close together in outer space, not touching but close together, that they will not attract/repel each other? That's the clear implication of your statement "force can't travel in vacuum"

ronric said:
Correct me if I'm wrong.Since the force can't travel in vacuum like for instance the gap between the sun and the earth. Isn't it more practical if we just say gravity only instead of gravitational force?

No. Forces don't 'travel'. In classical field theory, there is a value associated at every position in space that tells us what the magnitude and direction of a force exerted by the field will be. This holds true for both EM and Gravitational fields. A change in the field will move at c in the form of an EM or Gravitational wave. The 'gravitational force' is the force exerted by the gravitational field and 'gravity' is the name of the whole concept, similar to how 'electromagnetism' is the name of the whole concept of electrical charges, magnetic fields, etc.

Drakkith said:
In classical field theory, there is a value associated at every position in space that tells us what the magnitude and direction of a force exerted by the field will be. This holds true for both EM and Gravitational fields. A change in the field will move at c in the form of an EM or Gravitational wave. The 'gravitational force' is the force exerted by the gravitational field

Note that the term "force" here is being used in the Newtonian sense, not the GR sense. In GR, the term "gravitational field" is somewhat ambiguous--it can refer to different things in the math--but in any case it does not exert a "force" because objects moving under gravity are in free fall, with zero proper acceleration. Gravitational waves, similarly, are changes in the spacetime geometry that propagate at ##c##, not changes in the "force exerted". (In Newtonian gravity, there is no such thing as gravitational waves--gravity "propagates" at infinite speed, so a change in the source causes a change in the field everywhere instantaneously.)

Thanks, Peter. I actually meant to explain some of that, but somehow forgot all about it. Can I blame Phinds somehow?

PeterDonis said:
In Newtonian physics, the word "acceleration" means what, in GR, is called "coordinate acceleration" (with the intended implication that it is not "really" acceleration). This works in Newtonian physics because Newtonian physics has absolute space and absolute time, so there are "privileged" systems of coordinates in which acceleration "really is" acceleration. In such a system of coordinates, a rock freely falling towards Earth is "really" accelerating, and we attribute this to the action of a "force", namely gravity.

In GR, however, the word "acceleration" is properly used to denote "proper acceleration" (pun intended ;) ). Proper acceleration is a direct observable: you measure it with an accelerometer (your bathroom scale is an example of an accelerometer). A "force" in GR is then something which produces proper acceleration. Gravity does not do this: an object moving solely under the influence of gravity, like the rock falling, is in free fall, with zero proper acceleration, and therefore is not being subjected to any force. So in GR, gravity is not a force--period.

Point noted, thanks for the clarification! I was referring to "force" in the Newtonian sense. General relativity (in which as you point out gravity doesn't produce proper acceleration, but does produce coordinate "acceleration") explains why there appears to be a gravitational force in the Newtonian model, which is still useful for most intents and purposes, and must be discussed in schools before students can begin to understand GR. So I still stand by my statement that GR explains the source of Newton's gravitational force, even if gravity is no longer considered a force within GR. (Note also that the word "force" is also used in a rather loose sense by particle physicists to mean "interaction" in general, e.g. "the four fundamental forces." Outside of the context of Newtonian mechanics "force" is a pretty imprecise term!)

Amaterasu21 said:
the word "force" is also used in a rather loose sense by particle physicists to mean "interaction" in general, e.g. "the four fundamental forces."

Yes, this is yet another usage of the term "force".

Amaterasu21 said:
Outside of the context of Newtonian mechanics "force" is a pretty imprecise term!

I don't think it's imprecise--each of the meanings discussed in this thread is precise enough. It's just that there are different precise meanings depending on which theoretical framework you are using.

The way I see it, classical physics( Newtons Laws,Maxwells laws etc.) isn't wrong. Its just that the theories of relativity and quantum physics provide a more accurate picture of the universe.

They can't be "wrong",... Newton found us many planets and so on...
He was just unable to give correct numbers to more accurate measurements performed later on... as such, it's a good theory that works in some region [and it's much more easy to handle when you want to work in that region] ... I would say Newton was incomplete...So it's only natural to be taught. If we want to teach only the correct over all regions theories, we should start looking at Quantum Gravity and so on... because GR is also not expandable to all "regions" of "reality".
The rest problems from clashes between GR and Newton, come from interpretations and how you see the world...

ronric,

I think Amaterasu21 explained it well, with support from PF staff and others of course. I rank Asimov up there with Feynman as a great teacher. Asimov was not only an imaginative, prolific writer, but a prolific deep thinker as well.

Something will eventually have to give as Peter mentioned. Somebody will have to ask the right questions to reconcile Quantum Mechanics (QM) with General Relativity (GR). And the "intruding" conjecture will have to do for both what GR did for Newtons Classical Mechanics, at least in the respect that GR encompassed Newtonian views, yet vastly improved them. Therefore the new perspective will very closely have to basically agree with both QM and GR without totally invalidating either.

QM and GR are both too good to be wrong... but one foundation may have to reluctantly give more than the other. After all this time has passed, the new perspective, historically seen as an intruder of current science by nature, will likely have to be radical... but still fit like a fine glove. When it dawns upon us, we will probably marvel at it's simplicity... and wonder why we didn't think of it sooner.

With luck, we won't have to redefine too many physics terms again. Redefinition is a messy ad hoc business. The simplest explanation is generally the best explanation, aka http://en.wikipedia.org/wiki/Occam's_razor][/PLAIN] [Broken] Occam's razor .

Wes
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Drakkith said:
No. Forces don't 'travel'. In classical field theory, there is a value associated at every position in space that tells us what the magnitude and direction of a force exerted by the field will be. This holds true for both EM and Gravitational fields. A change in the field will move at c in the form of an EM or Gravitational wave. The 'gravitational force' is the force exerted by the gravitational field and 'gravity' is the name of the whole concept, similar to how 'electromagnetism' is the name of the whole concept of electrical charges, magnetic fields, etc.
Yes, indeed - and that is also the way Einstein used used those words in his theory. In contrast, Peterdonis is referring to modern GR.

Drakkith said:
Thanks, Peter. I actually meant to explain some of that, but somehow forgot all about it. Can I blame Phinds somehow?
Grrrrrr

phinds said:
Grrrrrr

Down boy, else your geodesic will come to an abrupt halt at a singularity. Whose name is Roger. He's the local vet. ;)

Drakkith said:
Down boy, else your geodesic will come to an abrupt halt at a singularity. Whose name is Roger. He's the local vet. ;)
I eat vets for breakfast and !

harrylin said:
Yes, indeed - and that is also the way Einstein used used those words in his theory. In contrast, Peterdonis is referring to modern GR.
Einstein's theory and modern GR are the same theory. Some minor evolution in terminology and a better understanding of the math hardly makes it a new theory.

harrylin said:
"Yes, indeed - and that is also the way Einstein used used those words in his theory. In contrast, Peterdonis is referring to modern GR."

DaleSpam said:
Einstein's theory and modern GR are the same theory. Some minor evolution in terminology and a better understanding of the math hardly makes it a new theory.
I took it that harrylin is referring to the relatively modern (new) language sometimes used to describe the same original GR rather than a new theory of GR.

As an example, the term "force" (gravitational) is now used (redefined, #12) in a way that did not exist in Newtons day to try to circumvent some awkwardness in our description of GR. The modified definition seems ad hoc¹ to me, which is why I referred to "ad hoc" earlier in #15. In my opinion, science is best served for clarity when no ad hoc support is needed, but it appears it cannot be helped in this instance.

1. formed, arranged, or done for a particular purpose only
Wes
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Wes Tausend said:
The modified definition seems ad hoc to me

Why? It's obvious once you understand that proper acceleration, not coordinate acceleration, is the direct observable that is associated with what we usually think of as "force". This is just as true of Newtonian gravity as it is of GR. So the GR definition of "force" is not chosen ad hoc, but is just a matter of recognizing something that was always there, but was ignored before.

Wes Tausend said:
The modified definition seems ad hoc¹ to me

However, PeterDonis is correct to point out that the issue addressed by the change in definition is not unique to GR but was inherent in Newtonian gravity from the beginning. Basically, even in pre-relativistic mechanics we use the word "force" to refer both to real forces, like the EM force, and also fictitious forces like the centrifugal force. All fictitious forces have the mathematical characteristic that they are proportional to mass and the related experimental characteristic that they cannot be detected by accelerometers. Gravity has those same characteristics.

The change with GR is to classify the force of gravity as a fictitious force like the centrifugal force. But the different meanings of the word "force" were already there, and the reclassification does not change any predicted experimental outcomes.

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• Wes Tausend
Wes Tausend said:
harrylin said:
"Yes, indeed - and that is also the way Einstein used used those words in his theory. In contrast, Peterdonis is referring to modern GR."

I took it that harrylin is referring to the relatively modern (new) language sometimes used to describe the same original GR rather than a new theory of GR.
[..]...
Yes indeed. Ronrit referred to the formulation of "Einstein's theory", which on face value means the theory as originally formulated by Einstein. In that formulation, gravitation is interpreted as a field (so that gravity appears as a local field force*), while in Newton's theory it was modeled (by lack of better) as a mysterious action at a distance. While it is certainly a matter of interpretation, the issue of calling gravity a force does not directly depend on the theory. IMHO it's a philosophical issue and not really physics.

*for example, he speculated (footnote in Relativity: The Special and General Theory, 1920 edition): "The general theory of relativity renders it likely that the electrical masses of an electron are held together by gravitational forces."

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harrylin said:
Ronrit referred to the formulation of "Einstein's theory", which on face value means the theory as originally formulated by Einstein.
Who is Ronrit?

We still call modern pre relativistic physics "Newton's theory" despite the much more drastic evolution in both terminology and math.

Wes Tausend said:
In Newtonian physics, the word "acceleration" means what, in GR, is called "coordinate acceleration" (with the intended implication that it is not "really" acceleration).

I don't think it's quite right to say that, because Newton's third law of motion says that forces come in pairs: If object A acts upon by object B by a force $\vec{F}_{AB}$, then B acts upon A with a force $\vec{F}_{BA} = - \vec{F}_{AB}$. This kind of pairing of forces does not apply to "fictitious" forces such as centrifugal force. So mere coordinate acceleration does not imply a force, in Newton's sense.

Of course, the third law is strictly speaking only true for instantaneous forces, so something has to give to accommodate relativity, and limits on propagation speed of forces.

Wes Tausend said:
As an example, the term "force" (gravitational) is now used (redefined, #12) in a way that did not exist in Newtons day to try to circumvent some awkwardness in our description of GR.

From the modern perspective, that's exactly backwards. Newton's theory, if formulated in terms of "coordinate acceleration" is awkward, because his laws of motion don't apply in noninertial coordinate systems (such as a rotating coordinate system). For a general coordinate system, the motion of an object floating in space is not simply

$m \frac{d^2 x^i}{dt^2} = 0$

$m (\frac{d^2 x^i}{dt^2} + A^i + B^i_j \frac{dx^j}{dt} + C^i_{jk} \frac{dx^j}{dt} \frac{dx^k}{dt}) = 0$

Now, you could try to make this consistent with Newton's second law by moving the extra terms to the right side of the equation:

$m \frac{d^2 x^i}{dt^2} = F^i_{inertial}$

where $F^i_{inertial} = - m (A^i + B^i_j \frac{dx^j}{dt} + C^i_{jk} \frac{dx^j}{dt} \frac{dx^k}{dt})$

But that doesn't work, either, because of Newton's third law, that forces come in pairs (action-reaction).

So coordinate acceleration doesn't work for Newton's physics, either, except in the special case of inertial, cartesian coordinates.

DaleSpam said:
Who is Ronrit? [..]
I meant the OP, ronric (sorry for the typo).

stevendaryl said:
This kind of pairing of forces does not apply to "fictitious" forces such as centrifugal force. So mere coordinate acceleration does not imply a force, in Newton's sense.

Yes, this is a good point. But the word "force" is still used in Newtonian physics even for fictitious forces to which the third law does not apply. So at the very least, the Newtonian usage of the word "force" is not very clear, physically. As DaleSpam pointed out, the change in usage in GR can be viewed as a reclassification of gravity with the fictitious forces, so that the link between force and acceleration (in the GR sense of proper acceleration) is now clear and consistent.

stevendaryl said:
So coordinate acceleration doesn't work for Newton's physics, either, except in the special case of inertial, cartesian coordinates.

Yes, this is a good point too. The GR usage is also clearer in this respect, since the link between force and proper acceleration is now independent of coordinates.

DaleSpam said:

However, PeterDonis is correct to point out that the issue addressed by the change in definition is not unique to GR but was inherent in Newtonian gravity from the beginning. Basically, even in pre-relativistic mechanics we use the word "force" to refer both to real forces, like the EM force, and also fictitious forces like the centrifugal force. All fictitious forces have the mathematical characteristic that they are proportional to mass and the related experimental characteristic that they cannot be detected by accelerometers. Gravity has those same characteristics.

The change with GR is to classify the force of gravity as a fictitious force like the centrifugal force. But the different meanings of the word "force" were already there, and the reclassification does not change any predicted experimental outcomes.
That is a particularily good insight, Dale, and I thank you for that. It has always bothered me that so many learned commentators still often casually refer to gravity as a "force" and I now better understand why.

It appears terminology will not change until inertia and the "mystery" of gravity can be more directly reconciled with the electromagnetic force. Perhaps at that time, all fictitious forces will no longer be fictitious.

Harrylin's footnote in #24 seems to imply that Einstein has already seen this "probable" connection of gravity/electrodynamics and speculated such. This is the first time I have come across this comment by Einstein, which I very much appreciate. This is since I already ended here from thought experiment, derived from a simple, but slightly different, but harmless angle on SR that has stuck with me throughout the years. It seems, with the right coordinate system, we could basically eventually get rid of at least one separate fundamental force, that of gravity. Some day in the future perhaps. The ultimate dream... one force and one force only.

Thanks also to PeterDonis and stevendaryl. Very enlightening thread.

Wes
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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.

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.

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.

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

PeterDonis said:
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
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Wes Tausend said:
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.

Wes Tausend said:
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).

Wes Tausend said:
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.

Wes Tausend said:
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.

Wes Tausend said:
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