# Einstein theory on bending of space

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 ?

Matterwave
Gold Member
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
PeterDonis
Mentor
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.

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?

phinds
Gold Member
2021 Award
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"

Drakkith
Staff Emeritus
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.

PeterDonis
Mentor
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.)

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

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!)

PeterDonis
Mentor
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".

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.

ChrisVer
Gold Member
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...

Wes Tausend
Gold Member
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
...

Last edited by a moderator:
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.

phinds
Gold Member
2021 Award
Thanks, Peter. I actually meant to explain some of that, but somehow forgot all about it. Can I blame Phinds somehow?
Grrrrrr

Drakkith
Staff Emeritus
Grrrrrr

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

phinds
Gold Member
2021 Award
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 !

Dale
Mentor
2021 Award
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.

Wes Tausend
Gold Member
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.
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
...

PeterDonis
Mentor
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.

Dale
Mentor
2021 Award
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.

Last edited:
• Wes Tausend
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."

Last edited:
Dale
Mentor
2021 Award
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.

stevendaryl
Staff Emeritus
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.

stevendaryl
Staff Emeritus
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.

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

PeterDonis
Mentor
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.

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.

Wes Tausend
Gold Member

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
...