Gravity: Force or Distortion of Spacetime?

[Lunct]

Einstein proved that gravity wasn't a force, but a distortion of spacetime, when he got some guy to take a photo of an eclipse in Africa. Also we have more proof today because time is slightly faster on the ISS than on earth. So when I google it, why does it say gravity is a force? Why does my science teacher say it is a force? Is it a force or not?

 

[BvU]

It is.

 

[Lunct]

It is.

then why did Einstein say it wasn't?

 

[russ_watters]

then why did Einstein say it wasn't?

This is mainly an issue of cause vs effect, or rather that gravity can be viewed as a force and more.
https://www.universetoday.com/108740/how-we-know-gravity-is-not-just-a-force/

...edit: You also might consider the grammar of the question/answer: is a spring a force?

 

[wtlee]

in a nutshell, general relativity says that matter tells 4-D spacetime how to curve according to the field equations; and the curvature of 4-D spacetime determines the trajectory of a particle according to the geodesic equations. The concept of force is abolished in general relativity, which is a more accurate theory than Newtonian mechanics that makes use of the concept of force in the explanation of gravity.

 

[dextercioby]

Gravity is the effect of 4D curved space time on mass-energy inside it. That is to say that, even if there was only a curved spacetime with no mass-energy in it, there would be no gravity, because this effect would not be felt by anything. "Force" is just the Newtonian word for the effect of an arbitrary interaction. One postulates an instant interaction between two masses described by a pair of forces which dictate the dynamics. In GR the dynamics is dictated by the curvature of spacetime whose intensity / geometry is in turn dictated by the actual matter content.

 

[Orodruin]

The concept of force is abolished in general relativity, which is a more accurate theory than Newtonian mechanics that makes use of the concept of force in the explanation of gravity.

The concept of a gravitational force does not exist in GR. Not the general concept of a force.

 

[PeterDonis]

Is it a force or not?

Mu. The question of whether gravity is a force is not a question about reality; it's a question about our models. We have a model (Newtonian physics) in which gravity is modeled as a force. We also have a more accurate model (General Relativity) in which gravity is modeled as spacetime curvature. The more accurate model is also harder to do computations with, which is why we use the less accurate model for many purposes, where ease of computation is more important than accuracy.

 

[PeterDonis]

even if there was only a curved spacetime with no mass-energy in it, there would be no gravity

I think this is somewhat misleading. First, GR has the concept of test particles, which have negligible mass-energy but can still be used, in theoretical models, to "mark" trajectories and show how they are affected by the geometry of spacetime. Such test particle trajectories are certainly affected by "gravity" (spacetime curvature), even in idealized solutions which are curved but have no mass-energy present anywhere (see below).

Second, in practical terms, the only way to have a curved spacetime is to have mass-energy present somewhere. Yes, there are idealized vacuum solutions which are curved but have no mass-energy anywhere, but nobody thinks those idealized solutions are exact descriptions of our actual universe. Solutions which describe our actual universe always have mass-energy present.

 

[dextercioby]

No, the concept of test particles is GR (just like the concept of test charges in classical electromagnetism) is simply a way to cheat, that is discarding the mutual effect of sources generating a field which in turn affects the dynamics of the charges. You either have matter (which experiences "gravity"), or you don't. In the latter case, space time curvature is devoid of physical meaning. That is to say one cannot reasonably answer the question: What does R_munulambdasigma physically mean? if you have matter, you can say: R_munulambdasigma is the mathematical description of the "entity" which causes the dynamics of matter inside spacetime.

The second paragraph you wrote comes against the idea of "test particle" you put forth in the first.

 

[Ibix]

@Lunct - you do hear people referring to gravity as one of the four fundamental forces. Don't take this too seriously - it's largely them being poetical.

Newton's theory models gravity as a force. Einstein's theory models gravity as not a force. We are certain that Newton's theory is not completely accurate. We strongly suspect that Einstein's theory is not completely correct. Of the various candidates for the next theory of gravity, some model it as a force and some do not. So the current answer is "maybe".

One note about scientific method. We never formally say that gravity is a force, or electromagnetism is a force. Informally we do say it, but it's just a slightly lazy shorthand. We have models, and in some of those models gravity is described as a force. And all we really know about the models is that they haven't been shown to be wrong yet. The point is that we can only ever describe the world around us and make predictions about it with as much accuracy as possible. We don't claim to be saying what it "actually is", and doing so is a stronger claim than science can, formally, make.

 

[PeterDonis]

the concept of test particles is GR (just like the concept of test charges in classical electromagnetism) is simply a way to cheat

This might be your opinion, but I don't think it's a fair description of how GR is developed as a theory or how it is used in practice. Test particles are used all the time, in exactly the way I described; their trajectories can be used, and are used all the time, to describe the effects of gravity. If you disagree, please give some mainstream references (textbooks or peer-reviewed papers) that support your view. I can give plenty--I'll just mention MTW and Wald for a start, two classic GR textbooks--that support what I'm saying.

Also, remember that this is a "B" level thread, and at the "B" level, statements like the one of yours that I objected to are misleading, not helpful. If we are going to get into the details of the technical points you raise, we should have a separate discussion in an "A" level thread.

 

[Lunct]

@Lunct We strongly suspect that Einstein's theory is not completely correct. Of the various candidates for the next theory of gravity, some model it as a force and some do not. So the current answer is "maybe".

Once we figure out quantum gravity, does that mean we can then say with more certainty that gravity is a curvature of spacetime? Is that what you are saying?

 

[Ibix]

Once we figure out quantum gravity, does that mean we can then say with more certainty that gravity is a curvature of spacetime? Is that what you are saying?

No. We always say "our current best theory does/does not [please delete as applicable] model gravity as a force, but makes no claim about what it actually is". New theories may or may not change the does/does not, but they won't change the bit where we say "model".

We don't know what the world is "really like". We don't even really know if that's a question that makes sense. All we know is that there is some maths called the Einstein field equation that predicts experimental results to the highest precision we can measure. We interpret that maths as a description of a curved spacetime, but that may be completely off track.

I think we may be getting more philosophical than is really helpful. Our usual interpretation of general relativity is that gravity is not a force. However, it is always worth keeping at the back of your mind that all scientific knowledge is provisional and this may be superceded at any time. As may whatever superceded it...

 

[pervect]

Einstein proved that gravity wasn't a force, but a distortion of spacetime, when he got some guy to take a photo of an eclipse in Africa. Also we have more proof today because time is slightly faster on the ISS than on earth. So when I google it, why does it say gravity is a force? Why does my science teacher say it is a force? Is it a force or not?

In the theory of non-relativistic Newtonian gravity, gravity is a force. That theory works very well, and is much easier to understand, and has been around for a long time. That's why gravity is treated as a force in many contexts, such as high school science, and in many places on the web.

The story of the development of General Relativity (henceforth GR) starts to unfold when we look at the development of special relativity. A review or what relativity says and why it's broadly accepted is probably needed, but it would be off-topic and long, so I'll omit it and hope for the best. The main point is that Newtonian gravity, even though it works very well in its realm of applicability, but Newtonian gravity simply isn't compatible with special relativity. Einstein realized this early on, one of the reasons is the existence of gravitational time dilation that you mention. Another reason Newtonian gravity isn't compatible with special relativity is that Newtonian gravity requires instantaneous action at a distance, an observation that bothered Newton enough that he said "I make no hypotheisis" as to how this could be. In General Relativity, gravity is NOT an instantaneous action at a distance, this issue doesn't arise in GR.

Attempting to reconcile gravity with special relativity led Einstein, after a very long search, to the concept of general relativity, where gravity isn't a force. Einstein made specific predictions from his theory, which were tested, and turned out to be true. The deflection of light is one of those predictions.

So in a nutshell (and this may be slightly oversimplified), in the context of Newtonian theory, gravity is considered to be a force, and is treated as such. In the context of general relativity, gravity is not considered to be a force, and is not treated as such. Both theories are actively used and taught - Newtonian theory is perfectly adequate for many applications, as is Newtonian gravity. Newtonian gravity is also much easier to learn, and usually only specialists who need it are taught General Relativity, typicially at a post-graduate level.

To really understand why gravity is a force in Newtonian gravity and isn't in General Relativity, one needs the necessary understanding of both theories. The later is a challenging and typically taught (if at all) at a graduate level, so there is a fair amount of confusion on the topic, especially among people with an interest in science but without a formal graduate level education.

While a full understanding of the topic of why gravity in GR, is not a force involves some highly technical points, it is reasonably safe to say that the student who tries to learn General Relativity and still treat gravity as a force will become very confused. So we can give such students and prospective students a heads-up warning in advance, that they will have to re-thinking some cherished notions to fully understand GR, that they will confuse themselves if they try to cling too tightly to the familiar rather than learn the new.

This answers the original question I hope, but there's one more point to be made. Relativity wasn't the only breakthrough in physics, another important breakthrough was quantum mechanics. Quantum mechanics has its own notion of what a force is, the popularized version of this notion is that a force is something that's carried by a virtual particle. I believe there is a bit of a linguistic issue here, I don't think the quantum notion of a force as something carried by a virtual particle is exactly the same as the classical notion due to Newton, even though we use the same name. Perhaps this point could be argued, I don't know for sure. The application of all this to gravity is the possible existence of a way to describe gravity as something carried by a virtual particle. The short answer to this is there are some proposals along this line , but I'd say that the consensus view is that we don't yet have a description of gravity in these terms.

Another way of talking about this issue is to say that we don't have a full theory of quantum gravity, even though there is a lot written about it. People sometimes ask for more of science than it can give. In the end, science is about what works, and it's possible that our current notions of what gravity is may in the future change as we get more data and more and better experiments. GR has become very well tested though, even the most extreme cases we have study (gravitational waves emitted from black hole inspirals) appear at this time to be compatible with GR, and do not suggest any new physics.

 

[Lunct]

In the theory of non-relativistic Newtonian gravity, gravity is a force. That theory works very well, and is much easier to understand, and has been around for a long time. That's why gravity is treated as a force in many contexts, such as high school science, and in many places on the web.

The story of the development of General Relativity (henceforth GR) starts to unfold when we look at the development of special relativity. A review or what relativity says and why it's broadly accepted is probably needed, but it would be off-topic and long, so I'll omit it and hope for the best. The main point is that Newtonian gravity, even though it works very well in its realm of applicability, but Newtonian gravity simply isn't compatible with special relativity. Einstein realized this early on, one of the reasons is the existence of gravitational time dilation that you mention. Another reason Newtonian gravity isn't compatible with special relativity is that Newtonian gravity requires instantaneous action at a distance, an observation that bothered Newton enough that he said "I make no hypotheisis" as to how this could be. In General Relativity, gravity is NOT an instantaneous action at a distance, this issue doesn't arise in GR.

Attempting to reconcile gravity with special relativity led Einstein, after a very long search, to the concept of general relativity, where gravity isn't a force. Einstein made specific predictions from his theory, which were tested, and turned out to be true. The deflection of light is one of those predictions.

So in a nutshell (and this may be slightly oversimplified), in the context of Newtonian theory, gravity is considered to be a force, and is treated as such. In the context of general relativity, gravity is not considered to be a force, and is not treated as such. Both theories are actively used and taught - Newtonian theory is perfectly adequate for many applications, as is Newtonian gravity. Newtonian gravity is also much easier to learn, and usually only specialists who need it are taught General Relativity, typicially at a post-graduate level.

To really understand why gravity is a force in Newtonian gravity and isn't in General Relativity, one needs the necessary understanding of both theories. The later is a challenging and typically taught (if at all) at a graduate level, so there is a fair amount of confusion on the topic, especially among people with an interest in science but without a formal graduate level education.

While a full understanding of the topic of why gravity in GR, is not a force involves some highly technical points, it is reasonably safe to say that the student who tries to learn General Relativity and still treat gravity as a force will become very confused. So we can give such students and prospective students a heads-up warning in advance, that they will have to re-thinking some cherished notions to fully understand GR, that they will confuse themselves if they try to cling too tightly to the familiar rather than learn the new.

This answers the original question I hope, but there's one more point to be made. Relativity wasn't the only breakthrough in physics, another important breakthrough was quantum mechanics. Quantum mechanics has its own notion of what a force is, the popularized version of this notion is that a force is something that's carried by a virtual particle. I believe there is a bit of a linguistic issue here, I don't think the quantum notion of a force as something carried by a virtual particle is exactly the same as the classical notion due to Newton, even though we use the same name. Perhaps this point could be argued, I don't know for sure. The application of all this to gravity is the possible existence of a way to describe gravity as something carried by a virtual particle. The short answer to this is there are some proposals along this line , but I'd say that the consensus view is that we don't yet have a description of gravity in these terms.

Another way of talking about this issue is to say that we don't have a full theory of quantum gravity, even though there is a lot written about it. People sometimes ask for more of science than it can give. In the end, science is about what works, and it's possible that our current notions of what gravity is may in the future change as we get more data and more and better experiments. GR has become very well tested though, even the most extreme cases we have study (gravitational waves emitted from black hole inspirals) appear at this time to be compatible with GR, and do not suggest any new physics.

But the thing is I am 13 and can understand general relativity (not the field equations), and in my head I can run through was space time would be like as it curves round a planet or moon or star. I may be above average in science, but I am not somme sort of child genius. I understand how it has been proven. I can run through thought experiments in my head that explain GR - like the one where you put the big ball in the middle of the trampoline and then the smaller ball and it will orbit around it. I think it is more simple than Newtonian gravity. Newtonian gravity says it is instant and we say entanglement is weird because it is instant, but no-one ever points out how strange Newtonian gravity is. There is no "why" in Newtonian gravity. But in GR it actually gives you a why. If it has more proof than Newtonian Gravity. Why do we not teach it in schools? I think it is far more simple than Newtonian gravity. It is kind of like you are taught classical physics, then if you do science to a more advance level, you are told that a lot of the stuff you learned is wrong. I think that is flawed.

 

[Ibix]

The so-called "rubber sheet model" has serious shortcomings. Notably: why does a particle at rest start to move? And on the subject of "why", why does spacetime curve near mass? There isn't an answer to that, any more than there is an answer to why mass attracts things in Newtonian gravity.

The basic reason we teach Newtonian gravity is that you cannot get quantitative answers from general relativity without using techniques you won't know enough maths to handle until you're well into your university career. And the answers you can get from Newton are close enough for NASA to run spaceflight.

Just to give you an idea, if there are two planets, one with mass ##M_1## a distance ##r_1## to your left and the other with mass ##M_2## a distance ##r_2## to your right then the total force on you is $$F=\frac {GM_1m}{r_1^2}-\frac {GM_2m}{r_2^2} $$Now using only a pen and paper you can work out the thrust a rocket needs to hover, and work out where you have to be to have the gravitational forces balance. In general relativity, however, the maths is so tough that there is no known way to describe that (really simple) situation using algebra. Your only option is to program a computer to give you a numerical approximation - all to make a difference on the seventh or eighth decimal place.

I do agree that we should be more clear about the limits of our models, and that they are simpler models. But we can't just jump into general relativity because you would never get any practice at problem solving if we did.

 

[Lunct]

"why", why does spacetime curve near mass? There isn't an answer to that, any more than there is an answer to why mass attracts things in Newtonian gravity.

The way I see it no matter what, with any answer, you can ask why. If we ever find out why it curves around mass, then you can still ask why. For our knowledge it is just a matter of how many why questions we can answer, and in GR you can answer one extra. You ask why does gravity attract objects, Newtonian gravity doesn't give an answer, but GR does. Then you ask one more why question.
I think why questions are the most important part of science, you should always ask them, and try to find answers. That is why I do not like the Copenhagen interpretation.

 

[fresh_42]

If we ever find out why it curves around mass, then you can still ask why.

My favorite answer to all "whys" is meanwhyle the following link:

 

[Lunct]

My favorite answer to all "whys" is meanwhyle the following link:

Dammit, now I have a question about magnets. Time for a new thread!

 

[Nugatory]

Dammit, now I have a question about magnets. Time for a new thread!

But also take a look at this classic essay: http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htm

 

[Lunct]

But also take a look at this classic essay: http://chem.tufts.edu/AnswersInScience/RelativityofWrong.htm

That was an amazing essay. Is it particularly famous?

 

[Nugatory]

That was an amazing essay. Is it particularly famous?

Depends on whether you hang out with me or not
It's famous enough that it's on the first page of Google hits for "relativity of wrong"

 

[fresh_42]

That was an amazing essay. Is it particularly famous?

You have your day of unanswerable questions, don't you? It is on PF, that's for certain, but beyond is a bit difficult to answer.

 

[Lunct]

You have your day of unanswerable questions, don't you? It is on PF, that's for certain, but beyond is a bit difficult to answer.

I pretty sure my science teacher wants to kill me because I ask so many questions.

 

[fresh_42]

I pretty sure my science teacher wants to kill me because I ask so many questions.

I seriously hope he wouldn't, for asking questions means you are curious and curiosity is the most important property to learn - anything. So stay curious and ask as much as you can. The difficult part is to memorize it.

 

[jtbell]

We don't know what the world is "really like". We don't even really know if that's a question that makes sense.

To make this more concrete, consider this: if we were to find out someday what gravity (or anything else) "really is", how would we recognize that we have done it?

 

[Dale]

I think it is far more simple than Newtonian gravity

Then you have never actually used it. Nothing wrong with that at age 13, but once you have actually used both you will find it very obvious why Newtonian gravity is still taught and taught first.

 

[CWatters]

All we can really do is make models of how we think the universe works and try to refine or improve them as much as possible. Even models we know to be wrong at one level of detail are still very useful at other levels. Much the same applies in a lot of other fields not just physics.

 

[maria_phys]

The concept of a gravitational force does not exist in GR. Not the general concept of a force.

Exactly. We assume that gravity is a force for systems with low masses (like our Earth and moon) . But for heavy objects (like stars etc.) the gravity is so strong that it curvatures the space time. So you can assume that the gravity is coincided with the space-time geometry. However, other forces may be occur in such events. If you drop an object inside the black hole it will feel the huge tidal forces from the black hole.

 

[Ibix]

If you drop an object inside the black hole it will feel the huge tidal forces from the black hole.

Note, though, that tidal effects are a manifestation of spacetime curvature (at least, as they are modeled in general relativity). So I'd be careful calling them forces if you're not modelling gravity as a force.

 

[Lunct]

Exactly. We assume that gravity is a force for systems with low masses (like our Earth and moon) . But for heavy objects (like stars etc.) the gravity is so strong that it curvatures the space time. So you can assume that the gravity is coincided with the space-time geometry. However, other forces may be occur in such events. If you drop an object inside the black hole it will feel the huge tidal forces from the black hole.

Is that like gravitational waves?

 

[PeterDonis]

We assume that gravity is a force for systems with low masses (like our Earth and moon) . But for heavy objects (like stars etc.) the gravity is so strong that it curvatures the space time.

No, that's not the point Orodruin was making, and it's not correct. In GR, gravity is not a force, period. It's spacetime curvature. But other interactions--electromagnetism, weak, and strong--are still forces in GR.

 

[maria_phys]

Note, though, that tidal effects are a manifestation of spacetime curvature (at least, as they are modeled in general relativity). So I'd be careful calling them forces if you're not modelling gravity as a force.

Hmm, ok I agree with you in general. But assuming that I am an astronaut and I'm traveling directly to the black hole. The effect of the tidal forces wouldn't be the same like the system Earth moon. I will stressed out or shrink in one direction. A force has a direction.

 

[maria_phys]

No, that's not the point Orodruin was making, and it's not correct. In GR, gravity is not a force, period. It's spacetime curvature. But other interactions--electromagnetism, weak, and strong--are still forces in GR.

Newtonian dynamics works really good for objects with low masses. Take for example the gravitational force between Earth and Moon. The space-time curvature is so negligible that has no meaning. In general I agree with you. Yes, in GR is not force. I said that before. But I've tried to clarify when GR has a meaning.