Is Gravity Really Just Curved Spacetime?

[markf]

I read somewhere that gravity is not a force. Is this true? What does it mean?

 

[rbj]

according to the theory of General Relativity, there is an equivalence to a body falling in free fall to an identical body out in free space traveling at a constant velocity.

what a big mass (like a planet) does is warp or curve space in such a way so that objects flying about freely in this curved space appears to us in our Euclidian space to be following a curve where it just appears that a force is acting on the body that causes its path to be curved toward the center of that big mass.

 

[Ravi Mandavi]

I read somewhere that gravity is not a force. Is this true? What does it mean?

where did you read

 

[Whovian]

where did you read

Actually, in a certain sense, it isn't.

 

[sophiecentaur]

For all practical purposes, we can say that Gravity 'produces' a force - because we can all feel it. Modern Physics takes matters further than that, of course, but the same 'force' effects are observable even when they are 'explained' slightly differently.

 

[K^2]

I read somewhere that gravity is not a force. Is this true? What does it mean?

There is a class of forces in physics known as fictitious forces or inertial forces. Whether they act as real force or not depends on your choice of coordinate system. If you chose surface of the Earth as your reference point, for example, you have to account for the force of gravity for all of your equations to make sense. But if you happen to be inside an elevator during a free-fall, you will not experience gravity. For all intents and purposes, gravity just goes away.

This is very similar to centrifugal force. It is also a fictitious force. If you are observing a rotating space station from an inertial frame, you can describe everything that happens in terms of forces of interaction between various objects. But if you are standing inside the station, measuring all positions relative to the station, and you don't take rotation into account, it appears that there is another force, very similar to gravity, that keeps pushing you away from center of the station.

 

[BruceW]

I read somewhere that gravity is not a force. Is this true? What does it mean?

In general relativity, they don't count gravity as a force, but its effects are taken into account in the equations of the spacetime curvature. In the limit of low speed and weak curvature, we can say that gravity acts approximately like a force (which is the physics that was around before Einstein's relativity).

 

[Khashishi]

I think physicists don't get too worked up about what exactly constitutes a force. Depending on the context, they will call gravity a fundamental force or a fictitious force. But it's not something to argue over. They'll just use the term that is more convenient at the time. Being too concerned with the terminology is just stupid, since physicists will agree on what gravity _does_.

So if one textbook says gravity is a force and another one says it's a figment of the coordinate system, it doesn't mean that one textbook is wrong and one is right. We are all just working with human-defined models and it's the observable phenomena that really count.

In GR, gravity is not a force, but in everything else, gravity is a force.

 

[D H]

For all practical purposes, we can say that Gravity 'produces' a force - because we can all feel it.

No, you can't. Newtonian POV: We can feel every real force but gravity. There is no way to directly sense the gravitational force. However, note that we don't "feel" fictitious forces.

General relativity POV: We feel every real force, period. Gravitation falls into the real of fictitious forces in general relativity. That gravitation can't be sensed -- no surprise. We can't sense any of the fictitious forces.


Put an accelerometer at rest on top of a table. That accelerometer will register an acceleration of 1g pointing upward, yet it's obviously not accelerating. It's standing still. That 1g upward acceleration that it is registering is the normal force exerted by the table on the accelerometer. Now push the accelerometer off the table. In free fall, the accelerometer registers an acceleration of near zero. Yet it obviously *is* accelerating. The gravitational force acting on the accelerometer hasn't changed. What has changed is that the normal force is now absent. The accelerometer doesn't measure gravity because there is no way to measure gravity.

The same goes for what you feel. You aren't feeling gravity. What you are feeling is the ground pushing up on your feet, your skeleton transmitting this upward force to the less rigid parts of your body, and eventually, your inner ear. Your inner ear is equipped with a natural accelerometer. It senses that upward acceleration.

Now imagine taking one of those zero g amusement park rides, or being a passenger on NASA's Vomit Comet. During those intervals of zero g, your stomach and your inner ear rebel at the loss of this upward acceleration that is normally sensed when you are standing on the ground. You aren't feeling those forces during those intervals of zero g.

I think physicists don't get too worked up about what exactly constitutes a force.

Exactly. Worrying about what different theories call things is just a semantics game. What really matters is how well physics predicts experimental outcomes. In those realms where Newtonian mechanics is (approximately) valid, Newtonian mechanics and relativity will agree on experimental outcomes, sensor readings, etc.

 

[ApplePion]

according to the theory of General Relativity, there is an equivalence to a body falling in free fall to an identical body out in free space traveling at a constant velocity..

This is the sort of thing laymen hear on Carl Sagan programs. Actually, I suspect that most professional physicists would get it wrong.

If you have a box falling in the Earth's gravitational field and you shine a light horizontally, the light will be deflected downwards with an acceleration of around 19.6 meters per second squared. the doubling is because in Relativity there are gravitational forces that go as the square of the velocity. So the box is falling at around 9.8 meters per secomnd squared and the light is falling at double thatr--it therefore is possible to distinguish between the box in free fall vs a box at rest without gravity.

what a big mass (like a planet) does is warp or curve space in such a way so that objects flying about freely in this curved space appears to us in our Euclidian space...

The is clearly incorrect. If you are standing here on Earth you are experiencing gravity, and as you yourself said, gravity invoves spacetime not being Euclidian. So we are not in "our Euclidian space".

 

[harrylin]

For all practical purposes, we can say that Gravity 'produces' a force - because we can all feel it. Modern Physics takes matters further than that, of course, but the same 'force' effects are observable even when they are 'explained' slightly differently.

I agree with that - the "force of gravity" acts on a spring scale when you stand on it. The "different explanation" is to say that that force is not due to gravitation but due to acceleration. And as others said, whatever you call it or how you interpret it, everyone agrees that the spring is compressed by a real force.

The situation is a lot more hazy when an object falls under the influence of a gravitational field; it then depends on one's exact definition of "force" (as well as on one's definition of "field"!).

 

[Muphrid]

Yes, the spring is being compressed by a force. GR just says that force is that of the Earth pushing upwards on the scale. There is a reason that a stationary accelerometer reads as though the acceleration it experiences is up, not down. This is not sleight-of-hand with jargon to confuse people. In a very material, concrete way, objects cannot and do not know about how gravity affects their motions.

 

[drphysica]

"I read somewhere that gravity is not a force. Is this true? What does it mean?"

Simple answer if gravity was not a force we wouldn't be here! Just because we haven't found graviton particle it dosn't mean gravity doesn't exit. 8)

 

[sophiecentaur]

The 'purist' view is strongly against allowing gravity to be a force. Fair enough, because a gravitational field 'causes' a force to act on a mass - rather than actually 'being' a force. But why is the same purist view not held so strongly in the case of EM fields? I appreciate that if you were in a charged ship with no windows then you could detect an acceleration due to the presence of an EM field (due to a measurable acceleration). This is different from the gravitational case, of course (an accelerometer wouldn't react because the Equivalence Princple is at work), but in both cases, the acceleration is actually measurable as soon as you can see (or reference) the outside world.
Why restrict the measuring conditions in order to 'classify' the gravitational effect as being different from the EM effect?
Weight is a readily perceived and measured force - given the appropriate equipment - so why are we not 'allowed' to treat gravity as a force? It is such a tangible thing that it seems to me that the purist tail is wagging the dog of experience.

 

[harrylin]

The 'purist' view is strongly against allowing gravity to be a force. [..].

I'm very much a 'purist' and I disagree with what you call the 'purist' view for reasons similar to the ones you mention.

It would be useful if opinionated people present their definitions of "force" and "field", and then explain how they reason that those definitions logically lead to their expressed opinions.

 

[sophiecentaur]

OK, my "opinion" is that a Force will produce an acceleration or change of shape. (That's Newtonian - based). How one measures these changes is, to my mind, irrelevant.
For a definition of Field in this context, I'd say that the presence of a Field will produce a Force on an object with a particular property - e.g. mass / charge / current. So F=mG and F=qE for instance. So the Field is force per unit of some property.
So we could continue the discussion with those definitions - or with others, perhaps(?).

 

[Markus Hanke]

Imagine two travellers standing at different points along the equator. Now both of them start walking north, towards the north pole. What happens ? The further north they walk, the closer they get to one another ! They approach each other not because of any force acting between them, but because of the geometry of Earth's surface. Gravity works the same - as time passes, two bits of matter will gravitate towards each other, not because of any force, but because of the geometry of space-time.

 

[sophiecentaur]

Imagine two travellers standing at different points along the equator. Now both of them start walking north, towards the north pole. What happens ? The further north they walk, the closer they get to one another ! They approach each other not because of any force acting between them, but because of the geometry of Earth's surface. Gravity works the same - as time passes, two bits of matter will gravitate towards each other, not because of any force, but because of the geometry of space-time.

If these two travellers stop walking, do they experience anything? Is there any Force acting on them to make them continue getting closer to the Pole? I do understand this is just an analogy but I feel it is too far away from the point about the 'reality' or otherwise of a gravitational force. You would need to say what the equivalent of a force is for these two travellers. It certainly couldn't be the same as the 'force' that pulls two masses together because the analogy is not 1:1.

I can see that GR tries to explain the origin of a force like the one that the proximity of two masses causes but, if the effect is the same as that which occurs between two charges, then why is it not allowed to be called a force? What distinguishes the one 'force' from the other force apart from the difficulty in detecting it?

 

[Markus Hanke]

If these two travellers stop walking, do they experience anything? Is there any Force acting on them to make them continue getting closer to the Pole? I do understand this is just an analogy but I feel it is too far away from the point about the 'reality' or otherwise of a gravitational force. You would need to say what the equivalent of a force is for these two travellers. It certainly couldn't be the same as the 'force' that pulls two masses together because the analogy is not 1:1.

You are right, it isn't at 1:1 analogy. However ( and I failed to mentioned that ), once one understands that the northward direction corresponds to time, and the distance between the travellers corresponds to spatial separation, then the situation is clear : there is a tendency for two bits of matter to approach one another over time, purely based on the geometry of space-time. This is, I believe, quantified via the Raychaudhuri equation.
The question as to whether you need a force for them to continue going north is rather meaningless, since one cannot stop moving through time.

 

[harrylin]

OK, my "opinion" is that a Force will produce an acceleration or change of shape. (That's Newtonian - based). How one measures these changes is, to my mind, irrelevant.
For a definition of Field in this context, I'd say that the presence of a Field will produce a Force on an object with a particular property - e.g. mass / charge / current. So F=mG and F=qE for instance. So the Field is force per unit of some property.
So we could continue the discussion with those definitions - or with others, perhaps(?).

Thanks for the precision!

If one uses either of those definitions then gravity is a force in GR that appears whenever a gravitational field is assumed. Einstein called in his 1916 GR paper the gravitational field a "field of force [..] which possesses the remarkable property of imparting the same acceleration to all bodies".

In a reference frame that is attached to the surface of the earth, your acceleration when you stand on a scale is zero so that the force that you feel is fully ascribed to gravitational field (and not acceleration)*.
Conversely, in a "free falling" GR frame the gravitational field has vanished and that same force is ascribed to acceleration instead.

*From the more standard ECI frame POV, it is gravity due to the mass of the Earth, which is partly reduced due to the acceleration of the rotating surface of the Earth.

 

[Naty1]

I found this quote from these forums illuminating:

Jambaugh:

However if we read the Equivalence Principle correctly (as I see it) then it is not that "gravity is just geometry" but rather that we only see dynamic evolution of test particles and so the boundary between gravity and geometry is indistinguishable. We can vary our choice of space-time geometry and introduce a "physical" force of gravity and not see any difference in predictions. I think this means that it is the geometry which is "not physical" rather than the gravitational force.

Gravitational forces (except tidal effects) don't exist in GR because forces cannot be 'transformed away' by going into free fall. This was Einstein's great insight.

 

[Naty1]

Einstein called in his 1916 GR paper the gravitational field a "field of force".

Yet Einstein's GR does not depend on traditional 'fields'...such fields are a different model than his final geometric interpretation of spacetime curvature.

 

[harrylin]

[..] such fields are a different model than his final geometric interpretation of spacetime curvature.

I cited him in the context of his explanation of fields in GR. Do you know by chance how with that geometric interpretation of GR the words "force" and "field" were redefined, so that those words have different meanings than the same words of 1916?

 

[Muphrid]

It's precisely because we identify the four-force as something that all freely-falling obsrevers agree on. An object that is freely falling experiences zero four-force, and hence, because the four-force is more useful than ordinary force, we tend to use that versus ordinary force.

We dismiss the idea of gravitational force because different freely-falling observers may disagree whether there was a gravitational force at all--not just its components, but whether it has any magnitude. The same cannot be said of the electromagnetic four-force, which all freely-falling observers agree on.

 

[sophiecentaur]

Gravitational forces (except tidal effects) don't exist in GR because forces cannot be 'transformed away' by going into free fall. This was Einstein's great insight.

Quote from whom, I'm not sure but it doesn't matter.
That bit has me flummoxed. You can explain the tides in terms of motion in a circle, with all the 'forces' we're familiar with. How can tidal forces not be taken care of in GR? They're only there because of what, presumably, GR predicts.

 

[harrylin]

It's precisely because we identify the four-force as something that all freely-falling obsrevers agree on. An object that is freely falling experiences zero four-force, and hence, because the four-force is more useful than ordinary force, we tend to use that versus ordinary force. [..]

Thanks for the clarification! You seem to say that "Gravity is not a force" really means "Gravity is not a four-force". That is a concept that may need more elaboration, in particular for non-falling observers. And what happened to Einstein's gravitational field?

 

[D H]

You can explain the tides in terms of motion in a circle, with all the 'forces' we're familiar with.

No, you can't. At least not correctly. The centrifugal force explanation of the tides is fundamentally flawed; it happens to get the right result thanks to a lucky cancellation of errors. That circular motion explanation utterly fails for a Moon-sized object falling straight toward the Earth. When that object is at a distance of 384,400 km from the center of the Earth, the tidal forces exerted by it on the Earth would be exactly the same as those exerted by the Moon itself when it is 384,400 km from the center of the Earth.

The right way to explain tides from the perspective of Newtonian mechanics is to examine at the difference between the gravitational acceleration at a point on the surface of the Earth toward some other object (the Moon, the Sun, Jupiter, ...) and the gravitational acceleration of the Earth as a whole toward that object. In other words, compute the gravitational acceleration at a point on the surface relative to the Earth as a whole. Another way of looking at it: An Earth-centered frame is a non-inertial frame since the Earth is accelerating Moonward (and Sunward, and toward Jupiter, ...). The apparent gravitational acceleration at a point on the surface of the Earth is identically equal to this aforementioned difference.

Note that the motion of the tide-inducing object does not come into play here. All that comes into play is that this object causes other objects to accelerate toward it due to gravitation, and that this gravitational acceleration is not uniform. (There are no tides in Newtonian mechanics in a uniform gravitational field). When that Moon-sized object falling straight toward the Earth and the Moon are equidistant from the Earth, those two objects will exert the same tidal force on the Earth.

You don't need something as big as the Earth to observe these tidal forces. Outfit a spacecraft with an accelerometer placed far from the spacecraft 's center of mass. If that accelerometer is sensitive enough, it will sense a tidal force because the spacecraft is a (more or less) rigid body and because gravitational acceleration at the accelerometer's location is falling at a slightly difference from that at the spacecraft 's center of mass.

How can tidal forces not be taken care of in GR? They're only there because of what, presumably, GR predicts.

The spacecraft example above leads to how tidal forces can be addressed in GR. Suppose the distance between the spacecraft 's center of mass and the accelerometer is many orders of magnitude less than the distance between the spacecraft and planet. This means we can linearize the tensor mathematics that describes the curvature of spacetime. What you'll get is the same prediction as the that predicted by in Newtonian mechanics. Things get hairier if that linearization isn't valid such as when the spacecraft is in the close proximity to an extremely massive object, but tidal forces can still be calculated. Tidal forces become much stronger than those predicted by Newtonian mechanics in case of extreme curvature of space-time.

 

[vijendra sing]

I read somewhere that gravity is not a force. Is this true? What does it mean?

really gravity is not a force it is property of object by virtue of an object attract other object

 

[Nugatory]

If these two travellers stop walking, do they experience anything? Is there any Force acting on them to make them continue getting closer to the Pole? I do understand this is just an analogy but I feel it is too far away from the point about the 'reality' or otherwise of a gravitational force. You would need to say what the equivalent of a force is for these two travellers. It certainly couldn't be the same as the 'force' that pulls two masses together because the analogy is not 1:1.

We are getting very far from OP's question, but the analogy is better than you're giving it credit for being; indeed, I've seen it used in serious introductions to GR. It works because in GR there's no such thing as standing still - in four-dimensional spacetime you're always moving in the time direction.

I can see that GR tries to explain the origin of a force like the one that the proximity of two masses causes but, if the effect is the same as that which occurs between two charges, then why is it not allowed to be called a force? What distinguishes the one 'force' from the other force apart from the difficulty in detecting it?

The essential difference is that with gravity you can always find a (local) frame of reference where the gravitational force is zero and test particles just continue moving inertially. This is the case for all the so-called "fictitious" forces; for example if you're standing on the surface of the Earth and in the northern hemisphere, you'll believe that there's a force that deflects south-moving objects towards the west, but viewing the situation from space it's clear that the southwards-moving object is just moving in a straight line while the surface of the Earth moves underneath it.

You cannot find a similar transformation with the so-called "real" forces; for example a charged and an uncharged particle test particle will always behave differently in the presence of an electric field.

The distinguishing characteristic of the "fictitious" forces such as gravity is that their strength is always proportional to the mass of the object being acted upon - this is why all objects accelerate at the same rate under the influence of gravity, regardless of mass. It is also why the fictitious forces can be made to disappear in some local frame, by choosing a suitable frame of reference.

 

[BruceW]

Weight is a readily perceived and measured force - given the appropriate equipment - so why are we not 'allowed' to treat gravity as a force? It is such a tangible thing that it seems to me that the purist tail is wagging the dog of experience.

Then we should be allowed to treat centrifugal force as a real force too. In general relativity, you can't have one defined as a real force and not the other.

Edit: that's the beauty of general relativity - you can use whichever coordinate system you want. But this means we must accept that gravity and fictitious forces are one and the same.

Edit again: You could say that the coordinate system comoving with the expansion of the universe is the only true coordinate system, and use this coordinate system to judge what is gravity and what is fictitious force. But this seems like an unnecessary extension to me, without much insight gained.