If gravity is not a force, what is holding us down?

[sawer]

OK. Gravity is not a force it is a contraction or curvature of space.
I was free-falling and now I hit the ground. Why don't I float through the universe, or go upward instead of still trying to go downward.
Because I hit the ground, and now there is no force(like gravity) and my free-falling must be stopped. What is holding us down?

 

[Ibix]

Gravity is not a force it is a contraction or curvature of space.

No - it's a curvature of spacetime. The distinction is important.

What is holding us down?

The point about gravity as spacetime curvature is that "things travel in a straight line unless acted on by a force" is no longer true. The correct statement is that "things travel along geodesics unless acted on by a force", and the available geodesics near Earth (or, more precisely, their spatial components) all curve towards the planet and eventually intersect it (unless you can jump upwards at about 11km/s or more). So no force is needed to hold you down - a force is only needed to stop you falling, and that's what the floor provides.

 

[Nugatory]

now there is no force(like gravity) and my free-falling must be stopped

Imagine that you and I are standing on the earth’s equator, one meter apart. Now we both start walking due north. As we’re moving north we will find ourselves pressed closer and closer to one another until we collide at the north pole. That’s curvature at work; the Earth is not flat so our initially parallel paths converge and eventually intersect.

The “force” that presses us down against the surface of the Earth is similarly a curvature effect: our path through spacetime is not parallel to the path of the earth’s surface.

 

[Dale]

What is holding us down?

Nothing. You are being pushed upwards by the ground, not held down by anything. The surface of the Earth accelerates continually upwards as measured by accelerometers. We are pushed up along with it

Here is an Insights I wrote explaining this topic in some detail:

https://www.physicsforums.com/insights/understanding-general-relativity-view-gravity-earth/

 

[sawer]

No - it's a curvature of spacetime. The distinction is important.

The point about gravity as spacetime curvature is that "things travel in a straight line unless acted on by a force" is no longer true. The correct statement is that "things travel along geodesics unless acted on by a force", and the available geodesics near Earth (or, more precisely, their spatial components) all curve towards the planet and eventually intersect it (unless you can jump upwards at about 11km/s or more). So no force is needed to hold you down - a force is only needed to stop you falling, and that's what the floor provides.

Thanks for answer. There is just one thing that I can not imagine is as you said it is geodesic, but I imagine even it is geodesic, it is line, why does it have to be just one way on the geodesic, even my free falling stopped? I was in the space something pushed me, I felt and I hit the ground. But still I am trying to go same way. I think I can not imagine the "one way" thing.

 

[sawer]

Imagine that you and I are standing on the earth’s equator, one meter apart. Now we both start walking due north. As we’re moving north we will find ourselves pressed closer and closer to one another until we collide at the north pole. That’s curvature at work; the Earth is not flat so our initially parallel paths converge and eventually intersect.

The “force” that presses us down against the surface of the Earth is similarly a curvature effect: our path through spacetime is not parallel to the path of the earth’s surface.

OK. Thank you. How can this analogy(walking due north) be adapted to a man standing on the ground and felt a force??

 

[sawer]

Nothing. You are being pushed upwards by the ground, not held down by anything. The surface of the Earth accelerates continually upwards as measured by accelerometers. We are pushed up along with it

Here is an Insights I wrote explaining this topic in some detail:

https://www.physicsforums.com/insights/understanding-general-relativity-view-gravity-earth/

I think, "pushing upwards by the ground" is not pushing or cause by any force. Am I right? This pushing effect must be result of curvature. Right?

 

[PeroK]

Thanks for answer. There is just one thing that I can not imagine is as you said it is geodesic, but I imagine even it is geodesic, it is line, why does it have to be just one way on the geodesic, even my free falling stopped? I was in the space something pushed me, I felt and I hit the ground. But still I am trying to go same way. I think I can not imagine the "one way" thing.

It isn't easy to imagine the effect of curved spacetime being equivalent to a force. But, ultimately, that is what results from the laws of physics in general relativity: the curved spacetime near the Earth causes an acceleration towards the centre of the Earth - almost exactly as a force would.

When you are off the ground, you fall towards the ground (that's a natural path, or geodesic). When you hit the ground, there is a real force from the ground that stops you and prevents you falling any further.

 

[vanhees71]

No - it's a curvature of spacetime. The distinction is important.

The point about gravity as spacetime curvature is that "things travel in a straight line unless acted on by a force" is no longer true. The correct statement is that "things travel along geodesics unless acted on by a force", and the available geodesics near Earth (or, more precisely, their spatial components) all curve towards the planet and eventually intersect it (unless you can jump upwards at about 11km/s or more). So no force is needed to hold you down - a force is only needed to stop you falling, and that's what the floor provides.

Maybe it's important to stress that these forces are of course not gravitational but mostly electromagnetic.

Concerning the debate, whether gravity is a "force" or not, it's a pretty semantic discussion. It depends on your point of view. Most physicists follow the idea by Einstein that the gravitational interaction is geometrized by General Relativity Theory, i.e., it's the spacetime structure itself that gets dynamical and that gravitational interactions are entirely due to the geometry of spacetime.

Other physicists have a somewhat different point of view and interpret the gravitational interaction as an interaction as all the others, described by a gauge theory, i.e., it is a making a global symmetry local by introducing a gauge field and introducing covariant derivatives via a corresponding connection.

What, however, makes gravitation distinct from the other fundamental interactions (electroweak and strong interactions, described by local gauge theories, where the gauge group acts in an abstract field space) is that what's "gauged" here is indeed the Poincare symmetry of the special-relativistic space-time model (flat Minkowski space), and this pretty formal procedure leads to a theory, which is very closely related to General Relativity. It's extending General Relativity, which assumes that the spacetime model is that of a Lorentzian manifold (i.e., a pseudo-Riemannian manifold with a fundamental form of signature (1,3) or equivalently (3,1) with the uniquely determined metric-compatible connection), to a socalled Einstein-Cartan manifold, where the connection has torsion and is related to the spin of the matter fields. On the macroscopic level, where the only relevant far-distant interaction despite gravity is the electromagnetic interaction, one ends up with a torsion-free connection, i.e., the same spacetime model as GR, and this then can of course immediately reinterpreted as providing the dynamical spacetime metric and thus geometrizing gravity.

One should, however, always be aware of the fact that the corresponding equivalence between inertial forces (i.e., forces occurring due to the use of an accelerating reference frame) is strictly true only locally, i.e., in a sufficiently small space-time region around an arbitrary point in spacetime, where you always can introduce an inertial frame. It's realized by some free-falling non-rotating object. E.g., the Internation Space Station is pretty close to such a local inertial reference frame, and indeed, over a small enough region there are (nearly) no gravitational effects. The astronauts operate in "weightlessness". If, however, you investigate the motion of (extended) bodies within such a free-falling reference frame with more accuracy, you'll realize that the gravitational field is not completely "transformed" away, but that there are still tidal forces left. Mathematically that's pretty obvious: Because at presence of matter spacetime gets a non-vanishing curvature tensor, and this curvature tensor is non-zero independently of the choice of your reference frame (simply because tensors and tensor fields are independent of the choice of a reference frame or coordinates and thus describe observables in GR). So you cannot in any way choose a reference frame, where there are no gravitaional interactions ("tidal forces" cannot be "gauged away").

 

[Nugatory]

OK. Thank you. How can this analogy(walking due north) be adapted to a man standing on the ground and felt a force??

Even when you are standing still in space, you can think of yourself as moving in spacetime: you are moving into the future at the rate of one second per second (this moving in spacetime" notion has some serious imitations, but it's good enough for present purposes). Just as moving in a straight line due north shoves you into the space occupied by your neighbor doing the same thing, when standing still on Earth your motion through spacetime is trying to shove you into the surface of the earth. The upwards force on your feet is the Earth resisting; if ground weren't there and getting in the way you would continue to move down towards the center of the earth.

You might try searchnig ths forum for the excellent and frequently posted video made by our member @A.T.

 

[PeroK]

How can this analogy(walking due north) be adapted to a man standing on the ground and felt a force??

What they have in common is that they are both the result of geometry. 3D spatial curvature in one case and 4D spacetime curvature in the other.

 

[stevendaryl]

OK. Gravity is not a force it is a contraction or curvature of space.
I was free-falling and now I hit the ground. Why don't I float through the universe, or go upward instead of still trying to go downward.
Because I hit the ground, and now there is no force(like gravity) and my free-falling must be stopped. What is holding us down?

Someone may have already answered this question, but to understand how gravity can act like a force, you need to think in terms of curved spaceTIME, not just curved space.

From the point of view of Special and General Relativity, we aren't moving through just space, we're moving through spaceTIME. Even if you are completely "still", you're still moving along the time axis. You pass through Saturday, then Sunday, etc.

Simplifying the discussion by just considering one space axis, the x-axis, you can plot your location as a point in the x-t plane. With each beat of your heart, you are at a different t-location, whether or not your are stationary (in the sense of being at a constant x-location).

So without gravity, you would have Earth at "rest" at a constant x-location, and you at "rest" at a constant x-location, and the plot of your trajectories through spacetime would look like two straight parallel lines oriented in the t-direction, never getting closer.

Now add spacetime curvature, and you have another effect: When spacetime is curved, inertial paths (that is, paths of objects that have no forces acting on them besides gravity) that start off parallel to each other do not remain parallel. So taking into account gravity/spacetime-curvature, the plots of your trajectory and that of the Earth don't remain parallel, they bend towards each other and eventually intersect.

So it's exactly analogous to travel along the surface of the Earth. If you have two travelers that start at the equator and travel North, their paths start off parallel (since they are both traveling in the same direction). But as they get closer and closer to the North Pole, their paths bend toward each other, until they finally meet at the North Pole.

 

[jbriggs444]

I think, "pushing upwards by the ground" is not pushing or cause by any force. Am I right? This pushing effect must be result of curvature. Right?

The pushing upwards by the ground is just a plain vanilla electromagnetic interaction. The same thing that you use when you lift a box or lean on a wall. Your feet push down on the ground and the ground pushes up on your feet.

The curvature of space-time is what makes it so that you stay in what seems like the same place despite the constant acceleration produced by this unbalanced force on your body.

 

[A.T.]

OK. Gravity is not a force it is a contraction or curvature of space.
I was free-falling and now I hit the ground. Why don't I float through the universe, or go upward instead of still trying to go downward.
Because I hit the ground, and now there is no force(like gravity) and my free-falling must be stopped. What is holding us down?

This might help:

 

[EPR]

You are traveling through curved spaceTIME, as has been stressed(capitalization mine). Curved spacetime feels like gravity. Go somewhere where there's no curved spacetime and you won't be falling down.

 

[jbriggs444]

Curved spacetime feels like gravity.

It's not gravity that you feel. What you feel is the crunch when the ground comes up and hits you in the face.

 

[EPR]

It's up to him to decide if he's falling down or if the Earth is rising up and is hitting him in the face.

 

[Dale]

I think, "pushing upwards by the ground" is not pushing or cause by any force. Am I right? This pushing effect must be result of curvature. Right?

No, the pushing upwards is caused by the normal force which pushes upwards in the bottom of your feet. The curvature just keeps the surface of the Earth from expanding.

Please read the link I gave you. It explains this concept well.

 

[paradisePhysicist]

Nothing. You are being pushed upwards by the ground, not held down by anything. The surface of the Earth accelerates continually upwards as measured by accelerometers. We are pushed up along with it

Here is an Insights I wrote explaining this topic in some detail:

https://www.physicsforums.com/insights/understanding-general-relativity-view-gravity-earth/

If the surface of the Earth is accelerating, wouldn't that result in the expansion of the Earth's crust? Granted, according to Newtonian gravity, the Earth does slightly accelerate towards a falling object, but not by much (maybe like 0.000001% and not detectable by an accelerometer, or at least the ones available on amazon), and I don't think that was the type of acceleration you were referring to.

Anyway, I have heard the explanations of how mass bends spacetime, creating a geodesic path for objects to move through, but what I don't get is how this actually creates gravity. What is actually pushing the object to move through the path in the first place? I'm not saying that the geodesic theory is "wrong", I am just saying the way its explained doesn't really make sense to me. Like why does it even move to begin with, is it pushed by time? How does time cause a push in the first place?

Maybe this is an explanation of why the object actually moves along the given path. Usually objects move because of some kind of pressure difference. Unfortunately I don't know the maths described here, but it seems whatever this is that is being described here, could lead to a more explainable axiom than just the usual explanation of a stationary object with no tangible forces acting on it suddenly deciding to move on a path.

What, however, makes gravitation distinct from the other fundamental interactions (electroweak and strong interactions, described by local gauge theories, where the gauge group acts in an abstract field space) is that what's "gauged" here is indeed the Poincare symmetry of the special-relativistic space-time model (flat Minkowski space), and this pretty formal procedure leads to a theory, which is very closely related to General Relativity. It's extending General Relativity, which assumes that the spacetime model is that of a Lorentzian manifold (i.e., a pseudo-Riemannian manifold with a fundamental form of signature (1,3) or equivalently (3,1) with the uniquely determined metric-compatible connection), to a socalled Einstein-Cartan manifold, where the connection has torsion and is related to the spin of the matter fields. On the macroscopic level, where the only relevant far-distant interaction despite gravity is the electromagnetic interaction, one ends up with a torsion-free connection, i.e., the same spacetime model as GR, and this then can of course immediately reinterpreted as providing the dynamical spacetime metric and thus geometrizing gravity.

 

[jbriggs444]

If the surface of the Earth is accelerating, wouldn't that result in the expansion of the Earth's crust?

No. The curvature of space-time is what allows the surface of the Earth to remain stationary (against a particular reasonable choice of coordinates) in spite of its non-zero proper acceleration.

 

[Ibix]

If the surface of the Earth is accelerating, wouldn't that result in the expansion of the Earth's crust?

In flat spacetime, yes. In curved spacetime it depends in general, but in this case no.

 

[paradisePhysicist]

No. The curvature of space-time is what allows the surface of the Earth to remain stationary (against a particular reasonable choice of coordinates) in spite of its non-zero proper acceleration.

Hmm. Idk, sounds confusing.

From the point of view of Special and General Relativity, we aren't moving through just space, we're moving through spaceTIME. Even if you are completely "still", you're still moving along the time axis. You pass through Saturday, then Sunday, etc.

Saturday and sunday are human constructs. In real life there is just a planet orbitting the sun at a particular location, this location determines the calendar. The location is caused by gravity. Thus this particular segment of text seems like explaining gravity by gravity (tautology.)

 

[Ibix]

Idk, sounds confusing.

Not really, once you start to get your head round the maths.

 

[jbriggs444]

Hmm. Idk, sounds confusing.

Yes. Curved space is tough to grasp. Popularizations such as "Sphereland" may help. Curved space-time is worse. But that's General Relativity for you. Built on differential geometry -- not for the faint of heart.

 

[paradisePhysicist]

Not really, once you start to get your head round the maths.

Even if I understood the maths (which I do not) I would at least like to see some kind of physical simulation or explanation. I have seen the trampoline one which seems like a tautotology (using gravity to prove gravity.)

Yes. Curved space is tough to grasp. Popularizations such as "Sphereland" may help. Curved space-time is worse. But that's General Relativity for you. Built on differential geometry -- not for the faint of heart.

Alright I will watch this Sphereland movie, looks interesting.

 

[jbriggs444]

Even if I understood the maths (which I do not) I would at least like to see some kind of physical simulation or explanation. I have seen the trampoline one which seems like a tautotology (using gravity to prove gravity.)Alright I will watch this Sphereland movie, looks interesting.

I was actually thinking of the book. It has been so long since I read it that I do not remember whether it was Flatland or Sphereland. But it got me to the point where I could wrap my head around curved space and higher dimensional geometries.

 

[Ibix]

I have seen the trampoline one which seems like a tautotology (using gravity to prove gravity.)

It is tautological. This by @A.T. is much better:

 

[Nugatory]

I would at least like to see some kind of physical simulation or explanation. I have seen the trampoline one which seems like a tautotology (using gravity to prove gravity.)

The trampoline analogy is horribly misleading because it shows curved space, as opposed to curved spacetime. The video linked in post 14 of this thread by our own @A.T. is what you're looking for.

 

[Ibix]

The video linked in post 14 of this thread by our own @A.T. is what you're looking for.

And I went and searched the whole site for that...

 

[ergospherical]

The trampoline analogy is horribly misleading because it shows curved space, as opposed to curved spacetime.

This is a bit of a non-issue, don't you think?

 

[PeterDonis]

This is a bit of a non-issue, don't you think?

No, it's a very important issue, as shown in many previous discussions here on PF of this very point.

The video by @A.T. is a much better way of understanding what is going on.

 

[ergospherical]

Don't think it's important, because it's literally just showing a curved space. Bit hard to visualise curvature and geodesics using anything other than one or two dimensional surfaces, haha.

 

[Ibix]

This is a bit of a non-issue, don't you think?

The usual problem is that people ask "if gravity is curved space then I can see why moving objects follow curved paths but why do stationary objects start moving?". The answer, of course, is that Newtonian gravity is what you get when you neglect everything the trampoline diagram is showing you and only use the stuff you can't embed in a Euclidean space. That makes it a bit hard to bridge the gap between "look at this pretty diagram, you understand everything now don't you" and the actual reality of the physics.

 

[stevendaryl]

Saturday and sunday are human constructs.

The fact that we call them that is a human construct, but the fact that Saturday is a different point on spacetime than Sunday is part of the nature of the universe (as we currently understand it; we could always be wrong…)

In real life there is just a planet orbitting the sun at a particular location, this location determines the calendar.

Orbiting means that its location changes as a function of time.

The location is caused by gravity. Thus this particular segment of text seems like explaining gravity by gravity (tautology.)

The location is caused by gravity? That makes no sense. In the absence of gravity, you still have time, and you still have space. If you do nothing at all, you are still moving in time.

As I said, in the absence of gravity, the paths through spacetime of two drifting objects that start off parallel will remain parallel. Curvature causes initially parallel paths to converge or diverge. An object falling is a specific example.

If you step off a cliff, initially you and the Earth are following parallel trajectories through spacetime. But curvature results in your spacetime paths bending towards each other.

 

[Dale]

If the surface of the Earth is accelerating, wouldn't that result in the expansion of the Earth's crust?

If spacetime were flat, then yes. It is the curvature of spacetime that allows different parts of the Earth to be continually accelerating away from each other without getting further away from each other.

I'm not saying that the geodesic theory is "wrong", I am just saying the way its explained doesn't really make sense to me.

Did you read the link I cited earlier? I really tried to walk through the origin of these concepts. No math is involved, but it is a verbal description of the actual theory and not a handwaving “rubber sheet” thing.