Gravity and the bending of spacetime

[SimonFunnell]

I have seen this visualisation expressing the suns gravitational effect on our planet quite a bit:

 

 

However, what I don't see, and what this question asks, is how does this work with the gravity and objects on the earth, me for example?

 

I was hoping somebody could provide a link or explain this. Thanks.

[ajb]

In the same sort of way. Gravity is understood in general relativity as the local geometry of space-time. On the scales we are talking about, Newtonian gravity gives very good results.

[SimonFunnell]

I guess I am just having trouble visualising spacetime bending and keeping me on the planet. For example, in the visualisation posted it looks like, its even stated, that spacetime is a like a flat surface warping. What I am struggling with is how that works on earth, are you saying that spacetime doesn't bend at the earth/human scale?

[ajb]

I guess I am just having trouble visualising spacetime bending and keeping me on the planet. For example, in the visualisation posted it looks like, its even stated, that spacetime is a like a flat surface warping.

Such images you cannot take too seriously. To properly understand this geometry of space-time you need to be comfortable with 4 dimensional manifolds, tensors and so on. None of this you can really visualise as there are too many dimensions.

 

 

What I am struggling with is how that works on earth, are you saying that spacetime doesn't bend at the earth/human scale?

There is curvature of the geometry on the Earth/human scale, just that it is tiny and so Newtonian gravity works very well.

[michel123456]

Such images you cannot take too seriously. To properly understand this geometry of space-time you need to be comfortable with 4 dimensional manifolds, tensors and so on. None of this you can really visualise as there are too many dimensions.

 

 

 

There is curvature of the geometry on the Earth/human scale, just that it is tiny and so Newtonian gravity works very well.

I don't understand your answer. Newton gravity is not of another nature, it is the same gravity as that of spacetime bending.

[Mordred]

I don't understand your answer. Newton gravity is not of another nature, it is the same gravity as that of spacetime bending.

Correct but the more curvature you get due to relativitistic effects the more Newtonian gravity becomes inaccurate. Newtonian gravity uses Euclidean (flat geometry)

[swansont]

I don't understand your answer. Newton gravity is not of another nature, it is the same gravity as that of spacetime bending.

Same effect, but not the same mechanism.

[SimonFunnell]

As I understand it Newton said that while he could model gravity mathematically he could not explain exactly what is was, however, with Einstien we now understand gravity to be (the geometry?) of spacetime bending/warping.

 

Does this mean that gravity is not a force as such?

[Sensei]

However, what I don't see, and what this question asks, is how does this work with the gravity and objects on the earth, me for example?

 

Have you heard about Sun tides?

https://en.wikipedia.org/wiki/Tide

 

https://en.wikipedia.org/wiki/Earth_tide

 

Tides on the Io moon, are great

https://en.wikipedia.org/wiki/Io_%28moon%29

Edited February 16, 2016 by Sensei

[ajb]

As I understand it Newton said that while he could model gravity mathematically he could not explain exactly what is was, however, with Einstien we now understand gravity to be (the geometry?) of spacetime bending/warping.

Yes, in general relativity we understand the gravitational field to essentially be the local geometry, there are a few ways of actually understanding this. In the 'standard' formalism the metric tensor is taken as the gravitational degree of freedom.

 

 

Does this mean that gravity is not a force as such?

In a technical sense we say that gravity is a pseudoforce. It comes down to the impossibility of picking frames that are not accelerated frames. Well, in a small enough region you can forget about the curvature, this is one way of looking at the equivalence principle.

 

I do not know how much you know about Lagrangian mechanics and the Euler-Lagrange equations. But basically, in the equations of motion for a test particle under the influence of gravity only, there is no term that corresponds to an external force. Yet the path of the particle is not a straight line line in general, but rather a geodesic, which is the shortest path between two points. Thus we have a pseudoforce.

[Thorham]

Yes, in general relativity we understand the gravitational field to essentially be the local geometry

 

Is that really what's happening physically, or is it a model?

[ajb]

Is that really what's happening physically, or is it a model?

 

The question is how would you make a clear distinction?

[Strange]

 

Is that really what's happening physically, or is it a model?

 

It is a model. How would you tell the difference between that and a what is happening physically?

 

We have models that match observation and measurement. All we can know about what is "really" happening physically is our observations and measurements and so, indirectly, we try and make models that are consistent with "physical reality".

 

Does the model describe that what is really happening? Who knows; it is impossible to answer that question. We can't even tell if there is such a thing as "reality", there is just what we measure. (Or, if you want to get away from realism completely, what we think we measure!)

[Thorham]

The question is how would you make a clear distinction?

I'm asking because it somehow came across as if it's what physically happens, which seems a little strange.

 

We can't even tell if there is such a thing as "reality"

That's not true. Everything that exists is collectively reality. What that reality is, is another question.

[Strange]

That's not true. Everything that exists is collectively reality. What that reality is, is another question.

 

It might all be a delusion.

 

Or, as suggested in another thread, a computer simulation.

Edited February 16, 2016 by Strange

[Thorham]

It might all be a delusion.

 

Or, as suggested in another thread, a computer simulation.

A computer simulation is simply running on a computer somewhere in reality. A delusion is part of reality, as well. Like I said, everything that exists, including computer simulations, delusions, illusions and what not, is part of reality.

[ajb]

I'm asking because it somehow came across as if it's what physically happens, which seems a little strange.

This borders on metaphysics. I really do not know if space-time and its curvature are real in any deep sense. What I do know is if I model gravitational phenomena using general relativity then I get great agreement between the theory and experiment. In this sense general relativity is a 'true' theory and space-time 'actually' bends.

 

The same kind of statements can be made about any physical theory, so general relativity is not unique in this respect.

[Thorham]

This borders on metaphysics.

Not necessarily. What if gravity is caused by a force that's measurable somehow, and we simply don't know how yet?

Edited February 17, 2016 by Thorham

[ajb]

What if gravity is caused by a force that's measurable somehow, and we simply don't know how yet?

So far all attempts to build a Lorentz invariant theory of gravity on a flat space-time have failed. People like Feynman spent some time on this question.

 

Anyway, if such a theory were realised and it was shown to be phenomenologically indistinguishable from general relativity, then how would we decide which theory is 'true'?

[Thorham]

So far all attempts to build a Lorentz invariant theory of gravity on a flat space-time have failed. People like Feynman spent some time on this question.

 

That doesn't mean that the nature of gravity is not measurable.

Edited February 17, 2016 by Thorham

[Strange]

 

That doesn't mean that the nature of gravity is not measurable.

 

But however you measure it and whatever model you use to describe it, that doesn't tell you any more about what is "really" happening. It just tells you that you have a good (and hopefully better) model

[ajb]

That doesn't mean that the nature of gravity is not measurable.

I don't understand your point.

 

Strange has it bang on. What you see will be fundamentally driven by the theoretical framework you are using.

Edited February 17, 2016 by ajb

[Thorham]

But however you measure it and whatever model you use to describe it, that doesn't tell you any more about what is "really" happening. It just tells you that you have a good (and hopefully better) model

We either measure what's happening or we don't. In the case of gravity we find a way to measure space as stuff that's curving somehow (or some force), or we don't.

 

I don't understand your point.

You said:

 

This borders on metaphysics.

I don't agree.

 

What you see will be fundamentally driven by the theoretical framework you are using.

That sounds like seeing what we want to see.

[SimonFunnell]

I have been following this thread and I don't feel like the original question has really been addressed, but I am going somewhere with this and a few of the posts made by people touch on the same point I am going to make now.

Prior to the Copernican Revolution we had theories that effectively modelled the motion of celestial bodies (Ptolemaic model), however following the revolution we discover the model, while having explanatory power, was not a reflection of the of the underlying reality.

Now people may have their opinions on this but my own is that relativity is a modern version of epicycles, basically a mathematical model that works but does not reflect the underlying reality.

Can physicists authoritatively say that, for example, spacetime is quite literally bending as modelled in relativity or would they accept there is a very small chance that relativity is nothing more than modern epicycles?

[swansont]

That sounds like seeing what we want to see.

 

No, not really. The theoretical framework has to match with observations. You don't get to disregard evidence.

 

If your theoretical framework that precisely matches what we observe includes invisible pink unicorns, then your explanation is going to include invisible pink unicorns. The problem is that there is generally no way to test for the unicorns, only the results of their actions.