# Gravity of planets, stars etc.

• Euclid Areti
In summary, General Relativity (GR) is a geometric theory that explains gravitation in terms of geometry. While it may not be the final theory of gravity, it is currently the simplest and most accurate theory that explains gravitational motion. The notion of "fabric" of space and time is mostly an analogy and the true description is purely mathematical. While it may be possible to come up with a different theory, it would likely be very complex and counter-intuitive. To truly understand GR, one must learn the mathematical description rather than relying on analogies.

#### Euclid Areti

Hello. I am by no means knowledgeable in General Relativity. With that said:

What if "curvature of space-time" actually is the force fields of massive objects, like the magnetic field of earth?
Why must space-time necessarily have to be "bent"? Is there really only one way to look at the nature of gravity between massive objects? That gravity is a "distortion of space-time"? I know that there's much experimental and observational evidence for GR, but how do we really know there is such a thing as "fabric" of space and time? What exactly is this fabric, at quantum level?

I want to get to the bottom of what gravity really is. Unfortunately, GR is taught like after you have a Bachelor's degree, in your masters.

Anyway, is it beyond a reasonable doubt, that the notion of "curvature" will never be replaced by another theory?
What if, as I speculate, force fields or acceleration fields, account for the bending of light near masses and all the other experimental data for GR? Is that completely impossible?

Actually, introductory GR courses are routinely offered as freshman university classes. Einstein preferred the curvature explanation for gravity because he habitually thought in geometrical terms to visualize mathematical relationships. This approach was highly successful and remains preferred by many because of its conceptual simplicity. Experiments show it works extremely well under all but extreme conditions. No one believes it is the 'final' theory of gravity, but, it is widely believed to be accurate enough for use in the low energy regime. Chances are all our best theories will be replaced, or supplemented by something else once we master testing them more rigorously.

Nugatory
Euclid Areti said:
What if "curvature of space-time" actually is the force fields of massive objects, like the magnetic field of earth?
Why must space-time necessarily have to be "bent"?

We used to think of gravity as a field similar to the magnetic field around the Earth. However, GR is a different approach. GR is a geometric theory, meaning that at its core, it explains gravitation in terms of geometry, which itself is "concerned with questions of shape, size, relative position of figures, and the properties of space". (Per wiki)

Euclid Areti said:
Is there really only one way to look at the nature of gravity between massive objects?

Certainly not. As I said, we used to look at gravitation as a classical field theory. The problem was that it wasn't accurate enough. Einstein's General Theory of Relativity is the simplest theory that explains gravitation and motion so accurately that current experiments have yet to find the limit of its applicability. To date, no other theory can do this. It's certainly thinkable that you can make up a more traditional field theory that explains gravitation as accurately, the problem is that it would be extraordinarily complex and non-intuitive, far more than GR is.

Euclid Areti said:
I know that there's much experimental and observational evidence for GR, but how do we really know there is such a thing as "fabric" of space and time?

Common explanations of GR talk about spacetime as a sort of "fabric" that bends and stretches and does all sorts of other weird things. Similarly, classical field theories talk about fields as if they are real entities. Whether spacetime is a fabric or fields really exist is mostly interpretation in my opinion. If you do the math, you get the right answer, no matter what you believe.

Euclid Areti said:
What if, as I speculate, force fields or acceleration fields, account for the bending of light near masses and all the other experimental data for GR? Is that completely impossible?

Impossible? Doubtful. So complex and counter intuitive that it would barely make any sense? Very likely.

Euclid Areti said:
I want to get to the bottom of what gravity really is. Unfortunately, GR is taught like after you have a Bachelor's degree, in your masters.

Yes, the math required to do the equations in GR is indeed complex and takes many years to master. However, you can gain an understanding of GR without knowing how to do all the math. I recommend one of the many, many books and articles you can find online or at a book store.

Euclid Areti said:
Hello. I am by no means knowledgeable in General Relativity. With that said:

What if "curvature of space-time" actually is the force fields of massive objects, like the magnetic field of earth?
Why must space-time necessarily have to be "bent"? Is there really only one way to look at the nature of gravity between massive objects? That gravity is a "distortion of space-time"? I know that there's much experimental and observational evidence for GR, but how do we really know there is such a thing as "fabric" of space and time? What exactly is this fabric, at quantum level?

I want to get to the bottom of what gravity really is. Unfortunately, GR is taught like after you have a Bachelor's degree, in your masters.

Anyway, is it beyond a reasonable doubt, that the notion of "curvature" will never be replaced by another theory?
What if, as I speculate, force fields or acceleration fields, account for the bending of light near masses and all the other experimental data for GR? Is that completely impossible?

The basic answer is that this view of space-time is very useful. Descriptions like "fabric" are only ever analogies to the true description which is purely mathematical. We use words like "fabric" because they help us to understand the behavior of the system at an intuitive level. But if you really want to understand what's going on, it is absolutely necessary to learn the true mathematical description. Analogies like "fabric" are imprecise and, therefore, not quite accurate.

The way in which space-time is most analogous to a "fabric" is that it can carry momentum and energy across space through gravitational waves.

And while we are likely to come up with a better theory of gravity that better-describes what goes on in the case of very strong gravitational fields and very short distances, General Relativity is experimentally-proven to be accurate across a tremendous range of scales.

TEFLing
Wow, thanks guy (or girls?) for clearing it up a bit.

Drakkith said:
Impossible? Doubtful. So complex and counter intuitive that it would barely make any sense? Very likely.

But isn't Special Relativity all about counter-intuition? What Einstein discovered through his thinking and math about the nature of light, if you travel at high speed, space and time changes? After all, nature doesn't care for our logical assumptions. Isn't it then possible that the true nature of gravity is something very counter-intuitive?

Chalnoth said:
The basic answer is that this view of space-time is very useful. Descriptions like "fabric" are only ever analogies to the true description which is purely mathematical. We use words like "fabric" because they help us to understand the behavior of the system at an intuitive level. But if you really want to understand what's going on, it is absolutely necessary to learn the true mathematical description. Analogies like "fabric" are imprecise and, therefore, not quite accurate.

So the truth of the matter is that we really can't "visualize" what gravity really is? It is too abstract to understand without mathematics? How can it be understood mathematically and not matter-of-factly? Isn't it then, much more theoretical than actual?

Precise descriptions require precise language. Math is more rigorously descriptive than verbal descriptions.

Euclid Areti
Euclid Areti said:
So the truth of the matter is that we really can't "visualize" what gravity really is? It is too abstract to understand without mathematics? How can it be understood mathematically and not matter-of-factly? Isn't it then, much more theoretical than actual?
The only way to fully grasp the implications of General Relativity is to understand the math behind it. Visualization can only ever give a fuzzy, imprecise picture, and is always prone to misunderstandings.

A verbal description is only ever an analogy of the true mathematical description.

Euclid Areti
Euclid Areti said:
Why must space-time necessarily have to be "bent"?

Because tidal gravity exists, and "spacetime curvature" is just another term for tidal gravity.

The reason why this viewpoint works is that the motion of a freely falling object is independent of its mass or composition; that means whatever governs its motion must be a property of spacetime, not of the object.

TEFLing
PeterDonis said:
Because tidal gravity exists, and "spacetime curvature" is just another term for tidal gravity.

The reason why this viewpoint works is that the motion of a freely falling object is independent of its mass or composition; that means whatever governs its motion must be a property of spacetime, not of the object.

Is that what Galileis experiment of two falling masses with unequal weight would have proven, if done in a vacuum chamber? The two unequal masses fall with equal acceleration, if you let them "free fall"?

Euclid Areti said:
Is that what Galileis experiment of two falling masses with unequal weight would have proven, if done in a vacuum chamber? The two unequal masses fall with equal acceleration, if you let them "free fall"?

Yes, with the proviso that the "acceleration" here is coordinate acceleration, not proper acceleration, and in GR it's often better not to use the word "acceleration" when coordinate acceleration is meant, because it can cause confusion. That's why I phrased it the way I did.

Euclid Areti
Is there any way of making the fabric analogy more precise / slightly less imprecise?

Is there any way of characterizing the hardness or ductileness of space time?

Is space time as stretchy as a rubber sheet, or more like / less unlike deformable but hard tempered steel? Or anything else like that?

Euclid Areti
Space doesn't have such properties. The only thing the analogy is for is the geometry.

TEFLing said:
Is there any way of characterizing the hardness or ductileness of space time?

Not in the context of GR, no. There are speculations in quantum gravity about spacetime and spacetime curvature arising from an underlying quantum medium that could be assigned properties like elasticity--see, for example, this Wikipedia article.

TEFLing
PeterDonis said:
Not in the context of GR, no. There are speculations in quantum gravity about spacetime and spacetime curvature arising from an underlying quantum medium that could be assigned properties like elasticity--see, for example, this Wikipedia article.

Can I rephrase and reword?

What about the Einstein constant in the GR equation

R = k T

k = " curvature per energy density "

If k was a lot larger, then the fabric of space-time would warp a lot more ( for a given density of mass energy )

And then the fabric of space-time would be ( qualitatively ) much more rubbery and elastic and stretchy...

Whereas if k --> 0, then space-time would never warp, would always be "straight" & "flat" , no matter how much mass energy was loaded onto it ( in the sense of loading bowling balls onto a rubber sheet )

In the second case, space-time would be a lot less rubbery and stretchy and elastic... And qualitatively a lot "harder" & "stronger" ( in the sense of replacing the rubber sheet with plywood or even steel plate, which would bend little or not at all, under the weight load of bowling balls )

Is there any qualitatively valuable way, of associating the Einstein constant, with a characterization of the " structural strength " of the space-time fabric / membrane ?

Simplistically, is space-time more like ( less unlike ) rubber? Or plywood? Or plate steel ? Or anything else like that?

TEFLing said:
Is there any qualitatively valuable way, of associating the Einstein constant, with a characterization of the " structural strength " of the space-time fabric / membrane ?

Same answer as before: not in the context of GR. In the context of GR, the constant in the Einstein Field Equation is just a conversion factor between curvature units and energy density units. It has no interpretation as "structural strength". That sort of speculation is a quantum gravity speculation.

Euclid Areti said:
I want to get to the bottom of what gravity really is. Unfortunately, GR is taught like after you have a Bachelor's degree, in your masters.

As others said, you really can't get to the bottom without the math. Verbal descriptions and analogies can never make it clear.

May I suggest Professor Leonard Susskind's video course on GR? He does the math, but he does it well enough that you need only freshman calculus to follow along.

The course consists of thirteen 90 minute lectures. I found that if I view just 10 minutes of one lecture each day, my
comprehension soars. I also find it very helpful to pause the playback whenever Susskind mentions an unfamiliar mathematical concept. Then I can switch to Wikipedia, look up that concept, read the article, then return to Susskind.

Those abilities and the magic number of 10 minutes per lesson (which I first heard articulated by Sal Khan of Khan Academy) make even difficult subjects accessible to ordinary mortals. I have been able to finish courses on video that I could never have kept up with in a live classroom.

Khan also recommends repetition as necessary to achieve 100%
comprehension instead of just 70-80%. He argues that 100% comprehension of step N makes study of step N+1 much easier.

Find the GR course
here on youtube. It is also available on iTunes.

anorlunda said:
As others said, you really can't get to the bottom without the math. Verbal descriptions and analogies can never make it clear.

May I suggest Professor Leonard Susskind's video course on GR? He does the math, but he does it well enough that you need only freshman calculus to follow along.

The course consists of thirteen 90 minute lectures. I found that if I view just 10 minutes of one lecture each day, my
comprehension soars. I also find it very helpful to pause the playback whenever Susskind mentions an unfamiliar mathematical concept. Then I can switch to Wikipedia, look up that concept, read the article, then return to Susskind.

Those abilities and the magic number of 10 minutes per lesson (which I first heard articulated by Sal Khan of Khan Academy) make even difficult subjects accessible to ordinary mortals. I have been able to finish courses on video that I could never have kept up with in a live classroom.

Khan also recommends repetition as necessary to achieve 100%
comprehension instead of just 70-80%. He argues that 100% comprehension of step N makes study of step N+1 much easier.

Find the GR course
here on youtube. It is also available on iTunes.

Thank you for the info. I have listened to other lectures of Susskind, amongst them his Cosmology course. He's a very good teacher. I will use your 10 minute tip as well!

russ_watters said:
Space doesn't have such properties. The only thing the analogy is for is the geometry.

What you probably meant is that modern physics still can not explain what exactly this fabric of space is. We will have to progress further in our research first...

Euclid Areti said:
What you probably meant is that modern physics still can not explain what exactly this fabric of space is.

Physical theories do not explain fundamental constituents.

Modern physics does not explain what electron is, either. It just says "there is a four-component complex spinor field permeating all space, whose behavior is governed by these equations. Let's call it electron field. Let's call its excitations (they are quantized) 'electrons'."

Euclid Areti said:
What you probably meant is that modern physics still can not explain what exactly this fabric of space is. We will have to progress further in our research first...

That is not correct. Modern physics uses General Relativity, which does not describe spacetime as a 'fabric'. That is just an analogy. GR explains gravity and spacetime in very specific ways that simply aren't easily translated from the mathematical language used to a language that a layman can understand.

That doesn't mean that GR is 100% accurate. We could develop a new theory of gravity that surpasses GR and can't be analogized into a 'fabric' at all.

The " fabric " of space-time exists separately from ( the wave functions of ) matter and energy, yes?

Cp. DeSitter empty space-time is flat

Like actors on a stage , ( the wave functions of ) mass and energy exist within space-time...

Space-time has an independent identity, or existence, or ontological reality... In the theory

Or something like that?

TEFLing said:
The " fabric " of space-time exists separately from ( the wave functions of ) matter and energy, yes?

It's not a "fabric", as others have pointed out. As for "existing separately", I'm not sure what you mean, but there are at least two senses in which the answer is yes:

(1) If we derive the Einstein Field Equation from a Lagrangian (this derivation was first done by David Hilbert in 1915, at the same time that Einstein was completing his derivation by another route), the term in the Lagrangian that describes spacetime is separate from the term that describes matter and energy.

(2) If we take a quantum field theory viewpoint (since you mentioned wave functions), the quantum field corresponding to spacetime (the graviton) is different from the quantum fields corresponding to matter and energy (all the others). Of course, this depends on our current heuristic understanding of quantum gravity being correct.

TEFLing said:
DeSitter empty space-time is flat

No, it isn't. There is a coordinate chart in which spatial slices are flat, but the spacetime is not flat.

TEFLing