Gravity and spacetime curve.

[scorpionkings123]

Elaborate on the fact that gravity exists due to space time curve. Also let me know whether moon has lesser gravity because spacetime is less curved there due to lesser mass than earth.

[swansont]

That's how gravity is represented in general relativity. The motion in curved space is what we perceive as motion in a gravitational field.

[elfmotat]

Elaborate on the fact that gravity exists due to space time curve.

 

I don't think anyone is going to write a textbook-length explanation of General Relativity. That's what textbooks are for.

 

Informally, the basic idea is that the geometry of spacetime is connected to the energy-momentum distribution in spacetime by the following equation:

 

[math]\begin{pmatrix} curvature\\ of\\ spacetime \end{pmatrix}=\begin{pmatrix} energy ~\\ momentum\\ density \end{pmatrix}[/math]

 

The actual equation is called the Einstein Field Equation:

 

[math]G_{\mu \nu}=\frac{8 \pi G}{c^4}~T_{\mu \nu}[/math]

 

where [math]G_{\mu \nu}[/math] is the Einstein curvature tensor, [math]T_{\mu \nu}[/math] is the stress-energy tensor, [math]G[/math] is the gravitational constant, and [math]c[/math] is the speed of light.

 

Once you know the geometry of spacetime, you can determine how things will move. If you remember Newton's first law: "If an object experiences no net force, then it travels along a straight line with constant speed." This law still applies, but now the idea of a "straight" line in curved spacetime becomes rather vague.

 

The generalization of a straight line into curved space is called a "geodesic." It's essentially the "straightest" possible line you can draw. The modified version Newton's First Law in curved spacetime becomes: "If an object experiences no net force, then it travels along a geodesic in spacetime." This creates the illusion that objects are pulled toward massive objects due to some gravitational force. What's really happening is that everything is simply trying to follow a straight line in curved spacetime.

 

 

Also let me know whether moon has lesser gravity because spacetime is less curved there due to lesser mass than earth.

 

That's pretty much the basic idea.

[ajb]

Elaborate on the fact that gravity exists due to space time curve.

 

I recommend Carroll's "Lecture Notes on General Relativity" [1].

 

 

References

[1] Sean M. Carroll, Lecture Notes on General Relativity, arXiv:gr-qc/9712019 (1997).

[Markus Hanke]

Elaborate on the fact that gravity exists due to space time curve.

 

In the above sentence, swap "due to" with "is" - that will give a more accurate statement.

 

Consider for a moment elfmotat's avatar, and imagine two observers standing on the equator of that sphere. Now let our observers start walking north, along the lines as drawn in the avatar picture. What happens ? The further north they get, the more they approach each other. At the north pole, they meet. This happens not because of any force between them, but simply because of the geometry of the surface they are moving on.

Likewise GR - two bodies will approach one another not because there are any forces between them, but because of the geometry of space-time itself. Gravity ceases to be a phenomenon external to a body, and becomes a geometric property of space-time.

[general1]

I think gravity Is just a product of the strong electromagnetic force . after all the electromagnetic force is what causes the dent in space time which everything revolves around.

[Markus Hanke]

I think gravity Is just a product of the strong electromagnetic force . after all the electromagnetic force is what causes the dent in space time which everything revolves around.

 

This is an old idea, and trivially wrong. Gravity and electromagnetism do not behave in the same fashion, and cannot be described by the same laws. In fact they differ in pretty much all aspects, most notably that one of them is a vector field and the other one a tensor field, and that gravity is self-interacting whereas electromagnetism is not. While it is true that electromagnetic fields are one possible source of gravity, so too are all other forms of energy. All forms of energy are sources of the gravitational field, not just electromagnetism.

 

Btw, the term "strong electromagnetic force" is physically meaningless. You have electromagnetism, and you have the strong interaction. They are physically distinct phenomena, and not the same thing. Again, these interactions behave in completely different ways.

 

I should also remind you that this section is not the place to present personal theories; the moderators will probably not take kindly to that. I suggest you open your own thread on this in the appropriate section, but you will find that the idea is old and has long since been shown to be wrong.

[xyzt]

 

It's worth a visit just for the synopsis alone, and it's free. I know there is a web site as well under the title name. If you have read this book please enter a post and let me know as there are some things that I do not quite understand regarding the E=MC2 section. That bit has me perplexed as I thought that this was nailed but after reading this I am in great doubt about how valid or invalid it is. Hoping to hear from someone soon,

Alan.

 

 

The "book" is totally crackpot, please stop pushing it.

[swansont]

 

For a brief on Space and Time, please click on link below.

Your comments are welcome.

link removed

 

!

Moderator Note

Linus, advertising a pet theory is against the rules of the forum; such a discussion should take place in its own thread in speculations. Further, and to avoid duplication of mod effort, we ask that the discussion take place here on not simply via links to papers. Links without discussion are subject to deletion.

[krash661]

!

Moderator Note

Linus, advertising a pet theory is against the rules of the forum; such a discussion should take place in its own thread in speculations. Further, and to avoid duplication of mod effort, we ask that the discussion take place here on not simply via links to papers. Links without discussion are subject to deletion.

just to inform you,

they posted it all through the physics section.

[swansont]

just to inform you,

they posted it all through the physics section.

 

!

Moderator Note

 

A) I'm on it, and

B) this is exactly what the report post function is for (it lessens the disruption of threads)

 

edit: FYI Linus has been banned as a spammer (a PM telling him to stop was ignored)

 

Back to your regularly scheduled program

 

[pears]

Is gravity still viewed as spacetime curve in modern physics? Has that idea disappeared with quantum field theory?

[ajb]

Is gravity still viewed as spacetime curve in modern physics? Has that idea disappeared with quantum field theory?

Today the best view of classical gravity is as space-time curvature. One would like to understand gravity as a quantum theory, but this has not be fully acheived.

 

It maybe the case that a proper full quantum theory of gravity will describe space-time and its geometry as emergent aspects in some kind of classical limit. But without a good theory at hand it is impossible to say exactly how this will work.

[pears]

Oh ok - so when people talk about gravitons and gravity waves that's really highly theoretical and an area of research more than discovery?

[ajb]

Oh ok - so when people talk about gravitons and gravity waves that's really highly theoretical and an area of research more than discovery?

Gravity waves are classical waves that arise when you linearise the equations of gravity. In simpler langauge they are small ripples in the geometry of space-time. These should be detectiable and would provide great evidence that general relativity is a good theory of gravity. We do have indirect evidence of gravitational waves from observations of binary pulsars.

 

Now, one would like to quantise these ripples and end up with a theory of gravitons. You cannot do this properly, but you can still think of gravitons if you are careful. We can work with a perturbative theory of quantum gravity as an effective theory.

 

Anyway, it may be the case that general relativity, or something close it, is asymptotically safe. This means that it maybe a good quantum theory, but not a perturbative quantum field theory. In laymans terms, quantum gravity may not be a theory of gravitons after all!.

[pears]

Oh ok. Thanks - I guess I don't know much about gravity I think I need to brush up my physics!

[md65536]

Anyway, it may be the case that general relativity, or something close it, is asymptotically safe. This means that it maybe a good quantum theory, but not a perturbative quantum field theory. In laymans terms, quantum gravity may not be a theory of gravitons after all!.

Is that reasonably expected? Or is it just a wild possibility?

 

This is above my head, forgive me if I'm rambling incoherently and off topic, but...

 

In quantum theory is it only observable aspects that must be quantized?

And the effects of gravity do not need to be observed locally (eg. an observer in freefall doesn't need to know if it's in empty space or approaching a mass)?

Could a quantized measurement of gravity (ie. a graviton) be an aspect of the observation or measurement of spacetime curvature, and not an aspect of spacetime itself? (ie. having no existence outside of observation.)

 

 

 

Edit: Oh wait... the only time gravitons would come into play anyway is when the gravitational field changes, which the observer would (or could) detect or "feel", which would constitute an observation... so there would be no point in separating observable effects from anything else... ?

Edited August 28, 2013 by md65536

[ajb]

Is that reasonably expected? Or is it just a wild possibility?

I would say reasonably expected. We see similar phenomenology with classical electrodynamics and the electron self-energy.

 

In quantum theory is it only observable aspects that must be quantized?

I am not sure what this really means.

 

It is quite possible for observables to have a continuous spectrum, if that is what you are asking?

 

And the effects of gravity do not need to be observed locally (eg. an observer in freefall doesn't need to know if it's in empty space or approaching a mass)?

Okay, that is basically one form of the equivalence principal.

 

Could a quantized measurement of gravity (ie. a graviton) be an aspect of the observation or measurement of spacetime curvature, and not an aspect of spacetime itself? (ie. having no existence outside of observation.)

Well in the early development of quantum mechanics, Planck said that electromagnetic radiation interacts in "lumps" (I paraphrase here). He did not say that the electromagnetic radiation itself comes only in "lumps". I think it was Einstein who first really understood the true particle nature of light in this way.

 

Today we think of electromagnetic radiation as consisting of photons rather than just interacting as photons. So with this analogy, and as I have said we may have to be very careful with the notion of a graviton, I would think of the quantum nature as being a true part of space-time.

 

However, I have no idea exactly what that will be.

 

 

Edit: Oh wait... the only time gravitons would come into play anyway is when the gravitational field changes, which the observer would (or could) detect or "feel", which would constitute an observation... so there would be no point in separating observable effects from anything else... ?

You won't be able to split things into time and space absolutely.

[md65536]

Well in the early development of quantum mechanics, Planck said that electromagnetic radiation interacts in "lumps" (I paraphrase here). He did not say that the electromagnetic radiation itself comes only in "lumps". I think it was Einstein who first really understood the true particle nature of light in this way.

 

Today we think of electromagnetic radiation as consisting of photons rather than just interacting as photons. So with this analogy, and as I have said we may have to be very careful with the notion of a graviton, I would think of the quantum nature as being a true part of space-time.

That's what I was trying to speak about.

 

We say photons exist as particles, but the only time we can say anything concrete about their existence is when we measure them. I was thinking (in the case of gravitons at least)... couldn't it be possible that they exist not in "lumps" but only interact or are measured in lumps? That is, whenever you look at them, the observation is lumpy, where the lumpyness (particleness) is a property of the observation, not the thing observed?

 

But then I second guess myself because what is the point of speaking of something's existence outside of its measurable effects?

 

In the case of quantum gravity could that make a difference? Could it be a continuous thing that affects mass continuously, but when you measure it you would theoretically get quantized measurements? Or is it nonsense to speak of effects of gravity and measurements of gravity as if they're different things?

 

 

Edit: I guess you already answered the question using the photon analogy. But in that analogy, why do we say photons exist as particles instead of only interact as such? Does it even matter if we said one or the other (since there's no measurable difference)? And would that be the same in the case of gravitons?

Edited August 28, 2013 by md65536

[Strange]

Gravity waves are classical waves that arise when you linearise the equations of gravity.

 

Strictly, gravitational waves (gravity waves are something very different).

[ajb]

Strictly, gravitational waves (gravity waves are something very different).

Yes, I should have corrected myself.

Edit: I guess you already answered the question using the photon analogy. But in that analogy, why do we say photons exist as particles instead of only interact as such? Does it even matter if we said one or the other (since there's no measurable difference)? And would that be the same in the case of gravitons?

It is what the standard interpretation of quantum field theory tells us.

 

If there are no observable effects of "something", then does that "something" exist in any meaningful way?

 

You have limits in quantum field theory in which you recover the classical waves, I would expect something similar in any quantum theory of gravity.

[Gitirana]

The curvature of space is an observable phenomenon. However as we have no evidence of that space is made, we can only have hypotheses. We can even create formulas based on the hypotheses tested in other premises, but the fact is: We do not know what space is made ​​of and how it behaves, and ignoring other aspects eg feonomeno called dark energy. But even without knowing this does not stop us from going to the moon or mars.

[Zvonko]

 

In the above sentence, swap "due to" with "is" - that will give a more accurate statement.

 

Consider for a moment elfmotat's avatar, and imagine two observers standing on the equator of that sphere. Now let our observers start walking north, along the lines as drawn in the avatar picture. What happens ? The further north they get, the more they approach each other. At the north pole, they meet. This happens not because of any force between them, but simply because of the geometry of the surface they are moving on.

Likewise GR - two bodies will approach one another not because there are any forces between them, but because of the geometry of space-time itself. Gravity ceases to be a phenomenon external to a body, and becomes a geometric property of space-time.

Following this analogy, could we then propose that like magnetic field lines merge as they near the north (or south) pole on a 3 dimensional (spacial) object such as a sphere, that gravity may be doing the same thing in the 4th spacial dimension (or on time maybe) such as a hypersphere? I'm simply extrapolating the logic in your analogy and it seems like a reasonable hypothesis. I'm cognizant that analogies are only representations and may only have a limited relevance, however I'm also open minded enough to believe that analogies are historically excellent starting points. If I'm off the mark, can you explain in what way? On a hunch, it feels like the math would support it.