Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 13/06/2014 14:30:02
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Geert Michiels asked the Naked Scientists:
Given by Einstein, gravity (I believe) is the bending of space/time.
The typical example given is that a star warps the space/time fabric
just as a bowling ball on a rubber sheet. Planets then get "trapped" in
this funnel and thus orbit the star.
Question: Particle physicists also talk about the "graviton" as being the particle
(force carrier) for the gravitational force. To me this seems to be incompatible
with the "folding of space/time" view of gravity. How do you combine these
2 views?
Being an engineer myself, I strongly believe there must be more science
in the media, radio, tv... I therefore love your podcast and all your initiatives.
Regards
Geert Michiels
Belgium
What do you think?
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A very insightful question, Geert, and one that physicists have been asking themselves for decades!
The short answer is that we don't know how to reconcile a quantized particle of gravity with the gravitational field. It is one of the major open questions in physics. As you point out, gravity is unique among the forces as being something intimately related to the curvature of space-time. This makes it a non-trivial problem to come up with a theory of gravitons. Moreover, gravity is such a weak force (you need really massive objects to generate strong gravitational fields) that it is well beyond our current experimental systems to look for the graviton directly.
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As you point out, gravity is unique among the forces as being something intimately related to the curvature of space-time.
So how is this different from the electrostatic field? The electrostatic field E is defined by how test particle having charge q behaves when placed in the field. In classical electrostatics
E = Felec/q
In classical gravity we have the same thing, i.e. the gravitational field G is defined by how it acts on a test mass m
G = Fgrav/m
In general relativity its similar. For the exact expression please see Eq. (8) at http://home.comcast.net/~peter.m.brown/gr/grav_force.htm
It should be noticed that there is no requirement that there be spacetime curvature be present in the field where the particle is located in order for there to be a gravitational force on the test particle. People often confuse the presence of a gravitational field with spacetime curvature. I worked out an example of the gravitational force on a particle in a uniform gravitational field, a field with zero spacetime curvature. See
http://home.comcast.net/~peter.m.brown/gr/uniform_force.htm
So just as the electrostatic force is mediated by photons so to do they expect the gravitational force be mediated by gravitons.
This makes it a non-trivial problem to come up with a theory of gravitons.
I don't follow. Please explain.
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As you point out, gravity is unique among the forces as being something intimately related to the curvature of space-time.
So how is this different from the electrostatic field? The electrostatic field E is defined by how test particle having charge q behaves when placed in the field. In classical electrostatics
E = Felec/q
In classical gravity we have the same thing, i.e. the gravitational field G is defined by how it acts on a test mass m
G = Fgrav/m
In general relativity its similar. For the exact expression please see Eq. (8) at http://home.comcast.net/~peter.m.brown/gr/grav_force.htm
It should be noticed that there is no requirement that there be spacetime curvature be present in the field where the particle is located in order for there to be a gravitational force on the test particle. People often confuse the presence of a gravitational field with spacetime curvature. I worked out an example of the gravitational force on a particle in a uniform gravitational field, a field with zero spacetime curvature. See
http://home.comcast.net/~peter.m.brown/gr/uniform_force.htm
So just as the electrostatic force is mediated by photons so to do they expect the gravitational force be mediated by gravitons.
This makes it a non-trivial problem to come up with a theory of gravitons.
I don't follow. Please explain.
As Pete has pointed out the equations for gravitation and electromagnetism are very similar. Also curvature, as Pete points out need not be present for gravity. If people took the trouble to look at some of Pete's pages then a lot more understanding would be gained all round. Gravitation is not simple to model but having at least a basic understanding of the mathematics gives insights.
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As you point out, gravity is unique among the forces as being something intimately related to the curvature of space-time.
So how is this different from the electrostatic field?
As you point out the equations look similar. However q can be negative. Mass cannot. The existence of two charges: +/- is a fundamental difference from gravity and is what makes coming up with a quantum theory of gravity tough and is also what makes coming up with a geometric theory of electromagnetism hard. In fact, both have been proposed but have problems.
The unification of electromagnetism and gravity into a single geometric theory is given by the Kaluza-Klein model and ends up requiring extra dimensions to deal with the charge: http://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory
This may be a fruitful direction in which to look, but certainly isn't straightforward.
As for the problems of a quantum theory of gravity, there are two issues I know of. The first is that all other quantum theories require quantization of a field in flat spacetime, whereas gravity should be agnostic to choice of a particular spacetime in which to quantize the theory. The second problem is renormalization: gravitions attract gravitons and the theory quickly runs into infinities when calculating interaction strengths. There are ways around this, but it places the theory on shakier ground already than other theories and hints that it is just an approximation to a deeper theory that would be free of these infinities (the infinities are a sign that the theory is a poor approximation to reality at a certain point).
One other major difference between Maxwell's equations and Einstein's field equations is that Maxwell's equations are linear, whereas Einstein's are not. I believe this is what's causing the renormalizability issue in quantum gravity, but that's way beyond my expertise. At any rate, thought the equations are similar on some level, they are fundamentally very, very different.
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Nice answer JP. As for the question of gravitons, if they exist then gravity would be a force, is that not so?
"Then in 1915, Einstein completed the General Theory of Relativity - the product of eight years of work on the problem of gravity. In general relativity Einstein shows that matter and energy actually mold the shape of space and the flow of time. What we feel as the 'force' of gravity is simply the sensation of following the shortest path we can through curved, four-dimensional space-time."
From http://www.hyperhistory.com/online_n2/History_n2/index_n2/einstein_theory.html
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As Pete has pointed out the equations for gravitation and electromagnetism are very similar.
I did? Where?
Also curvature, as Pete points out need not be present for gravity.
That’s correct. That’s what my paper on gravity is about in fact. Einstein commented on this point in a letter to Max Von Laue in fact. This was pointed out to me by the former editor of the Einstein paper’s project and a physics historian.
If people took the trouble to look at some of Pete's pages then a lot more understanding would be gained all round.
Thanks, Jeff. I appreciate that a great deal. I created and work on that site to help others. It’s an additional benefit to see people say nice things about it. So thanks! :D
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Nice answer JP. As for the question of gravitons, if they exist then gravity would be a force, is that not so?
Pete can go into it in more detail, but gravity is certainly a force. Our best model for gravity just works differently (space-time geometry) than our best models for other forces (particles). I think most physicists assume that an improved model of gravity will contain particles, but who knows? Maybe the particle model will be superseded.
Part of this comes back to the point I harp on a lot: in mid-19th century physics, a lot of terms had a single, precise, classical defiinition: mass, particle, force, length, etc. But modern physics in the form of quantum mechanics and relativity (general and special) changed the game. Now there are multiple definitions of these quantities that, in the limits of slow speeds, weak gravity or large objects, agree with our classical definitions. But in the extended, modern theories, we have to be more precise and they can take on multiple definitions. Not everyone agrees with these definitions.
Force is another example of this: Newton's gravity is defnitely a force as much as is electromagnetic force. But extending this to modern physics, these forces are described completely differently: gravity in terms of space-time geometry and electromagnetism in terms of particle exchanges. Does this mean gravity is suddenly not a force? Of course not. But it means we have to be careful when describing it to lay persons so that they know what makes it unique among the forces (at least in current models).
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Yes, make sense to think of it that way. Although it makes forces more diffuse to me I think I will agree on that gravity has the appearance of a force when acting on me, and me acting on it :) Then again, forces are strange things.