Relation between graviton and space curvature

[xMonty]

Hi,
i read a few books (pop ones) and one thing that left me thoroughly confused was the relation between graviton and space curvature, is there any relation between the two...

if we find a graviton then does it mean that space is not curved?

regards
Monty

 

[Bob_for_short]

One graviton cannot be detected, unlike one photon, because of too low energy in it.

What could be detected is a strong gravitational wave - stream of many coherent gravitons. But again, if photon's electric field "shakes" differently electrons and heavy ions (nuclea) and thus can be detected easily, the gravitational wave "shakes" any mass in the same way so no relative displacenemt of masses is observed. They move all together as if they do not move at all. So detection technique is quite tricky even in case of a strong wave.

In General Relativity the gravitational wave makes a part of the space-time curvature. It is of a geometrical nature.

In some other theories (RTG) the the gravitational wave is as physical as the other waves (photons) - it carries energy-momentum.

Thus two different interpretations.

 

[PeterDonis]

One graviton cannot be detected, unlike one photon, because of too low energy in it.

This isn't quite correct; in principle, as far as we know (and bear in mind we don't know a lot, since we don't have a good theory of quantum gravity, which is what we would need to know in detail the properties of gravitons), there is nothing in the laws of physics that rules out gravitons with arbitarily high energy. It's just that it's a *lot* harder to produce high-energy gravitons than high-energy photons, so in practice, we're unlikely to ever observe high-energy gravitons.

What could be detected is a strong gravitational wave - stream of many coherent gravitons. But again, if photon's electric field "shakes" differently electrons and heavy ions (nuclea) and thus can be detected easily, the gravitational wave "shakes" any mass in the same way so no relative displacenemt of masses is observed. They move all together as if they do not move at all. So detection technique is quite tricky even in case of a strong wave.

It's not correct that gravitational waves can't cause relative displacement of masses; they can. The http://www.ligo.caltech.edu/" . Previous "bar" detectors attempted to use the (very tiny) relative displacement of atoms in a bar to detect gravitational waves.

In General Relativity the gravitational wave makes a part of the space-time curvature. It is of a geometrical nature.

In some other theories (RTG) the the gravitational wave is as physical as the other waves (photons) - it carries energy-momentum.

Thus two different interpretations.

Gravitational waves are physical in GR too, and they do carry energy-momentum. The http://en.wikipedia.org/wiki/PSR_B1913+16" system gives off gravitational waves that carry away some of the orbital energy of the system; the rate of orbital decay has been measured for more than three decades now, and matches the GR predictions.

EDIT: The http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_radiation.html" gives a good introduction to the subject.

 

[Bob_for_short]

This isn't quite correct...It's just that it's a *lot* harder...

Gravitons are not produced by one but by coherent packets.

It's not correct that gravitational waves can't cause relative displacement of masses...

Seeing a very long-wave character of GW in the Universe, it is unlikely to observe the relative displacement of masses in a laboratory scale, that is why the detection technique is not trivial.

Gravitational waves are physical in GR too...

No, because in a curved space-time there is no energy-momentum conservation. GW in GR are perturbations of the geometry.

 

[PeterDonis]

Gravitons are not produced by one but by coherent packets.

Seeing a very long-wave character of GW in the Universe, it is unlikely to observe the relative displacement of masses in a laboratory scale, that is why the detection technique is not trivial.

You're right, it's certainly not trivial; but again, in principle, as far as we know, there is nothing preventing the production of single high-energy gravitons (or indeed single gravitons of any energy); it's just very, very much harder than producing single photons. In practice, we don't know of any source in the actual universe that could produce single gravitons, or short-wave gravitational radiation; all the sources we know of should produce long-wave, reasonably coherent gravitational radiation, yes.

No, because in a curved space-time there is no energy-momentum conservation. GW in GR are perturbations of the geometry.

You have to be careful talking about energy-momentum conservation in GR. There are some senses in which it *is* conserved, and others in which it is not. The http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html" gives a good overview of the issues involved.

One of the senses in which energy-momentum *is* conserved in GR is the following: the energy-momentum carried off from a bound system by gravitational waves must equal the energy-momentum lost by the system itself. The binary pulsar is an example of this. So even though gravitational waves are perturbations of the spacetime geometry, they can still carry energy-momentum, and that energy-momentum does have to come from somewhere.