# Graviton & Conservation of Energy etc.

1. May 29, 2010

### jaketodd

If an object absorbs a graviton, can it emit the same graviton? I would think that the gravitational energy would have to be transmitted to the object and if the object emitted the graviton again, it would lose the effect the graviton had on it. But I read somewhere that gravitons are not constrained by the conservation of energy. Please help.

If it can re-emit the graviton, which direction would it be emitted in? The same direction as when it was coming in? Random direction?

Thanks,

Jake

2. May 30, 2010

### tom.stoer

The whole concept of gravitons may be questioned as it is not clear if this concept applies in all domains of quantum gravity.

If one uses Feynman rules to calculate scattering of matter with gravitons I expect that the Feynman rules force energy-momentum conservation at each vertex; just like in QED, QCD, etc.

Unfortunately in a general spacetime geometry the whole concept of energy becomes invalid. The mathematical reason is that in dynamical spacetimes there is not enough symmetry to covariantly define energy (as a zero-component as a four vector) at all. This applies already to the standard Friedman Universes.

3. May 30, 2010

### jaketodd

So according to Feynman, QED, QCD, there is conservation of energy but there isn't even gravitational energy in Relativity? What about acceleration in Relativity; wouldn't that produce energy in spacetime? And since gravity is acceleration, then wouldn't that cause the curvature of spacetime to produce energy, in a sense, for something in it?

I really want to know:
If the graviton was added to the standard model as a boson, would it have to conserve energy?

Would a graviton boson transfer its gravitational energy as acceleration of something it hits and go away, not to be re-emitted?

Thanks,

Jake

Last edited: May 30, 2010
4. May 30, 2010

### ensabah6

If that is the case, what would be the ramifications for string theory's claim to be a QG based on spin-2 graviton?
Since GR predicts gravity waves, and in QM all waves are also particles, doesn't there have to be a particle?

5. May 31, 2010

### tom.stoer

There is local conservation of energy-momentum density, but in general cases no unique global notion of energy.

Yes, energy for a particle is a reasonable concept, but not energy of a finite volume of spacetime

Locally yes, globally not. (this is not an effect of the graviton but of general relativity; you don't need to quantize gravity in order to see these problems of global energy-momentum conservation).

The problem is the following. The Einstein equation reads (symbolically)

G = T

where G is the 4*4 Einstein tensor of spacetime and T is the 4*4 energy-momentum density of the SM fields. Energy-momentum conservation reads

(DT)a = 0

Where D is a covariant derivative and a is a spacetime index.

What one usually does in order to derive a global conserved quantity is to take this equation, perform an 3-space integration and derive a quantity E for which

dE/dt = 0

Unfortunately this is not possible here as the covariant derivative D adds new terms which do not allow to define the integral in the usual way.

Have a look here: http://relativity.livingreviews.org/Articles/lrr-2009-4/ [Broken]

Last edited by a moderator: May 4, 2017
6. May 31, 2010

### tom.stoer

First of all string theory does predict the existence of a graviton, but afaik is does so only in a perturbative manner. Afaik it is not clear if there is a reasonable non-perturbative formulation of string theory.

The concept regarding quantization of waves resulting in particles is nice but not always sensible. It is by no means clear if quantization of gravitational waves using the standard QFT approach is reasonable. There are theories of quantum gravity where gravitons are by no means elementary particles but only derived, emergent concepts based on new underlying structures not familiar from quantum field theory.

7. Jun 4, 2010

### kaksmet

Just a note: Think it is interesting that both QFT and General Relativity violates energy conservation, QFT during small times and General Relativity over large regions.

8. Jun 4, 2010

### tom.stoer

This is a misconception.

GR does not violate energy conservation over large regions. It simply does not allow for a well-defined global notion of energy. There is a big difference between "enery is not conserved" and "there is no energy at all". In addition the local conservation law is a much stronger requirement than a global one.

QFT (in flat spacetime basede on SR = w/o GR) does not violate energy conservation either. Again there is a local conservation law.

$$\partial_\mu T^{\mu\nu} = 0$$

One can derive a Hamiltonian

$$H = T^{00}$$

which is conserved.

$$\partial_0 H = 0$$

For each eigenstate of the Hamiltonian the energy is conserved as well

$$H|\psi> = E|\psi>$$

$$\partial_0 E = 0$$

In every Feynman diagram at each vertex 4-momentum is locally conserved. However the virtual particles are "off-shell", that means that a particles with rest mass $$m$$ appears in vacuum fluctuations as a virtual particle violating the equation

$$E^2 - \vec{p}^2 = m^2$$

Nevertheless energy $$E$$ and momentum $$p$$ are conserved in these vacuum fluctuations.

Last edited: Jun 4, 2010
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