Quantum Fluctuations of Spacetime and of Energy

[Curious6]

I'm just confused on this point. The Uncertainty Principle states that there is always a minimum of uncertainty on small scales, leading to quantum fluctuations. However, can we say that quantum fluctuations of spacetime are quantum fluctuations of energy or are they different?

 

[marlon]

I'm just confused on this point. The Uncertainty Principle states that there is always a minimum of uncertainty on small scales, leading to quantum fluctuations. However, can we say that quantum fluctuations of spacetime are quantum fluctuations of energy or are they different?

they are very different. the quantumfluctuations that give rise to the ground state-virtual particle sea in QFT arise from the ZPE's of all known interactions, apart from gravity. So they come from the zero point energy of the strong force, the weak force and the electromagnetic interactions...

I don't really know about the incorporation of ZPE-gravition field fluctuations but that certainly is not a QFT related matter and quite speculative to my knowledge. Perhaps others will elaborate on this specific argument

regards

marlon

 

[Kruger]

I think they are different. Think of the ground state of a harmonic oscillator or the electromagnetic field. These ground states or vacuum states aren't zero cause of momentum-position uncertainty and not cause of energy time uncertainty. Energy time uncertainty gets important in the case of creation of virtual photons or other particles (applications in QED or vacuum polarisation, ...).

 

[marlon]

I think they are different. Think of the ground state of a harmonic oscillator or the electromagnetic field. These ground states or vacuum states aren't zero cause of momentum-position uncertainty and not cause of energy time uncertainty. Energy time uncertainty gets important in the case of creation of virtual photons or other particles (applications in QED or vacuum polarisation, ...).

Well yes but you can apply the energy-time uncertainty onto the non-zero ZPE.

Vacuum polarization really is no direct consequence of all this. It really is an effect that follows from the vacuum being filled with charged virtual particle pairs and their "electric dipole-like" behaviour when electric fields are present, eg the vacuum polarization tensor

marlon

 

[Curious6]

Interesting, it was just that I was speculating about the possibility of virtual particles arising due to the quantum fluctuations of spacetime and therefore pondering whether there is any relationship at all.

 

[Kruger]

@marlon: I'm in trouble now. The electromagnetic field is a collection of harmonic oscillators. Each oscillator has infinity lifetime. So how can this oscillator's represent virtual particles that have not infinity lifetime?

 

[marlon]

@marlon: I'm in trouble now. The electromagnetic field is a collection of harmonic oscillators. Each oscillator has infinity lifetime. So how can this oscillator's represent virtual particles that have not infinity lifetime?

Ahum ?

The zero point energy has a fixed value , ok ? Well during a period of time, this energy can become uncertain. This implies that it can rise or lower to another value. This energy difference (ie this fluctuation) corresponds to a virtual particle. That's all

Just think of the ZPE as one big oscillation and the uncertainties in energy correspond to little oscillations that are superimposed onto the big oscillation that respects the Einstein energy relation
marlon

 

[Kruger]

@marlon: Well, thanks. Now I got it.