# B Does a field's vacuum density violate conservation of energy?

#### TheQuestionGuy14

The vacuum density, or the zero point energy, of a field, doesn't change as space expands, it remains constant. But, aren't particles and virtual particles just fluctuations of these fields? Meaning as space expands, more and more particles are being created, violating conservation of energy?

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#### PeterDonis

Mentor
Global conservation of energy does not hold in an expanding universe. Global conservation of energy only holds in spacetime with a timelike Killing vector field, and an expanding universe does not have one.

#### TheQuestionGuy14

Global conservation of energy does not hold in an expanding universe. Global conservation of energy only holds in spacetime with a timelike Killing vector field, and an expanding universe does not have one.

Does this mean there is more particles in the universe today than there was yesterday? Or is the energy being created not related to particles?

#### PeterDonis

Mentor
is the energy being created not related to particles?
The "energy being created" is due to a nonzero cosmological constant, which is not "related to particles".

#### Demystifier

2018 Award
Global conservation of energy does not hold in an expanding universe.
More precisely, global conservation of energy of matter does not hold in an expanding universe. But if energy of the gravitational field is added too, then total energy is conserved. The reason why such a view is not often used is the fact that such a view cannot be made general covariant, except in a trivial sense. http://de.arxiv.org/abs/1407.8028

#### A. Neumaier

But if energy of the gravitational field is added too, then total energy is conserved.
.... and is always exactly zero, hence uninteresting.

#### Demystifier

2018 Award
.... and is always exactly zero, hence uninteresting.
Well, the vanishing of the Hamiltonian is a consequence of the time reparameterisation invariance, which is very interesting to me.

#### A. Neumaier

Well, the vanishing of the Hamiltonian is a consequence of the time reparameterisation invariance, which is very interesting to me.
But time reparameterisation invariance is a pphnomenon quite different from a conservation law, which was the subject of my remark.

#### Demystifier

2018 Award
But time reparameterisation invariance is a pphnomenon quite different from a conservation law, which was the subject of my remark.
It's different, but very related.
time rep. invariance $\rightarrow$ vanishing total Hamiltonian $\rightarrow$ conserved total Hamiltonian

#### A. Neumaier

It's different, but very related.
time rep. invariance $\rightarrow$ vanishing total Hamiltonian $\rightarrow$ conserved total Hamiltonian
Sure, but the latter is as uninteresting as the conservation of total force following from Newton's third law. In both cases, only the premise is interesting, not the conclusion.

#### TheQuestionGuy14

The "energy being created" is due to a nonzero cosmological constant, which is not "related to particles".
Isn't the cosmological constant interpreted to be the zero point energy of all the quantum fields? Doesn't that mean as space expands, more electric field is being created, more electromagnetic field etc. Doesn't that mean more particles? Sorry if it's a dumb question.

#### PeterDonis

Mentor
Isn't the cosmological constant interpreted to be the zero point energy of all the quantum fields?
That's one hypothesis, but we don't know if it's correct.

Doesn't that mean more particles?
No. The fields are in their vacuum state, which means no particles.

#### TheQuestionGuy14

That's one hypothesis, but we don't know if it's correct.

No. The fields are in their vacuum state, which means no particles.
Oh right, that makes sense. But don't virtual particles fluctuate from the vacuum state? So there's more virtual particles

Also, don't virtual particles affect real particles? Meaning if you had a closed system, and more and more virtual particles were appearing, the total energy of the real particles would change.

#### PeterDonis

Mentor
don't virtual particles fluctuate from the vacuum state?
No. See this Insights article:

#### TheQuestionGuy14

No. See this Insights article:

Oh ok. Thanks. I read it, I understand where the myth came from, but I still don't quite understand, where virtual particles actually come from then?

Real particles are still high energy parts of a field though right?

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#### PeterDonis

Mentor
I still don't quite understand, where virtual particles actually come from then?
The other Insights articles linked to from that one explain what "virtual particles" actually are and how the concept is used in quantum field theory. Basically, "virtual particles" are internal lines in particular Feynman diagrams. They do not correspond to anything observable and are only used in the particular mathematical formulation, perturbation theory, that uses Feynman diagrams.

Real particles are still high energy parts of a field though right?
Real particles are excitations of the field above its ground state, yes.

#### TheQuestionGuy14

The other Insights articles linked to from that one explain what "virtual particles" actually are and how the concept is used in quantum field theory. Basically, "virtual particles" are internal lines in particular Feynman diagrams. They do not correspond to anything observable and are only used in the particular mathematical formulation, perturbation theory, that uses Feynman diagrams.

Real particles are excitations of the field above its ground state, yes.
Oh ok, thank you. Since virtual particles are purely mathematical, what really causes the electromagnetic force and other forces? People usually say the virtual photons are the force carriers.

#### PeterDonis

Mentor
Since virtual particles are purely mathematical, what really causes the electromagnetic force and other forces?
The electromagnetic field. There is nothing wrong with the general idea that fields like the EM field transmit forces. You just have to be aware that the more specific idea that the way fields like the EM field transmit forces is by exchanging virtual particles has limited usefulness and can be misleading if taken too literally.

#### TheQuestionGuy14

The electromagnetic field. There is nothing wrong with the general idea that fields like the EM field transmit forces. You just have to be aware that the more specific idea that the way fields like the EM field transmit forces is by exchanging virtual particles has limited usefulness and can be misleading if taken too literally.
Thank you, I appreciate the help. Just one last question though, what exactly is a quantum fluctuation then? A quantum fluctuation is the temporary change of energy in an area of space, but the wiki says it's the creation of virtual particles that causes this energy fluctuation. What is it really then?

#### haushofer

Virtual particles are conceptual aids to describe quantum fluctuations. Quantum fluctuations are just stochastic fluctuations of the field values.

#### haushofer

Mmm, conceptual aids...pun non intended for those abhorred by the usage of virtual particles in popular literature.

#### DarMM

Gold Member
Thank you, I appreciate the help. Just one last question though, what exactly is a quantum fluctuation then? A quantum fluctuation is the temporary change of energy in an area of space, but the wiki says it's the creation of virtual particles that causes this energy fluctuation. What is it really then?
Quantum Mechanics is statistical, so quantities have average values but deviations from that average can be observed. Like rolling a dice the average is 3.5, but you can get 1 or 6. Similarly when you observe quantum fields you have an average/expected value but you can observe values quite a bit away from this average.

These deviations from the average are called "fluctuations". They aren't caused by virtual particles they're just an intrinsic element of the theory since it involves probabilities.

#### A. Neumaier

Thank you, I appreciate the help. Just one last question though, what exactly is a quantum fluctuation then? A quantum fluctuation is the temporary change of energy in an area of space, but the wiki says it's the creation of virtual particles that causes this energy fluctuation. What is it really then?
It is nothing temporal, Wikipedia is poor on this topic.

#### PeterDonis

Mentor
what exactly is a quantum fluctuation then?
It is a sloppy and misleading way of describing the fact that, if you measure a quantum system using an observable that the system is not in an eigenstate of, the measurement result will be uncertain.

the wiki says
Wikipedia is not a good source for something like this.

"Does a field's vacuum density violate conservation of energy?"

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