# Zero-Point Energy and Gravitational Influence

• I
• frankinstien
In summary, attempts to identify the energy of the vacuum with the cosmological constant have been made, but our current understanding of quantum field theory does not provide a way to accurately calculate this energy density. Estimates suggest that it should be much larger than the observed value, indicating that there is still much we don't understand about this concept.
frankinstien
TL;DR Summary
Given that Zero-point energy is everywhere wouldn't it have a gravitational influence?
I ran into another article demonstrating the Casimir effect and it hit me that zero-point energy is real mass and therefore would have a gravitational influence on our universe. Is there something wrong with this idea, am I missing something?

frankinstien said:
Summary: Given that Zero-point energy is everywhere wouldn't it have a gravitational influence?

I ran into another article demonstrating the Casimir effect and it hit me that zero-point energy is real mass and therefore would have a gravitational influence on our universe. Is there something wrong with this idea, am I missing something?
Energy is not mass but it IS part of the stress energy tensor which is what determines gravity in GR:

It is tempting to try to identify the energy of the vacuum with the cosmological constant, in fact. They should behave similarly. But as I understand it nobody really knows how to do the maths and our best plausible estimates suggest that vacuum energy density should be around ##10^{120}## times higher than the observed upper bound on the cosmological constant.

So, in summary, maybe. But if so there's something we don't understand.

frankinstien
Moderator's note: Thread moved to the Beyond the Standard Model forum.

frankinstien said:
I ran into another article demonstrating the Casimir effect

frankinstien said:
zero-point energy is real mass and therefore would have a gravitational influence on our universe
As @Ibix notes, our best current understanding is that our universe has a positive cosmological constant, because the expansion of our universe is accelerating, and that is what the gravitational influence of a positive cosmological constant looks like.

An intuitively natural way of accounting for the positive cosmological constant is that it is an energy density associated with vacuum, which is similar conceptually to what you are calling "zero point energy"; however, attempts to calculate the value of this energy density based on our best current understanding of quantum field theory either give an infinite answer or give an answer that is some 120 orders of magnitude larger than the actual value we observed. So while there is probably something here, it is not something we currently understand very well.

bhobba and frankinstien
frankinstien said:
I ran into another article demonstrating the Casimir effect and it hit me that zero-point energy is real mass and therefore would have a gravitational influence on our universe. Is there something wrong with this idea, am I missing something?
Yes, and this is a problem creating a theory of quantum gravity.

frankinstien said:
I ran into another article demonstrating the Casimir effect

Which has nothing to do with zero-point energy.

Ibix said:
It is tempting to try to identify the energy of the vacuum with the cosmological constant, in fact. They should behave similarly. But as I understand it nobody really knows how to do the maths and our best plausible estimates suggest that vacuum energy density should be around ##10^{120}## times higher than the observed upper bound on the cosmological constant.

So, in summary, maybe. But if so there's something we don't understand.
There's always something we don't understand, the universe is a mysterious monster to be observed...

More stuff to learn, an endless quest...

frankinstien
I am being a little bit philosophical here...

frankinstien said:
I ran into another article demonstrating the Casimir effect and it hit me that zero-point energy is real
Casimir effect does not imply that zero-point energy is real.
https://arxiv.org/abs/1702.03291

PeroK and bhobba
QFT is an area I would say I only have intermediate knowledge of to the level of Student Friendly Introduction to QFT. Highly reccomended BTW as an approachable introduction after you have done QM:

http://www.quantumfieldtheory.info/

I am endeavouring to work up to Wienberg, but something always seems to come up.

Anyway, my understanding for several years now is normal ordering solves the issue ie there is no ZPE:

As explained above, you would want normal ordering, so Wicks's Theorem can be applied. No Wicks Theorem - no Feynman Diagrams - but those with a better understanding than I can comment on that - the books I have read always use normal ordering and Feynman Diagrams.

Thanks
Bill

Last edited:
bhobba said:
Anyway, my understanding for several years now is normal ordering solves the issue:
It's not that simple. See the paper in #9, the paragraph after Eq. (53).

bhobba
bhobba said:
As explained above, you would want normal ordering, so Wicks's Theorem can be applied. No Wicks Theorem - no Feynman Diagrams - but those with a better understanding than I can comment on that - the books I have read always use normal ordering and Feynman Diagrams.
There is also a version of Wick theorem without normal ordering. That creates additional Feynman diagrams, which however just change the phase of the S-matrix amplitude, without physical consequences.

PeroK and bhobba
Ibix said:
It is tempting to try to identify the energy of the vacuum with the cosmological constant, in fact. They should behave similarly. But as I understand it nobody really knows how to do the maths and our best plausible estimates suggest that vacuum energy density should be around ##10^{120}## times higher than the observed upper bound on the cosmological constant.

So, in summary, maybe. But if so there's something we don't understand.
In a recent paper I argue that the quantum vacuum energy does not contribute to cosmological constant if the diffeomorphism invariance of general relativity is emergent, rather than fundamental. https://arxiv.org/abs/2301.04448

ohwilleke, PeroK and bhobba
Demystifier said:
There is also a version of Wick theorem without normal ordering. That creates additional Feynman diagrams, which however just change the phase of the S-matrix amplitude, without physical consequences.
Now I noticed that the above was slightly wrong. There is no version of Wick theorem without normal ordering. There is a version without time ordering, but that's irrelevant here. What I really meant is that the interaction Hamiltonian can be taken either with or without normal ordering. Taking it without normal ordering creates additional Feynman diagrams, the bubble diagrams, which just change the phase of the S-matrix amplitude, without physical consequences.

I'm not sure if I should reply, as the OP has gone, and what he thinks of as ZPE isn't ZPE and the thread as started winding, but....

In a material system, ZPE gravitates like other forms of energy. If it didn't, you'd see Eotvos-type effects.

ZPE of vacuum is a very woolly concept, and I don't think there is a good answer for this. I'm not even sure there is a question

ohwilleke and bhobba

## 1. What is zero-point energy?

Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have. It is the energy that remains in a system even at its lowest possible energy state, due to the uncertainty principle in quantum mechanics.

## 2. How is zero-point energy related to gravitational influence?

Zero-point energy is believed to have a direct influence on the gravitational force between objects. According to some theories, the fluctuations in zero-point energy can create small changes in the curvature of space-time, which in turn can affect the strength of gravitational pull between objects.

## 3. Is zero-point energy a real phenomenon or just a theoretical concept?

Zero-point energy is a real phenomenon that has been observed and measured in various experiments. However, our understanding of it is still limited and there are ongoing debates and research about its true nature and properties.

## 4. Can zero-point energy be harnessed for practical use?

There is ongoing research and experimentation on how to harness zero-point energy for practical use, such as in energy generation and propulsion systems. However, it is still a highly theoretical and complex field, and there are many challenges and limitations to overcome before it can be effectively utilized.

## 5. What are the potential implications of zero-point energy and gravitational influence in our understanding of the universe?

If we are able to fully understand and harness zero-point energy and its relationship to gravity, it could potentially lead to a major shift in our understanding of the universe and the laws of physics. It could also open up new possibilities for space exploration and energy generation, among other things.

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