I Are the energy fluctuations in space real or virtual?

[jcap]

Heisenberg's uncertainty relation says:
$$\Delta x \Delta p \ge \hbar$$
If we assume a massless quantum object then we have the relationship $\Delta E = c\Delta p$ so that the above uncertainty relationship becomes
$$\Delta E \ge \frac{\hbar c}{\Delta x}.\tag{1}$$
I understand that if we have a real system with size $\Delta x$ then there is necessarily an uncertainty in the real energy, $\Delta E$, given by Equation(1).

But this relationship is commonly applied to otherwise empty space in order to argue that there is a fluctuation of energy $\Delta E$ in each interval of space $\Delta x$. As we take $\Delta x$ to be arbitrarily small then $\Delta E$ becomes arbitrarily big. If we apply a cutoff at the Planck scale then general relativity implies that space should expand exponentially at an enormous rate which is not observed (the cosmological constant problem).

But surely in the analysis regarding empty space there is no real object with size $\Delta x$ and therefore no real energy fluctuation $\Delta E$?

Instead it seems to me that the arbitrary interval of space of size $\Delta x$ is a virtual construct so that by the uncertainty principle it should only lead to a virtual energy fluctuation $\Delta E$.

Surely such a virtual energy fluctuation cannot be expected to lead to any real effects like exponential space expansion?

P.S. However I could imagine differences in virtual energy leading to real effects.

 

[Jilang]

I would ask what is confining it in the first place.

 

[bhobba]

The energy of empty space is zero by a process called Normal Ordering:
https://en.wikipedia.org/wiki/Normal_order

Forget what you read in popularization's - you can only find out about Quantum Field Theory by reading decent textbooks on it.

That empty space has energy is a very common but incorrect misconception.

Please, do not post this or that link that says otherwise. They are wrong - or rather sometimes physicists speak loosely.

If you want to argue it, mods like me will keep a careful eye on it to ensure it doesn't develop into a long thread along the lines of - but so and so says - yes but he is speaking loosely - its actually zero. Such threads really don't go anywhere and are just long meandering reads of no actual value.

And to ensure you don't bring up the Casmir Effect, be aware it's explanation does not involve vacuum fluctuations:
https://arxiv.org/abs/1605.04143
https://arxiv.org/abs/hep-th/0503158v1

Thanks
Bill