According to Crowell, vacuum fluctuations probably can be observed - the issue is a fundamental problem with our technology to do so. I am in agreement with him, I believe the short timescale existence of the fluctuation should not be taken to mean they cannot be described by a Hermitian matrix. If we actually had the technology to probe space to lengths either very close or at the Planck scale, we would be able to probe the same amount of time they exist for and effectively see them in progress, albeit for a short fraction of a fraction of a fraction of a second. The fact we do not deal with off-shell particles in quite the same manner as normal matter has troubled me for a while - one example is that the off-shell (virtual) particle does not obey the same mass-energy relationships as normal matter. When investigating a fundamental length from the Einstein field equations in the context of the uncertainty principle, I arrived at the following description: \(\frac{N}{\delta L^2_P} \geq k <\frac{Gm}{\delta L}> \mathbf{n}m\) (1) The LHS is (just a quantum corrected) contracted Einstein tensor \(G\) which can also be seen from the context theoretically as a string theory uncertainty as (Yoneya 1987, 1989, 1997), \(\delta L\ c\delta t = \ell^2_P\) (2) What I deducted from my investigation is that fluctuations arises in the quantum operator form of the gravitational potential \(<\frac{Gm}{\delta L}>\) (3) And that the more you probe down to the inverse Planck area will result in large fluctuations in expression (3). We must assume that the Planck area is observable and if this is the case as I suspect it is, virtual particles will also been observed at around the same scale if not, exactly this scale. Equation (1) is equivalent to a fluctuation with a proportional curvature \(\delta L_P \propto \frac{L}{L^3_P}\) (4) Interestingly, Noether's theorem is what's called an ''on-shell theorem'' and if virtual particles do correspond to vacuum energy, then we won't be able to conserve energy in a universe, yet for another reason. ref. https://books.google.co.uk/books?id=w8ZoDQAAQBAJ&pg=PA6&lpg=PA6&dq=do fluctuations have a temperature in spacetime?&source=bl&ots=CS7Oe7LJ7U&sig=-x4h21-AsDMrjTRr2-FsckVg9is&hl=en&sa=X&ved=0ahUKEwi0nJKcn9LRAhWMDcAKHY73D_oQ6AEIKDAC#v=onepage&q=do fluctuations have a temperature in spacetime?&f=false
Bingo! Also worth noting if we had such technology to probe at the quantum/Planck scale, we maybe able to validate or otherwise string theory or one of its derivitives. Please Register or Log in to view the hidden image!
It will be a very sensitive apparatus whatever we come to use and may very well be a hundred years from now.
