Pick, Flick And A Flux - A Summary Of Vacuum Fluctuations

[Dubbelosix]

The Ricci curvature is related to the d'Alembertian operator (aka. the box operator) given in literature in first derivative as

 

R = g^μv R_μv = g^μv ∇_μ∇_v = g^μv □_μv

 

Will be a relationship to be remembered for future reference because we will enter physics in this work respectively in terms of the square of the tensor R^2 itself. The square of the curvature holds a number of important possible interpretations which will not be discussed in this work.

 

The Sakharov fluctuation field contribution to the background curvature is given by a correction term

 

L = ℏc k ∫ dk ⋅ R + ℏc ∫ dk/k ⋅ Rⁿ

 

In which the density of those modes are

 

ρ = ℏc dk ∫ dk³ = ℏc R²

 

And is specifically non-zero from the postulation of quantum field theory of ground state fields (keep in mind the existence of a free vacuum is an experimentally-falsified assumption of classical physics). For instance we can detect those ground state fluctuations even inside of vacuum chambers when they are supposed to be empty according to classical mechanics. Reinterpreting the derivative or aka. the connections of the gravitational field Rⁿ as a second derivative formula satisfying

 

Rⁿ f(x) = d/dx ⋅ (d/dx) f(x)

 

This defines the usual relationship, albeit, we redefine the function of the space derivative as the wavelength respectively

 

d²/dx² λⁿ = n(n - 1) ⋅ λ^(n - 2)

 

The term additionally ℏc is called the Planck charge, but it can be considered related to the rest gravitational charge as approximately related to the wavelength as

 

Gm² ≈ ℏc ≈ Mc² ⋅ λ

 

Just as the energy is obtained from the wave number

 

Gm² k ≈ ℏc k ≈ mc²

 

They may be considered the reciprocal of each other in this sense. The Langrange density is in terms of those wave length approximations as

 

L = (mc² ⋅ λ(A)) k ∫ dk ⋅ R + (mc² ⋅ λ(B )) ∫ dk/k ⋅ Rⁿ

 

If we can define the connections as

 

g^μv □_μv = ∇^μ ∂_μ √-g ∇^v ∂_v

 

□_μv = [∇^μ, ∇^v] = (∂_μ + Γ_μ)√-g(∂_v + Γ_v)

 

More compactly we wish to think of the connections related to the scalar curvature as the derivatives,

 

R = d²/dx²

 

And derive from using the usual relationship,

 

R² λⁿ = n(n - 1) ⋅ λ^(n - 2)

 

Then the same rule should manifest when considering the structure of Sakharov's equation. For Rⁿ = R² the gravitational correction takes on the form as would be expected from the Sakharov equation as

 

L = ℏc k ∫ dk ⋅ R + ℏc ∫ dk/k ⋅ R²

 

With the last term made from the wave number density,

 

≈: ℏc dk ∫ dk³ ≝ ℏc d(log k) R²

 

If we notice that in the last term it is ℏc that encodes the wavelength then

 

L =... + mc² ∫ dk/k ⋅ R² λⁿ = ... + mc² ∫ d(log k) ⋅ n(n - 1) ⋅ λ^(n - 2) + C

 

*I assume there is nothing wrong with taking the scalar curvature and writing it as the derivatives as this is freely done in many quantum gravity papers.

 

While it is written in terms of constants concerning ℏc, the energy of a system varies with the wavelength and respectively so does the charge (or mass-energy content) of the system, from the observables of the system it does not always appear to be a constant but something that can vary with length and certainly velocity as found in relativity (ie. Moving objects appear more massive and equally moving objects experience the length contraction) . So here, the rest energy always remains the same but a dynamic wavelength must mean the velocity is variable naturally for any system with a mass,

 

ℏv ≈ Gm² ≈ mc² λ(x, v)

 

*maybe this should be less than a surprise since many of the Planck parameters are simply too fundamental for even nature, for instance, the Planck mass term may appear to have no particle analogue. The Planck mass turns out to be a quantity however very important in black hole dynamics. The Planck mass equally is a measurement independent of the density, a system does not need to be a black hole to have a Planck mass as it is roughly equivelent to the same mass as a human eyelash.

 

How does a wavelength depend on position? Moreover can the wavelength depend on the velocity? The short answer is yes, since the wavelength can have a position so long as both the wave and the particle coexist. Equally the particle with greater velocity will have wavelengths corresponding to their appropriate energy. In quantum mechanics, it is argued that the sense of position is in fact lost when dealing with waves, but this really is a strict definition because it seems largely an assumption since pilot waves can easily explain how something appears to be a wave and a particle depending on whether a locator detects it. Even if the particle model was to be abandoned, there is nothing in the books saying that such a position for a wave cannot exist, but likely a position is something that can fluctuate around the absolute square of the wave function. This slight smearing gave rise to an outdated terminology known as the Planck cell, an idea in which a particle cannot exist in quantum mechanics, but instead the wave function smears it into a cell like system. It seems though we should say a little on the phenomenon regarding extended objects vs. particle like objects, especially when we attempt to measure the "shape of electrons" because what we actually measure is a charge distribution in space. To understand why it causes such a headache requires that we delve into the uncertainty principle and what it really means.

 

However, it seems likely also we may need to accept the wave function may be in all regards gravitational waves interacting at the subatomic and atomic scales and possibly even nano scales where quantum tunnelling is observed. It was suggested in the event of discovering gravitational waves that even the detector is capable of producing the gravitational wave, so even the instruments we use to detect them are capable of creating them. This sort of interaction would hold significant importance when considering the true nature behind the wave function. Even inside an atom, it is possible gravitational waves can move electrons between energy levels from a perturbation involving the absorption or emission of radiation. Funnily it would also explain why we do not see a wave function when we attempt to locate a particle but instead we can only indirectly measure small disturbances it leaves in its wake. It would also mean the wave itself is not physical but a response of the medium with respect to physical interactions, similar to how matter affects space by curving it. In a way, the gravitational wave could easily become the pilot wave because matter tells space how to curve whereas space is responding by telling it how to move. I wrote out a mathematical basis for a gravitational wave function and ended up realising that deBroglies empty wave prediction would turn out to be a not so empty gravitational wave. But when we speak of empty in this sense, we should think of it as being empty of gravitons or any detectable particle with energy but not devoid of the fluctuations which makes up spacetime, which certainly is not empty.

 

A particle is never at rest, no matter how cold we make the system from any ideal vacuum chamber. And the existence of virtual particles has been pretty much tested with good accuracy that there is no such thing as a true classical vacuum, indeed, quantum mechanics insists that these little particles of energy should exist all the time. The fact that a particle is never at rest is often recited to be related to the uncertainty principle, but as we explore the following we will see that the uncertainty principle doesn't mean that the system acts in purely random ways but instead is a limitation of the information we can extract from a system. Sadly in our experimental prowess, we can only get certain information at the expense of other information... A good example comes from the identity

 

d/dx f(x)

 

One could use larger neighborhoods around the point of location to get a better estimate of the derivative at x, which would have to trade off accuracy against the fact that larger neighborhoods are also more likely to include unrelated surface details. While certain information in physics is often traded at the expense of knowing another, it has lead to a crisis of understanding the fundamental world, adding an aspect of mysticism allowing physicists to ignore that we live in a macroscopic world where cause and effect holds reality together. Even quantum entanglement has caused headaches over the years, adding a new type of mysticism concerning how particles at a distance is affected by an observation. Einstein was right in my opinion, quantum mechanics is incomplete and a proper understanding may require the non local hidden variable theory, something which even Bell himself endorsed. Even if pilot waves turned out to be a complete waste of time, it is the closest theory (in my opinion, see also analogue experiments depicting the existence of pilot waves in nature) that we have had that has been capable of making sense of the apparent contradictory nature of the results and sure enough, when the scientist thinks of a particle as a wave and a wave as a particle, contradictions arise in a particular set of theories classed as being continuous and discrete. It was until recently that it has been shown a system can be continuous and discrete at the same time. Again, the choice of model really depends on any progress being made because contradictions should not arise in a theory and if it does, it is usually a breakdown of an understanding somewhere.

 

If there is no such thing as a system truly at rest, position itself becomes ill defined and even then you have to ask what position do we speak of? I have a well defined classical position on the X-Y coordinate but I consist of many systems, is that many particles, waves or both? (1) I would render the answer as both and posit that the particle and wave are inexorably linked and exist side by side but this doesn't answer the question of how to define the position. So why should both exist? Because the double slit experiment literally shows us that both exists and the choice to observe the particle in a certain position has to be impossible simply because there is no position of rest. To give up any notion that there is no such thing as a well defined position does not need to boil down to wave mechanics alone - if the wave was absent, would the particle no longer be able to move?

 

The uncertainty principle isn't even as uncertain as it used to be, with technology becoming more accurate we have experiments showing that the uncertainty principle as given by Heisenberg is violated quite often which seems to be telling us that something deterministic is happening at these scales. Even the double slit experiment when reduced to a single particle beam still displays a diffraction pattern over a given finite length of time, an age old question since this was discovered was why, and how? How did the non-entangled particle know where the previous particles had landed on the screen to create the interference pattern? This is still an unresolved question that would add great insight if ever rectified and may have something to do with the measuring apparatus acting itself as a quantum system.

 

There is also another possibility to why particles are always in motion, simply because they are constantly interacting with the virtual particles. This is the same kind of argument which preserves all the requirements, such as detection by an observer/fluctuation causing uncertainty. In fact this kind of theory arose a while back when deBroglie, later Schrodinger and Dirac believed that the electron was a photon moving in a zig zag path as to give the illusion it had a mass. Even though Dr. Wolf later gave up this idea, it still seems appealing for a number of reasons that would be interesting to get into at a later date.

 

(1) - Even though my body consists of many particles, my body is constantly filled with entangled systems. Systems that naturally collapse is known as decoherence, demonstrates that consciousness is nothing special when it comes to the collapse of a wave function, assuming anything collapses at all. Interestingly however, an entangled system acts like one system, and it is perhaps here we may see how a collection of particles we call the brain may give rise to the self, from a collection of entangled particles acting as one system. This would give a natural explanation as to why we cannot detect consciousness in any single region of the brain.

Edited January 28, 2020 by Dubbelosix

[Dubbelosix]

You missed a possibility ref photons and wave particle duality etc  :shocked:  all the ideas above are connected and all are correct to a certain extent, they are simply describing different aspects of the same complex motion. 

 

I do not think anyone has a clear picture of how the photon moves through space, it can be modeled as having both wave and particle like properties, but its movement through space might be better described by bohemian mechanics, and pilot waves.  

 

We know Virtual particles can and do acquire energy from other particles momentarily, before giving up the energy to other virtual particles around them. 

 

I view the photon rightly or wrongly as moving via emission and absorption through a soup of virtual particles giving the appearance of having frequency. Which I think is in line with the pilot wave version of the double slit experiment https://www.quantamagazine.org/pilot-wave-theory-gains-experimental-support-20160516/

 

The speed of sound in air is limited to 340m/s as the medium becomes more dense it speeds up. The speed of light through the vacuum is 2.98x10^8m/s as the medium of virtual particles becomes more dense away from mass it speeds up, but the measured lengths change as well maintaining a constant c.

 

Could a pilot wave be described as a shock wave following a sonic boom.

 

Is it possible that information ref a physical pilot wave exists outside space time, whilst the point energy of the photon rides the wave but exists in space time or vice versa.? 5 dimensional pilot wave thingy sort of thing .

 

You are good at these questions, but I do not profess to have all the answers, only that some physics was so ridiculous the physicists must have been too high at the time. As far as something outside spacetime, it is not very well defined and general relativity makes a statement that nothing can exist outside of spacetime.

 

If it is any help, I view the photon as a wave inside the medium, or is the medium and things which detect this are bradyons in nature. The fact a photo has a finite speed funnily within deBroglies pilot wave, it was shown mathematically even a photon should have a mass due to coherence within his theory... But the idea lacked proper experimental varification... And the mass of a photon would be ridiculously small anyway as to detect it would be difficult.

[Dubbelosix]

Now that it has been proven that non locality is a fact, by separate experimenters leaving no loop holes is the Copenhagen interpretation even viable anymore.

 

The Bohemian approach seems more likely. I was pondering your point 1 at the bottom of the post whilst stuck in a traffic jam consisting mostly of cows!. Various analogies popped into mind. None locality would seem to support a instantaneous conveyor/conduit connecting two points in space. The photon being a particle on the conveyor/conduit restricted to c. 

 

Your point 1 seemed a little religious, and since I have buddhist/pantheist sympathies https://puredhamma.net/quantum-mechanics-buddhism-buddha-dhamma/quantum-mechanics-a-new-interpretation/photons-are-particles-not-waves/ The links are good reading.

 

Yes non local pilot waves is the Bohmian extension. It was even created before we knew about non locality. It's actually the only theory which can make sense of the physics at hand.

[Dubbelosix]

Does it follow then that there is another dimension that is none spacial that can connect different points in space directly. Perhaps limited to transmitting information such as inertia/spin etc

Maybe, in a way, parallel universes try do the same by explaining wave functions as signatures of other interactions somewhere else.

[Dubbelosix]

Written through tex command now looks better, easier to follow https://physics.stackexchange.com/questions/527749/sakharov-gravitational-correction

[Dubbelosix]

Yes this is it, the sort of idea we have in place. It's not perfect just yet but that is because no one is looking into the elasticity of space properly resulting in either an absorption or emission of electromagnetic fluctuations.

[Dubbelosix]

Care to discuss any point in the paper?

 

Of course but I need to read the whole thing very carefully because if the paper holds merit like I expect it does, then I will need to read more by this author.

[Dubbelosix]

The paper is fine, but could use a lot more detail.

[Dubbelosix]

We need I thought, to consider the operator value of the gravitational potential in order to quantize those fluctuations according to Bogoliubov transformations. For a while I had arguments with a freshman out of university that their understanding on these transformations was just a mathematical process in which I explained very clearly, the quantization of the potential means we are dealing with real particles, whether we call them virtual or not. The word vurtual has misled a lot of physicists to think somehow they are not real.

[Dubbelosix]

Or just a flux... Everything boils down to the fluctuation, even the long lived fluctuation becomes what we call observable matter.

[Dubbelosix]

It's because I have been writing very hard... Interesting conversations require time, and sometimes we are not always the best at explaining things, but since I have written an article, I will get to your questions tomorrow. Well, I'll try.