[Dubbelosix (OP)]

Bryce DeWitt suggested a radical idea that has since became core of how we not only understand quantum mechanics, but how the same laws extend to cosmology. Related, when dealing with a wave, confined to a small region, will have corresponding small momentum, imposed also by the very small value of . He showed that only small systems through his equations, would exhibit wave behaviour. In fact, he predicted electrons would be the best particle to measure such wave properties. He later won the Nobel prize for his efforts, when he extended the wave nature of the electron to all particles.

It would be reasonable then, to investigate a universe when the radius is the deBroglie wave length . Though I object to full quantization of the gravitational theory of evolution prescribed by the Friedmann equation, I don't mind some partial quantization methods, such as identifying non-commutating variables. The following suggests such a proposal:





For those who are interested in string theory, there is a certain string uncertainty relationship for spacetime. Strings are said to vibrate, but equally, this may just be another way to speak about its wave function. In the limit of a universe beginning as a ''Planck wave'' which I will investigate in depth later, but for now takes the form:



The basic of idea of the preliminary approach is:




Later, I will do a more extensive research into these approaches and make a write up. For now, here are some external links




https://en.wikipedia.org/wiki/Matter_wave

https://www.thenakedscientists.com/forum/index.php?topic=71124.0

[Dubbelosix (OP)]

So this now leads to a more in-depth interpretation of the equations. Quickly, just to rehash, this replacement:



Isn't added in add hoc, it is simply the universes size corrected to the deBroglie wavelength. This is what justified the following relationships:



Going to the inequality equation extended into Friedmann cosmology we may understand something a bit deep within the structure of the relationships.



The contracted Einstein equations are just where is a stress energy density.  If one wanted to, it's completely legal to consider the effective density as a stress energy term. Replacing we can see subtle relationships between Einsteins equations and the deBroglie wave length



Should this be expected maybe? Is it surprising, maybe just to me, because it does give a possible link between the wave length and the response of spacetime curvature in its presence.

[Dubbelosix (OP)]

This equation has another important consequence. The physics of the ''small'' momentum, resulting in the reason why only small systems exhibit wave duality, must also result in gravity equally being small, encoded in . This rules out any strong gravity theory of particles, in which the strength of gravity increases on the particle scale. Of course, electromagnetism will dominate gravity by something of order magnitudes, one can only wonder if this muffles the effects of gravity out sufficiently that detection of it on the quantum scale will be near impossible to measure properly.

[Dubbelosix (OP)]

Thermal energy is related to equipartition as



This too would be encoded in the stress energy of a system.

The thermal  de Broglie wavelength is denoted as . When the thermal de Broglie wavelength is  smaller than the inter-particle distance, the gas can be considered to be a classical. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the inter-particle distance, quantum effects will dominate and the gas must be treated with Fermi or Bose statistics. Letting we get a thermodynamic interpretation of the non-commutation, a temperature-time relationship:



The phase transition obeys the following considerations:



and



(see wiki references). In my previous work, I investigated a pre-big bang phase which was indeed a type of condensed, liquid superfluid state, thinking of the configuration of the system in terms of the physics above may help pave the way for a better foundation towards those arguments/theories.


https://en.wikipedia.org/wiki/Thermal_de_Broglie_wavelength

[Dubbelosix (OP)]

In a post or two back, I said the curvature must be small to correspond to the small value on the RHS. That wasn't entirely the case, as I forget to include this following passage:

However, maybe the spacetime curvature does not need to be weak at all, remember, the LHS imposed by the inequality is either greater or equal to the RHS. The amount of deviation of spacetime curvature is not only related to the non-commutating variables, but must be encoded in the amount of stress energy density in spacetime.

[guest39538]

You seem to know a lot about waves, I wonder if you could please answer me a question?

If an electromagnetic ''wave'' was permeating through space, would it still be a wave or would it be a linearity (flat-line)?

My reason I ask is because surely   λ=Fµ and µ=0 in/of space.

Δ=µ

[Dubbelosix (OP)]

As noted before, if this had been a direct equality like deBroglies wavelength term



Then the wave length strictly applies to noticeable wavelengths for small systems. However, the equation above strictly said this is not the case, because the LHS could be greater or equal to the RHS. I suggested it must be linked to the uncertainties existing in the energy term - or in the case above, we have written the commutation related to the termperature. If the temperature are really high, for instance, would correspond to a large curvature. And if large temperatures in this equation corresponds to curvature, it must correspond to gravity, then there is a possible connection to this as well.

[fthomposon]

Dark matter is a smoothly distributed superfluid sea that is displaced by ordinary matter. What physicists mistake for the 'clumpiness' of the dark matter is actually the state of displacement of the superfluid dark matter sea. Particles of ordinary matter move through and displace the superfluid sea causing it to wave, including 'particles' as large as galaxy clusters. The superfluid sea is what ripples when galaxy clusters collide and is what waves in a double slit experiment. The superfluid sea displaced by ordinary matter relates general relativity and quantum mechanics.