Tuesday, May 20, 2014

Spacetime Expansion (i.e. Dark Energy) is due to the production of Quantum-Degenerate Active Neutrinos

(Note: Aug 14 2015:   I no longer find my argument regarding light neutrinos as dark energy convincing. I think that I was trying to find a connection between the fact that the energy density of dark energy is roughly (2 meV)^4, and this value is close to the value of the lightest neutrino.

Even though I don't agree with my arguments regarding dark energy, I have kept this page up to show my thinking at that time...and because there are a number of discussions about warm dark matter. As of Aug 2015, warm dark matter is still looking like a better explanation than cold dark matter.
As for light neutrinos bring dark energy. the problem is that fermi degeneracy pressure is positive. In order to explain why the Hubble expansion rate is reaching a positive, constant value. One needs to include a form of energy in which the pressure is negative, and with an equation of state of roughly the following: pressure = -1 * energy density. Instead, the equation of state for decaying dark matter into relativistic particles is the following:     pressure = 1/3 * S(a) * energy density
where S(z) is like the sigmoid function...it goes from a value of zero at small size, a, to a value of 1 at large size, a.

Also, I found a paper written in April 2015 that models dark matter decaying into relativistic matter...such as light neutrinos. http://arxiv.org/pdf/1505.05511v1.pdf
There are some tight constraints on this model. For example, the decay rate of the dark matter to relativistic species would have to be <0 .015="" an="" average="" decay="" gyr="" i.e.="" of="" time="">70 Gyr...which then makes it hard to explain why so much has happened in the first 13 Gyr.)
Original post from 5/20/2014
I'd like to summary what I've been trying to put into words over the last few years at this site. This article is still in rough draft form, and I will likely be editing it over the next few weeks as I improve the main argument.

Dark energy is not actually actual energy. Dark energy is just the expansion of spacetime because matter (mostly keV sterile neutrinos dark matter) is slowly turning into active neutrinos, which are relativistic & quantum degenerate.

Assuming that the rest mass of lightest active  neutrino is 0.001 - 0.06 eV and assuming that their temperature right now is 2 Kelvin, then their de Broglie wavelength is between 0.3 mm and 2 mm.

Also, using estimates for the electron neutrino density of 60-200 per cubic cm,  the average spacing between electron neutrinos is between 1.7 and 2.5 mm. These two numbers are extremely close to each other, which means that the lightest neutrino is quantum Fermi-degenerate, i.e. you can't pack more into a region than given by their de Broglie wavelength cubed. (Just as you can't pack more electrons into a metal than its de Broglie wavelength cubed, without increasing its temperature.)

The pressure of a relativistic Fermi quantum gas is only a function of the number density of fermions. The pressure (in units of mass per volume) is proporitonal to planck's constant divided by the speed of light, all multipled by the number density to the 4/3rd power. By starting with the density of dark matter at the recombination time (z ~ 1100), and assuming that the number of light neutrinos that can be created from a heavy neutrino is equal to the ratio of their rest masses, then I estimate a degenerate pressure of 10^-30 grams per cubic cm. This number is surprisingly close to the current mass density of dark matter (~5*10^-30 grams per cubic cm) and is only a factor of 10 less than the required dark energy pressure of 10^-29 grams per cubic cm. This means that with a few(somewhat) minor tweaks to my calculations, I could derive the dark energy "pressure" from the equations of relativistic, quantum degenerate neutrinos. (Note: here's a link to an article saying that relativistic, quantum degenerate neutrinos can't be the source of dark energy because the pressure is way too low. However, in that article, they assume a rest mass of the neutrino of 0.55 eV and don't assume that neutrinos can be generated from dark matter. When you change the rest mass to ~0.01 eV and include other sources of neutrinos from the decay of dark matter into many light neutrinos, then the quantum degeneracy pressure of neutrinos is large enough to explain dark energy. To be clear, my argument rests on a still on proven statement:  that a ~2 keV sterile neutrino can slowly convert into ~10^5 active neutrinos of ~0.02 eV rest mass. If this statement is true, then we can explain why neutrinos have mass, what is dark matter, and what is dark energy.)

So, if dark matter can slowly turn into active neutrinos over time, then dark energy might just be the quantum degeneracy pressure of relativistic, quantum degenerate neutrinos. I'll continue in the rest of this post to make this argument stronger.

During the Big Bang, there would be a large amount of active neutrinos produced, and then some more would be produced as sterile neutrinos (i.e. dark matter) slowly converts/oscillates into light active neutrinos. Spacetime expands as active neutrinos are generated because it can't be any smaller than that which would be required to keep the de Broglie wavelength cubed times the number density less than 1.

As seen in the image below, there is stringy areas and clumpy areas. It is entirely possible that the stringy areas are regions in which the dark matter is mostly light neutrinos (formed after recombination via break down of heavier, sterile dark matter) and the clumpy areas (i.e. galaxies) are regions that mostly hold the keV sterile dark matter. What is keeping the whole universe from collapsing might be the quantum degenerate pressure of the lightest active neutrino.

Monday, May 19, 2014

What is the curvature of spacetime?

This post was updated on June 30 2014. (And see news update added to the bottom of the post on May 2015 regarding BICEP2+Planck2015 estimates of gravitational waves.)
The astrophysicists community is currently in a heated debate about the implications of the BICEP2 measurements of B-mode waves in the cosmic microwave background (CMB.)
[For non-experts, the CMB is the nearly spatially-uniform (isotropic) radiation that we receive in whichever direction we look. The radiation matches with the radiation of a blackbody at a temperature of 2.726 /- 0.0013 Kelvin. This radiation is nearly uniform, with only small fluctuations. This near uniformity can be contrasted with the extreme density fluctuations we see in matter. Before the temperature of the universe cooled to below 3000 K (~0.3 eV), the density of hydrogen and helium in the universe was rather uniform because the hydrogen and helium were ionized (i.e. plasma), and in constant contact with the photons that today make up the CMB. Only after the temperature dropped below 3000 K, could the helium and hydrogen decouple from the radiation, and clump together to form local dense spots (which eventually turned into galaxies, stars, and planets.) It appears that the dark matter was already much more lumpy than photons and non-dark-matter at this point in time, so when the non-dark-matter decoupled from the photons, it started to fall into the local gravitational wells caused by the lumpy dark matter. (Note that my guess of why dark matter did not become extremely clumpy is that dark matter has a rest mass of ~2-10 keV and is prevented from being clumpy due to Fermi quantum degeneracy as neutrons are in neutron stars.)]

Thursday, May 8, 2014

Dynamic Simulation of the Universe

I noticed that the BBC ran an article this morning about a Dynamic Simulation of the Universe with Cold Dark Matter that was recently published in the journal Nature.

The simulation produces galaxies of different shapes and sizes that astronomers see in the real Universe

I think that simulations like this are fascinating and I encourage more people to run simulations like this.
However, I find it extremely odd that the researchers didn't state in the paper what was the mass of the dark matter particle in their simulations. They just mention Cold Dark Matter. It seems odd that the reviewers in a journal as well-recognized as Nature would have let this paper be published without requesting that the authors provide the mass of the Dark Matter particle.
If anybody knows what is the mass of the Dark Matter particle they used in their simulations, please comment on this post and provide us with the value of the rest mass of the Dark Matter particle.
Thank you

Also, to those people who work in this field, I have a request:
Try running a simulation in which the universe is simulated with all of the following properties: (1) a wrinkled surface on an expanding 4D sphere (i.e. General Relativity in 4D with non-isotropic mass density), (2) the radius of the 4D sphere expands only when there are time irreversible collisions (i.e. collisions involving the weak nuclear force are the cause of the expansion of space-time while GR tells how space-time is curved), and (3) the dark matter particle has a mass between 2-10 keV.

It seems to me that simulations that are missing (1), (2), and (3) above are missing major components required to actually simulate the evolution of the universe.

Wednesday, May 7, 2014

Center of Mass of the Universe: More thoughts on Symmetries and Conservation Laws

I was re-reading Feyman's "The Character of Physics Law" when I stumbled upon some interesting sentences. (Chapter 3, Pg 82 starting just above Figure 22.)
"In this way the conservation of angular momentum implies the conservation of momentum. This in turn implies something else, the conservation of another item which is so closely connected that I did not put it in the table. This is a principle about the centre of gravity...The point is that of all the stuff in the world, the centre of mass, the average of all the mass, is still right where it was before."

If you take a large collection of particles, the forces of interaction between the particles is not capable of changing the center of mass. The position of the center of mass only changes if the center of mass was already moving with a certain velocity, V. This velocity, V, is unaffected by the forces of repulsion and attraction between the particles. If this velocity, V, were zero to start, then it would always stay that way, unless acted upon by particles that weren't included in the original set when calculating the center of mass. But what if we take the collection of particles to be all of the particles in the universe?

In my understanding of our universe (which is different than most astrophysicists and physicists), the universe is a wrinkled, expanding surface of a 4D sphere,where the radius of the sphere is the time dimension. The center of mass of such a surface is the center of the sphere. The center of the 4D sphere is the location in space-time of the Big Bang  (r=t=0.) So, while the surface my be wrinkled (due to local variations in the density of matter), the variations have to cancel exactly on average, so that the center of the mass of the universe is still exactly the the center of the 4D sphere. If there were any fluctuations (i.e. fluctuations such that there is an increase in mass/energy that is not exactly balanced on the opposite side of the sphere), then the location of the center of mass would be offset from the center of the sphere.

One can hopefully see that this has major implication for quantum gravity as well as R-type quantum theories that require a collapse of the wavefunction. The introduction of uncertainty into the location of massive objects might cause us to have to drop an important conservation law (i.e. the conservation of the momentum...which leads to the conservation of the center of mass in specific circumstances.) For example, if the mass inside of a blackhole were to randomly fluctuate, then this could cause the center of mass of the blackhole to change, and then would in turn cause the center of mass of the universe to go off center.

There are clearly some problem reconciling quantum mechanics with certain conservation laws, such as the conservation of momentum, because if the location of an electron in an atom were truly random (i.e. stochastic) before we measure it, then this could cause the center of mass of the universe to be ever so slightly off center (unless there were an completely symmetry fluctuation on the opposite side of the universe that kept the center of the mass constant. Of course, such a symmetric fluctuation would imply that electrons on opposite sides of the universe can communicate with each other at speeds much greater than the speed of light.) This is one of the many reasons why I'm skeptical of introducing stochastic (i.e. probabilistic) processes into the laws of physics. In order to introduce stochastic processes into nature, you run into potential problems of either (a) communication at infinite speed in order for the fluctuations to cancel out, or (b) throw out the conservation of momentum...i.e. allow of the center of mass of the universe to move stochastically around the origin as particles randomly appear here and disappear there. (Note U-type Quantum mechanics is deterministic, it's only R-type Quantum mechanics that is stochastic. For more discussion of U vs. R QM, see Chapter 22 of Penrose's The Road to Reality.)

Another interesting question is:  what is the total angular momentum of the universe? Is there an axis about which the 4D sphere is rotating?
I think that this question is similar in nature to following questions:  what is the total electrical charge of the universe? what is the total weak charge and total color charge of the universe? It is entirely possible that the answer to all of these questions is zero.

In the remainder of this post, I'll be summarizing the concepts discussed in \Figure 14 in Chapter 3 of Feyman's "The Character of Physical Law."  The ideas that Feynman discuss here can be found on any website (such as wiki) that covers Emmy Noether's Theorem that Conservation Laws imply continuous symmetries of differential equations (and vice versa.)