Monday, March 23, 2015

Concordance Cosmology? Not yet

The term "Concordance Cosmology" gets thrown a round a lot in the field of cosmology. So too does the term "Precision Cosmology."
However, I'm a little hesitant to use these terms when we don't know what is 95% of the matter/energy in the universe. Cosmologists use the term  "Precision Cosmology" to describe the fact they can use data from a number of data sets to constraint variables, such as the rest mass of neutrinos, the spacetime curvature of the universe, or the number of neutrino species. However, many of these constraints are are only valid when assuming a certain, rather ad hoc model.

In many respects, this Standard Model of Cosmology,  i.e. Lambda CDM, is a great starting point, and most people who use it as a starting point are fully aware of its weakness and eagerly await being able to find corrections to the model. The problem is that it's sometimes referred to as if it were one complete consistent model (or referred to as a complete model once there's this small tweak over here or over there.) However, LCDM is not consistent and is rather ad hoc. The goal of this post is to poke holes in the idea that there is a "Standard Model of Cosmology" in the same sense that there's a "Standard Model of Particle Physics." (Note that the SM of particle physics is much closer to being a standard model...with the big exception being the lack of understanding of neutrino physics, i.e. how heavy are neutrinos and is there CP violation in the neutrino sector?)

So, let's begin with the issues with the Standard Model of Cosmology:  i.e. Lambda CDM:

(1) There is no mechanism for making more matter than anti-matter in Standard Model of Cosmology. The LCDM model starts off with an initial difference between matter and anti-matter. The physics required to make more matter than anti-matter is not in the model, and this data set (i.e. the value of the baryon and lepton excess fractions) is excluded when doing "Precision Cosmology."

(2) Cold Dark Matter is thrown in ad hoc. The mass of the dark matter particle is not in the model...it's just assumed to be some >GeV rest mass particle made in between the electro-weak transition and neutrino decoupling from the charged particles. The mechanism for making the cold dark matter is not consistent with the Standard Model of Particle Physics. So, it's interesting that the "Standard Model of Cosmology" so easily throws out the much more well known "Standard Model of Particle Physics." This means that there is no "Standard Model of Cosmo-Particle Physics."
There's also the fact that Cold Dark Matter over-predicts the number of satellite galaxies and over predicts the amount of dark matter in the center of galaxies. But once again, this data set is conveniently excluded when doing "Precision Cosmology" and, worse, the mass of the 'cold dark matter particle' is not even a free variable that Planck or other cosmology groups include in the "Standard Model of Cosmology." There are ten's of free variables that Planck uses to fit their data, but unfortunately, the mass of the dark matter particle is not one of the free variables.

(3) Dark Energy is a constant added to Einstein's General Theory of Relativity, and as such, it is completely ad hoc. The beauty of Einstein's General Theory of Relativity was its simplicity. Adding a constant to the theory destroys part of the simplicity of the theory.
It also appears that, if Dark Energy is not just a constant, then it's not thermodynamically stable (for most values of Wo/Wa.) (See the following article
http://arxiv.org/pdf/1501.03491v1.pdf)
So, this element of the "Standard Model of Cosmology" is an ad hoc constant added to GR. And while it's true that dark energy could just be the energy density of the vacuum of space-time, the particular value favored by LambdaCDM is completely ad hoc. The energy density of space-time appears to be on the order of (2 meV)^4.  What's so special about 2 meV?

Wednesday, March 11, 2015

The Two-Step Method for Controlling Inflation and Maintaining Steady Growth Rates

Given that I've focused a lot of attention recently on Dark Matter & Dark Energy, I've decided to switch gears and get back to topics of Energy&Currency.

The recent crisis in Russia has demonstrated the problems with basing a currency on any one commodity. In the case of Russia, approximately 26.5% of its GDP comes from the sale of petroleum products. The contribution of oil/tax taxes to the Russian government is roughly 50% of the total revenue for the government, which means that Russia's currency is strongly impacted by changes in the price of oil/natural gas.
But not all oil/gas producing countries are feeling the shock of low gas prices. The key to avoiding the shocks is to make sure that a large portion of the revenue from oil/gas needs is invested into stocks/bonds of companies/governments that will benefit from lower oil/gas prices. So, it's fine for a oil/gas-producing country to be specialized in one area production, provided that its revenue goes into investments that will make money when oil/gas prices drop.

So, this leads me to the question I've been trying to answer for years:  how can a country maintain constant inflation rates while also maintain steady growth rates?

There are some bad options available: (a) Gold-based currency  (b) Fiat currency without rules (c) Any currency based by only one commodity...such a PertroDollars

Second, I'd like to discuss the problem with leaving the control of the currency to just a Federal Board of Bankers. For example, there is a famous economist at Stanford named John Taylor. (You can check out his blog here.) He is credited with inventing the Taylor Rule to determine how Federal Reserves should change the interest rate as a function of the inflation rate and the growth rate of the economy.
While I'm a proponent of making the Federal Reserve rule-based, there is a clear flaw in John Taylor's Rule for controlling inflation and GDP:
There are two measured, independent variables (inflation and real GDP growth), but only one controlled, dependent variable (the federal funds rate.)

As such, the Taylor rule is doomed to fail. You can't control the fate of two, independent variables by changing only one dependent variable. In order to control both the inflation rate and the real GPD growth rate, then you need two free variables. The focus of the rest of this blog is on how to use 2 input variables to control the 2  output variables (inflation and real GDP growth rate.)

You need two keys, and the keys should be held by different people.

Tuesday, March 10, 2015

Review of "A World Without Time" and an Argument against Time Travel (Neutrino Drag)

Over the holidays, I read a book written back in 2005 titled "A World Without Time."
It's a good read for over the holidays because the first half of the book is largely biographical chapters on Albert Einstein and Kurt Gödel, and the second half is a step-by-step presentation of  Godel's argument that, if the General Theory of Relativity is true, then our perceived "flow of time" is not real.

This is an interesting argument, so I'd like to discuss it further in this post. It's actually quite similar to the argument that has been made by Julian Barbour for the last couple of decades. (In this prior post, I discuss Dr. Barbour's latest addition to his last-standing argument that there is no such thing as time because 'time' in General Relativity is nothing more than another spatial dimension.)

So, let's look at Kurt Gödel's argument in more detail:
What Kurt Gödel did was to build a hypothetical universe that was consistent with GR. (While the universe was nothing like our universe, it was entirely consistent with the laws of GR.) In this hypothetical universe, there were closed space-time paths. In other words, there were closed space-time paths in the same way that the Earth has a 'essentially' closed space path around the Sun. In other words, on this closed space-time path you would wind up right back where you started. Meaning that you could revisit the past and it would be exactly the same as before,
Kurt Gödel then argued that in this hypothetical universe, there can be no such thing as 'flow of time' because you could easily go back in time or forward in time, just as easily as you can go left or go right at a T-intersection.
Kurt Gödel then argued that, since the 'flow of time' does not exist in this universe and since this universe is entirely consistent with General Relativity, then the 'flow of time' does not exist in our universe because our universe is governed by the laws of  General Relativity.

So, I think that this is a valid argument, except for the last step. The problem with this last step is that there are four laws of physics in our universe (gravity, E&M, weak nuclear, and strong nuclear.) I would agree with Kurt Gödel if the only law of physics had been gravity, but the weak nuclear force just doesn't cooperate so easily.

It's well known that the weak nuclear force violates both CP and T symmetry. In other words, there is an arrow of time associated with the weak nuclear force, and this arrow of time does not exist in the other forces of nature. So, what keeps us from ever being able to make a closed space-time path is the weak nuclear force, because we are ultimately surrounded by particles that interact via the weak nuclear force, i.e. neutrinos (and perhaps dark matter particles interact via the weak nuclear force.) While the interaction of space-ships with neutrinos is negligible at normal velocities, the interactions is extreme when the space-ship starts moving at relativistic velocities...i.e. having a directed energy per nucleon on the ship of around ~10 GeV.) For example, I calculated that, when traveling at a speed where your kinetic energy is equal to your rest mass energy, then the protons in your start converting into neutrons at a rate of 1 proton every 2 milliseconds. (While this isn't particularly fast given the number of protons in your body, you can hopefully see that there's no way for you to travel anywhere near the speed of light without having neutrinos significantly destroy the structure of your body.)
So, there's no way to get a space-ship up to the required velocity/energy to create a closed space-time loop without bumping into neutrinos who will create a drag force on the space-ship as they bump into electrons. The irreversibly of drag (due to collisions with particles that interact via the weak nuclear force) is what prevents us from creating a closed space-time path.

But what if there were no neutrinos for use to run into? Would time travel be possible? (i.e. would a closed space-time path be possible?)
I would answer that that time travel would be possible in a world without the weak nuclear force. However, we live in a world with the weak nuclear force, and there is no way to get around it. In fact, the real question is: are the background neutrinos a requirement of our time asymmetric world?

I don't think that it's coincidental that we are surrounded by neutrinos (the very particles that prevent us from traveling back in time.)  It's the neutrinos and dark matter particles that carry most of the entropy in the universe. It's the high-entropy, diffuse nature of neutrinos that pushes back against attempts to create closed space-time loops (just as it's impossible/difficult to create vortexes in extremely viscous liquids like honey.)


So, in summary, I think that Kurt Gödel has a valid point that there is no flow in General Relativity (alone.) But when you combine GR with the weak nuclear force, then space-time travel is not possible.