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Showing posts from August, 2016

Do Surrealist Trajectors in Bohmian Mechanics Prove the Universe is Eternal?

I decided to interrupt what I had planned to write in order to address one issue I've been asked about over the weekend, specifically if a paper that appeared on arXiv in April 2014 titled "Cosmology from Quantum Potential" had shown the universe is eternal. One of the authors Ahmed Fang Ali is also the author of other another publications arguing that a speculative approach to quantum gravity called "Rainbow Gravity" lends further credence to pre-Big Bang eternal cosmologies.

The argument they make involves replacing geodesics in cosmology with the particle trajectories of Bohmian mechanics, these trajectories have certain properties that prevent their paths from crossing and so prevents them from forming an initial singularity.

Bohmian mechanics is an alternative to ordinary quantum theory that in addition to postulating a wave function that evolves according to some dynamic equation (Schrodinger, Dirac, Klein-Gordan etc,) posulates classical variables (co…

Can inflation be eternal into the past?

Back in 2003 a paper appeared on the arXiv titled "Inflationary spacetimes are not past complete" that was published by Arvind Borde, Alan Guth and Alexander Vilenkin which has had considerable amounts of attention online. The theorem is rather uninteresting but simple and doesn't require a very complicated understanding of math. So I thought I'd explain the result here.

It's purpose is to demonstrate that inflationary models are geodesically incomplete into the past which they take as "synonymous to a beginning" but Vilenkin stresses that the theorem can be extended to non inflationary models so long as the condition of the theorem that the average rate of expansion is never below zero is met. These models too then are incomplete into the past. Consider the metric for an FRW universe with an exponential expansion


Where the scale factor is


Since the eternal inflation model is a "steady state cosmology" the mass density and the Hubble paramet…

Friedmann's Acceleration Equation

The second Friedmann equation describes the universe's rate of expansion, how quickly the expansion is speeding up or slowing down. In short the equation tells us that if there is matter present in the universe then either its expansion rate is decreasing or its contraction rate is increasing. Friedmann originally solved Einstein's field equations with the Robertson-Walker metric and found two solutions, one was the Friedmann equation and the second was an equation which when subtracted by the first Friedmann equation gave the second Friedmann equation. However I want to explain how I first learned about the acceleration which I believe is he most easy and accessible way to derive it. We still need to use the first Friedmann equation that I spoke about previously.


Now multiply each term of the equation by the scale factor squared and you get 

If you differentiate this equation with respect to time 

Then divide by 
Then the equation becomes

Finally substitute in the following …

Hardy's Paradox

I want to discuss one further argument against local realism from Lucien Hardy in another well known set of publications, that were submitted in 1992 and 1993. In two papers titled "Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories" and "Nonlocality for two particles without inequalities for almost all entangled states". These papers present what is more commonly known as "Hardy's paradox".

These must be the nail in the coffin for any reasonable person who wants to still defend local realism. The experiment shows that the predictions of quantum mechanics differ from that of any local realist and local hidden variable theory.

The experiment involves using a stream of positions and electrons both sent through separate beam splitters on the left and the right. The wave function of each particle "splits" along the w path and the v path. These are then rejoined at the second beam splitter in phase so that if th…

GHZ Experiment vs Local Realism

Today I want talk about a famous paper titled "Bell's theorem, quantum theory and the conception of the Universe" which contains a thought experiment by Greenberger, Horne and Zeilinger that creates real problems for anyone who understands fundamental physics in terms of local realism, assuming it could even survive the difficulty captured in Bell's inequality theorem. The GHZ argument is not so reminiscently, simple at least as far as fundamental physics goes. I first came across the argument listening to an online lecture by the physicist Sidney Coleman but the argument against local realism here is unique in that it does not involve the derivation of any inequality over a statistical series of measurements like Bell's theorem does.

Most physicists believe the GHZ experiment is problematic for realist and hidden variable theories, the only way to make these compatible with the experiment is to appeal to exotic non-localities. The experimental set up involves t…

On the Einstein-Podolsky-Rosen Paradox

The Einstein-Podolsky-Rosen (here after EPR) paper published in 1935 argues that the wave function in quantum theory cannot give a complete description of a quantum system, and some "local hidden variables" must be added. The title of their paper "Can quantum mechanical description of physical reality be considered complete?" is treated somewhat as a philosophical question on the nature quantum mechanics that is answered in the negative.

We'll follow each step of the argument to make it clear what the paradox contains and then we'll briefly discuss Bell's inequality theorem which is a formal refutation of the argument. EPR open their paper by stating a "criterion of reality" they state "in a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system" this statement seems t…