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Showing posts from December, 2016

### How much Information can you Store on the Surface of a Black Hole?

In the currently best understood theory of gravity, spacetime is a physical entity which curves, bends, dips and expands. In some regions where gravity is so strong, light can't escape and the region has formed a black hole. When one just skims through any physics journal there are a plethora of papers published on the "entropy" of black holes, on Hawking radiation and on "holograms". But why do so many cosmologists believe in the holographic principle? The arguments in favor are really rather convincing, so lets try and follow the logic behind it. The radius of a black hole is

The energy of any given photon that cuts across the even horizon is given as

Normally, the formula includes the Greek symbol Lambda for wavelength but in our case, we are throwing in photons with a wavelength equal to the radius of the black hole. Such that

We use this equivalence because we only want one bit of information to be associated with each photon, a photon with much smaller w…

### Can a Lorentz Aether theory Explain the Michelson-Morley Experiment?

A theory of relativity already governed Newtonian mechanics. It's impossible according to Galilean relativity, to perform a mechanical experiment that tells one if she is in constant motion or at rest. Galileo's transformation equations were as follows

A problem became apparent when Maxwell published his equations of electromagnetism. He discovered that the speed of light is constant and propagates through an "aether". Motion through the aether of space is absolute and not relative and thus one could discover using light rays if they were traveling at a constant motion or at rest, violating Galieo's thesis. The Michelson-Morley experiment was the failure to detect such motion. Something was obviously wrong.

Galileo had not understood the effects of time dilation and length contraction. Today most physicists explain these effects as simply the result of time and spatial coordinates. These are not invariant and change from coordinate system unlike proper coordinat…

### Special Relativity and Time

Up till now I've discussed a few arguments for or against a cosmic beginning, so I thought I'd continue to and turn to a famous paper "Time and Physical Geometry" by the philosopher Hillary Putnam. Therein Putnam was the first to argue that the special theory of relativity implies an eternal universe. The meaning of the word "eternal" refers to "eternalism" or the block-universe, a timeless static view of time where temporal becoming is an illusion. Such a universe may still exist eternally, in a timeless sense without needing to extend back to past infinity.
There are philosophical arguments in favor of this proposal like the paradox of how "time flows" without introducing a meta-physical time. There's also an argument to be made in general relativity and quantum cosmology for a bock universe but I want to restrict our scope to Putnam's argument from special relativity. The spacetime relevant for special relativity, is Minkows…

### A Brief Look at One of John von Neumann's Beliefs about Quantum Mechanics

John von Neumann's argument for quantum logic was based on the Hilbert space formulation of quantum mechanics. In essence a Hilbert space is the quantum analog of phase space used in classical mechanics. In quantum mechanics the basis of interest are not just classical variables like position and momentum but also include spin and super positions of those variables. If there are N possible states a system can be in, then the Hilbert space of that system is the collection of all possible super positions of those N possible states. Where the sub space of a Hilbert space represent the properties of a given quantum system.

Consider the following 2-Dimensional Hilbert space for particle of half integer spin (all given in units of reduced Planck's constant)

Quantum mechanics uses complex, rather than real Hilbert spaces but this will be sufficient to illustrate von Neumann's argument.

In the Hilbert space the component P is a projection operator and operators orthogonal to each…