# physics

## Basic ideas of general relativity

General Relativity (GR) is a classical field theory (whatever that means, could be something like Electrodynamics or something like Fluiddynamics) There is no gravitational force. Principle of Mach: The distribution of matter and energy defines the geometry of space-time Principle of Equivalence: Acceleration = homogenous (in time and space) gravitational field; Principle of Covariance: All coordinate systems are equal. The equations of physics should have the same form in all coordinate systems.

## Classical limit of quantum mechanics

The semi-classical limit corresponds to $h\rightarrow 0$, which can be seen to be equivalent to $m\rightarrow\infty$ , the mass increasing so that it behaves classically. (from http://en.wikipedia.org/wiki/Dynamical_billiards ) An increasing mass can be seen as an increase in the number $N$ of involved particles with mass $m_0$. So is the limit of a $N$-particle quantum system for $N\rightarrow\infty$ a classical system?

## Fluid Dynamics of Spacetime

Bibliography Christopher Eling (2008) : Hydrodynamics of spacetime and vacuum viscosity Christopher Eling et al. (2006) : Non-equilibrium Thermodynamics of Spacetime Ted Jacobson (1995) : Thermodynamics of Spacetime: The Einstein Equation of State

Cherenkov Radiation is a very interesting phenomenom. Recently I asked myself, if such a phenomenom allso exists for gravity in the sense, that if a particle moves faster than the speed of gravity in a medium, it should radiate gravitational cherenkov radiation. I found an article [((bibcite 1))], that precisely predicts that. However in there article the theorists use it to constrain vacuum speed of gravity. They do not consider the case that gravity in a medium might(?

## Gravity

The basic equations are: $$G_{\mu \nu} + \Lambda g_{\mu \nu}= \frac{8\pi G}{c^4} T_{\mu \nu}$$ with $$G_{\mu\nu} = R_{\mu\nu} - \frac{1}{2} g_{\mu\nu}R$$ and $$T_{\mu \nu} = g_{\mu \alpha} g_{\nu \beta} T^{\alpha \beta}$$ and $$T^{\alpha \beta} \, = \left(\rho + \frac{p}{c^2}\right)u^{\alpha}u^{\beta} + p g^{\alpha \beta}$$ Eq.([[eref field]]) is the famous Einstein field equation connecting the Einstein tensor ([[eref ein]]) with the energy-momentum tensor ([[eref energy]]). The energy-momentum tensor in the form here is the stress-energy tensor of fluid (and I think this is the form Einstein used originally) and basically represent the relativistic euler equations.

From calculations of quantum tunneling through the horizon of a metric (black hole, Rindler..) Hawking/Unruh temperature can be calculated! [http://arxiv.org/abs/arXiv:0710.0612 Ryan Kerner: Fermions Tunnelling from Black Holes] _ Using this method it is recently claimed that the so called Black hole information paradox can be solved: Zhang et al. (2009): Hidden Messenger Revealed in Hawking Radiation: a Resolution to the Paradox of Black Hole Information Loss The answer is, that the information that seems to be lost when matter falls into a black hole is in fact completely carried away by Hawking radiation.

## Korteweg-de Vries equation

From [http://mathworld.wolfram.com/Korteweg-deVriesEquation.html]: In fact, a transformation due to Gardner provides an algorithm for computing an infinite number of conserved densities of the KdV equation, which are connected to those of the so-called modified KdV equation through the Miura transformation v_x+v^2=u (Tabor 1989, p. 291). The Korteweg-de Vries equation also exhibits Galilean invariance. See also [http://www.math.uwaterloo.ca/~karigiannis/papers/ist.pdf]: In the course of attempting to solve the KdV equation exactly, it was discovered that the equation has an infinite sequence of nontrivial conservation laws, which we shall presently define.

## Quantum entanglement

Before the measurement the positions of the photons in space are not defined, thus the distance between them also makes no sense and without distance one cannot really speak about the speed of information transfer. So IMO finding the properties of two entangled photons correlated is no more and no less surprising than finding the exact position of just one photon: the particle that was kind of “spread out all over space” before the measurement suddenly and instantaneously (basically “with infinite speed”, if one can dare to define a notion of “speed” in this case) “gathers itself together” in one particular spot.

## Relativistic Boltzmann equation

[Google Scholar: relativistic Boltzmann equation] [Literature citing Cercignani: The relativistic Boltzmann equation: theory and applications] [G. Kaniadakis (2006): Towards a relativistic statistical theory] [Garcia-Perciante (2006): Generalized Relativistic Chapman-Enskog Solution of the Boltzmann Equation] [Tsumura (2009): Second-order Relativistic Hydrodynamic Equations for Viscous Systems; how does the dissipation affect the internal energy?]

## Physik

Fortgeschrittenenpraktikum Teil A SS 2003 Meine Protokolle aus dem Fortgeschrittenenpraktikum Teil A im Sommersemester 2003 kann hier jeder downloaden der will. Die *.ps.gz-Files enthalten nur das Protokoll, die *.tar.gz-Files enthalten den gesamten Latex-Sourcecode, Bilder und Mathematica4-Notebooks. hall.ps.gz, hall.tar.gz laser.ps.gz, laser.tar.gz nmr.ps.gz, nmr.tar.gz optik2.ps.gz, optik2.tar.gz optpump.ps.gz, optpump.tar.gz roenmoes.ps.gz, roenmoes.tar.gz Master Thesis Enstanden während meines Auslandsaufenthaltes an der Rutgers University (Ansicht von oben) in den USA von 2001- 2002: thesis.