Basic Idea , Matveev A.N.
on Tue Jan 12, 2016 12:16 am
Basic idea:
Physical models are mathematical, but mathematics is not what
they are based on. The quantitative relations between physical
quantities are clarified through measurements, observations and
experimental investigations. Mathematics only serves as the
language in which these relations are expressed. There is no
other language for constructing physical theories.
ΒΑΣΙΚΗ ΙΔΕΑ
ΤΑ ΦΥΣΙΚΑ Πρότυπα είναι μαθηματικά  άλλα δεν βασίζονται
στα μαθηματικά. Οι ποσοτικές σχέσεις μεταξύ φυσικών μεγεθών
καθορίζονται απο τις μετρήσεις  πάντα μέσω προσεχτικής
παρατήρησης και πειραματικής έρευνας. Τα Μαθηματικά είναι
το όργανο για την περιγραφή αυτών των συναρτήσεων.
There is no royal road to Geometry.
There is a Rose in Spansih Harlem.
Physical models are mathematical, but mathematics is not what
they are based on. The quantitative relations between physical
quantities are clarified through measurements, observations and
experimental investigations. Mathematics only serves as the
language in which these relations are expressed. There is no
other language for constructing physical theories.
ΒΑΣΙΚΗ ΙΔΕΑ
ΤΑ ΦΥΣΙΚΑ Πρότυπα είναι μαθηματικά  άλλα δεν βασίζονται
στα μαθηματικά. Οι ποσοτικές σχέσεις μεταξύ φυσικών μεγεθών
καθορίζονται απο τις μετρήσεις  πάντα μέσω προσεχτικής
παρατήρησης και πειραματικής έρευνας. Τα Μαθηματικά είναι
το όργανο για την περιγραφή αυτών των συναρτήσεων.
There is no royal road to Geometry.
There is a Rose in Spansih Harlem.
Re: Physicks
on Tue Jan 12, 2016 2:18 am
Links.
http://arxiv.org/
papers
http://arxiv.org/list/grqc/new
Living Reviews
in relativity
http://relativity.livingreviews.org/
The Max Planck Institute for Gravitational Physics
http://www.aei.mpg.de/
nature physics :
http://www.nature.com/nphys/index.html
Webpages :
http://hyperphysics.phyastr.gsu.edu
http://www.physics.org/
http://www.physicscentral.com/
http://www.feynmanlectures.caltech.edu/
http://arxiv.org/
papers
http://arxiv.org/list/grqc/new
Living Reviews
in relativity
http://relativity.livingreviews.org/
The Max Planck Institute for Gravitational Physics
http://www.aei.mpg.de/
nature physics :
http://www.nature.com/nphys/index.html
Webpages :
http://hyperphysics.phyastr.gsu.edu
http://www.physics.org/
http://www.physicscentral.com/
http://www.feynmanlectures.caltech.edu/
Re: Physicks
on Tue Jan 12, 2016 2:33 am
Inside Black Holes
http://jila.colorado.edu/~ajsh/insidebh/intro.html
[This is not an artist's impression.
It is a general relativistic volumerendering
of a supercomputed simulation.]
Larger version

Andrew Hamilton's Homepage
http://jila.colorado.edu/~ajsh/insidebh/intro.html
[This is not an artist's impression.
It is a general relativistic volumerendering
of a supercomputed simulation.]
Larger version

Andrew Hamilton's Homepage
sxs
on Fri Feb 12, 2016 5:34 pm
Edwin F. Taylor's Website

http://www.blackholes.org Simulating eXtreme Spacetimes 
Visualizations of Quantum Chromodynamics (QCD)
on Fri Apr 01, 2016 3:31 pm
The animations above illustrate the typical fourdimensional structure of gluonfield
configurations averaged over in describing the vacuum properties of QCD. The volume
of the box is 2.4 by 2.4 by 3.6 fm, big enough to hold a couple of protons.
http://www.physics.adelaide.edu.au/theory/staff/leinweber/VisualQCD/Nobel
[High quality animations are available]
Big Bang / Current Research
on Thu Apr 21, 2016 11:46 am
Struggles with the Continuum
on Mon Jun 05, 2017 5:35 pm
Gravitational lensing by a nonrotating black hole
Combining electromagnetism with relativity and quantum mechanics led to QED.
But combining gravity with relativity led Einstein to something equally interesting : general relativity.
General relativity does not take quantum mechanics into account, so the story is not yet over. Many Colleagues hope that quantum
gravity will eventually save physics from its struggles with the continuum! Since quantum gravity far from being understood, this
remains just a hope. This hope has motivated a profusion of new ideas on spacetime.
Tolman–Oppenheimer–Volkoff limit
Above this limit, gravity overwhelms the repulsive forces that hold up the neutron star. And indeed, no neutron stars heavier than 3 solar masses have been observed. Thus, for very heavy stars, the endpoint of collapse is not a neutron star, but something else: a black hole, an object that bends spacetime so much even light cannot escape.
If general relativity is correct, a black hole contains a singularity. Many physicists expect that general relativity breaks down inside a black hole, perhaps because of quantum effects that become important at strong gravitational fields. The singularity is considered a strong hint that this breakdown occurs. If so, the singularity may be a purely theoretical entity, not a realworld phenomenon. Nonetheless, everything we have observed about black holes matches what general relativity predicts. Thus, unlike all the other theories we have discussed, general relativity predicts "infinities" that are connected to striking phenomena that are actually observed.
The Tolman–Oppenheimer–Volkoff limit is not precisely known, because it depends on properties of nuclear matter that are not well understood. However, there are theorems that say singularities must occur in general relativity under certain conditions.
One of the first was proved by Raychauduri and Komar in the mid1950’s. It applies only to ‘dust’, and indeed it is a precise version of our verbal argument above. It introduced the Raychauduri’s equation, which is the geometrical way of thinking about spacetime curvature as affecting the motion of a small ball of test particles. It shows that under suitable conditions, the energy density must approach infinity in a finite amount of time along the path traced out out by a dust particle.
The first required condition is that the flow of dust be initally converging, not expanding. The second condition, not mentioned in our verbal argument, is that the dust be ‘irrotational’, not swirling around. The third condition is that the dust particles be affected only by gravity, so that they move along geodesics. Due to the last two conditions, the Raychauduri–Komar theorem does not apply to collapsing stars.
The more modern singularity theorems eliminate these conditions. But they do so at a price: they require a more subtle concept of singularity! There are various possible ways to define this concept. They’re all a bit tricky, because a singularity is not a point or region in spacetime.
For our present purposes, we can define a singularity to be an ‘incomplete timelike or null geodesic’. As already explained, a timelike geodesic is the kind of path traced out by a test particle moving slower than light. Similarly, a null geodesic is the kind of path traced out by a test particle moving at the speed of light. We say a geodesic is ‘incomplete’ if it ceases to be welldefined after a finite amount of time. For example, general relativity says a test particle falling into a black hole follows an incomplete geodesic. In a roughandready way, people say the particle ‘hits the singularity’. But the singularity is not a place in spacetime. What we really mean is that the particle’s path becomes undefined after a finite amount of time.
We need to be a bit careful about what we mean by ‘time’ here. For test particles moving slower than light this is easy, since we can parametrize a timelike geodesic by proper time. However, the tangent vector of a null geodesic has so a particle moving along a null geodesic does not experience any passage of proper time. Still, any geodesic, even a null one, has a family of preferred parametrizations. These differ only by changes of variable like this: By ‘time’ we really mean the variable in any of these preferred parametrizations. Thus, if our spacetime is some Lorentzian manifold we say a geodesic is incomplete if, parametrized in one of these preferred ways, it cannot be extended to a strictly longer interval.
The first modern singularity theorem was proved by Penrose in 1965. It says that if space is infinite in extent, and light becomes trapped inside some bounded region, and no exotic matter is present to save the day, either a singularity or something even more bizarre must occur. This theorem applies to collapsing stars. When a star of sufficient mass collapses, general relativity says that its gravity becomes so strong that light becomes trapped inside some bounded region. We can then use Penrose’s theorem to analyze the possibilities.
Shortly thereafter Hawking proved a second singularity theorem, which applies to the Big Bang. It says that if space is finite in extent, and no exotic matter is present, generically either a singularity or something even more bizarre must occur. The singularity here could be either a Big Bang in the past, a Big Crunch in the future, both—or possibly something else. Hawking also proved a version of his theorem that applies to certain Lorentzian manifolds where space is infinite in extent, as seems to be the case in our Universe. This version requires extra conditions.
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