Some of the differences between the familiar Newtonian equation of gravity and the predictions of general relativity flow from the fact that gravity in general relativity bends both time and space, not just space. In normal circumstances, gravity bends time so slightly that the difference between Newtonian gravity and general relativity that results is so slight that it is impossible to detect without scientific instruments.

— Wikipedia on Anti de Sitter space

2010.06.26 Saturday ACHK

In physics, Gravitation is a very important reference book on Einstein’s theory of gravity by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler. Often considered the “Bible” of General Relativity by researchers for its prominence, it is frequently called MTW after its authors’ initials, or “the Phone Book” due to its immense size. It was published by W.H. Freeman and Company in 1973. The book, a massive tome of over 1200 pages, covers many aspects of the General Theory of Relativity and also considers some extensions and experimental confirmation. The book is divided into two “tracks”, the second of which covers more advanced topics for more capable or determined students. MTW uses the -+++ metric convention. The book is famous/infamous for its use of boxes to add supplementary substance to the already thorough main text.

* Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973-09-15 1973), Gravitation, San Francisco: W. H. Freeman, ISBN 978-0-7167-0344-0

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— Wikipedia on Gravitation (book)

2010.06.25 Friday ACHK

Thus, the relationship between aprioricity, necessity, and analyticity is not easy to discern. However, most philosophers at least seem to agree that while the various distinctions may overlap, the notions are clearly not identical: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.

— Wikipedia on A priori and a posteriori

2010.06.24 Thursday ACHK

Like all nice physical theories, we can in principle derive everything about our theory of superstrings once we know the formula for the action. For bosonic strings, the action is very simple. As time passes, a string traces out a 2-dimensional surface in spacetime called the “string worldsheet”. The action is just the area of this worldsheet.

— John Baez

2010.06.22 Tuesday ACHK

Beyond black holes

Hawking and Page showed that black hole thermodynamics is more general than black holes, that cosmological event horizons also have an entropy and temperature.

More fundamentally, ‘t Hooft and Susskind used the laws of black hole thermodynamics to argue for a general Holographic Principle of nature, which asserts that consistent theories of gravity and quantum mechanics must be lower dimensional. Though not yet fully understood in general, the holographic principle is central to theories like the AdS/CFT correspondence.

— Wikipedia on Black hole thermodynamics

2010.06.19 Saturday ACHK

* There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.

There is another theory which states that this has already happened.

— The Restaurant at the End of the Universe

— Douglas Adams

2010.06.16 Wednesday ACHK

Physicists are coming up with lots of exciting mathematical “results” – often NOT rigorously proved! – and mathematicians are getting very interested.

— John Baez

2010.06.14 Monday ACHK

Einstein’s equation in plain English:

Given a small ball of freely falling test particles initially at rest with respect to each other, the rate at which it begins to shrink is proportional to its volume times: the energy density at the center of the ball, plus the pressure in the x direction at that point, plus the pressure in the y direction, plus the pressure in the z direction.

— John Baez

2010.06.12 Saturday ACHK

In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization refers to a collection of techniques used to take a continuum limit.

When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, the continuum limit has to be taken carefully.

— Wikipedia on Renormalization

2010.06.11 Friday ACHK

Gauge invariance also implies that most force particles interact with themselves: …

— Fundamental Physics: Where We Stand Today

— John Baez

2010.06.10 Thursday ACHK

This is dictated by `gauge invariance’, a principle linking the Standard Model and general relativity.

— Fundamental Physics: Where We Stand Today

— John Baez

2010.06.09 Wednesday ACHK

A mathemagician is a mathematician who is also a magician.

— Wikipedia

2010.06.08 Tuesday ACHK

Another interesting discovery is that 11-dimensional supergravity is related to the exceptional Lie group E8: …

— John Baez

2010.06.06 Sunday ACHK

Any meaningful theory of quantum gravity that makes sense and is predictive at all energy scales must have some deep principle that reduces the infinitely many unknown parameters to a finite number that can then be measured.

* One possibility is that normal perturbation theory is not a reliable guide to the renormalizability of the theory, and that there really is a UV fixed point for gravity. Since this is a question of non-perturbative quantum field theory, it is difficult to find a reliable answer, but some people still pursue this option.

* Another possibility is that there are new symmetry principles that constrain the parameters and reduce them to a finite set. This is the route taken by string theory, where all of the excitations of the string essentially manifest themselves as new symmetries.

— Wikipedia on Quantum gravity

2010.06.04 Friday ACHK

Points of tension

There are two other points of tension between quantum mechanics and general relativity.

* First, classical general relativity breaks down at singularities, and quantum mechanics becomes inconsistent with general relativity in the neighborhood of singularities (however, no one is certain that classical general relativity applies near singularities in the first place).

* Second, it is not clear how to determine the gravitational field of a particle, since under the Heisenberg uncertainty principle of quantum mechanics its location and velocity cannot be known with certainty. The resolution of these points may come from a better understanding of general relativity.

— Wikipedia on Quantum gravity

2010.06.03 Thursday ACHK

Many first principles in quantum field theory are explained, or get further insight, in string theory: …

— Wikipedia

2010.05.30 Sunday ACHK