Since the coupling charge and the response coefficient for gravity are identical, it follows that gravity can only operate in a single directional sense, because changing the sign of m for a particle would reverse the sense of both the coupling and the response, leaving the particle’s overall behavior unchanged. In other words, if we considered gravitation to apply a repulsive force to a certain particle by setting the particle’s coupling charge to -m, we would also set its inertial coefficient to -m, so the particle would still accelerate into the applied force.

— 2.2  Force Laws and Maxwell’s Equations

— Reflections on Relativity

— mathpages

2013.06.09 Sunday ACHK

So one can show that all of physics of M-theory, if studied in the light-cone gauge, is equivalent to an ordinary non-gravitational matrix model – a quantum mechanical model with matrix degrees of freedom.

The eigenvalues of the X^i matrices may be viewed as the positions of the gravitons (or their superpartners) in 11 dimensions; a threshold (zero-binding-energy) bound state of several such eigenvalues (which can be proved to exist, a remarkable property of SU(N) supersymmetric quantum mechanics) are gravitons that carry a higher number of units of the quantized light-like (longitudinal) momentum.

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— Physics Stack Exchange
   
— answered Mar 6 ’11 at 8:02

— Lubos Motl

2013.06.06 Thursday ACHK

Albert Einstein was a pioneer of relativity and has actually made major contributions to early quantum mechanics, too. (And he also encouraged people to think about entanglement etc.) However, he didn’t really accept quantum mechanics because he has never understood it. Paul Dirac, a big shot from a newer generation, understood relativity as well as quantum mechanics (he was a major co-father of it) but he has never accepted renormalization. Of course, this theme gets repeated all the time. Richard Feynman was a big shot guy from another younger generation who understood and accepted relativity, quantum mechanics as well as renormalization but he was already too old to understand and accept string theory.

— Regularization and renormalization

— Lubos Motl

2013.06.03 Monday ACHK

In this sense, topology is a vital arbiter in the “discrete vs continuous” wars. The very existence of topology as a discipline shows that “discrete properties” always exist even if you only work with continuous objects. On the other hand, topology always assumes that these features are “derived” – they’re some of the properties of objects and these objects are deeper and that may have many other, continuous properties, too. The topological, discrete properties of these objects are just projections or caricatures of the “whole truth”.

— Euler characteristic

— Lubos Motl

2013.06.02 Sunday ACHK

The required modification of the couplings and masses linked to a small change of the typical energy scale \E_{\max} which is needed to preserve all the low-energy physical phenomena is what is referred to as the Renormalization Group flow.

— Regularization and renormalization

— Lubos Motl

2013.06.02 Sunday ACHK

Recall that the UV divergences allow you to divide theories to renormalizable and nonrenormalizable ones – the renormalizable ones only force you to choose a finite number of parameters and cancel their corresponding infinite parts by counterterms.

— Regularization and renormalization

— Lubos Motl

2013.05.29 Wednesday ACHK