But the main message is that the IR divergences can never tell you that a physical theory is inconsistent: they just tell you that the IR, long-distance physics may be different than you expected (or than you wanted to see). Production of soft photons in QED and confinement in QCD (and marginally also in conformal theories) are two examples of infrared effects you have to be careful about. But they will never allow you to throw away a theory as an inconsistent one.

— Regularization and renormalization

— Lubos Motl

2013.05.27 Monday ACHK

Renormalizable theories can be extrapolated to high energies

The main feature of renormalizable theories is that their physics may be extrapolated to and remains well-behaved at arbitrary high energy scales – or at least up to energy scales that are exponentially higher – e.g. \exp(1/e^2) times – than the typical scales in your theory. Because of that, any contributions of new particles or, more generally, new physics at these extremely high energy scales Λ are suppressed by 1/Λ^k where k is a positive exponent.

— Regularization and renormalization

— Lubos Motl

2013.05.25 Saturday ACHK

Indeed, if certain objects could move infinitely fast, we might expect to find the universe populated with large sets of indistinguishable particles, all of which are really instances of a small number of prototypes moving infinitely fast from place to place, so that they each occupy numerous locations at all times. This may sound implausible until we recall that the universe actually is populated by apparently indistinguishable electrons and protons, and in fact according to quantum mechanics the individual identities of those particles are ambiguous in many circumstances. John Wheeler once seriously toyed with the idea that there is only a single electron in the universe, weaving its way back and forth through time. Admittedly there are problems with such theories, but the point is that causality and the directionality of time are far from being straightforward principles.

— 1.7  Staircase Wit

— Reflections on Relativity

— mathpages

2013.05.17 Friday ACHK

Any particle can be exchanged in some context or another. So every kind of particle in one way or another produces a force.

In molecular physics, it’s the exchange of electrons which creates force [in covalent bond]. In electrodynamics, it’s the exchange of photons back and forth which creates force.

So [every] particle is connected with a force when that particle can be exchanged or jump back and forth between two something else.

There are people say that there are [only] four forces of nature.

No.

There is a force of every possible kind of particle.

— Lecture 1 | New Revolutions in Particle Physics: Standard Model 

— Leonard Susskind

2013.05.13 Monday ACHK

Now, you have to realize that the cosmological constant is the energy density of the vacuum.

— The enigmatic cosmological constant

— Lubos Motl

2013.05.10 Friday ACHK

Oddly enough, the clearest statement of this insight came only as an afterthought, appearing in Einstein’s second paper on relativity in 1905, in which he explicitly concluded that “radiation carries inertia between emitting and absorbing bodies”. The point is that light conveys not only momentum, but inertia. For example, after a body has absorbed an elementary pulse of light, it has not only received a “kick” from the momentum of the light, but the internal inertia (i.e., the inertial mass) of the body has actually increased.

Once it is posited that light is inertial, Galileo’s principle of relativity automatically implies that light propagates isotropically from the source, regardless of the source’s state of uniform motion.

— 1.6  A More Practical Arrangement

— Reflections on Relativity

— mathpages

2013.05.06 Monday ACHK

To summarize, black holes are the most universal localized objects in any theory that includes general relativity. They’re not just random siblings of comets, planets, stars, and quasars: they’re special. They maximize the density of many things. Despite the large matter densities that are needed to produce them, black holes are connected with “apparently empty” space, space without matter. Their properties therefore have something to do with the properties of the empty space itself.

— Event horizons and thermodynamics: more than an analogy

— Lubos Motl

2013.05.04 Saturday ACHK

The black hole entropy is a fundamental property of quantized space. The information may be generally attributed to surfaces – the event horizons. In Jacobson’s derivation of Einstein’s equations via Rindler spaces – much like in the case of the “cosmic horizon” of the anti de Sitter space – these event horizons depend on the observer. But there are also event horizons that are shared by pretty much everyone who lives in the Universe – the event horizons of localized black holes that causally separate their finite internal volume from the rest of the Universe.

— Event horizons and thermodynamics: more than an analogy

— Lubos Motl

2013.04.30 Tuesday ACHK

In early 1995, Ted Jacobson found an intriguing way to “localize” the relationship between the temperature and entropy on one side, and the acceleration and areas on the other side. In fact, he derived Einstein’s equations from a well-known thermodynamic equation. See also Einstein’s equations as equations of state.

— Event horizons and thermodynamics: more than an analogy

— Lubos Motl

2013.04.29 Monday ACHK

There is another consequence of the UV/IR connection: this connection makes the black hole microstates simultaneously composite as well as elementary.

They’re elementary because they can be thought of as some excitations of a collection of strings and branes. Even if you had a different theory, it would have to be able to calculate the black hole entropy from the number of excited states of “something”. This “something” would play the very same role as strings in perturbative string theory. And differently excited strings must be interpreted as different fields in spacetime – in an effective field theory. The same has to hold for “something” whatever it is.

On the other hand, the number of black hole microstates is so large that there must exist many ways to excite the “something”, some internal degrees of freedom.

— Event horizons and thermodynamics: more than an analogy

— Lubos Motl

2013.04.27 Saturday ACHK

Now, it was known that some portion of a charged object’s resistance to acceleration is due to self-induction, because a moving charge constitutes an electric current, which produces a magnetic field, which resists changes in the current.

— 1.5  Corresponding States

— Reflections on Relativity

— mathpages

2013.04.18 Thursday ACHK