String theory which is the state-of-the-art culmination of all the human knowledge about Nature provides us with very many “dimensions” of unification of previously unrelated phenomena, types of phenomena, objects, types of objects, and even unification of methods how to unify things, whether those things are objects, phenomena and principles that play a key role in the previous advances in physics or whether they are just notions in mathematics or whole subdisciplines of maths.

— Unification as a source of certainty

— Lubos Motl

2013.04.16 Tuesday ACHK

However, there’s still some difference between the light elementary particle species – and the numerous heavy elementary particle species such as the black hole. The latter may still be described as some kind of “composites” of the former ones. However, string/M-theory has made the notion of compositeness more subtle. Compositeness has been de facto replaced by the UV/IR-mixing.

What is that? It’s a rule that in a theory that is as powerful as string theory and/or quantum gravity, the spectrum of elementary particles is far from arbitrary. In fact, the statistical details of the high-mass spectrum (and the properties of high-mass particles) is fully encoded in the properties of the low-mass excitations and vice versa!

— Unification as a source of certainty

— Lubos Motl

2013.04.10 Wednesday ACHK

However, the individual microstates of the black holes may also be viewed as “elementary particles”, something that can be localized just like the electron. So string theory i.e. quantum gravity tells you that there are many species of elementary particles. The light ones are well-described by the quantum field theories – an approximate, effective description. However, you may continuously try to increase the mass of the particles, look for ever heavier species, and when you get to very high particle species, they may be viewed as higher excited, “large” strings or branes and, when they’re even heavier, as black hole microstates!

Some of the previous steps in the unification – such as S-duality – have found rigorous maps between seemingly elementary objects (such as electrically charged “electrons”) – and the seemingly composite objects (such as “solitons”, e.g. magnetic monopoles). So it’s not quite a new insight that elementary and composite objects can’t be strictly separated – an aesthetically appealing intuition that was promoted by people such as Werner Heisenberg when he was older and the S-matrix school but that didn’t lead to any solid insights prior to the birth of string theory.

— Unification as a source of certainty

— Lubos Motl

2013.04.06 Saturday ACHK

Symmetry dictates interactions.

—

Yang once summarized the fundamental laws in physics deduced in this century by a simple slogan “symmetry dictates interactions”.

— Symmetry & Modern Physics: Yang Retirement Symposium

— Alfred S. Goldhaber

2013.04.02 Tuesday ACHK

The observer is not disturbing the individual particles, influencing the individual measurement results.

Instead, by joining the system, the observer is replacing the original system by a bigger one. The observer is not just disturbing, but actually changing the whole system, influencing the statistics of the measurement results of that system.

— Me@2013-03-22 01:32:47 PM

2013.03.25 Monday (c) All rights reserved by ACHK

In another sense, the quantum uncertainty that the uncertainty principle refers to is due to the observer effect.

To measure a physical quantity of system, you have to add a measurement device into the original system, forming a bigger system. In other words, the disturbance is so huge that you do not call it “disturbance” anymore. Instead, you are actually changing the system.

Since the system has been replaced by a new one, the statistical patterns of the potential measurement results change.

— Me@2013-03-11 3:40 PM

2013.03.22 Friday (c) All rights reserved by ACHK

The quantum uncertainty that the uncertainty principle refers to is not due to the observer effect in the sense that the uncertainty is not due to the disturbances caused by any measurements on a system. The uncertainty principle is about the intrinsic statistical properties of the system.

For one single measurement, or even one single system, you cannot talk about the quantum uncertainty. The uncertainty principle is about the statistical patterns of a lot of identical measurements on a lot of systems which are all identical to the single system you are observing.

— Me@2013-03-11 3:40 PM

2013.03.14 Thursday (c) All rights reserved by ACHK

Topology is an important branch of mathematics that studies all the “qualitative” or “discrete” properties of continuous objects such as manifolds, i.e. all the properties that aren’t changed by any continuous transformations except for the singular (infinitely extreme) ones.

— Euler characteristic

— Lubos Motl

2013.03.12 Tuesday ACHK

The energy is a property of a system at a fixed moment of time – and because it’s usually conserved, it has the same values at all moments. On the other hand, the action is not associated with the state of a physical object; it is associated with a history.

…

the energy is universally defined in such a way that it is conserved as a result of the time-translational symmetry; and the action is defined in such a way that the condition δS=0 (stationarity of the action) is equivalent to the equations of motion. These are the general conditions that define the concepts in general and that make them important; particular formulae for the energy or action are just particular applications of the general rules.

— May 11 ’11 at 9:20

— Lubos Motl

2013.03.05 Tuesday ACHK

Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 180 degrees (and so to the rotation of one particle’s frame by 360 degrees), the symmetric nature of the wave function depends on the particle’s spin after the rotation operator is applied to it. Integer spin particles do not change the sign of their wave function upon a 360 degree rotation — therefore the sign of the wave function of the entire system does not change. Semi-integer spin particles change the sign of their wave function upon a 360 degree rotation (see more in spin-statistics theorem).

— Wikipedia on Exchange symmetry

2013.02.27 Wednesday ACHK

Tommaso Dorigo’s comrade Vladimir Lenin believed that an electron was a galaxy with many electrons, and so on, indefinitely. That’s what he meant by the statement that matter was “inexhaustible”. This hierarchical picture of the Matryoshka Universe was clearly indefensible already during Lenin’s life. First, it has to stop at the Planck scale because distances shorter than the Planck scale are unphysical, or at least don’t follow the normal laws of geometry. Second, two electrons must be exactly identical to allow chemistry to work, so they can’t carry any substructure that would be as variable as one of a galaxy (or even a high entropy, which must be zero).

— Composite vs elementary particles

— Lubos Motl

2013.02.27 Wednesday ACHK

As I suggested in the article about the solution of the Hydrogen atom using the SO(4) symmetry, one of the reasons why almost no people properly learn the “foundations of quantum mechanics” is the textbooks’ and teachers’ excessive focus on the Schrödinger picture (and the wave functions) and their disrespect for the Heisenberg picture (and the operators) even though operators – the observables – is what quantum mechanics is all about.

— Celebrating the Heisenberg picture

— Lubos Motl

2013.02.17 Sunday ACHK