Monday, January 24, 2011

Answers to some 200+ physics questions

In the past days, I had to do various things. One of them was an emergency fix in my bathroom.

Imagine a disgusting concrete block that was built right after the Soviet occupation sometimes in the late 1960s or early 1970s but whose exterior was recently renovated. Many details in the building and in my apartment - including the main door to the building, the elevator, and the kitchen unit - are closer to a 21st century capitalist economy than the 20th century communist mess in which the building was created.

However, there are still many annoying traces of the sloppy socialist architecture. The thick "boxboard" that separates the kitchen from the bathroom is one of them. Two weeks ago, I noticed that the "cardboard" on another "boxboard" on the bathroom side began to crack. Experts told me that there is still some wood and construction that will prevent the kitchen unit from collapsing ;-) so I decided it was a cosmetic imperfection and we glued a fake wall with ties in the bathroom; click to zoom in.

The product bought in Baumax for \$100 was made in the U.S. - no China - so the U.S. readers may feel particularly proud about the continuing competitiveness of the U.S. economy.

Physics Stack Exchange

However, my user profile at the Physics Stackexchange suggests that I had to spend some significant time on that server in the recent 11 days, too. There are 200+ questions where I posted answers and yes, some of them are pretty long, detailed, comprehensive, and they contain formulae in TeX - something that I try to avoid on this blog for many reasons.

If you click at the link, you may get to any of those questions. But let me present some "superconcise" versions of the 30 top-rated answers I posted over there. Of course, the actual answers over there are much more detailed and technical haha.

12 Why quantum entanglement is considered to be active link between particles?

Because most people are silly. The entanglement is just a correlation and there is no active aspect of the link.

10 Is it theoretically possible to shield gravitational waves?

No, unlike the boundaries of a conductor, the analogous gravitational objects would curve the space in an unacceptable way and they would require negative energy density, too.

10 What Is Energy? Where did it come from?

Noether's theorem guarantees that there's a number that's conserved whenever there's time translational symmetry.

8 What experiment would disprove string theory?

An extensive list of 12 categories of possible ways to disprove string theory. Most of them are very unlikely to occur - which really means that string theory has already passed the general tests so it's unlikely to be disproved by new general tests.

8 Why does a ballerina speed up when she pulls in her arms?

Conservation of angular momentum; her moment of inertia of order I=MR^2 goes down when she pulls in her arms, so the angular frequency omega has to go up for J=I.omega to be conserved.

6 Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?

Yes, Coulomb's law may be attributed to the electric field which has to transform in some way in relativity. The only consistent way is to extend it to an antisymmetric tensor with two indices which also includes the magnetic field. The guy who asked the question doesn't want to believe that the magnetic field is independent of (and equally real as) the electric one.

5 Difference between thermodynamics and statistical mechanics

Thermodynamics is the older macroscopic description of heat and work etc. based on principles that were assumed to hold, statistical physics is the framework that explains thermodynamics by statistics applied on many atoms.

5 Why do leptons and quarks mix?

Because the particles that mix have the same charges and quantum numbers and nothing (such as a conservation law) bans the mixing, and if nothing bans it, it will happen with a generic coefficient. The matrices are generic and they can't be fully diagonalized. I analyze the insufficient freedom to do so.

5 How are the calories in food calculated?

It turns out that the content of food is chemically analyzed for the amount of far, sugars, etc., which are believed to be usable by our bodies. And each of them has been measured by calorimeter - full burning - to find out the calories (e.g. 9 kcal per gram of fat). The components' calories are summed at the end - just like if they were fully burned in a calorimeter. Those components that are believed to be unusable by bodies - dietary fibers that go to the excrements etc. - are just not counted to the calories of food. Burning the whole food would give us a big overestimate because our bodies can't burn much of it.

5 How can a photon have no mass and still travel at the speed of light?

The total mass is a 0/0 indeterminate form. However, one may also explain that the squared mass is E^2-p^2 and it is simply equal to zero for photons.

5 Can spacetime be non-orientable?

No in the real world - because of the P- and CP-violation; yes in more general theories. In particular, M-theory on the Klein bottle and the Möbius strip produces well-behaved and well-understood vacua.

4 Discussion of the Rovelli's paper on the black hole entropy in Loop Quantum Gravity

It's invalid - a few links to his LQG colleagues who found serious errors are mentioned. However, the very proportionality of the entropy to the area in LQG is incorrect, too. The volume-extensive term can only be "hidden" but it is there, among other pathologies. Even when it's subtracted, the coefficient of the area-extensive term is just wrong.

4 How do electrons interact if one of them had just exited the two slits of the double-slit experiment?

The other electron can effectively measure the interfering one, and depending on how much it does so, the interference pattern of the intefering electron will get less sharp: a classical case of complementarity.

4 Where does the 10^{500} estimate for the number of stringy vacua come from?

Links to Bousso-Polchinski and KKLT papers are written down. It's mentioned that there are hundreds of cycles and each of them may carry a dozen of different values of generalized magnetic fluxes which is how one gets a power of googol of possibilities.

4 Why do galaxies and water going down a plug hole spin?

For the same reason as the ballerina above: the moment of inertia decreases by concentrating the matter or water closer to the axis, so the angular frequency has to increase.

4 Does the equivalence between inertial and gravitational mass imply anything about the Higgs mechanism?

It implies that the masses produced by the Higgs mechanism have both gravitational and inertial effects with the usual ratio - but it's also true for all other forms of mass and energy, not only the Higgs mechanism.

4 Summing over topologies

Well-defined in string theory i.e. 2-dimensional gravity; probably a wrong way to approach 3+1-dimensional or higher-dimensional quantum gravity because the metric is not a good degree of freedom at the Planck scale. However, some applications and reasons are discussed in some detail, anyway.

4 Why do the formulas for planck's units use h instead of hbar?

They don't - some typos and errors are found in the encyclopedias etc. However, the reduced Planck units - with "8 pi G = 1" - are explained as well.

4 Can/has string theory solved cosmological constant problem?

If shows that vacua with a rather generic C.C. exist but it hasn't explained why we live in the particular tiny C.C. vacuum, unless the anthropic people are right and our C.C. is just a random number chosen from the set of possibilities that is only contrained by the condition that intelligent observers have to arise.

4 Energy, power and action

The guy who asks is explained that if an equation is dimensionally correct, it doesn't mean that it's correct, and that power is less fundamental and more derived in physics than action or energy.

4 What does second quantization mean in the context of string theory?

It's explained why string theory interactions may be computed in the first-quantized form and the second quantization formalism is unnecessary - but string field theory gives the same results in a second-quantized language. However, it seems that it doesn't give us anything beyond that.

4 what is tension in string theory?

Coefficient analogous to the mass that multiplies the proper area in the Nambu-Goto action. Similarities and differences between piano strings and fundamental strings are discussed in detail.

4 Evidence for black hole event horizons

Narayan et al. look at Sgr A* and see that too much matter seems to be disappearing from sight; if there were a surface, the accreting matter would heat up, fall to the surface, and the surface would radiate a lot. The Sgr A* at the galactic center just seems way too dim.

4 Cherenkov radiation in nuclear bomb

Impossible in the air because the speed of light in the air is just a tiny fraction of a percent smaller than in the vacuum - and the charged particles are just not energetic enough to be faster than light. But possible in water etc.

4 Superselection sectors and p+1 form potentials in String Theory

Subspaces of the Hilbert space that don't evolve into each other by the evolution operators; either because of conservation laws or, more often, because of infinite changes - changes of the asymptotic structure of the spacetime.

4 Why do things that are far away seem smaller?

Similar triangles; eyes can only see the directions from which light rays are coming. Some people ask even these seemingly (and truly) silly questions but it's good to patiently answer. At least once.

4 If two ultra-relativistic billiard balls just miss, will they still form a black hole?

Probably yes, if there's a moment in which the whole energy fits into a region that is smaller than C times the Schwarzschild radius corresponding to the total energy/mass. C is of order one.

4 Binary Black Hole Solution of General Relativity?

Analytic solution of this is impossible because the black holes radiate gravitational waves, changes their distance, eventually collapse on each other etc. Comments on the 1993 physics Nobel prize pulsar.

3 Why are von Neumann Algebras important in quantum physics?

They are less important than von Neumann wanted to think and physicists rarely use this term.

3 Tesla's theory of gravity

A crackpot model unrelated to gravity based on a version of the aether - that Tesla was calling with another silly name - and supported by some flashy experiments. It turned out that the most important experiment was not only unrelated to gravity but was unrelated to the material filling the vacuum, too: he showed some properties of the solidified air.

Sorry, I can't fix the typos - too much stuff and this blog entry is not even the "main" place where the answers are posted.

1. Lubos, do you plan to write an article about new ideas in the last Witten's preprint concerning knots?

Why this works are considering so important?

2. Dear Victor81,

no, sorry, I am not an expert in this part of maths. Note that his paper has knots and fivebranes in the title. Compare with Knitted fivebranes we wrote in 1998.

But just to be sure, they're different knots haha.

So far, I don't know whether this work is "considered important" so I can't tell you why. It's surely important by having Edward Witten in the author list - but that's true for 330 other papers, not exactly a fully elite club anymore. Of course, almost all of them are extremely good papers.

Cheers
LM

3. Hey Lubos,

I agree that quantum entanglement is not an "active link", although certainly there is something interesting to be said.

(For example, the use of entanglement in the BB84 protocol to share random numbers at a distance, i.e. a cryptographic key.)

-Jon