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Hi, I am a string theorist and a publicist.


Sep
21
comment Can a single classical particle have any entropy?
The real purpose of entropy, regardless of its definitions in statistical physics, is the role it plays in thermodynamics: it never (macroscopically) decreases and $T\,dS$ and similar things appear in the equations of thermodynamics. The letter $S$ from these contexts is what we're calculating microscopically because it has consequences for thermal engines, life, and processes in the Universe in general. A good definition of entropy has to agree with thermodynamics. On the other hand, subtleties about entropy that can't be measured by thermodynamics don't belong to natural science.
Sep
21
comment Can a single classical particle have any entropy?
There is a difference between entropy and e.g. energy. Energy is a high-precision observable that may be measured and calculated with any accuracy, for arbitrarily small systems, and so on. But the entropy is simply not. Entropy is not an observable in the quantum mechanical sense: it is not an operator on the Hilbert space. That's why it doesn't make any sense to attribute sharp values of entropy to small systems. You may link the entropy to someone's being "ignorant" but then the whole quantity becomes subjective which is much worse than its being ill-defined for small objects.
Sep
21
comment Can a single classical particle have any entropy?
Dear @Ron, could you please explain in what sense the definition is "inconsistent"? What is true is that it doesn't allow one to attribute sharp values to the entropy of objects away from the thermodynamic limit. Indeed, it doesn't allow that. And it's a good thing, too, because those things don't have any physical meaning. You may choose a particular formula or prescription or value of the entropy of 1 particle but others may choose different prescriptions and values and there's no general principle that would say that one answer is better than the other.
Sep
21
comment Can a single classical particle have any entropy?
The undetermined additive shift to the entropy, as seen in classical physics, is actually "echoed" in quantum mechanics of a free particle as well. If you have a free particle in infinite coordinate space, it may occupy an arbitrarily large volume in the phase space. The entropy you would get according to your method is spurious, however. $S$ only becomes meaningful if one talks about the states of a bound state, internal degrees of freedom of an object, not the center-of-mass ones. How the center-of-mass d.o.f. are treated depends on many things; the dependence disappears as $N\to\infty$.
Sep
21
comment Can a single classical particle have any entropy?
But even if adopted your dogmatic $S=0$ definition of the entropy for pure states, you will not be able to give a positive answer to the original question because the original question asks about a single classical particle: read it carefully. In classical physics, the number of states isn't integer. Instead, one must measure the volume on the phase space. A strictly well-defined point on the phase space has $V=0$ which means $S=-\infty$. Yes, you may assign finite $S$ to distributions on the phase space but the additive shift in $S$ in classical physics remains undetermined, anyway.
Sep
21
comment Can a single classical particle have any entropy?
Dear @Ron, yours is just one way of defining the entropy, and not the usual one. The usual way to define the entropy calculates the number of macroscopically indistinguishable states with a given state, according to some convention, and the logarithm of this number is the entropy. In this way, one gets a nonzero entropy even for pure states (both in classical and quantum physics). Assigning just $S=0$ to single-particle states doesn't solve anything because it gives you no method to actually get a sensible, i.e. nonzero, entropy of larger objects.
Sep
20
comment Can a single classical particle have any entropy?
This question has nothing to do with "tracking" and with "sight". Even if I define a particular state of a particle, Marek or you won't be able to assign it with a unique value of entropy. The most naive definition would assign $S=0$ to any pure state: but this is clearly incorrect for pure states of big multi-body objects. One has to decide what the ensemble of macro-indistinguishable states is; log of their number is the entropy. This number is hugely uncertain for a low $S$ but becomes well-defined and independent of the choices in the thermodynamical i.e. large $S$ limit.
Sep
20
comment Can a single classical particle have any entropy?
Apologies, @Ron, but it isn't clear what you exactly think is wrong. sb1 asked whether a single particle - or an object with a similarly low entropy comparable to 1 bit - may be attributed an exact value of entropy. The answer is obviously No, it can't. The "statistical error" in the magnitude of the entropy is of order 100 percent when it's low. This is what the question by sb1 was about and this is what I answered. My answer is obviously right, as confirmed by Marek's inability to quantify the entropy even in the simplest situations.
Sep
6
awarded  Enlightened
Sep
6
awarded  Nice Answer
Aug
28
awarded  Nice Answer
Aug
28
awarded  Good Answer
Aug
27
awarded  Nice Answer
Aug
21
comment Why are the antimatter compositions of neutrons and protons different? Why by about 1%? References?
Hi, the keyword you may want to search is "parton distribution functions" (acronym PDF; too many references). They are functions telling you how many quarks, antiquarks, and gluons with various momenta are included in the proton or neutron. Because $p$ and $n$ differ by one quark, $u$ and $d$, and because the mass of these two quarks differs - 4 or 7 MeV and equally for the antiquarks, it follows that the heavier antiquark (anti d) will start to disappear faster etc.
Aug
21
comment What are the details around the origin of the string theory?
Dear @Ron, it's very interesting. But could you please be a little bit specific what the "hidden [bootstrap] assumptions" are? It's hard to imagine anything real behind your words at this point. I was just innocently stating that the particular deformation of string interactions you proposed was inconsistent. As far as I can say, one can prove it without any assumptions that would have to remain "hidden". You: "The fractal dimension of the embedding might be nonsense for real strings, but that's not the point." - OK, but what is your point then? Fractal dimension depends on UV physics.
Aug
20
comment What are the details around the origin of the string theory?
By the way, your "counting of the intersection dimension" in string theory is crap, too. There is absolutely no reason why such ad hoc concepts should be well-defined in a physical theory and they're not. Much more generally, the concept of "total spacetime dimension" is extremely subtle - the number of "Planckian" or "stringy" sized dimensions is always ambiguous and different dual descriptions generally yield different answers: ST isn't a fully local QFT, after all. Only large dimensions - much larger than the string/Planck scale - can be "unambiguously" counted.
Aug
20
comment What are the details around the origin of the string theory?
Dear Ron, you write: "I can construct an example field theory with low energy 'strings' and high energy crap". Great. You may construct such a "theory". But I may easily prove why it is crap and not a consistent theory i.e. not string theory. You can't modify string theory at high energies or low energies without spoiling its consistency. Of course, you may produce lots of crap but crap isn't the same thing as a theory in physics. One may prove that string theory can't be added ad hoc point-like-particle-like interactions without spoiling its consistency.
Aug
20
comment What are the details around the origin of the string theory?
Dear @Ron, Brandenberger-Vafa or string gas cosmology etc. isn't a paper about the existence and character of fundamental interactions in string theory; it is a paper about the "derived" impact of geometrical arrangement of strings on cosmology. Whether the strings are intersecting or not is irrelevant and the rules for the interactions of strings are independent of the spacetime dimension and they work in such a way that you may neglect the possibility of self-intersection as a measure-zero problem: the world sheet is always smooth around the interaction "point", even in $d=2$.
Aug
20
comment What are the details around the origin of the string theory?
Dear @Marek, the statement that string theory is a single theory is not ideology: it is a key technical property of the theory. Even if you decided to call it ideology - be my guest - it is a totally crucial ideology to understand what the theory actually is and what it is not. So it's just too bad if someone cannot learn these crucial technical things without "allergies". Arivero, Ramond's string - and Neveu-Schwarz string - wasn't really an "origin of string theory". String theory had "origin" as bosonic string theory which has no fermions. All SUSY/fermioncs strings are "new".
Aug
19
comment What are the details around the origin of the string theory?
What I want to say is that it is the opposite of the truth to suggest that string theory might be a theory of "anything". All previous theories in physics admitted some deformations or continuous parameters that were labeling different theories - but string theory doesn't. For example, interactions of rubber bands that would be nonlocal on the world sheet would also break spacetime locality and spacetime unitarity and spacetime Lorentz symmetry, and so on. Consistency prohibits all pathological mutations of the theory and string theory is totally determined by consistency.