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Hi, I am a string theorist and a publicist.


Jan
23
comment Does vacuum (empty space) exist?
Zero is natural in the physics sense. By the way, even in a different interpretation of "natural numbers", zero is usually considered a natural number, too: en.wikipedia.org/wiki/Natural_number - In the whole Universe, energy may take any real value, at least any value above the energy of the ground state. Particular physical systems may be affected by a discrete spectrum of energy but their union always has energy with a continuous spectrum.
Jan
23
comment Occam's razor on spin statistics theorem?
Dear @Propaganda, yes, if there are more particles, this gets extended to $\psi(x_1,x_2,\dots , x_n)$. It is completely antisymmetric, so it's enough for two of the arguments to coincide for the function to vanish (all the other arguments that don't participate in the permutations just sit at their place and don't do anything). There's nothing new happening about these simple rules for large $N$, and surely nothing hard.
Jan
23
comment How does Newton's 2nd law correspond to GR in the weak field limit?
Good point, WIMP. Still, deriving mechanics out of field theory of solitons is a bit advanced way for a beginner who wants to see his or her old equations of mechanics...
Jan
23
comment Basic question about law of gravitation
The time needed for two balls to collide by the action of gravity: It's an analytically solvable problem but too mathematically contrived one for a beginner. The resulting formula is pretty messy. One has to find the solution to the Kepler problem (differential equations) etc. Yes, the acceleration is accelerated because the force (and therefore acceleration) itself is increasing as the particles get closer to each other.
Jan
23
answered Conceptual puzzles when using Coulomb's potential in solving the hydrogen atom in non relativistic QM
Jan
23
comment Axiomatic statistical mechanics
To say that physics is just a collection of facts - like botany (and it's not quite true even for botany) - means to misunderstand physics completely. Physics doesn't have to become a nitpicking formalized branch of mathematics if it wants to unify the phenomena in the natural world. It does it without formalities; it really does.
Jan
23
comment Axiomatic statistical mechanics
Some comments showing that physicists - in this case Feynman - don't consider the axiomatization of physics useful or important: sciencehouse.wordpress.com/2009/07/23/more-on-feynman - In particular, Feynman often said that there's no reason to try to "minimize" a set of axioms completely. A finite set of rules that is self-consistent is just equally OK. Which of the axioms are "more fundamental" than others is often just a convention, anyway. At any rate, physics has done an amazing job in reducing billions of diverse observations to simple rules.
Jan
23
comment Axiomatic statistical mechanics
Here you have a monography on axiomatic classical statistical mechanics: amazon.com/… - it isn't a particularly well-known book and given the dull topic, there's no reason why it should be.
Jan
23
answered Occam's razor on spin statistics theorem?
Jan
23
comment Axiomatic statistical mechanics
Moreover, questions about literature for pure formal mathematicians are arguably off-topic on a physics forum. Physics is not an enterprise in which one is obsessed by formalities such as the need to write down proofs using quantifiers. The latter is purely mathematics, and even in mathematics, your purely formal and superficial interests are among the least important parts of the discipline.
Jan
23
comment Axiomatic statistical mechanics
I find this kind of questions annoying. In this case, statistical mechanics is one of the most rigorously treated subjects of mathematical physics - mostly because there are no conceptually confusing issues in it. That's why it's studied by many people employed by maths departments who can do these things very rigorously and formally. But the basic content is still the same as the content of the introductory books; they just get much further by analyzing more complex systems. In contrast to the OP's assumptions, stat. mech. isn't about some formal subtleties because there aren't any.
Jan
23
answered An odd relation with the epsilon/delta invariant tensors of SO(3)
Jan
22
revised What is the meaning of speed of light $c$ in $E=mc^2$?
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Jan
22
comment Calculating gravity when taking into account the change of gravitational force
Let me say Steven's lesson in different words. The first equation of yours, using $gt^2$, is only OK if the acceleration $g$ is constant, i.e. in the "uniform" gravitational field. For example, on the surface of Earth, the field and acceleration are approximately uniform. The accuracy is so high that we don't need to talk about $g$ being height-dependent in any everyday applications. However, $g$ does depend on $r$ and therefore on $t$, so $y=gt^2/2$ for a fixed $g$ isn't the right description anymore. Instead, it must be replaced by the solution of the differential equation, $g\to\ddot y$.
Jan
22
comment Calculating gravity when taking into account the change of gravitational force
Dear @Frxstrem, differential equations are equations for whole functions $r(t)$ which relate the so-called "derivatives". The equation with $\ddot{r}$ is actually the right way to write your equation for the acceleration. I think that if you don't know at all what differential equations are, this thread on Physics SE isn't the right arena to learn this rather extensive subdiscipline of maths. Steven: I disagree that the analytic solution to the Kepler problem etc. is useless and infinitely contrived; after all, Newton mastered it to explain Kepler's laws, the first big success of his theory.
Jan
22
revised What is the meaning of speed of light $c$ in $E=mc^2$?
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Jan
22
answered What is the meaning of speed of light $c$ in $E=mc^2$?
Jan
22
comment Source term of the Einstein field equation
Otherwise what the mass "including the pressure" is depends on what we exactly calculate; Feynman's was an estimate. But in various situations, the mass may be modified by $\pm C \int p\,\, {\rm d}V/c^2$ where $C$ is a numerical constant. In other contexts, it's important that the influence of the pressure is nonlinear, and therefore only in higher orders, and so on.
Jan
22
comment Source term of the Einstein field equation
Dear @Kernel, it seems to me that you are repeating the same pre-existing opinions of yours and you didn't really pay much attention to Kyle who explains what the actual core of Penrose's complaint was, and in my opinion, correctly so. When you have a star, it has not only mass density inside; it also have a pressure because the particles are moving somewhat quickly. In GR, the very presence of pressure - inside the matter (so "pressure on what" is a totally irrelevant question here) - is affecting the properties of the gravitational field because the whole $T_{\mu\nu}$ including $p$ is RHS.
Jan
21
awarded  Enlightened