kleinwolf

I heard a photon was a vector-particle, how do we prove this ? btw, Do spin 1/3 particle exist ?

Yes, liver

Does this mean that the polarization is 2-dimensional, and hence a photon is like a spin 1/2 particle ?

Since politics (except in France) do not like "foie gras" (fatty leather) creation, by over-feeding birds (this stores fat in their leather) does anyone know how to transform normal leather (cheaper to buy) into this..?

It's widespread that moon phase influence the speed of nails (or hair) growing size...(experimentally seen)...but has someone an explanation of this ?

Why do we represent nucleons as small sphere when they are build of 3 quarks....this describes a plane (2-dimensions) ?

There is no information transfer, this you can understand classically via Bertelmann's socks argument : -imagine 2 socks a blue and a yellow -EPR paradox is not a paradox, it's really easy to understand that if you choose one sock, the remaining sock has the other color...this 100% sure..even before you know or see (i.e. "measure with your eyes") the color of yours... however, in quantum mechanics, the possibilities remain after you measure once, by changing the angles of measurement, like you measure at A +/- and B -/+...then you remeasure a second time after B by changing the angle , you can again find + or -..whereas classically if the color of your sock is yellow...it remains yellow, even if you look at it again

The equivalence is locall..this means your rocket should have a different acceleration depending on space and time...for example : In the gravitational field of a point (or sphere), the equivalent acceleration at a certain (constant) radius is constant a®=GM/r², if you are farther away the acceleration of your rocket changes

Yes, I meant tensor Suppose we had spherical coordinates [math](r,\theta,\phi)[/math] : then is [math]d\theta[/math] dimensionless, the euclidean metric diag(1,1,1) transforms into [math] (1,r^2,r^2\sin(\theta))[/math], so the units should be 1,L^2,L^2 (?)

An error occured in my question : In fact [math]\Lambda_1[/math] should be understood as independent of "g" (the unknown, i.e. the metric), but can depend on space-time, since for example in spherical coordinates, [math]\Lambda^1_{\mu\nu}=-\Lambda \textrm{ diag}(1,-1,-r^2,-r^2\sin(\theta)^2)[/math]

What are the units of the metric : It seems components can have different ones ?

Matrix mechanics is also a geometrization of the axioms of probabilities : (Axiom a) p(1)+...p(n)=1 (Axiom b) p(i)>=0.... (b)=>so we could write p(i)=a(i)^2, with a(i) a real number, or a(i)=¦b(i)| hence (a) is just the squared norm of an n-dimensional [normalized] vector...this vector is the state-vector, or wave-function in infinite dimensional space

Some wide public books write like : position were [math] \vec{r} [/math]. Since the time has now to be local (the time is kept on the particle) get [math] \vec{p}=m_0\frac{d\vec{r}}{d\tau}=\gamma m_0\vec{v}[/math] [math]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/math] Kin. power is [math] P=\vec{F}\vec{v}=\frac{d\vec{p}}{d\tau}\vec{v}=\gamma\vec{v}\frac{d\vec{p}}{d t}[/math] In order to get the energy we need to integrate P over time.... It can be shown that [math]\frac{d m c^2}{d t}=\frac{d(\gamma m_0 c^2)}{d t}=...(*)...=P[/math] (*) calculation left to the reader. Then, the kinetic energy is non-zero even if speed is zero...!!? This means that a new energy concept that is not classical has to be introduced : rest energy [math] m_0 c^2 [/math]

[math]e=mc^2 [/math] could be a mnemotechnic for general relativity too : e=energy density m=a constant depending on the gravitational constant and the celerity of light c^2=curvature squared

Is it allowed to write : [math] G_{\mu\nu}(g)=R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R+\Lambda g_{\mu\nu}+\Lambda^1_{\mu\nu}=\kappa T_{\mu\nu} [/math] where [math]\Lambda^1_{\mu\nu}[/math] is a constant symmetric tensor (depending neither on space nor time)...and other symbols well-known in GR. We find, since in vacuum the Minkowski metric is a particular solution in cartesian coordinates, that [math]\Lambda^1_{\mu\nu}=-\Lambda \textrm{diag}(1,-1,-1,-1)[/math]. Else, could someone give a comprehensive summary of the conditions on [math]G_{\mu\nu}[/math] forbidding similar constant (of integration?) ?

In the original EPR article, it's written, "If, [...], we can predict [...]" I'm not a native english speaker, but shouldn't it be written "If, [...], we COULD predict [...]" ?? "can" in this case is like a grammatical error ? Or sound that negative from the onset and the present version could be, at the limit right...since we still don't know if we can predict or not ?? Thanks in advance

Let suppose we admit physics formulas represent physical reality, and we had an equation described by : Lf(x,t)=0 where L were an operator. Suppose we get a constant of integration C independent of x and t I can however write C=1 and C=2... and hence vary the constant...but if we believe t is physical time and x space, then this would contradict the fact C is a constant ....and hence C is either a function of "t" or "x" (where x is for example the position of C in the present text.....hence whole physics breaks down ??? Or do meta-time, or global time, or "experiment-intern time" (C could depend on the initial condition you could vary)...or do C depend on hidden parameter C(u)...where u represent a parametrization of universes or human free will....

The next step in quantum entanglement is a very profound result : *) the value of the result of measurement is not set at the time of the separation of both particles. Classically, this is like if you had 2 coins, then person A throws a coin far away from B, who throws the other coin too, and A can predict the result of B with 100% accuracy...which could be very useful to earn a lot of money at random games (bertlmann's socks are a classical model in which the color of the sock is set from the separation on, even if the observer does not know it)

This is right, a often made supposition on the solution. Let see the next steps : Now take the space-dependent part : [math] X''(x)=C*X(x) [/math] with C the given constant. (indep. of x and t) But the boundary condition is "time-dependent" and X(x) should be a function of time too. hence a contradiction, and we deduce the separation Ansatz is not the right hypothesis on the solution. Note : for example that the brownian motion, which is a solution of parabolic problem, is not separable (gaussian of the type exp(x²/t)<>X(x)*T(t)) The general solution Ansatz, which is just a change of basis (Fourier basis, aso.) is just using the linearity of the equation : [math] f(x,t)=\sum_n X_n(x)T_n(t) [/math] with [math] X_n [/math] basis functions, often the eigenvectors of the space-operator. The time-dependent part is found out of projection on [math] X_m(x)[/math]. However here the BC (boundary condition) makes that [math] X_n=X_n(x,t)[/math].

How to compute the solution of a partial differential equation problem of the type : a) [math] \frac{\partial^2 f}{\partial x^2}(x,t)=D\frac{\partial f}{\partial t}(x,t)[/math] D is a non vanishing constant and b) an initial condition, for example [math] f(x,t=0)=\delta(x)[/math] c) a boundary condition [math]f(at,t)=f(-at,t)[/math] with 'a' nonzero it can be seen that * separation of variables does not work because of the time-dependence of the boundary * pseudo spectral method fails due to the non-orthogonality of the eigenvectors of the space-operator and their time derivatives. Is there another way to solve that kind of differential problem ? thx