Recent content by gerald V

The force two static electric charges exert on each other fulfills (velocity of light set unity) \begin{equation} F r^2 = N_1 N_2 \alpha \hbar \;, \end{equation} where ##F## is the force, ##r## is the mutual distance, ##\alpha## is the dimensionless fine structure constant, ##\hbar## is Planck's...

The Gauss formula for the induced metric reads ##g_{\mu \nu} = G_{ab}\frac{\partial X^a \partial X^b}{\partial x^\mu \partial x^\nu}##, where ##G## is the metric of the embedding space, the capital ##X## are positions in the embedding space, the little ##x## are positions inside the embedded...

With the algebra so(3) are associated the spherical harmonics. I would assume that comparably with the algebra so(2,1) are associated functions that can be addressed as hyperbolic harmonics. But I nowhere found any reference to them. Do they exist and if so, where can they be found? Thank you...

Thank you very much. I was aware of what you are saying. But, is this the correct sign for bosons? Does current quantum physics think the vacuum energy density of bosons is positive (and huge, namely of Planckian order of magnitude; forget observation), and is there a simple argument why?

My head is spinning when it comes to the sign of the vacuum energy density and the cosmological constant. The cosmological term can be put at the left or the right side of Einsteins equation, energy density is not pressure and energy density is not action density. There is a historic theory...

In textbooks, Bekenstein-Hawking entropy of a black hole is given as the area of the horizon divided by 4 times the Planck length squared. But the corresponding basis of the logarithm and exponantial is not written out explicitly. Rather, one oftenly can see drawings where such elementary area...

The Kerr solution describes the gravitational field of a rotating black hole. Oftenly, the hole is said to be „spinning“, what appears as misleading to me. My questions: 1.) Is it correct to say that angular momentum in this way is treated like orbital angular momentum, not like spin? 2.) Can...

I am aware that one usually starts from the Maxwell equations and then derives the masslessness of a photon. But can one do it the other way round? The action of photon would be ##S = \hbar \int \nu (1 - \dot{x}^2) \mbox{d}t##, where ##\nu## is the frequency acting as a Lagrange multiplier...

Now, in a texbook I found an explanation, which is embarrasingly simple. To embed n-dimensional space parametrized by coordinates x into N-dimensional space parametrized by coordinates X, there are exactly N embedding equations. This is because for any point on the embedded manifold it must be...

I am confused about the shape of the de Sitter universe. The Misner-Thorne-Wheeler says it can be regarded as the submanifold given by ##-x_1^2 + x_2^2 + x_3^2 +x_4^2 + x_5^2 = k## of a flat space with lineelement ##\mbox{d}s^2 = -\mbox{d}x_1^2 + \mbox{d}x_2^2 + \mbox{d}x_3^2 +\mbox{d}x_4^2 +...

In a textbook, which is not in Englisch language unfortunately, I found a passage saying that intrinsic curvature of spacetime is just a specific definition. The alternative definition is that spacetime is flat, whereas clocks and rods have variable lengths - which is just Feynman’s bug...

The term for the electromagnetic interaction of a Fermion is ##g \bar{\Psi} \gamma_\mu \Psi A^\mu##, where ##g## is a dimensionless coupling constant, ##\Psi## is the wave function of the Fermion, ##\gamma## are the gamma matrices and ##A## is the electromagnetic field. One can quite simply see...

In the following, I set the velocity of light unity. I refer to theories of gravities in higher-dimensional spacetimes. Newton` s constant converts the curvature scalar with dimension ##lenght^{-2}## into the matter Lagrangian with dimension ##energy/length^3##. So its dimension is...

Many thanks, George Jones. Maths can surprise me again and again. In differential geometry - Isometric embedding - Mathematics Stack Exchange it is discussed that the notions used can refer to quite different mathematical structures. I mean embedding in the very pedestrian sense of a...

It is mathematically proven that any intrinsically curved manifold can be derived from embedding in a flat space of sufficient number of dimensions. I heard somewhere, but lost that reference, that for our universe 10 flat dimensions are needed in the most general case.. May I ask - Is the...