Recent content by Antonio Lao

My addition to the last post is that there might be a much deeper connection between all these undetectable fundamental particles and the invariance of magnetic helicity. It is known that magnetic helicity comes in two varieties: positive and negative. So, without giving any mathematical proof...

selfAdjoint, Thanks. You have given me the most informative and clearest discussions of the invariance of linked curves so far. But if I have to apply it into the quantum domain instead of celestial domain, I am hoping for some mathematical tools that can describe quantum of mass or magnetic...

Turbo-1, Thanks. But did he called it magnetic? I think I need to get Epple M 1998 Math. Intelligencer 20 45 as mentioned by Berger.

When the physical volume increase because of expansion, does this imply that relatively speaking, the volume of an electron is decreasing? This volume decrease of the electron does not affect its inertial mass or energy so that local gauge invariance is possible for the fine structure constant...

Who is the person that started the concept of magnetic helicity? Is it Gauss? Is it Woltjer? I was trying to obtain a copy of Woltjer's paper of 1958 Proc. Natl Acad. Sci. USA 44 480. Can anybody help me get a copy of this paper? I did purchased a paper by Mitchell A. Berger called "Introduction...

Thanks for the math. Gonna work on it some more till I am eligible for a PhD.

But for all relativistic mechanics, it is the square of energy that can describe the linear momentum of light E^2 = c^2 \mathbf{p}^2 + m^2 c^4 when the mass is zero, such as that for a photon, its energy becomes purely kinetic, then its momentum is p =\frac{E}{c} this implies...

This general covariance of alpha and beta might be capable of explaining the factor of 1/2 in kinetic energy for the total energy of an isolated system. E = \frac{1}{2} mv^2 + V where V is the energy potential. In relativity, as v -> c, the energy is mc^2. The factor of 1/2 becomes unity.

InvariantBrian, I would say half not double. The reason for this is that given \alpha and \beta for what values will the following be true? \frac{\alpha - \beta}{\alpha \beta} = 1 This is where \alpha = 1 is the potential energy and \beta = 1/2 is the kinetic energy. For higher...

InvariantBrian, Please check out the virial theorem and let me know why you think the potential is only half of the kinetic by using Newton's 3rd law? Thanks.

InvariantBrian, Bottomline is that in any given system, there are many forces of interaction between components. Whichever is the force that dominate the system, its law can be shown correct by experiments. For the solar system, Newton's mechanics is correct because in this system, both...

Newton's 2nd is correct for all inertial forces wherever they exist in a system. But there are also other forces: gravitational forces, electrical forces, magnetic forces, frictional forces, weak forces, strong forces, electromagnetic forces, elastic forces, molecular forces, atomic forces...

InvariantBrian, Once you are faced with an engineering problem, then you will start to realize that Newton's 3rd law is not enough to model physical reality. Specially in situation where static forces are in equilibrium, there is no obvious momentum because all velocity components are zero...

InvariantBrian, I agree with what you said. But in almost all experiments of modern quantum physics, it is the change in energy that can be detected not so much as the force. While in classical mechanics, forces are disguised in all forms of vibrations and oscillations (damped or undamped)...

InvariantBrian, No. But let me be more specific about it. In analytical mechanics, there are many ways that force is defined. One definition is that force is the negative gradient of a scalar potential function. F = -\vec{\nabla} V This force depends only on the coordinates of the...