## How Magnetic Fields Can Bend Space

According to classical concepts in Physics, Gravitational Fields can bend space, while Magnetic Fields are orthogonal to them, and as long as that model does not break, no intensity of Magnetic Field, will do what a Gravitation Field does.

But there are many ways in which the classical theories of Physics have been replaced by more-controversial ones, based on Quantum Mechanics.

(Revised 10/19/2016)

One subject which Quantum-Mechanics describes, is that of Virtual Particles. And this is my best stab at explaining ‘how they work':

The ‘normal state’ of matter, is to have positive energy, which is really just a confusing way to say that matter has positive mass, since mass and energy are equivalent, and since photons, that are generally perceived as only consisting of energy, can collide with nuclei, and cause matter-antimatter particle-pairs to be created, the combined mass of which must not exceed the energy of the incident gamma-ray photon.

This concept of matter possibly having positive energy can be misread, because the particle in question could be an electron, the electrical charge of which is defined as negative. This negative electrical charge does not prevent the electron from being positive matter, in the sense that its electrical properties are orthogonal to its mass, as a property.

But there was a famous Physicist named Dirac, who discovered quite by accident, that in correspondence with the positive-energy / mass -state of a particle, a negative-energy state is also ‘possible’, because that negative state by itself does not lead to contradictions.

The ‘inverse electron’ is positively charged, and opposite the regular electron in every way, including that the inverse one has positive charge, (and negative mass and energy). If the electron was left-handed, the positron will be right-handed.

Quite by accident, Dirac had discovered antimatter.

(Edit 05/25/2017 : It should be pointed out that this initial theory of Antimatter stands in contradiction with the modern, observed fact, that antimatter has positive mass, even though in some ways, it’s supposed to exist in opposition to ‘regular matter’. Hence, the paradox has already been commented on in depth, that while in the laboratory, Scientists are only able to convert energy into matter and antimatter simultaneously, the observed Universe consists almost entirely of matter.

Scientists cannot explain why this inconsistency takes place; they can only measure that it does.

It’s assumed that the reader is already familiar with this, and this posting is designed to have a liberal look at the subject, which could open up ways to rethink it. Trying to rethink a subject, while clinging to every assumption we may make about it, will usually not lead to any new insights. )

But under normal circumstances, the properties of empty space are defined such, that the energy-state of the electrons equals zero, which simply means that they do not exist. Yet, there is some small probability, that both a negative a positive-energy electron exist simultaneously, yet temporarily. Over slightly longer distances, relative to their distances of uncertainty, their properties cancel out. “Virtual Particle Phenomena” arise, when these particle-properties fail to cancel out completely. This usually requires some catalyst to happen, that catalyst having to consist of positive energy.

An extremely strong magnetic field – which would have to be stronger, even, than the magnetic field of a regular neutron star – is capable of evoking an asymmetry, in the paired, virtual particles of empty space. And then, if the magnetic field becomes as strong as that observed belonging to a type of start called a ‘magnetar’, a gamma-ray photon that crosses it, can cause a particle-antiparticle pair to be formed, which consume the photon, and which promptly annihilate, thus leaving behind two or more photons, that are less-energetic than the original photon was.

And so by distorting the relationship between a particle and its inverse, as belonging to a virtual-particle pair, a magnetic field can in fact have an effect on empty space. I do not know whether this meets the criteria of distorting space adequately.

Dirk

I have a piece of personal speculation to add. It might be that Dirac had an incorrect way of working with this subject.

## Whether the Columns of Matrices have a Natural Order

Are the columns of matrices in a given, natural order, as we write them? Well, if we are using the matrix as a rotation matrix in CGI – i.e. its elements are derived from the trig functions of Euler Angles – then the column order depends, on the order in which we have labeled coordinates to be X, Y and Z. We are not free to change this order in the middle of our calculations, but if we decide that X, Y and Z are supposed to form a different set, then we need to use different matrices as well.

(Edited 02/15/2018 :

OTOH, We also know that a matrix can be an expression of a system of simultaneous equations, which can be solved manually through Gauss-Jordan Elimination on the matrix. If we have found that our system has infinitely many solutions, then we are inclined to say that certain variables are the “Leading Variables” while the others are the “Free Variables”. It is being taught today, that the Free Variables can also be made our parameters, so that the set of values for the Leading Variables follows from those parameters. But wait. Should it not be arbitrary for certain combinations of variables, which follows from which?

The answer is, that if we simply use Gauss-Jordan Elimination, and if two variables are connected as having possibly infinite combinations of values, then it will always be the variables stated earlier in the equations which become the Leading, and the ones stated later in the equations will become the Free Variables. We could restate the entire equations with the variables in some other order, and then surely enough, the variable that used to be a Free one will have become a new Leading one, and vice-versa. (And if we do so, the parametric equations for the other Leading variables will generally also change.)

As of 02/15/2018:

This is an observation which I once made, based on certain exercises in Linear Algebra, as taught, having been simplified in the way I described. Eventually, systems of solutions will come up in the real world, in which a Free Variable actually precedes a Leading Variable, both in the order they get mentioned in equations, as well as according to the order of matrix-columns. The corresponding row with a single 1, corresponding to those Free Variables, will not occur, so that it also cannot be added to or subtracted from what will be the earlier row, in such a case.

The later observation follows from the fact that such solutions have infinitely many solutions:

1. If the Free Variables are just given a set of values that follow from the solution-set, Then the Leading variables would still need to have definite values, as defined by the same solution-matrix,
2. If the Free Variables are given a set of values, that no longer follow from the solution-set, it will not follow that a different set of values for the Leading Variables, will make such extraneous solutions viable.

End of edit, 02/15/2018 )

The order of the columns, has become the order of discovery.

This could also have ramifications for Quantum Mechanics, where matrices are sometimes used. QM used matrices at first, in an effort to be empirical, and to acknowledge that we as Humans, can only observe a subset of the properties which particles may have. And then what happens in QM, is that some of the matrices used are computed to have Eigenvalues, and if those turn out to be real numbers, they are also thought to correspond to observable properties of particles, while complex Eigenvalues are stated – modestly enough – not to correspond to observable properties of the particle.

Even though this system seems straightforward, it is not foolproof. A Magnetic North Pole corresponds according to Classical Principles, to an angle from which an assumed current is always flowing arbitrarily, clockwise or counter-clockwise. It should follow then, that from a different perspective, a current which was flowing clockwise before, should always be flowing counter-clockwise. And yet according to QM, monopoles should exist.