Is There a Formula for Non-Material Objects? Solving the Mystery of X=sqrt (-1)

[Thor]

E=mc^2 is the simplified form of an equation given to us by Albert Einstein to describe the relationship between energy and mass. Translated into words, it says the amount of change (E) that we may expect a material subject to be able to produce is directly proportional to a it's mass (m) and the square of the speed of light (c^2). It is certainly a very useful formula; however, in order for it to work, the subject of the equation must have the property of mass. But what about things which have no mass - things like space, for example?

The motion of a substance which has no mass would still require the subject to displace whatever lies in front of it and this change would certainly take an instance of time (t). Mr. Einstein's equation may be accurate, but it is incomplete. It addresses only the special case of subjects with the attribute of mass. I wonder if there is an equation which addresses both material and ethereal substances. I wonder if the additional terms that such a formula would require might finally resolve the issue of that pesky imaginary number X=sqrt (-1)

 

[StatusX]

First of all, how can space move? Relative to what? And what could you possibly mean by "the issue of that pesky imaginary number X=sqrt (-1)," and how is that related?

 

[selfAdjoint]

E=mc^2 is the simplified form of an equation given to us by Albert Einstein to describe the relationship between energy and mass. Translated into words, it says the amount of change (E) that we may expect a material subject to be able to produce is directly proportional to a it's mass (m) and the square of the speed of light (c^2). It is certainly a very useful formula; however, in order for it to work, the subject of the equation must have the property of mass. But what about things which have no mass - things like space, for example?

The full equation in special relativity is $$E^2 = p^2c^2 + m^2c^4$$. This equation is invariant under Lorentz transformations, i.e. it holds in every inertial frame. The content of the two sides of the equation varies from frame to frame, but the two sides remain equal in every frame. Notice the right side has 2 terms, and the second one is valid in the rest frame of a massive particle ("rest" meaning that in this frame, the momentum p of the particle is zero). So in this rest frame, the first term drops out and we have $$E^2 = m^2c^4$$ which is our old favorite $$E = mc^2$$ after taking a square root. Now consider a massless particle, this amounts to setting m = 0. So now the second term drops out, and that means that for a massless particle there IS NO REST FRAME; its momentum can never be zero!. Thus only the first term is valid and we have $$E^2 = p^2c^2$$; the energy of a a massless particle is the magnitude of its momentum multiplied by the speed of light. And this is the correct formula for such a particle.

Space does not move in special relativity. In general relativity space curves dynamically to reallize local physics. In cosmology space expands. But we do not need the concept of "speed of space".

The motion of a substance which has no mass would still require the subject to displace whatever lies in front of it and this change would certainly take an instance of time (t). Mr. Einstein's equation may be accurate, but it is incomplete. It addresses only the special case of subjects with the attribute of mass. I wonder if there is an equation which addresses both material and ethereal substances. I wonder if the additional terms that such a formula would require might finally resolve the issue of that pesky imaginary number X=sqrt (-1)

This is an attempt to apply prescientific concepts to a scientific subject. The mathematics of relativity is consistent and will deal with these cases. The square root of minus one comes in naturally where it naturally comes in and doesn't need to be pushed in.

 

[Jonny_trigonometry]

I'm beginning to wonder if maybe the concept of speed of space, or flux of space moving through a cross section of a referance frame could be used to develop the relations behind the speed of an atom through space (or flux of space through it), and the actual mechanics of it's behavior as a function of translation in space (or, space flowing through the atom). To put it more clear, I believe that atoms (at least the hydrogen atom) behave(s) differently (has different Psi functions) when it is traveling through space rather than when it is at rest. Right now, my hypothesis is that as it's sped up approaching C, the "orbital radius" of the electron moving around the nucleus stays the same in the direction of travel (counteracting length contraction in the direction of travel), but the "orbital radius" increases in the direction perpendicular to the direction of travel. It increases to infinity at C, and the radius in the direction of travel at C is still the same radius as when the atom is at rest. I'm betting that a more comprehensive derivation of the spin-orbit interaction when accounting for translation (of the entire atom) through space (or space moving through it) is the roadmap toward this relation.