Torsion and the Dirac Equation

[Dubbelosix]

As some of you may remember, I did investigate the Dirac spinors in the style of torsion, but I realised, I hadn't actually spoke about the Dirac equation itself and how gravity and then torsion would enter this brilliant and beautiful equation. The four equations which summed up the previous investigation was

∇x Γ = - 1/2c² ⋅ ∂Ω/∂t

Ω = 1/2mc² ⋅(dU/dt)

B x v = 1/2emc² ⋅ 1/r ⋅ dU(r)/dt ⋅ Jv

e(B x v) = 1/2mc² ⋅ 1/r ⋅ dU(r)/dr ⋅ Jv

The first equation is my take on how the gravitational field is related to the torsion, remember... torsion should be taken as important, since it encompasses the full Poincare group of spacetime symmetries, which means its a phenom that should occur in nature, and as my arguments have progressed, its something that may be important on the scale of particles, where acceleration and the tightly bound curvilinear trajectories are analogous to large gravitational contributions. Acceleration will be a major feature of our second treatise. The second equation, is how I define torsion explicitly, related to a central potential in which a particle can travel round a fixed axis. The third equation described the coupling of gravity and magnetism through a cross product of velocity, so that gravimagnetism arises from motion in the gravitational field, analogous to how a particle can experience an electromagnetic field as it has motion through it. In fact, an early pet theory of a gravitational mass was explained by me as a possible reason to why certain particles experience an inertial mass as opposed to some all pervading Higgs field, but such an alternative model would certainly be difficult for an academia to swallow, so I dropped the idea a while back. The fourth equation unified the third, with that of an analogous Lorentz gravimagnetic force equation, but as always in my own professing, we must be clear that gravity is not a real force from the first principles of relativity. So, what can we now say about a particle, that is following a curved path, and how do we translate these ideas into gravity carefully?

In order for a particles trajectory to be following a tightly curved path in space it must have a maximum of gravity that is translatable from GR, the maximum acceleration it can have will be approximate, or possible equal to (though this does not include the idea of black holes, which is the true upper limit using a gravitational classical upper bound) as,

a ~ mc³/ħ

acceleration did appear in one of the derivations i made, which was itself modelled from the work of Sciama, whose own paper was also on gravimagnetism, titled the "origin of inertia" and we implemented it into the spin orbit equation while defining a torsion directly from acceleration in the rotating frame 

a =  Ω x v

 Lets not toy too much as I really want to move on to the Dirac equation. There are many types of connections in mathematical physics, in fact, its one of the most complicated aspects of physics, I can't remember now off the top of my head how many there are, but its over a dozen. Whats unique about the connection though, is that they don't just come in different components, they are often written under different dimensions. For instance, in our work above, we defined the gravitational field as having units of an inverse length

∇x Γ = - 1/2c² ⋅ ∂Ω/∂t

These dimensions are most commonly found in literature, mostly because two connections define the Ricci curvature R, with dimensions of inverse length squared. Its also possible however, to define it under the j its of acceleration, in fact, because gravity and acceleration are phenomena that are coupled and for that matter, unified as the same thing under relativity, you might argue it is more accurate to measure it in these dimensions. If we were to create a gravitational field with these dimensions the next task would be to define how that itself is related to torsion. It can't be done in any ad hoc way, we need an argument to explain why the torsion would be related to it, just like how we related the gravitational field to torsion by a curve round some central potential. Keeping the torsion Ω as an artifact of motion, then we know from basic physics that (a change in velocity) divided by (a change in time) is the acceleration, so by redefining the connection as acceleration, we can now accutely redefine the torsion with dimensions of (a change in) velocity, so in a theoretical sense, the argument holds merit by such a remodelling. Such an equation would look like

Γ = ΔΩ/Δt

In this case, the gravitational field is taken in the rotating frame of reference, so that it can be related torsion. Now we want to write the Dirac equation in terms of a gravitational field. In can remember roughly how to do this from earlier essays a few years back when investigating how spin 1/2 particles would be written when interacting with some external gravitating mass, it is in the most simplest form

[pc ⋅ α + (mc² + mΓ ℓ ) β] = 0

where α and β are the usual Dirac matrices, following the unique properties of the Clifford algebra, where  ℓ is some affine length. We recall now that the gravitational field, is the ratio of the torsion with time, where again the numerator is measured as a velocity and the denominator with time. Since it is an acceleration, the maximal acceleration of the torsion field must be

 ΔΩ/Δt ~ mc³/ħ

 

Edited June 23, 2021 by Dubbelosix

[Vmedvil2]

On 6/22/2021 at 5:17 AM, Dubbelosix said:

As some of you may remember, I did investigate the Dirac spinors in the style of torsion, but I realised, I hadn't actually spoke about the Dirac equation itself and how gravity and then torsion would enter this brilliant and beautiful equation. The four equations which summed up the previous investigation was

∇x Γ = - 1/2c² ⋅ ∂Ω/∂t

Ω = 1/2mc² ⋅(dU/dt)

B x v = 1/2emc² ⋅ 1/r ⋅ dU(r)/dt ⋅ Jv

e(B x v) = 1/2mc² ⋅ 1/r ⋅ dU(r)/dr ⋅ Jv

The first equation is my take on how the gravitational field is related to the torsion, remember... torsion should be taken as important, since it encompasses the full Poincare group of spacetime symmetries, which means its a phenom that should occur in nature, and as my arguments have progressed, its something that may be important on the scale of particles, where acceleration and the tightly bound curvilinear trajectories fe analogous to large gravitational contributions. Acceleration will be a major feature of our second treatise. The second equation, is how I define torsion explicitly, related to a central potential in which a particle can travel round a fixed axis. The third equation described the coupling of gravity and magnetism through a cross product of velocity, so that gravimagnetism arises from motion in the gravitational field, analogous to how a particle can experience an electromagnetic field as it has motion through it. In fact, an early pet theory of a gravitational mass was explained by me as a possible reason to why certain particles experience an inertial mass as opposed to some all pervading Higgs field, but such an alternative model would certainly be difficult for an academia to swallow, so I dropped the idea a while back. The fourth equation unified the third, with that of an analogous Lorentz gravimagnetic force equation, but as always in my own professing, we must be clear that gravity is not a real force from the first principles of relativity. So, what can we now say about a particle, that is following a curved path, and how do we translate these ideas into gravity carefully?

In order for a particles trajectory to be following a tightly curved path in space it must have a maximum of gravity that is translatable from GR, the maximum acceleration it can have will be approximate, or possible equal to (though this does not include the idea of black holes, which is the true upper limit using a gravitational classical upper bound) as,

a ~ mc³/ħ

acceleration did appear in one of the derivations i made, which was itself modelled from the work of Sciama, whose own paper was also on gravimagnetism, titled the "origin of inertia" and we impleme ted it into the spin orbit equation while defining a torsion directly from acceleration in the rotating frame 

a =  Ω x v

So that we get after plugging it in

B = 1/2mc² ⋅ 1/r ⋅(m/r² + 1/c² [Φ + φ]Ω x v) ⋅ J

In a similar fashion, this maximal acceleration would enter as

B ~ 1/2mc² ⋅ 1/r ⋅(m/r² + 1/c² [Φ + φ]mc³) ⋅ J/ħ 

[see footnote 1.]

And by simplifying the like terms we get

B ~ c/2r ⋅(m/r² + 1/c² [Φ + φ]) ⋅ J/ħ

And simplifying further through the parenthesis 

B ~ 1/2r ⋅(p/r² + 1/c [Φ + φ]) ⋅ J/ħ

where p=mc is the momentum. Lets not toy too much as I really want to move on to the Dirac equation. There are many types of connections in mathematical physics, in fact, its one of the most complicated aspects of physics, I can't remember now off the top of my head how many there are, but its over a dozen. Whats unique about the connection though, is that they don't just come in different components, they are often written under different dimensions. For instance, in our work above, we defined the gravitational field as having units of an inverse length

∇x Γ = - 1/2c² ⋅ ∂Ω/∂t

These dimensions are most commonly found in literature, mostly because two connections define the Ricci curvature R, with dimensions of inverse length squared. Its also possible however, to define it under the j its of acceleration, in fact, because gravity and acceleration are phenomena that are coupled and for that matter, unified as the same thing under relativity, you might argue it is more accurate to measure it in these dimensions. If we were to create a gravitational field with these dimensions the next task would be to define how that itself is related to torsion. It can't be done in any ad hoc way, we need an argument to explain why the torsion would be related to it, just like how we related the gravitational field to torsion by a curve round some central potential. Keeping the torsion Ω as an artifact of motion, then we know from basic physics that (a change in velocity) divided by (a change in time) is the acceleration, so by redefining the connection as acceleration, we can now accutely redefine the torsion with dimensions of (a change in) velocity, so in a theoretical sense, the argument holds merit by such a remodelling. Such an equation would look like

Γ = ΔΩ/Δt

In this case, the gravitational field is taken in the rotating frame of reference, so that it can be related torsion. Now we want to write the Dirac equation in terms of a gravitational field. In can remember roughly how to do this from earlier essays a few years back when investigating how spin 1/2 particles would be written when interacting with some external gravitating mass, it is in the most simplest form

[pc ⋅ α + (mc² + mΓ ℓ ) β] = 0

where α and β are the usual Dirac matrices, following the unique properties of the Clifford algebra, where  ℓ is some affine length. We recall now that the gravitational field, is the ratio of the torsion with time, where again the numerator is measured as a velocity and the denominator with time. Since it is an acceleration, the maximal acceleration of the torsion field must be

 ΔΩ/Δt ~ mc³/ħ

 

 

[1.] Footnote

We notice that we where able to take a more fundamental maximum expression for the acceleration and we plugged it into our gravimagnetic equation as

B = 1/2mc² ⋅ 1/r ⋅(m/r² + 1/c² [Φ + φ]mc³) ⋅ J/ħ

we plugged in the values in certain ways for a specific reason, for instance, you will find the ratio J/ħ related to magnetic moments from usual quantum theory, or in this case, the extended gravimagnetic moment, though its now quite that. We did investigate how it arises in the first investigation by noticing the following derivation: 

 

1/G = Φ/c²

a/G = 1/r ⋅ ∂m/∂r = ω²r/G

1/e⋅ ∂U/∂r = c²/e⋅ ∂m/∂r

In CGS units. A gravielectro field now defined as

E = 1/2emc² ⋅ 1/r ⋅ ∂U/∂r ⋅ Jc = 1/2e ⋅ ∂U/∂r

Plugging in now the inverse Bohr mass we get

E = 4π²eB/2mc⋅ 1/r ⋅ ∂U/∂r ⋅ J/h

Here we can identify an important term arising as the magnetic dipole:

μ = eJ/2mc

So we can write

μ(S) = -g μ J/h

This now gives

E = -4π²μB⋅ 1/r ⋅ ∂U/∂r ⋅ J/h

Notice how beautifully it roles out, it was one basic achievement of this theory which appears to show a consistency in the coherence of the dynamics involved. A similar result is found in the wiki article on spin orbit interaction, similar, but not quite the same, so it was a unique discovery in itself.

 

Okay, It's time for the brass tax on your equations dubbel, what evidence do you have that gravimagnetic effects are displayed in physical reality? This is all interesting and the equations look to be balanced and good however just math isn't good enough I could make a equation that says the universe is a cube but if the universe isn't actually a cube it doesn't speak about this universe, you get where I am coming from. What is the hard evidence that the universe behaves in the way your equations describe that you are speaking about our physical reality? A example of such is that you can solve string theory a million different ways however there is only one version that shows our universe, what evidence do you have that our universe is being shown by these equations and not just another universe that could exist or do you indeed say you are describing another alternate universe in hyperspace with different initial conditions of the big bang along with space/time/force dimensions such that it has gravimagnetic dimensions as a force dimension much like my model includes a Flavour Force Dimension/Quantum Number in the (https://www.scienceforums.com/topic/35724-wormhole-metric-continued/) thread to explain Dark Matter which recently has some evidence for its existence(https://www.bbc.com/news/56643677)? So basically, What besides math do you have to show that this exists in that manner?

 

Edited June 23, 2021 by VictorMedvil

[Dubbelosix]

OK, so first of all I argue that torsion must play a role in some way in physics, because it encompasses the Full Poincare group of space symmetries. So its a natural thing to do.

Second, the vanishing of torsion in GR is a actually just an assumption in academia, you can if you do some investigation, find that many top authors have argued that its only speculation that we make torsion vanish, and there is the Cartan Einstein model, which as far as observation goes, explains reality just as well, maybe arguably more accurately than our current model which can be thought of as a limited version of the Full Poincare group. Heres what wiki has to say about the issue

"

Einstein–Cartan theory differs from general relativity in two ways: (1) it is formulated within the framework of Riemann–Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian geometry, which does not; (2) an additional set of equations are posed that relate torsion to spin. This difference can be factored into

general relativity (Einstein–Hilbert) → general relativity (Palatini) → Einstein–Cartan

by first reformulating general relativity onto a Riemann–Cartan geometry, replacing the Einstein–Hilbert action over Riemannian geometry by the Palatini action over Riemann–Cartan geometry; and second, removing the zero torsion constraint from the Palatini action, which results in the additional set of equations for spin and torsion, as well as the addition of extra spin-related terms in the Einstein field equations themselves."

Thirdly, I have no proof as of yet whether torsion plays a role in particle dynamics, but I did show my preliminary work to Ruth Kastner who has rightly said, that according to current view, electromagnetism and gravity are usually considered "different animals" and this is mostly based on the assumed force difference between the two... but... I went on to explain that the Nobel prize winner Abdus Salam had invented an alternative model for the strong force, where gravity becomes a scale dependent phenomenon, so that gravity only appears weak on galactic scales. Moreover, and something I never did explain in that conversation gravity and magnetism are incredibly "similar animals" because  both share a common feature, that is that they are motion and frame dependent phenomena. For instance, early field theories that where extremely ambitious in their attempts to unify gravity with the rest of the forces, they went and quantized gravity, suggested it not only had a particle mediator (the graviton) but because electromagnetism unified with the weak forces achiever energies (which has since been has perimentally varified), it is believed then that gravity would do the same thing. There may be no reason to doubt this, but the biggest error physics has ever made concerning gravity in the modern age, at least in ju opinion, and some other physicists I have spoke to, is that gravity isn't even a force, its a frame dependent, motion dependent pseudo force. When we say this, it has huge implications to our search for unification, because it essentially means that field theories about gravity being quantized has to be wrong, because it breaks the first principles of relativity when it speaks about gravity as a manifestation of curvature.

So why is magnetism is a "similar animal?" Well, in relativity, to was shown that magnetism arose from a motion and frame dependent phenomenon, just as the coil and wire experiment showed, and so magnetism is more like gravity than the electroweak and the theoretical electrostrong unification. Magnetism was once thought to be quantized, it was Dirac who said it was theoretically possible that magnetism was quantized and its quantization was going to be called the monopole, but after decades of experimentation, just like gravity, neither have been found to have any particles which mediate these phenomenon. Because of this, I think unification has better possibilities in the case of gravity and magnetism, this linearized theory of gravity doesn't just end with magnetism, being gravimagnetism, it may speculatively hold onto a fuller unification to a gravielectric field as well.

Hat evidence do we have of gravimagnetism? We have a lot of evidence, but there is one particular phenomenon which has a mathematical representation that eerily similar to magnetism, called the Coriolis effect, which is also gravitational in nature when spin is included. There's a paper out there, titled, "why is the coriolis effect like gravimagnetism,"or something to that effect, which is the first seriou investigationj know of that has picked up on the fact that magnetism and gravity are coupled in a weak way through the presence of spin, because of this, I argue we need to go back to the basics of similar phenomena, such as frame dragging. While frame dragging is a prediction from GR without a theoretical need for torsion, it is in fact true that Einstein once admitted that his theories failed to properly account for torsion because he found it difficult to visualise. Today, we know it to be a type of twisting of space, a distortion of space that is dragged around a body of mass. Frame dragging to conclude, could be just a weak approximation of torsion, because frame dragging is the local dragging of space around the best tested object we have, which Earth. Because of the twisting of the space around the local vicinity of Earth, we also have magnetic fields round the vicinity of Eartg, which is believed to arise from a spinning iron core. But Earth is not the only system that we have found that has twisted space around it, just a year or so back, I made a point of keeping a news article in my essay database on quora, which explained that they had discovered strong evidence of a star literally dragging space round with it. I was strongly impelle by it, because an alternative theory of dark matter, which I not only adopted but later extended mathematically, was the idea that rotation curves where partly a phenomenon caused by the strong gravitational binding energies found in the center of galaxies, from two different model types, huge collections of semi large black holes which we know have condensed to most typical spiral galaxies, and those which still harbour their supermassive black holes, which are mechanically dragging space sound with it. It became the cosmic seeds in my theory which helped to form the first primordial galaxies and keep them held together.

I found even more evidence of this, where I studied several known galaxies whose suoermassive black holes had been ejected to find that the rotational effects of those galaxies where slowly ripping them apart due to the internal centrifugal forces, which is analogous to an antigravity effect. You might come to realise, why I became angry, at an article only in the last year where a group of scientists said that if dark matter was a gravitational local effect of galaxies, then gravity would have to be acting extremely weird. Its not acting weird in a rational mind where upermassive black holes  which are now many times more solar masses than first expected, is twisting space analogous to frame dragging and torsion, but on much larger scales. The best way to visualise these dynamics, is that the black holes is what we call space, so the black hole does not rotate in space, it is the rotation of space, thats a crucial difference! Its like a drain, in which water being the matter around it, is twisted round a common center,

Edited June 23, 2021 by Dubbelosix

[Dubbelosix]

I've removed the simplifications, in the Op, well do it here  because we can do it in a nicer way.

 

...So that we get after plugging it in

B = 1/2mc² ⋅ 1/r ⋅(m/r² + 1/c² [Φ + φ]Ω x v) ⋅ J

In a similar fashion, this maximal acceleration would enter as

B ~ 1/2mc² ⋅ 1/r ⋅(m/r² + 1/c² [Φ + φ]mc³) ⋅ J/ħ 

write everything out we get

B ~ 1/2mc² ⋅ 1/r ⋅mmc³/r² ⋅ J/ħ + 1/2mc² ⋅ 1/r ⋅ 1/c² [Φ + φ]mc³ ⋅ J/ħ 

now combine like terms we get

B ~ 1/2mc² ⋅ 1/r ⋅m² c³/r² ⋅ J/ħ + 1/2mc⁴ ⋅ 1/r ⋅ [Φ + φ]mc³ ⋅ J/ħ 

now we simplify the numerator with all terms on the denominator and we get

B ~ m² c³/2mc² ⋅ 1/r³ ⋅ J/ħ + mc³/2mc⁴ ⋅ 1/r ⋅ [Φ + φ] ⋅ J/ħ 

~  p/2⋅ 1/r³ ⋅ J/ħ +  c/2r ⋅ [Φ + φ] ⋅ J/ħ 

~ p/2 ⋅ J/ħ +  c/2r ⋅ [Φ + φ] ⋅ J/ħ 

where  is the momentum p density, now we replace all like terms outside the parenthesis again,

~ 1/2 (p +  c/r ⋅ [Φ + φ]) J/ħ 

why does our gravimagnetic field have units of a momentum density from the first term in the parenthesis? I will check the dimensions. I know that from the cgs units Sciama used, the expression Φ + φ has units of 1/Newtons constant, or 1/G so we can experiment mathematically, say we have

rc² = Gm

Which is the gravitational parameter. Invert, 

1/rc² = 1/Gm

And multiply through by the mass

m/rc² = 1/G

Let's plug it it check dimensions

c/r x m/rc² = m/c

So here the dimensions are popping up wrong again, it's missing a factor c in the numerator and also missing a factor of r squared in the denominator... why are these things happening to me lol. I swear I've been very careful deriving these things carefully, maybe it's a matter of the issue that I've used Sciama's slightly odd cha u its of 1/G for the value of Φ, which in ordinary standard units has a value of c²? I'll tell, you what, without checking it, let's do a smudge factor, I know what the missing factors so far are under our usual units, putting one factor of c in the denominator and an extra factor of r²,

~ 1/2 (p +  c²/r⋅ [Φ + φ]) J/ħ

Now let's plug in m/rc² for the Φ + φ and see if turns into a momentum density

~ 1/2 (p +  c/r² ⋅ m/rc²) J/ħ) 

Combining now 

~ 1/2 (p +  mc/r³) J/ħ

OK  so thats right now... but is it right to define the gravimahnetic field as a momentum density? There's a less dubious way to test this, because it seems like Sciamas units has completely messed up the original investigation  I'd say we'd be much safer to ignore his model and work fro  the conventional spin orbit equation.

For anyone reading this and wondering how this happened  welcome e to world of units where equations are a matter of trial and error, which need to be fixed! I won't finish today until its done either.

[Dubbelosix]

OK, so know my first four equationsare absolutely correct, we know this because we investigated the spin orbit equation for its dimensions and found that the central potential was written with a derivative of time, which was fine unless I admitted one inverse unit of speed of light which we fixed and we got the correct equation as

e(B x v) = 1/2mc² ⋅ 1/r ⋅ dU(r)/dr ⋅ Jv

To get an acceleration this equation, important for the maximal acceleration we were investigating  we can take the derivative of the equation, which is just a time derivative of the force,

e(B x v') = 1/2mc² ⋅ 1/r ⋅ dU(r)/dr ⋅ J(dv/dt)

where v' would be our usual dot notation. Now the equation has on the RHS an acceleration term

e(B x v') = 1/2mc² ⋅ 1/r ⋅ dU(r)/dr ⋅ Ja

Plugging in the maximal acceleration

a ~ mc³/ħ

we get

e(B x v') ~ J/2mc² ⋅ 1/r ⋅ dU(r)/dr  ⋅ mc³/ħ

Now we can do two things, each unique in their own separate ways, we can identify the Josephson constahtby using  mc² ⋅r = e giving

e(B x v') ~ J/2e ⋅ dU(r)/dr  ⋅ mc³/ħ

which is probably the most attractive version, or we can simplify a term of mass

e(B x v') ~ J/2c² ⋅ 1/r ⋅ dU(r)/dr  ⋅ c³/ħ

both these equations are absolutely accurate terms of dimensional analysis. 

[Dubbelosix]

There's two concise way and identify to measure the units of c³/ħ 

e(B x v') ~ J/2c² ⋅ 1/r ⋅ dU(r)/dr  ⋅ c³/ħ

The Planck length is

ℓ =  √ħG/c³

so inverting we get

1/ℓ =  √c³/ħG 

and squaring before rearranging we get

G/ℓ² =  c³/ħ

or from a previous identity in the OP we also have it related to torsion  as

(ΔΩ/Δt)/m ~ c³/ħ

where again, the torsion Ω has units of velocity so you can take your pic which set of identities you'd like to associate with the ratio.

Edited June 23, 2021 by Dubbelosix

[Dubbelosix]

Either way, whether you take it to be the gravitational constant divided by the Planck length squared or by torsion x time divided by mass, both interpretations have roots in gravitational physics.

Edited June 23, 2021 by Dubbelosix

[Dubbelosix]

Also one last curious prediction, in contrast to the Jospephson constant J/2e which is about the mechanics of magnetic flux, 

e(B x v') ~ J/2e ⋅ dU(r)/dr  ⋅ mc³/ħ

One thing I did obtain from the simplification alternative, is yet a third gravitational interpretation by combining J/2c² ⋅ 1/r and doing so leads to a gravitational parameter 

e(B x v') ~ J/2c² ⋅ 1/r ⋅ dU(r)/dr  ⋅ c³/ħ

μ =Gm = c²r

leading to 

e(B x v') ~ J/2μ ⋅ dU(r)/dr  ⋅ c³/ħ

Edited June 23, 2021 by Dubbelosix

[Dubbelosix]

Right im off to go back to my chess training, I've established to keep Sciamas a bit mystical equations out of my investigation because our units are clashing with each other, nice though to know though that my spin orbit interpretations are holding up. No clash in dimensions there.

Edited June 23, 2021 by Dubbelosix

[Dubbelosix]

It just occurred there from playing a chess, game, the Unruh temperature! I'm sure you're thinking 'and?'

[Vmedvil2]

7 minutes ago, Dubbelosix said:

It just occurred there from playing a chess, game, the Unruh temperature! I'm sure you're thinking 'and?'

How did playing chess make you think of Unruh temperature? It seems pretty not connected.

[Dubbelosix]

well, let's take the equation

e(B x v') = 1/2mc² ⋅ 1/r ⋅ dU(r)/dr ⋅ Ja

The general understanding of heat comes from the kinetic motion, and thus, jnternal accelerations of systems in the surrounding space or object. I just realised that there is a temperature dependant interpretation encoded in the (Ja) part of the equation. OK, so J completes the total angular momentum, while ħ Is a quantum version, so an analogous Unruh temperature dependant version 

well, let's take the equation

e(B x v') = 1/2mc² ⋅ 1/r ⋅ dU(r)/dr ⋅ Ja

The general understanding of heat comes from the kinetic motion, and thus, jnternal accelerations of systems in the surrounding space or object. I just realised that there is a temperature dependant interpretation encoded in the (Ja) part of the equation. OK, so J completes the total angular momentum, while ħ Is a quantum version, so an analogous Unruh temperature dependant version 

T = Ja/2πck

Rearranging we get

2πckT = Ja

This is a natural unification, because the spin orbit equation is an equation of circular kinetic motion, so we have, after plugging it in

e(B x v') = π ⋅ mc³/r ⋅ dU(r)/dr ⋅kT 

where k is the Boltzmann constant.

 

 

Edited June 25, 2021 by Dubbelosix

[Dubbelosix]

3 minutes ago, VictorMedvil said:

How did playing chess make you think of Unruh temperature? It seems pretty not connected.

well I was thinking about the peices where moving about and I instantly thought about the particles moving about in a system.

[Vmedvil2]

2 minutes ago, Dubbelosix said:

well I was thinking about the peices where moving about and I instantly thought about the particles moving about in a system.

Okay, so explain it to me, how do I make a Gravimagnetism weapon, what is the strength of it? Can I like blow up black hole or something with it?

Edited June 23, 2021 by VictorMedvil

[Dubbelosix]

Good question, let me think about it. It would have to be in the style of a very theoretical science.

[Dubbelosix]

I should also note, we can also state that a centripedal acceleration is encoded in the equation

e(B x v') = π ⋅ mc³/r ⋅ dU(r)/dr ⋅kT 

As 

 mc²/r

and this will probably lead to new investigations, anyway, how can we make a gravimagnetic weapon?

[Vmedvil2]

3 minutes ago, Dubbelosix said:

I should also note, we can also state that a centripedal acceleration is encoded in the equation

e(B x v') = π ⋅ mc³/r ⋅ dU(r)/dr ⋅kT 

As 

 mc²/r

and this will probably lead to new investigations, anyway, how can we make a gravimagnetic weapon?

Does it have a force equation like the coulomb's law or newton's law of gravity, To make a weapon I need something that explains the parameters and what effects it. what is dU?

Edited June 23, 2021 by VictorMedvil