New Equivalence Principles?

[Shustaire]

You can have adjoints of a tensor though your right about the example above being poor as you would more likely use unitary vectors I,j,k . The linear transformations of inner products spaces or transpose of a tensor is one example a way to look at it is symmetric tensors with real value element are self adjoint.

The x,y,z example above would fall into a symmetric orthogonal space hence Hermitean and consists of real values so is  self adjoint

The Minkoskii tensor has a self adjoint for another example.

 

This isn't as good as a textbook on the topic obviously but it covers the basis of self adjoint operators

https://en.wikipedia.org/wiki/Self-adjoint_operator

 

Another memory rule is Any linear operator metrically equivalent to a symmetric contravariant tensor is self-adjoint. Under math I would use the descriptive a linear operation T on vector space V with scalar product ( inner products are scalar) [math] \langle\dot,\dot\rangle[/math] is self adjoint if

[math] \langle Tx,y\rangle=\langle x,Ty\rangle[/math] for all [math](x,y)\in V[/math]

 

a vector space with a Euclidean metric has a nondegenerate scalar product [math]\langle x,y\rangle =\displaystyle\sum_{x=1}^{n}x_iy_i[/math]

Edited July 31, 2018 by Shustaire

[Super Polymath]

I've literally given you an avenue to peer into your own future & you're still trying to divert attention to the thermodynamics of black hole systems

[Super Polymath]

This is a crystal ball, a quantum computer can be a gateway to get rich quick pyramid scheme brute force crack bitcoin

[Vmedvil2]

I agree with Dubbel, Polymath stop invading Dubbel's thread, I have considered getting moderators on you about doing this, Thankfully you don't do it to my threads. He has been much more patience then I would have been with you.

Edited August 1, 2018 by VictorMedvil

[Vmedvil2]

Ya,  I like polymath but man, he does tend to disturb threads with his own ideas, that is why you create your own thread, I feel the same way while I like polymath his thread hijacking gets old and butting into conversations where legit research is happening with his own ideas gets very old. In any case, I am still interested to see how you treat the forces in their current state within the universe model you have been working on.

[Vmedvil2]

Shustaire:

 

 

I have decided from the last link, that the transformation laws will apply only to the direction of motion. I am expecting the direction of motion needs to satisfy both red shift and blue shift corrections. I am also expecting for red-shifted systems, they will need to obey the logical consistency somehow of heat flows in a Riemannian metric - I actually think far ahead these were my ideas but I have no one that mathematically- headed that have done much work into my investigations, though some considerable discussions, here and from a few physicist-friends. 

 

The consistency we seek may even require just an additional understanding, such as corrections to show which system is truly cooler. Will look more into the at a later point as its pretty difficult this one.

 

I know this was directed toward shustaire but I will answer with my opinion, if I were you I would just directly relate it to the Cosmological constant and Dark Energy Expansion mathematically that will solve those issues.

[Vmedvil2]

this is partially why I had to knock bad one suggestion to get the theory into gauge groups, the problem is, gravity is a [pseudo] field and is not a gauge phenomenon from quantization of fields. I have been open to suggestions that curvature however is affected by a wave function. I have also suggested that the phase space applies to gravitational systems - one example I explored and wrote to the gravitational research foundation was that systems have decay rates which may depend on geometric properties of the system dictated by UP effects. One thought experiment was how a cloud of atoms not influenced by any other force but gravity, raised the question of an inequilibrium of the states leading to a Penrose gravitational collapse and collapse time. 

 

I know nothing of Quantum Mechanics so I will leave that to you, but I know that the cosmological constant and curvature will solve for Red and Blue shift.

Edited August 1, 2018 by VictorMedvil

[Vmedvil2]

I can't, because dark energy isn't actually good at explaining anything. We think a very small amount covers a square meter, but we don't even know what it is. We think its related to vacuum energy but even then we are not sure.

 

Dark energy is about acceleration rather than expansion, the truth is no theory explains expansion, unless you were willing to believe that entropy always increasing is actually a by-product of something that irreversible that happened in the early stages of bi bang. I don't see right now, if there is any... acceptable link between the thing we don't understand very well ''dark energy'' --- the acceleration however, does have an implication over global scales perhaps leading to a tired light hypothesis, but this needs to be taken with a pinch of salt. It is completely adequate to explain the physics from local dynamics were redshift and blueshift is measured from relative motion which has nothing to do with the accelerated expansion per se, it is basically the general relativistic analogy of the Doppler effect for light and that really can be explained by motion alone. 

 

But unfortunately, it is relative motion to curvature and expansion being part of red and blue shift does come from Expansion of the universe at some point you will have to explain it for your theory to be truly UFT. I know for me, it was one of the more difficult properties to quantify but you will come across the fact that it does contribute as well at some point.

Edited August 1, 2018 by VictorMedvil

[Vmedvil2]

Plus dark energy or even inflation explains why expansion happens at all. In a loose sense it related to entropy but I think that is only partly the case, since as I have explained, irreversible early dynamics could  have been the initial one-way drive of entropy (as opposed to seeing the law violated). 

 

Ya, I never worked on how it related to entropy but I know it contributed to the Forces of nature and their current state, I found as expansion happened the Dimensions that cause the forces started to expand as well causing them to decouple, but to entropy no idea how that DE/Expansion effects it, I suppose it allows more chaotic behavior in general as the system expands due to increase in potential movement, but it will be something you will have to tackle.

[Vmedvil2]

This isn't my understanding, I could be wrong. It is very true that distant objects subjected to the dynamics of the expansion of space will project very large redshifts. But it is not only distant objects, I am sure objects in our own milky way are affected by redshifts?

 

Surely the definition of red shift is that it applies to any body moving away from an observer?

 

Again, correct me if I am wrong.

 

Well, distant objects are effected more but objects even a planck length apart are gradually effected as the effect accumulates, it happens at every point in space equally, thus even objects that are close are slightly effected by expansion.

Edited August 1, 2018 by VictorMedvil

[Vmedvil2]

But expansion has no effects on the local dynamics inside a galaxy. If it could do that galaxies would be ripped apart internally.

 

That is correct, it has not major effect on the local dynamics but even now as we speak the points of space between those galaxies are expanding the more points of space that between objects the more this effect is noticed but gravity easily binds the galaxies together being much more prominent than expansion, expansion actually being overpowered by gravitational attraction, the weakest of all the forces, but even though you barely notice it, it is still there.

[Shustaire]

The usual boundary condition for a galaxy is when the strength of gravity exceeds that of the critical density by a factor of 200. This is chosen mainly as the value leads to a measurable mass density via luminosity to mass ratio.

[Vmedvil2]

Oh, dubbel I like that Power equation, I am stealing that. I am going to use that in my BH dyson sphere design for the QCD beam laser's yield (relativistic jet).

Edited August 1, 2018 by VictorMedvil

[Shustaire]

 

Just been trying to find an equation which will satisfy both the Ott and Einstein (et al.) transformations for both warmer and cooler bodies with respect to relativistic motion.

 

[math]\mathbf{S} = \frac{S}{k_B} = 2T \sqrt{1 - \frac{v^2}{c^2}} \frac{1}{1 - \frac{v^2}{c^2}} = \frac{2T}{\sqrt{1 - \frac{v^2}{c^2}}}[/math]

 

In which the Ott covariant transformation is 

 

[math]T = T_0 \sqrt{1 - \frac{v^2}{c^2}} = \gamma T[/math]

 

And the suggestion by Einstein and Planck was 

 

[math]T = \frac{2T_0}{\sqrt{1 - \frac{v^2}{c^2}}} = \frac{T}{\gamma}[/math]

 

par a factor of two that we have picked up through this derivation. I also notice these transformation laws linked like this together could maybe implemented into the equation I developed earlier on for the power emitted by an accelerated black hole with a mass, charge and angular momentum:

 

[math]P = \frac{2}{3}\frac{a^2}{(1 - \frac{R}{r})^2}(\frac{Q^2}{c^3} + \frac{J^2}{Gm^2c}) \leq \frac{2}{3} \frac{mr_g}{c}\frac{a^2}{(1 - \frac{R}{r})^2} = \frac{2}{3} \frac{r_g}{mc}\frac{1}{(1 - \frac{R}{r})^2}(\frac{dp}{dt})^2 [/math]

 

 

If temperature is covariant, is entropy covariant? I don't think so, I think the laws have to follow the contraction of the volume of the system, just as we applied to the black hole to satisfy the Penrose theorem of rotated spheres in relativity. The temperature in such a case, has to transform in the same way as the four volume. It seems fair to do this, since entropy can be either dimensionless or have units of the [math]k_B[/math] (the Boltzmann constant) which is well known to be a constant.

 

We may see how the change in entropy becomes dependent on the only covariant object which can lead to a variation in the temperature due to Lorentz contractions:

 

[math]\Delta S = \log_2(\frac{V_2}{V_1}) = \log_2(2) = 1[/math]

 

Or as a more compact argument, 

 

[math]\Delta S = Nk_B\ \log_2(\frac{V_2}{V_1})[/math]

 

Which reminds me a four-dimensional entropy equation which measured a the temperature through a similar ratio. In such cases, a ratio like

 

[math]\frac{V_0}{V} = \frac{T_0}{T}[/math]

 

is something I suspect can be formed. 

 

 

 

 I suspect your thinking of entropy in terms of amount of heat, its usual to treat the entropy as the effective number of degrees of freedom with the Maxwell-Boltzmann equations. This relies upon the particle species cross sections involved in the system state being examined.

 

For example a photon cloud of photons with its anti photons (photons being their own antiparticle) has S=2 S for entropy. So a state of thermal equilibrium such as the BB prior to symmetry breaking under strictly SM model of particles would be described via temperature itself. Photons as the mediator gauge boson for EM which temperature falls under would be a low entropy beginning of 2.

 

 Entropy today of the known particle family is something like 196 if memory serves correct.

Edited August 1, 2018 by Shustaire

[Vmedvil2]

BH QCD Matter Beam Yield

 

P_{BH  *} Δt(1- (V_{QCD Matter}²/C²))^1/2/C²  = M_jet

 

Edited August 1, 2018 by VictorMedvil

[Dubbelosix]

Ah, here we are:

 

https://ricciflow.quora.com/

 

the equations are in fact identical in the sense, it is totally possible to equate the two, will do in a moment while I take a smoke break.

[Dubbelosix]

This one I mean https://ricciflow.quora.com/The-Entropy-of-Heat-Flow