Time is the potencial?

[Kuyukov Vitaly]

Perhaps time can be expressed as

 

$$ t=\frac{Gh}{c^4} \int \frac{dS}{r} $$

Where S is the entropy of entanglement of an arbitrary closed surface. r is the radius to the surface point. Integration over a closed surface.

This is very similar to the analogy. Time behaves as a potential, and entropy as a charge.

From this formula there are several possible consequences.

1. Bekenstein Hawking entropy for the event horizon. Light cone case

$$ ct=r $$

$$ S=\frac{c^3r^2}{Gh} $$

 

2. Gravitational time dilation. The case if matter inside a closed surface processes information at the quantum level according to the Margolis-Livitin theorem.

$$ dI=\frac{dMc^2t}{h} $$

$$ \Delta t=\frac{Gh}{c^4} \int \frac{dI}{r}=\frac{GM}{rc^2}t $$

 

3. The formula is invariant under Lorentz transformations.

4. If this definition is substituted instead of time, then the interval acquires a different look, which probably indicates a different approach of the Minkowski pseudometric with a complex plane

5. $$ s^2=(l^2_{p} \frac{S}{r})^2-r^2 $$      $$ l^2_{p}=\frac{Gh}{c^3} $$

6. Is such an interpretation possible? Sincerely, Kuyukov V.P.

 

 

 

1812.0145v1.pdf

Edited January 16, 2019 by Kuyukov Vitaly

[studiot]

I can't see how your first equation is dimensionally consistent.

How do you achieve this?

The dimensions are

G is ................M^-1L³T^-2

h is ................ML²T^-1

(velocity)4 is...L⁴T^-4

r is .................L

S is ................ML2T^-2K^-1

 

In any case four out of the five right hand side variables require time in their definition so your argument is circular.

 

Edited January 16, 2019 by studiot

[Kuyukov Vitaly]

Entropy dimensionless

S = tr (p In p) 

Edited January 16, 2019 by Kuyukov Vitaly

[swansont]

11 minutes ago, Kuyukov Vitaly said:

Entropy dimensionless

S = tr (p In p) 

S = -k_B tr (p In p)

Entropy has the same units as the boltzmann constant (joules per kelvin, in SI units)

[Kuyukov Vitaly]

Von Neumann entanglement entropy and Shannon entropy are dimensionless

[studiot]

3 minutes ago, Kuyukov Vitaly said:

Von Neumann entanglement entropy and Shannon entropy are dimensionless

Actually they are not.

They are related to the oft missed dimension of number N - in the case of non physical 'entropy' - the number of states.

However it still falls to you to answer properly my comments about the rest of the dimensional analysis and the question of circularity of definition.

[Kuyukov Vitaly]

1811.0134v1.pdf

[swansont]

A paper in Russian is not particularly helpful

[Phi for All]

!

Moderator Note

We need some clarity. There is obviously a language problem, but there are also some misconceptions that need to be adjusted, so posting a paper that predates those corrections is worthless. Please be more clear about your idea, or I'll have to shut this speculation down.

 

[Kuyukov Vitaly]

I'm trying to explain. Obviously there is a language problem. First, there are no contradictions in the dimensions of the first formula, everything converges there, if the entropy is dimensionless (according to Shannon, bits). Second, this naturally new formula raises questions, sometimes trivial. Thirdly, it is really difficult to understand if you do not know the current results of Beckenstein-Hawking.

I repeat once again, there are no any contradictions in the dimension of the first formula, carefully consider.