Theories on quantum geometry and entropy

[Paul Roberts]

Theories on the nature of quantum geometry and entropy. 

I am not sure whether or not you are familiar with the theory of quantum geometry, but I think it is rather interesting. Naturally, we are used to operating in the third dimension, as with the interaction of 3-D objects. In the 2nd dimension, we would only observe three-dimensional objects from the view of a two-dimensional plane. All we would see is the cross-section of a ball going through our plane, as though it were a shadow. It would, therefore, makes sense that geometry is also pervasive through higher dimensions. 

In theoretical physics, Albert Einstein postulated that there may be an affect on gravity in the 4th dimension of space-time, characterized by the einstein-rosen bridge or wormhole (elongated geometry into the 4th dimension?). This bridge may (as some theoretical physicists have wondered)  make possible phenomena such as entanglement. This may help explain the transference of information, which is not limited by the speed of light. 

Going further on the subject of geometry: Platonic solids, for example, have particular properties such as congruent sides, and shapes that come together in very precise and symmetrical ways. Most fascinating among the platonic solids is the sphere. What seems most evident is the fact that this is an eloquently simple, yet profoundly elaborate shape. What I mean to say is that there is a self-contained aspect, but for which allows for an infinite expansion in size and quantity (or variation). This seems to be verified by the consistent nature of Pi. I postulate that this principal may have to do with a persistent containment of entropy. If a shape were asymmetrical, there would be no self-containing aspect, and entropy would continue to chaos, the likes of which could not be adequately preserved. In other words, the universe would be unstable (but we know it to be stable). 

Conservation of Entropy

If the theory is correct, this would suggest that entropy is ultimately conserved as a function of expansion/contraction. Contraction would continue to the point of singularity (0). I postulate that going further beyond the singularity would result in imaginary numbers (of an inverse nature?).  There must be a way to express a sphere in variable mathematical terms (accounting for characteristics and size) and taking this expression, perhaps times the known expression for entropy, and maybe also accounting for the constant for Pi? We know that Pi is approximately equal to 3.14159 (though it is theorized that it is nearly infinite). 

If correct, this result would effectively tell you the degree of complexity within the system (our universe) at a given state. Interestingly, zero is both real and imaginary in mathematical terms. Perhaps the quantum world lies beyond the point of singularity and this is an inverted universe to that which we know. Interestingly, entanglement is equal and opposite. The theory is that, in order for a system to maintain connectivity, the system needs self containment. Otherwise, entropy resulting in infinite chaos cannot remain connected, and results in unstable collapse.

*I am not particularly gifted in mathematics but perhaps someone here is?

Considerations:

Applying the function of contraction to the idea of entropy, it seemed to me that there should be a way of considering what the idea of negative entropy would suggest. This is where I arrived at the notion of possible imaginary numbers (more appropriate to quantum physics) as the inverse form of entropy. If true, that would suggest a non-classical quantum mechanics lies on the other side of the singularity as an inverse universe to this one.

There is some discussion over whether or not entropy should be considered a measure of thermodynamics or else a more mechanical description. Some would say that the second law of thermodynamics prevents conservation but the flip side is that information is conserved, so why should entropy not also be conserved?

Mathematical expression for a sphere (as derive from a circle, but adding the 3rd dimension of additional space): (x−h)2+(y−k)2+(z−l)2=r2.  There would also need to be a variable added for the 4th dimension of time (perhaps a term involving relativity). 

Deriving the mathematical formula for entropy:

https://arxiv.org/pdf/physics/0301048.pdf

Edited February 10, 2023 by Paul Roberts
Misspelled

[joigus]

20 minutes ago, Paul Roberts said:

Most fascinating among the platonic solids is the sphere.

The sphere is not one of the platonic solids. Platonic solids are regular polygons:

https://en.wikipedia.org/wiki/Platonic_solid

21 minutes ago, Paul Roberts said:

Conservation of Entropy

Entropy is not a conserved quantity. See,

https://en.wikipedia.org/wiki/Second_law_of_thermodynamics

Quote

An increase in the combined entropy of system and surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.^[5]

If entropy was conserved, time would cease to exist as we know it, and I would look exactly as I did 50 years ago, and 50 years before that, and..., and...

24 minutes ago, Paul Roberts said:

Mathematical expression for a sphere (as derive from a circle, but adding the 3rd dimension of additional space): (x−h)2+(y−k)2+(z−l)2=r2.  There would also need to be a variable added for the 4th dimension of time (perhaps a term involving relativity). 

There is. It corresponds to a hyperbolid, not a sphere:

https://en.wikipedia.org/wiki/Spacetime#Spacetime_interval

[Paul Roberts]

Thank you, some good observations. 

Edited February 10, 2023 by Paul Roberts

[joigus]

11 minutes ago, Paul Roberts said:

Thank you, some good observations. 

Thank you, and no problem.

[sethoflagos]

49 minutes ago, Paul Roberts said:

Deriving the mathematical formula for entropy:

https://arxiv.org/pdf/physics/0301048.pdf

You claim to derive the 2nd Law from the 1st Law in this (unreviewed?) reference.

However to do this you rely on the relation dU = dQ_rev = TdS, which is a 2nd Law statement. 

Therefore your claim is undermined by a very obvious fallacy.

 

[Paul Roberts]

That is appreciated, sethoflagos. I realize the second law of thermodynamics is considered rather set in stone. However, I do believe it was used as a convenience of sorts with regard to entropy. 

 

The formula for entropy most likely was introduced to provide a convenient way to  calculate the changes in the internal energy of a system and to convert the thermal and mechanical energies into each other. 

[sethoflagos]

35 minutes ago, Paul Roberts said:

The formula for entropy most likely was introduced to provide a convenient way to  calculate the changes in the internal energy of a system and to convert the thermal and mechanical energies into each other. 

No. The 1st Law treats W & Q as equivalent. The 2nd Law was introduced to help explain their observed differences. eg why it is possible to convert W into Q completely while the reverse is not true.

 

 

[Paul Roberts]

I used to think this way too and I enjoy a healthy and respectful debate. Classical physics may be different than quantum physics with regard to states of matter changing in the backward direction of time (at least after exhausting all probabilities). I invite you to review this link, as an example.

https://www.google.com/amp/s/phys.org/news/2020-08-time-reversal-unknown-quantum-state.amp

I think what I am insinuating is the fact that there is a compatibility issue between classical and quantum with regard to the potential conservation of entropy. It seems to me that something is missing in the reconciliation of the two.

[joigus]

8 hours ago, Paul Roberts said:

with regard to the potential conservation of entropy.

What potential conservation of entropy? There is no such thing as conservation of entropy. You have a physical system. It has myriads upon myriads of microstates that have all the fine-detail distincions. Then you introduce coarse-grained distinctions, or cells, that include many microstates in them. That's information --of some kind-- for you. Perhaps because you don't know the fine details, perhaps because you don't care, or perhaps both, you don't know what's in the cells. No matter how you create the distinctions, if the system has the possibility to change --it hasn't reached thermal equilibrium yet-- your entropy will increase for the universe as a whole. It will also increase for an isolated system that hasn't reached thermal equilibrium yet. Example: A box, thermally isolated, with rigid walls. You have two different gases and a wall separating them. You remove the separating wall. The gases will mix, the system will reach a common temperature, pressure, volume, chemical composition, etc. All the information that you had stored in your system will have disappeared. Entropy has to do with information in the last analysis.

Only when your system has reached thermal equilibrium, your entropy will stay the same.

So no, there is no conservation of entropy, potential or factual. Entropy conservation would imply time, in a way, has ceased to exist. That's what people call thermal death of the universe.

[studiot]

The op claims to be new

 

Has anyone else the feeling of deja vu ?

I'm sure i've seen this junk before and I can't thik where else I might have seen it.

Does anyone else remember such a post ?

 

[Paul Roberts]

I understand what you are saying. Yet, time is relative. There is no actual absolute sense of time. Our understanding of time is incorrect. Everything is happening in the now moment and our observation is what changes. As you said, entropy is conserved at the point of thermal equilibrium. The concept is that eventually entropy is conserved. 

[joigus]

1 hour ago, Paul Roberts said:

I understand what you are saying. Yet, time is relative. There is no actual absolute sense of time. Our understanding of time is incorrect. Everything is happening in the now moment and our observation is what changes. As you said, entropy is conserved at the point of thermal equilibrium. The concept is that eventually entropy is conserved. 

If you mean the concept is that entropy is not conserved, and 'eventually' could mean 'infinitely far ahead in the future,' and that nobody is actually sure whether that will actually happen, among other things due to gravity being exceptional in almost every sense concerning entropy, and being the fundamental mechanism behind the evolution of the universe, I guess you're right.

3 hours ago, studiot said:

Has anyone else the feeling of deja vu ?

Indeedy!

[Paul Roberts]

We know that time is relative to the observer and there is no absolute sense of time. Suppose for a moment that the "lost information" we know as thermodynamic/mechanical entropy is ultimately harnessed and conserved, even though current physics states that the second law of thermodynamics (from relative microcosmic observation in the third dimension) indicates that lost information escapes and is never recovered. How would it make sense that energy is conserved but not entropy? If correct, this would imply that everything is happening in the now moment and may even suggest that expansion and contraction have occurred an infinite number of times in the past.

Granted, there is debate concerning the late Stephen Hawking's conclusions regarding whether or not information is actually lost inside of a black hole. However, it was once thought that information was lost, only to be concluded (at least by Stephen), that it was not.

Since it needs to be said, I will go ahead and say it (a bold claim no doubt): I propose that quantum geometry is the critical link for the marriage of quantum and classical physics and the pursuit of the "theory of everything". It is the preservation of quantum entropy we are referring to, by way of quantum uniform geometry. 

Edited February 12, 2023 by Paul Roberts

[Paul Roberts]

Going further: We know there are many paradoxes in physics.  Suppose that the reason for expansion and contraction actually has to do with the relationship between classical energy/quantum entropy. As established earlier in this post, I have proposed the notion of an inverse reality beyond the singularity, represented in quantum physics with imaginary numbers. Some theoretical physicists have already proposed that there may be an inverse universe where the arrow of time moves in the opposite direction as ours. We have seen in our own reality that quantum computers have been able to calculate algorithms consistent with states of matter changing in the reverse arrow of time. In this version of reality, we see that the nature of the universe wants to conserve energy, preferring a lower electron valence in chemistry, for example.  We know in this reality that, as energy is conserved, entropy is increased. This would account for expansion, perhaps. However, what if the opposite were true beyond the singularity (allowing for contraction)? In that sense, the entire system would be self-contained.

Edited February 12, 2023 by Paul Roberts

[swansont]

12 hours ago, Paul Roberts said:

Going further: We know there are many paradoxes in physics

True paradoxes, or just things called paradoxes because they require proper application of a concept, and are not actually paradoxical? (rather, they are not intuitively obvious)

[exchemist]

On 2/10/2023 at 1:33 PM, studiot said:

The op claims to be new

 

Has anyone else the feeling of deja vu ?

I'm sure i've seen this junk before and I can't thik where else I might have seen it.

Does anyone else remember such a post ?

 

I have the same feeling. There are the hallmarks of crankdom all right (principal ≠ principle, affect ≠ effect, "the 3rd dimension" ≠ 3 dimensions, etc.) plus of course the nonsensical notion of entropy being conserved. But I can't yet place it. 

12 hours ago, Paul Roberts said:

Going further: We know there are many paradoxes in physics.  Suppose that the reason for expansion and contraction actually has to do with the relationship between classical energy/quantum entropy. As established earlier in this post, I have proposed the notion of an inverse reality beyond the singularity, represented in quantum physics with imaginary numbers. Some theoretical physicists have already proposed that there may be an inverse universe where the arrow of time moves in the opposite direction as ours. We have seen in our own reality that quantum computers have been able to calculate algorithms consistent with states of matter changing in the reverse arrow of time. In this version of reality, we see that the nature of the universe wants to conserve energy, preferring a lower electron valence in chemistry, for example.  We know in this reality that, as energy is conserved, entropy is increased. This would account for expansion, perhaps. However, what if the opposite were true beyond the singularity (allowing for contraction)? In that sense, the entire system would be self-contained.

What do you mean by "electron valence" and what is meant preferring a lower value of this, whatever it is?

If - hazarding a wild guess - you mean what determines the preferred oxidation states of elements, this has nothing to do with energy conservation. (It has more to do with entropy, actually.)  

[joigus]

14 hours ago, Paul Roberts said:

Since it needs to be said, I will go ahead and say it (a bold claim no doubt): I propose that quantum geometry is the critical link for the marriage of quantum and classical physics and the pursuit of the "theory of everything".

I see no way in which anybody could disagree with it. And that's not good, I think.

[Paul Roberts]

What we need at this point is to resolve the mathematics, and then attempt to test the theories through experimentation.

[Paul Roberts]

Could it be that quantum information passes through the black hole while the physical mass is retained on this side of the singularity?

I have a saying,"To not think out of the box is to always be in the box". There has been a longstanding conundrum with regard to the notion of nothingness represented by zero. As we have seen, zero is both real and imaginary. If what I am saying is correct, there is an inverse universe equal and opposite to ours. This helps to explain entanglement. We should also consider the fact that there is no such thing as "nothingness". This has been pointed to by theoretical mathematicians. If there is an inverse relationship, then all that can exist closest to nothingness is both real and imaginary.

By the way, my apologies for incorrect grammar at times. I often use dictation software. 

[Paul Roberts]

I have a saying,"To not think out of the box is to always be in the box". There has been a longstanding conundrum with regard to the notion of nothingness represented by zero. As we have seen, zero is both real and imaginary. If what I am saying is correct, there is an inverse universe equal and opposite to ours. This helps to explain entanglement. We should also consider the fact that there is no such thing as "nothingness". This has been pointed to by theoretical mathematicians. If there is an inverse relationship, then all that can exist closest to nothingness is both real and imaginary.

By the way, my apologies for incorrect grammar at times. I often use dictation software. 

It seems to me that the first resolution should concern the "divisibility by zero conundrum". Instead of having zero represent nothing, a better representation should be an infinitely small, but not zero, superposition of real and imaginary -- (Schrodinger's Cat).

[exchemist]

19 minutes ago, Paul Roberts said:

I have a saying,"To not think out of the box is to always be in the box". There has been a longstanding conundrum with regard to the notion of nothingness represented by zero. As we have seen, zero is both real and imaginary. If what I am saying is correct, there is an inverse universe equal and opposite to ours. This helps to explain entanglement. We should also consider the fact that there is no such thing as "nothingness". This has been pointed to by theoretical mathematicians. If there is an inverse relationship, then all that can exist closest to nothingness is both real and imaginary.

By the way, my apologies for incorrect grammar at times. I often use dictation software. 

It seems to me that the first resolution should concern the "divisibility by zero conundrum". Instead of having zero represent nothing, a better representation should be an infinitely small, but not zero, superposition of real and imaginary -- (Schrodinger's Cat).

Why do you consider it necessary to duplicate this gibberish? 

[Paul Roberts]

Infinity is a difficult topic, granted. Effectively, it is the superposition we are trying to find. The point of superposition probability in quantum physics (equal probability of the cat being both alive and dead at the same time).

Exchemist, is it you alone who can think about these issues? Must you squander out of the box thinking in a speculative forum? A great service to science you are.

[Bufofrog]

1 hour ago, Paul Roberts said:

The point of superposition probability in quantum physics (equal probability of the cat being both alive and dead at the same time).

You do realize that a cat cannot be in a superposition state, don't you? 

[joigus]

57 minutes ago, Paul Roberts said:

Infinity is a difficult topic, granted

No. Sometimes infinity appears in a mild form, that can be tamed. That's why we teach those instances to teenagers (eg limits.)

Other times it's like you say. Still other times finite problems are every bit as difficult.

And quantum superpositions are not superpositions of 'real' and 'imaginary.'

What are you on about?

[Genady]

8 minutes ago, joigus said:

... teenagers ... limits

Pun intended?