I think it is better to understand that black holes undergo Infinite Entropy, not 'maximum entropy,' as there is no definition whatsoever of what maximum entropy would be.

Infinity means literally 'increasing without bound.' thus, this suggests that change is a constant increase in entropy, which would involve consuming more mass-energy to accommodate that.

as Infinite Entropy, constat change would then be part of the definition.

William, thank you for sharing your perspective. I see that we both agree on one crucial point: describing black holes as being in a state of “maximum entropy” is misleading, because that implies a static endpoint where no further change is possible. Yet observations show that black holes clearly do change.

Your framing of black holes as undergoing “infinite entropy” is interesting, because it naturally incorporates constant change — entropy increases without bound, and therefore absorption and radiation are expected behaviors.

From my QTIP Cosmology perspective, I interpret the same issue slightly differently. Rather than calling it “infinite,” I view black holes as regions where expression into the observable (real-number) domain has halted, while internal computation and entropy growth continue in the imaginary domain. To outside observers, this looks like a frozen surface, but internally, change is ongoing.

In this way, your “infinite entropy” view and my “halted expression but ongoing computation” view converge: both reject the static maximum-entropy model, and both insist that black holes must remain dynamic systems. We simply describe the mechanism in different terms.

@Seungyoung Choi:

This is where conventional delta-S entropy and Shannon Entropy diverge. I've attached a pdf that you may find interesting if not useful to your work.

William, I appreciate your suggestion to consider Shannon entropy. Indeed, your description — that Shannon entropy applies to systems of more than one causal path, always unobservable — resonates strongly with my own QTIP interpretation of black holes.

In QTIP Cosmology, I describe black holes not as static endpoints of “maximum entropy,” but as regions where expression into the observable real domain fails due to computational overload, while internal information processing continues in the imaginary domain. From an external perspective, this “expression failure” looks like a frozen surface, but internally, the system is still evolving dynamically.

This seems very close to what Shannon entropy implies: once a system moves beyond a single causal path, its state becomes unobservable, and entropy no longer corresponds to a tangible trajectory but to hidden informational multiplicity. In this sense, the QTIP view of expression failure and Shannon’s view of >1 causal path unobservability might be two descriptions of the same underlying reality.

In my recent work on particle properties under QTIP Cosmology, I described the wavefunction’s probabilistic state as an absolute domain of imaginary information. I believe this probabilistic framework can also help to interpret Shannon entropy as a form of probabilistic load increase, which seems directly relevant to your point.

Thus, I find your reference to Shannon entropy to be a valuable reinforcement of my own interpretation, and I will consider integrating this information-theoretic framing into my broader development of QTIP Cosmology. Thank you again — for an independent researcher like myself, such a reference is especially valuable.

@Seungyoung, youre right, they do seem to express the same concpts. I have a Probabilistic set of expressions in Markov Mechanics that i will dig out tomorrow and post here for you to look at. perhaps you can gleen something useful from it.

William Bray William, thank you so much for taking such genuine interest in this discussion. It really means a lot to me, especially as an independent researcher, to have someone engage thoughtfully and even offer to share their own work. I truly appreciate it.

@Seungyoung, here is the PDF file of the Markov Mechanics fine structure probabilities, etc.

William Bray William, thank you very much for sharing your PDF on Markov Mechanics — I truly appreciate the effort and generosity. I will go through it carefully, and I’m sure I can learn something valuable from your approach.

As an independent researcher, it means a lot to me to have this kind of exchange. My own work in QTIP Cosmology approaches physics as an information-based cosmology — an “information universe” framework where black holes, particles, and even time itself are redefined through information processing and expression.

I also hope you might take a look at some of my QTIP papers when you have time — especially the ones on particle properties and the fundamental nature of time. They might offer another perspective that connects with your ideas.

Thank you again for this generous collaboration. By the way, I am based in Korea, and as I write this it is about 1 a.m. on September 11 here — but exchanges like this make the late hours feel worthwhile.

William Bray By the way, I have also opened a separate new discussion on the fundamental nature of time, focusing on whether it is truly continuous or discrete (tick-based). Since it connects closely with our current topic, you might find it interesting:

"What Is the Fundamental Nature of Time: Continuous Flow or Discrete Ticks?"

Seungyoung Choi

Quantum Information Dynamics in 3 volumes:

Preprint Quantum Information Dynamics Volume I and II

Preprint Quantum Information Dynamics Vol III: The Delayed Choice Lunar Landing

As for quantized time on a Planck scale:

Preprint The Evolution of Spacetime on a Planck Scale

William Bray I have not yet read your papers in full detail, but I have looked through them with great interest. I found them profound and impressive, and I believe they will be of great help in expanding the conceptual framework of my QTIP cosmology. Your approach to information dynamics and entropy resonates with my own research and has given me much inspiration. In particular, regarding the concepts and mechanisms of black holes, white holes, and wormholes, I think the structural ideas of QTIP may, albeit modestly, also contribute to your research. I would be grateful for your thoughts on these aspects.

Seungyoung Choi , building on prior works is what physics is all about. you can't reinvent the wheel with every paper. there are some very serious researchers right here on RG you should look into.

in any case, take your time with the papers and if you have any questions it is much easier to email me, don't be shy:

[email protected]

i'll help you with any questions you may have.

William Bray I sincerely appreciate your kind offer to help with my QTIP research. I am not trying to create an entirely new wheel, but rather to make the existing wheel more efficient in its structure.

I have the deepest respect for modern physics and have built my work upon the achievements that have been accumulated so far. However, I found that by reconstructing a few concepts in a different way, it is possible to provide clearer and more compelling interpretations without denying existing theories. My current research, therefore, seeks to include and honor established physics while at the same time reinterpreting parts that have been mathematically vague or only conceptually defined, and to reshape them into a clearer mathematical structure through QTIP.

For example, by dividing the continuity of time into discrete ticks (T4), I was able to distinguish the domains of quantum theory and relativity. By then locating the absolute storage of information in the imaginary domain and structuring it with Quell sets, I found that a new level of interpretation became possible.

In particular, this approach allowed me to reinterpret the characteristics of particles, the foundation of which lies in a redefinition of the wave function. I modified the wave function so that it applies only within the discrete T4 intervals. As a result, I was able to newly define the essence of the wave function as an absolute domain, and from this, reinterpret Vev—previously used only conceptually as the basis of mass calculation—as the volume of a virtual sphere that sets probabilistic boundaries.

As an independent researcher, I recognize that such attempts may appear rather bold. I also fear that because my framework simplifies the beautifully complex mathematics of conventional physics, it may feel unfamiliar or even unsettling to many physicists. Furthermore, I worry that some of these ideas might simply reflect errors caused by my own limited mathematical ability.

Yet at the same time, I cautiously believe that this new perspective can lead to more avenues of interpretation than existing theories. I see myself only as a child standing before the lake of truth, tossing a small stone into its still surface and creating ripples. By myself, I can never be enough; the help of many others who take an interest in QTIP is indispensable.

In this sense, the advice of experienced experts like you would be of immense value to me. Once again, I am truly grateful for your kindness.

And finally, is it not both thrilling and deeply moving to discover structures hidden by time itself within the universe? I hope we may work together to uncover that hidden structure of time.

A maximum entropy state simply does not mean that nothing can change anymore. Entropy can decrease in open systems (by flowing out of them). Maximum entropy implies no change only in an isolated system, which a black hole in vacuum simply isn't. It emits Hawking radiation, decreasing the entropy of the black hole and increasing the entropy of the universe at large. The balance is not zero, the total entropy of a black hole plus its Hawking radiation is bigger than the entropy of the black hole before it emitted the radiation.

Constant-velocity motion would not be a change of state, btw.

K. Kassner I also do not regard a black hole as an isolated system. However, since in modern physics it is still often described as being in a state of maximum entropy, I raised this question. From the perspective of my QTIP research, I agree with your statement. Inside a black hole, the processes of information computation and integration continue, but remain in a state that cannot be expressed in the real (observable) universe.

As you pointed out, in a system under constant velocity no change occurs, which can indeed be regarded as equivalent to rest. However, my concern is that even if acceleration exists inside a black hole, the results of such processes are not expressed in the observable world. For this reason, I find it problematic to describe the state of a black hole solely in terms of entropy as observed externally.

Hawking radiation, in my view, can likewise be understood as the residual output of these computations at the event horizon, expressed externally. Moreover, if a singularity truly existed within a black hole, it would be akin to driving a nail into the fabric of spacetime and fixing it permanently. From the perspective of QTIP Cosmology as an informational cosmology, I consider that singularity convergence should not be mathematically determined at all, because the universe is structured by discrete information into finite forms. Singularities appear only in an infinite continuum. For this reason, I do not regard singularities as existing inside a black hole; rather, the event horizon itself appears as the boundary where expression becomes impossible, a structure as I see it.

Therefore, describing a black hole solely as a state of maximum entropy seems incomplete; it may be more appropriate to interpret it from an open-system perspective. In QTIP Cosmology, this process is regarded not as the cessation or loss of information, but as information that remains unexpressed and later becomes expressed externally under certain conditions. In this sense, my QTIP papers may be modest, but if you could kindly take a brief look and share your opinion, it would be of great help to me. I would also be very grateful if you could share your own view on the issue of black hole singularities.

Guys, Maximum Entropy is not even a defined thing. the form of entropy cant be coneventional delta-S because, if you abide by AdS/CFT , the entropy is defined as infinite, increasing without bound, and every Q-bit is being Multiply Connected. delta S entropy cannot describe systems that are connected by more than one causal path. only Shannon Entropy can describe the system; Shannon Entropys lower bound is two causal paths, extending to infinity.

since Hawking based his model on conventional delta S, and since the otherwise very detectable hawking radiation has never been detected, there is no hawking radiation. furthermore, hawking radiation borrows its information from beyond the Schwarzschild Surface of the black hole, not from the black hole itself.

ive read your QTIP papers and the underlying thing that is absent is a causal source, informing the information what to do with itself. your phase diagrams cut spacetime finer than the Planck limit will allow. you cant have a smooth transition across two Planck lengths of space or time. there are no curves at the Planck limit, only ones and zeros.

William Bray Thank you for taking the time to read my paper. The phase diagrams I presented are not intended to “cut” time into fragments, but rather to express the structure of time itself. What we perceive in our universe as continuous time is represented in the diagrams by the green blocks labeled as “frames,” and between these frames lies the tick (T4).

Within each T4 interval, the Information PR performs computations based on information existing in both the real and imaginary domains, and then delivers the results to the Expression PR. The Expression PR subsequently renders them into physical reality. In this structure, a causal source naturally emerges. Moreover, the branching structure of Shannon entropy can also be understood as arising naturally within the T4 interval, through probabilistic information.

The “frozen state” you mentioned can indeed be defined as the state within this T4 interval. That is, when the universe expresses something based on information, we perceive its sequence as time. However, the T4 itself cannot be directly observed.

What I am asserting through QTIP goes beyond the conventional notion of Planck time: it is about how time itself is structurally organized. Therefore, the Planck time—defined only with respect to the time we can observe—is not fundamentally relevant here. The diagrams are simply structural representations of time, not subdivisions constrained by the Planck scale.

Although it is admittedly a very unfamiliar concept, structuring time in this way made it possible to clearly distinguish the domains in which quantum phenomena are realized. In QTIP, the states of 0 and 1 that you referred to are determined within the T4 interval, and it is the Expression PR that maps these into the real domain. In this respect, I believe my view aligns with yours.

Ultimately, through QTIP, I only aim to show that what we experience as continuous time is in fact discrete, and to illustrate the mechanism by which it operates.

@seungyong, you need to establish a quantitative minimum parcel for time. think of it like a Planck interval, which is quantized time, but you say is a different value. establish a minimum and see how it relates to the Planck intervals of time (tp) and of space (Lp).

there is no possibility to be of lesser magnitude than Planck time. if it is greater than tp, then it is composed of some Integer Quantity of tp. it is not possible to have a non integer value as that would require slicing time finer than what is possible in normal spacetime.

if you dont equate your Temporal Units to tp, you wont be able to derive anything related to quantum mechanics.

William Bray Thank you for your comment. Once again, I would like to clarify that the Tick (T4) concept in QTIP is not the same as the continuous three-dimensional time we are familiar with. A Tick is the process by which the universe prepares the phenomena it will reveal to us in the gaps between what we perceive as continuous time and events.

Within this Tick process, quantum expressions are prepared to emerge as actual phenomena in the real world, and only when they are expressed and observed do we perceive them as time and events.

Thus, the Tick is an indicator of how each frame of our continuous experience arises, and for this reason it is independent of the Planck time. What we perceive as time and phenomena is only the sum of the green blocks shown at the bottom of the diagram, while the structural process that generates those frames is the Tick itself. Even the Planck time can only have meaning within the continuity of these green blocks.

This perspective resonates with the concept of time in Loop Quantum Gravity (LQG). In LQG, time does not exist as an independent background but is defined only as events. In other words, time is understood not as a continuous flow but as a network of relations between events. QTIP’s Tick shares this viewpoint but goes one step further by describing how such events are prepared and expressed. While LQG emphasizes the background-independence of time, QTIP extends this by including the absolute information-processing stage (the Tick) prior to the manifestation of events.

When I first conceived this idea, I also wondered whether it might sound too much like science fiction. However, through QTIP research I realized that considering information processing in this structural way makes entirely new interpretations possible. In particular, it allowed me to distinguish clearly between quantum theory and relativity, and thereby to conceptualize, at least in part, a framework for their possible unification.

I sincerely hope for your understanding of this Tick (T4) concept, and I would greatly appreciate your continued advice and insights.

William Bray Additionally, what I would like to emphasize is that the limitations encountered in Shannon entropy and in Markov mechanisms can both be addressed within the Tick (T4) concept.

The Tick does not deny Planck time; rather, it reinterprets it as a projection value within the observable frame of phenomena. In this view, entropy is not merely statistical uncertainty, but an indicator of what kind of phenomena are being prepared within the Tick process.

Likewise, a Markov mechanism is not bound only by dependence on past states, but can change according to how the Tick process prepares the next phenomenon to be expressed. In other words, the very structure of transition probabilities can be expanded by one more dimension.

Thus, the limitations of both entropy and Markov chains can be reinterpreted and extended when Tick is accepted as a structural process. I would also be grateful if you could take a look at the concept I proposed in my particle characteristics paper regarding the absolute domain in which the wave function arises, as I believe this may be helpful for the understanding and interpretation of Shannon entropy and Markov mechanisms.

In these two contexts, it may be more fruitful not to treat Planck time as a fixed absolute minimum unit, but instead to view it as a projection value that only appears within the observable frame of phenomena.

@seungyoung, you should take all of these discussions and build a paper that explains your hypothesis in greater detail, based on the comments and so on. this forum is aleays a good place to remodel your descriptions, with both sides of the comments in mind.

William Bray Thank you for your comment. As an independent researcher, I am well aware that there are many shortcomings in my work. The purpose of opening this discussion is precisely to address those weaknesses.

In particular, I would like to hear your thoughts on the tick (T4) concept I proposed in QTIP. I would be especially grateful if you could consider the possibility of applying it to your work on Shannon entropy and the Markov mechanism. Of course, since it is an unprecedented concept, it may seem like something of a waste of time. But isn’t that what research is about? Even as an intellectual exercise, such an application would be a great honor for an independent researcher like myself.

I sincerely welcome further comments, whether in agreement or in opposition.

Seungyoung Choi Your QTIP hypothesis is not in a condition where it can be applied to anything as of yet. This is why I have been encouraging you to equate a unitary interval of time for your 'tick,' to some common value such as the Planck intervals, quantize your work so that it is compatible with Quantum Mechanics in general, and explain the process in terms of having some motive causal component. By that I mean, there doesn't seem to be any reason why nature would proceed in the manner you hypothesize. there is always some causal component in quantum processes.

You are at the earliest stages of your work. you have a lot of work to do and a lot of explaining the processes in common terms compatible with quantum mechanics.

William Bray Thank you for your advice. I will continue my research. Since QTIP is a very new theory, quite different from modern physics, I myself have many concerns as well. For this reason, it is difficult to fit it directly into existing physical concepts. Rather, I am trying to reinterpret them, not to deny them. The result of that effort is my paper on particle characteristics. In that work, I reinterpreted the spin, charge, mass, and orbital of particles based on QTIP, turning concepts that had remained at the level of definitions into structures of information. In this way, I wanted to show that QTIP can serve as a framework to reinterpret existing physical and quantum concepts. In particular, what is important in this interpretation is the mechanism within the tick (T4) interval. Through such processes, I believe that a new approach to quantum theory becomes possible.

The same applies to the topic of this forum discussion: the problem of black hole entropy. As another participant pointed out, changes arising from extending the conventional concept of maximum black hole entropy—especially Hawking radiation—can be seen as a natural phenomenon within QTIP.

Moreover, after establishing the basic concepts of QTIP, I have reviewed many theories in modern physics—especially recent information-based cosmologies—and I have found that many of them in fact contain hints consistent with QTIP. This is also the main reason I find it fascinating to pursue QTIP concepts. Surprisingly, I have found many such hints in existing research—in LQG, in QMM, and, though it may sound presumptuous, even in string theory.

The tick (T4) and the mechanism of absolute information in the imaginary domain, which form the foundation of my QTIP cosmology, are not physical processes that we can directly observe at present. However, I believe that, when concepts in modern physics are extended and reinterpreted, there are in fact a great many indirectly observable indications. I regard this as a fundamental domain that the universe has not yet revealed. Therefore, like many other researchers, I intend to continue my work on the premise that my theory might be correct.

Once again, I sincerely thank you for your heartfelt advice.