I had the pleasure earlier this month of giving a plenary lecture at a meeting of the American Astronomical Society. Unfortunately, as far as I know they don’t record the lectures on video. So here, at least, are the slides I showed during my talk. I’ve been a little hesitant to put them up, since some subtleties are lost if you only have the slides and not the words that went with them, but perhaps it’s better than nothing.

My assigned topic was “What We Don’t Know About the Beginning of the Universe,” and I focused on the question of whether there could have been space and time even before the Big Bang. Short answer: sure there could have been, but we don’t actually know.

So what I did to fill my time was two things. First, I talked about different ways the universe could have existed before the Big Bang, classifying models into four possibilities (see Slide 7):

**Bouncing** (the universe collapses to a Big Crunch, then re-expands with a Big Bang)
**Cyclic** (a series of bounces and crunches, extending forever)
**Hibernating** (a universe that sits quiescently for a long time, before the Bang begins)
**Reproducing** (a background empty universe that spits off babies, each of which begins with a Bang)

I don’t claim this is a logically exhaustive set of possibilities, but most semi-popular models I know fit into one of the above categories. Given my own way of thinking about the problem, I emphasized that any decent cosmological model should try to explain why the early universe had a low entropy, and suggested that the Reproducing models did the best job.

My other goal was to talk about how thinking quantum-mechanically affects the problem. There are two questions to ask: is time emergent or fundamental, and is Hilbert space finite- or infinite-dimensional. If time is fundamental, the universe lasts forever; it doesn’t have a beginning. But if time is emergent, there may very well be a first moment. If Hilbert space is finite-dimensional it’s necessary (there are only a finite number of moments of time that can possibly emerge), while if it’s infinite-dimensional the problem is open.

Despite all that we don’t know, I remain optimistic that we are actually making progress here. I’m pretty hopeful that within my lifetime we’ll have settled on a leading theory for what happened at the very beginning of the universe.

*Related*

What Sean has presented here reflects the current state of knowledge about the conditions surrounding evidence for the Big Bang and various theoretical supposition about universal Creation within that scientific context. Each model represents an approach to the problems of Causality, and by extension, all causal explanations. Philosophically, the four models avoid the question of “first cause” by hiding it in postulations of a ground state that is given without explanation for its existence. They are scientific theories because each is an effort to explain the mechanics behind the known or observed expression of our Universe, as a statement involving space, time, matter, and energy.

Categorically, the Universe exists. As improbable or preposterous as it might seem, the dynamics of our Universe dynamically represents a certainty. Its probability equals one. That would not be if its probability equaled zero, or state of absolute oblivion.

No differential information is not the same thing as nothing. The causal question in terms of Creation centers on this issue about associated states relating the dynamics of information. In this context, a Universal singularity could be described as a potential infinite energy state with zero entropy. It includes the potential for everything that can exist. Lawful processes and paths for genetic evolution are the only missing components.

From this perspective, the dynamics for space, time, matter, and energy are all emergent properties.

Hi Sean,

I spent almost a month in hospital in Nov/Dec, and once off the “critical list” I had the unusual luxury of some time to read. I enjoyed your “From Infinity to Here” and found a several points which, for me, as a “hitch-hiker” on the journey of scientific discovery, needed clarification. One such seems relevant to this discussion, namely your insistence on the necessity for a low entropy “boundary condition”.

In the FLRW model the Universe in its first instant is miniscule (a single quantum, as Lemaître described it). This “Primordial Atom” contained all the matter and energy of the Universe, and completely filled the tiny space it occupied. When it expanded, Lemaître saw it as space expanding, and its contents remaining stationary relative to space, but becoming further apart as the expansion took place; a concept that is still with us In that first “quantum” matter/energy occupied all the available space; there was no room for manoeuvre; entropy could not have started evolving until more space became available. What, then, does it mean to talk of a low entropy boundary condition? Surely, in that first instant, entropy was at the maximum possible for the conditions.

Sean comes close to the idea of initial conditions when he along with others attempt to run time backward towards the conditions which existed during the Big Bang. That conceptual process reaches a low-entropy boundary condition within the parameters generally cited for classical physics and supposed by quantum mechanical interpretations of events. Those thoughts become the subject of Sean’s lecture. However, I would argue that the state reached by running time backward does not go far enough. It remains conventionally dependent on time and notions about space. It represents an effort that tries to make do with the tools we mostly understand. That effort fails to recognize that the Universe is a consequence of genetically induced emergence properties in a self-referential process that brings order out of potentially chaotic conditions.

I would observe that going beyond that artificial threshold requires a deeper understanding of topological evolution. Placed in that context, you must be able to define the simplest order of topology that can exist. Only then can you examine the phased consequences of its evolution in terms of mechanistic processes and byproducts, which must then lawfully define the meaning of measurement and scale. The first limit is defined by the fact that the Universe must logically come from a pre-dimensional singularity. Mathematically, it will always equal one. It must be highly unstable as genetically implied. Then mathematically, the question becomes what are the other topological limitations on potentially chaotic processes of evolution. Without presupposing any conventional means, how are those processes and products defined?

If you run time, and the expansion of the Universe, backwards far enough in the context of GR, you reach a singularity, and I suspect that few people are really happy with that idea. Christopher Baird expresses it rather succinctly:

“In general, singularities are the non-physical mathematical result of a flawed physical theory. When scientists talk about black hole singularities, they are talking about the errors that appear in our current theories and not about objects that actually exist.”

This still seems to leave us with an initial state in which the entropy of the Universe is, albeit momentarily, at its maximum possible.

I was lucky enough to attend your lecture. It was a smidge over my head but it was intriguing and I very much enjoyed it. These slides will help me go back and fill in the parts that I didn’t catch. So thank you for sharing them Sean. Looking forward to your next course with the Teaching Company (hint hint).

Using GR is a presupposition about how to run time backward. The singularity that is produced is an artifact of that assumption’s distorted emphasis. Understanding that both space and time are emergent properties immediately tells you that the effects of gravity are a byproduct of other processes. A singularity hypothesized by that kind of process is simply not the singularity topologically associated with the Big Bang. Specifically, a process of compression is not a process of disassembly and reconstitution.

Stars and stellar aggregations entail gravitational and electromagnetic effects. They are not fundamental objects in the sense of being related to initial conditions. GR defines a process of relationships, specifically between matter and energy. That relationship is an emergent property, not a cause in that sense. Again, as stated, it depends upon other emergent properties, like space and time. It fails because it is an incomplete concept. So, categorically, it is not even a proper expression of space-time.

That GR is not a proper expression of space-time only means that it has a limited range of application and that it might not produce a completely accurate description of our universe. The same holds true for QM in terms of quantum field theory, constructs related to Hilbert Space, and other technical problems relating to bulk and quantum entanglements. Those problems are immediately identified by how well the issue of dark matter and energy are addressed. More fundamentally, these issues are dynamically related to topology and the geometric question of dimension. All related to genetic properties of emergence. As Sean would easily note, genetics trace a self-referential line of evolution from Universal beginnings to the manifestations seen in the self-consciousness of Life, or literally everything.

Thanks for the response, Charles. You raise some interesting points. However, possibly as a result of my lack of scientific expertise, I’m not clear as to how this links to the original question about the entropy of the Universe in the initial instant.

Bill S. in this arena, we all lack scientific expertise.

The notion of entropy is a thermodynamic measure of how much energy is available for mechanical work. Outside of specific formalism, it is generally related to the idea that pressure times volume equals temperature. It is also considered as measure of disorder in a closed system which relates to the amount of information within the system. In that sense, high-entropy would indicate that there is less energy within the system to do work. Low-entropy expresses a differential state where systemic work can be done. Consequently, when a system reaches thermal equilibrium no more work can be done and the system is in a state of maximum entropy.

In a very general sense, if the universe represents a closed system. Then a low-entropy state must have existed to allow the thermal dynamic properties within our universe which depend upon thermal disequilibrium to dynamically exist. Again, if the universe is indeed a closed system, then once it reaches thermal equilibrium, all those dynamics stop. That state is frequently described as the “heat death of the universe.”

The universe need not be a closed system. The four scenarios presented by Sean are hypothetical means by which those universal models begin a universe in a relatively low-entropy state. Required for thermodynamic outcomes like those seen in our universe. In contrast to those models, as I have strongly suggested, thermodynamics is an emergent property and the entropy of the initial state is zero.

Bill S., in this arena we all lack scientific expertise.

The notion of entropy is a thermodynamic measure of how much energy is available for mechanical work. Outside of specific formalism, it is generally related to the idea that pressure times volume equals temperature. It is also considered as measure of disorder in a closed system which relates to the amount of information within the system. In that sense, high-entropy would indicate that there is less energy within the system to do work. Low-entropy expresses a differential state where systemic work can be done. Consequently, when a system reaches thermal equilibrium no more work can be done and the system is in a state of maximum entropy.

In a very general sense, if the universe represents a closed system. Then a low-entropy state must have existed to allow the thermal dynamic properties within our universe which depend upon thermal disequilibrium to dynamically exist. Again, if the universe is indeed a closed system, then once it reaches thermal equilibrium, all those dynamics stop. That state is frequently described as the “heat death of the universe.”

The universe need not be a closed system. The four scenarios presented by Sean are hypothetical means by which those universal models begin a universe in a relatively low-entropy state. Required for thermodynamic outcomes like those seen in our universe. In contrast to those models, as I have strongly suggested, thermodynamics is an emergent property and the entropy of the initial state is zero.

[quote=Charles] The notion of entropy is a thermodynamic measure of how much energy is available for mechanical work [/quote]

Agreed! So, if in the instant before the before the Universe began to expand, there was no room for change, there would have been no potential for mechanical work. Effectively, the Universe would have been in thermal equilibrium until more space became available.

I would not presume to argue with Sean’s insistence on a low entropy boundary condition, I just wondered if this could be considered as a possible alternative. I.e. the Universe came into being in a state of maximum entropy, but a low entropy state was (instantly) imposed on it by rapid expansion.

Bill S., I understand your concern about “no room for change.” But unfortunately, it is based on a false assumption about initial conditions, specifically in physical terms of structure. Rather than a notion based on a lack of room for change, I would think more in terms of possibilities for displacements. A singularity of the sort I am talking about is “unbounded,” which means it is a pure continuity. A pure continuity would have some interesting properties. Since it has no structure, it cannot be in any kind of equilibrium, thermal or otherwise. On the contrary, it is infinitely unstable and so has unlimited degrees of freedom for movement. There are no countervailing forces which could constitute a differential which could come into balance. It is pre-dimensional.

To give it an artificial thermal dynamic description, and with apologies to Sean, one could possibly say it is in an indeterminate state between infinitely hot and infinitely cold. To borrow the metaphor, perhaps inflation marks the collapse of a Universal wave function. It cannot be both, it must change.

Thanks again, Charles. I have a feeling that if we are to have a chance of coming close to speaking the same language we need a look at terminology.

Let’s start with your statement: “one could possibly say it is in an indeterminate state between infinitely hot and infinitely cold.”

How would you define infinitely hot, or infinitely cold? Surely, neither can exist in reality, and if they did, all possible temperatures would be intermediate between the two. So, unless there is some esoteric interpretation, to which you are privy, in spite of your aligning yourself with those who “lack scientific expertise”; that statement has no real meaning.

Bill S., your observations here about terminology and meaning are both valid ones, and critical for understanding topological consequences. So, why are we talking and what are we talking about?

First, to be perfectly honest, I am not a scientist nor a mathematician; but I do know how to think scientifically and I am aware of many of the technical problems which must arise in aligning mathematical models to careful observation. In that sense, I do have high aptitudes for those areas of study and several productive insights which are currently missing in the search for a comprehensive and coherent understanding of our empirical observations. We are having this conversation because I have something to say that the professional community of researchers needs to hear. In effect, you are asking me what that is.

Second, the baseline for this conversation is Sean’s presentation. Your questions here dance on the edge of the problems suggested by slide 22, more specifically the paradox posited by ‘Boltzmann brains.’ It goes to the heart of the discussion which establishes the methodological, epistemological, and ontological basis for the theories under examination.

So, to directly respond to your question. Let’s start with methods. My understanding comes from an informal study of combinatorics, an odd branch of topological questions which looks at how things are related. The point of view is esoteric. Which, in this conversation, places us at a threshold about how things are connected. It also places us at the state of QM and quantum field theories and the dynamic nature of physical associations. We are both looking at phase states in the abstract. Schrodinger/Hilbert formalisms and what I have simply referred to in my thinking as the hypoform/hyperform nexus. The connection between the two methods is the question about genetically emergent properties which lead to physical manifestations and related properties, in terms of what I categorize in my thinking as genetic lawfulness. Science typically works statistically from the top—down; my point of view deliberately works from the bottom—up.

Let’s literally take my hypothetical statement as a fact of reality. Then the consequences would be like the ones you suggest. But, I would counter with what is not considered are the genetic limitations on physical processes. So, underlying that question is an even more abstract one. How does one go from the unbounded infinite to the finite? Remember, we are looking at a singularity defined by physical unity. That topological unity will not change over time. However, it can go through phases of genetically based evolution.

In general, the demonstrable genetic limitations on physical processes causally emerge through the properties of space and time in conjunction with the relationship between matter and energy. These processes setup the conditions that define observable matter and energy, dark matter and energy, distributions between matter and anti-matter, and the quantum oscillations of quantum chromodynamics and quantum electrodynamics which through polarization relate time to causality in an associated loop with the effects of gravity. These structural relationships mostly emerge in conjunction the proportional manifestation of spatial dimensions in a causal process of topological folding and mixing. All these relationships fall out of topological limitations on displacements and physical mechanisms for traversable paths.

The ratio of 4% to 96% between observable matter/energy and dark-matter/dark-energy immediately fell out of the applied mode for displacements, not expected in my initial assessments of applied topological principles. That ratio is clearly pointed out in the book I wrote, as is the explanation for matter/antimatter distributions. What I just recently realized, is the fact that the 23% dark-matter and 76% dark-energy distribution is fully implied in the argument that relates to the oscillating dynamics of time and space. Note that these are quantum distributions that partly relate to the incomplete postulations of slide 15, but contain far more detail.

Let’s begin with Hilbert space and fill it with the topological conditions of state for a reconstituted singularity, an unbounded continuity with zero entropy. Looking at any one of an infinite number of Euclidian planes which slice through that space will be perfectly smooth—with no differential information as already discussed beyond Unity. That defines the ground state of Universal existence that as indicated is structurally unstable. Instability must lead to a process of folding and mixing. At that point a slice through Hilbert space will reveal the onset of differential information. It will emerge from an indicator of empty space and will begin to reveal the onset of greater structural complexity. It will begin to express domains and boundaries. Since a folding and mixing process is an expression of complexity that grows exponentially, the number of domains and boundaries within the slice rapidly approaches a limit towards infinity. The ultimate expression of complexity is not bound by that process. It would seem chaotic. Also, in the infinite expanse of any one of those Euclidian planes, that statement of complexity would be homogenous and isotropic. However, it does represent an entangled bulk of associations with specific properties. It also represents the initial emergence of a quantum field with precise topological limits of association. This phase also creates a space where we can take a Hamiltonian walk. It is meaningfully traversable—which is not true for the initial phase of singularity. However, it is not quite sufficient for a dynamically interactive Universe. It has no relative scale. It is not yet gauged in terms of coupling and decoupling.

One of the first things impressed on those undertaking Courtroom training as professional witnesses is that whatever question the “opposing” Barrister asks; you should use it as an opportunity to say what you need to say. Would I be right in suspecting the same technique at work here?

Whilst what you say is interesting, it doesn’t really address the question: “How would you define infinitely hot, or infinitely cold?”

Answer to the first question, is yes and no. To setup a common language for a technical dialog we need to come to an understanding about what each of us is conceptually thinking and lock in the meaning of the words we are using to talk about the topic, professional jargon if you will. My agenda is to meaningfully communicate specific aspects of applied principles. To do that, I must work to put the ideas into a form that we mutually understand in terms of a common technique.

The answer to the second question can be hypothetically obtained by using the ideal gas law (PV=T) and by taking a sample of our continuity and making V a constant. The value for P is not actually determinate. However, infinitely hot would be defined when P equals infinity and infinitely cold would defined when P = minus infinity.

Slide 4: “Of all the states that look macroscopically like our universe, only a tiny fraction evolved from smooth states. Most were chaotic, Planckan, singular.”

Just from the slides, it is hard to tell what you are saying here. Is your conclusion

1) “Therefore the Universe wasn’t smooth”

2) “Therefore the smoothness of the early Universe is a problem because the smooth state is lower entropy than you would expect”

Conclusion 1) is unsupported. It would only be supported by a (incorrect?) statement: of all the smooth early universes, only a tiny fraction evolve into a Universe like ours (compared to the fraction of all initially unsmooth universes).

Against conclusion 2), I would say that the smooth state is the highest entropy state for conditions under which gravity variations do not dominate. (This is because gravity is the only relevant situation that leads to negative-heat-capacity systems.)

For a given set of conserved quantities and Universe volume, you can get higher entropy by segregating the mass into tightly-gravitationally-bound chunks: with the highest entropy found in a universe that includes a single black hole with the rest of the volume filled with radiation in thermal equilibrium at the Hawking temperature. But it is hard to see how such a highly segregated situation is likely to come about from the local physics of any spatially-distributed creation event.

If you have a hot big bang, then the volume of a density fluctuation large enough to collapse despite the intense thermal effects is much larger than I would expect as the coherence length of the statistical fluctuations.

Charles, you say: “The answer to the second question can be hypothetically obtained……”

I have to take issue with that. You used the terms “infinitely hot” and “infinitely cold”. What I asked for was your definition, in the context of that specific usage. Attempting to obtain an answer “hypothetically” would be tantamount to guessing your meaning, which would be a waste of time.

Your response was an irrelevant tautology which leaves such questions as:

What do you mean by “P equals infinity”?

Do you mean that P tends to infinity, or are you saying P is finite, but becomes infinite at some juncture?

How do you define “minus infinity”?

Follow up to my previous comment: What does gravity do when the temperature is well above the Higgs Scale? When the Higgs Boson is just another particle in thermal equilibrium, does that mean that its mass-giving (hence gravity-giving) properties are muted or cancelled?

Without gravity, the smooth universe IS the highest entropy configuration for a given density and volume.

As our latest Nobel laureate said, you have to worry about what happens `when gravity fails and negativity (of the thermal capacity of gravitationally bound systems) don’t pull you through’ to a higher entropy state.

To Bill S., I would say that it is a tautology; but doesn’t that category of relationship apply to all valid mathematical equations? Consequently, the fact that it is a tautology does not invalidate any of those equivalencies. It’s hypothetical because the actual value of P is not determinate in this state. The context of superpositioning should have explained the application of that meaning. However, even though P is not specifically determined does not void the fact the value for P will be found on a scale that runs from minus to plus infinity. Infinity is not an actual point on any scale, it is a direction or process that never terminates.

I don’t know how Sean would respond to David Palmer’s questions, but I would respond by saying that all persistent particles are in a fixed state of maximum entropy. I also believe his questions are fair ones for the consequence predicted by our current set of assumptions.

Let’s put all of this in a proper context and back into the context of Sean’s presentation.

The argument for maximum entropy holds in the argument of emergence at the point where topological evolution turns from causally driven processes to interactive ones. It reacts that way because dimensional evolution hits a profound limit on associative processes; but that limit can only be reached from a pre-dimensional state through phased evolution of dimensional associations which must, in terms of complexity, run from zero entropy to maximum entropy. The events which evolve from the phase of maximum entropy entail processes of coupling and decoupling. Those events are defined by the mechanisms of lawful association which become set by the point of maximum entropy.

Bill S.’s push for a definition relates to the logical problem of circular arguments. It also relates to the issues of scale and comparative measurement, which is postulated by the problem of pulling the finite out of the infinite. Our exchange isolates the issue from both sides of the question about entropy and the nature of inflation at and before the “Big Bang.”

To return to our exchange over the hypothetical definition for “Hot” and “Cold,” the information required to give a definitive answer does not exist in the singularity with zero entropy. However, it does exist at the point of maximum entropy. In the first case, Pressure (P) and Temperature (T) are completely indeterminate. We set Volume (V) to a constant because V in this hypothetical case is already partly determined. Volume is the dominating variable. The hypothetical situation clarifies the circumstances of the topological problem we are discussing. What is inside and outside the box? What sets the boundary between the inside and outside? What determines the related volumes for the inside and outside? The clue to the answer is formulated by topology of the question. That question involves the dimensional mechanics of displacement. We are looking at a geometric problem and a scalar question about measurements. It is gauged by meaning of dimensionality. In the real universe, these are determined by the measurement of fundamental constants. Parameters that must currently be ‘plugged’ into our existing theoretical models. In a coherent and comprehensive model, these ratios must be geometrically buried in the topology that comes to dynamically limit those values in evolutionary processes of emergence. How do you topologically determine those limits?

Charles, “To return to our exchange over the hypothetical definition for “Hot” and “Cold,””

Could it be that you missed my point? I was asking specifically what you mean by INFINITELY hot & cold.