A very interesting talk. Do you have references for the theories you mentioned (the string gas cosmology, primordial degravitation, baby universes etc).

Thank you

]]>I have always liked the mirror universe option. It could (obviously) explain any and all asymmetries that we see, or will ever see, in our universe.

However, there are very massive questions that remain, and they are largely overlapping with the same ones as in several of the other options.

Just as an example…

How is this at all different from other universe options? The only hint is that every particle in ‘this half of the universe’ has to have be somehow balanced by an antiparticle in the other half. But… except within the tiniest bit of ‘time’ when it arose, there was no interaction at all. Why the balance at all? What if the big bang was just slightly asymmetric? Etc.

Overall, when you factor in what a person thinks of when they think they say ‘time’, there is little difference.

A ‘symmetrical universe’ in your #5 iimagination is identical to an anti-universe that collapses and then explodes as our positive universe at the big bang in someone elses’ who is thinking of time as common people do.

The general nature of symmetry in everything else is a strong indication, but not really proof.

]]>The Topology of Quantum Timespace (TQM) equals P(5) in terms of N and Q (functions for the GR formulation for mass and energy [in terms of QM] as well as the QM formulation for the notion of wave-particle duality). Ohwilleke’s post (A Mirror Universe) is essentially very much like your observations about the potential for a for ‘reproducing’ cosmology, albeit on a slightly smaller scale. Returning to the context for Schrödinger’s functions in terms of probabilities within Hilbert space (specifically your discussion of Eigenstates in slides 21 to 24 in reference to time, as well as the physical notion of clocked states (slide 25) and dimensional compactification (slide 15), ‘you’ should note that the conjunction of space-time and matter—anti-matter is well served. Or, in general, Schrödinger’ perspective, such that in the conjunctions for ‘now’, the components of TQM oscillate topologically. Where TQM^t defines the dimensional limits of those oscillations, such that the exponent of ‘t’ oscillates between the values of +1 and -1 in the systemic progressions of conjunctions that generate differential exchanges (bosonic attributes) between the physical states of structure (fermionic attributes)—nature’s means for handling information. If you like, ‘you’ can think in terms of ‘qubits.’

]]>In that sense, live in two worlds. An objective one, which expresses all the ‘lawful’ physical limitations in which we exist and subsist; and, a subjective one, in which we compound all our personal understandings and interpretations about the dynamics of our lives.

Our perceptions of an objective, physical reality is tested daily through personal experience in our interactions with everything around us. It can also be more empirically tested and scientifically examined through careful measurements in repeatedly demonstrable and controlled circumstances. Within the limits of objective laws, we can even manipulate those lawful circumstances to our advantage. But, we cannot change the fundamentals of those laws due to the lawful nature of the mechanism which enable our existence. Those are dimensionally wrapped up in a series of ‘quantum’ entanglements which mostly defy any of our technical abilities to fully isolate.

The subjective world is a highly-biased construct of assimilated and recollected experiences which is retained and constantly modified through our limited capacities for reason and memory. As individuals, that process helps us navigate the world we discover around us. It enables each of us to place ourselves in individual and communal contexts. We are self-aware.

Due to this context, I will agree and disagree on certain points of your statement.

1. “. . . mathematical “infinities” are convenient approximations which have their value in the appropriate context, but probably have little relevance to your specific question.”

[I tend to agree with the first part of the statement; but disagree about the relevance of “infinities” to my specific question.]

2. “Beyond mathematics, infinity is not a number and eternity is not an expanse of time.” Time and quantity may be unbounded, but this relates only to our finite perception. Infinite is an entirely different concept.”

[I would argue that “infinity” in not a number, both inside and outside the context of mathematics. I would argue in the same sense, that “eternity” is not a number so cannot specifically define a duration. However, it can refer to an “unbounded” duration. Both relate to our ‘finite’ perceptions.]

3. “This cosmos is eternal, infinite and changeless.”

[True, for “eternal” and “infinite.” But only in the very limited sense of “singularity” and “continuity.” However, not true for “changeless.” Anyone would be hard-pressed to explain all the processes of “change” relating to events before and after the “Big Bang” and the aggregations of matter and energy which complement spatial expansion.]

4. “Our perception of a finite Universe existing in linear time is a “shadow” of that underlying physical reality. It arises from our 3+1D perspective, and is essential to our ability to form any understanding of our world.”

[For the reasons cited above in an explanation of ‘objective’ and ‘subjective’ perceptions, I would agree. However, having that philosophical understanding, does nothing to enlighten our physical understanding about how that circumstance comes into ‘being’ and ‘becoming.’]

]]>* In this fifth alternative, the Second Law of Thermodynamics runs in the opposite direction prior to the Big Bang, and the part of the universe on the opposite side of the time dimension from us with respect to the Big Bang is made up predominantly of antimatter. The universe extends both forward and backward in time, in each of the two cases away from the Big Bang and towards lower entropy. The Mirror Universe on the other side of the Big Bang would be basically like our own.

* This would solve the matter-antimatter asymmetry problem, would eventually allow the universe to expand indefinitely in both directions, and would also make it possible to think about the explosion of the Big Bang itself as being associated with the brief time period in which matter and antimatter are not well sorted and annihilating like crazy.

]]>Let’s start by creating a mathematical shorthand. Infinite-dimensional Hilbert space equals H1. Finite-dimensional Hilbert space equals H2. The bottom up view holds that H2 is a subset of H1.

The relationship is revealed by some additional shorthand. For this demonstration, I will use the idea of phased field evolutions, starting with the initial singularity (the concept of unity) as P(0). P(0) must equal 1. If you wish, you can think of it as Schrodinger’s conception of certainty based on distributions of probability. As you know, H1 also has potential as an unknown volumetric, which can be expressed by H1^0, such that P(0)<H1^0 as a subset of H1.

To maintain unity in generic evolutions of complexity [P(0) to P(x)], where x is a process that goes from zero(information) within the unity of P(0) towards infinity. In that process, P(x) must reflect two basic characteristics of fundamental association. First, a ‘quantitative’ function basically related to the complexity of compounded forms; let’s simply label it as N. In that sense, N has an equivalency to H1 as a subset. And second, a ‘qualitative’ function related to fundamental limits on association, let’s simply label it as Q. In that sense, Q = H2. Q is not a subset of H2 for this definition.

Following the context for that point of view, H1 is functionally populated by a process which runs from zero information towards a potential for unlimited information.

We can now state a phased function for P(x). P(x) = NQ. Since P(0) must equal 1, then specifically, as a phased process within the context of P(0) (the singularity of unity), P(x) must also always equal 1 to retain that meaning of a profound limit. Consequently, N represents a simple count of ‘reproductive’ complexity in terms of Q. To ensure that N always equals 1, N must be written in terms related to x, but in a process of inversions. Hence, N = n1/n2, n2=n1. Or to be more precise, N takes the form that counts functional reiterations (reproductions) of Q. As a simple count related to Q, the value of n1 runs from 1 towards infinity. However, since n1 is also a byproduct in a compounded series of associations means n1 is also entails an exponential function, say a function(x), where f(x) precisely reflects the limited structures and processes entailed in Q. During inflation, these are recursive processes. So, H1 and N are related in restricted terms of process (specifically, closure on the dimension evolutions of ‘local’ space now expressed in H2). So broadly, in contrast, H1 is infinitely dimensional in a mathematical sense; which is mathematically consistent, but not necessarily reflective of the physical processes defined by the subset of P(x). To properly express physicality, the variables of those mathematical functions must reflect dimensional limitations globally within the bulk of P(x) due to entanglements, again specifically, by the finite processes entailed in H2=Q. Therefore, there is an important substantive conceptual difference between the mathematic potential of dimensions in H1 and the physical dimensions in P(x) which are formulated by N in the limited evolution of physical dimensions entailed in Q.

H2=Q determines the limitations which define the emergent properties which are functionally related to our conventional notions of space and time. In that context, N determines the extent of those physical distributions. That P(0) in some way equates to the infinite reach of Euclidian fields postulated by states in quantum field theory (QM), approaches the correct point of view for physical interpretations of P(0) in H1, especially as N expresses the global extent for physical modes of inflation.

Consequently, the reduced formulation of H2=Q is the primary focus for this discussion. It is responsible for how inflation locally terminates at a point of decoupling. The function and operations of Q also enable the interactive interactions (coupling and decoupling) seen in the observable universe in conjunction with the associated dynamics of a universal ‘now’, a phase of state indicated by P(5).

P(5) is a failure of a fifth spatial dimensional to emerge and is directly related to the emergent functions of dynamic time within four-dimensional spatial displacements. These interactions are arbitrated through displacements related to three-dimension space. This formulation of interactive dynamics is captured by Q = {(q1+q2)/(q2+q1)} = 1. In this case, the components of Q represent an average between two oscillating states. For the purpose of demonstration, phase(1)=q1/q2 and phase(2)=q2/q1. Phase(1) times phase(2) = 1. The fields represented by q1 and q2 are similar, but not quite equal. The two persist as instabilities within Q as temporal oscillations relating to the structure and emergence of time—specifically as clock states. Consequently, Q also synchronizes events within P(5), defined and detailed just below.

In looking at the basic components of any two-dimensional quantum field, a field cannot be bound by limits on complexity. It can only bound by the number of unique associations which are formed between domains expressed within the plane, despite the potential for unlimited extents. That degree of ‘uniqueness’ is numerically defined by the type of association. Types of association form a unique set, let’s label it U (it is conceptually related to symmetry groups). In this context, U expresses the degree of saturation within the field and can only run from zero to four. This fact holds true whether the space is opened as in a Euclidian plane, or closed as in the surface of a sphere (caveat, the expression of a sphere also requires a volumetric space in which to exist). The property of ‘unique’ associations underlies the solution and proof in the ‘Four Color Theorem.’ [Not liking the method of the original ‘proof,’ I did another proof using different methods.] However, what is important here is that all simple two-dimensional fields are limited in terms of uniqueness, U(1), U(2), U(3), and U(4), an extension of association to U(5) does not exist with in the field, except perhaps in modified terms of U(0). Then, U(5) = U(0) only in the sense that each reflects a potential association which does not properly exist as a domain or boundary within the field.

The corollaries to the physical dimensions of space follow this sequence: U(0) equates to pre-dimensional space; U(1) equates to non-dimensional space; U(2) equates to one-dimensional space; U(3) equates to two-dimensional space; U(4) equates to three-dimensional space; and U(5) equates to the dynamics of four-dimensional space. However, in the phasing of P(x) the relationship is staggered due to limitations on topology that are not a conditional limitation on fields. P(0) implies U(1); P(1) implies U(2); P(2) implies U(3); P(3) implies U(4); P(4) implies U(5); but, by the rules of unique association, P(5) cannot exist in terms of U(6). U(6) cannot be a field related association in terms of unique associations. Or in strict terms of U(5) or U(0) for existing as a proper associations within a two-dimension field. In evolutionary processes of progression, this means that U(5) and U(0) only exist as a genetic part of the self-associated processes which enable the dimensional emergence of fields in QM. The operative connection between U(5) and U(0) forms a looped circuit which expresses the gravitational effects of ‘causality (spatial expansions)’ and ‘gravity (spatial contractions).’ Consequently, the process underpins and sets up the emergence of GR couplings.

To reiterate, if the topology required for existence fails, then the expressed case for no topology or zero topology means physical oblivion. So, in the evolutions of H(2), P(0) must equal a state defined by U(1). In terms of quantum fields, the meaning of U(5) and U(0) expresses an allowable process for the creation and destruction of local fields. Essentially, in field evolutions, U(0) creates a potential for a field that is then extended by processes of U(5). It is in the dynamic sense of field relationships that U(0)=U(5). The topology expressed by P(0), which through intrinsic instability, fundamentally relates to the phases of global folding and mixing. Overall, as the foundational state, it refers to physical continuity and the phased processes of a singularity. Again, that process comes to dimensional closure at P(5). Closure on dimensional evolution does not terminate systemic instabilities. It only defines a point of dimensional saturation which can easily be viewed as a form of thermal equilibrium.

A U(5) association can only be defined in the interactive relationship between two saturated fields. Geometrically, those relationships are orthogonal. The saturation point of all fields is U(4). The minimum of associations which permits a Hamiltonian walk within a field or between fields is defined by U(2). Both are fundamental to folding and mixing processes. U(1) and U(3) potentially define emplacements [combined form (neutron)], [decoupled form (proton and electron)] and as specific processes [consequences of coupling and decoupling (neutrino)] within fields, but are not strictly a byproduct of global or local folding and mixing processes. They arise due to polarization within H2 and between the coupled fields of H1 and H2. In the collection of couplings expressed by H1 and H2, are five fermionic inflection points (think ‘quarks’) and two sets of eight gluon-like bosonic processes (think gluons, photons) which are dynamic reflections of internal and external processes (exchanges of energy)—all patterns of perpetual recursion within a saturated field. The energy comes from the potential energy and instabilities of the initial continuity through continuous inflationary processes.

In saturation, after closure on dimensional inflation, U(1), U(2), U(3), U(4), and U(5) are no longer variables but constants of association. At that point, folding and mixing processes can be expressed as a mostly fixed functional series in terms of U(2) and U(4). Topologically U(2) relates to electromagnet processes and U(4) relates to what might be called the Higgs field, both are related to spatial expansions and, physically, are properly ‘dimensional’. The dynamic of U(5) relates to gravitational processes in terms of expansions and contractions of and within fields. Consequently, U(5) also represents a failure for a fifth dimensional of uniqueness to be manifested within any two-dimensional field. However, {U(5), U(0)} still forms a circuit of displacements which produces and binds all fields together, it links ‘causality’ (a process of expansion) to ‘gravity’ (a process of contraction). The functional series, as an expression of spatial saturation, illustrates the relationship between ‘expansion’ and ‘contraction’. Expansion (the sum of the series) is related to inflation. Contraction (the product of the series) can be correlated to the formation of mini black-hole singularities by being related to unity. The sum and product of the series illustrate the ‘cycle’ and ‘bounce’ of between the maximum and minimum limits of these operations of dimensional compression and dimensional inflation.

As constant terms, these relationships can be easily stated. The function, f{U(2)}, is defined by the set of terms {2^8, 2^4, 2^2, [2^1, 2^-1], 2^-2, 2^-4, 2^-8}—a two-fold process. And the function, f{U(4)}, is defined by the set of terms {4^4, 4^2, 4^1, [4^0.5, 4^-0.5], 4^-1, 4^-2, 4^-4}—a four-fold process. In orders of uniqueness, f{U(2)} precedes f{U(4)}. Note that f{U(2)} = f{U(4)} = 1 as products of each series. To jointly gauge and scale these function, the two function need to be related, but also considered in the inflationary process which leads up to the point of saturated displacements. Zero Point Unity (ZPU) allows the functional series in terms of U(2) and U(4) to be dimensionally equated and aligned according to centers of displacement within Q and points of coupling and decoupling between N and Q. The centers of differential displacement within f{U(2)} and f{U(4)} are offset by square brackets. The offset value in f{U(2)} has a combined expectation value of 2.5, a sum of the bracketed set, {2, 0.5}. The offset value in f{U(4)} has a combined expectation value of zero, a sum of the bracketed set, {+2, +0.5, -2, -0.5}. This condition within the square brackets, sets up the potential for functional constants of displacement. The sums of f{U(2)} and f{U(4)} minus the expectation values for each spatial field are essentially equal. Let’s set that value to a constant and arbitrarily label it as, D. The expectation values can be combined as constants of differential displacement, C1. Note that the expectation value for C1 cannot be zero. A value of zero, would defeat the potential of the function under the resulting product of compression.

To include the evolutionary processes between N and Q and to place them in the analysis of the functions which define Q. Let’s define the results of the folding and mixing processes from P(0) to P(5). This number is another constant of displacement, C2. A final statement of analysis produces an inflated set of terms which can be written as, {[C2], D+[C1], [C2]} with C2 setting and the external points of processes which set at the limits in expression of Q, but which also must be included in the gauging defined by ZPU. The process which defines the differential constant of displacement between N and Q shows up in two places in the analysis. The first is directly reflected global processes of folding and mixing during inflation. What happens precludes Sean’s notion of a reproducing cosmology on universal scales.

Basically, half of the gross field defined by P(0) to P(5) goes to zero while the other half doubles in number. The past and future share the same topological space in the local and global conjunctions of now. The amount of positive matter and energy is doubled, while the temporal displacement of antimatter cease to exist in persistent forms, except ephemerally in the durable dynamic vacuum relate to space. In the expression of Q, this doubling appears in consolidation as a masked factor, 2/2. Within ZPU, it shows up as a phased oscillation related to the dimensional synchronizations of time between N and Q that persists as a differential constant of offset as a percentage of those active relationships that locally span the coupling and decoupling within P(5).

The combinations give you a precise statement about the functions of energy, q1; as well as a precise statement about matter, q2. Those relationships lead to the common equation generally expressed by E=mc^2. However, there is a hidden factor in that relationship which express the structural ratio between q1 an q2.

In short, q1 and q2 specifically defines the structural density of P(5) in terms of dimensional constants as abstracted from the principles of unique associations. Those parameters are inherent to the genetic processes of dimensional evolution. The geometric structure of P(5) exhibits all the structural properties of our universe and entails all fundamental constants as already indicated. Those constants can be mathematically extracted from the saturated field density as defined.

The book I wrote is an informal demonstration of this application of principle. The title, “The Topology of Quantum Timespace: A Theory of Everything,” is an accurate statement. However, it is not ‘The Theory of Everything.” To finish the project, it must be turned into a formal statement. To do that, I would have to invent a new field of study that might be titled as, “Quantum Vector Mechanics.” Mathematically, it would be a subset of vector analysis. The project is within the reach my capabilities. Fortunately, since I am short of time and inclination, I do not have to take on that project by myself. I can share what I have done or pass it on to others who, as a professional community, already have the necessary qualifications and techniques as scientists and mathematicians. Any volunteers?

]]>Thank you.

]]>Action without energy – perpetual motion – run away. 🙂

Perhaps you could say a bit more about time-symmetric crystals for those of us who have not met them, and seriously lack “research” time.