The theory of everything: Help wanted

When Scientific American writes that physicists are working on a theory of everything, does it sound ambitious enough to you? Do you lie awake at night thinking that a theory of everything should be able to explain, well, everything? What if that theory is founded on quantum mechanics and finds a way to explain gravitation through the microscopic laws of the quantum realm? Would that be a grand unified theory of everything?

The answer is no, for two different, but equally important reasons. First, there is the inherent assumption that quantum systems change in time according to Schrodinger’s evolution: i \hbar \partial_t \psi(t) = H \psi(t). Why? Where does that equation come from? Is it a fundamental law of nature, or is it an emergent relationship between different states of the universe? What if the parameter t, which we call time, as well as the linear, self-adjoint operator H, which we call the Hamiltonian, are both emergent from a more fundamental, and highly typical phenomenon: the large amount of entanglement that is generically found when one decomposes the state space of a single, static quantum wavefunction, into two (different in size) subsystems: a clock and a space of configurations (on which our degrees of freedom live)? So many questions, so few answers.

The static multiverse

The perceptive reader may have noticed that I italicized the word ‘static’ above, when referring to the quantum wavefunction of the multiverse. The emphasis on static is on purpose. I want to make clear from the beginning that a theory of everything can only be based on axioms that are truly fundamental, in the sense that they cannot be derived from more general principles as special cases. How would you know that your fundamental principles are irreducible? You start with set theory and go from there. If that assumes too much already, then you work on your set theory axioms. On the other hand, if you can exhibit a more general principle from which your original concept derives, then you are on the right path towards more fundamentalness.

In that sense, time and space as we understand them, are not fundamental concepts. We can imagine an object that can only be in one state, like a switch that is stuck at the OFF position, never changing or evolving in any way, and we can certainly consider a complete graph of interactions between subsystems (the equivalent of a black hole in what we think of as space) with no local geometry in our space of configurations. So what would be more fundamental than time and space? Let’s start with time: The notion of an unordered set of numbers, such as \{4,2,5,1,3,6,8,7,12,9,11,10\}, is a generalization of a clock, since we are only keeping the labels, but not their ordering. If we can show that a particular ordering emerges from a more fundamental assumption about the very existence of a theory of everything, then we have an understanding of time as a set of ordered labels, where each label corresponds to a particular configuration in the mathematical space containing our degrees of freedom. In that sense, the existence of the labels in the first place corresponds to a fundamental notion of potential for change, which is a prerequisite for the concept of time, which itself corresponds to constrained (ordered in some way) change from one label to the next. Our task is first to figure out where the labels of the clock come from, then where the illusion of evolution comes from in a static universe (Heisenberg evolution), and finally, where the arrow of time comes from in a macroscopic world (the illusion of irreversible evolution).

The axioms we ultimately choose must satisfy the following conditions simultaneously: 1. the implications stemming from these assumptions are not contradicted by observations, 2. replacing any one of these assumptions by its negation would lead to observable contradictions, and 3. the assumptions contain enough power to specify non-trivial structures in our theory. In short, as Immanuel Kant put it in his accessible bedtime story The critique of Pure Reason, we are looking for synthetic a priori knowledge that can explain space and time, which ironically were Kant’s answer to that same question.

The fundamental ingredients of the ultimate theory

Before someone decides to delve into the math behind the emergence of unitarity (Heisenberg evolution) and the nature of time, there is another reason why the grand unified theory of everything has to do more than just give a complete theory of how the most elementary subsystems in our universe interact and evolve. What is missing is the fact that quantity has a quality all its own. In other words, patterns emerge from seemingly complex data when we zoom out enough. This “zooming out” procedure manifests itself in two ways in physics: as coarse-graining of the data and as truncation and renormalization. These simple ideas allow us to reduce the computational complexity of evaluating the next state of a complex system: If most of the complexity of the system is hidden at a level you cannot even observe (think pre retina-display era), then all you have to keep track of is information at the macroscopic, coarse-grained level. On top of that, you can use truncation and renormalization to zero in on the most likely/ highest weight configurations your coarse-grained data can be in – you can safely throw away a billion configurations, if their combined weight is less than 0.1% of the total, because your super-compressed data will still give you the right answer with a fidelity of 99.9%. This is how you get to reduce a 9 GB raw video file down to a 300 MB Youtube video that streams over your WiFi connection without losing too much of the video quality.

I will not focus on the second requirement for the “theory of everything”, the dynamics of apparent complexity. I think that this fundamental task is the purview of other sciences, such as chemistry, biology, anthropology and sociology, which look at the “laws” of physics from higher and higher vantage points (increasingly coarse-graining the topology of the space of possible configurations). Here, I would like to argue that the foundation on which a theory of everything rests, at the basement level if such a thing exists, consists of four ingredients: Math, Hilbert spaces with tensor decompositions into subsystems, stability and compressibility. Now, you know about math (though maybe not of Zermelo-Fraenkel set theory), you may have heard of Hilbert spaces if you majored in math and/or physics, but you don’t know what stability, or compressibility mean in this context. So let me motivate the last two with a question and then explain in more detail below: What are the most fundamental assumptions that we sweep under the rug whenever we set out to create a theory of anything that can fit in a book – or ten thousand books – and still have predictive power? Stability and compressibility.

Math and Hilbert spaces are fundamental in the following sense: A theory needs a Language in order to encode the data one can extract from that theory through synthesis and analysis. The data will be statistical in the most general case (with every configuration/state we attach a probability/weight of that state conditional on an ambient configuration space, which will often be a subset of the total configuration space), since any observer creating a theory of the universe around them only has access to a subset of the total degrees of freedom. The remaining degrees of freedom, what quantum physicists group as the Environment, affect our own observations through entanglement with our own degrees of freedom. To capture this richness of correlations between seemingly uncorrelated degrees of freedom, the mathematical space encoding our data requires more than just a metric (i.e. an ability to measure distances between objects in that space) – it requires an inner-product: a way to measure angles between different objects, or equivalently, the ability to measure the amount of overlap between an input configuration and an output configuration, thus quantifying the notion of incremental change. Such mathematical spaces are precisely the Hilbert spaces mentioned above and contain states (with wavefunctions being a special case of such states) and operators acting on the states (with measurements, rotations and general observables being special cases of such operators). But, let’s get back to stability and compressibility, since these two concepts are not standard in physics.

Stability

Stability is that quality that says that if the theory makes a prediction about something observable, then we can test our theory by making observations on the state of the world and, more importantly, new observations do not contradict our theory. How can a theory fall apart if it is unstable? One simple way is to make predictions that are untestable, since they are metaphysical in nature (think of religious tenets). Another way is to make predictions that work for one level of coarse-grained observations and fail for a lower level of finer coarse-graining (think of Newtonian Mechanics). A more extreme case involves quantum mechanics assumed to be the true underlying theory of physics, which could still fail to produce a stable theory of how the world works from our point of view. For example, say that your measurement apparatus here on earth is strongly entangled with the current state of a star that happens to go supernova 100 light-years from Earth during the time of your experiment. If there is no bound on the propagation speed of the information between these two subsystems, then your apparatus is engulfed in flames for no apparent reason and you get random data, where you expected to get the same “reproducible” statistics as last week. With no bound on the speed with which information can travel between subsystems of the universe, our ability to explain and/or predict certain observations goes out the window, since our data on these subsystems will look like white noise, an illusion of randomness stemming from the influence of inaccessible degrees of freedom acting on our measurement device. But stability has another dimension; that of continuity. We take for granted our ability to extrapolate the curve that fits 1000 data points on a plot. If we don’t assume continuity (and maybe even a certain level of smoothness) of the data, then all bets are off until we make more measurements and gather additional data points. But even then, we can never gather an infinite (let alone, uncountable) number of data points – we must extrapolate from what we have and assume that the full distribution of the data is close in norm to our current dataset (a norm is a measure of distance between states in the Hilbert space).

The emergence of the speed of light

The assumption of stability may seem trivial, but it holds within it an anthropic-style explanation for the bound on the speed of light. If there is no finite speed of propagation for the information between subsystems that are “far apart”, from our point of view, then we will most likely see randomness where there is order. A theory needs order. So, what does it mean to be “far apart” if we have made no assumption for the existence of an underlying geometry, or spacetime for that matter? There is a very important concept in mathematical physics that generalizes the concept of the speed of light for non-relativistic quantum systems whose subsystems live on a graph (i.e. where there may be no spatial locality or apparent geometry): the Lieb-Robinson velocity. Those of us working at the intersection of mathematical physics and quantum many-body physics, have seen first-hand the powerful results one can get from the existence of such an effective and emergent finite speed of propagation of information between quantum subsystems that, in principle, can signal to each other instantaneously through the action of a non-local unitary operator (rotation of the full system under Heisenberg evolution). It turns out that under certain natural assumptions on the graph of interactions between the different subsystems of a many-body quantum system, such a finite speed of light emerges naturally. The main requirement on the graph comes from the following intuitive picture: If each node in your graph is connected to only a few other nodes and the number of paths between any two nodes is bounded above in some nice way (say, polynomially in the distance between the nodes), then communication between two distant nodes will take time proportional to the distance between the nodes (in graph distance units, the smallest number of nodes among all paths connecting the two nodes). Why? Because at each time step you can only communicate with your neighbors and in the next time step they will communicate with theirs and so on, until one (and then another, and another) of these communication cascades reaches the other node. Since you have a bound on how many of these cascades will eventually reach the target node, the intensity of the communication wave is bounded by the effective action of a single messenger traveling along a typical path with a bounded speed towards the destination. There should be generalizations to weighted graphs, but this area of mathematical physics is still really active and new results on bounds on the Lieb-Robinson velocity gather attention very quickly.

Escaping black holes

If this idea holds any water, then black holes are indeed nearly complete graphs, where the notion of space and time breaks down, since there is no effective bound on the speed with which information propagates from one node to another. The only way to escape is to find yourself at the boundary of the complete graph, where the nodes of the black hole’s apparent horizon are connected to low-degree nodes outside. Once you get to a low-degree node, you need to keep moving towards other low-degree nodes in order to escape the “gravitational pull” of the black hole’s super-connectivity. In other words, gravitation in this picture is an entropic force: we gravitate towards massive objects for the same reason that we “gravitate” towards the direction of the arrow of time: we tend towards higher entropy configurations – the probability of reaching the neighborhood of a set of highly connected nodes is much, much higher than hanging out for long near a set of low-degree nodes in the same connected component of the graph. If a graph has disconnected components, then their is no way to communicate between the corresponding spacetimes – their states are in a tensor product with each other. One has to carefully define entanglement between components of a graph, before giving a unified picture of how spatial geometry arises from entanglement. Somebody get to it.

Erik Verlinde has introduced the idea of gravity as an entropic force and Fotini Markopoulou, et al. have introduced the notion of quantum graphity (gravity emerging from graph models). I think these approaches must be taken seriously, if only because they work with more fundamental principles than the ones found in Quantum Field Theory and General Relativity. After all, this type of blue sky thinking has led to other beautiful connections, such as ER=EPR (the idea that whenever two systems are entangled, they are connected by a wormhole). Even if we were to disagree with these ideas for some technical reason, we must admit that they are at least trying to figure out the fundamental principles that guide the things we take for granted. Of course, one may disagree with certain attempts at identifying unifying principles simply because the attempts lack the technical gravitas that allows for testing and calculations. Which is why a technical blog post on the emergence of time from entanglement is in the works.

Compressibility

So, what about that last assumption we seem to take for granted? How can you have a theory you can fit in a book about a sequence of events, or snapshots of the state of the observable universe, if these snapshots look like the static noise on a TV screen with no transmission signal? Well, you can’t! The fundamental concept here is Kolmogorov complexity and its connection to randomness/predictability. A sequence of data bits like:

10011010101101001110100001011010011101010111010100011010110111011110

has higher complexity (and hence looks more random/less predictable) than the sequence:

10101010101010101010101010101010101010101010101010101010101010101010

because there is a small computer program that can output each successive bit of the latter sequence (even if it had a million bits), but (most likely) not of the former. In particular, to get the second sequence with one million bits one can write the following short program:

string s = ’10′;
for n=1 to 499,999:
s.append(’10’);
n++;
end
print s;

As the number of bits grows, one may wonder if the number of iterations (given above by 499,999), can be further compressed to make the program even smaller. The answer is yes: The number 499,999 in binary requires \log_2 499,999 bits, but that binary number is a string of 0s and 1s, so it has its own Kolmogorov complexity, which may be smaller than \log_2 499,999. So, compressibility has a strong element of recursion, something that in physics we associate with scale invariance and fractals.

You may be wondering whether there are truly complex sequences of 0,1 bits, or if one can always find a really clever computer program to compress any N bit string down to, say, N/100 bits. The answer is interesting: There is no computer program that can compute the Kolmogorov complexity of an arbitrary string (the argument has roots in Berry’s Paradox), but there are strings of arbitrarily large Kolmogorov complexity (that is, no matter what program we use and what language we write it in, the smallest program (in bits) that outputs the N-bit string will be at least N bits long). In other words, there really are streams of data (in the form of bits) that are completely incompressible. In fact, a typical string of 0s and 1s will be almost completely incompressible!

Stability, compressibility and the arrow of time

So, what does compressibility have to do with the theory of everything? It has everything to do with it. Because, if we ever succeed in writing down such a theory in a physics textbook, we will have effectively produced a computer program that, given enough time, should be able to compute the next bit in the string that represents the data encoding the coarse-grained information we hope to extract from the state of the universe. In other words, the only reason the universe makes sense to us is because the data we gather about its state is highly compressible. This seems to imply that this universe is really, really special and completely atypical. Or is it the other way around? What if the laws of physics were non-existent? Would there be any consistent gravitational pull between matter to form galaxies and stars and planets? Would there be any predictability in the motion of the planets around suns? Forget about life, let alone intelligent life and the anthropic principle. Would the Earth, or Jupiter even know where to go next if it had no sense that it was part of a non-random plot in the movie that is spacetime? Would there be any notion of spacetime to begin with? Or an arrow of time? When you are given one thousand frames from one thousand different movies, there is no way to make a single coherent plot. Even the frames of a single movie would make little sense upon reshuffling.

What if the arrow of time emerged from the notions of stability and compressibility, through coarse-graining that acts as a compression algorithm for data that is inherently highly-complex and, hence, highly typical as the next move to make? If two strings of data look equally complex upon coarse-graining, but one of them has a billion more ways of appearing from the underlying raw data, then which one will be more likely to appear in the theory-of-everything book of our coarse-grained universe? Note that we need both high compressibility after coarse-graining in order to write down the theory, as well as large entropy before coarse-graining (from a large number of raw strings that all map to one string after coarse-graining), in order to have an arrow of time. It seems that we need highly-typical, highly complex strings that become easy to write down once we coarse grain the data in some clever way. Doesn’t that seem like a contradiction? How can a bunch of incompressible data become easily compressible upon coarse-graining? Here is one way: Take an N-bit string and define its 1-bit coarse-graining as the boolean AND of its digits. All but one strings will default to 0. The all 1s string will default to 1. Equally compressible, but the probability of seeing the 1 after coarse-graining is 2^{-N}. With only 300 bits, finding the coarse-grained 1 is harder than looking for a specific atom in the observable universe. In other words, if the coarse-graining rule at time t is the one given above, then you can be pretty sure you will be seeing a 0 come up next in your data. Notice that before coarse-graining, all 2^N strings are equally likely, so there is no arrow of time, since there is no preferred string from a probabilistic point of view.

Conclusion, for now

When we think about the world around us, we go to our intuitions first as a starting point for any theory describing the multitude of possible experiences (observable states of the world). If we are to really get to the bottom of this process, it seems fruitful to ask “why do I assume this?” and “is that truly fundamental or can I derive it from something else that I already assumed was an independent axiom?” One of the postulates of quantum mechanics is the axiom corresponding to the evolution of states under Schrodinger’s equation. We will attempt to derive that equation from the other postulates in an upcoming post. Until then, your help is wanted with the march towards more fundamental principles that explain our seemingly self-evident truths. Question everything, especially when you think you really figured things out. Start with this post. After all, a theory of everything should be able to explain itself.

UP NEXT: Entanglement, Schmidt decomposition, concentration measure bounds and the emergence of discrete time and unitary evolution.

18 thoughts on “The theory of everything: Help wanted

  1. Pingback: The theory of everything: Help wanted | Φ&u...

  2. Spyridon Michalakis posts thirty questions, provides zero answers, and remarks “So many questions, so few answers!”

    Spyridon, this fine post surely reflects the Great Truth that your questions already have not zero answers, but rather many answers. So let’s revisit the history of quantum physics with a view toward discerning some of these answers through the lens of engineering. Some snappy quotations that provide guidance are:

    * The Guidance of Knuth  “Science is what we understand well enough to explain to a computer. Art is everything else we do. […] Science advances whenever an Art becomes a Science. And the state of the Art advances too, because people always leap into new territory once they have understood more about the old.”

    * The Guidance of Amati and Witten (extended version)  “Thermodynamics is part of 21st century physics that fell by chance into the 19th century.”

    * The Guidance of Feynman  “We are struck by the very large number of different physical viewpoints and widely different mathematical formulations that are all equivalent to one another. The method used here, of reasoning in physical terms, therefore, appears to be extremely inefficient. […] Sometimes an idea which looks completely paradoxical at first, if analyzed to completion in all detail and in experimental situations, may, in fact, not be paradoxical. [And thus] a very great deal more truth can become known than can be proven.”

    * The Guidance of Klein  “Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.”

    * The Guidance of Borges  “Suele estar muy cerca lo que buscamos (what we seek usually is nearby)”

    * The Guidance of Grothendieck  “Our thirst for knowledge and discovery indulges itself more and more in a logical delirium far removed from life, while life itself is going to Hell in a thousand ways—and is under the threat of final extermination. High time to change our course!”

    Knuth’s guidance directs our attention to large-scale simulations as (per Knuth’s guidance) the sole aspect of quantum physics that qualifies as science. The guidance of Amati and Witten focuses our attention upon thermodynamics and information theory — including transport theory as the dynamical manifestation of thermodynamics and information theory — as the present-century boundary between quantum art and quantum science.

    Then Feynman’s guidance authorizes us to write Schroedinger’s equation in modern mathematical language as X\lrcorner\,\omega = dh, where X is the dynamical flow, \omega is the symplectic form, and h is the Hamiltonian symbol. Klein’s guidance encourages us to pullback this equation onto the only state-space manifolds that we understand scientifically (in Knuth’s sense): low-dimension algebraic manifolds. Of course, not every Hamiltonian is thermodynamically natural under pullback, but (again per Knuth’s guidance) the sole Hamiltonians that we understand scientifically — namely gauge field theories — do pullback thermodynamically.

    To state this principle another way, Hilbert space is the sole state-space that resolves singularities for all Hamiltonian symbols, but to the extent that we are willing to restrict our set of gauge-invariant Hamiltonian symbols (as the Standard Model directs), then the lower-dimension algebraic (non-Hilbert) state-spaces that our computers actually understand are thermodynamically natural.

    Thus space and time emerge informatically, even In existing engineering quantum simulation formalisms, as coarse-grained descriptions of the transport properties of (h,\omega), and it becomes computationally natural that black-hole interiors have no fine-grained space-time description at all, and that black-hole horizons appear to external observers as informatic fire-walls.

    And so Spyridon, from this already-existing engineering perspective — and per the guidance of Knuth/Amati/Witten/Feynman/Klein — a great many of your quantum questions already are finding natural answers … per the guidance of Borges that “what we seek usually is nearby.”

    Plenty of practical details remain to be worked-out (needless to say), and achieving a mathematically natural appreciation of these interlocking considerations already is requiring considerable work, from many people, spanning many disciplines. This is good news for young researchers.

    As for Grothendieck’s guidance, that is a separate meditation … a very challenging one.

    Thank you, Spyridon Michalakis, for a thought-provoking post!

  3. “… time and space as we understand them, are not fundamental concepts. We can imagine an object that can only be in one state, like a switch that is stuck at the OFF position, never changing or evolving in any way…”
    Yes, we can imagine a more fundamental multiverse consisting of many universes – why not even a multitude of multiverses? However, in the universe that we can observe, time and space do appear to be fundamental constructs…

  4. A fundamental theory must start from well selected first principles from which everything else (such as space, progression, speed of information transfer, space curvature, diversity of elementary particles, existence of fields) emerge..
    Such a theory will be completely deduced and for that reason it will meet fierce resistance, because physicists use to require experimental verification of any significant physical statement.
    For that reason I formatted my research project as a game: “The Hilbert Book Model Game”.
    I advice you to do the same.

  5. Couldn’t you also regard complexity as the ability of a larger function to incorporate smaller functions. Even though it would be an easy matter to reduce this process to a computer program I think from a common sense perspective an automobile is more complex than a bike. According to your definition randomness is complexity.

  6. Theory of everything :-

    As the science of cosmology is progressing, we have a better understanding of universe day by day.

    When we talk about grand unification of two theories (GR & QT), we find ourselves stuck up at the set of equations and fail to find a common solution to both from small scale to the large scale structure of universe.

    But at least we know from these theories that…

    1) Quantum theory proposes an active vacuum i.e. all space is filled up with some extremely fine dynamical fluid like substance which produces some sort of activities called quantum effects throughout the universe.

    2) General relativity proposes a singularity at the beginning of universe
    But how this beginning of universe took place, GR remains silent on this issue.

    By summing up two theories, at least we know that there are two types of independent realities present before the beginning of universe …..
    A) An active or dynamic vacuum which is single,continuous & particle-less and always existing
    in space time
    B) Singularity- Perfect symmetry of four fundamental forces having
    zero space time (Laws of physics breakdown in this state)

    (Here, Modern science has assumption that only one reality exists before beginning which gives incomplete solution for existence of universe)

    With two realities before the beginning, singularity was stretched apart by instant inflationary epoch of dynamic vacuum thereby breaking the symmetry of four fundamental forces and hence the elementary particles are generated.

    These elementary particles then combine to form bigger structures under the influence of dynamic vacuum and it continued for long period of time to develop large scale structures like stars, galaxies, clusters etc. what we see in present day universe.

    It is important to note that laws of physics came into existence after the inflation broke the symmetry of four fundamental forces and these keep the universe in state of existence till the expansion of space continues.
    After inflation reverses, universe will undergo in contraction phase and nobody will be witness to see changing state of the universe.

    Inflation is not driven by the physics but it acts in such a way so as to cause the very existence of everything in the universe.

    It is also important to note that there must be substantial amount of information contained in dynamic vacuum for choice of inflation and to set the universe into state of existence.

    Rest will be discussed in later post…
    Ajay saini

  7. Give up your precious notions of time and space. They do not exist. You seem to experience a sequential “life”. You do not. At the Quantum level you are just a simulation. All is little jolts of energy zooming around and around. There is no mind. There is no reality. Your equations fall far short explaining anything. Enjoy the ride. It will end soon enough.

  8. The following statement from this article is convoluted nonsense, and the argument that follow in the article are worthless (I have included comments in parenthesis):

    “So what would be more fundamental than time and space? Let’s start with time: The notion of an unordered set of numbers, such as \{4,2,5,1,3,6,8,7,12,9,11,10\}, is a generalization of a clock (nonsense), since we are only keeping the labels (numbers have no meaning as only labels), but not their ordering (numbers are ordering, the sequence above only has meaning as a mapping or function of numbers). If we can show that a particular ordering emerges from a more fundamental assumption about the very existence of a theory of everything (this statement has so many undefined or misdefined concepts that it is impossible for me to understand what is meant), then we have an understanding of time as a set of ordered labels (numbers are ordered labels), where each label (number?) corresponds to a particular configuration in the mathematical space containing our degrees of freedom (how can you define a mathematical space that is more fundamental than numbers? Are degrees of freedom a concept more fundamental than numbers?). In that sense, the existence of the labels in the first place corresponds to a fundamental notion of potential for change (doesn’t use of the word change itself imply a notion of time which is just as fundamental as numbers or labels?), which is a prerequisite for the concept of time (nonsense), which itself corresponds to constrained – ordered in some way – change from one label to the next. Our task is first to figure out where the labels of the clock come from, then where the illusion of evolution comes from in a static universe – Heisenberg evolution, and finally, where the arrow of time comes from in a macroscopic world – the illusion of irreversible evolution.

    I don’t understand how anyone could consider this approach coherent.

  9. Even though these thoughts are logical extensions of current thinking I had the impression that they were a little far afield. I think before we should attempt a theory of everything we ought to figure out what gravity is. From what I gather, scientists have an excellent notion of how gravity behaves but not the foggiest notion of why. If the Bicep2 data turns out to be valid, than the pattern for our universe was imprinted by gravity within the first 10 to the -35 seconds. And, somehow I keep getting the feeling that the fundamental truths about the universe are hidden, behind a curtain that is waiting to be pulled back. We see graphical representations of space time to explain general relativity, depicting moving curvature and their interactions. And my own personal view is that the four dimensional universe is a process of resolving those curves in four dimensions; a telescopic gird of ordered magnitudes that resolves curvature in real time. And this view is in direct contrast to the Kolmogorov principle, which equates complexity with randomness rather than higher functioning mathematics. By my reckoning, space is nothing more than another four dimensional construct, as is time whose complexity depends on the curvature of the functions they are resolving. We observer spatial relations; four dimensional models of higher spatial functions; temporal relations in which time has a myriad of characteristics. I think this view is superior to the notion that statistically, out of an infinities of infinities, a monkey will type Hamlet.

    • “If the Bicep2 data turns out to be valid, than the pattern for our universe was imprinted by gravity within the first 10 to the -35 seconds.”

      As I understand, the primordial gravitational waves thought to have been produced by inflation are _not_ the products of any proper gravitational interaction, as stable particles of matter had not yet condensed. IMO, these are considered to be gravitational waves only because they are expected to be manifested as temporally oscillating tensor fluctuations in the gravitational metric – the dimensional coordinates of spacetime. It’s not clear to me how these effects produced by inflation might provide any useful information regarding the physical nature of gravitational interactions among cosmological objects…

      I do think your point regarding or ignorance of the physical mechanism that produces gravitational effects is well taken – while quantum theorists are strongly motivated to fit gravity into the framework of quantum field theory, I’m not at all certain that gravity is one of the fundamental ‘forces’ of quantum interactions at all! I suspect it may be an emergent state produced by accretion – the localization of mass-energy and the necessarily opposing action of mass-energy extraction from the vacuum… In this case. gravitational effects are not directly caused by massive objects – but the spacetime that is contracted by their accretion.

  10. Excellent essay! I agree that starting out with the most fundamental ideas as possible, as few assumptions as possible, and using those to reason towards theories of everything is the way to go to make faster progress towards a deeper understanding of existence. My view, as an amateur, is that if metaphysics is the study of being and existence, and the universe “be”s and exists, and physics is the study of the universe, then the laws of physics must be derivable from basic concepts of metaphysics. In my own thinking as a hobby, I try to figure out why anything exists (why does a book exist, for instance?), apply the results of this thinking to the question “Why is there something rather than nothing?” (because “something” seems to exist) and then use the results of this to build a primitive model of the universe. As mentioned in this essay, this model must be stable and eventually be able to make testable predictions. Because I’m a biochemist, and not a physicist, and work on this in my spare time, this goal is, predictably, a long way away.

    If anyone is interested, my proposed solutions to the questions of “Why do things exist?” and “Why is there something rather than nothing?” are at:

    sites.google.com/site/whydoesanythingexist

    As this essay pointed out, I also consider set theory to be important, and some of my views on that are at:

    sites.google.com/site/ralphthewebsite

    Thank you for listening!

    Roger

    • My Dear friend,
      What you want to do with nothing? If there is nothing, you will not be here to ask question.Why?
      Nothing can not produce something because it is direct violation of fundamental law of physics & metaphysics.
      Reality can neither be created nor be destroyed but it exists in space time eternally.
      For physics, Reality is sum of matter-energy content of universe and constitutes 25% of universe.
      For Metaphysics, Reality is filled like an infinite ocean in space. It is conscious in nature, self driven & extremely powerful and dominates all activities of universe from smallest to largest scale.
      So, be kind to something that exists and you are here to ask question, why?
      Thanks.
      Ajay

  11. Pingback: Question everything? People who say that almost never really mean it | Uncommon Descent

  12. Every physicist in Munich knows the TOE candidate that Schiller calls the strand model. http://www.motionmountain.net/research.html He seems to derive both quantum theory and general relativity from a simple microscopic model. Hilbert space and time emergence is part of it, and entropic force was in his model even before Verlinde. He derives the three gauge groups and the spectrum of elementary particles. He is now calculating the parameters of the standard model, and we are curious what he will achieve next.

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