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Zuma's avatar

Might fractal geometry finally reconcile general relativity and quantum theory?

Asked by Zuma (5908points) December 1st, 2009

Lately I’ve been awed by how often chaos theory and its fractal geometry turn up.

In this article it appears that quantum space-time and the curvature of Euclidean space may be explained by fractal dimensions. And here is an article on how fractals may make sense of quantum weirdness. Here is another more technical article.

Fractals and chaotic dynamics also seem to keep turning up in the structures and dynamics of brains, nervous systems, and possibly even consciousness itself. EEGs, for example, have fractal properties (“noise” in general has a fractal distribution). And fractals also seem to be intimately in all sorts of information exchange, and seem to reconcile wave-like and particle phenomena, as in photosynthesis and the fractal design of antennae. Fractals also have a temporal dimension, which would seem to be key to any study of consciousness.

I don’t understand it all, but it looks to me as though some major pieces of the puzzle of the ultimate nature of reality are starting to come together. Is anyone else getting this sense?

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41 Answers

Sonnerr's avatar

I believe that over the years, there have been more and more questions, and with that more and more answers. Even is helping with this. Its discoveries like this that made me think of questions myself. In regards to your question, it might be audacious to say that everything is possible 100% of the time. And have a temporal dimension could been that we would be able to see it with the right pair of glasses.

FireMadeFlesh's avatar

At the moment the differences between Quantum Mechanics and General Relativity stand unresolved. Physicists have been proposing strange theories for decades as unification becomes more and more frustrating. The way things stand, anything could solve it and it is premature to place a bet on any one theory. Fractals are certainly interesting and are widely reflected in nature.

I will read those articles when I have the time and presence of mind to do them justice.

Christian95's avatar

Even a dog from a pet store might unify general relativity and quantum mechanics.Both theories are very good and interesting and fractal geometry seems a very good unifier too but it also might be wrong.In history science there have been theories which seemed right and they proofed to be totally wrong.So fractal might turn to be wrong and the pet shop dog to be right.Everything is possible and a unifier will be totally accepted only when the proof will be perfect.

DrBill's avatar

I would agree it is starting to come together, but it still falls short of rectifying all the differences. The temporal dimension fractals could help the understanding of the
“two places at once” (although I have my own theory to explain this)

One place fractal theory can be used effectively is light theory, when we need to treat light as both a particle and a wave simultaneously.

virtualist's avatar

“The task is not to make sense of the quantum axioms by heaping more structure,
more definitions, more science fiction imagery on top of them, but to throw them away
wholesale and start afresh. We should be relentless in asking ourselves: From what
deep physical principles might we derive this exquisite structure? These principles
should be crisp, they should be compelling. They should stir the soul.”

Chris Fuchs, in Louisa Gilder’s (2008 hardcover and 2009 paperback ) entitled “The Age of Entanglement: When Quantum Physics Was Reborn”

The review of this book, in the Washington Post, by a respected theoretical physicist , presents a nice layman’s overview of some of the mysteries in theoretical physics. It can be found at the same link in the paragraph, above this one:

“From The Washington Post’s Book World/washingtonpostDOTcom Reviewed by James Trefil.

Evolutionary biologists tell us that the human brain developed for one purpose: to allow our ancestors to survive in the African savannah millions of years ago. And yet this organ, whose main duty was to keep us from the attention of the neighborhood carnivores, seems capable of comprehending almost any environment it finds, from galaxies billions of light years away to the cells in our bodies. With one exception: the world inside the atom.

I would suggest that this strange world is one place the brain is simply not wired to understand. Oh sure, we can write equations and predict the results of experiments to umpty-ump decimal places, but there remains something essentially unknowable about the inside of the atom. It is the challenge of taking on this world and, if not explaining it, at least explaining why it is unexplainable that Louisa Gilder tackles in The Age of Entanglement.

Some background: Inside the atom everything, including matter and energy, comes in little bundles called “quanta.” (The name derives from the Latin for “bundle” or “heap.”) The old word for the science of motion is “mechanics,” so the science that applies inside the atom, the study of the motion of things that come in bundles, is called “quantum mechanics.” The basics of the science were developed in the early 20th century, and a major shift in the field took place with the discovery of what is now called “entanglement,” in the 1960s and ‘70s.

Gilder, therefore, splits her narrative into two parts, one dealing with early developments, the other with entanglement and its ramifications. She has an unusual technique for handling historical figures. She puts together imaginary conversations using actual quotations from letters and other writings. I’m sure this will give historians fits, but aside from some stilted language, it worked for me. She also displays the ability to capture a personality in a few words, as when she characterizes the Viennese physicist Erwin Schrödinger as someone who “grew handsome, cultured, charming, brilliant, and devoid of any sense that the world did not, in fact, revolve around him.” The first wave of quantum mechanics, centering on the Heisenberg Uncertainty Principle, is built on the realization that in the world of the atom you cannot measure something without changing it in the process. As a result, quantum events have to be described in probabilities—a fact that drove Albert Einstein to object that “God does not play dice with the universe.” The second wave started in 1964, when Irish theoretical physicist John Bell published a theorem that showed that once two subatomic particles interact, they remain entangled. “No matter how far they move apart,” Gilder explains, “if one is tweaked, measured, observed, the other seems to instantly respond, even if the whole world now lies between them.” This is quite unlike the world that our brains are wired to understand. If you hold two baseballs in the palm of your hand, then throw one to the left and the other to the right, you expect that clocking the speed of one ball will not affect the other. In the jargon of physicists, the baseballs are “local.”

Not so with electrons. Once two electrons have come into contact, they never seem to forget that this has happened. It would be as if, by making a measurement on the left-hand baseball, you could determine what the right-hand baseball was doing. Trying to picture this is virtually impossible. But if you test the predictions that arise from entanglement, the theory works. Gilder picks a couple of laboratories to describe how the process of experimental verification took place. It is the only time I can think of when a theory led to an outlandish prediction, the prediction was confirmed by a series of brilliant experiments, and everyone was unhappy with the result.

We really don’t like it when Nature tells us that our comfortable view of the universe doesn’t hold. Gilder concentrates on telling the stories of the people who developed the theories of uncertainty and entanglement, rather than on explaining the theory itself. I would have preferred more science, but then, I’m just an old-line physics prof.

The bottom line for this book is simple: The world of the quantum is so strange, so alien to our experience, that it will never seem right to us. Indeed, I have three simple laws for interpreting quantum mechanics: (1) every physicist knows that his or her interpretation is right, (2) every physicist knows that every one else’s interpretation is wrong, and (3) no two interpretations are the same. ‘Nuff said.

Copyright 2008, The Washington Post. All Rights Reserved.”

hiphiphopflipflapflop's avatar

My first thought is that I don’t think so. The defining characteristic of fractals is self-similarity over an infinite range of scale. Fractal-like properties of nature (a coastline, a mountain range, a snowflake) eventually break down at extremely fine scale due to the atomic nature of matter. I think the general trend is that natural structures simplify as one reaches extremes in fine scale.

The cosmological constant is the same thing as the energy density of the vacuum. The conventional picture of spacetime due to quantum field theory is: not only do you have virtual particles of all kinds popping in and out of existence, but also the very metric goes haywire. Einstein’s smooth membrane gets foamy at the Planck scale. All attempts to calculate the vacuum energy density end up with huge positive quantities. The observed cosmological constant appears to be slightly positive, but many, many orders of magnitude smaller. To me this seems to indicate that at some point as you zoom in, rather than getting rougher, spacetime starts smoothing out and become simpler again.

Blondesjon's avatar

If it does, I owe James Gleick 20 bucks.

go albert

mattbrowne's avatar

I have this gut feeling that something totally new will solve the problem. I’m very doubtful about all the string theories, loop quantum theory, twistor theory and so forth. Some might be good approximations. But I think in 2020 some genius will come up with something that will seem very odd at first. The LHC will help inspire a new generation of physicists. And we might know more about dark matter and higgs, but will it be enough to marry general relativity and quantum theory?

Zuma's avatar

@hiphiphopflipflapflop “Fractal-like properties of nature (a coastline, a mountain range, a snowflake) eventually break down at extremely fine scale due to the atomic nature of matter. I think the general trend is that natural structures simplify as one reaches extremes in fine scale.”

Is this smoothing-down effect really so? I thought that this article was arguing that the quantum froth of spacetime may have fractal properties all the way down to the Planck level. Even if not, when you have waves colliding with particles (as in the case of sunlight and the green pigment chlorophyll) it throws off fractal patterns (in this example, photosynthesis). Also, one of the things we know from dripping faucets and other oscillators is that fractals can have a temporal dimension, and that information can be exchanged or translated from one dimension to another in fractal structures.

So, at the very least, it would seem, that fractal geometry is fundamental to our understanding of the universe. I wish I understood this better. I have a hunch that quantum weirdness has something to do with the imaginary number component to the complex numbers fractals are made up of. (By the way, thanks for turning me on to the Mathematical Universe Hypothesis in our last exchange.)

@mattbrowne “The LHC will help inspire a new generation of physicists.”

I’m not so sure. It may disillusion them with the reigning paradigm of science and send them off in a different but not completely new direction. The Large Hadron Collider represents the ultimate expression of the reductionist paradigm in science. The great hope of particle physics has always been that if we can just go smaller, we will find a particle (or force) that will explain everything. So far, we have discovered a bewildering array of particles, and it is likely that we will find the predicted Higgs boson and whatever other particles are necessary reconcile it to the standard model; and at that point, we can say that supersymmetry is fundamental to our understanding of the universe but, by no means, constitutes our whole understanding.

I think that the reductionist paradigm is about to play itself out, and that the really exciting work will come from the holistic or “emergence” paradigm, of which fractal geometry is one of the first fruits. I think that pretty much all the pieces are on the table and that it is now a matter of assembling them. Here, I think, the biggest unsolved problems have to do with the nature of consciousness and the ultimate nature of reality. With regards the latter problem, I think that Max Tegmark’s Mathematical Universe Hypothesis is the kind of work that will start pulling things together into a comprehensible whole.

What I find interesting about this sort of work is that it doesn’t proceed by empirical investigation and hypothesis testing so much as by bootstrapping from what we already know. The “proof” of the pudding, as I think David Deutsch would say, is in whether a new theoretical formulation is more comprehensive, compact, and coherent than the last.

When it gets down to multiple competing interpretations, as in the case of quantum theory, I think the edge will go to whichever interpretation can explain any of the following: life, consciousness, the unreasonable effectiveness of mathematics, or the ontological nature of the noumenal world. Given how many people who are independently inching their way along in this direction, I don’t think it will take very long before the chunks start coming together. It’s only been about 30 years or so that nonlinear, dynamic, holistic thinking has been quietly revolutionizing scientific disciplines.

hiphiphopflipflapflop's avatar

@Zuma “Is this smoothing-down effect really so?” When you consider matter as such, yes, at least the way I see it. Zoom in on a coastline. Eventually you’re dealing with individual grains of sand touching the water. Sand grains aren’t nearly as rough as a typical coastline. Even given unnaturally gnarly sand grains, zoom in more and eventually you’re looking at individual atoms (actually the electron probability density distributions) which are smooth (continuous) by quantum mechanical law. Once inside the atom, it’s a whole new ballgame as I see it! You’re no longer dealing with matter but it’s constituents. Suppose I let you insist it is still the same ballgame, then things don’t get very interesting again until you close on the Planck scale if the “foam” model is correct. This produces a huge gulf from at least 10^-9 to 10^-35 meters where we are missing anything resembling self-similarity.

Fractals are nice models of given pieces of nature over certain ranges of scale.

Power laws, which are also ubiquitious in nature, eventually breakdown at low and high extremes in frequency.

I’ve already given my intuitive argument against fractal spacetime: the tiny observed cosmological cosmological constant as contrasted to what we get if we try to to apply quantum field theories to this question. This suggests to me that the vast majority of the expected roughness/foaminess is not actually there.

hiphiphopflipflapflop's avatar

@mattbrowne “I have this gut feeling that something totally new will solve the problem.” I agree. “The LHC will help inspire a new generation of physicists.” @Zuma “I’m not so sure.” I agree. Direct evidence of subquantum spacetime structure(s) will never be obtainable through accelerators. The best we can hope for is something very subtle and indirect and my own gut feeling is that this is more likely to come through some future astronomical/cosmological investigations.

One pet hope of mine is that part of the solution will involve the mathematical machinery of category theory (or more likely its proposed elaboration into “weak n-categories”)...

“Samuel Eilenberg and Saunders Mac Lane introducesd categories and functors into mathematics in 1945. These concepts represent a “triumph of generalization” (to quote John Fowles) as Darwin’s theory of evolution. In the latter half of the twentieth century, they have not only changed the language of mathematical discourse, but also the nature of mathematical inquiry.” ... “By stressing relationships across classes, functoriality deftly sidesteps the centention described above between generality and richness. Thus it achieves a measure if unity without retreat into banality. Moreover, functorial relationships often allow one to bring the full knowledge of one class of objects on the analysis of another. In this way categories and functors provide within mathematics itself a service that mathematics has long provided for science. And finally in purely asthetic terms, the exquisite balance between the objectified and the relational manifest in this approach revels one of the most beautiful designs ever conceived by the human mind.”
(from Robert Valenza’s Linear Algebra, final chapter.)

“A mathematician is a person who can find analogies between theorems, a better mathematician is one who can see analogies between proofs and the best mathematician can notice analogies between theories. One can imagine that the ultimate mathematician is one who can see analogies between analogies.”
(Stephen Banach, functional analyist)

“I didn’t invent categories to study functors. I invented them to study natural transformations.”
(Saunders Mac Lane)

“For every analogy, a functor. For every anology between analogies, a natural transformation.”
(n-category theory slogan)

My other pet hope is that Andrei Sakharov was right and gravity is induced and emergent, analogous to situations in condensed matter physics, rather than a fundamental quantum force.

Zuma's avatar

@hiphiphopflipflapflop Can you recommend any sources that might explain any of this in simpler terms? This is way over my head.

hiphiphopflipflapflop's avatar

I looked at some of places I first read about it and I have to say, they will probably be much, much more confusing than just reading the Wikipedia article…

I do not understand the topic in depth at all yet, I’ve merely placed it in relation with other concepts I have read about. It appears intuitively to me to occupy something of a “strategic high ground” in mathematics. I have two books Lawvere co-wrote that I’d like to work through fully some day to wrap my mind fully around the nuts and bolts.

mattbrowne's avatar

A while ago I read an interesting article written by Lee Smolin called the unique universe in which he argues against Tegmark and Deutsch’s multiverse. It takes a while to get access on this physics site. Here it is:

Three decades ago, talk of other universes was not seen by most physicists to be part of science. Most research in theoretical physics and cosmology concerned observable features in our universe and most papers and seminars referred to experimental results. However, since then there has been a gradual shift, during which it first became acceptable to work on theories that described not only our universe, but other possible universes, universes with less or more dimensions, or universes with different kinds of particles and forces. In the last few years, we have moved further away from theories of our one universe, as these other worlds went from being logically possible to hypothetically actual. It is now common to hear about the multiverse a quantum cosmology that takes for granted that the visible universe that we see around us is just one of a vast or infinite number of universes.

The multiverse assumption often comes hand in hand with a metaphysical assumption regarding the nature of time. It has been argued by many experts in quantum cosmology that time is not a fundamental concept, but an approximate and emergent one. If this is correct, then we experience time in a timeless universe for reasons similar to why we, who live in a quantum universe, experience one that obeys classical physics: we are composed of very large numbers of fundamental particles and emergent statistical regularities determine much of what we experience. Furthermore, the combination of the multiverse assumption and the timeless assumption effectively gives us a static meta-universe. Even if our own universe evolves in time, at a deeper level it is part of a timeless, eternal, ensemble of universes.

There are good reasons for these conclusions, and like many others in the field of quantum cosmology I have explored them. However, in the last few years I have come to believe that these conclusions are profoundly mistaken. In collaboration with the Brazilian philosopher Roberto Mangabeira Unger, we have been trying to understand the source of the problems and develop an alternative notion of time and law on the cosmological scale. Our reasons for doing so are based partly on concerns about whether these theories are testable by doable observations, partly on the current results of attempts to realize the timeless approach and partly on philosophical considerations. In a timeless world in which our universe is just one of many equally real universes, the laws of physics must be very different from those that most physicists can ever have conceived. This is because the laws of physics are no longer determinable by what we observe in our own universe, for they must apply to all of the vast ensemble of universes. A fundamental law then no longer proscribes what happens in our universe; instead it gives probability distributions for properties of the ensemble of universes.

To understand why, it is helpful to distinguish between the notion of a fundamental law and an effective law. A fundamental law is posited to hold meta-universally from first principles and must be unique. String theory, for instance, is an attempt at discovering such fundamental laws of nature. Effective laws, at the other extreme, govern experiments at scales that we observe directly within one universe, down to the small scales probed by the Large Hadron Collider and up to the scales probed by observations of the cosmic microwave background. We can only observe the effective laws, but we hope that it should be possible to derive them from fundamental laws — otherwise the latter has no connection with what we observe. The question is whether that indirect connection provides enough ground for experimentally testing the fundamental laws so that they are relevant for our scientific understanding of the world.

Unfortunately, it appears that if string theory, or a similar theory, is true, then the fundamental theory does not in fact predict what the effective laws of nature are. Instead, it gives rise to a vast landscape of possible effective laws, a concept I introduced in my book Life of the Cosmos (the word landscape was meant to be evocative of fitness landscapes in biology). We then must have hypotheses for how the single effective laws that describe our universe are chosen from the vast list of possibilities allowed by the fundamental theory. This is one of the major motivations for speculation about multiverses.

Several ideas have been suggested for how to select the effective laws that apply to our universe from the larger set of possibilities. One possibility, which has been much studied, is that the ensemble of universes is populated by laws by an effectively random process. An example is eternal inflation. In this scenario the process that produces the ensemble occurs at energy scales so high that they swamp any processes we have experimental access to. The result is that a universe like ours, populated by structures that depend on physics at much lower energy scales, is very atypical in the ensemble of universes. One then has to depend on the anthropic principle to pick out the very few universes hospitable to life, which are very rare in the actual ensemble. Not surprisingly, given that the characteristics of the ensemble can be postulated at will and are not subject to experimental tests, the result is that we cannot make precise and unambiguous predictions about anything observable in our own universe.

An alternative approach, which does lead to at least a few falsifiable predictions, is cosmological natural selection, which I introduced in 1992. This is based on a cosmological scenario that is constructed to be analogous to population biology. Universes are born from bounces deep inside black holes, which replace their singularities, where time had been hypothesized to end, with new expanding universes. This leads to a prediction that a typical universe is one where the parameters are tuned to maximize the production of black holes. There is in fact evidence that this is true of the laws that govern our universe. Most importantly, in this theory our universe is supposed to be typical of the ensemble, which leads to several genuinely testable predictions, all of which have held up since they were first published, such as the prediction that the upper mass limit of stable neutron stars is about 1.6 solar masses.

The contrast between these two kinds of multiverse theories leads to a question: why is the theory based on natural selection predictive, but not the one based on random production of universes? This helps us understand why the reality of time is necessary to explain how the laws of physics are chosen. It is apparent that a scenario in which a population of universes evolves, rather than just being a random timeless distribution, requires a notion of time that is real at a level above individual universes. But to understand why the timeless picture fails, we have to go deeper to the foundations of quantum theory. For example, without time, and without the assumption that what exists is the single universe that we observe, it is hard to make sense of statements about probability relevant to what we observe in our universe. Since quantum mechanics is a probabilistic theory, we then run into trouble by trying to extend it to a realm where probability appears to make no sense. A number of authors have attempted to address this question, by proposing ad hoc measures for deducing predictions from ensembles of multiverses. At least up to the present time, none of these appears to be justified by anything other than the need to reproduce what we observe.

A related issue is the recovery of classical space and time, which general relativity describes, as part of an effective theory. These must be emergent aspects of a fundamental quantum theory, much like the classical notions of a particle being at a definite place and travelling on definite trajectories is emergent from quantum mechanics. This is non-trivial because the notions of quantum spacetime, which arise in quantum theories of gravity, are very different. So far, approaches to quantum gravity that assume that both space and time are emergent fail to reproduce the spacetime that we know. On the other hand, two approaches that assume that time is fundamental and non-emergent succeed, at least to some extent, in describing how spacetime may emerge. The most developed of these is causal dynamical triangulations, which has impressive results indicating the emergence of classical spacetime. A more recent attempt, quantum graphity, also has preliminary indications for the emergence of space given the existence of time. Furthermore, fundamental time is also needed to make sense of probability and describe the evolution of effective laws, which ties to the earlier issue.

These results were the first evidence that led me to consider the idea that there might have to be a fundamental global notion of time in any fully consistent approach to quantum gravity that can recover general relativity in the approximation in which the universe is large. This hypothesis is strengthened by recent results in unimodular gravity, which several authors have argued solves the long-standing problem of the cosmological constant, something that is necessary for a large classical spacetime to emerge. What is remarkable, as pointed out by the physicists Rafael Sorkin of the Perimeter Institute for Theoretical Physics, William Unruh of the University of British Columbia, Vancouver, and others, is that this approach describes evolution in a global time related to the spacetime volume of the past.
What is a cosmological law?

To understand the difference between the two paradigms of emergent time versus fundamental time we need to appreciate how much of our usual notion of physical law has evolved historically from our experience of laboratory observations. In the laboratory we do not, by definition, study the whole universe. We study a small subsystem of the universe that, to some reasonable approximation, can be regarded as isolated (apart from the measuring instruments that we use to observe it). When we do this, we explore the possibility that we can prepare that closed system over and over again, at different times and in different places, with the same elements and different configurations. We abstract physical laws from what is common in a large set of experiments, and study what becomes different when the initial conditions are different. This allows us to make a clean distinction between laws and initial conditions. The laws are held to be invariant, at least over scales of time and space larger than the scales pertaining to our experiments.

This situation is almost the same for most astronomical observations. We cannot prepare stars and galaxies in any state that we want, but we can observe vast numbers of them and we can treat them as approximately isolated. Hence, in astronomy we also have a justification for distinguishing between laws and initial conditions. The separation of scientific explanation into law and initial conditions leads to one of the most universal and powerful notions in physics the notion of configuration space. This is the space of all possible configurations, or states, of the system. In classical and quantum physics we assume that this space exists a priori and outside of time, and that it can be studied independently of the laws of motion. These laws then specify the rules for how the point that describes the initial conditions in configuration space evolves in time. We call this the Newtonian schema for explanation.

The Newtonian schema is the basis for the claim that time is not fundamental in cosmology. From this point of view, time is seen merely as a parameter on a trajectory in configuration space, and not as an intrinsic part of the physical law. The present moment, the time we experience, has no place in this description. The philosopher who does not believe in the flow of time points to the trajectory in the configuration space and says that the only thing that is real is that the whole history of the universe exists timelessly, what in general relativity is called the block universe picture. Many physicists and philosophers have fallen for the temptation of believing in the block universe picture. To them, our experience of the flow of time is just an illusion.

This argument is faulty for two reasons. First, it does not prove that time is not fundamental. When we observe motion, we record a series of measurements of a system’s position. These can be graphed on the configuration space, resulting in a curve that represents the record of the motion. This graph is timeless, because it is a representation of a record of a past motion, which is, of course, no longer changing. The correspondence is between a mathematical object, which is static, and a series of records of observations, which is also static. The fact that we can make this correspondence between a mathematical object and a record of past motion does not imply that the actual motion that the observations sampled is timeless. Nor does it imply that behind the real evolution in time of the real world there exists a complete correspondence to a timeless mathematical object. To posit this further relation is a pure metaphysical fantasy, which is not implied by anything in the science (see “The fourth principle: mathematics and Platonism” below).

The second failure of the argument for time not being fundamental is that it is far from clear that the Newtonian schema applies on the scale of the universe as a whole. Almost all work in classical and quantum cosmology assumes that it does. But given the difficulties that these subjects encounter, I think it more likely that the answer is no. One reason for suspecting that the Newtonian schema does not apply to cosmology is that the experimental context that gives meaning to the separation of causes into laws and initial conditions is completely missing. There is no possibility of preparing the universe in different initial configurations, and there is no way to determine by observation the full initial conditions. Any observer, within the universe, can only see a fraction of any initial-value surface. Thus, the notion of initial conditions is simply not realizable in cosmology. If there is just one universe, there is no reason for a separation into laws and initial conditions, as we want a law to explain just the one history of the one universe.

The same is true for the configuration space of the cosmos. The universe happens once, so what is the meaning of all the states that exist in state space but are never realized in the history of the universe? The notion of the quantum state of the universe is a fiction, divorced from anything that could be prepared or measured in practice. These considerations suggest that the notions of configuration space and state space correspond to measurements and preparations that can be operationally realized only in the case of a small subsystem of the universe. These concepts or at least their operational basis fail us when we try to extend them to the whole universe.

The issue of time also looks different from this perspective. Time in the Newtonian schema is a parameter used to label points on a trajectory describing the system evolving in configuration space. When the system is small and isolated, this time parameter refers to the reading of a clock on the wall of the observer’s laboratory, which is not a property of the system. When we try to apply this notion to the universe as a whole, the time parameter must disappear. Some have attempted to argue that this means that time itself does not exist at a cosmological scale, but that is the wrong conclusion. What disappears is not time, but the clock outside of the system which would be an absurd object since the system is the whole universe.

Indeed, it may be that sticking to the Newtonian schema, when it has no operational significance, leads us to take the multiverse scenario seriously. If our scientific methodology only makes sense when applied to subsystems of a vaster universe, then it is tempting to react to the problems that arise when we try to extend it uncritically to that whole universe by positing that our universe is in fact a subsystem of an even vaster multiverse. We get to do physics as we have been trained to, but this is a trap because to do this we must employ structures that have no operational significance. Better, in our view, to regard the Newtonian schema as inapplicable to cosmology, and to look for another notion of law that can make sense when applied to our entire, but single, universe.

But once we state that the distinction between laws and initial conditions has no counterpart in the cosmological context, this renders moot several puzzles that the extension of the Newtonian paradigm to cosmology has brought about. What is the initial quantum state of the universe? How do we interpret it? How do we define probabilities in quantum cosmology? How do we do physics when time has disappeared? By discarding the Newtonian schema for cosmology and dispensing with the notion of the multiverse, we also no longer have any reason to suspect that time is an illusion. This led Unger and me to consider the implications of a natural philosophy based on a different set of principles.

1. There is only one universe. There are no others, nor is there anything isomorphic to it.
This logically implies that there are no other universes, nor copies of our universe, whether within or without. The first is impossible as no subsystem can model precisely the larger system it is a part of, while the second is impossible because the one universe is by definition all there is. This principle also rules out the notion of a mathematical object isomorphic in every respect to the history of the entire universe, a notion that is more metaphysical than scientific.

2. All that is real is real in a moment, which is a succession of moments. Anything that is true is true of the present moment.
This says that not only is time real, but also that everything else that is real is situated in time. Nothing exists timelessly.

3. Everything that is real in a moment is a process of change leading to the next or future moments. Anything that is true is then a feature of a process in this process causing or implying future moments.

The third principle incorporates the notion that time is an aspect of causal relations. A reason for asserting it is that anything that just existed in a moment, without causing or implying an aspect of the state at a future moment, would be gone in the next moment. Things that persist must be thought of as processes leading to newly changed processes. An atom in a moment is a process leading to a different or a changed atom in the next moment.

This alternative metaphysical framework has implications for the nature of physical law. Since nothing is true or real outside of time, there is no possibility of speaking of eternal laws. Laws are regularities that we discover hold for very long stretches of time, but there is no reason for laws to be true timelessly indeed, there is no way to make sense of that notion. This opens the door to the possibility that laws evolve in time, which is an idea that has been on the table ever since the great American logician Charles Sanders Peirce wrote in 1891 that to suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for. Law is par excellence the thing that wants a reason. Now the only possible way of accounting for the laws of nature, and for uniformity in general, is to suppose them results of evolution.

From this point of view, the notion of transcending our time-bound experiences in order to discover truths that hold timelessly is an unrealizable fantasy. When science succeeds, we do nothing of the sort; what we physicists really do is discover laws that hold in the universe we experience within time. This, I would claim, should be enough; anything beyond that is more a religious urge for transcendence than science.

So, what is physics without a clean separation into laws and initial conditions, and hence, without the notion that there is a space of configurations that exists timelessly? We do not know the full answer to this, but we have a few observations. First, by discarding the Newtonian schema for cosmology we have much less reason to consider our universe one of many other actual universes. Indeed, we may also be able to dispense with the notion of a vast number of other possible universes, that somehow are never realized. We can imagine instead a notion of law that applies only to the single universe that really exists. We also no longer have any reason to suspect that time is an illusion because, as outlined above, the main arguments from physics for time being emergent and not fundamental come from the misapplication of the Newtonian schema to the universe as a whole.

As we attempt to realize those principles, we seek a notion of law that cannot be applied to an imagined universe within a multiverse, and which cannot be imagined to hang around timelessly waiting for a universe to begin that it can then govern. Given that the universe only happens once, we must try to imagine a new kind of law that applies only that one time. Such a law need not and should not have any sense in which it exists outside of time. Nor could it be conceived of as apart from the universe it describes. It might indeed be a law that evolves in time; that is, a law where the distinction between a one-time narration of the history of the one universe and the statement of principles governing that history weakens.

If the timeless multiverse paradigm now ascendant is correct, then we are approaching the end of a process that will eliminate the reality of time and replace it with a shadowy kind of existence within an eternal frozen world consisting of vast numbers of possibilities. If, on the other hand, the principles that Unger and I propose are closer to the truth, then we are at the beginning of a new adventure in science where we have to reconceive the notion of law to apply to a single universe that happens just once. In either case we will end up conceiving our universe in very different and less familiar terms than before.

But did we really imagine that completing the revolution started by Einstein would be possible without having to discard some of our comfortable beliefs in favour of disturbing and almost inconceivable new ideas? At this level we do science not for ourselves, but for the future generations that will live comfortably in conceptual worlds that we can at best only point roughly towards. Many cosmologists today believe that we live in a timeless multiverse a universe where ours is just one of an ensemble of universes, and where time does not exist. The timeless multiverse, however, presents a lot of problems. Our laws of physics are no longer determinable from experiment and it is unclear what the connection is between fundamental and effective laws. Furthermore, theories that do not posit time to be a fundamental property fail to reproduce the spacetime that we are familiar with. Many of these puzzles can be avoided if we adopt a different set of principles that postulates that there is only one universe and that time is a fundamental property of nature. This scenario also opens the way to the possibility that the laws of physics evolve in time.

Believers in eternal truth often point to mathematics as a model of a realm with timeless truths. What is called the Platonic view of mathematics holds that mathematical objects (the things that the theorems of mathematics are about, such as numbers, spheres, planes, curves and so on) exist in a separate timeless realm of reality. Mathematicians explore this realm with their minds and discover truths that exist outside of time, in the same way that we discover the laws of physics by experiment. But mathematics is not only self-consistent, it also plays a central role in formulating laws of fundamental physics, which the physics Nobel laureate Eugene Wigner once referred to as the unreasonable success of mathematics in physics.

One way to explain this success within the dominant metaphysical paradigm of the timeless multiverse is to suppose that physical reality is mathematical, i.e. we are creatures within the timeless Platonic realm. The cosmologist Max Tegmark calls this the mathematical universe hypothesis. A slightly less provocative approach is to posit that since the laws of physics can be represented mathematically, not only is their essential truth outside of time, but there is in the Platonic realm a mathematical object, a solution to the equations of the final theory, that is isomorphic in every respect to the history of the universe. That is, any truth about the universe can be mapped into a theorem about the corresponding mathematical object. If nothing exists or is true outside of time, then this is all wrong. However, if mathematics is not the description of a different timeless realm of reality, what is it? What are the theorems of mathematics about if numbers, formulas and curves do not exist outside of our world? This leads Unger and me to a new view on mathematics that can be summarized in a fourth principle.

Mathematics is derived from experience as a generalization of observed regularities when time and particularity are removed. Consider a game, for example chess. It was invented at a particular time, before which there is no reason to speak of any truths of chess. But once the game was invented, a long list of facts became demonstrable. These are provable from the rules, and can rightly be called the theorems of chess. These facts are objective, in that any two minds that reason logically from the same rules will reach the same conclusions about whether a conjectured theorem is true or not.

Now a Platonist would say that chess always existed timelessly in an infinite space of mathematically describable games. We do not achieve anything by believing that, except an emotion of doing something elevated. Moreover, it is clear that a lot is lost; for example, we have to explain how it is that we finite beings embedded in time can gain knowledge about this timeless realm. We find it much simpler to think that at the moment the game was invented a large set of facts become objectively demonstrable, as a consequence of the invention of the game. We have no need to think of them as eternally existing truths, which are suddenly discoverable, instead we can say they are objective facts that are evoked into existence by the invention of the game of chess. Our view is that the bulk of mathematics can be treated the same way, even if the subjects of mathematics such as numbers and geometry are inspired by our most fundamental observations of nature. Mathematics is no less objective, useful or true for being evoked by and dependent on discoveries of living minds in the process of exploring the single, time-bound universe.

LostInParadise's avatar

@mattbrowne , The laws of science follow mathematical principles that operate independently of humans. I would go along with the idea that the basic numerical and geometric properties of the universe have been extended by man and that a portion of mathematics, like chess, may be considered our invention. However, a complete understanding of the universe would have to include an explanation of where numbers come from and why they are so universally applicable.

LostInParadise's avatar

@Zuma , I too believe that the reductionist paradigm has about run its course. I am hoping that such a paradigm switch would have consequences beyond the scientific community. The rise of reductionist science coincides with a highly individualistic view of society. Might a holistic view usher in a more community oriented view of humanity?

mattbrowne's avatar

@LostInParadise – Good point. What’s also missing in the article is an explanation about the double slit experiment and quantum interference. What if there’s a third explanation no one has thought about today? Which means that neither the Copenhagen nor the many-worlds interpretation are good models of reality.

Shuttle128's avatar

@mattbrowne Well, technically there are infinite explanations that no one has thought about yet. The underdetermination of theories means that there are not just many but infinite alternate explanations for phenomena. Sure, most of them are absurd, but none-the-less possible.

mattbrowne's avatar

@Shuttle128 – True indeed.

Zuma's avatar

@hiphiphopflipflapflop I thought of another reason why what you were saying about fractals becoming simpler at smaller scales is true. Martin Rees in his book “Just Six Numbers” points out that the scale level we humans inhabit just so happens to be the scale in the universe at which the maximum complexity occurs. Animals very much larger than ourselves run into problems with gravity and the limits of pushing blood uphill, and organisms at, say, the viral level tend to become smoother due to the limits of molecular bonding (as you mentioned).

Even so, a great deal of information can be encoded on surfaces. I don’t understand it all that well, but theories about the holographic universe seem to rely on this principle. Here is a sampling of my own fractal art, which shows how readily fractals can model wave interference patterns.

hiphiphopflipflapflop's avatar

@Zuma Are you familar with Jos Leys?

The holographic principle and Wheeler’s notion of “It from Bit” have some provocative overlap.

Zuma's avatar

@hiphiphopflipflapflop His name and his work look familiar. Very beautiful—and impressive—considering that the software he works with does not readily yield up such orderly structures. I’ve been out of the fractal art scene for almost 8 years now, which is a long time in that field.

Back in the 90s, I was known as the fractal artist O and was considered one of the top artists publishing on, which was the main venue back then. The webhosting company I had signed up with went bankrupt and took the gallery of my work with them. However, I just now discovered that it has been restored; so I’m really quite pleased to learn that my work has managed to survive.

There is something about fractals that speaks directly to our intuition and our aesthetic sense. Fractals are absolutely everywhere in nature; so it seems entirely credible to me that they—and math—are somehow fundamental to the nature of reality.

Zuma's avatar

@mattbrowne I’m not entirely sure what we are supposed to make of Lee Smolin’s Unique Universe, which you can also find quoted in full here. Is this intended to be an example of the kind of “totally new” approach that will explain everything in the future? Or, is this a continuation of an an earlier debate we were having on the status of the multiverse?

This critique of the timeless multiverse is less than 6 months old; so it hasn’t had much time to attract much notice or commentary. I was only able to find a few thoughtful comments and one refutation. I’ve been reading for the better part of two days now trying to get enough background to understand it. I don’t mind the effort, since I am learning a lot. But it does seem a bit much to offer this up in such a way that I have to take on someone of Smolin’s stature in order to reply.

From what I understand, Smolin is considered quite a maverick in physics. Apparently, he’s rankled quite a few physicists with his outspoken criticisms of string theory and its purported strangle hold on the imagination of “big science” funding agencies and the physics establishment in general. Up until very recently, Smolin was known for his theory of Cosmic Natural Selection, which, as I understand it, he proposed as an alternative to the anthropic principle.

Interestingly, Smolin’s Cosmic Natural Selection model postulates a population of universes that very closely resembles Tegmark’s Level II multiverse—when a star goes supernova, it creates a black hole which pushes out another expanding universe on the other side of the wormhole—sort of like a circus elephant taking a high wire dive and disappearing into its own asshole, and then turning inside out again to become a new expanding universe. Even more interestingly Smolin offers the same criterion that Tegmark offers for the falsification of his multiverse prediction. (See Susskind’s critique)

However, Smolin’s present critique of the timeless multiverse is even more radical, insofar as he seems to be rejecting mathematical physics altogether—and doing so just as empirically-driven method of “doing physics” appears to be on the verge of playing itself out. Once the Hadron Collider experiments have been done, there simply won’t be any way to “look deeper” into the quantum world in the traditional reductionist way. After all, the situation we are in with string theory is that there simply aren’t any experiments one can do that are capable of deciding empirically which interpretation is best.

The Copenhagen interpretation, for example, is an explicitly positivist view which does not care about the ontological nature of the quantum substrate, or the bedrock “stuff” of reality. Both the Copenhagen interpretation and the multiverse interpretation of quantum mechanics are equally valid insofar as they are both based on the same set of empirical observations and experiments. In this respect, multiple universes are neither a theory nor a hypothesis; they are a direct prediction of quantum mechanics. And to the extent that quantum mechanics is confirmed empirically—and QM has been confirmed empirically more than any other scientific theory—so too we can trust in its predictions.

Thus, it makes no sense to say that there is “insufficient evidence” to believe in other worlds because you can’t see them or visit them or whatever would make them seem intuitively obvious to you. They are real in the same sense that a quantum wavefront is real. A quantum wavefront is a mathematical object (as is spacetime). It should therefore not be all that implausible that multiverse theorists might be attracted to the proposition that the fundamental nature of reality is math—that mathematical objects have physical reality and physical reality is an isomorphic manifestation of math.

Now, obviously, this isn’t “scientific” in the sense of being experimentally testable. Nonetheless, as you should remember from your recent reading of David Deutsch, we are now at a point in human knowledge where the boundaries of science, math and philosophy are becoming increasingly blurred; where the very act of observation tends to have profound epistemological and ontological implications; and where scientific theories are becoming increasingly self-referential. Hut, Alford and Tegmark in their paper On Math, Matter and Mind get into a discussion of the various strategies that are possible. (Tegmark, takes the role of what he calls a “mathematical fundamentalist”; Alford takes the role of a “secular” scientist; and Hut takes a “mystic” view of science. Given your love of typologies, I think you may really going to enjoy this article.)

Now, the reason the multiverse interpretation occupies such a prominent place in mainstream physics is that it explains more than the generic Copenhagen interpretation with respect to why we have the laws we do in this universe and not some other laws. Basically, the gist of it is that, short of supernatural creation, it is extremely improbable that a universe occurring at random would be as finely tuned as our universe is in being able to support intelligent life. So, a multiverse consisting of all possible universes is much easier to explain than a one-off finely tuned universe, such as ours.

As for the timeless aspect of the multiverse, timelessness is a characteristic of all mathematical objects and spaces. But timelessness applies in the universe as well as the multiverse for reasons explained here and here. It also seems implausible that there would be a phenomenon like the big bang and that it would only happen once.

LostInParadise's avatar

This is all very heady stuff to me and I appreciate all the time and effort you and matt have put into this. The question I have, is how much of this stuff is verifiable? I heard some time ago that theories of physics are going to be judged not on how well they verify things but as a kind of beauty pageant based on elegance. If this is the case then the extent to which beauty is in the eyes of the beholder, there may never be an agreed upon ultimate theory.

Zuma's avatar

@LostInParadise As I understand it, QM is the most verified theory in all of science, but there are interpretations of it that are predicted by the theory that do compete on the basis of 1) explanatory power (comprehensiveness, coherence); 2) parsimony; and 3) aesthetic preference (elegance). Some of these interpretations are at pains to specify criteria by which they might be falsified and I have even seen cases where two competing interpretations will invoke the same thing as a falsification criterion. For example, the many worlds or multiverse interpretation would be considered falsified by an observation of the cosmological constant (or some other key parameter) being substantially above what would be optimum to sustain life in the universe. But it would also falsify Cosmic Natural Selection as well.

I recommend the On Math, Matter and Mind link above to draw out the nuances of all this. What happens is that the physicists seem to diss the mathematicians for “doing philosophy” instead of science and generally formulating things that are not empirically testable; while the mathematicians ding the physicists for proposing theories that are not rigorously specified in a formal mathematical terms. The trouble is that we are getting to the point in our theories where the “it” that is supposed to be empirically verified could be either a mathematical construct or a physically real thing (a wave or a particle) depending on how you choose to look at it.

To complicate matters further is how our theories fit with our baggage which is now actually a technical term in the parlance of theoretical physics. No doubt one of the things that animates Matt’s dogged skepticism over the multiverse is that if the multiverse exists, there is very little room for God in the scheme of things. The multiverse, together with the anthropic principle provide a satisfying naturalistic explanation as to how our universe can be so finely tuned across the 31 dimensions and constants that are necessary to support intelligent life.

The Intelligent Design folks are very clear about how a multiverse would minimize the necessity for a supernatural creator. Atheists like Lee Smolin simply dismiss creationist explanations out of hand on the ground that it is an explanation that fails to explain. If other universes are really as common as black holes, that might go a long way toward why they exist. If black holes of different masses forming under slightly different quantum initial conditions yield different universes with differently tuned parameters, that would be a plausible mechanism for how the population of universes is generated.

Naturally, some universes fail to achieve the escape velocity necessary to sustain an expansion, and others explode with such force that they fly apart, but there is a range in between where ”[t]he fabric of the multiverse is an inflationary field that’s filled with quantum fluctuations. These fluctuations can interfere with each other, creating high inflation at the peaks. The low points of the interference are where stable universes can pop out of the field. Conveniently, the high points continue to inflate, producing more multiverse fabric, which undergoes its own quantum fluctuation, making it an endless producer of universes; Linde describes it as a fractal process.”

Ah, fractals. To my mind that is almost a mathematical proof that the process of universe creation giving rise to the multiverse is correctly specified.

mattbrowne's avatar

I guess I need to print all the new replies and think really hard about it before I can reply.

Zuma's avatar


One more thing about testability. I recently came across a Scientific American article published in July of 08 called The Self-Organizing Quantum Universe by Ambjorn, Jurkiewicz and Loll. It’s a promising new approach to quantum gravity that may have already reconciled Quantum Mechanics with General Relativity. (Given how entrenched string theory is as the dominant paradigm, it may well take until 2020, according to Matt’s timeline, before it is all worked out and widely accepted.)

In their approach, called Causal Dynamical Triangulations, they approximate spacetime as a mosaic of triangles, which have a built-in distinction between space and time, and so permit a representation of causality. On small scales, spacetime takes on a fractal shape—and apparently a smooth one, as @hiphiphopflipflapflop predicted. They describe it, “a landscape composed of microscopic triangular structures that constantly rearrange themselves into new patterns. Seen from afar, the landscape looks perfectly smooth, but up close it is a churning cauldron of strange geometries.”

Interestingly, the way they tested it was through computer simulations. They ran variously parameterized models and compared their results to the real world. I suppose that if we really do live in a fundamentally mathematical universe, then computer simulations—which are basically ways of making predictions—may make the problem of empirical observation more tractable. This, I think, is what David Deutsch had in mind in The Fabric of Reality when he included computer science as one of the four root disciplines that will converge in a theory of everything.

Dynamic modeling is how you do studies of “emergent” phenomena. And I am sure it will come into its own as a form of theory testing/validation/proof as holistic approaches science gains ascendancy over the reductionist paradigm, or as reductionist science runs into the physical limits of empirical observation.

Intuitively, I think it’s a very good sign when theories and models turn up fractal structures. I think it tells you that the system is self-organized and therefore a natural part of the fabric of the universe. If space-time is self-organizing and fractal, and galactic clusters are self-organizing and fractal, perhaps everything in between is too—we certainly see it everywhere in Life. I wonder if there isn’t some sort of mathematical test of “fractality,” that might enable one to quantify the “goodness of fit” between an observed and expected fractal pattern.

In any case, Wikipedia lists Lee Smolin as a popularizer of CDT, and John Baez is also some kind of contributor. So, there may be something for everyone here.

mattbrowne's avatar

Okay, I need to study all this.

Just to be clear, I’m not against the idea of a multiverse. It has a lot of elegance, but we should treat it as exactly what it is, a very interesting hypothesis that needs further research. The multiverse could turn out to be a far better model than the unique universe. I just thought a debate would be very boring if everyone agrees about the multiverse. And Lee Smolin certainly is a heavy-weight quantum physicist.

Zuma's avatar

@mattbrowne the idea of a multiverse… is a very interesting hypothesis that needs further research.

We keep coming back to this same point. I wouldn’t have a problem if you said you didn’t know enough about theoretical physics to have a firm opinion on the multiverse, but that’s not what you say. When you say that the idea of a multiverse “needs further research” you strongly imply that you have reviewed the available evidence, that you are qualified to render an assessment, and that you have found this evidence is “lacking” in some specific but as yet unspecified respect.

I suspect, however, that you haven’t actually evaluated all this evidence yourself; but are instead relying on Smolin as your proxy and champion in this matter. Fair enough. But, it seems to me, in substituting his understanding for your own that you should actually understand and be willing to defend his critique of the multiverse, especially after you have quoted it in full above.

This may seem like an idle quibble, but neither Smolin nor Tegmark refer to the multiverse as a hypothesis. A hypothesis is a proposed explanation for an observable phenomenon, and the multiverse is not observable, not even in principle. The multiverse is a prediction. That is to say, it is required as a matter of logical necessity if you accept the assumptions of certain theories. If those theories have empirical support, the predictions move away from being purely speculative logical possibilities, and become “hypothetical actualities.”

Is a prediction that the sun will rise tomorrow a merely speculative logical possibility? No, it isn’t. This is not an actuarial prediction whose accuracy depends on the depth and quality of past observations. It is a hypothetical actuality because it is predicted by an empirically well-supported theory; namely, classical Newtonian mechanics. Once we know the relative position and velocities of the bodies in motion, and determine that no extraneous variables will intrude into the model, the model predicts with mechanical efficiency that there is actually no chance that the sun will not come up tomorrow. We are warranted in accepting the prediction as a hypothetical actual because because classical mechanics applies everywhere in the universe—in the future as well as the past.

This may seem like metaphysical sleight of hand—and, ultimately, maybe it is—but hypothetical actualities are everywhere in physics, especially mathematical physics. The big bang, the block universe, singularities, and even spacetime itself are all mathematical objects—as is the whole of Quantum Mechanics—the quantum wavefront, superposition, decoherence, and the rest of it. In the case of the multiverse, there are four separate and distinct empirically grounded theories that predict the multiverse; so this is one of the better established “hypothetical actualities.” And one that is not likely to change or improve with “further research.”

One thing you may have noticed is that Smolin does not take the position that “we need more research” before we can accept the multiverse. Quite the contrary, his rejection of the multiverse is far more radical insofar as it consists of a rejection of the entire class of “hypothetical actualities” as an “unreal” class of phenomena—which pretty much rejects the bulk of mathematical physics, including Quantum Mechanics. As you can see above, he explicitly rejects the unreasonable effectiveness of mathematics, and the mathematical Platonist notion that mathematical objects and laws are real and exist in a timeless reality. He also explicitly rejects the Newtonian schema, which assumes (among other things) that physical laws apply universally and do not vary depending on context or scale.

In short, it appears that Smolin is proposing a wholly different physics than the one we have now. Presumably, after we throw out all the “hypothetical actuals,” we no longer need to explain everything and for all time. We need only concern ourselves with what we can observe the present universe in the here and now. So, at about this point one might reasonably be ask, “Where’s the rest of it?” What does physics look like without timeless mathematical formalisms? In particular, how does one explain everything that was formerly explained by Quantum Mechanics? Well, so far as I can tell, the long passage Matt quoted above, is the whole thing in its entirety!

Where is the empirical evidence for the unique universe? It is, after all, a hypothesis and not a hypothetical actuality—or is it? How does one conclusively show that there is one universe and one universe only, beyond simply denying all the alternatives? Smolin may be a brilliant guy, but his unique universe proposal is nothing you would call an accredited theory; so it must be regarded as a kind of skeptical riff rather a serious critique of the multiverse, which at least is predicted by four separate empirically sound theories.

mattbrowne's avatar

The multiverse hypothesis cannot be falsified, but this doesn’t mean that future research cannot come up with more evidence in its support. We already have the double-slit experiment and quantum inference (“shadow photons”). There is research about singularities. Does a hypernova really result in a black hole? What about black stars which might not be singularities (because quantum processes create vacuum polarization, which creates a form of degeneracy pressure, preventing spacetime from occupying the same space at the same time)? What about baby universes inside them? Are they possible?

I’m more optimistic when it comes to finding alternatives to the Copenhagen interpretation or corroborative evidence for the multiverse. The notion of the unique universe might not be the end of the story. Smolin could be wrong of course.

Presently the multiverse is seen as a hypothesis not because of Smolin, but because of the vast majority of cosmologists and astrophysics out there. You might ridicule Wikipedia again, but this encyclopedia is not the only one calling the multiverse a hypothetical set of multiple possible universes.

LostInParadise's avatar

For what it is worth, I just came across this article from the online Scientific American, that talks about the possibiity of life in alternative universes:

Zuma's avatar

@mattbrowne “Presently the multiverse is seen as a hypothesis not because of Smolin, but because of the vast majority of cosmologists and astrophysics out there. You might ridicule Wikipedia again, but this encyclopedia is not the only one calling the multiverse a hypothetical set of multiple possible universes.”

Actually Matt, the multiverse is not seen as a hypothesis by the “vast majority of cosmologists and astrophysicists out there.” Here is a fair summary the changing status of the multiverse in physics:

Three decades ago, talk of other universes was not seen by most physicists to be part of science. Most research in theoretical physics and cosmology concerned observable features in our universe and most papers and seminars referred to experimental results. However, since then there has been a gradual shift, during which it first became acceptable to work on theories that described not only our universe, but other possible universes, universes with less or more dimensions, or universes with different kinds of particles and forces. In the last few years, we have moved further away from theories of our one universe, as these other worlds went from being logically possible to hypothetically actual. It is now common to hear about the multiverse a quantum cosmology that takes for granted that the visible universe that we see around us is just one of a vast or infinite number of universes.” (emphasis added)

If this sounds a bit familiar to you, it’s because it is from the long passage from Smolin which you quoted to me just a few posts above! Note the term “hypothetically actual.” I just spent a couple of hours and the better part of my last post trying to explain to you the subtle but important difference between a hypothesis and something that is “hypothetically actual.”

If you read your Smolin quote closely, you will find that he never refers to the multiverse as a hypothesis. But, even more telling, he does not treat the multiverse as a phenomenon that we can learn more about through information gathering and hypothesis testing. Now, if the “vast majority” of physicists actually regarded the multiverse as a hypothesis, their discussions of it would be dominated by talk about what kinds cosmological observations they could make or what kind of experiments the could do that would shed light on some aspect of the matter. And that simply isn’t the case—and it will never be the case—since other universes are unobservable in principle.

Here for example, is an announcement for a conference titled “A Debate in Cosmology – The Multiverse” at Peter Woit’s Not Even Wrong blog. As you will notice, nowhere in that announcement—or the in the discussion which follows—is the multiverse referred to or treated as a hypothesis. Instead, you will find mention of “The Many Worlds interpretation of QM” or “the idea that our observable universe is part of a multiverse.”

If you do a Google search on “multiverse hypothesis” you will find that, aside from Wikipedia, the only people who refer to “the multiverse hypothesis” are non-physicists. Moreover, they are non-physicists who appear to be engaged in philosophical debates about theism and “cosmic design.” Indeed, the Discovery Institute seems to have helped frame some of these discussions. No doubt, they think that if they can get people to think of the multiverse a “hypothesis,” they can frame it as something for which proof will always be found “lacking.”

So, I challenge you. If there is a “vast majority” of theoretical physicists who regard the multiverse as a testable hypothesis, name one. Find me one who has published on the subject in, say, the past five years. You may find passing reference to Boltzmann’s (1897) “multiverse hypothesis” in papers like P.C.W Davies’ Multiverse Cosmological Models but you won’t find any discussion of the multiverse as a testable hypothesis.

As for Wikipedia, go look at the profiles of the people who contributed to their Multiverse article and tell me if you can find even one working scientist among them, much less a theoretical physicist. As you can tell from the graphics, the folks at Wikipedia are all quite well acquainted with Max Tegmark’s Scientific American article on the subject—in fact they seem to rely upon him quite heavily. But in both the Sci Am. article and elsewhere, he states that the multiverse is not a hypothesis but a prediction. So, please tell me why you think the motley crew at Wikipedia is right and Tegmark is wrong.

And, finally, the multiverse can be falsified. In fact, each level has its own separate way of being falsified. (Essentially, you are falsifying the theories that predict the multiverse.) See here and here.

LostInParadise's avatar

What is meant by “hypothetically actual”? And in plain English, how does one go about falisifying the multiverse (prediction/hypothesis/conjecture/whatever)?

Zuma's avatar

@LostInParadise Take the Mathematical Universe Hypothesis, for example. Its an hypothesis because we can look to see if the unreasonable effectiveness of mathematics applies in every instance where we think it should apply. If it applies, then it is predicted—i.e., it is hypothetically actual—that the Level IV multiverse exists. If there is ever an observed case where the unreasonable effectiveness of mathematics does not apply, then the theory is falsified and the Level IV multiverse can be ruled out.

Level I parallel universes are based on the assumption that space is infinite and that our Hubble volume constitutes only an infinitesimal fraction of all space. This is supported by observations of cosmic microwave background radiation which shows that space has almost no curvature. Furthermore, the observed “hot” and “cold” spots are too large to be consistent with the previously popular “steady state” or “open universe” model. This theory makes the firm prediction that Omega = 1 to an accuracy of order 10^{-5}, this model (and all those level I parallel universes with it) would have been ruled out if we had measured say Omega=0.70+0.02. Instead, our latest constraints are Omega=1.01+-0.02.

Level II parallel universes are based on the notion that whatever mechanism caused the big bang in our universe continues to produce inflationary bubbles that give rise to other universes and even whole Level I multiverses. This can occur though the repeated cycling of our own universe. Or, as Smolin proposed, there could be some mechanism whereby black holes forming in a parent universe can sheer off and sprout baby universes which then expand out the other side of their wormholes. Or, there could be some sort of braneworld scenario in which there are other 3-dimensional worlds quite literally parallel to ours parked in a dimension offset from ours.

Whatever the exact mechanism, when quantum effects act on singularities during the initial moments of its big bang, the resulting geometry of the universe’s spacetime will be slightly different from universe to universe, causing it to self-organize in ways that result in different parameters—i.e., different particles, fields, dimensions and effective physical laws. So, a Level II multiverse implies a huge population of universes, the vast majority of which would not be able to support life.

Fortunately, the question of what parameter values can support life can only come up in a universe that is already finely tuned enough to support life. As it turns out, there are 31 dimensionless physical constants that have to be finely tuned “just so” in order for life like ours to exist. So the prospect of a single universe with its parameters tuned exactly right so as to support a unique universe with us in it occurring entirely by chance is so extremely improbable that it scarcely bears consideration. So, either there is an intelligent creator who steps into the breech and creates our “one-off” universe, or there is a very large multiverse which undergoes fine tuning by way of anthropic selection.

The God Hypothesis is untenable because there is no other empirical evidence to support it; it makes no other verifiable predictions; and it still fails to explain why this universe and not some other universe. The anthropic selection hypothesis (or some other selection hypothesis) is preferable because it is empirically testable. So, if we observe any of the key parameters of our universe falling outside the range of what would support us, then the idea of a multiverse selection process is falsified and so the Level II multiverse can be ruled out.

The Level III multiverse is predicted by Hugh Everett’s interpretation of Quantum Mechanics and involves the “non-communicating parts of the so-called Hilbert space into which the universe can ‘split’ during certain quantum events.” That discussion is a bit too technical for me to explain here, but Tegmark has a crisp three-page paper called Many lives in Many Worlds which explains the whole thing. “Everett’s theory is falsifiable by future lab experiments: no matter how large a system they probe, it says, they will not observe the wavefunction collapsing.”

There is also the prospect of a Level 0 multiverse. If the present universe is large enough, there may be exact copies of yourself elsewhere. Or, if Moore’s Law continues unabated, there may well be quantum computers sufficiently powerful to simulate all possible variations on this universe, giving rise to a virtual copy of you that is indistinguishable from the “real” you. Indeed, there may be another advanced civilization that has already developed this technology—and we may all be living in the Matrix and not even know it.

Only one of these possibilities actually has to pan out in order for you be bound by the moral implications of the multiverse. If there is a multiverse, there are almost certainly different versions of yourself. In one universe you may be a saint or a scholar; in another you may hold up gas stations for a living. What you do to someone in one universe may be done to you in another, so that you suffer the same cruelties you inflict on others.

The multiverse also logically entails a kind of immortality, especially if the multiverse is timeless. The multiverse opens the possibility of getting Pascal’s wager seriously wrong. Suppose that simply believing in God is not enough to secure you an eternity in heaven, and you don’t die a permanent death. Suppose you live on, and on, and on in some future version of the world you have shaped through your day to day choices. What if the quality of your future depends on how much ignorance, cruelty and oppression you contribute (or spare) the world from? And instead of doing what you can to improve the world, you abandon it in the mistaken belief that it is too corrupt to save, or that your life really doesn’t begin until you get to Heaven?

These are the conversations I would like to have with @mattbrowne (and yes, I’m still interested in talking with him) but there is no point in having such a discussion with someone who is so dead set against the idea that he can’t envision the possibility that he may be living in one.

mattbrowne's avatar

Someone who is so dead set against the idea? Innuendos like this make debates very unpleasant. How do you know what other people envision or not envision? I’m interested in deep debates and I appreciate it when opinions differ but everyone should act professionally. There’s a difference between talking about various subjects and talking about the people who participate. Sorry to say this, but I’m not interested in this kind of conversation.

Zuma's avatar

@mattbrowne What I am saying very directly (and without any innuendo) is that if you review our exchange above, and our other exchanges elsewhere, you have done nothing but raise reason after reason why you shouldn’t have to take the idea of living in a multiverse seriously. First, there is your insistence that it is (just) a hypothesis; then there is your full frontal assault by Smolin denying its existence; and then there’s your preference for Wikipedia over actual experts, etc., etc. Nothing in our long exchanges—and we have been going at this for months now—shows me that you are any closer to accepting the multiverse as a live option than when we began.

I don’t know why you are feeling put out my statement of the obvious. If you don’t really believe there is a multiverse, how can you possibly envision yourself living in one? And how can you meaningfully discuss the moral, ethical and spiritual implications of living in a multiverse? That, I think, is a far more interesting conversation than the interminable quibbles we have been having over whether the multiverse actually exists.

Now, if I am mistaken as to your position, then I apologize.

mattbrowne's avatar

Look, I think it’s very simple. When we discuss science we stick to scientific method and the findings of observations and potential future findings of observations. When we discuss metaphysics, philosophy, spirituality and religion we keep in mind that we are stepping on turf outside of the realm of scientific method. We respect each others views and beliefs, although we don’t have to agree with everything that’s been said of course. We discuss topics and viewpoints, not participants of the discussions. You can’t know everything that’s going on in my head and I can’t know everything that’s going on in your head. Our posts here always show just a small fraction. And even then there can be misinterpretations.

I’m almost never dead set against any ideas, except for perverse ideologies like Nazism. I’ve said repeatedly that I see a lot of value in the multiverse concept. I even said, if it turns out to be the best explanation of reality, so be it. Why would I be against anything for which there’s overwhelming evidence? I’m just not ready to accept it as mainstream science yet like general relativity or evolutionary biology. If no one in the future can think of clever experiments within the realm of scientific method i.e. in addition to observable quantum interference, so be it. Then the multiverse concept will be in part science and in part metaphysics (a prediction).

I also never said I completely agree with what Lee Smolin wrote. One cannot assume if someone brings an article into a discussion this someone is a zealous supporter of the unique universe concept. I regarded the article as food for thought.

Moving on to religion. I also never said I have an issue with a “minimal” role of a deity. On the contrary I said if our universe and its big bang is the result of a larger structure, than this larger structure (not a god) explains our universe. There’s still the ultimate why question about any larger structures and there are two ways of answering them. I think this won’t go away. I’m also a vocal opponent of the intelligent design movement. I don’t believe in an interfering god and I don’t support movements that violate the basic principles of scientific method. I also see religion as more than the belief in a deity.

I don’t have anything against heated debates. It’s the fuel of progress. But I have something against debates that turn out to be very unpleasant. Good manners and etiquette do matter to me. I avoid the pronoun “you” in Fluther posts whenever possible, especially when there’s a lot of disagreement. I would never use a sentence like @Zuma or @LostInParadise or @Blondesjon is dead set against this or that. Because I don’t know. I might suspect this or that, but I could be wrong. Another reason is that this approach can hurt people’s feelings. Who wants to get a label of being close-minded? Especially people who are passionate about science and philosophy.

Zuma's avatar

@mattbrowne “I’m almost never dead set against any ideas… I’m just not ready to accept [the multiverse] as mainstream science…”

I see, it’s not that you’re actively resisting the evidence I have presented to you, you’re just “not ready” to give it any weight. In other words, you’re not being thick-headed, or ignoring my arguments on purpose, you’re just “not ready” to give them any credence. I could understand your lack of readiness were simply due to incomplete information. In that instance, you could exercise due diligence, find out more, and make up your mind. But, in this case, not being “ready” means not being ready to accept credible bonafide evidence or argument.

For example, when one of the world’s leading proponents of the multiverse tells you in a 2003 peer-reviewed scientific journal that Parallel Universes are now considered mainstream science, you find it okay to dismiss this out of hand because, apparently, you’re not “ready” to accept it:

“One might expect the notion of a multiverse to be forever in the domain of metaphysics. Yet the borderline between physics and metaphysics is defined by whether a theory is experimentally testable, not by whether it is weird or involves unobservable entities. The frontiers of physics have gradually expanded to incorporate ever more abstract (and once metaphysical) concepts such as a round Earth, invisible electromagnetic fields, time slowdown at high speeds, quantum, superpositions, curved space, and black holes. Over the past several years the concept of a multiverse has joined this list. It is grounded in well-tested theories such as relativity and quantum mechanics, and it fulfills both the basic criteria of an empirical science: it makes predictions and it can be falsified. Scientists have discussed as many as four distinct types of parallel universes. The key question is not whether the multiverse exists but rather how many levels it has.” (emphasis added)

Whether or not the multiverse is mainstream or is fringe science is not a matter of opinion, it is a matter of fact. And it can be settled by looking at current work on the subject. Here, for example, is another more recent article in Scientific American called Looking for Life in the Multiverse. It couldn’t be clearer on this point:

“Amazingly, the prevailing theory in modern cosmology, which emerged in the 1980s, suggests that such “parallel universes” may really exist—in fact, that a multitude of universes would incessantly pop out of a primordial vacuum the way ours did in the big bang.”

In fact, no discussion of modern cosmology is now complete without a discussion of parallel universes. Even the History Channel recognizes Parallel Universes as mainstream science. Indeed Smolin, whom you quote to me above, acknowledges that “over the past few decades… there has been a gradual shift, during which it first became acceptable to work on theories that described not only our universe, but other possible universes.” But now you inform me that you “don’t necessarily agree” with your own expert, presumably because you’re “not ready” to face the fact that “many worlds” has become a mainstream feature of modern cosmology, along with black holes and electromagnetic fields.

Maybe, just maybe (you say), you would be convinced if there were some sort of clever table top experiment like the double-slit experiment that would “provide experimental support” for the existence of parallel universes. I don’t see how, if you’re “not ready” to give any weight to the existing evidence. For your information, “many worlds” is a direct implication of the two-slit experiment—which was the subject of an hour-long PBS documentary on NOVA called, Parallel Worlds, Parallel Lives—this was also fully explained to you in a book by David Deutsch that I know you’ve read.

You complain about how unsatisfying it is when people accuse you of being close-minded. Well, maybe you could pause a minute and reflect on how satisfying it is to have a conversation with someone who someone says, in effect, “I’m not close-minded, I’m just ‘not ready’ to consider anything you have to say.”

I’ve gone to great lengths to explain to you how the multiverse is not a hypothesis. I might as well be talking to a fence post, because you simply ignore my argument and keep on referring to the multiverse as a hypothesis. How satisfying a discussion do you think that is for me? When I remark on your unseemly resistance to argument and your “unreadiness” to accept the abundant credible evidence presented to you, you get your knickers all in a twist and complain bitterly about how your feelings all hurt—which may actually believe, but is nonetheless a shabby way of changing the subject and wiggling out of the argument just when it starts to press.

You aren’t debating. You’re just sitting there saying, “I don’t believe it.” “I deny it.” or “I’m not ready.” to whatever is being offered to you. It’s not the lack of credible evidence or argument that is the problem. It is either your unwillingness or your inability to consider that which is being offered. Of course you don’t find the conversation satisfying! You aren’t ready to change your mind, and so you just dismiss everything that is presented to you out of hand. You’re right. I don’t know why. Maybe it’s because you don’t really have any firm beliefs about cosmology. It’s all just a haze of conjecture and theoretical possibility to you. Whatever the case, there simply isn’t any point in arguing this point with you any further, at least until you do some reading and settle in your own mind whether the multiverse is mainstream science or not.

To that end, I would like to recommend a website that I think you will find right up your alley: Closer to Truth. It contains dozens and dozens of top-notch interviews with many of the world’s top theoretical physicists, cosmologists, philosophers and theologians. I think you will find the theological discussions particularly enjoyable. (Keep in mind, however, that whenever they discuss the anthropic principle, they are implicitly accepting the multiverse as a matter of logical necessity.)

LostInParadise's avatar

@Zuma, I do not know anything of quantum mechanics, but the impression that I get is that the multiverse idea is on about the same level as string theory. It may eventually be possible to test but currently it is just a conjecture. There is an article in the current Scientific American written by physicists who I assume are reputable.

Quote from near the beginning of the article:
Amazingly, the prevailing theory in modern cosmology suggests such “parallel universes” may really exist – in fact that a multitude of such universes would pop out of a primordial vacuum the way ours did in the big bang.

Concluding paragraph:
We may never find any direct evidence of the existence of other universes, and we certainly will never visit one. But we may need to learn more about them if we want to to understand our place in the multiverse – or whatever it is that is out there.

Maybe the scientists are being overly cautious in their statements, but it seems to me that they are saying that the evidence to date of the existence of a multiverse is not yet conclusive.

Zuma's avatar

@LostInParadise If you want to get a better sense of what quantum mechanics is, this is the best website I have found on the subject (and many others we have been discussing here). As you probably know, string theory is an interpretation of quantum mechanics that seeks to explain gravity and thereby reconcile QM with general relativity theory. There are five distinct mathematically self-consistent versions of string theory, each of which is an approximation of a yet-to-be determined underlying reality. However, whatever the final theory is, it is likely going to be closer to one the five interpretations which approximate it than something completely different.

So, saying that parallel universes is on a par with string theory is actually quite a strong statement—certainly much stronger than calling it “just” a conjecture. Newtonian physics produces predictions that are on the order of seven decimal places of precision; QM produces predictions that are precise to the fourteenth decimal place. So, as approximations of ultimate reality, they QM and String Theory are both far more accurate and more empirically grounded than our old Newtonian gold standard in these matters.

I heartily recommend the Closer to Truth: Cosmos. Consciousness. God. website to you as well. So far, Robert Lawrence Kuhn has interviewed around 120–130 famous scientists, philosophers and scientifically trained theologians. These are some of the most brilliant and civilized people on the planet, and many of them talk about the spiritual implications of their scientific theories and vice versa.

One of the things that immediately becomes clear in these interviews is that no one seriously disputes the idea of a multiverse. In fact, one could say that “many worlds” is a generally accepted view of the cosmos, and certainly a preferred view given the current array of alternatives. Of course, not everyone is satisfied with this explanation, and some are deeply unhappy about the lack of direct empirical evidence. But most seem to regard it as a weird but inescapable implication of empirically well-verified theories; notably, chaotic inflation, quantum mechanics, and the unreasonable effectiveness of math.

Do we really prove anything in science “conclusively”? Certainly we do in math and logic. And it is through logic that we predict that the various levels of the multiverse exist (what makes other universes “other” is the fact that they are cut off from us and therefore unobservable in principle.)

So, what is it that prevents you from concluding that you live in a multiverse? Is it lack of direct evidence? No, because there are lots of other things we can’t observe directly that we seem to have no problem accepting (like black holes, the curvature of space, time dilation at high speeds, quantum wavefronts, etc.). Is it because we have plenty of robust alternative theories? No, it’s actually been the lack of alternative theories that has driven most physicists (some very reluctantly) into the fold. Is it because the idea sounds weird? Well, actually, that does seem to be the final sticking point of doubt for most people. But, nowadays, the multiverse is a well-vetted and perfectly respectable idea in theoretical physics—which I urge you and Matt to verify for yourself at the Closer to Truth website (which I think you will find mind-blowing anyway).

flutherother's avatar

Curioser and curioser. I found the above exchanges fascinating though most of it went way over my head. I would like to thank everyone who took part.

Scientific method is taking us to some strange places. Who could have thought that an investigation into black body radiation would lead to quantum theory which in turn predicts an infinite number of parallel universes. Are there an infinite number of copies of myself each believing himself to be unique and each with a different history to mine? Surely this cannot be.

And yet just because something seems strange doesn’t mean it is not true. Quantum computing is being taken very seriously by governments who are funding research and it may soon become a reality. Maybe I am wrong but quantum computing seems to me to rely on calculations taking place in more than one universe simultaneously and so the first quantum computer will be a proof of the existence of the multiverse.

Maybe, but it would be wise to bear in mind these words of G K Chesterton

“The madman is not the man who has lost his reason. The madman is the man who has lost everything except his reason.”

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