E Pluribus Unum
Nov. 26th, 2013 12:11 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mtvesselMay 2013
The Hidden Reality - Brian Greene - Penguin Books, 2012
* * * *
Warning: Very long article ahead. Also probably inaccurate summations of complex ideas in physics.
The author showed an engaging modesty when he appeared in an episode of The Big Bang Theory and was mocked by the Sheldon Cooper character for the sometimes left-field similes that are a feature of his writing style. They are certainly present here - cosmic cheese, wild partyers shaking buildings in San Francisco, the cosmological principle as a cup of tea and probability waves explained via New York landmarks all make an appearance - but they aren't annoying. The most irritating thing about this book is its title, which is a lie.
For this is a book about multiverses, and we have no direct evidence that any multiverse exists. So to say that it describes "the hidden reality" is wrong. To make matters worse, Greene doesn't just describe one possible multiverse but nine different possible formulations with varying degrees of likelihood. But then he is a physicist studying string theory, an area of research of which many scientists are suspicious because of its lack of testable hypotheses. A subject into which, to be fair, Greene goes in some detail.
And it's true that there has to be something out there because the two best theories we have for describing the behaviour of matter don't fit. Special and general relativity brilliantly explain the movement of large objects and the sometimes paradoxical effects of motion on causality. Their predictions of gravitational lensing and time dilation match exactly with observation. But the mathematical model is Newtonian in nature and there is not a probability in sight. Whereas quantum mechanics, which explains the properties of elementary particles and which matches some observations to a ridiculously high level of accuracy, is all about probabilities. The certainties of spacetime cannot be explained by the jitters of quantum mechanics, and vice versa. There must be something else that links the two.
What that something is is the big unanswered question in physics, and a multiverse could be the answer. Though to understand what a multiverse is, it is important to understand how physicists define the word "universe", which is slightly different from its casual usage. Physicists regard a universe as being everything that we can see, everything that is in our light cone. A universe is not "everything there is". Stuff that exists outside our light cone is part of a multiverse but not our universe.
This definition of a universe as having a "cosmic horizon" (defined as the maximum distance that light could have travelled since the big bang) leads to the "quilted multiverse" which is perhaps the most straightforward version of the idea. If space is infinite and every point in it has a cosmic horizon, and if the same laws apply throughout, there will be points that are so far apart that their cosmic horizons do not overlap and which therefore, up to now, have never communicated. Greene makes an interesting point about these separated universes. If the matter in them can only be arranged in a finite number of ways, some must necessarily be copies of others, for the same reason that infinite repetitions of a randomly sorted pack of playing cards must inevitably have some duplications. And of course we know from relativity and quantum mechanics that the possible arrangements of matter are indeed finite. There can only be a finite number of particles in a universe because particles have mass and if you try to cram too much mass into a small area, you get a black hole. And particles can only arrange themselves in a finite number of ways because of the Uncertainty Principle, which constrains their possible positions and velocities. So, if this view is correct, there is an infinite number of universes out there that are exactly like ours, containing carbon copies of ourselves. And an infinite number that are almost like ours but with small variations. Somewhere there is a universe in which a green, three-armed version of me is typing this exact review. And because all universes are constantly expanding, one day that universe and ours may meet.
The introduction of the concept of inflation, necessary to explain the uniformity of the night sky, also introduces a potential multiverse because the postulated inflaton field that drives it interacts with other quantum processes in such a way that its value varies in space. This is where the Swiss cheese analogy comes in. Regions of space with low inflaton field values become separate universes which are separated from other universes by rapidly expanding areas with a high inflaton field, like the holes in a Swiss cheese. These universes will be radically different from one another and will never interact. Interestingly, it turns out that each one, from the point of view of its inhabitants, has infinite space, and so can contain its own quilted multiverse.
Greene next moves on to string theory, which gives rise to three more possible multiverses. The one most fans of popular science will have heard of is M-theory in which "branes" float in multidimensional space. The four-dimensional (or, if string theory's hidden dimension exist, ten- or eleven-dimensional) spacetime with which we are familiar could be one such brane and there could be many others. Each brane would have its own physics dependent on its dimensionality and the fields permeating it. Collisions between branes could also correspond to big bang events, yielding a set of cyclic universes that end in fiery conflagrations as the branes bounce apart and meet again. Finally, string theory's extra dimensions can be bundled up in 10500 possible ways (the number of possible six-dimensional Calibi-Yau shapes) and all these conformations can be generated by quantum tunnelling in the inflation model's "Swiss Cheese" multiverse, which results in a set of universes each with its own unique arrangement of dimensions. Greene calls this the "landscape" multiverse.
And we're still not done, for all the multiverses proposed so far come from the relativistic side of the physics fence. On the other, quantum mechanics yields Everett's famous "many worlds" hypothesis, an interpretation of the Schrödinger wave function that posits that its various eigenstates all co-evolve in separate universes. An even more outré idea is the holographic multiverse, which arises from consideration of quantum effects in the physics of black holes and the application of the classic Second Law of Thermodynamics that entropy increases (something I have understood from a very young age thanks to the utter brilliance of Flanders and Swann). The Hawking radiation postulated to arise when one particle of a vacuum-generated quantum pair falls into a black hole's event horizon and the other escapes allows a black hole to have entropy, and hence to store information about the things that fall into it (a system's information content - the number of yes-no questions that its microscopic components have the capacity to answer - is directly proportional to its entropy). Juan Maldacena pointed out that the amount of information a black hole can store is proportional to its surface area, not its volume. This turns out to be a general result. The physical phenomena of any region of space, represented as information, can be encoded on the surface of a two-dimensional sphere surrounding that space.
When I was about twelve years old, I remember going to an exhibition of holography. It was one of the most extraordinary things I had ever seen. Laser light, shining through flat plates of glass, created magical glowing three-dimensional images of pots and flowers and footballs. Maldacena and others are suggesting that the n-dimensional universe that we see could be just such a projection of events on a distant lower dimensional surface.
The last two multiverses that Greene considers are definitely more philosophical than scientific. Extrapolation of computing power suggests that a simulated universe indistinguishable from our own (at our level of perception, at least) will soon be possible. Since simulations are by definition easier to create than the things they simulate, it is far more probable that we are constructs living in a simulated universe than that we are entities living in a real one. Beings capable of creating simulated universes could easily create multiple copies with variations. Hence a simulated multiverse.
Finally we come to the ultimate or "Library of Babel" multiverse. Many of the arguments in physics are over which mathematical description of the universe is correct, but what if they all are? Consider a library of all the logically consistent mathematical systems that could be used to describe a universe and imagine a universe for each one. Greene calls this the ultimate multiverse (though "omniverse" might be a better term), incorporating all the multiverses previously described and more. The great advantage of this is that you no longer have to explain why the particular set of laws that govern our universe (or the multiverse our universe is in) is "privileged" above any other set of laws that you could imagine, because it isn't.
So, an entertaining collection of ideas, but how can we find out if any of them are true? After all, by definition, no information from another universe in a multiverse can reach ours. Does this mean that models involving multiverses are fundamentally unscientific? Do they fail Popper's criterion of falsifiability? Well, not entirely. Greene points out a few ways in a which a multiverse hypothesis can be tested even on the evidence of the single universe that we can see. For example, if the mechanism for generating the multiverse requires that all universes have certain features (or correlations between features) in common, and if we don't see those features (or correlations) in our universe, we can conclude that it is false. Secondly, one can extend the Cosmological Principle - that physical laws are the same across the entire cosmos and so the bits of the universe we have looked at so far are typical of the whole - and say that a multiverse-generation mechanism that results in a set of universes in which the features of our universe are highly atypical is unlikely to be correct.
A few examples: the quilted multiverse becomes unviable if space can be shown not to be infinite in extent (though it's hard to imagine how this could be done empirically). More precise measurements of cosmic microwave background radiation could rule out simpler forms of inflation and make the swiss cheese multiverse unlikely. The failure to discover supersymmetric particles, energy gaps or mini black holes at the Large Hadron Collider could eliminate the most common varieties of string theory needed to support braneworld multiverses (and the preliminary evidence is not looking good for supersymmetry). The holographic multiverse effectively says that two mathematical models of physics (four-dimensional quantum field theory and ten-dimensional string theory) describe the same physics from different perspectives, and this mapping can in principle be tested. It has already provided an explanation for an otherwise anomalous measurement of the shear viscosity of a quark-gluon plasma at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven.
I have to say that as a good Popperian, I am more skeptical than Greene. For a start, calls to the extended cosmological principle fail if the multiverse generation mechanism produces an unlimited number of universes - you cannot talk about "typical" and "atypical" configurations if you have infinitely many instances to choose from. It's also characteristic of the "heads I win, tails you lose" shiftiness that surrounds the subject that some string theorists are arguing that the absence of supersymmetric particles at the LHC is increased evidence for a string-y "landscape" multiverse. They say that it strengthens the Standard Model and therefore demands an explanation of why the highly fine-tuned values that have to be ascribed to the Higgs Boson bare mass and to the Cosmological Constant in it are not an incredible coincidence.
Ultimately, many of the ideas about multiverses described in this book seem to me to have the same explanatory power as many religious explanations of the origin of the universe. Nice just-so stories, and not demonstrably false, but not much use either. After all, these multiverses exist as deduced consequences of mathematical models, and if by definition we can't empirically detect their existence or anything about their properties, they can't be used to test the models from which they derive. Which means that they are not worth thinking about, other than as an intellectual curiosity or as a playground for science fiction writers.
There is also Occam's Razor to consider. If two cosmological models exist that fit the established facts, and one requires a multiverse to exist and the other doesn't, the more parsimonious should be the front runner where time and money are spent. The parallel between the elaborate Ptolemeic model of the solar system and the elegant Copernican one seems pretty exact to me.
My personal view is that we have not got to the bottom of quantum mechanics yet and that some clever formulation of quantum gravity, possibly stringy, possibly loopy, will encompass the certainties of relativity and the problems of the Standard Model into the probabilistic fold without the necessity to call on a multiverse that effectively stops scientific enquiry with the parental "it just is, okay?" (despite Greene's optimistic assertion that it doesn't).
Multiverses as a calculation tool, rather than as a description of the "hidden reality", may still have a place, however, in much the same way as the wave function describes what an electron does but not what it is. Malcadena's holographic formulation does seem to be a useful way of making intractable calculations possible. And what if you could apply Feynman's sum over histories idea to the evolving wavefunctions of Wheeler's quantum multiverse, cancelling them out in an orgy of interference and leaving ours as the only one standing? E pluribus unum. Now that's a multiverse I could live with. And in.
The Hidden Reality - Brian Greene - Penguin Books, 2012
* * * *
Warning: Very long article ahead. Also probably inaccurate summations of complex ideas in physics.
The author showed an engaging modesty when he appeared in an episode of The Big Bang Theory and was mocked by the Sheldon Cooper character for the sometimes left-field similes that are a feature of his writing style. They are certainly present here - cosmic cheese, wild partyers shaking buildings in San Francisco, the cosmological principle as a cup of tea and probability waves explained via New York landmarks all make an appearance - but they aren't annoying. The most irritating thing about this book is its title, which is a lie.
For this is a book about multiverses, and we have no direct evidence that any multiverse exists. So to say that it describes "the hidden reality" is wrong. To make matters worse, Greene doesn't just describe one possible multiverse but nine different possible formulations with varying degrees of likelihood. But then he is a physicist studying string theory, an area of research of which many scientists are suspicious because of its lack of testable hypotheses. A subject into which, to be fair, Greene goes in some detail.
And it's true that there has to be something out there because the two best theories we have for describing the behaviour of matter don't fit. Special and general relativity brilliantly explain the movement of large objects and the sometimes paradoxical effects of motion on causality. Their predictions of gravitational lensing and time dilation match exactly with observation. But the mathematical model is Newtonian in nature and there is not a probability in sight. Whereas quantum mechanics, which explains the properties of elementary particles and which matches some observations to a ridiculously high level of accuracy, is all about probabilities. The certainties of spacetime cannot be explained by the jitters of quantum mechanics, and vice versa. There must be something else that links the two.
What that something is is the big unanswered question in physics, and a multiverse could be the answer. Though to understand what a multiverse is, it is important to understand how physicists define the word "universe", which is slightly different from its casual usage. Physicists regard a universe as being everything that we can see, everything that is in our light cone. A universe is not "everything there is". Stuff that exists outside our light cone is part of a multiverse but not our universe.
This definition of a universe as having a "cosmic horizon" (defined as the maximum distance that light could have travelled since the big bang) leads to the "quilted multiverse" which is perhaps the most straightforward version of the idea. If space is infinite and every point in it has a cosmic horizon, and if the same laws apply throughout, there will be points that are so far apart that their cosmic horizons do not overlap and which therefore, up to now, have never communicated. Greene makes an interesting point about these separated universes. If the matter in them can only be arranged in a finite number of ways, some must necessarily be copies of others, for the same reason that infinite repetitions of a randomly sorted pack of playing cards must inevitably have some duplications. And of course we know from relativity and quantum mechanics that the possible arrangements of matter are indeed finite. There can only be a finite number of particles in a universe because particles have mass and if you try to cram too much mass into a small area, you get a black hole. And particles can only arrange themselves in a finite number of ways because of the Uncertainty Principle, which constrains their possible positions and velocities. So, if this view is correct, there is an infinite number of universes out there that are exactly like ours, containing carbon copies of ourselves. And an infinite number that are almost like ours but with small variations. Somewhere there is a universe in which a green, three-armed version of me is typing this exact review. And because all universes are constantly expanding, one day that universe and ours may meet.
The introduction of the concept of inflation, necessary to explain the uniformity of the night sky, also introduces a potential multiverse because the postulated inflaton field that drives it interacts with other quantum processes in such a way that its value varies in space. This is where the Swiss cheese analogy comes in. Regions of space with low inflaton field values become separate universes which are separated from other universes by rapidly expanding areas with a high inflaton field, like the holes in a Swiss cheese. These universes will be radically different from one another and will never interact. Interestingly, it turns out that each one, from the point of view of its inhabitants, has infinite space, and so can contain its own quilted multiverse.
Greene next moves on to string theory, which gives rise to three more possible multiverses. The one most fans of popular science will have heard of is M-theory in which "branes" float in multidimensional space. The four-dimensional (or, if string theory's hidden dimension exist, ten- or eleven-dimensional) spacetime with which we are familiar could be one such brane and there could be many others. Each brane would have its own physics dependent on its dimensionality and the fields permeating it. Collisions between branes could also correspond to big bang events, yielding a set of cyclic universes that end in fiery conflagrations as the branes bounce apart and meet again. Finally, string theory's extra dimensions can be bundled up in 10500 possible ways (the number of possible six-dimensional Calibi-Yau shapes) and all these conformations can be generated by quantum tunnelling in the inflation model's "Swiss Cheese" multiverse, which results in a set of universes each with its own unique arrangement of dimensions. Greene calls this the "landscape" multiverse.
And we're still not done, for all the multiverses proposed so far come from the relativistic side of the physics fence. On the other, quantum mechanics yields Everett's famous "many worlds" hypothesis, an interpretation of the Schrödinger wave function that posits that its various eigenstates all co-evolve in separate universes. An even more outré idea is the holographic multiverse, which arises from consideration of quantum effects in the physics of black holes and the application of the classic Second Law of Thermodynamics that entropy increases (something I have understood from a very young age thanks to the utter brilliance of Flanders and Swann). The Hawking radiation postulated to arise when one particle of a vacuum-generated quantum pair falls into a black hole's event horizon and the other escapes allows a black hole to have entropy, and hence to store information about the things that fall into it (a system's information content - the number of yes-no questions that its microscopic components have the capacity to answer - is directly proportional to its entropy). Juan Maldacena pointed out that the amount of information a black hole can store is proportional to its surface area, not its volume. This turns out to be a general result. The physical phenomena of any region of space, represented as information, can be encoded on the surface of a two-dimensional sphere surrounding that space.
When I was about twelve years old, I remember going to an exhibition of holography. It was one of the most extraordinary things I had ever seen. Laser light, shining through flat plates of glass, created magical glowing three-dimensional images of pots and flowers and footballs. Maldacena and others are suggesting that the n-dimensional universe that we see could be just such a projection of events on a distant lower dimensional surface.
The last two multiverses that Greene considers are definitely more philosophical than scientific. Extrapolation of computing power suggests that a simulated universe indistinguishable from our own (at our level of perception, at least) will soon be possible. Since simulations are by definition easier to create than the things they simulate, it is far more probable that we are constructs living in a simulated universe than that we are entities living in a real one. Beings capable of creating simulated universes could easily create multiple copies with variations. Hence a simulated multiverse.
Finally we come to the ultimate or "Library of Babel" multiverse. Many of the arguments in physics are over which mathematical description of the universe is correct, but what if they all are? Consider a library of all the logically consistent mathematical systems that could be used to describe a universe and imagine a universe for each one. Greene calls this the ultimate multiverse (though "omniverse" might be a better term), incorporating all the multiverses previously described and more. The great advantage of this is that you no longer have to explain why the particular set of laws that govern our universe (or the multiverse our universe is in) is "privileged" above any other set of laws that you could imagine, because it isn't.
So, an entertaining collection of ideas, but how can we find out if any of them are true? After all, by definition, no information from another universe in a multiverse can reach ours. Does this mean that models involving multiverses are fundamentally unscientific? Do they fail Popper's criterion of falsifiability? Well, not entirely. Greene points out a few ways in a which a multiverse hypothesis can be tested even on the evidence of the single universe that we can see. For example, if the mechanism for generating the multiverse requires that all universes have certain features (or correlations between features) in common, and if we don't see those features (or correlations) in our universe, we can conclude that it is false. Secondly, one can extend the Cosmological Principle - that physical laws are the same across the entire cosmos and so the bits of the universe we have looked at so far are typical of the whole - and say that a multiverse-generation mechanism that results in a set of universes in which the features of our universe are highly atypical is unlikely to be correct.
A few examples: the quilted multiverse becomes unviable if space can be shown not to be infinite in extent (though it's hard to imagine how this could be done empirically). More precise measurements of cosmic microwave background radiation could rule out simpler forms of inflation and make the swiss cheese multiverse unlikely. The failure to discover supersymmetric particles, energy gaps or mini black holes at the Large Hadron Collider could eliminate the most common varieties of string theory needed to support braneworld multiverses (and the preliminary evidence is not looking good for supersymmetry). The holographic multiverse effectively says that two mathematical models of physics (four-dimensional quantum field theory and ten-dimensional string theory) describe the same physics from different perspectives, and this mapping can in principle be tested. It has already provided an explanation for an otherwise anomalous measurement of the shear viscosity of a quark-gluon plasma at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven.
I have to say that as a good Popperian, I am more skeptical than Greene. For a start, calls to the extended cosmological principle fail if the multiverse generation mechanism produces an unlimited number of universes - you cannot talk about "typical" and "atypical" configurations if you have infinitely many instances to choose from. It's also characteristic of the "heads I win, tails you lose" shiftiness that surrounds the subject that some string theorists are arguing that the absence of supersymmetric particles at the LHC is increased evidence for a string-y "landscape" multiverse. They say that it strengthens the Standard Model and therefore demands an explanation of why the highly fine-tuned values that have to be ascribed to the Higgs Boson bare mass and to the Cosmological Constant in it are not an incredible coincidence.
Ultimately, many of the ideas about multiverses described in this book seem to me to have the same explanatory power as many religious explanations of the origin of the universe. Nice just-so stories, and not demonstrably false, but not much use either. After all, these multiverses exist as deduced consequences of mathematical models, and if by definition we can't empirically detect their existence or anything about their properties, they can't be used to test the models from which they derive. Which means that they are not worth thinking about, other than as an intellectual curiosity or as a playground for science fiction writers.
There is also Occam's Razor to consider. If two cosmological models exist that fit the established facts, and one requires a multiverse to exist and the other doesn't, the more parsimonious should be the front runner where time and money are spent. The parallel between the elaborate Ptolemeic model of the solar system and the elegant Copernican one seems pretty exact to me.
My personal view is that we have not got to the bottom of quantum mechanics yet and that some clever formulation of quantum gravity, possibly stringy, possibly loopy, will encompass the certainties of relativity and the problems of the Standard Model into the probabilistic fold without the necessity to call on a multiverse that effectively stops scientific enquiry with the parental "it just is, okay?" (despite Greene's optimistic assertion that it doesn't).
Multiverses as a calculation tool, rather than as a description of the "hidden reality", may still have a place, however, in much the same way as the wave function describes what an electron does but not what it is. Malcadena's holographic formulation does seem to be a useful way of making intractable calculations possible. And what if you could apply Feynman's sum over histories idea to the evolving wavefunctions of Wheeler's quantum multiverse, cancelling them out in an orgy of interference and leaving ours as the only one standing? E pluribus unum. Now that's a multiverse I could live with. And in.