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recent Edge postings, "Time
Loops: a Talk with Paul Davies" and Phil Anderson's response to
Jaron Lanier's "One-Half
a Manifesto" are rich in stimulating ideas. However, when they touch
on quantum computation, they both make statements that I question.
What is known about searching large databases on a quantum computer? Grover(1996) discovered a quantum algorithm for finding a single item in an unsorted database with N items in time proportional to the square root of N. The same problem takes time N to solve on a classical computer. For example, if there are 10 to the 100 items in the database (thats 1 followed by 100 zeros) it would take time 10 to the 100 on a classical computer and time about 1 to the 50 (thats 1 followed by 50 zeros) on a quantum computer. I would not call that "searching enormous databases with extraordinary efficiency".
Speaking technically, Grover's algorithm show quantum search is only polynomially faster than classical search. Part of my research is solving continuous problems on a quantum computer and here there are problems which can be solved exponentially faster on a quantum computer.
Grover (1997) shows that one can find an item in one step on a quantum computer, provided that the query is sufficiently complicated, but i don't think that this theoretical result would help Paul, since we wouldn't know how to frame the query.
I'll turn to Phil's remarks. He says "Why does the quantum computer do new things? Why is complexity theory such a poor quide to the real world of problems?"
I infer from the juxtaposition of these two sentences that Phil believes that computational complexity theory is incorrect for quantum computation. I surmise that Phil is thinking of complexity theory for a classical computer. But complexity theory always depends on the model of computation which states what operations are permitted and how much they cost. Think of it as the rules of the game. The model of computation for a quantum computer is ofcourse different than for a classical computer. Thus Phil's two sentences form a non sequitor.
In his comments on my book The End of Time and my suggestion
that time does not exist, I feel that Paul Davies does not really confront
the points I am making, but instead demolishes a straw man, justifying
thereby the conclusion: "To say that it [time] doesn't exist at all
is nonsensical." I welcome the invitation to respond.
As Copernicus and Galileo showed, the senses proclaim that the earth rests and the epicycles run, but inferences must be drawn with care. To quote Copernicus, one "should not attribute to the heavens what is in the observer". All the revolutions in physics, starting with terrestrial mobility, have shown that well-supported first inferences can be wrong. Stand back from the hurly-burly of the jet-setting world. Time could go the way of the epicycles.
The universe exhibits extraordinary order (very low entropy), one consequence of which is our sense of time. All statistical arguments based on current dynamics indicate that our state is exceptional. In the standard account, it makes possible, among much else, the formation of natural records like fossils, our memories and, above all, brain function. I argue that this special state could be misleading us about time as much as the epicycles misled Ptolemy. However, I am not arguing that mental flux is the sole reason we believe in time.
There are three sources of information about time: 1) mental flux; 2) records (both natural and man-made) redolent of a lawful process in time; 3) the structure of our best dynamical theories: general relativity and quantum mechanics. What does general relativity, which has a far more subtle treatment of time than quantum mechanics, tell us? Here we must consider its orgin and subsequent elaboration.
It is usually said that general relativity was created almost in its entirety by Einstein. This is not quite true. What he did do practically single handedly was realize that his highly original heuristic ideas could be implemented through already known mathematics. The mathematics itself he took over more or less ready made. He almost 'bought it off the shelf'. Somewhat surprisingly (as the late Chandrasekhar used to emphasize), Einstein made little attempt to understand the full implications of his theory. Its deep dynamical structure only emerged after his death in the work of Dirac and Arnowitt, Deser and Misner and in a little known paper by Baierlein, Sharp and Wheeler (1962). This last is the nub of my case: It shows that general relativity is as timeless as Newtonian dynamics would be if you considered only the paths bodies follow (for example, the planetary ellipses in the solar system) and not their speeds as well. History in the Einsteinian universe is not a path traversed in time at some speed but simply a path. This is a complete elimination of time.
This may seem to conflict with statements like Paul's "We know that time is real at one level because it can be manipulated - stretched and shrunk". However, in strict fact we never see time, only the readings of clocks. There is no contradiction between the elasticity of clock readings and history as a timeless path. The clocks are part of the landscape through which the path of history passes. They are milestones.
At the practical level Paul is right. So was Ptolemy. Virtually all the movements we make are predicated on the assumption that the earth rests (pilots, astronauts, and gunners are among the few people who have to worry about the earth's rotation). The change I envision is not at the practical (classical) level at which Paul dismisses my proposal. It is not even in the notion of history as a path, which still belongs to the domain of classical physics, though it is a step. The big one comes at the quantum level.
The case is as yet far from conclusive but cannot at all be dismissed out of hand: the universe may not only be static and timeless but even without a path that one might call history. There are just Nows, individual instants like locations in a landscape. Quantum mechanics simply makes some more likely to be experienced than others. This falls out as a distinct possibility from one perfectly respectable approach to the unification of quantum mechanics with the inner timeless structure of general relativity.
In my book, I address the consequences of timelessness and make suggestions how our experience of time, motion and records can be explained. I suggest how the first two sources of temporal evidence listed above arise from timelessness. Since that is more speculative, I will not go into it here. But timelessness in a far more radical sense than Paul sketches is a real possibility.
Incidentally, since Paul was mainly commenting on the possibility of time travel (at the practical classical level), I may mention that the work of Dirac and Arnowitt, Deser, and Misner might kill it. For the dynamical Hamiltonian form in which they recast general relativity is more restrictive than its original spacetime formulation and does not allow the more bizarre solutions of Einstein's theory with closed time loops and the seemingly paradoxical possibility of time travel. Most relativists and particle physicists are committed to the spacetime picture and tend to dismiss the Hamiltonian approach as not being fundamental. But if physics in its entirety is considered the Hamiltonian approach is just as worthy a candidate for being fundamental as the spacetime approach. Indeed, it could well be that the main reason why we do not yet have a theory of quantum gravity is because theoretical physicists have not yet been able to "call" the contest between these two great principles. At the present milestone in the path of history (November 13th 2000), it is rather like the presidential election.
Responding to a different comment in the same Edge number, could Philip Anderson please give details of the book in which "it is shown that the Alexandrians had reached a level of scientific sophistication by 150 BC which was close to that of 17th century England; for instance, that much of Newton's Principia borrowed ideas from Greek texts"? I find it a somewhat surprising claim even though it is probably true that Newtonian science would have been impossible without Greek antecedents.
Last, on my recent trip to the United States I made a linguistic discovery
that might make a small contribution to eliminating trans-Atlantic misunderstandings.
It concerns the use of 'quite'. In British English, the 'quite' in "He
is quite wrong", enhances 'wrong' (as in American English). But in "Her
talk was quite good," the 'quite' implies "somewhat, to some extent"
(Concise Oxford Dictionary). According to Webster's (which I take to
reflect American usage), the weakest implication of 'quite' is "to a
considerable extent". I finally started to suspect some mismatch after
repeated emails from an American colleague in which 'quite' was used
about some ideas I had put to him in a manner that left me quite disappointed
(sometimes in the British sense, sometimes even in the American sense).
Shortly before calling on him in Maryland, it occurred to me what might
be the cause, and I questioned a passing jogger. "Oh he certainly means
'a lot'" was the reassuring response. Our meeting went quite well (American
I have great respect and affection for Paul Davies, and often find that I agree with his take on things. But in this case I find myself in disagreement. As it happens Paul and I were just at a conference in the Vatican where we discussed these questions, so this is a continuation of a friendly discussion. Paul finds himself undecided on the possibility of time travel, my view is that the evidence we have from both classical general relativity and quantum theories of gravity is that time travel is not possible in any realistic theory of space and time. The evidence for this conclusion comes independently from classical general relativity, statistical physics and quantum theories of gravity. I would like to briefly describe some of this evidence and then raise the question of why, given its evident unlikelihood, there is so much interest in the possibility of time travel.
Classical general relativity contains a theory of a dynamical system which describes how the geometry of space evolves deterministically given the state of the universe at one time. The topology of space cannot change under this deterministic evolution. A wormhole represents a change in the topology of space, and so one cannot be created in the evolution described by Einstein's equations. If there are wormholes they have been there for all time (which is very unlikely given that the universe itself has evolved from a much different earlier state) or they have been created by quantum processes.
It is true that there are closed timelike loops in certain classical solutions of Einstein's equations, and these cannot then be described in the language of a system evolving in time deterministically from initial data. But these are very special solutions and there is good evidence that the existence of closed timelike loops is an artificial consequence of the imposition of certain symmetries. Among these symmetries is one which requires that these universes never change in time. The real universe has no such symmetry. Further, the evidence is that any small deviation from the exact symmetries turn the solutions with closed time like loops into solutions without them, but with singularities. Even if such an exactly symmetric solution were to exist in nature the symmetry, and hence the existence of a closed timelike loop, would be destroyed by any attempt to send any matter or information around the loop.
One might be inspired to thinking about time travel by contemplating the arguments for the elimination of time as a fundamental concept raised by Julian Barbour. However, as I think Julian has indicated in his response to Paul's piece, that view of quantum gravity does not seem to have a place for time travel as it is rooted in a three dimensional configuration space that does not allow topology to change. Neither is there any support for time travel coming from other approaches to quantum cosmology and gravity that rely on the notion of a spacetime history. Some of these approaches (such as those that come from loop quantum gravity, which are generically called spin foam models) provide descriptions of the world on the Planck scale that are consistent with everything we know and make no artificial assumptions such as symmetry. So far as I know, time travel is impossible in all these models.
There are several reasons for the failure of these detailed studies of classical and quantum theories of gravity to find a realistic possibility for time travel. Some of these were discussed in a previous Edge piece with Stuart Kauffman ("A Possible Solution For The Problem Of Time In Quantum Cosmology"), others of which are discussed in a paper I will shortly post on the archive gr-qc, to be found at xxx.lanl.gov. I believe that a fair summary of the evidence is that the possibility of time travel rests on an incorrect interpretation of general relativity. According to this interpretation, which is sometimes called the "block universe", time is really no different from space and the whole universe in some sense exists "at once", so that a history is just a path in an already existing world. From this point of view, why can't a timelike path make a loop as easily as a spacelike loop?
The answer, I think, is that this view is derived from the study of vastly over-simplified models, rather than the real theory. When one gets to a detailed, realistic description, rather than a model, the complexity of the world (and here I am thinking of the spacetime geometry and not life....) makes it impossible for any reasonable sized part of the universe to ever return to the same state. The reason is that the list of things one would have to know to make even a small part of the universe return to a previous state are vastly (in Dan Dennet's sense) larger than could ever be could be coded into any present state of any subset of the universe. Another way to say this is that the interruption in the web of causal processes that at any moment are in progress, which would be caused by the sudden appearance of a person, or even a camera, from the future, is so vast that it is impossible to imagine engineeering the insertion of the bit of the future into the present. What would be required is vastly more complex than transplanting a brain into a new body.
My own view is that when we are done making the quantum theory of gravity the block universe idea will be as dead as Ptolemy and we will have a view of time in which the future has a very different status than the past and the notion of time travel will be logically impossible. This is described in the papers I mentioned and in a forthcoming book. But one does not need to agree with my view to come to the conclusion that time travel is very unlikely; there is sufficient evidence for this already in what we know about general relativity and quantum theory, so long as one considers their application to the real universe, rather than vastly oversimplified models.
Now, having said this, why is time travel such a popular subject, among both experts and laypeople? One possibility is that it represents another in a genre of ideas that may be called the technological transcendent fantasies. Among these are the idea of achieving immortality by "uploading our brains into computer software", which was recently discussed by Jaron Lanier in his "halfesto". These ideas have three things in common: 1) they take over the logical form of a religious promise of transcendence (as has been pointed out by Margaret Wertheim in her recent book), 2) they promise an escape from mortality and from the general situation of being an animal making a living in a biological world. 3) The more they are investigated in detail the less plausible they look.
I am not sure of the proper response to these technological transcendent fantasies, given that arguing from the evidence produced by research so far seems insufficient. One might ask, as did a certain Italian scientist, "Before you upload yourself into software (or step into your time machine) will you give me the phone number of your girlfriend?" But sitting in the Vatican discussing these things I was struck that transcendent fantasies that promise escape from our time bound mortal existences may be just the thing to fuel the work necessary to establish powerful institutions that perpetuate both the fantasies and the people who teach them. Perhaps in a thousand years priests from the Church of Time Travel and the Church of AI will meet in the Vatican with their Jesuit brothers to discuss the present status of their still unfulfilled hopes. Meanwhile the rest of us will still be transcending time and perpetuating and improving the human race the old fashion way.
I enjoyed Paul Davies' remarks on time a problem foregrounded in physics since Einstein's General Relativity, which apparently allows truly paradoxical events. His kind reference to my novel Timescape, published 20 years ago (so even its future in Cambridge, UK lies now in the past, as did my 1963 California) highlights the interplay between literary imagination and hard science in the last century. The deepening interest in other dimensions that began in the late 19th century foreshadowed the higher dimensionality of 20th C. physics.
Application of quantum mechanical ideas to the time problem led me to suggest in the concluding dramas of Timescape that time loops did not connect to the same universes, so that quite truly one could not go home again. I was aware of the quantum loop problem, and encouraged when my scheme came to be used by David Deutsch in his quantum-logical formulation. His adroit calculations showed that these ideas are compatible with quantum mechanics as we know it, but as far as I know have not engendered any further experiment or tests.
So: the difficulty is how to assign scientific value to such ideas. How can they be falsified? This problem occurs also in the meta-universe models for perpetual inflation of Linde and others. Descriptions that are perhaps more aesthetically satisfying but lead to no new experimental tests cannot advance the argument very far. I would be pleased if Paul Davies could suggest a direction we might pursue to make such ideas more satisfyingly concrete. Measurement should lead.