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FQXi FORUM
CATEGORY: Essay Contest
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TOPIC: The Garden of Forking Paths: Time as an Expanding Labyrinth by Paul Halpern
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The voting deadline has been extended to January 1, 2009.
Please vote for your favorite essays soon!
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Essay Abstract
We speculate that the arrow of time stems from the growth of an information space housing the full gamut of quantum states in the universe. As this information space dynamically expands, in conjunction with the growth of the physical universe, the network of alternatives would become increasingly complex, explaining why wave-function collapse is future-directed and why causality due to conscious decision-making is in the forward direction. In other words, an arrow of information entropy increase would set the order of cause and effect. Because the labyrinth of possibilities could grow in a deterministic fashion, yet the choices themselves could be arbitrary, our model could offer a means of reconciling mechanistic, probabilistic, and freely-chosen aspects of how natural interactions transpire. We examine how this model bears on the question of time travel, and contrast its implications with those of earlier descriptions of time as a cycle or as a steady stream.
Author Bio
Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. After receiving a PhD from Stony Brook University, he has published a number of articles in the fields of general relativity, complexity theory, cultural aspects of science, and the history of physics. The author of 11 popular science books, he has been the recipient of a Guggenheim Fellowship, a Fulbright Award, and an Athenaeum Literary Award.
Download Essay PDF File
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Hello Paul,
Thanks for the cool paper!
You write, "Classical mechanics offers a clockwork view of a steady rhythm of causes followed by effects. It is eminently deterministic and fully reversible."
Classical mechanics is not always fully reversable. Drop a coffee mug on the ground and it shatters. Although described by classical mechanics, it will never reassamble as it was, even with glue. And how about friction? Friction slows things down but doesn't generally speed them up. We teach this in classical mechanics.
You write, "Special relativity, particularly in the version framed by Hermann Minkowski, solidified the concept of time as being on par with space as members of a dimensional quartet—what became known as a spacetime manifold."
Well, "on par" is not quite "equal to," and this is the scene of the crime which has given us the huam construct of the block universe, frozen time, and implied time travel.
Be careful here, as time is very different from the spatial coordinates.
You would enjoy my essay, "In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time’s physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify. Beginning with the postulate that time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c, diverse phenomena from relativity, quantum mechanics, and statistical mechanics are accounted for. Time dilation, the equivalence of mass and energy, nonlocality, wave-particle duality, and entropy are shown to arise from a common, deeper physical reality expressed with dx4/dt=ic. This postulate and equation, from which Einstein’s relativity is derived, presents a fundamental model accounting for the emergence of time, the constant velocity of light, the fact that the maximum velocity is c, and the fact that c is independent of the velocity of the source, as photons are but matter surfing a fourth expanding dimension. In general relativity, Einstein showed that the dimensions themselves could bend, curve, and move. The present theory extends this principle, postulating that the fourth dimension is moving independently of the three spatial dimensions, distributing locality and fathering time. This physical model underlies and accounts for time in quantum mechanics, relativity, and statistical mechanics, as well as entropy, the universe’s expansion, and time’s arrows."
--http://fqxi.org/community/forum/topic/238 : Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken
If you look at Einstein's RELATIVITY,
http://www.scribd.com/doc/3409/eBook-PDF-Science-Albert-Einstein-Relativity-1
you will see
x1=x
x2=y
x3=z
x4=ict
Ergo x4 = ict, naturally implying MDT's postulate and equation reflecting a hitherto unsung universal invariant: dx4/dt = ic--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c.
How else would one weave change into the fundamental fabric of spacetime (where it has been longing to be, as without change there is no measurement, and thus no physics), unfreezing time and liberating us from the block universe and granting us free will, while also accounting for quantum nonlocality and entanglement, while providing a *physical* mechanism underlying relativity, entropy, and time and all its arrows and assymetries, thusly unifying physical reality with a simple postulate and equation?
Such is the nature of that more heroic physics.
You write, "general relativity implies a far more rigid
determinism by freezing all of history into a solid immutable block. The reason is that the division of spacetime into space and time is arbitrary."
Acutally, time is not the fourth dimension, but rather a parameter that emerges because the fourth dimension is expanding relative to the three spatial dimensions.
The attached paper shows how MDT, while embracing the hitherto unsung universal invariant of a fourth dimension expanding at c, accounts for the gravitational slowing of light and time, as well as the gravitational redshift.
You write, "If one could somehow step outside of the
spacetime manifold, all moments would be as accessible as all locations. In its purest form this “block universe idea” offers the startling conclusion that travel through time ought to be as simple as traveling along any spatial direction, and that the passage of time is an illusion. Such implications clash with our intuition, placing us in the situation of either denying the framework of Einstein’s elegant theory, slicing in a manner it to reflect our own experience of time (such as in the ADM formalism of Arnowitt, Deser and Misner [3]), or proclaiming that our feeling of moments passing is fallacious."
But there is another way on this brand new day! It seems you did not yet read my paper before writing yours.
MDT liberates us from the block universe, while retaining all of relativity, and providing a *physical* mechanism for change! Change has at long last been woven into the fundamental fabric of spacetime with dx4/dt=ic, and too, the very same physical model accounts for nonlocality, entropy, quantum entanglement, relativity, and time and all its arrows and assymetries across all realms.
You write, "Yet another directional arrow of time pertains to quantum measurement. According to the Copenhagen interpretation of quantum mechanics, whenever an observer measures a particle’s property, its wave function collapses into one of a spectrum of eigenstates 3 corresponding to a particular eigenvalue pertaining to that property. For example, measuring an electron’s spin forces it into one of its two spin states, each matched up with a different spin eigenvalue. Such wave function collapse is generally irreversible; that is, one cannot directly “undo” the measurement to restore a mixed spin state."
In the simplest case of the photon, the act of measurement removes Wheeler's momenergy from the fourth expanding dimension, which represents an expanding sphere of nonlocality, and it localizes the photon in the three spatial dimensions, on a photographic plate.
By going back to Einstein's 1912 paper, MDT has saved us from the perpetual-motion and everlasting reign of anthropic multiverse/parallel universe/anti-theories/information spaces, whose theorists exist because if they didn't exist, they wouldn't exist, and they get tenure for this logic, because if they didn't, they wouldn't. I think that is how it goes.
You write, "If each of these paths represents a parallel universe, then there is no contradiction with determinism—because all possibilities that can occur will occur."
There is no evidence for a parallel universe, let alone an infinte number of such universes; while there is plenty evidence for MDT--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c.
You write, "Past-directed time travel would be permitted, consistent with general relativistic anomalies such as wormholes, in so far as the information space in the past possessed available “slots’ to accommodate the material traveling back in time. As a result, those attempting pastdirected time travel would be forced into alternative timelines rather than those already occupied by actual events. Effectively, therefore, they would be unable to interfere with existing structures (such as anything familiar), making it a rather meaningless excursion."
So the block universe is real, you say, and we can travel back in time, but we can't travel back in time where things actually happened.
I hope you enjoy Moving Dimensions Theory, which stays away from "rather meaningless excursions," by proposing a hitherto unsung universal invariant--the fourth dimension is expanding relative to the three spatial dimensions at the rate of c. All of relativity is derived from this, while a *physical* model is given for time and its arrows across all realms.
Best,
Dr. E (The Real McCoy)
P.S. You write, "Although our model is hypothetical, some of its elements could conceivably emerge through a fuller
understanding of quantum gravity."
I think it is funny how every modern physicist concludes with:
1) our theory reagarding time is hypothetical and young.
2) as soon as they figure quantum gravity out, our theory will be proven to be true.
But there is no need to quantize gravity, as space is continuous, and all quantum action derives from the Planckian wavelength of the fourth expanding dimension, which sets both h and c. Please see the attached paper. below.
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7_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf |
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Professor Halpern,
That is a well and clearly stated history of the understanding of time and how it naturally leads into your view of time as branching out into ever expanding possibilities. It also offers me the opportunity to point out why this concept of time has diverged from the real world.
This sea of energy that is the basis of reality is constantly changing form. So while this energy goes from one form to the next, the particular forms go from being in the future to being in the past. Tomorrow becomes yesterday.
The sun moves east to west, but the reality is the earth rotating west to east.
There are natives of South America who view the past as in from of the observer, with the future behind them. That is because their point of reference, the hand of their clock, is the energy, which first causes the event, then presents it to the observer and then travels past the observer. As opposed to our more anthropological assumption that the observer is traveling from past to future, so the past is behind and the future is in front. Put this in the context of Schrodinger's Cat; The arrow goes from the quantum event to the cat, to the door of the box, to the observer and beyond. Makes more sense than the observer moving forward into the alternative possibilities?
So, yes, the series of events do branch out in the future, but we, existing as a momentary state in the sea of energy, are not traveling toward the future. It is coming to us, like a wave crashing on the beach. Even our individual lives are units of time which start in the future, are carried along for awhile and are deposited in the past, while the larger organism of life moves onto the next generation. To the hands of the clock, it's the face going counterclockwise.
Energy and information are like two sides of the same coin. Energy manifests some amount of information, by its existence, while information requires energy to exist, yet they travel in opposing directions of time.
What this means is that time is a consequence of motion, like temperature, rather than the basis for it, like the vacuum of space. Since temperature is an average of motion, it can be stable at a point, but as a unit of motion, time cannot be described as a dimensionless point, as that would be the cessation of motion, like a temperature of absolute zero. Time is variable because the rate of change is variable. A hotter candle burns faster. Atomic activity in a vacuum is faster than such activity in a gravity field.
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Dear Dr. E,
Thanks for your remarks and a presentation of your ideas. On the question of classical mechanics and reversibility I was referring to the strict application of Newton's laws of motion without taking the dissipation of energy into account.
Dear John,
Thanks for sharing your insights. In speaking of the human sense of motion toward the future that is from the perspective of conscious perception rather than from a retrospective view. However, you are correct that, in hindsight, what was once the present recedes into the past.
Much appreciation for both of your comments!
Regards,
Paul
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Professor Halpern,
Thank you for taking the time to think through and comment favorably on my observation, even though it is at odds with your own perspective. It's been my experience, in discussing science, that others are far more willing to point out logical flaws than acknowledge what does seem reasonable. Given the objectivity, cooperation and mutual benefit to which science aspires, I find this somewhat surprising. Though as a student of history, politics, nature, human and otherwise, as well, I'm not entirely surprised.
We live in interesting times and this has been an interesting discussion about time.
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John,
It is my pleasure. I think an open-minded approach toward philosophical issues offers the surest path toward a deeper understanding.
Best wishes,
Paul
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Paul,
Agreed. We have to be objective about ourselves before we can really be objective about anything else.
Although our knowledge will always be finite, while our ignorance will always be infinite. Just not absolute.
Regards,
John
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Dear Paul,
What an intriguing idea. One cannot help ruminate on it, especially the deterministic vs. undetermined aspect. Your essay is very well written too. You managed to cover a remarkable amount of ground, while I thought your analogies were great as well.
Best of luck
Peter
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Dear Peter,
Thanks for your kind remarks. I very much appreciate your insights.
Best wishes,
Paul
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Paul, thanks for a thoroughly delightful tour of the labyrinth of time. Borges is also one of my favorites, and I would choose "The Library of Babel" for my metaphor.
Borges writes, in describing the universe as "...an indefinite and perhaps infinite number of hexagonal galleries" that "The Library is a sphere whose exact center is any one of its hexagons and whose circumference is inaccessible."
Showing that his library is a perfectly physical possibility with objectively measurable results, Borges adds, "(The mystics claim that their ecstasy reveals to them a circular chamber containing a great circular book, whose spine is continuous and which follows the complete circle of the walls; but their testimony is suspect; their words, obscure. This cyclical book is God.)"
My ICCS 2007 paper (attached) agrees point for point with your conjecture of time as information.
All best,
Tom
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ICCS2007.pdf |
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Dear Tom,
Thanks for your detailed comments. Glad you enjoyed my paper. Yes, I agree that "The Library of Babel" offers an excellent metaphor for the labyrinth of time. Looking forward to reading your article.
Best wishes,
Paul
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Dear Prof. Halpern,
Very captivating history of the various modes of time proposed during the development of science. I especially like your idea of time as an expanding labyrinth, in an information space or multiverse.
Best wishes,
Cristi Stoica
“Flowing with a Frozen River”,
http://fqxi.org/community/forum/topic/322
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Dear Professor Halpern,
Family trees bifurcate backwards. From your essay I conclude you a an expert in history of science. I largely share your points of view. May I ask you for comments on what you might not accept in my essay?
"Let's benefit from special mathematics for elapsed time"?
Sincerely,
Eckard Blumschein
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Dear Cristi,
Thanks so much for your kind comments about my essay!
Dear Eckard,
I appreciate your remarks. Yes I am interested in the history of science.
Best wishes,
Paul
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Dear Professor Halpern,
I found your essay highly readable and containing much food for thought as well as interesting historical tidbits. As I read these essays, I always try to think in the back of mind how one might be able to test the many new ideas they offer.
In the spirit of this thought, let me ask you the following question:
Suppose we take two boxes of equal volume and try to isolate what happens inside from outside as much as possible, so that the boxes can constitute closed systems. We fill the first box with a certain quantity of one kind of unstable particle, and the second box with exactly twice as many of the same kind.
Ordinarily, we would expect that the half-life of the particles is the same in both boxes.
If time is really to be modeled as an expanding labyrinth of diverging word-lines, should we not expect the half-life of the particles in the second box to be shorter, or at least different? The rationale is that since there are more unstable particles in the second isolated system of equal volume, there are more possibilities, therefore the labyrinth is more complicated, the information space is larger. If time is really a parameterization of these quantities, then it would appear to me that it should be different in the two systems, and the half-life is the most convenient measure I can think of to quantify this difference.
I tried to identify as many assumptions built into my thought experiment as I could, for if any one of them is incorrect, then it may render my conclusion invalid.
I assumed
1. It is possible to realistically have such isolated systems
2. the particles do not interact with each other (or at least, the interactions are independent of particle density)
3. Any gravitational effects are negligible
4. The process of putting the particles into the box and measuring the number of remaining particles after some time in each case has no effect on the outcome of the experiment.
Also, you write "a profound mystery about time is why do we experience its progression at a certain speed". I find this statement a little surprising because the special theory of relativity seems to offer a clear explanation for this insofar as we take any kind of periodic change in our environment (and perhaps even internal periodic changes, such as the pulse) as a standard against which to calibrate our sensory experience of time. I am, of course, referring to the Lorentz Factor (The issue of time's "progression at a certain speed" is of special interest to me because it is central to the main hypothesis in my paper).
Armin
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Dear Armin,
Thanks for your comments and interesting thought-experiment.
The expansion of the labyrinth of possibilities (growth of the information space) would be a universal effect, not a local effect. Therefore placing more decaying particles in a region would not affect the rate of temporal progression (as measured by decay rates) in that domain.
You raise an interesting point about the perception of time being connected to "periodic changes" in our enviroment. However, even in the absence of external indications of change (such as someone confined to a windowless room) we still sense that time is moving forward.
Best regards,
Paul
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