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Abdun: on 7/25/09 at 11:24am UTC, wrote TIME EXPLAINED To understand time, it is...

Paul Halpern: on 12/10/08 at 14:22pm UTC, wrote Dear Armin, Thanks for your comments and interesting thought-experiment. ...

Armin Nikkhah Shirazi: on 12/10/08 at 0:19am UTC, wrote Dear Professor Halpern, I found your essay highly readable and containing...

Paul Halpern: on 12/9/08 at 2:41am UTC, wrote Dear Cristi, Thanks so much for your kind comments about my essay! Dear...

Eckard Blumschein: on 12/8/08 at 11:29am UTC, wrote Dear Professor Halpern, Family trees bifurcate backwards. From your essay...

Cristi Stoica: on 12/8/08 at 10:50am UTC, wrote Dear Prof. Halpern, Very captivating history of the various modes of time...

Anonymous: on 11/29/08 at 16:05pm UTC, wrote Dear Tom, Thanks for your detailed comments. Glad you enjoyed my paper. ...

T H Ray: on 11/29/08 at 13:33pm UTC, wrote Paul, thanks for a thoroughly delightful tour of the labyrinth of time. ...


Georgina Woodward: "On obtaining the singular, relative, measurement product it replaces the..." in The Present State of...

Steve Dufourny: "The paper of Wilczek of course is very relevant considering the idea about..." in The Noise of Gravitons

Georgina Woodward: "Material neuronal structure in which memory is encoded, physical records..." in Quantum Physics and the...

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The Entropic Price of Building the Perfect Clock: Q&A with Natalia Ares
Experiments investigating the thermodynamics of clocks can teach us about the origin of time's arrow.

Schrödinger’s A.I. Could Test the Foundations of Reality
Physicists lay out blueprints for running a 'Wigner's Friend' experiment using an artificial intelligence, built on a quantum computer, as an 'observer.'

Expanding the Mind (Literally): Q&A with Karim Jerbi and Jordan O'Byrne
Using a brain-computer interface to create a consciousness 'add-on' to help test Integrated Information Theory.

Quanthoven's Fifth
A quantum computer composes chart-topping music, programmed by physicists striving to understand consciousness.

The Math of Consciousness: Q&A with Kobi Kremnitzer
A meditating mathematician is developing a theory of conscious experience to help understand the boundary between the quantum and classical world.

February 5, 2023

CATEGORY: The Nature of Time Essay Contest (2008) [back]
TOPIC: The Garden of Forking Paths: Time as an Expanding Labyrinth by Paul Halpern [refresh]
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Paul Halpern wrote on Nov. 25, 2008 @ 10:00 GMT
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.

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Dr. E (The Real McCoy) wrote on Nov. 25, 2008 @ 16:36 GMT
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,...

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John Merryman wrote on Nov. 25, 2008 @ 18:19 GMT
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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Paul Halpern wrote on Nov. 25, 2008 @ 19:32 GMT
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!



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John Merryman wrote on Nov. 25, 2008 @ 21:25 GMT
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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Paul Halpern wrote on Nov. 25, 2008 @ 22:55 GMT

It is my pleasure. I think an open-minded approach toward philosophical issues offers the surest path toward a deeper understanding.

Best wishes,


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John Merryman wrote on Nov. 26, 2008 @ 02:03 GMT

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.



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Peter Lynds wrote on Nov. 28, 2008 @ 22:24 GMT
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


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Paul Halpern wrote on Nov. 29, 2008 @ 04:01 GMT
Dear Peter,

Thanks for your kind remarks. I very much appreciate your insights.

Best wishes,


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T H Ray wrote on Nov. 29, 2008 @ 13:33 GMT
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 " 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,


attachments: ICCS2007.pdf

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Anonymous wrote on Nov. 29, 2008 @ 16:05 GMT
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,


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Cristi Stoica wrote on Dec. 8, 2008 @ 10:50 GMT
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”,

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Eckard Blumschein wrote on Dec. 8, 2008 @ 11:29 GMT
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"?


Eckard Blumschein

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Paul Halpern wrote on Dec. 9, 2008 @ 02:41 GMT
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,


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Armin Nikkhah Shirazi wrote on Dec. 10, 2008 @ 00:19 GMT
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).


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Paul Halpern wrote on Dec. 10, 2008 @ 14:22 GMT
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,


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Abdun wrote on Jul. 25, 2009 @ 11:24 GMT

To understand time, it is necessary to understand its components.

Time is energy (virtual), with the same energy density as solid mass. Time is a function of energy, and so identical to energy.Energy in three-dimensional space is understood as mass, energy in the fourth Minkowski axis (the Minkowski axis is a limited mathematical...

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