Incompatible Arrows, III: Lewis Carroll

By Sean Carroll | April 2, 2008 11:15 pm

As far as I know (and I’d love to hear otherwise), one of the earliest examples of literary characters with incompatible arrows of time (as opposed to a simple reversed-chronology narrative) is from Lewis Carroll (no relation), in Through the Looking Glass. When Alice first meets the White Queen, she learns that the Queen experiences time backwards.

`I don’t understand you,’ said Alice. `It’s dreadfully confusing!’

`That’s the effect of living backwards,’ the Queen said kindly:

`it always makes one a little giddy at first –

`Living backwards!’ Alice repeated in great astonishment. `I never heard of such a thing!’

` — but there’s one great advantage in it, that one’s memory works both ways.’

`I’m sure MINE only works one way.’ Alice remarked. `I can’t remember things before they happen.’

`It’s a poor sort of memory that only works backwards,’ the Queen remarked.

I agree, and I wish someone would do something about that. Carroll doesn’t emphasize this device much in the book, but does offer one classic illustration of the phenomenon.

Alice was just beginning to say `There’s a mistake somewhere-,’ when the Queen began screaming so loud that she had to leave the sentence unfinished. `Oh, oh, oh!’ shouted the Queen, shaking her hand about as if she wanted to shake it off. `My finger’s bleeding! Oh, oh, oh, oh!’

Her screams were so exactly like the whistle of a steam-engine, that Alice had to hold both her hands over her ears.

`What IS the matter?’ she said, as soon as there was a chance of making herself heard. `Have you pricked your finger?’

`I haven’t pricked it YET,’ the Queen said, `but I soon shall – - oh, oh, oh!’

`When do you expect to do it?’ Alice asked, feeling very much inclined to laugh.

`When I fasten my shawl again,’ the poor Queen groaned out: `the brooch will come undone directly. Oh, oh!’ As she said the words the brooch flew open, and the Queen clutched wildly at it, and tried to clasp it again.

`Take care!’ cried Alice. `You’re holding it all crooked!’ And she caught at the brooch; but it was too late: the pin had slipped, and the Queen had pricked her finger.

`That accounts for the bleeding, you see,’ she said to Alice with a smile. ‘Now you understand the way things happen here.’

`But why don’t you scream now?’ Alice asked, holding her hands ready to put over her ears again.

`Why, I’ve done all the screaming already,’ said the Queen. `What would be the good of having it all over again?’

Both Alice’s Adventures in Wonderland and Through the Looking Glass rely on nonsense to tell a gripping story. Reversing an individual arrow of time is sufficiently nonsensical to qualify as automatically amusing, but also provocative. Why does everyone remember the same direction of time, anyway? (Actually that one’s not hard to answer. If two systems with incompatible arrows were to noticeably interact, the one with more degrees of freedom would swamp the other one and quickly “correct” its arrow of time. No being that “remembered the future” would survive very long in the real world.)

  • Sam Cox

    Enantiomorphy has its applications in biology, physics and geometry. I think it important to remember that science is observational and descriptive. We observe the universe a certain way from our frame of reference. It makes sense that way, and following empirically, we deduce (and find testable and reducable to a technology) the laws of physics and their mathematical framework…which by the way and by definition are logically consistent.

    When we assume that the universe everywhere must be as we observe it, we are making a very large assumption indeed! L. Carroll was a pre-Einsteinian mathmetician, as well as a teacher and story-teller. He used his story telling ability, not only to entertain children, but to challenge the basis of our assumed ideas about the way the universe is…or more profoundly, seems to us.

    The reason Carroll challenges our assumtions is his knowledge of the reality of dualism in the mathematical framework by which we define (and precisely measure) our world and derive our technology.

    Might not the universe be more than what we observe? The math of SR/GR/QM- even the basic “mirror” geometry of Schwarzschild certainly imply that the universe may be very different from the way we observe it…the math leads us down a winding, counterintuitive and seemingly bizarre path which leads to Schwarzschild, Dirac, Bohr-and Einstein.

    That same path leads to determinism in a universe which seems anything BUT deterministic, and a universe with the foundational quality of a quite rigid…quasi-static, “engineering” stability.

    A very interesting and challenging post…

  • Super Toll

    Isn’t the wizard Marlin who was the advisor of king Arthur an earlier example of someone living backwards in time, or do I get the literature history wrong… ?

  • Steve Denham

    I have the following quote on my bulletin board: “The best book on programming for the layman is “Alice in Wonderland”, but that’s because it’s the best book on anything for the layman.” I don’t know who to attribute it to (probably some Berkeley-based Unix wizard), but the Alice series is remarkably applicable to so many fields that I have to believe there is some truth to the quote.

  • Scott H.

    Isn’t the wizard Marlin who was the advisor of king Arthur an earlier example of someone living backwards in time, or do I get the literature history wrong… ?

    That was apparently an innovation of T.H. White in The Once and Future King (1958).

  • Scott H.

    Whoops, 1958 was just the date in which The Once and Future King was completed. Big chunks of it (including some of the Merlin stuff) were published before that. (Patchy memory plus Wikipedia = semblance of knowledge!)

    Anyhow, Lewis Carroll predates it by a few decades.

  • Llorrac

    “Lewis Carroll predates it ”

    So Carroll was a predator. I knew it!

  • roland

    > If two systems with incompatible arrows were to interact, the one with more degrees of freedom would swamp the other one (..)

    Is that physics or nonsense?
    And if the queen has both ways memory, wouldn’t she have “more” degrees of freedom.

  • Reginald Selkirk

    Why does everyone remember the same direction of time, anyway?

    A biologist suggests: Maybe because our thoughts and memories are part of those physical systems that are apparently subject to the arrow of time? In all of the examples you have described, extra-mental events run backwards in time, but the character was somehow able to perceive and think about these in a forward manner. What would experiencing a thought backwards even feel like?

  • Joshua Spitz

    Check out Faulkner’s “Sound and the Fury”. The first part is told from the point of view of an autistic (or retarded) man-child who has no concept of time–past or present. The section of the book is one of the hardest in all of literature.

  • Rat Poison

    Mind/brain duality versus e.g. emergentism is interesting but doesn’t seem to have much predictive power in cosmology.

    The three Incompatible Arrows posts all seem to revolve around the question of whether an actor/observer relationship is even possible between entities that have a very different view of the pastness and futureness of other events they each observe at some point.

    Let’s clump together particles into a pair of reasoning cosmologists, one of which observes evidence of a universe expanding from a surface of last scattering, and the other of which sees a contracting universe heading towards a hot dense coupling phase. The individual particles “travelling along together” with each cosmologist share compatible views of pastness/futureness, in that they receive signals from their past and transmit signals into their future. The cosmologists perform their own physical experiments locally, obtaining results consistent with their best theories about how physics operate.

    Are the theories held by each cosmologist comparable?

    Can we, sharing the view of the first scientist, make predictions about what the “backwards” (to us) scientist’s theories are like?

    If there were such a scientist, could we interact at all? Could we communicate? What would be the effects of the communication from our perspective, and from the other perspective?

    Or, is any interaction with any “backwards-moving” entity, whether reasoning scientist or particle, “forbidden”?

    The fictional treatments in these three posts are interesting because the communication is all consistent with one character’s past->future direction, even if that character’s counterparties occasionally or usually have a very different view of pastness/futureness.

    Alice moves like us, the Queen communicates with Alice in Alice-friendly forward-moving expressions. Billy moves like us except when he jumps around, but everyone he interacts with moves like us (and Billy) between jumps. In fictional works that sound like Amis’s (which I haven’t read) most backwards-moving characters tend to communicate forwardly from time to time, or have forward-moving “vignettes” from the persepective of a forward-moving character. Red Dwarf’s Backwards is constructed this way.

    Unfortunately the people in the backwards/forwards interactions in fictional treatments don’t seem to behave realistically as collections of unthinking particles/fields/whatevers. How does the weak nuclear force work in the backwards-moving people’s bodies, for example? Do they experience spontaneous nuclear integrations?

    One point I’m wondering about is how a writer could take on a reasonably hard science fiction treatment of a backwards-moving cosmologist. Maybe a conventional Earth cosmologist who “switches” the pastness/futureness of some reasonably isolated environment (like a space ship) she’s embedded in? Does the “switched” scientist still observe Galilean invariance? (“Yes” would be useful for plot purposes, followed by “what’s the view out the window?”, but “no” is probably the more interesting answer for a cosmologist thinking about T-symmetry. :-) )

  • CWhite

    I love this site!

    Often I feel too inadequate to post.

    But, this subject fascinates me. I have read “Wu Li Masters” and “A Brief History of Time” a number of times.

    When this “time” question comes up, I never fail to try and imagine an environment in which time and the other three dimensions don’t exist (pre-Big-Bang).

    The fact that my brain can even conceive of a realm that would exclude the existence of the very brain imagining it is endlessly fascinating.

    I must wonder how much we DON’T know.

  • John R Ramsden

    I think “Tristram Shandy”, an 18th century novel by Laurence Sterne, involves some time incompatibility, for comical effect, between author and reader.

    There may be some other examples at

  • f15mos

    Check out Strugatsky brothers classic “Monday Begins on Saturday”. There is a character that is in fact two persons – one living along the normal time arrow, the other in reverse. The catch was that the skip back in time happened only at midnight, during the day the time was going in the same direction (so the person look normal to normal people)

  • blanton

    Dear Sean, These are amusing posts, but I am worried
    about what precisely you mean by the last comment:
    presumably it is not a statement about a consequence
    of the laws of physics, but instead a philosophical inference?
    I don’t mean that to be a derogatory term, just one
    that distinguishes it from a theoretical inference
    from physical law, which you appeared to strongly imply
    it was — was that your intent?

  • Sam Cox

    RS said,

    “Why does everyone remember the same direction of time, anyway?

    A biologist suggests: Maybe because our thoughts and memories are part of those physical systems that are apparently subject to the arrow of time? In all of the examples you have described, extra-mental events run backwards in time, but the character was somehow able to perceive and think about these in a forward manner. What would experiencing a thought backwards even feel like?”

    This is very thoughtful reasoning. Even in a dual 7D and up quasi-static model of the universe fully incorporating the duality of SR/GR/QM and Schwarzschild, it could well be that there is no actua experience of the part of the universe which exists in decreasing thermal and increasing informational entropy (the “younging” “hemisphere”). In such a universe, though foundationally dual, our conscious existence would eternally remain on the “same side” IE, we would “die” (actually only others are observed to experience death, not ourselves) and then gradually awaken to our own childhood, increase in awareness again, die and repeat the process eternally.

    The caveat is the fact that photons do work…lower informational entropy- and likely spin in a certain direction in the 4D particulate cross-section (Schwarzschild “hemisphere”) which we observe. Anything which collectively (and individually) spins in a certain direction relative to our reality could very well be observed to spin in the opposite direction from other, equally particulate coordinates in the system. If our universe exists this way, there might well be an “Allice in Wonderland” 4D cross-section of the universe where thermal entropy would be observed to decrease and informational entropy would increase.

    In such a universe, our consciousness would not cease or radically change at death, but would rather “shift”…we would become in some way which would take some “getting used to”, aware of another side, where the physics and way of life would be different. We would become more childlike and then ultimately and eternally become re-aware of our childhood and maturing experience in the reality we all “now” inhabit.

    I think it appropriate that we not only remember Lewis Carroll, but also the late Arthur Clarke and Carl Sagan, all of whom, in very provocative ways, popularized some of the implications of the standard cosmological models of our era.

  • Sean

    blanton, it is a consequence of the laws of physics. We are only able to remember the past because the entropy was lower back then. When two macroscopic systems interact, even if the smaller one has delicately-tuned correlations in its constituents so that its entropy decreases toward the future (as defined by the larger system), those correlations would rapidly be destroyed by the interactions with the larger system. You can’t maintain interacting systems with opposed arrows of time.

  • John Merryman

    Maybe the problems encountered in these narrative explorations of temporal disconnect might lead to a reconsideration of time as a dimensional phenomena that enables traveling about as if it were a form of space. That the rate of activity is influenced by physical context makes devices use to measure this rate of activity(clocks) equally dependent doesn’t mean the rate of activity is subject to whim. The amounts of energy and dislocation required to effect even the most minimal change is large. Why is it that some plot devices and flights of fancy, such as time travel, or reversed time, are more credible than others, such as omnipotent deities, resurrection or talking, burning bushes? Maybe Jesus hit a time loop.

  • Celestial Toymaker

    “No being that remembered the future would survive very long in the real world”

    No. But how about a world where all physical processes operated in reverse?
    Physical systems now absorb energy and become more organised with time, prexistent biological forms devolve.
    The “past” of such an organism would be our “future”.
    Would an intelligent being, somewhere in the “anthropic” phase of such a universe, actually be able to distinguish one arrow of time from its reverse?
    Think out the implications consistently all the way through and I think the answer is no.

  • blanton

    Sean, I guess what I am wondering is whether either of your
    statements (“We are only able to remember the past because
    the entropy was lower back then”, or “You can’t maintain interacting
    systems with opposed arrows of time”) are summaries of results
    from the vetted physics literature. I’d be very surprised if there is
    a clean experimental test of either statement; I’d be less surprised
    if there was a theoretical calculation supporting the latter one.
    I probably *believe* either statement as reasonable, but that’s
    different than them being established consequences of the laws of
    physics. I admit I’ve never searched the literature for this sort
    of thing, so I stand ready to be corrected with the appropriate

  • MedallionOfFerret

    Enough of these metaphysical speculations. Here’s all ye on earth know, or need to know, about time:

  • Brody Facoum

    (19) blanton…

    His wording was a pretty naked use of the anthropic principle, but in essence his argument is based on using measurements of entropy as a privileged clock since it is always increasing at the largest scales.

    This is reasonable when one considers a phase in which the universe was a hot, dense, nearly ideal gas, as WMAP/COBE/BOOMERANG data have been suggesting for some time, which has more recently been expanding to fill the growing “container” provided by the metric expansion of spacetime, cooling on the largest scales as it grows.

    This is in line with local explorations of the second law of thermodynamics. Shown a film clip of gas in a box with no indication of whether it was showing the explosion of gas from a compact form, or the condensation of a large volume of gas into a small pellet. Normally we would choose as the initial conditions the most compact, least uniform end of the clip, and as the final conditions the least compact, most thermally equilibriated filling of the box.

    We run into trouble if we end up with a film clip where there is no obvious change in entropy when running the clip in either direction. We also run into problems if the entropy at both ends of the clip is substantially similar.

    Observations preclude a steady state universe, so the first film-clip trouble isn’t applicable cosmologically. There is compelling evidence against a future “big crunch”, which eliminates the second trouble too.

    Thus we have some conditions at or very near the Big Bang which lead to a Universe whose overall geometry leads to a clearly defined directionality in our entropy clock. Less entropy in one “direction” (pastwards), more in the other direction (futurewards).

    That we “remember” anything at all is also due to the early conditions of the Universe in that the formation of large structures — galaxies, stars, our planet, our brains — fell out of the distribution of energies and the behaviour of spacetime at or very soon after the bang.

    Thinking about why our memories seem well aligned with an entropy-based Universal clock is interesting, but to me not obviously germane to other distant not-human-memory-equipped users of the same idea of clocking things relative to the overall entropy of the observable universe, with futureward being the direction of increasing entropy.

    Most of this arrow of time stuff is an attempt to reason about the initial conditions of the observable universe, and especially about the amazing orderliness suggested to us by observation of the CMBR and also of increasingly ancient astronomical structures.

    As to theoretical calculations… Cosmic Inflation is consistent with very low entropy initial conditions. That’s the first argument in a nutshell, just reframed without the anthropic reasoning about memory. “You can’t maintain interacting systems with opposed arrows of time” seems to fit with various ideas involving destructive interference wiping out the initial quantum fluctuations that lead to a change in entropy in the first place (whichever direction entropy moves in). Sean’s “the one with more degrees of freedom would swamp the other one and quickly “correct” its arrow of time” is a very terse way of saying that there are some events that are possible (and demonstrable) in a less-entropy->more-entropy direction that do not seem possible in the reverse direction. The most physical of these involve the weak nuclear force (KTeV – BaBar – Belle explorations of CP violation).

    This is where we could quickly go into ratholes looking for what’s eating gaps in the standard model, so I actually appreciate the terseness somewhat. :-)

  • ike

    Celestial toymaker: The principle of microscopic reversability does state that at a certain level, one cannot distinguish the arrow of time, for example:

    “Since evaporation and condensation are in general thermodynamically
    reversible phenomena, the mechanism of evaporation must be the exact reverse
    of that of condensation, even down to the smallest detail.”

    The simple test for such phenomenon is the movie test: if you can’t tell if the movie is going in reverse or not, you might be looking at a manifestation of the principle of microscopic reversibility.

    This was blogged about here, and I’ll quote them quoting C.V., to clarify the issue raised above:

    “The observed macroscopic irreversibility is not a consequence of the fundamental laws of physics, it’s a consequence of the particular configuration in which the universe finds itself. In particular, the unusual low-entropy conditions in the very early universe, near the Big Bang. Understanding the arrow of time is a matter of understanding the origin of the universe.”

    As far as Lewis Carroll goes, perhaps he was influenced by the thinking of the day, which was spelled out by Laplace:

    “We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”

    So, in that mentality, people would be able to “remember backwards” if they had access to the “clockmaker’s blueprint”. We know now that such deterministic visions are a myth, and that even if one had such complete knowledge, one’s ability to predict the future would be very limited, due to chaos and Q.M.

    However, one might be able to “remember backwards” for very short periods of time in one’s local environment. If you drop a glass and see it heading for the floor, you can anticipate it smashing to bits. Human response times, from sensory stimulation to registering and responding in the higher cortex, is about half a second – so that’s probably about the limit within which we will ever be able to remember (process mentally) backwards (or is it forwards? so confusing…).

    If we were to remember backwards for longer than that, we would probably have all been eaten by saber-tooth tigers long ago.

  • John Ramsden

    LLorac (#6) wrote:
    > So Carroll was a predator. I knew it!

    Tongue in cheek in the circs perhaps, but most people take it for granted that Lewis Carroll may have been a bit of a kiddie fiddler on the quiet, in thought if not in deed.

    However, a recent Dodgson biography (a review of which I read but not the actual work) apparently makes a good case that he befriended young girls mostly as a pretext to get to “know” their mothers more intimately .. !

    But after his death his niece, in characteristic Victorian fashion, tore from his voluminous diaries every page which might have shed light on his true predilections. So I guess we’ll never know for sure.

  • Arun M Thalapillil

    “If two systems with incompatible arrows were to noticeably interact, the one with more degrees of freedom would swamp the other one and quickly “correct” its arrow of time. No being that “remembered the future” would survive very long in the real world.” :

    Interesting…is there an quick way to see this ? Can this statement be made more precise starting from the H-theorem or something ?

  • Sean

    I think that these statements wouldn’t appear in published papers, only because they are too straightforward, once you define your terms. The bit about memory is a piece of conventional wisdom, although you do have to be careful to define what you mean by “form a memory” in purely mechanical terms. I don’t remember seeing it discussed in a physics paper, but I’ll take a look.

    The fact that two systems with oppositely-pointed arrows of time would interfere with each other follows from basic stat mech. If you have a system whose “initial” conditions are chosen so that it has a large (coarse-grained) entropy, but if you evolve it forward the entropy decreases, that means you have delicately tuned all of the momenta so that the system “aims” at a much tinier region of phase space, one with lower entropy. If you perturb it by just a little bit, you will generically deflect it away from that path, and the entropy won’t go down by as much; the bigger the perturbation, the less it will go down.

    None of this has anything to do either with the anthropic principle, nor with CP violation!

  • John Merryman


    This is in line with local explorations of the second law of thermodynamics. Shown a film clip of gas in a box with no indication of whether it was showing the explosion of gas from a compact form, or the condensation of a large volume of gas into a small pellet. Normally we would choose as the initial conditions the most compact, least uniform end of the clip, and as the final conditions the least compact, most thermally equilibriated filling of the box.

    Isn’t this essentially a convective cycle, where heat/energy radiates/expands, while mass/stucture coalesces out of the cooling field?

    The arrow of time for the energy is to radiate from past structure to coalsce into future structure, while the direction of time for specific structural units goes from being future potential to past circumstance.

    Essentially the energy is the hand of the clock, being the physical reality that goes toward the future, as the structure is the face of the clock, going the other way, as particular units of time go from being in the future to being in the past.

    Think of it in terms of life cycles; The future of the species is in the birth of the next generation, while the future for the individual is old age and death.

    Energy goes past to future. Information goes future to past.

  • Paul Valletta

    “Starting from the assumption that Lewis Carroll’s nonsense means something, the author of WHITE KNIGHT makes a determined attempt to find out what lies behind it. Conclusions are reached which are revolutionary in their nature yet self-evident once attention is drawn to them,C.L.Dodgson, it is suggested, was a normal, though retiring, individual who fell in love with ALICE LIDDELL, the daughter of his proud and aristrocratic dean. Darkly beautiful, Alice while still a child, acted upon Dodgson as a powerful stimulus and catalyst,fusing all his powers into effort to charm and amuse” ..All his life Dogson was puzzled by the nature of TIME, which he knew from the start “would come and take his love away,” not into old age and death but into womanhood and marrage.”

    The above is extracted from THE WHITE KNIGHT a study of C.L.DODGSON (LEWIS CARROLL) by A.L.TAYLOR.

    The future has not happened yet, so it cannot influence in any way the present time “now”, and thus have any available information that can be recorded as a history past,: there is nothing in the future, that can influence the present,and thus can be recorded as a past.

    Events happen, the future has NOT happened yet, there is no way one can record “non-events”, the future has to fall in line, with the rest of Time! In the same sense that the unavailable_not-yet-happened_ future cannot interact and influence with present time events, the past does not follow you where-ever you go(turn around when you walk from any A to B and you will not see yourself in a kalidascope multidude frozen images)

    The arrows of time must have interaction, influence, paramiters, and nature makes sure you cannot know the location of future particles, present particles and FAIP past particles! The PAST-PRESENT-FUTURE are locations of “area”, thus spread out in “volume” terms one can derive some pretty airtight assumptions.

    There are no events still occurring in the long ago PAST?..the influence is close to the changing events of the PRESENT. To alter/change the present time, one would need “miracle” performing tachyonic “future-arrow” particles, sending a certain volume of these particles across the “now” without them coming into contact of local “now” particles, and hopefully they have a direct hit on the “target_location_area” of the past. You would know if your tachyonic bow has proppelled “arrows of time”, by the fact of change in present time events.

    Come back Boltzman all is forgiven!

  • Sam Cox

    From today:

    “Are animals stuck in time?
    Dog owners, who have noticed that their four-legged friend seem equally delighted to see them after five minutes away as five hours, may wonder if animals can tell when time passes. Newly published research from The University of Western Ontario in London, Canada may bring us closer to answering that very question.”

    The substance of the above research is that animals live in a kind of eternal present and have only certain very restricted perception of the passage of time.

    I have spent many years living in neolithic, oral and tropical human cultures. Birthdays were made up only to place something on an imported and required, legal record. Many of the aspects of the vagrancy of the memory of time passage in other beings, also applied to humans in these tropical circumstances. There was a sense of living in an eternal present. I studied local navigation and sailed on Wa Ceris (sailing canoes with outriggers). The perception, so long as the island destinations were visible and close was that of movement, however on the open ocean, we spoke of “bringing our destination island to ourselves”.

    Our family is also a flying family. I have done millions of commecial miles, mainly traveling from the east coast to the western Pacific rim region, but I’ve owned and operated corporate aircraft too. One thing I have learned is that our sense of the passage of time and place is closely related to our biological propriatary sense…what we see with our eyes, hear with our ears, the motion we detect with our inner ear…even our senses of touch and smell.

    When we enter a realm where we cannot see where we are going, flying in clouds for example, our ability to correctly orient ourselves in space and time is immediately compromised. For example, it is madness, sheer lethal madness to attempt to fly an airplane in clouds without instruments to orient ourselves- or to ignore those instruments.

    A pilot can have 60 hours or 6,000 hours…flying “by the seat of ones pants” under IFR conditions is ALWAYS lethal. Yet pilots still try to fly VFR flight rules while IFR- and die…and not just the inexperienced Joe Kennedy either. Experienced pilots flew a well equipped 747 into Nimitz Hill on Guam a few years back while attempting a VFR landing under marginal IFR conditions.

    The realm of the astronomical and sub-microscopic, although we learn more about those places every day, is veiled, to a large extent, and prevents us from completely and correctly orienting ourselves in the universe. Like that 747 on approach to Guam in marginal IFR, we would do very well to carefully follow the models which have been proven to accurately measure- and define- reality.

    We ignore the duality and marginally closed geometry of our mathematical models at our own conceptual peril. For example, in a GR universe, we stay at the same set of invariant coordinates forever and so does everything else in the universe. Time and space…our position in space and time is something we observe and measure from where we happen to observe (our coordinates). Because of the eternal nature of the antipodes of the geometry, neither we nor anything else actually goes anywhere at any time.

    Space and time are the holographic, electromagnetic constuctions of information- organized, complex energy density structures, we call “ourselves”.

    When no observation takes place in our universe, there is no universe, though the universe is eternally observed at some coordinates and is therefore continuously existing. The universe can only be said to exist as we (all information and biological complexity) observe and measure it from a vast array of different perspectives. The eternal timeless and placeless Planck Realm and Photonic matrix link all information in the universe. The most distant galaxies are, in an important sense, at our fingertips…we measure them as distant only because of the propriatary sense our baryonic existance bestows.

    What we see and feel is real. We can build a technology upon it. In fact, it is highly likely that we ourselves represent an intermediate step in the information building process which has brought about the existence of high complexity in the universe in the first place. It is also highly likely that we live in a universe where everything which can be done technologically, has been done- and exists at coordinates somewhere.

    In such a universe as we inhabit, and considering our own nature and the mathematical qualities and predictive accuracy of our models, I think we should be extremely cautious making any assertions about the nature of time, other than the facts that it is linked to space- and coordinate related.

    In engineering the sum of the moments in a structure must be 0 to (at least to begin to) insure its stability. The sum of the fractional terms in binomial expansion equal 1, and, given an infnite (or near infinite) and random set of events, the predictive value of the mathematics is certain (or near certain). For Statistical Mechanics to exist, it must exist within a manifold. That is where and how QM and GR relate, and integrate.

    If we live in a universe in which its baryonic component, at the quark level, undergoes a matter/antimatter occillation 2.8 trillion times per Earth second, and if we observe that baryonic universe, in a marginally closed two/sphere geometry, electromagnetically in extreme gavitational time dilation (creating our impression of the vastness of space and time), and if we, and all information exist at eternal invariant frames of reference, it is easy to understand why the tall tales of one Lewis Carroll are so intuitively attractive!

  • Sam Cox


    John F. Kennedy Jr.

  • Celestial Toymaker

    #22 “The simple test for such phenomenon is the movie test: if you can’t tell if the movie is going in reverse or not, you might be looking at a manifestation of the principle of microscopic reversibility.”

    The reverse movie test assumes that the observer’s mental processes aren’t affected by the time-reversed scenario.

    The problem with all of the fictional scenarios (I only dipped into this thread, so one of them may have it covered), is that they always assume a conscious observer which thinks using the same arrow of time we do. This allows full use of the novelty effect of the situation.

    My point in #18 though, is that this would not be the case in a time-reversed universe. The observer’s thought processes would also be reversed: Mental images would precede their perception. So, to a conscious observer, causality would not appear to be violated and the “reverse movie” would thus look just the same as it does to us.

    So I’m suggesting that if the rules of time-reversal are consistently applied, nothing very interesting would be seen at all. What’s at “either end” of time’s arrow in such a universe might be an interesting
    question though!

  • anonymous

    #16 – “You can’t maintain interacting systems with opposed arrows of time.”

    I’m still a little confused… Are you referring to a system of two individuals (who presumably need consensus in order to communicate), or are you referring to two directions of information flow within a single mind?

    I ask because it occurs to me that there might be a survival advantage if a single mind is able to process information outside the arrow of time. For example, let’s say two rather primitive people have chosen to engage in a battle of fisticuffs over a critical supply of food. The winner survives another month; the loser has to find another source of food.

    Would it be to the advantage of one of them to be able to deflect the subjective experience of the pain of any injuries sustained into the past, so that it has been processed before the fight occurs, thereby rendering that person less likely to be inhibited while fighting? (The injuries would still occur, however the subjective experience of pain would not follow the injury, but would have already been processed.)

  • Professor R

    I always loved that book, but I never really understood the passage

    ?Living backwards!’ Alice repeated in great astonishment. `I never heard of such a thing!’
    ` — but there’s one great advantage in it, that one’s memory works both ways.’
    `I’m sure MINE only works one way.’ Alice remarked. `I can’t remember things before they happen.’

    Both ways? Surely it is not entirely consistent that the Queen’s memory would work in both directions – it implies she is experiencing time both forwards and backwards, instead of a symmetric experience to Alice! For the same reason, her conversation with Alice wouldn’t make sense from her frame of reference…
    Or have I missed something?
    Regards, Cormac

  • Sean

    anonymous– it refers to any form of interaction. If you have two directions of information flow within a single mind, that wouldn’t do you any good unless they could actually share information, which implies that they are interacting. Which implies that they could not sustain mutually incompatible arrows of time.

    Cormac– it’s definitely not consistent! Carroll didn’t try very hard to come up with consistent behavior for the White Queen, even granting the freedom of inventing new laws of physics and logic.

  • Professor R

    It always irked me a little, even as a child ..s.uch a good book otherwise. Did you know Looking Glass was inspired by a different Alice? Today’s piece of trivia….Cormac

  • anonymous

    #33 – “If you have two directions of information flow within a single mind, that wouldn’t do you any good unless they could actually share information, which implies that they are interacting. Which implies that they could not sustain mutually incompatible arrows of time.”

    As the girl said, “Curiosity often leads to trouble.” :)

    Now I’m wondering what you mean by ‘share information’… If two directions of influence were flowing, any single instance of time would reflect the predominate direction of influence (usually past to future), but if the information flow from future to past could experience a temporary surge in strength, and/or the information flow from past to future were diminished enough to allow the normally-weaker stream of influence from the future to exert the dominating influence, then a single subjective moment in time might reflect the future moreso than the past. There is no need for the streams of influence themselves to be mutually held in awareness or directly compared. The ‘interaction’ would be a simple summation function that resulted in a single moment of awareness. (Does that make sense?)

  • John Merryman


    What determines the future is where the energy goes. Usually past order incorporates and adapts fresh energy and the future is a continuation of the past, though sometimes the past is too rigid to incorporate anything new, so energy accumulates elsewhere and the future becomes a reaction to the past. Life incorporates this cycle of growth and corruption through regeneration. Frequently the future is hard to predict because the compass points we tend to take for granted are also adjusting to forces and energies we are not aware of. The result is that what we tend to consider the most durable and and unchanging aspects of our sense of order are also potentially the most rigid and brittle. The consequence is that when we are young, we see and think in terms of objects, but as we get older and understand we were born into one world that is constantly dying off, as another grows up in its place, we learn to think in terms of process. So that by the time our alloted time is up, we see beyond the limits of definition and understand that death, like the absolute, is as much about everything as it is about nothing.

    Could you imagine space as any less “linked” to the concept of temperature than it is to time? How many arrows of time, such as entropy, universal expansion, gravitational contraction, anthropic aging, atomic decay, etc. are not a consequence of some manifestation of temperature? Yet we understand temperature as a consequence and description of motion, not some dimensional basis for it. As for space, what would you consider as the default description of space, the dimensionless point, or the featureless void? I tend to think it’s the void, yet it seems cosmology and geometry consider it the dimensionless point.


    An interesting point this discussion brings to mind is that there are natives of South America who consider the past as what is in front of them and the future as behind them. This is because their point of reference, the center of their four dimensional coordinate system, if they used one, is the energy, not the observer. So that the event happens, they observe it and then the information goes past them, thus the arrow of time goes from event to observation. We think of the future as in front of us because we are the center of our coordinate system and we are moving from previous events to future ones, much as the hand of the clock moves from previous time units to future ones.

  • W. Arfarin

    Sean (re 25) -

    I see where you’re going with the entropy-only arrow of
    time argument, but I don’t think you can keep it strictly
    classical and large scale.

    *Is* there macroscopic irreversibility? Can it be
    proven without resort to quantum? Is only our initial
    boundary condition important?

    Let’s think about things from the perspective of some
    reverse colleagues out there. (This is going to result in
    messed-up pronouns; sorry. I’m also not even going to try
    to handwave a map between their observational tools and

    Observations of (their) past show a tendency towards
    the collapse of cold, randomly distributed gasses and cold
    photons into hotter, denser, metastable arrangements that
    “sink” heated photons, neutrinos and free electrons into
    baryonic matter. Star-forming nebulae coalesce into stars
    – the final infall before stellar ignition is sometimes
    quite rapid — the stars in turn heat up, fission metallic
    elements thanks to free neutrinos and the like, which are
    attracted to dense, high-energy objects like stars. Stars
    eventually cool and dissolve into nebulae. This is
    cyclical, with increasing proportions of lighter elements
    released in each star-dissolving cycle.

    The best observations of the CMBR and the relative
    motions of celestial objects suggest a future big crunch,
    which likely will involve only the final hydrogen-rich
    diffuse gas that evaporated out of the final cycle of stars.
    The end result is likely to be a hot dense gas which will
    (similar to stellar fission) break apart atoms and
    nucleons into simpler particles. These may in turn form
    structures within the plasma, but unfortunately behind the
    veil of the final breakdown of baryons, we can only guess
    that metastable configurations can’t last very long
    because of the heat leading up to the final explosive
    infall of the quark-gluon plasma. One big problem about
    the future is how the energy that drives the metric
    contraction of spacetime can overcome the tendencies of
    the hot post-baryosis phase members to resist contraction.

    There is another boundary condition strangeness,
    namely the highly unlikely distribution of the matter and
    energy universe in the distant past. We know from
    observation that more objects appear within the limit of
    visibility over time; the new material is essentially
    homogeneous and arrivals are distributed isotropically
    across the sky. Regression suggests that at some point
    there was a relatively small amount of very cold matter
    within the limits of photon-mediated interactions. That
    the combination of the primordial gas (and/or black holes)
    fell into metastable large structures is uncontroversial,
    since that happens in labs at smaller scales, and at
    middle scales in astronomical structures. However, there
    is a fine tuning problem with the initial distribution of
    causally-connected local matter and energy at the “time of first

    Back to us… how do we objectively decide which of
    these history->future progressions has greater degrees of
    freedom? In their view of the universe, the tendency
    towards condensation into systems with reduced
    availability of microstates is a given, just as the
    tendency towards an increase is a given in our stat mechs.

    Yes, these are incompatible views. We think that a
    tendency towards reducing available microstates is
    impossible, they think that it is not only perfectly
    natural, but derive that isolated systems always do this.
    Each party has an apparent fine-tuning of boundary
    conditions that underlie their respective derivations,
    with the initial one being critical. Theirs is thermal
    equilibrium, which comes to an end thanks to a metric
    collapse of spacetime. Ours is a false vacuum fluctuation
    which is magnified by a metric inflation of spacetime.

    Is their view just backwards from ours, or is it
    somehow objectively invalid? Can that be shown without
    also showing the presence or absence some underlying
    irreversibility in microscopic interactions?

  • Plato

    I’ve heard most of the sideline issues noted in this comment section about Lewis Carroll. I really enjoyed the attention paid to the nonsensical while underneath it’s facade there is a mathematical relation being spelt out? Logic forming? I’m not sure.

    But this has been a troubling issue of late for me in terms of this arrow time. The memory issue, the whole works.

    Kurt Gödel Time 100

    Soon it dawned on a few insightful souls, Gödel foremost among them, that this way of looking at things opened up a brand-new branch of mathematics — namely, metamathematics. The familiar methods of mathematical analysis could be brought to bear on the very pattern-sprouting processes that formed the essence of formal systems — of which mathematics itself was supposed to be the primary example. Thus mathematics twists back on itself, like a self-eating snake. Bold added for emphasis

  • Paul Valletta

    John, the future is bleak and empty, it has not yet happened, thus there is nothing there to change?

    The past has gone, it will not happen over and over again, therefore there can be no change occuring in any system’s past. The only change is the present time? To change the past, is to change the future, think about it, if you changed yesterday in any way, it would certainly have reprocusions for “today”, thus any change of past is a change of the future “today”?

    Now we can make statements such as:”There was change in the past”..but how do we narrow it down to “ago”? long ago did changes happen?..10seconds ago?…five seconds ago?..1 second ago?..

    Truth is, at every instant of “ago” there was change, infact the whole of the past was really changing events, there was never any moment in one’s past wherby no change occured!

    This now begs the question of:Will all future events involve “change”?

    When you look back at today, from tomorrow, you will notice change, you cannot, repeat cannot!..record events 100%, that is the incomplete nature of Relativity?

  • Plato

    Is there a possibility of a “relativistic interpretation” based at the QGP?

  • John Merryman


    My point is what is happening in the now that decides among all the potential futures. That which will happen will be what is manifested by the energy of the universe. All other possibilities are the paths not taken. The question is what determines the path that the energy chooses. Often times it is like a meandering stream, pulled by larger forces of gravity, heat and convection, not going fast enough to force a straight path, bouncing off the hard spots, curving around, washing over the small stuff. As I said, if the order of past events is still vital and flexible to absorb new energy and the information it contains, even if it is simply a message of raw force, then the future is in many ways a continuation of past events, but if the old order is too rigid to accomodate fresh energy, this energy pushes the old out of the way and starts a new system of order. The first way is like the passage from spring to winter, as the new grows, aborbing sun, water and minerals, but necessarily becoming more rigid as it gets bigger. The second way is like the passage from winter to spring, as the dried out husk of the old is pushed aside by new life, cracking through where the shell is weak, or brittle. Action and reaction. In terms of current politics, you might say that McCain is winter, Obama is spring and Hillary is somewhere inbetween.

  • Paul Valletta

    John, think of a rubik cube and its many configurations, or permutations. Now, from 1 second ago, to this very moment NOW, the “second” has a certain value, and from NOW to 1 “second” into the future, this “second” has certain value. Are the two moments past_to_now now_to_future “seconds” identical? the previous second compatable with the first “second”?

    If there is no change, then there is no history, no past in time. There may be many molecular or atomic manouvering, permutations for every piece of matter in existence, but look at any single moment anywhere on Earth, and there is a vast amount of change happening, no two “seconds” are identical?

    Although the measuring clock is identical, the fact one can go back 13 billion ly’s and find a Universe that has totally changed, means that locally “second_to_second” time NEVER changes, or there is never any recordable evidence to such changes, but Universe_to_Universe Bang_to_Rip, then there a not only vast amount of changes, the local Laws of Physics must have changes emmbedded into every local interaction, like a “new” geometric rubik cube appearing with a new set of rules and regulations?

    Gravity for instance has today, “NOW” has four signatures, there are FOUR FOURCE’S ;) two of inner force (short range)we and two that can be demmed outer force (long range), these have been set sometime in the long distant past, just what changes occured to configure Gravity into this sequence, or order of sequence?

    What if Gravity was a positive inner force “NOW”, and the strong molecular “now” force, relagated to the Atomic extreme?

    Is there a time in the Universe, where all force’s interchange locally?

  • John Merryman


    To the extent I consider time a measure of motion, rather than the basis for it, the concept of “now” as a point is meaningless. To actually freeze motion would require a temperature of absolute zero, at which point measureable reality ceases to exist, since measurement requires a degree of interconnectivity and transition, which don’t exist without motion. So since the concept of a point in time can only be approximate, any measurement from or to such a point is equally approximate. To suppose otherwise, you end up with a form of Zeno’s Paradox, where nothing happens, although it is obvious that much happens, as you seem to be hinting at.

  • Qubit

    You can’t maintain interacting systems with opposed arrows of time.

    Black holes can, otherwise they would not be able to evaporate. IMO Hawking radiation must escape along parrallel surface reflections, allowing it to escape unseen and able to freely interact with each arrow of time; marrying the two together so they seem like a seamless past and escaping up imaginary potentials, as the universe observes the real objects it creates.

    I don’t see how they are incompatible, if they are incompatible then that’s because one is from another universe. Which does not mean you can’t make them compatible; esp. if you can convince the other direction your past matches its interactions.

  • Adam S

    Towards the end of chapter VII in Through the Looking-Glass, there’s another instance of time reversal (kind-of)
    ‘You don’t know how to manage Looking-glass cakes,’ the Unicorn
    remarked. ‘Hand it round first, and cut it afterwards.’

    I always figured that this was kind of like reversing parity and as a result needing to reverse time as well. (I guess the looking-glass world wasn’t antimatter, or Alice wouldn’t have fared so well)

  • John Merryman

    testing access…

  • Plato

    Lewis Carroll’s Logic Game

    Lewis Carroll’s fame is universal. I can easily cite a couple dozen books that mention him or quote from his books. Temptation to quote from Alice’s experiences with which so many people can identify, is indeed great. But the trend may be reversing. In the introduction to a book I have recently come across, the author found it necessary to mention that in the whole of the book there is not a single reference to either Alice in Wonderland or Through the Looking Glass – the two books that made the name of Lewis Carroll a household item the world over. However, his other works are either forgotten or known far less. In real life he was a mathematician C. L. Dodgson with deep interest in symbolic logic and logical reasoning. I have described elsewhere one of his probability and the doublets puzzles.

  • Adam Stephanides

    I just came across this thread yesterday. Sean, doesn’t your argument in 16 and 25 assume that the correct direction of time is already fixed? That is, the effects of the interaction propagate into the “future” of the system with more degrees of freedom, but not into the “future” of the system with fewer degrees.

    Suppose two systems with opposite directions of time and equal degrees of freedom were to interact. What would happen?


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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