Greetings from Paris! Just checking in to do a bit of self-promotion, from which no blog-vacation could possibly keep me. I’ve written an article in this month’s Scientific American about the arrow of time and cosmology. It’s available for free online; the given title is “Does Time Run Backward in Other Universes?”, which wasn’t my choice, but these happenings are team events.
As a teaser, here is a timeline of the history of the universe according to the standard cosmology:
- Space is empty, featuring nothing but a tiny amount of vacuum energy and an occasional long-wavelength particle formed via fluctuations of the quantum fields that suffuse space.
- High-intensity radiation suddenly sweeps in from across the universe, in a spherical pattern focused on a point in space. When the radiation collects at that point, a “white hole” is formed.
- The white hole gradually grows to billions of times the mass of the sun, through accretion of additional radiation of ever decreasing temperature.
- Other white holes begin to approach from billions of light-years away. They form a homogeneous distribution, all slowly moving toward one another.
- The white holes begin to lose mass by ejecting gas, dust and radiation into the surrounding environment.
- The gas and dust occasionally implode to form stars, which spread themselves into galaxies surrounding the white holes.
- Like the white holes before them, these stars receive inwardly directed radiation. They use the energy from this radiation to convert heavy elements into lighter ones.
- Stars disperse into gas, which gradually smooths itself out through space; matter as a whole continues to move together and grow more dense.
- The universe becomes ever hotter and denser, eventually contracting all the way to a big crunch.
Despite appearances, this really is just the standard cosmology, not some fairy tale. I just chose to tell it from the point of view of a time coordinate that is oriented in the opposite direction from the one we usually use. Given that the laws of physics are reversible, this choice is just as legitimate as the usual one; nevertheless, one must admit that the story told this way seems rather unlikely. So why does the universe evolve this way? That’s the big mystery, of course.
The origin of the 2nd law of thermodynamics is no mystery. It’s been solved for decades at least.
Here are some references for those interested.
http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf
http://bayes.wustl.edu/etj/articles/gibbs.paradox.pdf
http://www.ucl.ac.uk/~ucesjph/reality/entropy/text.html
Sean…
A very interesting and thoughtful article! It would be, I think, interesting to conjecture on how many frames of reference in the universe it would be necessary to conceive, assume, describe and understand before we could get an accurate mental pictorial concept of the true nature of cosmological reality.
Perhaps it would be appropriate to conceive of our “multiverse” as a progressive, eternal and infinite set of universes almost identical to our own, even including ourselves, but gradually and phylogenically developing along a single, single process time dimension, and increasing in informational complexity….
Garth Barber said: “So, if for the sake of argument, no other universe other than our own exists, then what test would falsify the multiverse hypothesis?”
That depends on how the work I mentioned progresses. It could easily happen, for example, that the theory will predict that new universes will nucleate at a rate and collide with ours with such effect that the theory can be ruled out by observations *already* made. Or, in the specific scenario considered by Sean, it may be possible to prove that new universes never look like ours. The point, as also made by Jason D, is that it is just not true that these theories are non-falsifiable *in principle*.
Peter Woit said: “On the other hand, there are a lot of people who want to see specific arguments about a multiverse make some sort of standard, testable (even if only in principle) scientific prediction before they agree that these specific arguments are science.
Look at the articles I cited. Seeing the patterns in the CMB described there would of course be very difficult — but you have no complaints about that, right?
“I don’t see how the arguments being sold in Scientific American lead to any possible predictions that would allow one to test them in any conventional sense of scientific testability.”
Exactly what people said — on better grounds — 25 years ago about Inflation. If I had been around 25 years ago, I would have been prepared to bet serious money that nothing observable would come out of such a theory within 25 years. And I would have been wrong.
There is nothing *in principle* unverifiable about Sean’s theory. One universe is born from another. Personally I would bet that a deeper investigation of this theory will show [sorry SC !] that it is actually not able to produce a universe like ours, except by some kind of Boltzmann-style massive fluctuation. Thinking about Boltzmann-style fluctuations has convinced most of us that it is not what happened. So at that point I would conclude that SC’s theory has been proved false. If that is not science then what is?
In short, nothing special is going on here philosophically. We have theories that posit *currently* unobservable things, just like any speculative theory. So what?
Anyway you might look again at Sean’s comprehensive demolition of John Horgan a couple of months back. He said it all better than I can.
I don’t see how anyone wouldn’t see how much more believable the standard cosmological model is than to hypothesize an “original intelligence” which created everything.
@ Ed,
Just because we are yet to understand something and at the present don`t have the technology to do that, it does`t mean that we shouldnt try….
Good point.
Can anyone help me imagining time going backwards?? If I reverse processes, I can only visualise it (the reversed process) as a going forward…..
“You should definitely not translate articles without permission!”
AHHH??!!!
Might as well be, “Quit thinking!”
You can’t read the article if english is your second language and you translate it first?
Just got the new issue of SciAm in the mail yesterday. Flipped to Sean’s article and started to read it out loud in the car while my 16 year old was driving to school this morning, thinking she might find it interesting (and having my eyes averted from the road keeps me from thinking about all the various possibilities of increasing entropy that she, as a beginning driver, narrowly avoids).
Unfortunately, I was unable to finish the article because, arriving at school, she asked to borrow it to share with her physics teacher today. The opening paragraphs completely grabbed her! This is the kind of stuff that gets her really excited and has her wanting to pursue physics/astronomy/cosmology in college in a couple years (She recently got the opportunity to spend the afternoon with your colleague Mike Brown at CalTech which she loved!).
So, thanks, Sean, for putting out this “high school-accessible” article. You definitely set the hook in at least one young reader! I look forward to finishing the article for myself tonight.
Khan, I think it’s great that you’ve offered to translate the article into Bengali. Send me an email offline and I’ll help you get the necessary permission. My email address is my first initial plus last name at sciam dot com.
manyoso, the problem isn’t the translation but the publishing! But actually I doubt there will be any problem at all.
George
Pete,
Here is a way to visualize time as going from the future into the past.
Rather then viewing time as a directional dimension along which we move from past to future, consider just a bunch of quantum energy that simply exists, with no time dimension at all. Suppose this energy developed the tendency to clump, then break apart and scatter, then clump again.
What this energy has done is to create a time dimension of events. Now since this dimension isn’t fundamental, but is created by the process of clumping and scattering, the quantum energy isn’t moving along it, but is creating it as each successive stage replaces the previous one. Since the only thing that exists is the energy, these stages go from being present to being past. The result is that this timeline is going from future potential, to present manifestation to past circumstance. This is one way to imagine time as going from future to past.
Sort of like tomorrow becomes yesterday.
Is it really that surprising that equations do not fully describe reality? A multiverse could be the difference in behavior/description at different scales within this universe.
Pete, I wholeheartedly, support and commend the activity of increasing our knowledge about our current and past environment (universe). That was not my point. I was pointing out that there isn’t much real difference in saying “in the beginning was void” and saying in the beginning was a tiny amount of vacuum energy.
Ed, thanks for explaining it, my mistake. 🙂
John,
So, what is going to happen has already happened and therefore isnt going to happen at all? Or am I approaching this in a wrong way?
This has twisted my brain.
Thought I just posted something, got a thank you, but, now I don’t see it.
Hoek
Pete,
I’m just making the point that the one dimensional, linear cause and effect narrative that we call time is better explained as a consequence of motion, similar to temperature, rather than the basis of it.
As a measure of motion, the concept of a specific dimensionless point in time is meaningless, as there would be no motion to measure, so nothing measured in time can be said to have an exact location. Reality really is fuzzy.
Sean
I liked your Scientific American article, but it seems to me that you
have neglected a significant component of the “time’s arrow” problem,
the part that some philosophers call the “now” problem.
Your article focused mainly on questions related to why the “beginning”
of the universe has more or less entropy than the other end, which is an
inherently interesting and non-trivial problem. But it misses the vital
question of what it is that “moves” under time’s arrow. The simple
answer is that what moves is an odd moment of time that we call “now.”
The problem of course is that there is nothing in physics that specifies
any particular instant of time as special in any way, and in particular,
nothing that specifies an instant called “now” that separates a
determined past from an indeterminate future. This might not be the
best definition of “now,” in that it opens up a set of difficult problems
about determinism that we don’t need just yet.
To sidestep these questions (for now), perhaps a better definition of
“now” is this: the moment of time that separates the time intervals that
all of us can remember from those intervals than none of us can
remember. At first we should probably assume that “now” is the same
moment for all of us, at least to some (poorly specified) accuracy. We
could define a separate “now” for each individual, but I don’t think we
need to do that just yet. We get into serious philosophical difficulties if
we assume that “now” for any one of us is separated by a “large” amount
of time from that for the rest of us, where “large” means something like
significantly greater than the light-travel-time between observers.
You touch on this question when you ask: “Why do we remember the
past but not the future?” You state that: “to form a reliable memory
requires that the past be orderly, that is, have a low entropy.” This
answer seems completely inadequate. Tomorrow may have a slightly
higher entropy than today, but not by an amount that explains the
radical difference in the behavior of memory over the two intervals. In
general, the difference in entropy in my surroundings between yesterday
and today isn’t very much different than the difference between
today and tomorrow. But there is a radical difference in what I can
remember about these days.
This raises another difficulty. Clearly there are large differences in the
change of entropy of our surroundings from day to day, as in the case,
say, of my house burning down compared to a more normal diurnal
interval. But I personally do not notice much difference in my memory
abilities, nothing that correlates with the magnitude of the change in
entropy from day to day.
It seems to me that a complete understanding of “time’s arrow” would
require an understanding of the “now” problem. It may even be the
more fundamental part of the problem, in that a theoretical
understanding of “now” might entail a full understanding of time’s arrow,
but an understanding of the entropy differences across the universe’s
lifetime would not appear to require an understanding of “now.”
Some philosophers, called “nowists,” attempt to resolve this difficulty by
assuming that “now” is the only instant of time that exists. This strikes
me as simply defining away the problem without explaining it. And it
has clear difficulties with special relativity. But I don’t have a
particularly better explanation.
Your very use of the words “past” and “future” assume the existence of
a “now” moment, but you do not deal with this problem at all.
Sean –
Heh, cool, I obviously like your timeline with respect to large
scale reverse cosmology. 🙂 Within our conventional
direction of time, I think you probably wrote your version first,
given how gaps between publication deadlines and “ink on
paper” usually work. I promise I have not hacked
into your ‘puter or travelled from your future after
having read your SciAm timeline!
A number of minutes ago I began typing a handwave about the weirdnesses of the two boundary conditions from the perspective of observers like us versus observers who see the evolution of the cosmos in reverse. This was derailed by two things, viz. conclusions that can be drawn about cosmic evolution in a Big Crunch direction, and whether reasoning about that end is really easier in either direction (forward physics or backwards physics) given a similar need for extrapolations in constucting timelines that include both boundary conditions.
It’s going to take a long hot shower to think about some of this.
One of the things that hit me was what the Hubble flow looks like to a reverse observer rather than a forwards observer who can simply play the “tape” backwards.
(Also there is another plausible case that is both helpful and distracting, namely, a pair of observers who are in a universe much like ours except that both boundary conditions are strongly predicted to be hot and dense. One observer looks “forwards” and one looks “backwards”. The differences between what either observer sees after his peculiar expansion-collapse transition and what the other observer sees after her peculiar expansion-collapse transsition is worth a thought.)
The second thing to hit me involved my immediate reaction was that the boundary condition of Big Collapse is easier to think about than either starting condition (Big Bang or “Horizon Decay”) because we only have to consider a couple oddities:
A. changes in the metric collapse of spacetime — e.g. it may be slowing down towards the big crunch, rather than proceeding at an even, “inertial” rate. (Here’s one place where backwardsverse!observer broke my brain, since I really get stuck thinking that their metric collapse of spacetime looks to them a lot like what we in forwardsverse think of as gravitational collapse).
B. it is not clear how the metric collapse can squish everything together to match the CMBR — we need a lot of energy to dissociate baryons (as we know from watching stellar reductions), but the energy from the metric collapse force seems insufficient, especially with respect to singularity models of the Big Collapse.
In point (B) I wanted to predict “cosmic deflation” but my brain bent less because of mechanism (just play it backwards) than because of what could suggest it to any of our Big Crunch predictors.
I also am tired and easily distracted by trying to add in things like possible quintessence, predictions from QM (dehadronization) and the like. You can have a lot of fun running various models backwards and forwards! Maybe everyone should do this out of habit if “Given that the laws of physics are reversible” is true.
Penultimately, I wanted to avoid dragging everyone into long debates about the nature of reason (I’m in the “it’s an emergent property of brain structure/function/mechanics” camp), since that doesn’t obviously help with the thinking about boundary conditions, but is one of those interesting distractions. 🙂 This started getting very hard when thinking about how our backwards counterparts would perceive CMBR, for example.
Finally, notch up another commenter who likes before-bedtime activities, even if he is a total outlier in your timezone-to-posting-hour distribution (UTC+1).
Your friendly neighbourhood rodent toxin of many names.
3 Meta points:
1. Add me to the list of people who wish for a preview button!
2. I obviously did not foresee the mangling of the link to my previous comment, but I figure you are smart and can figure it out. 😀
3. As one way to sidestep the problems of observation and communication involving people with incompatible arrows of time, how about pretending there exists a translation system that lets you write down the observations and reasonings of a “foreign” (in the evolution of the universe sense) cosmologist acting just as his/her/it’s agent? I wish I could find a more concise and academic description than here:
http://tvtropes.org/pmwiki/pmwiki.php/Main/LiteraryAgentHypothesis
in which it is argued that some proper scientists have employed the device at least when writing hard science fiction.
I was using it earlier without really thinking about it or acknowledging it.
Perhaps someone will have a “conversation” with a scientist in backwards-universe and report back details? Or at least bury the use of such a reasoning device behind something more conventional and rigorous, along the lines of what you might find on arXiv or at least main postings on cosmicvariance.com?
Finally: Warning: tvtropes.org will ruin your life, or annoy you, or both. It says so itself on the front page. Apologies in advance.
Here’s a Sci Am article on the arrow of time that is interesting on quite a number of levels:
http://www.sciam.com/media/pdf/2008-05-21_1975-carroll-story.pdf
One of the reasons why it’s interesting is because it’s 1/3 century old. Another is that it doesn’t treat it’s readers as if they are terminally afflicted with ADD.
No offence, Sean, but I wistfully long for the days when Sci Am published elegant articles that served up some actual meat in them, “articles” that didn’t resemble a television commercial with eye-catching and monumentally irrelevant cgi artwork. Then one looks “under the hood” and finds watered-down soup that looks as if it was hammered out over a weekend rather than the hoped-for beefy stew. I spent as much time – maybe ten minutes total – admiring the opening art as it took me to read the article, which provides almost no further elaboration of the concepts that isn’t already encapsulated by the 3 so-called “infographic” boxes. Unfortunately, the article fails miserably in terms of actually learning anything new.
Just how far can they possibly push this “simplification” gambit before anyone notices that the “articles” are basically appetizers for what readers REALLY want in a magazine subscription – you know, like a satisfying meal?
Though they can still work up a fair sweat with biological topics, in terms of physics and astronomy articles, Sci Am has become a dreadful waste of the precious resource of paper. Looking over how the magazine has diluted the information content in it’s articles over the last 20 years or so, it’s apparent that they’ve finally settled on identifying their market: moderately bright grade-schoolers who have the attention-span of a gnat.
Doug,
The entropy problem would go away if cosmology wasn’t trying to define the universe as a sungular unit with an internal timeline that goes from beginning to end, as its external position goes from being in the future to being in the past. If it’s infinite there is universal energy exchange and all energy is conserved.
“Now” makes much more sense if we consider that only energy in space exists and time is a consequence of measuring change. Therefore, as I previously mentioned, “now” cannot be a dimensionless point, as there would be no motion to measure.
W. Arfarin,
If you think of energy expansion as the source of redshift, it is the hands of the clock of constituent energy going from one temporal unit to the next, as as gravitational structure is the face of the clock, with its units of measure going from being in the future to being in the past. That way, you have a convective cycle of expanding energy and collapsing mass, rather than a universe as a singular unit of time.
Anchor,
Maybe the material they have to work with is at fault.
The apparent symmetry of time in physics could well be due to the inability of equations to fully capture and describe time. The convention is just that, a convention.
I hope I am not being annoying…
John Merryman –
No, my thinking rathole about the Hubble flow, specifically from
the point of view of an observer who sees *this* universe (more precisely, our Hubble volume) in the
opposite time-like direction from us, went like this:
1. Can a biology arise in reversed standard cosmology?
(a) We can guess what it looks like — the (generic) luciferase
process looks a lot like the chloroplast membrane proton gradient-ATP Synthase process in reverse!universe: photons are
absorbed and used to phosphorylate AMP; the resulting ATP
can do work (e.g. breaking apart polymers in ribosomes,
synthesizing carbohydrates in mitochondria,
bioluminescing in chloroplasts…)
(b) Origin of life problem seems pretty damn hard, but it’s
not exactly easy in forwards universe
(c) Adaptation and natural selection is a bit
confounding in reverse, especially if we look at it
forwardsly — it seems like a spectacularly
unsuccessful species whose population dwindles rapidly
towards zero would be well adapted to a niche in reverse
2. Can a biology in reverse standard cosmology result in a
brain that reasons like our brains?
I have nothing other than resorting to the law of large
numbers, which as we know produces Boltzmann Brain
problems in forwardsverse; my poor brain needs some
pencils and paper to think about it backwards. My “yes”
is purely intuitive.
3. “Seeing”
An obvious development in sensory equipment comes down to
“sourcing” photons from biomechanical processes that emit
them with a nonthermal distribution that can be tracked
from point of emission. (No feedback in backwardsverse is
an assumption to help preserve Galilean invariance and
Lorentz covariance).
In backwardsverse we would want to evolve strucuress which emit
photons in such a way that the resulting work preserves
(“encodes”) very fine grained angular distribution
information about the photons (as well as their energies).
“Seeing” reversed: photons stream out of phototransmissors
in all sorts of directions with anisotropies at different
frequencies. At point of emission we can preserve
information about the direction of distant photon sinks.
Using this to examine the sky we would see large areas
which “suck” only low numbers of low frequency low
temperature photons from our photoemissors. We would see
quite a few pointlike and smearlike objects which would
“suck” out larger numbers of much higher energy photons,
and so forth. A hot blackbody sinker has a well defined
photon sucking behaviour in terms of photon frequencies;
many other hot objects (especially in the sky and in labs)
do not take a full blackbody spectrum. Doppler effects
shift these spectral lines towards higher frequencies or
lower frequencies depending on the relative motions of the
observer and distant photon attractor.
Rotating and elliptical galaxies and huge stellar implosions are pretty
uniformly distributed across the sky. When we send out
photons to them we notice a correlation between decreasing
angle and increasing blueshift, corresponding to a metric
collapse of space time of approximately 71 km/s/Mpc.
When we send out very blueshifted galactic spectra to a
narrow angle of sky we are really transmitting photons
into the distant past, where they will ultimately meet up
with their appropriate photon sinks, in line with what we
know about the second law of thermodynamics.
Unfortunately we cannot say much about the present state
of the sinks of these distant photons, except that they
are probably further away from us now (and probably more
filled with metal) than is suggested by the outgoing spectra.
4. This is far from rigorous and hinges on forward
reasoning informed by backwards perception (i.e., something that thinks like us but which we would probably guess was thinking backwards — “remembering the future” when it is really remembering its own past).
This is not forbidden by an emergentist view of reasoning, but I have no idea how likely or unlikely it could be. Is it more or less likely than our own reasoning?
This point also lends itself to metaphysical thinking which,
frankly, annoys me.
Lastly, with respect to your paragraph staring with “if
you think of energy expansion as the source of
redshift”…
I don’t want to do that; that’s not an approach that
is interesting to me. I am not trying to disprove the
concordance model AT ALL, I am trying to better understand
it by inverting the timelike direction of observation with
a few assumptions (reversibility of physical processes, fundamentally).
As a result, I am (trying to be) thinking of the Hubble
flow in standard cosmology terms (without being
particularly rigorous), just in a timelike direction that
leads to the Big Crunch (i.e. what we call the Big Bang).
That is, the “clock” direction in this is with respect to
the boundary conditions, particularly the one which is
strongly predicted (our hot dense early universe). The
clock metric favoured in Sean’s threads is entropy
(specifically the log relation of microstates to
macrostates), which increases in one direction and
decreases in the other.
Trying to predict the observations of a human-like
reasoner who happens to be used to the reverse direction
(i.e., entropy decreases over time) is hard, particularly
since I am scratching my head about things like
thermodynamic favourability versus forward logic, and
whether when we flip the thermodynamic arrow we also flip
*whether* things like electron transport chains, osmosis,
exclusive or logic gates, and so forth *can* work, rather
than *how* they could work.
Particularly with respect to this rathole, I’m
not especially keen on considering possible states outside
the Hubble volume or beyond the BB/BR (and even the Big
Rip (or Long Asymptotic Isolation) end is a bit fuzzy)
without good reason.
So, to reiterate, thinking about time reversal like this is at best an exercise that might be useful to explore the standard cosmology, and at worst is Anchor’s “dreadful waste of [some] precious resource”. Science-shattering? No. Interesting? I think so, otherwise I’d be doing something else with this. Useful? I dunno. Ask Sean Carroll. 😀
– Your friendly neighbourhood etc.
I wonder if the answer to this might not be hiding in plain sight. E=MC(Squared). A useful formulation that even Einstein had to tinker with, even if just a little. Our physics have no explanation for what happens past the “speed” of light. On the other hand our physics, certainly on our own little macro level, depends upon a formula that includes 3 elements, one of which clearly does not exist — the speed of light squared. What might energy, matter, time, or space be, or would they be, in a multiverse where one “sector” was ordered on laws of physics where the speed of light squared was the rule rather than the exception?
Brody,
My problem is the path down this particular hole started with a question about the expanding universe. Many years ago I happened to read that the sum of total expansion is very close to, if not evenly balanced by the contraction of gravity. So I’ve raised the issue of how can the entire universe be expanding, if this spatial expansion on which the assumption is based is being effectively neutralized by gravity. Now I can certainly understand why you wouldn’t want to question BBT, as it classifies one as a crackpot to do so.
On the other hand, I’m not a scientist and in fact my main interests tend toward politics and history and I only started reading up on physics as a way to gain insight as to what motivates the larger forces in society. So when I come across bunches of people all marching in the same direction because the best and brightest told them it’s the way to go, even though the logic is incomplete, incoherent and full of patches, my impression is decidedly less then credulous. When the adherents try an enlighten me by by pointing out that it’s ordained by a higher power, in this case, mathematics and I’m just too simple to understand, I don’t necessarily assume I’m just too thick to appreciate that we are living in a new era, but tend to consider the crowd might just be falling for another version of the same old song and dance. As far as I’m concerned, equations are another form of smoke and mirrors when those promoting them cannot explain what they mean in another language. In this case, english.
As for cosmology and time, if gravitational collapse is an inward curvature of space, than I am of the opinion the radiation and other forms of energy being ejected from gravitational wells amounts to an outward curvature of space and redshift is evidence of this cosmological constant. The result being an old fashioned convective cycle of collapsing mass that heats up and starts expanding, until it cools sufficiently to start the cycle over. As structure, mass is the face of the clock, with its units starting as future potential and ending up as past circumstance, while the outward flow of radiation/energy is the hands of the clock, the raw essence that is constantly shedding/radiating away from old forms and starting new ones. It is both of these directions of time coexisting, the outward expansion into the future and the inward collapse of the past, that forms this infinitely dimensional reality we live in.
As for math, it is a model, not an ideal.
Anchor sneered: “No offence, Sean, but I wistfully long for the days when Sci Am published elegant articles that served up some actual meat in them, “articles” that didn’t resemble a television commercial with eye-catching and monumentally irrelevant cgi artwork.”
Yeah, well, Anchor, “no offence”, but you are neglecting one tiny point: that article from 1975 is wrong, though at least it correctly identifies cosmology as the source of the Arrow — incredibly, there are still some people who dispute this obvious fact. Nevertheless the solution proposed is indeed wrong. Here’s a free clue: the theory advanced there sank without a trace.
Sean’s article may seem simplistic, but that’s the point: what he is trying to draw to your attention is something which is indeed amazingly obvious, yet people —- I mean professional physicists, not just crackpots like Last Mohican —- just don’t get it. Quite recently I had a discussion with a distinguished physicist. I asked him what he thought about the old idea that the arrow might reverse if the universe began to contract. His response: “that’s ridiculous, it would require incredible correlations, etc etc etc” But he didn’t think that there was anything ridiculous about the fantastic correlations that you see if you trace the history of our universe back to the big bang! So you see that even the simplest errors in this subject live on, and Sean is doing great work in alerting everyone — not just the public — to those errors.
ps. No, I don’t believe that the arrow will reverse if the universe contracts. The point is that the history we observe is just as bizarre as that would be, and cries out for an explanation. Meta-point: there is obviously some major gap in our understanding of the early universe. If we can’t understand this, then we are probably getting lots of other things wrong too.