The Frozen Stream of Time

by Luke Muehlhauser on September 8, 2010 in Science

drescher good and real smallI’m blogging through Good and Real by Gary Drescher, perhaps the best book on naturalism I’ve read yet. (See the series index.)

So far I’ve summarized Drescher’s views on the mind and consciousness. Next, Drescher turns to some paradoxes in physics, starting with the nature of time.

Talk of spacetime can be confusing, so we’ll rely on pictures. Drescher asks us to

Imagine that space is just two-dimensional. And imagine that it is a (huge) finite square… So the total state of the universe, at a given moment, can be drawn on a square piece of paper… The piece of paper shows the state of every particle in the universe [at that moment].

By applying patterns that say how the state of each particle changes over time (as a function of other nearby particles), we can generate a stack of pieces of paper, each next page describing the next state of the universe, so that pieces of paper form a three-dimensional box shape… we have used two dimensions to represent space, and a third to represent time.

Drescher provides the following illustration:

If determinism is true, then any cross-section in the box could be used to figure out what the very next cross-section would be like, and so on “for the entire future of the universe. And to an external observer looking at the… universe from outside the three-dimensional box, everything is just sitting statically, unchanging, within the box.”

Motion within this box would, like motion across several frames of a film strip, be represented by the fact that an object in one frame is in a slightly different position in the next frame, and a different position still in the frame after that. Unmoving objects would appear in the same place in frame after frame after frame.

This box of time slices is a loose analogy for the real universe. The real universe has three (or more, according to string theory) dimensions of space, which are represented as two dimensions in the box analogy. Also, space in the real universe may not be finite like a super-huge sheet of paper would be. Finally, some interpretations of quantum mechanics are non-deterministic, such that each knowledge of the whole state of the universe could not be used to predict exactly the next state of the universe, but only a probability distribution for the next state of the universe. (But Drescher endorses an interpretation of quantum mechanics that preserves determinism, which is the subject of the next chapter.) Finally, special relativity says that no time-axis is preferred, so of course the time-axis used in the box merely represents some chosen time-axis. The box of the universe would look different if we chose a different time-axis. But the analogy of the box to the real universe is close enough to illustrate what Drescher wants to say about the nature of time.

Drescher notes that the box-universe view

contrasts sharply with our perception of time. To us, there is always a present moment that is somehow more real than the past and the future. The past is just a memory, the future just a potentiality. And crucially, which moment is the present one changes, moving steadily forward in time. It is as though the cross sections in the… box were indeed frames in a reel of film, and the film is being shown one frame at a time – the present frame.

Indeed, we can imagine another universe analogy that seems to fit better with how we experience time than the box-universe view does. In this universe

successive frames are generated (by a process external to the universe) on the fly and quickly discarded, each frame computed from the previous one using the laws of physics. There is only one frame at a time, just as in our intuitive model of the progression of time.

But here’s the thing: both versions of the universe are equally compatible with our experience of time:

Since all depicted events are the same in both versions, it follows… that if either version contains beings like ourselves who perceive an apparent flow of time as you and I do, they will do so and say so in both versions of the universe (because their perceptions, and their commentary on those perceptions, are among the events identically depicted in the two versions). Most importantly, they will do so for the same reason in both versions – namely, because their doing so is somehow part of what their universe’s laws of physics ultimately dictate will happen.

But the laws of physics give no support to the notion that there is a process external to the universe that generates each frame, one at a time, and discards the one just before it. We have no reason to posit such process. And since both models of the universe fit our experience, we can go with the simpler hypothesis.

But golly, it just feels like time flows from one moment to the next. Why would we feel that way, if that is not the universe physics describes? Drescher returns to this after considering another paradox.

The Direction of Time

Another paradox is this: Why does time seem to point in one direction? The laws of physics are symmetric between past and future, so why should time move in only one direction – from the past into the future? Why is time asymmetric while space is symmetric?

Drescher claims that

The underlying symmetry is real, but there is also something real about the perceived asymmetry. And it is precisely by… figuring out how the symmetric laws give rise to the perceived asymmetry [that] we can understand how the two are compatible.

Thus, the strategy below is to construct a simple, artificial universe that has time-symmetric laws, and to show that perplexingly time-asymmetric events do somehow arise from those laws.

To begin, consider a video of two billiard balls bouncing off each other. The 6 ball comes from the left edge of the screen, the 8 ball comes from the right edge of the screen, they collide, and the 6 ball is ejected out the top of the frame and the 8 ball disappears out the bottom of the frame. Now consider the same video in reverse: The 8 ball appears from the bottom of the frame and the 6 ball appears from the top of the frame. They collide, ejecting the 6 ball out the left edge of the frame and the 8 ball out the right edge of the frame.

Which video is being played forward in time, and which one is being played backward in time? If what I’ve described is all you see in the video, there would be no way for you to tell, because the laws of physics are time-symmetric.

But now, consider a different video. In this video you see a bunch of small balls bouncing around within the frame. So far, you have no way of knowing whether this video is being played forward or backward in time. Suddenly, a giant ball rolls through the frame, leaving behind it a “wake” that is later filled in again by the smaller balls, still bouncing around. Now you can tell the video is playing forward in time:


The key to understanding the direction of time is entropy.

Consider a large collection of particles:

It turns out there are vastly more [possible] configurations with an approximately uniform distribution than [possible] configurations with areas of conspicuous concentration or sparseness. For example [in a Newtonian universe] there are vastly more… arrangements that are roughly uniform than exhibit sparse “wakes”… Thus, we expect a wake formed by the passage of a giant [ball] to fill in as the random motions of the [smaller balls] tend toward arrangements of greater entropy [meaning, less order]. Likewise, we do not expect wakes to form spontaneously.

Of course, entropy can decrease locally, but “only at the cost of a greater increase elsewhere.” So the direction of time is observed by an average increase in entropy.

How can we explain this? It is tempting to appeal to statistics: higher-entropy states are by definition more numerous than lower-entropy states, and so more likely to be achieved at random, and thus more likely to result when particles are reshuffled by random collisions. But this explanation doesn’t work, because it implies that running time backward should also lead to higher-entropy states. But that’s not what happens.

A better explanation for why entropy increases with time is to appeal to the initial state of the universe. If the universe began in a state of extremely low entropy, and after that, entropy is highly likely to increase just by chance.

But we haven’t solved the paradox yet:

Consider a time-slice of the universe a few moments after the initial state. Entropy has increased some, but we still find a very low-entropy arrangement… Why, then, do we not see an increase in entropy when we apply physics backward from that low-entropy state, as we see when we apply physics forward? Why do we instead see decreasing entropy… when we watch backward from there for a few moments?

But wait a minute. Maybe we’re looking at this too simply. The seemingly “forward” direction is not a fixed direction. Rather, it can be seen as a pair of opposite directions, both pointing away from the initial state:

After all, what we see as we watch the movie backward past the initial state is identical to what we would see watching the movie forward if each object in the initial state had been assigned the negative of whatever velocity it in fact had…

Now we can see that the “futureward” direction, the “increasing entropy” direction, is not really a “forward” direction specifically but instead an away-from-the-initial-state direction. Drescher explains:

Just as terrestrial up… once seemed to be a single direction – back when the earth was thought to be flat – but later turned out ot be all directions pointing away from the center of the earth, so too does futureward (the temporal direction [of increasing entropy]) turn out… to consist of both directions away from the initial state…

Thus, neither the physical laws nor the initial state itself needs to have any time symmetry to account for the seeming time asymmetry of [experience]… [there is] an entirely symmetric arrangement with respect to the two directions [on either side of the initial state].

Still, there’s something special about the initial state. Suppose we took some other time-slice and designated it as the initial state. We would no longer see entropy increasing on both side of that “initial state.” As Drescher puts it, “Merely moving the label ‘initial’ to one of the other states does nothing to change what’s already depicted in the spacetime of the universe.”

Again, we will be tempted to say that what is special about the initial state is its extremely low entropy. But Drescher disagrees:

…it is not the initial state’s entropy level per se that distinguishes it as the point from which the apparent arrows of time emanate; rather, that distinction comes from the lack of coordination among the constituent objects’ states.

What he means is this: The positions of particles in the initial state are defined (whether randomly or otherwise) independently of the time-slice on either side of the initial state. As soon as you move in either direction of the initial state, the particles start interacting with each other and affecting each other. They begin to “coordinate”:

It is because of… that coordination that if we were to run the universe backward from that subsequent state – applying laws to generate each successive previous state rather than each next one – we would find [small balls] “conspiring” to get out of the way in advance of the passage of each [big ball]. That conspiracy would be unlikely to the point of virtual impossibility if it were to unfold from applying physical laws to a universe-state generated at random, because very few possible configurations lead to that spontaneous evacuation compared ot the exponentially vast number that do not.

Drescher recaps:

The time asymmetry in the events we perceive is not really between one time-direction and the other… Rather, the asymmetry is between the direction away from the initial (uncoordinated) state and the direction toward the initial state. And that asymmetry is itself symmetric with respect to the positive and negative temporal directions (since the futureward arrow bifurcates, pointing away from the initial state in both the positive and negative directions). Because of that symmetry with respect to the positive and negative temporal directions, the perceived events are not inconsistent at all with the underlying laws that are symmetric with respect to the positive and negative directions.

If my summary is unclear, which I suspect it is, please do read the second chapter of Drescher’s book, which toward the end contains another thought experiment which may help explain the “coordination” issue. Also see David Albert, Time and Chance.

Back to the Flow of Time

Let us return at last to the question of what creates the impression of a flow of time:

…to move a minute into the future, you need only wait a minute, and there you are. Not so with moving into the past. But why the difference? Could you not, after all, just wait -1 minute and then find yourself a minute earlier? If we define waiting n minutes simply as comparing your present state to your state n minutes from the present, then it is indeed just as easy to wait -1 minute as it is to wait +1 minute: you simply compare your present state to your state in -1 minute, that is, a minute ago.

Surely, though, comparing your present state to your state a minute ago does not correspond to what we think of as waiting from now until that other state. The notion of waiting n minutes thus smuggles in some additional meaning beyond a mere comparison between the present state and the state n minutes from the present. The additional meaning is intuitively clear: to wait entails in part that at the end of the wait, you can remember the beginning of the wait and the events in between.

Thus, the version of you at 10:00 can anticipate, but cannot remember, what it will be like at 10:01 the same morning. The version of you at 10:01 can remember what it was like at 10:00… This subjective ordering of time, based on the sequence of inclusions of memory, points in the same temporal direction as the apparent futureward direction that is exhibited by diverse physical phenomena such as wakes, waterfalls, and splattering eggs – and not coincidentally… any mechanism for memory harnesses some such physical process to make its recordings, so it too points in the same direction.

From the point of view of physics, with its static spacetime, there is merely a collection of different versions of you, thinking and saying different things at different moments. Nothing ever designates one of those moments as the present and then changes the designation, sliding it futureward along the time axis, implementing a flow of time. But there is a sequence defined by the inclusion of memories. The version of you at one moment has memories of the versions of you of many previous moments… and no version remembers any of the future moments’ versions…

…The distinction between memory and anticipation imposes a subjective ordering of the moments we experience, creating the illusion that time itself flows in sequence according to that ordering. In reality, though, the laws of physics prescribe instead a collection of different temporal versions of ourselves, some remembering others, but all sitting statically in spacetime, with no flow of time at all.

Of course, we need not stop talking of time as if it flows as we go about through our days, as long as we understand it really doesn’t work that way – just as we may talk about the sun “rising” and “setting” even though we know it does neither.

But if physicists are right about time – that all events are just sitting there already, then what room is there for our “choices” to “change” anything? We’ll discuss that later. First, we must tackle quantum mechanics.

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{ 15 comments… read them below or add one }

Bill Maher September 8, 2010 at 6:28 am

For anyone interested, Sean Carroll wrote an entire book on this subject.

It is a fun read.


MichaelPJ September 8, 2010 at 8:22 am

Do you ever hear about/read a book and then think “Oh shit, he wrote the book I was going to write (when I got around to it :P)”. I’m getting that vibe from this book. Bastard. Definitely going to read it, though, looks fascinating!


Garren September 8, 2010 at 9:16 am

Definitely interested in the Drescher book now.

Two observations:

* While it may seem like this ‘whole reel’ style time is a simpler hypothesis than ‘frame creation/discarding’ style because the former is static overall, it also implies a much more populated ontology. To use the analogy, a reel takes up more space than a frame.

* I wonder if the ‘whole reel’ version of time is attractive to Atheists because it allows for a kind of eternal existence for human beings. (Not implying that’s the only thing going for it; more of a perquisite.)


Mindyourmind September 8, 2010 at 9:34 am

My “Good and Real” is just sitting there in my study, next in line in my reading list. Can’t wait.


lukeprog September 8, 2010 at 9:56 am

Yeah, Carroll’s book will be enjoyable to anyone who liked Brian Green’s bestsellers on contemporary physics.


Julia Galef September 8, 2010 at 11:34 am

Luke, I love “Good and Real” — so glad you’re blogging it!
Drescher makes some pretty ambitious arguments in the later part of the book, about Newcomb’s Paradox and morality, which ultimately I just couldn’t get behind (although they’re fun to chew over). But the first part of the book, in which he’s talking about how to clarify your thinking and resolve paradoxes, was just so refreshing. I kept smacking the page and exclaiming “Yes, THANK you!”


Reginald Selkirk September 8, 2010 at 11:49 am

I’ve seen things you people wouldn’t believe. Attack ships on fire off the shoulder of Orion. I watched c-beams glitter in the dark near the Tanhauser Gate. All those moments will be lost in time, like tears in rain. [pause] Time to die.


Tony Hoffman September 8, 2010 at 12:09 pm

When will the seemingly endless stream of cool tidbits that people are writing about end here? When!?!?


lukeprog September 8, 2010 at 12:38 pm


That was precisely my reaction to the book. :)


Bill Maher September 8, 2010 at 5:14 pm


You rule for quoting Blade Runner.


cl September 8, 2010 at 5:38 pm

If my summary is unclear, which I suspect it is,

Parts of it were clear, all of it was interesting, but I was wondering what “the bottom line” was, or if there even was one. What was the main point you wanted us to take from the post? Can you write it as a single sentence?


Lamplighter Jones September 8, 2010 at 6:19 pm

Re: Symmetry/asymmetry.

Are the various forces (gravity, electromatetism, etc.) time-symmetric? Wouldn’t gravity appear to repel objects if time was reversed? That’s my intution, but I was never very good at this sort of thing.


Beelzebub September 9, 2010 at 2:40 am

Wouldn’t gravity appear to repel objects if time was reversed?

Picture something falling to earth from a point way out in space. It starts out stationary and picks up speed faster and faster (ignore friction). Eventually it collides with the surface at its surface “escape velocity.” Now reverse time. You see an object propelled off the surface at its escape velocity which moves slower and slower as it travels out into space, the exact inverse of its motion coming in.

Granted, the fact that an object suddenly changed from zero to finite velocity would break other laws of physics, but you can’t tell from the film which direction is forward or backward.


Lampligther Jones September 9, 2010 at 9:41 am

Thanks Beelzebub. I guess it makes more sense when you think of gravity in terms of geodesics rather than in terms of “acceleration due to gravity.” It seems like geodesics are time-symmetric, while it seems like “acceleration due to gravity” is time-anti-symmetric. Of course, if first derivatives all get multiplied by (-1) when you reverse time, then second derivatives should remain unchanged, so forces also look time-symmetric when explained in terms of acceleration.


Yair September 10, 2010 at 10:22 am

Sounds good. Looking forwards to hear what he says about QM, as I’m an advocate of MWI over hidden variables.


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