running time backward: a thought experiment
David Madore
I wish to describe a thought experiment and then ask two questions,
one on physics and one on epistemology (but related to physics) about
it. Thought the thought experiment itself is rather simple, I will
describe it at a certain length in order to emphasize certain points.
There is one essential prerequisite to the experiment: namely that the
laws of physics are completely deterministic in both future and past,
and reversible. By "reversible", I do not require that the laws
remain identically the same when time is reversed, but merely that
there exist certain laws predicting the past from the present, having
roughly the same form as the laws predicting the future from the
present. For example, CPT invariance is quite sufficient, T
invariance is not necessary. However, all aspects of non-determinism
or irreversibility in the laws of physics, whether in thermodynamics
or in quantum mechanics (e.g., measurement of observables), must be
statistical in nature, not in the "true" laws of physics, or else this
thought experiment will be meaningless. Beyond that, there are little
constraints on the laws of physics, and I have even tried the
experiment on a (reversible) cellular automaton with some interesting
results (and some nice pictures).
If you do not accept this prerequisite that the laws of nature are
deterministic and reversible in some form, there is no use going on
with reading. :-)
Here now is the experiment.
Call U our present Universe. Let t=0, the origin of time, be a moment
just after someone has dropped a light bulb and it has shattered on
the floor. Say the bulb was dropeed at t=-3s and just afteward it has
fallen on the floor and broken. But at t=0 the shards are still lying
there, waiting to be dumped away. At t=-3s, perhaps, Mr. John Doe
lets out an exclamation, something like "Oh dear! How clumsy of me!",
and at t=60s perhaps, Mr. John Doe cleans the mess.
Now consider a Universe U' much similar to ours. In fact, at t=0,
this Universe U' is absolutely identical to ours except for one small
fact: the pieces of glass from the broken light bulb are replaced by
other pieces of glass that are macroscopically indistinguishable from
the pieces in U (having the same position and temperature), but
microscopically quite different (and quite generic for this
macroscopic aspect).
If we evolve U and U' for t>0, we believe that, inside the forward
(future) light cone of the glass fragments, differences will exist and
will eventually diverge (this is the "butterfly" effect). However,
both the future of U and the future of U' seem quite "reasonable" to
us: for example, in both U and U', Mr. John Doe will remove the
splinters from the floor and perhaps fetch a new bulb or something of
the kind. Differences between U and U' for t>0, we expect, will occur
for seemingly "random" events, where a small perturbation can make a
big difference. On the whole, if an observer were to view the future
of U and that of U', she would have some difficulty deciding which
belongs to U and which to U'.
But now I have assumed that the laws of physics are reversible: this
means that from the initial condition at t=0 in U and U' I can
determine not only a future (t>0) but also a past (t<0).
As for the past of U, we know what it looks like: if we run time
backward (increase -t), we will see the glass fragments on the floor
come together to form a light bulb, which will rush up to Mr. Doe's
hand, while he is uttering (backward) something like "How clumsy of
me", and so on. We also know that, in the waterfall near the broken
bulb, the water will rush up from the basin to the fountain's mouth,
and similar strange phenomena. This happens because the state of U
for t=0 is extremely peculiar: it is a state for which entropy
_decreases_ in one direction of time (viz. t<0), an extremely special
state therefore. Although the laws of physics are, if not identical,
at least very similar, when time is reversed, phenomena happen in the
past (t<0) of U for t reversed (-t>0) that we have no chance of
reproducing in a laboratory (nobody can make water flow _up_
spontaneously from a basin).
Now these phenomena are wildly unstable: consider now the past of the
Universe U'. The first obvious difference we notice around t=-3s is
that the pieces of glass remain stupidly on the floor like all generic
pieces of glass do, and certainly do not try anything foolish like
becoming a light bulb. But of course this is not the only difference!
For t=-240s perhaps the light bulb was shining in the Universe U, and
it certainly does not shine - in fact, it does not even exist - in the
Universe U'. As a matter of fact, we are led to believe that the
seemingly (i.e., macroscopically) small difference we have introduced
between U and U' will wreak tremendous havoc when time is run
backward. All the very subtle - and highly unstable - equilibrium
that caused, e.g., waterfalls to flow _up_, is now broken and
waterfalls will very soon start flowing _down_ again, as they ought to
(except that I am talking for time reversed, i.e., -t increasing,
which means that if we view things for t increasing the waterfalls in
U' flow up, up to about t=0 when they start flowing down).
So I believe, and I hope I am not too much in error in this (and my
experiments with cellular automata seem to confirm my beliefs), that
the arrow of time, which in Universe U points toward increasing t, in
Universe U' points toward increasing t for t>0 and decreasing t for
t<0 - whatever this means. There is a time reversal for t=0 in
Universe U'.
Of course, this time reversal does not affect all things. It affects
waterfalls but does not affect, for example, celestial mechanics: the
Earth's path around the sun is, we are tempted to believe, very
similar in U and in U' - at least for t>t0 where t0 is the time of
formation of the solar system in U which should correspond to nothing
remarkable in U', or, if it does, more to the death of the sun than to
its birth. Also, the expansion of the Universe in U is preserved in
U' which means that the size of U' increases (as that of U) when t
increases, but that makes the "big bang" of U look more like a "big
crunch" around t=-15Gyr.
This leads me to my first question, which is, as I see it, a true
question of physics. Namely, what does U' actually "look like" for
t<0? I am concerned with several aspects. For example, how does the
waterfall look like around the point of time reversal? How fast does
the time reversal take place for macroscopic objects like a waterfall?
When does the Bethe cycle of the Sun change direction of time in the
Universe U'? And what happens to living organisms in U'? As to that
last question, if I may hazard a guess, it would be that microscopic
organisms do not care much for the direction of time and can live
quite happily through a time reversal, whereas more complex organisms
die quite rapidly and quite violently - but I would be curious to know
what a "death by time reversal" actually looks like. (Of course, I
call it "death" because I look at -t increasing, following the arrow
of time in U' in that region, but if we look at it with t increasing,
it is a very, very peculiar kind of "birth".)
At this point you can guess where I'm going next. I point out that
human beings in U', for t>0, are persuaded that their past is that
which actually happens in U. But they are utterly wrong. Mr. Doe in
Universe U' may think that he has been alive for 42 years, but in fact
mere seconds before he was a gooey mass of organic substances with
very little life-like properties; and all his memories are fake, are
made fake simply because I have replaced a little shard of glass by
another. A strange thought, is it not?
But things are even wilder than that. Consider our alien friends the
Alphacentaurians: living at a distance of four light-years from us,
the Alphacentaurians observe the Earth with their powerful telescopes
and record all of what is happening on it, of course with a four-year
delay due to the speed of light. Now in the Universe U, at t=-2yr,
the Alphacentaurians have observed Mr. Doe, alive and well (and aged
36) resting near his favorite waterfall, that is falling in the usual
direction. Note that this point of space-time (Alpha Centauri at
t=-2yr) is outside of the past _or_ future light-cone of the broken
light bulb at t=0. By causality we must conclude that U and U'
coincide completely at that point. So in U' the Alphacentaurians have
observed exactly the same thing about Mr. Doe, and conclude that
Mr. Doe exists and is well in shape at t=-6yr (and aged 36) and that
waterfalls fall like they are expected to fall; perhaps they even
observed the prophetic light bulb shining in its expected place. This
is, however, entirely false: it may be the way of things in Universe
U, but in Universe U' things are entirely different, and waterfalls
fall the other way. How strange: so why are the Alphacentaurians
seeing something that is simply wrong in their Universe? So even if
Mr. Doe goes to them and asks to see the recording (to get his mind
off these ridiculous theories about having been a gooey mass of
organic chemicals for t=-240s, let alone t=-6yr), he might see what he
hopes to see but it does not prove a thing. Can someone explain this
paradox?
Now I turn to the epistemological question. As I have said, Mr. Doe
in Universe U' is quite wrong about the way he pictures his past. I
moreover argue that Universes like U' are ___far___ more common than
those like U, because shards of glass are ___far___ more likely to
remain on the floor when they are there (whatever way time flows) than
to suddenly aggregate to form a light bulb. So how do I know that _I_
live in Universe U and not U' or similar? We might call Occam's rasor
for help, but my point is, precisely, that Universes like U' are far
more common than those like U, so it is far simpler a hypothesis to
imagine that we are in one like U' than one like U.
But the conclusion is embarrassing: we should believe that you, I, or
anybody alive at this time, has never been born in the sense that we
picture it, but came into existence by some kind of fiat, in a time
reversal instants from now. All our theories about the origin of
species, for example, are dead wrong: there has never been such a
thing as a dinosaur on this planet, nor Charles Darwin, for that
matter. :-)
Needless to say, one is tempted to be prudent in accepting such
conclusions.
But how do we escape them? Should we give up the reversibility of the
laws of physics to avoid problems? This seems like a cowardly thing
to do.
I would appreciate any light on this strange problem and experiment,
whether from the metaphysical or simply physical point of view.
---
David A. Madore
(david....@ens.fr,
http://www.eleves.ens.fr:8080/home/madore/ )
[Moderator's note: since this is sci.physics.research, let's
try to stick to the physical point of view. - jb]
Ed Fredkin
news:<GwOMZir1...@clipper.ens.fr>...
> I wish to describe a thought experiment and then ask two questions,
> one on physics and one on epistemology (but related to physics) about
> it. Thought the thought experiment itself is rather simple, I will
> describe it at a certain length in order to emphasize certain points.
[rest of post deleted]
You might get a better understanding of this problem by taking a look
at www.digitalphilosophy.org Introduction to Digital Philosophy,
Chapter 30 on DM (Digital Mechanics) and CPT.
In the SALT model cellular automaton there is t reversibility, which
results in the physics having CPT reversibility. Chapter 30 goes into
the microscopic happenings of how time gets reversed within the laws
of physics. The net result of stopping time, tinkering with something
and then restarting time ought to be basically the same whether time
is restarted in the forwards direction or the backwards direction!
The result is that something non-physical may have been done, and the
consequences would very likely spread out at velocity equal to c.
When discussing "something non-physical", we are inventing new science
fiction. However, like other good science fiction authors, such
invention can be done carefully or sloppily.
It is possible that a small amount of tinkering might have little
effect, but it is also likely that the effect might be as large as
imaginable. The main reason that the effect might be small has to do
with the conserved quantities remaining the same along with the chance
that the tinkering resulted in a physically realizable state. On the
other hand, the change might be the R-Pentomino of the rule, similar
to the first stage of the big bang... who knows? So the change might
not be limited to the butterfly effect; it all depends on the
relationship between the most microscopic process in physics, and
whether or not physics is robust enough to calmly carry on, in a more
or less normal fashion from any most microscopic initial condition.
This would more likely be the case if, in nature, every possible local
state can occur naturally. On the other hand, if only a subset of
local most microscopic states can occur naturally, then non-physical
tinkering is likely to produce a rift; a sphere that grows at the
speed of light (or faster) within which the laws of physics are not
the same as outside the sphere.
As to your 2 questions, did you really imagine that someone just
happens to know the correct answers? On the other hand, you may get a
lot of responses from people willing to ramble on about things they
don't really understand (like me).
Ed F
Patrick Van Esch
> experiments with cellular automata seem to confirm my beliefs), that
> the arrow of time, which in Universe U points toward increasing t, in
> Universe U' points toward increasing t for t>0 and decreasing t for
> t<0 - whatever this means. There is a time reversal for t=0 in
> Universe U'.
Let's say that this is a great plot for good science-fiction :-))
>
> Of course, this time reversal does not affect all things. It affects
> waterfalls but does not affect, for example, celestial mechanics: the
> Earth's path around the sun is, we are tempted to believe, very
> similar in U and in U' - at least for t>t0 where t0 is the time of
> formation of the solar system in U which should correspond to nothing
> remarkable in U', or, if it does, more to the death of the sun than to
> its birth.
There is however a major difference. When running t backwards,
in U as well as in U', you have a problem with radiation: the sun
is receiving photons from the universe, to convert He into hydrogen
again and so on. So U' for sufficiently large -t, and t decreasing,
does NOT look like a normal universe....
The sun appears like a "light sucker" in a focal point of some
remotely emitted radiation. This problem appears on a larger scale
in the whole universe, so things do not really look like a
gravitational big crunch.
I don't think that the replacement of the piece of glass will
end up reversing stellar processes...
There is also that other question: how did your changed piece
of glass get there without violating any laws of physics ?
If it came "from the future", then the microstate of that piece
of glass also is very peculiar and will evolve for t>0 into
something which put it there. And now one starts to see why
U' is so bizarre: in the PAST lightcone of that future event
which prepared our experiment, for t >> t1, everything has to
arrange so that this event is indeed prepared. That's why Mr.
Doe can appear out of a gooey in a few seconds and so on.
[...]
> Mr. Doe goes to them and asks to see the recording (to get his mind
> off these ridiculous theories about having been a gooey mass of
> organic chemicals for t=-240s, let alone t=-6yr), he might see what he
> hopes to see but it does not prove a thing. Can someone explain this
> paradox?
I think the paradox comes from the fact that there is only
one way to replace those pieces of glass in a way that doesn't
violate the laws of physics, at t = 0, and for t>0 and that
is: they "come in" from the future. But in that case, the
universe U' is actually normally seen with t evolving
from +inf down to t = 0.
However, now the laws of physics are not respected for t<0
(because where the hell did that light bulb come from :-).
You cannot just "stop the film", change something, and
"let it run again" without violating the laws of physics ;
once you've violated them, they shouldn't be consistent
anymore, of course !
A similar, much simpler, thing happens in electrodynamics:
the question, in classical EM, of: what happens when a
charge disappears suddenly ? will give
rise to a lot of paradoxes, because you simply violate
conservation of charge, which is build into the dynamics.
Here, the change of the microstate in your piece of
glass amounts to the same thing. Indeed, at the
exact moment t=0, the flip from the "bulb piece of glass"
into the "common piece of glass" means an enormous
violation of the laws of physics for every atom involved: they change
instantaneously position, momentum etc... (thinking classically).
So you have the laws of physics obeyed from
t = -inf -> t=0- and from t = 0+ to t = +inf, but
at t=0 there is a tremendeous violation.
>
> Now I turn to the epistemological question. As I have said, Mr. Doe
> in Universe U' is quite wrong about the way he pictures his past. I
> moreover argue that Universes like U' are ___far___ more common than
> those like U, because shards of glass are ___far___ more likely to
> remain on the floor when they are there (whatever way time flows) than
> to suddenly aggregate to form a light bulb.
Except that the laws of physics are violated at t=0 in those universes
U'.
> But the conclusion is embarrassing: we should believe that you, I, or
> anybody alive at this time, has never been born in the sense that we
> picture it, but came into existence by some kind of fiat, in a time
> reversal instants from now.
Philosophically, you cannot exclude the possibility of course that the
laws of physics have been violated 1 second ago in such a way that we
think they haven't. But the true application of Occam's razor, in my
opinion, is to say that there are no such violations. In that case,
your thought experiment cannot be executed.
cheers,
Patrick.
David Hillman
David Madore wrote:
> I wish to describe a thought experiment and then ask two questions,
> one on physics and one on epistemology (but related to physics) about
> it. Thought the thought experiment itself is rather simple, I will
> describe it at a certain length in order to emphasize certain points.
Basically this comes down to what I think is called "Hume's problem"
(David Hume, philosopher, several hundred years ago). He could see no
reason whatsoever why the state of the world outside of himself at a given
instant in time was any particular way. You might "remember" various
things, but that is just some state of your current self; who is to say
that those things actually happened? You might believe that you are in New
York City, but are you? Might you not be a brain in a vat on Alpha
Centauri, being fed various neural inputs by alien scientists? And so on.
All of this is seemingly in the realm of physical possibility. I disagree
with another poster who said that this was the problem with your thought
experiment. I heard a talk by Steven Weinberg some years back in which he
claimed that one of the two main principles of physics (unfortunately I
forget the other one) was that stuff on a Cauchy surface can be arranged
freely. (He had a name for this principle, but I forget that too.) It
seems a reasonable enough claim. Maybe not entirely freely, but at least
freely enough so that we could position your brain as it is now in one
place and surround it by a computer feeding you various neural inputs that
you are going to have in real life in the next five minutes, and then put
Alpha Centauri around that. Extend that to a whole Cauchy surface, evolve
it backwards and forwards in time, and you have a universe. (Or: replace
those glass shards with other glass shards.)
Given what you are experiencing right now, yes, you could be in any of a
presumably infinite number of possible universes. That's true even if we
don't imagine all these exotic possibilities. So how do you make a
decision? You make estimates of likelihoods. Somehow you weigh the
probabilities. You say things like: maybe the planet Earth is just a
momentary fluctuation, in which case it doesn't matter whether I take out
the garbage or not. But "probably" it isn't.
Does this probability business make any sense? Is there a natural
probability distribution over the set of possible universes? Who knows? We
don't even know what the set of possible universes is. But suppose that
there is one. Then it seems to me that any reasonable definition of
probabilities would rate a possible universe as being more probable if it
has a simpler description. The simplest description is roughly equivalent
to the lowest-entropy Cauchy surface, because specifying a Cauchy surface
plus the laws of nature gives you a universe. In your universe U' this
lowest entropy Cauchy surface is an extremely complicated object. In U it
is the big-bang singularity, which presumably is a very simple object. So
U is way more likely than U'.
Your assumption that a state like U' is much more probable than a state
like U just because there are more states like U' than U is just that: an
assumption. You are assuming some sort of rule about assigning
probabilities to possible universes which may be incorrect. (Not that I
have a clue about how one would know that a rule was correct, because I
don't.)
Charles Francis
<david....@ens.fr> writes
>If you do not accept this prerequisite that the laws of nature are
>deterministic and reversible in some form, there is no use going on
>with reading. :-)
>
>Here now is the experiment.
In so far as I can see you are just asking the standard question in
statistical mechanics, why does entropy increase? To we have the same
answer whether the universe is deterministic or not, and whether it is a
cellular automaton or not. Whichever way you run time an ordered
situation will become a disordered one by the application of statistics.
The reason entropy goes the way it does is because you can arrange for
an ordered initial condition by bringing in outside influences, but you
cannot arrange an ordered final condition in an isolated system.
Regards
--
Charles Francis