Time asymmetry. was: This Week's Finds (Week 25)
john baez
>In article <2d5kpe$8...@nntp.ucs.ubc.ca> isr...@math.ubc.ca writes:
>>If it weren't for the fact that the universe started with very low entropy,
>>stones would neither fly into nor out of ponds, because everything would be
>>pretty much in a state of thermal equilibrium. All you would see would be
>>small fluctuations due to chance, and these would look more or less the same
>>forwards as backwards.
>Actually, you wouldn't see anything at all, since you could not be there
>to see anything. The anthropic principle seems to be quite relevant to
>this issue. Not satisfying, but relevant.
Of course Israel would be right if instead of "you'd see" he'd said
"that would occur." As for the anthropic principle, it is indeed true
that "observers" of the kind we know and love can only hang out in
highly nonequilibrium situations. Still, as always with the anthropic
principle, it would be dangerous to be satisfied with it as an
explanation and give up looking for other insights. The arrow of time
is quite possibly a very big clue when it comes to understanding
cosmology. E.g., it seems (to me) to fit in better with a cosmology
with big bang and no big crunch than the symmetric big bang/big crunch
cosmology implicit in Hawking's "no boundary condition" proposal for the
wavefunction of the universe. (One can however try to wiggle out of this as
Gold did by proposing a cosmology in which there is low entropy at both
"ends".) This is connected with the "missing mass" problem and other
juicy cosmology puzzles, so it is probably worth pondering a bit more.
Ron Maimon
|>
|> Of course Israel would be right if instead of "you'd see" he'd said
|> "that would occur." As for the anthropic principle, it is indeed true
|> that "observers" of the kind we know and love can only hang out in
|> highly nonequilibrium situations. Still, as always with the anthropic
|> principle, it would be dangerous to be satisfied with it as an
|> explanation and give up looking for other insights.
Not only dangerous, but in this case, wrong.
The anthropic principle can only be used to justify just enough
lack-of-entropy so that we can exist, not an iota more. That would
mean, as Feynman said so eloquently, that everytime astronomers point
their telescopes someplace new, we would expect to see objects in
thermal equilibrium. Weve been looking out at new things all the time,
and this is never the case, so there has to be some other reason why
the entropy of our region of the universe is low.
Ron Maimon
john baez
I was going to mention this but it seemed a secondary point, plus I
thought of a possible counterargument, which I didn't want to get
entangled with. But since you seem interested, it's this. Perhaps the
probability of smart life forming is so low that there needs to be lots
and lots of the universe that looks rather like our patch in order for
one civilization (ours) to form.... e.g., out to as far as we can see
now, or farther. Of course, why couldn't there be occaisional *patches*
of thermal equilibrium? Etc. etc. - this kind of thing seems pretty
tiring to me.
David Wayne Ring
>>The anthropic principle can only be used to justify just enough
>>lack-of-entropy so that we can exist, not an iota more. That would
>>mean, as Feynman said so eloquently, that everytime astronomers point
>>their telescopes someplace new, we would expect to see objects in
>>thermal equilibrium. Weve been looking out at new things all the time,
>>and this is never the case, so there has to be some other reason why
>>the entropy of our region of the universe is low.
>
>I was going to mention this but it seemed a secondary point, plus I
>thought of a possible counterargument, which I didn't want to get
>entangled with. But since you seem interested, it's this. Perhaps the
>probability of smart life forming is so low that there needs to be lots
>and lots of the universe that looks rather like our patch in order for
>one civilization (ours) to form.... e.g., out to as far as we can see
>now, or farther. Of course, why couldn't there be occaisional *patches*
>of thermal equilibrium? Etc. etc. - this kind of thing seems pretty
>tiring to me.
This seems to me to be unlikely. By how much do we improve our odds of
existing by having 10^20 of extra stars around? A factor of 10^20 of course.
This is about 40 units of entropy! Hardly enough to explain why a rock
falls downhill instead of up. A bit handwavy perhaps, but look at it this
way: you would not be _too_ surprised if out of 10^20 rocks, one were to roll
uphill.
As far as an anthropic principle explaining low entropy, I would say it is
probably inevitable, but we don't know enough yet to give the details.
On the other hand, I do not take the view that the AP can apply directly
to explain the enormous low entropy of the universe, but can help to
'direct' the early universe into a scenario which produces low
entropy naturally, an inflationary model, perhaps.
Dave Ring
Cd...@phys.tamu.edu
john baez
>john baez <ba...@guitar.ucr.edu> wrote:
>>>The anthropic principle can only be used to justify just enough
>>>lack-of-entropy so that we can exist, not an iota more. That would
>>>mean, as Feynman said so eloquently, that everytime astronomers point
>>>their telescopes someplace new, we would expect to see objects in
>>>thermal equilibrium. Weve been looking out at new things all the time,
>>>and this is never the case, so there has to be some other reason why
>>>the entropy of our region of the universe is low.
>>I was going to mention this but it seemed a secondary point, plus I
>>thought of a possible counterargument, which I didn't want to get
>>entangled with. But since you seem interested, it's this. Perhaps the
>>probability of smart life forming is so low that there needs to be lots
>>and lots of the universe that looks rather like our patch in order for
>>one civilization (ours) to form.... e.g., out to as far as we can see
>>now, or farther. Of course, why couldn't there be occaisional *patches*
>>of thermal equilibrium? Etc. etc. - this kind of thing seems pretty
>>tiring to me.
>This seems to me to be unlikely. By how much do we improve our odds of
>existing by having 10^20 of extra stars around? A factor of 10^20 of course.
>This is about 40 units of entropy! Hardly enough to explain why a rock
>falls downhill instead of up. A bit handwavy perhaps, but look at it this
>way: you would not be _too_ surprised if out of 10^20 rocks, one were to roll
>uphill.
I *really* don't understand this argument. 40 extra units of entropy?
(Entropy being an extensive quantity, 10^20 times as big means 10^20
times as much entropy, or, if one prefers, the fact that a region 10^20
times as big as our solar system has entropy X less than it would in
equilibrium means that there is 10^20 times X less entropy around than
there would be if the universe were in equilibrium.) 10^20 rocks???
I actually would be quite shocked if out of 10^20 rocks *around here*
one were to roll uphill; I imagine this has nothing to do with your
point (since I don't understand your point at all) but I bet a standard
thermodynamical calculation would show the probability of the heat
energy of a rock turning into motion sending it uphill would be far far
lower than 1/10^20.
>As far as an anthropic principle explaining low entropy, I would say it is
>probably inevitable, but we don't know enough yet to give the details.
I doubt that any time in the next few centuries or so will we understand
the conditions under which intelligent life arises well enough to
calculate its probabilities of its formation well enough to make the
anthropic principle into a useful tool.
>On the other hand, I do not take the view that the AP can apply directly
>to explain the enormous low entropy of the universe, but can help to
>'direct' the early universe into a scenario which produces low
>entropy naturally, an inflationary model, perhaps.
Many people have argued that an inflationary model does not really
produce low entropy naturally. I am inclined to sympathize, but I have
neither references nor enough knowledge to argue well about this.
David Wayne Ring
>>>probability of smart life forming is so low that there needs to be lots
>>>and lots of the universe that looks rather like our patch in order for
>>>one civilization (ours) to form.... e.g., out to as far as we can see
>
>>existing by having 10^20 of extra stars around? A factor of 10^20 of course.
>>This is about 40 units of entropy! Hardly enough to explain why a rock
>>falls downhill instead of up. A bit handwavy perhaps, but look at it this
>>way: you would not be _too_ surprised if out of 10^20 rocks, one were to roll
>>uphill.
>
>I *really* don't understand this argument. 40 extra units of entropy?
>(Entropy being an extensive quantity, 10^20 times as big means 10^20
>times as much entropy, or, if one prefers, the fact that a region 10^20
>times as big as our solar system has entropy X less than it would in
>equilibrium means that there is 10^20 times X less entropy around than
>there would be if the universe were in equilibrium.) 10^20 rocks???
I shouldn't post when I'm in a hurry. :-)
In order to exist we need a certain amount of entropy lower than equilibrium
in our neighborhood (solar system for example). Call this amount Y. Y is a
measure of the unlikeliness of this local fluctuation. Given one such unlikely
solar system, let Z be the probability that intelligence forms. The anthropic
principle says that our universe may be in an unlikely state if that state
is necessary for us to exist. But it must take the most likely (or nearly)
such possibility. I believe the phrase was "not one iota more...". Imagine
two strategies: 1) Have a universe with one fluctuation and have this
fluctuation produce intelligence. Probability exp[-Y]*Z. 2) Have lots of
solar systems so that we have lots of chances. Probability
exp[-10^20*Y]*Z*10^20. I leave it as an exercise which is bigger.
40 units of entropy is what you get taking the 10^20 inside the bracket.
It is meant to be compared with the entropy needed for all those solar
systems.
As far as the rock goes:
If the anthropic principle needed a rock to roll uphill, instead of a
solar system, then your argument might work. As you point out, this is
wrong. I got my orders of magnitude confused. Perhaps a speck of dust
is more appropriate. :-)
>>As far as an anthropic principle explaining low entropy, I would say it is
>>probably inevitable, but we don't know enough yet to give the details.
>
>I doubt that any time in the next few centuries or so will we understand
>the conditions under which intelligent life arises well enough to
>calculate its probabilities of its formation well enough to make the
>anthropic principle into a useful tool.
We don't need to know _all_ the conditions for life, to apply the AP to
the arrow of time, we just need to know that _the arrow_ is necessary.
Then the universe MUST select a scenario which has low entropy. Whether
the AP is necessary depends on how natural such a scenario is.
>>On the other hand, I do not take the view that the AP can apply directly
>>to explain the enormous low entropy of the universe, but can help to
>>'direct' the early universe into a scenario which produces low
>>entropy naturally, an inflationary model, perhaps.
>
>Many people have argued that an inflationary model does not really
>produce low entropy naturally. I am inclined to sympathize, but I have
>neither references nor enough knowledge to argue well about this.
Personally, I don't know anything about it. It was just an example.
It is certainly not inconcievable that human imagination can come up
with some such scenario (especially considering that one must almost
certainly exist)
Dave Ring
Cd...@phys.tamu.edu
john baez
In article <2dhn92$3...@TAMUTS.TAMU.EDU> dwr...@TAMUTS.TAMU.EDU (David Wayne Ring) writes:
>john baez <ba...@guitar.ucr.edu> wrote:
>>>>probability of smart life forming is so low that there needs to be lots
>>>>and lots of the universe that looks rather like our patch in order for
>>>>one civilization (ours) to form.... e.g., out to as far as we can see
>>>This seems to me to be unlikely. By how much do we improve our odds of
>>>existing by having 10^20 of extra stars around? A factor of 10^20 of course.
>>>This is about 40 units of entropy!
>>I *really* don't understand this argument. 40 extra units of entropy?
>>(Entropy being an extensive quantity, 10^20 times as big means 10^20
>>times as much entropy, or, if one prefers, the fact that a region 10^20
>>times as big as our solar system has entropy X less than it would in
>>equilibrium means that there is 10^20 times X less entropy around than
>>there would be if the universe were in equilibrium.)
>In order to exist we need a certain amount of entropy lower than equilibrium
>in our neighborhood (solar system for example). Call this amount Y. Y is a
>measure of the unlikeliness of this local fluctuation. Given one such unlikely
>solar system, let Z be the probability that intelligence forms. The anthropic
>principle says that our universe may be in an unlikely state if that state
>is necessary for us to exist. But it must take the most likely (or nearly)
>such possibility. I believe the phrase was "not one iota more...". Imagine
>two strategies: 1) Have a universe with one fluctuation and have this
>fluctuation produce intelligence. Probability exp[-Y]*Z. 2) Have lots of
>solar systems so that we have lots of chances. Probability
>exp[-10^20*Y]*Z*10^20. I leave it as an exercise which is bigger.
Okay, good. Note that you are hinting at what may be a novel sharpening of
the anthropic principle. Basically, it's this: to calculate the
expectation value of an observable, restrict to the ensemble of
universes in which intelligent life exists and calculate its average
over all these.
On a tangent...
These days I prefer to skip reference to the anthropic principle and
say, "this is the expectation of the observable given that intelligent
life exists." We can typically get a better answer by inputting more
information into the "given," so it is unclear what the special status
of the anthropic principle is, unless one is fixated on the notion that it's
ones intelligence and only that that is a necessary condition for
worrying about such issues. It might be better to calculate
expectation values given that life which believes in the anthropic
principle exists. Whether such life is necessarily intelligent is unclear.
Or better yet, it might be better to calculate expectation values
given that life that calculates expectation values given that life that
calculates... .... ...exists exists exists. A complicated fixed point
problem for future generations to solve.
Warren G. Anderson
>
> Okay, good. Note that you are hinting at what may be a novel sharpening of
> the anthropic principle. Basically, it's this: to calculate the
> expectation value of an observable, restrict to the ensemble of
> universes in which intelligent life exists and calculate its average
> over all these.
I don't think this is too new an idea. Don Page (the person here who likes
to bring up the anthropic principle the most) has expressed the idea of
this kind of usage on several occassions (as far as I can make out). The
problem is that it is no more straightforward to put a measure on
the set of all universes that support intelligent life than it is to put
a measure on the set of all universes. In either case, there is no way I
know of to measure probability with anything but the vaguist of guesses,
given that we are necessarily restricted to basing our imagined ensemble
on a sample of one. This is why I find the use of the weak anthropic
principle so much less disconcerting. We have some basis for comparing the
densities of places and times like ours to all the places and times in
the universe, so we can realistically estimate what the probability
of seeing what we see is with respect to both the ensemble of all
places and times and with respect to places and times that could
support life. After all, the anthropic principle simply a balance
against the overuse of the Copernican principle. The Copernican principle
is sometimes taken to imply that we are in the most generic of circumstances.
The anthropic principle simply reminds us that we can at best expect to be
in the most generic of circumstances that allow intelligent observers.
Without a measure of probability, what does generic mean?
--
########################## _`|'_ ##############################################
## Warren G. Anderson |o o| "... for its truth does not matter, and is ##
## Dept. of Physics ( ^ ) unimaginable." -J. Ashbery, The New Spirit ##
## University of Alberta /\-/\ (ande...@fermi.phys.ualberta.ca) ##
SCOTT I CHASE
>This seems to me to be unlikely. By how much do we improve our odds of
>existing by having 10^20 of extra stars around? A factor of 10^20 of course.
>This is about 40 units of entropy! Hardly enough to explain why a rock
>falls downhill instead of up. A bit handwavy perhaps, but look at it this
>way: you would not be _too_ surprised if out of 10^20 rocks, one were to roll
>uphill.
I, for one, would not be astonished. :-)
-Scott
-------------------- Physics is not a religion. If
Scott I. Chase it were, we'd have a much easier
SIC...@CSA2.LBL.GOV time raising money. -Leon Lederman
SCOTT I CHASE
>After all, the anthropic principle simply a balance
>against the overuse of the Copernican principle. The Copernican principle
>is sometimes taken to imply that we are in the most generic of circumstances.
>The anthropic principle simply reminds us that we can at best expect to be
>in the most generic of circumstances that allow intelligent observers.
>Without a measure of probability, what does generic mean?
Furthermore, with only one data point in the sample, how are we to know
what conditions are inconducive to the existence of intelligent observers?
If you mean "homo sapiens," then we are, in some sense, in the only place in
the Universe where we could have evolved. But if you mean a more
general intelligence, then I would argue that we have barely the foggiest
clue about what's out there and why. So the anthropic principle
tells us very little. I.e., exactly what conditions are you sure you
can rule out as impossible for the inhabitation by intelligent beings?
We can make educated guesses, but barely more than that. Even the simpler
question of the probability of any kind of life at all outside the
solar system has "experts" giving estimates many orders of magnitude
different from one another.
Ron Maimon
|>
|> I shouldn't post when I'm in a hurry. :-)
|>
|> In order to exist we need a certain amount of entropy lower than equilibrium
|> in our neighborhood (solar system for example). Call this amount Y. Y is a
|> measure of the unlikeliness of this local fluctuation. Given one such unlikely
|> solar system, let Z be the probability that intelligence forms. The anthropic
|> principle says that our universe may be in an unlikely state if that state
|> is necessary for us to exist. But it must take the most likely (or nearly)
|> such possibility. I believe the phrase was "not one iota more...". Imagine
|> two strategies: 1) Have a universe with one fluctuation and have this
|> fluctuation produce intelligence. Probability exp[-Y]*Z. 2) Have lots of
|> solar systems so that we have lots of chances. Probability
|> exp[-10^20*Y]*Z*10^20. I leave it as an exercise which is bigger.
|>
yup youre right. The anthropic principle may be able to explain why the
entropy of the universe is so low. I am starting to believe it.
What you have to show is that out of all the possible universes, most of the
intelligent beings live on ones with low entropy initial conditions. That
doesn't seem as impossible as I first thought...
Ron Maimon
Ranjan S Muttiah
Let t = f(T).
dt/dT = f'(T).
mv(t) = P
m dx/dt = P
m dx/dT *dT/dt = P
m V(T) = f'(T) P
Momentum is a function of some general function f'(T) i.e.,
t = f(T) + k for arbitary k. Therefore, momentum is time
independent. No time assymmetry here folks!
:-).
Find the problem.
Jon J Thaler
I only want to address one aspect of the discussion of the anthropic
principle, so I've deleted most of DWR's post.
dwr...@TAMUTS.TAMU.EDU (David Wayne Ring) says:
>
>In order to exist we need a certain amount of entropy lower than equilibrium
>in our neighborhood (solar system for example). Call this amount Y. Y is a
>measure of the unlikeliness of this local fluctuation. Given one such unlikely
>solar system, let Z be the probability that intelligence forms. The anthropic
>principle says that our universe may be in an unlikely state if that state
>is necessary for us to exist. But it must take the most likely (or nearly)
>such possibility. I believe the phrase was "not one iota more...". Imagine
>two strategies: 1) Have a universe with one fluctuation and have this
>fluctuation produce intelligence. Probability exp[-Y]*Z. 2) Have lots of
>solar systems so that we have lots of chances. Probability
>exp[-10^20*Y]*Z*10^20. I leave it as an exercise which is bigger.
Calculation of probabilities requires confidence that one knows the
a priori situation. In the case of cosmology, such confidence is
unwarranted. One can obtain any result one wants by changing some
underlying assumptions which are not constrained by data.
For example, the mechanism of baryogenesis (why the universe has
more protons than antiprotons) is not understood. It is possible
that baryogenesis requires a low entropy initial condition, in which
case this whole discussion of thermodynamic fluctuations becomes
irrelevant - every universe with matter would be a low entropy one.
For all we know, physical law requires this.
Archimedes Plutonium
The difference for me in writing a textbook on physics rather than mathematics or chemistry or biology, is that I have to invent new concepts, not there before. For example, I replace the entire 4 Maxwell Equations with 6 Equations of AP - EM theory, and making 6 laws. And reinventing the Electromagnetic Spectrum. Of course in AP physics, a atom has no nucleus for the inside of an atom consists of true electrons as muons thrusting through a proton torus tube producing Dirac magnetic monopoles by converting Space into electricity. All of the Maxwell equations are wrong in some aspect, worst of all is the Gauss's law of no magnetic monopole, that is the worst of them. And of course the particle that JJ Thomson found in 1897 was not the atom's electron, but was what Dirac was searching for by the 1930s-- the magnetic monopole as 0.5MeV particle.
So, well, in writing my TEACHING TRUE PHYSICS, 1st year College, I have to produce an entirely different book of teaching physics, one that no one who took College Physics in the past can recognize.
I have made it student friendly by making mathematics ultra ultra easy. And it is the shameful mathematics of Old Physics that has turned many students off of and away from physics.
As promised, the world needs the successor textbook of Physics since the Feynman Lectures of the 1960s, and that is what AP's textbook promises. The New Age physics textbook that will carry physics forward for the next 30 years, perhaps 1,000 years if fate is kind to me.
AP, King of Science, especially Physics