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Unformatted text preview: 46 Ratchet and pawl 46—1 How a ratchet works In this chapter we discuss the ratchet and pawl, a very simple device which
allows a shaft to turn only one way. The possibility of having something turn
only one way requires some detailed and careful analysis, and there are some very
interesting consequences. The plan of the discussion came about in attempting to devise an elementary
explanation, from the molecular or kinetic point of view, for the fact that there is
a maximum amount of work which can be extracted from a heat engine. Of
course we have seen the essence of Carnot’s argument, but it would be nice to ﬁnd
an explanation which is elementary in the sense that we can see what is happening
physically. Now, there are complicated mathematical demonstrations which
follow from Newton‘s laws to demonstrate that we can get only a certain amount
of work out when heat ﬂows from one place to another, but there is great difﬁculty
in converting this into an elementary demonstration. In short, we do not under
stand it, although we can follow the mathematics. In Carnot’s argument, the fact that more than a certain amount of work
cannot be extracted in going from one temperature to another is deduced from
another axiom, which is that if everything is at the same temperature, heat cannot
be converted to work by means of a cyclic process. First, let us back up and try
to see, in at least one elementary example, why this simpler statement is true. Let us try to invent a device which will violate the Second Law of Thermo
dynamics, that is, a gadget which will generate work from a heat reservoir with
everything at the same temperature. Let us say we have a box of gas at a certain
temperature, and inside there is an axle with vanes in it. (See Fig. 46—1 but take
T1 = T2 = T, say.) Because of the bombardments of gas molecules on the vane,
the vane oscillates and jiggles. All we have to do is to hook onto the other end of
the axle a wheel which can turn only one way——the ratchet and pawl. Then when
the shaft tries to jiggle one way, it will not turn, and when it jiggles the other, it
will turn. Then the wheel will slowly turn, and perhaps we might even tie a ﬂea
onto a string hanging from a drum on the shaft, and lift the ﬂea! Now let us ask
if this is possible. According to Carnot’s hypothesis, it is impossible. But if we
just look at it, we see, primafacie, that it seems quite possible. So we must look
more closely. Indeed, if we look at the ratchet and pawl, we see a number of
complications. First, our idealized ratchet is as simple as possible, but even so, there is a pawl,
and there must be a spring in the pawl. The pawl must return after coming off a
tooth, so the spring is necessary. Another feature of this ratchet and pawl, not shown in the ﬁgure, is quite
essential. Suppose the device were made of perfectly elastic parts. After the pawl
is lifted off the end of the tooth and is pushed back by the spring, it will bounce
against the wheel and continue to bounce. Then, when another ﬂuctuation came,
the wheel could turn the other way, because the tooth could get underneath during
the moment when the pawl was up! Therefore an essential part of the irreversibility
of our wheel is a damping or deadening mechanism which stops the bouncing.
When the damping happens, of course, the energy that was in the pawl goes into
the wheel and shows up as heat. So, as it turns, the wheel will get hotter and hotter.
To make the thing simpler, we can put a gas around the wheel to take up some of
the heat. Anyway, let us say the gas keeps rising in temperature, along with the
wheel. Will it go on forever? No! The pawl and wheel, both at some temperature 46—1 46—1 How a ratchet works 46—2 The ratchet as an engine 46—3 Reversibility in mechanics
46—4 Irreversibility
46—5 Order and entropy Fig. 46l .
machine. The ratchet and pawl T, also have Brownian motion. This motion is such that, every once in a while, by
accident, the pawl lifts itself up and over a tooth just at the moment when the
Brownian motion on the vanes is trying to turn the axle backwards. And as
things get hotter, this happens more often. So, this is the reason this device does not work in perpetual motion. When
the vanes get kicked, sometimes the pawl lifts up and goes over the end. But some
times, when it tries to turn the other way, the pawl has already lifted due to the
ﬂuctuations of the motions on the wheel side, and the wheel goes back the other
way! The net result is nothing. It is not hard to demonstrate that when the
temperature on both sides is equal, there will be no net average motion of the
wheel. Of course the wheel will do a lot of jiggling this way and that way, but it
will not do what we would like, Which is to turn just one way. Let us look at the reason. It is necessary to do work against the spring in
order to lift the pawl to the top of a tooth. Let us call this energy 6, and let 0 be
the angle between the teeth. The chance that the system can accumulate enough
energy, 6, to get the pawl over the top of the tooth, is e"/"T. But the probability
that the pawl will accidentally be up is also e_‘/kT. So the number of times that
the pawl is up and the wheel can turn backwards freely is equal to the number
of times that we have enough energy to turn it forward when the pawl is down.
We thus get a “balance,” and the wheel will not go around. 46—2 The ratchet as an engine Let us now go further. Take the example where the temperature of the
vanes is T1 and the temperature of the wheel, or ratchet, is T2, and T 2 is less than
T1. Because the wheel is cold and the ﬂuctuations of the pawl are relatively in
frequent, it will be very hard for the pawl to attain an energy 6. Because of the
high temperature T1, the vanes will often attain the energy 6, so our gadget will
go in one direction, as designed. We would now like to see if it can lift weights. Onto the drum in the middle
we tie a string, and put a weight, such as our ﬂea, on the string. We let L be the
torque due to the weight. If L is not too great, our machine will lift the weight
because the Brownian ﬂuctuations make it more likely to move in one direction
than the other. We want to ﬁnd how much weight it can lift, how fast it goes around,
and so on. First we consider a forward motion, the usual way one designs a ratchet to
run. In order to make one step forward, how much energy has to be borrowed
from the vane end? We must borrow an energy 5 to lift the pawl. The wheel turns
through an angle 0 against a torque L, so we also need the energy L0. The total
amount of energy that we have to borrow is thus 6 + L0. The probability that
we get this energy is proportional to e_(‘+L’”/kT1. Actually, it is not only a ques
tion of getting the energy, but we also would like to know the number of times
per second it has this energy. The probability per second is proportional to
e_(‘+L‘”/’°Tl, and we shall call the proportionality constant 1/1. It will cancel
out in the end anyway. When a forward step happens, the work done on the
weight is L0. The energy taken from the vane is e + L0. The spring gets wound
up with energy 5, then it goes clatter, clatter, bang, and this energy goes into heat.
All the energy taken out goes to lift the weight and to drive the pawl, which then
falls back and gives heat to the other side. Now we look at the opposite case, which is backward motion. What happens
here? To get the wheel to go backwards all we have to do is supply the energy to
lift the pawl high enough so that the ratchet will slip. This is still energy 6. Our
probability per second for the pawl to lift this high is now (l/r)e"/"T2. Our
proportionality constant is the same, but this time kT2 shows up because of the
diﬂerent temperature. When this happens, the work is released because the wheel
slips backward. It loses one notch, so it releases work L0. The energy taken from
the ratchet system is e, and the energy given to the gas at T1 on the vane side is
L6 + c. It takes a little thinking to see the reason for that. Suppose the pawl has
lifted itself up accidentally by a ﬂuctuation. Then when it falls back and the spring 46—2 Table 46—1 Summary of operation of ratchet and pawl. 1
Forward: Need energy 6 + L6 from vane. Rate = — e*(”+‘>/"Ti
1
Takes from vane L0 + 6
Does work L0
Gives to ratchet e
 1  /er
Backward: Needs energy 6 for pawl. . .Rate = — e e ' 2
T
Takes from ratchet e
Releases work L6 same as above with sign reversed. Gives to vane L0 + e . . L0 lf system Is reversnble, rates are equal, hence e + = ~5— 
T1 T2 Heat to ratchet 6 Q2 T2 ———— =  Hence — = — Heat from vane L6 + e Q1 T1 pushes it down against the tooth, there is a force trying to turn the wheel, because
the tooth is pushing on an inclined plane. This force is doing work, and so is the
force due to the weights. So both together make up the total force, and all the
energy which is slowly released appears at the vane end as heat. (Of course it
must, by conservation of energy, but one must be careful to think the thing
through!) We notice that all these energies are exactly the same, but reversed.
So, depending upon which of these two rates is greater, the weight is either slowly
lifted or slowly released. Of course, it is constantly jiggling around, going up for a
while and down for a while, but we are talking about the average behavior. Suppose that for a particular weight the rates happen to be equal. Then we
add an inﬁnitesimal weight to the string. The weight will slowly go down, and
work will be done on the machine. Energy will be taken from the wheel and given
to the vanes. lf instead we take off a little bit of weight, then the imbalance is
the other way. The weight is lifted, and heat is taken from the vane and put into
the wheel. So we have the conditions of Carnot’s reversible cycle, provided that
the weight is just such that these two are equal. This condition is evidently that
(e + L0)/T1 = e/Tg. Let us say that the machine is slowly lifting the weight.
Energy Q1 is taken from the vanes and energy Q2 is delivered to the wheel, and
these energies are in the ratio (6 + L0)/e. If we are lowering the weight, we also
have Q1/Q2 = (e + L0)/e. Thus (Table 46—1) we have Q1/Q2 = Tl/TZ Furthermore, the work we get out is to the energy taken from the vane as L6
is to L0 + 6, hence as (T 1 — T2)/T1. We see that our device cannot extract
more work than this, operating reversibly. This is the result that we expected from
Carnot’s argument, and the main result of this lecture. However, we can use our
device to understand a few other phenomena, even out of equilibrium, and there
fore beyond the range of thermodynamics. Let us now calculate how fast our oneway device would turn if everything were
at the same temperature and we hung a weight on the drum. If we pull very, very
hard, of course, there are all kinds of complications. The pawl slips over the
ratchet, or the spring breaks, or something. But suppose we pull gently enough
that everything works nicely. In those circumstances, the above analysis is right
for the probability of the wheel going forward and backward, if we remember 463 Fig. 46—2. Angular velocity of the
ratchet as a function of torque. that the two temperatures are equal. In each step an angle 0 is obtained, so the
angular velocity is 6 times the probability of one of these jumps per second. It
goes forward with probability (l/r)e‘“+L”’kT and backward with probability
(l/T)e_‘/kT, so that for the angular velocity we have M = (0/T)e—(€+L9)/kT _ e—e/kT = (o/r)e—°”°T(e—L“/” — 1). (46.1) If we plot a; against L, we get the curve shown in Fig. 46—2. We see that it makes a
great difference whether L is positive or negative. If L increases in the positive
range, which happens when we try to drive the wheel backward, the backward
velocity approaches a constant. As L becomes negative, to really “takes off”
forward, since e to a tremendous power is very great! The angular velocity that was obtained from different forces is thus very un
symmetrical. Going one way it is easy: we get a lot of angular velocity for a little
force. Going the other way, we can put on a lot of force, and yet the wheel hardly
goes around. We ﬁnd the same thing in an electrical rectifier. Instead of the force, we have
the electric ﬁeld, and instead of the angular velocity, we have the electric current.
In the case of a rectiﬁer, the voltage is not proportional to resistance, and the
situation is unsymmetrical. The same analysis that we made for the mechanical
rectiﬁer will also work for an electrical rectiﬁer. In fact, the kind of formula we
obtained above is typical of the currentcarrying capacities of rectiﬁers as a func
tion of their voltages. Now let us take all the weights away, and look at the original machine. If
T2 were less than T1, the ratchet would go forward, as anybody would believe.
But what is hard to believe, at ﬁrst sight, is the opposite. If T 2 is greater than T1,
the ratchet goes around the opposite way! A dynamic ratchet with lots of heat
in it runs itself backwards, because the ratchet pawl is bouncing. If the pawl, for
a moment, is on the incline somewhere, it pushes the inclined plane sideways.
But it is always pushing on an inclined plane, because if it happens to lift up high
enough to get past the point of a tooth, then the inclined plane slides by, and it
comes down again on an inclined plane. So a hot ratchet and pawl is ideally
built to go around in a direction exactly opposite to that for which it was originally
designed! In spite of all our cleverness of lopsided design, if the two temperatures are
exactly equal there is no more propensity to turn one way than the other. The
moment we look at it, it may be turning one way or the other, but in the long run,
it gets nowhere. The fact that it gets nowhere is really the fundamental deep
principle on which all of thermodynamics is based. 46—3 Reversibility in mechanics What deeper mechanical principle tells us that, in the long run, if the tempera
ture is kept the same everywhere, our gadget will turn neither to the right nor to
the left? We evidently have a fundamental proposition that there is no way to
design a machine which, left to itself, will be more likely to be turning one way
than the other after a long enough time. We must try to see how this follows from
the laws of mechanics. The laws of mechanics go something like this: the mass times the acceleration
is the force, and the force on each particle is some complicated function of the
positions of all the other particles. There are other situations in which forces
depend on velocity, such as in magnetism, but let us not consider that now. We
take a simpler case, such as gravity, where forces depend only on position. Now
suppose that we have solved our set of equations and we have a certain motion
x(t) for each particle. In a complicated enough system, the solutions are very
complicated, and what happens with time turns out to be very surprising. If we
write down any arrangement we please for the particles, we will see this arrange
ment actually occur if we wait long enough! If we follow our solution for a long 464 enough time, it tries everything that it can do, so to speak. This is not absolutely
necessary in the simplest devices, but when systems get complicated enough, with
enough atoms, it happens. Now there is something else the solution can do. If
we solve the equations of motion, we may get certain functions such as
t + t2 + t”. We claim that another solution would be —t + t2 — t3. In other
words, if we substitute ——t everywhere for t throughout the entire solution, we will
once again get a solution of the same equation. This follows from the fact that
if we substitute —t for t in the original differential equation, nothing is changed,
since only second derivatives with respect to I appear. This means that if we have
a certain motion, then the exact opposite motion is also possible. In the complete
confusion which comes if we wait long enough, it ﬁnds itself going one way some
times, and it ﬁnds itself going the other way sometimes. There is nothing more
beautiful about one of the motions than about the other. So it is impossible to
design a machine which, in the long run, is more likely to be going one way than
the other, if the machine is sufficiently complicated. One might think up an example for which this is obviously untrue. If we take
a wheel, for instance, and spin it in empty space, it will go the same way forever.
So there are some conditions, like the conservation of angular momentum, which
violate the above argument. This just requires that the argument be made with a
little more care. Perhaps the walls take up the angular momentum, or something
like that, so that we have no special conservation laws. Then, if the system is
complicated enough, the argument is true. It is based on the fact that the laws of
mechanics are reversible. For historical interest, we would like to remark on a device invented by
Maxwell, who ﬁrst worked out the dynamical theory of gases. He supposed the
following situation: We have two boxes of gas at the same temperature, with a
little hole between them. At the hole sits a little demon (who may be a machine
of course!). There is a door on the hole, which can be opened or closed by the
demon. He watches the molecules coming from the left. Whenever he sees a fast
molecule, he opens the door. When he sees a slow one, he leaves it closed. If we
want him to be an extra special demon, he can have eyes at the back of his head,
and do the opposite to the molecules from the other side. He lets the slow ones
through to the left, and the fast through to the right. Pretty soon the left side will
get cold and the right side hot. Then, are the ideas of thermodynamics violated
because we could have such a demon? It turns out, if we build a ﬁnitesized demon, that the demon himself gets so
warm that he cannot see very well after a while. The simplest possible demon, as
an example, would be a trap door held over the hole by a spring. A fast molecule
comes through, because it is able to lift the trap door. The slow molecule cannot
get through, and bounces back. But this thing is nothing but our ratchet and pawl
in another form, and ultimately the mechanism will heat up. If we assume that
the speciﬁc heat of the demon is not inﬁnite, it must heat up. It has but a ﬁnite
number of internal gears and wheels, so it cannot get rid of the extra heat that it
gets from observing the molecules. Soon it is shaking from Brownian motion so
much that it cannot tell whether it is coming or going, much less whether the
molecules are coming or going, so it does not work. 46—4 Irreversibility Are all the laws of physics reversible? Evidently not! Just try to unscramble
an egg! Run a moving picture backwards, and it takes only a few minutes for
everybody to start laughing. The most natural characteristic of all phenomena
is their obvious irreversibility. Where does irreversibility come from? It does not come from Newton’s laws.
If we claim that the behavior of everything is ultimately to be understood in terms
of the laws of physics, and if it also turns out that all the equations have the
fantastic property that if we put I = —t we have another solution, then every
phenomenon is reversible. How then does it come about in nature on a large
scale that things are not reversible? Obviously there must be some law, some 465 obscure but fundamental equation, perhaps in electricity, maybe in neutrino
physics, in which it does matter which way time goes. Let us discuss that question now. We already know one of those laws, which
says that the entropy is always increasing. If we have a hot thing and a cold
thing, the heat goes from hot to cold. So the law of entropy is one such law. But
we expect to understand the law of entropy from the point of view of mechanics.
In fact, we have just been successful in obtaining all the consequences of the argu
ment that heat cannot ﬂow backwards by itself from just mechanical arguments,
and we thereby obtained an understanding of the Second Law. Apparently we
can get irreversibility from reversible equations. But was it only a mechanical
argument that we used? Let us look into it more closely. Since our question has to do with the entropy, our problem is to try to ﬁnd a
microscopic description of entropy. If we say we have a certain amount of energy
in something, like a gas, then we can get a microscopic picture of it, and say
that every atom has a certain energy. All these energies added together give us
the total energy. Similarly, maybe every atom has a certain entropy. If we add
everything up, we would have the total entropy. It does not work so well, but
let us see what happens. As an example, we calculate the entropy difference between a gas at a certain
temperature at one volume, and a gas at the same temperature at another volume.
We remember, from Chapter 44, that we had, for the change in entropy, In the present case, the energy of the gas is the same before and after expansion,
since the temperature does not change. So we have to add enough heat to equal
the work done by the gas or, for each little change in volume, dQ = PdV.
Putting this in for dQ, we get V2 V2
/ dV NkT d_V As: V1 7: VI V T
_ V2 as we obtained in Chapter 44. For instance, if we expand the volume by a factor
of 2, the entropy change is Nk 1n 2. Let us now consider another interesting example. Suppose we have a box with
a barrier in the middle. On one side is neon (“black” molecules), and on the other,
argon (“white” molecules). Now we take out the barrier, and let them mix. How
much has the entropy changed? It is possible to imagine that instead of the
barrier we have a piston, with holes in it that let the whites through but not the
blacks, and another kind of piston which is the other way around. If we move
one piston to each end, we see that, for each gas, the problem is like the one we
just solved. So we get an entropy change of Nk 1n 2, which means that the entropy
has increased by k In 2 per molecule. The 2 has to do with the extra room that
the molecule has, which is rather peculiar. It is not a property of the molecule
itself, but of how much room the molecule has to run around in. This is a strange
situation, where entropy increases but where everything has the same temperature
and the same energy! The only thing that is changed is that the molecules are
distributed differently. We well know that if we just pull the barrier out, everything will get mixed
up after a long time, due to the collisions, the jiggling, the banging, and so on.
Every once in a while a white molecule goes toward a black, and a black one goes
toward a white, and maybe they pass. Gradually the whites worm their way, by
accident, across into the space of blacks, and the blacks worm their way, by
accident, into the space of whites. If we wait long enough we get a mixture. 466 Clearly, this is an irreversible process in the real world, and ought to involve an
increase in the entropy. Here we have a simple example of an irreversible process which is completely
composed of reversible events. Every time there is a collision between any two
molecules, they go oh" in certain directions. If we took a moving picture of a colli
sion in reverse, there would be nothing wrong with the picture. In fact, one kind
of collision is just as likely as another. So the mixing is completely reversible, and
yet it is irreversible. Everyone knows that if we started with white and with black,
separated, we would get a mixture within a few minutes. If we sat and looked at
it for several more minutes, it would not separate again but would stay mixed.
So we have an irreversibility which is based on reversible situations. But we also
see the reason now. We started with an arrangement which is, in some sense,
ordered. Due to the chaos of the collisions, it becomes disordered. It is the change
from an ordered arrangement to a disordered arrangement which is the source of
the irreversibility. It is true that if we took a motion picture of this, and showed it backwards,
we would see it gradually become ordered. Someone would say, “That is against
the laws of physics!” So we would run the ﬁlm over again, and we would look at
every collision. Every one would be perfect, and every one would be obeying
the laws of physics. The reason, of course, is that every molecule’s velocities are
just right, so if the paths are all followed back, they get back to their original condi
tion. But that is a very unlikely circumstance to have. If we start with the gas in
no special arrangement, just whites and blacks, it will never get back. 46—5 Order and entropy So we now have to talk about what we mean by disorder and what we mean
by order. It is not a question of pleasant order or unpleasant disorder. What is
different in our mixed and unmixed cases is the following. Suppose we divide the
space into little volume elements. If we have white and black molecules, how many
ways could we distribute them among the volume elements so that white is on one
side, and black on the other? On the other hand, how many ways could we dis
tribute them with no restriction on which goes where? Clearly, there are many
more ways to arrange them in the latter case. We measure “disorder” by the
number of ways that the insides can be arranged, so that from the outside it looks
the same. The logarithm of that number of ways is the entropy. The number of
ways in the separated case is less, so the entropy is less, or the “disorder” is less. So with the above technical deﬁnition of disorder we can understand the
proposition. First, the entropy measures the disorder. Second, the universe al
ways goes from “order” to “disorder,” so entropy always increases. Order is not
order in the sense that we like the arrangement, but in the sense that the number
of different ways we can hook it up, and still have it look the same from the outside,
is relatively restricted. In the case where we reversed our motion picture of the
gas mixing, there was not as much disorder as we thought. Every single atom had
exactly the correct speed and direction to come out right! The entropy was not
high after all, even though it appeared so. What about the reversibility of the other physical laws? When we talked
about the electric ﬁeld which comes from an accelerating charge, it was said that
we must take the retarded ﬁeld. At a time t and at a distance r from the charge,
we take the ﬁeld due to the acceleration at a time t — r/c, not t + r/c. So it
looks, at ﬁrst, as if the law of electricity is not reversible. Very strangely, however,
the laws we used come from a set of equations called Maxwell’s equations, which
are, in fact, reversible. Furthermore, it is possible to argue that if we were to use
only the advanced ﬁeld, the ﬁeld due to the state of affairs at t + r/c, and do it
absolutely consistently in a completely enclosed space, everything happens exactly
the same way as if we use retarded ﬁelds! This apparent irreversibility in electricity,
at least in an enclosure, is thus not an irreversibility at all. We have some feeling
for that already, because we know that when we have an oscillating charge which
generates ﬁelds which are bounced from the walls of an enclosure we ultimately 46—7 get to an equilibrium in which there is no onesidedness. The retarded ﬁeld ap
proach is only a convenience in the method of solution. So far as we know, all the fundamental laws of physics, like Newton’s equa
tions, are reversible. Then where does irreversibility come from? It comes from
order going to disorder, but we do not understand this until we know the origin
of the order. Why is it that the situations we ﬁnd ourselves in every day are always
out of equilibrium? One possible explanation is the following. Look again at our
box of mixed white and black molecules. Now it is possible, if we wait long enough,
by sheer, grossly improbable, but possible, accident, that the distribution of mole
cules gets to be mostly white on one side and mostly black on the other. After
that, as times goes on and accidents continue, they get more mixed up again. Thus one possible explanation of the high degree of order in the presentday
world is that it is just a question of luck. Perhaps our universe happened to have
had a ﬂuctuation of some kind in the past, in which things got somewhat separated,
and now they are running back together again. This kind of theory is not un
symmetrical, because we can ask what the separated gas looks like either a little
in the future or a little in the past. In either case, we see a grey smear at the inter
face, because the molecules are mixing again. No matter which way we run time,
the gas mixes. So this theory would say the irreversibility is just one of the acci
dents of life. We would like to argue that this is not the case. Suppose we do not look at
the whole box at once, but only at a piece of the box. Then, at a certain moment,
suppose we discover a certain amount of order. In this little piece, white and black
are separate. What should we deduce about the condition in places where we have
not yet looked? If we really believe that the order arose from complete disorder
by a ﬂuctuation, we must surely take the most likely ﬂuctuation which could
produce it, and the most likely condition is not that the rest of it has also become
disentangled! Therefore, from the hypothesis that the world is a ﬂuctuation, all
of the predictions are that if we look at a part of the world we have never seen
before, we will ﬁnd it mixed up, and not like the piece we just looked at. If our
order were due to a ﬂuctuation, we would not expect order anywhere but where we
have just noticed it. Now we assume the separation is because the past of the universe was really
ordered. It is not due to a ﬂuctuation, but the whole thing used to be white and
black. This theory now predicts that there will be order in other places——the
order is not due to a ﬂuctuation, but due to a much higher ordering at the beginning
of time. Then we would expect to ﬁnd order in places where we have not yet
looked. The astronomers, for example, have only looked at some of the stars. Every
day they turn their telescopes to other stars, and the new stars are doing the
same thing as the other stars. We therefore conclude that the universe is not a
ﬂuctuation, and that the order is a memory of conditions when things started.
This is not to say that we understand the logic of it. For some reason, the universe
at one time had a very low entropy for its energy content, and since then the entropy
has increased. So that is the way toward the future. That is the origin of all ir
reversibility, that is what makes the processes of growth and decay, that makes us
remember the past and not the future, remember the things which are closer to
that moment in the history of the universe when the order was higher than now,
and why we are not able to remember things where the disorder is higher than
now, which we call the future. So, as we commented in an earlier chapter, the
entire universe is in a glass of wine, if we look at it closely enough. In this case
the glass of wine is complex, because there is water and glass and light and every
thing else. Another delight of our subject of physics is that even simple and idealized
things, like the ratchet and pawl, work only because they are part of the universe.
The ratchet and pawl works in only one direction because it has some ultimate
contact with the rest of the universe. If the ratchet and pawl were in a box and
isolated for some sufficient time, the wheel would be no more likely to go one way
than the other. But because we pull up the shades and let the light out, because 468 we cool off on the earth and get heat from the sun, the ratchets and pawls that
we make can turn one way. This onewayness is interrelated with the fact that the
ratchet is part of the universe. It is part of the universe not only in the sense that
it obeys the physical laws of the universe, but its oneway behavior is tied to the
oneway behavior of the entire universe. It cannot be completely understood until
the mystery of the beginnings of the history of the universe are reduced still further
from speculation to scientiﬁc understanding. 46.9 ...
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This note was uploaded on 06/18/2009 for the course PHYSICS Physics taught by Professor Limkong during the Spring '09 term at Uni. Nottingham  Malaysia.
 Spring '09
 LimKong
 Physics

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