| Topic: |
Science > Physics |
| User: |
"Edward Green" |
| Date: |
24 Aug 2005 08:38:49 PM |
| Object: |
Yet another entropy paradox... |
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
In considering a time reversal of the force law f = q v x B, the
convention is that B be flipped, so that the time reversed law has the
same form. Suppose we don't adopt this convention, so now the law has
lost its time reversal symmetry. Is this proper? We don't have to
argue whether this alternate convention is proper, we can model it!
Consider a plasma of electrons and protons in a parallel magnetic and
gravitational field, and also consider a plasma of positrons and
anti-protons in the same set-up. The charge conjugated version then
obeys the proposed dynamics of the time-reversed system (gravitation
merely defines a distinct vertical).
Well, before we seemed to be bothered that symmetric microlaws led to
assymetric macrolaws, and now we have some asymmetric microlaws, so we
should be all set, right? Well, not quite: the two systems are time
reversed models of each other, yet both stubbornly evolve towards
increasing entropy in lab time.
So besides asking how symmetric microlaws fail to produce a symmetric
macroworld, we also may ask how reversed asymmetric microlaws fail to
produce asymmetric macroscopic results.
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| User: "Ken Muldrew" |
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| Title: Re: Yet another entropy paradox... |
25 Aug 2005 02:42:28 PM |
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"Edward Green" <spamspamspam3@netzero.com> wrote:
In considering a time reversal of the force law f = q v x B, the
convention is that B be flipped, so that the time reversed law has the
same form.
If B is put in by hand in the first place, then it will have to be
flipped "by hand" when time is reversed. If we include whatever is
generating B within our system (e.g. electrons going through a
solenoid) then time reversal automatically leads to a reversal of B.
Suppose we don't adopt this convention, so now the law has
lost its time reversal symmetry. Is this proper?
I don't think it is.
We don't have to
argue whether this alternate convention is proper, we can model it!
Spoiler.
Consider a plasma of electrons and protons in a parallel magnetic and
gravitational field, and also consider a plasma of positrons and
anti-protons in the same set-up. The charge conjugated version then
obeys the proposed dynamics of the time-reversed system (gravitation
merely defines a distinct vertical).
I think it's a mistake to consider one the time-reversed complement of
the other.
Well, before we seemed to be bothered that symmetric microlaws led to
assymetric macrolaws, and now we have some asymmetric microlaws, so we
should be all set, right? Well, not quite: the two systems are time
reversed models of each other, yet both stubbornly evolve towards
increasing entropy in lab time.
Where is the entropy increasing in this model?
So besides asking how symmetric microlaws fail to produce a symmetric
macroworld, we also may ask how reversed asymmetric microlaws fail to
produce asymmetric macroscopic results.
I'd need to see an asymmetric microlaw first.
Ken Muldrew
kmuldrezw@ucalgazry.ca
(remove all letters after y in the alphabet)
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| User: "Edward Green" |
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| Title: Re: Yet another entropy paradox... |
25 Aug 2005 06:16:33 PM |
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Ken Muldrew wrote:
"Edward Green" <spamspamspam3@netzero.com> wrote:
In considering a time reversal of the force law f = q v x B, the
convention is that B be flipped, so that the time reversed law has the
same form.
If B is put in by hand in the first place, then it will have to be
flipped "by hand" when time is reversed. If we include whatever is
generating B within our system (e.g. electrons going through a
solenoid) then time reversal automatically leads to a reversal of B.
Yes, I agree. I think this leaves open the question of whether
thinking of B as representing some local property of space, it "should"
be flipped (and what "should" means here) or not, but...
Suppose we don't adopt this convention, so now the law has
lost its time reversal symmetry. Is this proper?
I don't think it is.
We don't have to
argue whether this alternate convention is proper, we can model it!
Spoiler.
I hoped to side step this issue.
Consider a plasma of electrons and protons in a parallel magnetic and
gravitational field, and also consider a plasma of positrons and
anti-protons in the same set-up. The charge conjugated version then
obeys the proposed dynamics of the time-reversed system (gravitation
merely defines a distinct vertical).
I think it's a mistake to consider one the time-reversed complement of
the other.
It's a thought problem, set up so the explicitly considered laws of
motion in the physical analogues are precisely time reversals of each
other. Now, if I say something like "these aren't real plasmas, but
plasmas which are fully described by the laws I posit for them", you
will say I am cheating -- I am just a bit, but I think with
justification. I am appealing to real plasmas to motivate the idea
that both systems evolve in the normal entropic direction. I'm
asserting that these model systems are sufficiently physical or complex
that the second law will apply to them regardless of the accuracy of
the physical model (model of the model?).
Well, before we seemed to be bothered that symmetric microlaws led to
assymetric macrolaws, and now we have some asymmetric microlaws, so we
should be all set, right? Well, not quite: the two systems are time
reversed models of each other, yet both stubbornly evolve towards
increasing entropy in lab time.
Where is the entropy increasing in this model?
It could increase in any of the usual ways -- by expansion or
homogenization or condensation (if that happens to be the favored
process) -- in which macroscopic systems spontaneously evolve. Unless
of course we start the systems in equilibrium.
So besides asking how symmetric microlaws fail to produce a symmetric
macroworld, we also may ask how reversed asymmetric microlaws fail to
produce asymmetric macroscopic results.
I'd need to see an asymmetric microlaw first.
Sheesh -- I just explicitly constructed one for you!*
If you want to argue "but B really flips", call it the $-field, and say
that in the force law "f = q v x $", $ doesn't flip under time
reversal. It just so happens that we can model the behavior of
particles subject to the mysterious "$-field" by various systems of
charged particles subject to the B-field.
What _is_ going to happen to entropy in a many body model system with
explicitly time-asymmetric microlaws?
* (You may want a time-reversal asymmetric microlaw to be a little 2nd
law, which idea you reject: how can a particle expand in phase space or
lose information when the state is completely represented by only a few
variables? But that's not what this kind of asymmetry means -- it's
about what happens to the form of the equation under the change of
variables "t' = -t").
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| User: "Uncle Al" |
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| Title: Re: Yet another entropy paradox... |
25 Aug 2005 10:06:23 AM |
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Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
Feynman's sprinkler. Angular momentum is an irreversible arrow of
time.
In considering a time reversal of the force law f = q v x B, the
convention is that B be flipped, so that the time reversed law has the
same form. Suppose we don't adopt this convention, so now the law has
lost its time reversal symmetry. Is this proper? We don't have to
argue whether this alternate convention is proper, we can model it!
Consider a plasma of electrons and protons in a parallel magnetic and
gravitational field, and also consider a plasma of positrons and
anti-protons in the same set-up. The charge conjugated version then
obeys the proposed dynamics of the time-reversed system (gravitation
merely defines a distinct vertical).
Well, before we seemed to be bothered that symmetric microlaws led to
assymetric macrolaws, and now we have some asymmetric microlaws, so we
should be all set, right? Well, not quite: the two systems are time
reversed models of each other, yet both stubbornly evolve towards
increasing entropy in lab time.
So besides asking how symmetric microlaws fail to produce a symmetric
macroworld, we also may ask how reversed asymmetric microlaws fail to
produce asymmetric macroscopic results.
Learn something about CPT conservations.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
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| User: "michaeld" |
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| Title: Re: Yet another entropy paradox... |
25 Aug 2005 01:46:51 PM |
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Uncle Al wrote:
Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
Feynman's sprinkler. Angular momentum is an irreversible arrow of
time.
What? The Feynman sprinkler is purely Newtonian, and there is no
violation of time reversal symmetry in Newtonian physics. If you take a
video of the Feynman sprinkler and reverse the footage then the laws of
physics are still obeyed.
[...]
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| User: "Edward Green" |
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| Title: Re: Yet another entropy paradox... |
25 Aug 2005 05:12:37 PM |
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michaeld wrote:
Uncle Al wrote:
Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
Feynman's sprinkler. Angular momentum is an irreversible arrow of
time.
What? The Feynman sprinkler is purely Newtonian, and there is no
violation of time reversal symmetry in Newtonian physics. If you take a
video of the Feynman sprinkler and reverse the footage then the laws of
physics are still obeyed.
[...]
Well, other than entropy creation, of course -- assuming you really
meant "reverse the footage". In this case the Feynman sprinkler simply
becomes the Sears brand sprinkler, since there is no monkey business
about reversing the flow in forward time.
I too am mystified by the claim regarding angular momentum and time
reversal -- and I doubt subject can form a coherent argument supporting
this claim: although learned droppings of "Feynman sprinkler" and "CPT
symmetry" might form the suggestion in easily cowed minds.
As for the Feynman sprinkler, I will admit I never was clear for very
long in my mind whether it doesn't move in reverse because of rigid law
or fortuitous near cancellation of terms.
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| User: "Andy Resnick" |
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| Title: Re: Yet another entropy paradox... |
26 Aug 2005 10:04:41 AM |
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Edward Green wrote:
<snip>
As for the Feynman sprinkler, I will admit I never was clear for very
long in my mind whether it doesn't move in reverse because of rigid law
or fortuitous near cancellation of terms.
American Journal of Physics 60 (1992) 12
American Journal of Physics 58 (1990) 352
American Journal of Physics 59 (1991) 349
American Journal of Physics 57 (1989) 65
American Journal of Physics 56 (1988) 307
American Journal of Physics 55 (1987) 488
American Journal of Physics 46 (1978) 1194
American Journal of Physics 44 (1976) 1106
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "John Sefton" |
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| Title: Re: Yet another entropy paradox... |
26 Aug 2005 10:57:29 AM |
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Andy Resnick wrote:
Edward Green wrote:
<snip>
As for the Feynman sprinkler, I will admit I never was clear for very
long in my mind whether it doesn't move in reverse because of rigid law
or fortuitous near cancellation of terms.
American Journal of Physics 60 (1992) 12
American Journal of Physics 58 (1990) 352
American Journal of Physics 59 (1991) 349
American Journal of Physics 57 (1989) 65
American Journal of Physics 56 (1988) 307
American Journal of Physics 55 (1987) 488
American Journal of Physics 46 (1978) 1194
American Journal of Physics 44 (1976) 1106
3
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| User: "Edward Green" |
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| Title: Re: Yet another entropy paradox... |
28 Aug 2005 11:17:03 AM |
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Andy Resnick wrote:
Edward Green wrote:
<snip>
As for the Feynman sprinkler, I will admit I never was clear for very
long in my mind whether it doesn't move in reverse because of rigid law
or fortuitous near cancellation of terms.
American Journal of Physics 60 (1992) 12
American Journal of Physics 58 (1990) 352
American Journal of Physics 59 (1991) 349
American Journal of Physics 57 (1989) 65
American Journal of Physics 56 (1988) 307
American Journal of Physics 55 (1987) 488
American Journal of Physics 46 (1978) 1194
American Journal of Physics 44 (1976) 1106
Thank you.
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| User: "Edward Green" |
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| Title: Sprinkler cools dog days... |
29 Aug 2005 06:45:05 PM |
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Andy Resnick wrote:
Edward Green wrote:
As for the Feynman sprinkler <...>
American Journal of Physics 60 (1992) 12 <...>
Unfortunately, or not, my local physics library is closed on weekends
for intersession. Once more to the envelopes, dear friends.
Abstract: the direction of torque is found to be indeterminate under
reasonable assumptions.
The statement:
Consider an initially static L-shaped section of pipe joined at an open
end of a radial arm to a hollow hub, the distal, tangential, pipe arm
being perpendicular to the hub axis. The apparatus is immersed in a
fluid reservoir and a frictionless and incompressible flow is
established through the open pipe end towards the hub.
Q: Is non-zero torque generated, and if so, what is its sign?
Envelope #1:
Consider a boundary surface enveloping the pipe and entering its open
end to a depth at which the flow is characterized by a single v
parallel to the walls. It suffices to compare momentum transfer across
this reentrant surface element to that on the projected opposite area
of the elbow.
Assume Bernoulli's law applies, and distant areas of the reservoir are
nearly static at pressure P_0, so
P_0 = P + 1/2 rho v^2 (I)
Force (density) across the inside surface element, aka momentum flux
(density), has two components; a dynamic pressure*, rho v^2, and a
static pressure, P = P_0 - 1/2 rho v^2, so we have to compare
P_0 + 1/2 rho v^2 net surface momentum transport flux density
P_0 pressure on opposite projected area of elbow
Clearly the difference is always positive, and tending to torque the
pipe in the forward direction of the sprinkler.
Envelope 2:
But flow may not be simple within the pipe. In particular, the fluid
may be swirling, so that the a speed v_m characterizing mean mass
transport along the pipe axis may be different from and smaller than a
speed v_s characterizing the mean v in the Bernoulli equation. In
particular, starting with a situation with given v_m = v characterizing
mass transport, we may increase the v_s characterizing swirling until P
~ 0 sets a maximum absolute speed for the flow, thus eliminating the
static pressure term. In this case we may compare the magnitudes of
P_eff = rho v^2 dynamic momentum transport
P_0 static pressure on opposite face of elbow
for any feasible value of v characterizing simple flow: swirling flow
can keep the dynamic pressure constant while eliminating the static
pressure.
To perform this comparison reexamine eq. (I)
P_0 = P + 1/2 rho v^2
and notice that P can take any value between 0 and P_0, so that 1/2 rho
v^2 can also. Dynamic pressure rho v^2 is twice that term, so it can
take any value from 0 to 2P_0, hence the sign of P_eff - P_0 is
indeterminate. If mean mass flow v_m is small but the fluid is
swirling down rapidly, then torque on the sprinkler arm may be in
reversed.
Conclusion: Static torque has an algebraic minimum when v_m is zero and
v_s at a maximum, goes through a zero as v_m increases (and the
available swirling pressure drop decreases), and reaches a maximum when
v_m = v is the maximum speed permitted by Bernoulli's law for given
P_0, and the flow is simple. Torque can be controlled by controlling
vorticity in the pipe.
*taken here as a label for rho v^2, rather than 1/2 this quantity
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| User: "Andy Resnick" |
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| Title: Re: Sprinkler cools dog days... |
30 Aug 2005 07:43:25 AM |
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Edward Green wrote:
Andy Resnick wrote:
Edward Green wrote:
As for the Feynman sprinkler <...>
American Journal of Physics 60 (1992) 12 <...>
<snip>
Here's how I have come to understand the result: The flow within the
pipe is not what to examine; that is clearly symmetric. The real answer
lies within the pressure field at the exit port to the sprinkler.
When water jets out, the pressure distribution is not isotropic; hence
the sprinkler turns. When suction is applied, the pressure at the (now
inlet) port is isotropic, thus there is no net momentum carried by the
water into the sprinker, the sprinkler does not turn.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
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| User: "Edward Green" |
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| Title: Re: Sprinkler cools dog days... |
30 Aug 2005 09:18:31 PM |
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Andy Resnick wrote:
Here's how I have come to understand the result: The flow within the
pipe is not what to examine; that is clearly symmetric. The real answer
lies within the pressure field at the exit port to the sprinkler.
When water jets out, the pressure distribution is not isotropic; hence
the sprinkler turns. When suction is applied, the pressure at the (now
inlet) port is isotropic, thus there is no net momentum carried by the
water into the sprinker, the sprinkler does not turn.
I prefer my analysis, though I can see some similarity here. ;-}
Flow inside the pipe is not necessarily symmetric: it might be straight
out forward, but swirling in reverse. If flow comes in from all angles
as suggested, conservation of energy _requires_ vorticity within the
pipe: the extra kinetic energy for given mass flow can't simply
disappear.
We should be able to consistently analyze momentum balance across any
control surface, whether transversing the exit or somewhere inside the
pipe. And we have to consider the entire control surface. If water
comes in from all angles vs. a single angle across a surface at the
exit, internal pressure is reduced for a given mass flow, tending to
cancel the torque -- same effect suggested, different language.
But is this necessarily an _exact_ cancellation? I don't see why yet.
The so-called "reverse" sprinkler is misleadingly compared to an above
ground sprinkler: the reversed-reversed sprinkler is still surrounded
by a fluid reservoir. The analysis is the same as for the submerged
reversed case. I look forward to reading those papers: like Uncle Al,
I too can dream of revolutionizing an important field. ;-)
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| User: "Bob Cain" |
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| Title: Re: Sprinkler cools dog days... |
30 Aug 2005 03:31:15 PM |
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Andy Resnick wrote:
Here's how I have come to understand the result: The flow within the
pipe is not what to examine; that is clearly symmetric. The real answer
lies within the pressure field at the exit port to the sprinkler. When
water jets out, the pressure distribution is not isotropic; hence the
sprinkler turns. When suction is applied, the pressure at the (now
inlet) port is isotropic, thus there is no net momentum carried by the
water into the sprinker, the sprinkler does not turn.
That seems so obvious (and did so when I first heard of the
issue) that I've long wondered why there was any question
about it. Anybody know?
Bob
--
"Things should be described as simply as possible, but no
simpler."
A. Einstein
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| User: "michaeld" |
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| Title: Re: Yet another entropy paradox... |
26 Aug 2005 07:06:57 AM |
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Edward Green wrote:
michaeld wrote:
Uncle Al wrote:
Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
Feynman's sprinkler. Angular momentum is an irreversible arrow of
time.
What? The Feynman sprinkler is purely Newtonian, and there is no
violation of time reversal symmetry in Newtonian physics. If you take a
video of the Feynman sprinkler and reverse the footage then the laws of
physics are still obeyed.
[...]
Well, other than entropy creation, of course -- assuming you really
meant "reverse the footage".
The increase in entropy is not a violation of the laws of physics. The
second law of thermodynamics is a statistical rule that holds (to high
probability) assuming reasonable physical boundary conditions. It is
actually the 'physical boundary conditions' not the fundamental laws of
physics that break time reversal invariance in classical mechanics. If
you take any classical solution and reverse it in time you get another
solution whether or not entropy/angular momentum are involved.
In this case the Feynman sprinkler simply
becomes the Sears brand sprinkler, since there is no monkey business
about reversing the flow in forward time.
I too am mystified by the claim regarding angular momentum and time
reversal -- and I doubt subject can form a coherent argument supporting
this claim: although learned droppings of "Feynman sprinkler" and "CPT
symmetry" might form the suggestion in easily cowed minds.
Of course the standard model of particle physics is not invariant under
time reversal. The standard model is CPT invariant but it is well known
that CP (and hence T) are violated by the electroweak force. However
this has little to do with the macroscopic violation of time reversal.
[...]
Michael
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| User: "michaeld" |
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| Title: Re: Yet another entropy paradox... |
26 Aug 2005 07:36:00 AM |
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michaeld wrote:
Edward Green wrote:
michaeld wrote:
Uncle Al wrote:
Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
Feynman's sprinkler. Angular momentum is an irreversible arrow of
time.
What? The Feynman sprinkler is purely Newtonian, and there is no
violation of time reversal symmetry in Newtonian physics. If you take a
video of the Feynman sprinkler and reverse the footage then the laws of
physics are still obeyed.
[...]
Well, other than entropy creation, of course -- assuming you really
meant "reverse the footage".
The increase in entropy is not a violation of the laws of physics.
Oops. That should have said: the _decrease_ in entropy is not a
violation of the laws of physics. Sorry.
The
second law of thermodynamics is a statistical rule that holds (to high
probability) assuming reasonable physical boundary conditions. It is
actually the 'physical boundary conditions' not the fundamental laws of
physics that break time reversal invariance in classical mechanics. If
you take any classical solution and reverse it in time you get another
solution whether or not entropy/angular momentum are involved.
In this case the Feynman sprinkler simply
becomes the Sears brand sprinkler, since there is no monkey business
about reversing the flow in forward time.
I too am mystified by the claim regarding angular momentum and time
reversal -- and I doubt subject can form a coherent argument supporting
this claim: although learned droppings of "Feynman sprinkler" and "CPT
symmetry" might form the suggestion in easily cowed minds.
Of course the standard model of particle physics is not invariant under
time reversal. The standard model is CPT invariant but it is well known
that CP (and hence T) are violated by the electroweak force. However
this has little to do with the macroscopic violation of time reversal.
[...]
Michael
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| User: "michaeld" |
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| Title: Re: Yet another entropy paradox... |
26 Aug 2005 08:31:26 AM |
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Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
In considering a time reversal of the force law f = q v x B, the
convention is that B be flipped, so that the time reversed law has the
same form. Suppose we don't adopt this convention, so now the law has
lost its time reversal symmetry. Is this proper?
Maxwell's equations also wouldn't be obeyed.
We don't have to
argue whether this alternate convention is proper, we can model it!
Consider a plasma of electrons and protons in a parallel magnetic and
gravitational field, and also consider a plasma of positrons and
anti-protons in the same set-up. The charge conjugated version then
obeys the proposed dynamics of the time-reversed system
I don't see why it's the same.
You have to reverse the sign of B. If E = f(t,x,y,z) and B = g(t,x,y,z)
solve Maxwell's equations then so do E' = f(-t,x,y,z), B' =
-g(-t,x,y,z) (if you also reverse the sign of the current J). However
your E' = f(-t,x,y,z), B' = g(-t,x,y,z) don't. If E,B satisfy Faraday's
law of induction:
curl E = -@B/@t
then your E',B' instead satisfy:
curl E' = @B'/@t
i.e. they violate Faraday (unless the B field is static).
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| User: "Gregory L. Hansen" |
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| Title: Re: Yet another entropy paradox... |
26 Aug 2005 12:31:49 PM |
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In article <1125063086.735678.16830@o13g2000cwo.googlegroups.com>,
michaeld <michaeld@cantab.net> wrote:
Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
In considering a time reversal of the force law f = q v x B, the
convention is that B be flipped, so that the time reversed law has the
same form. Suppose we don't adopt this convention, so now the law has
lost its time reversal symmetry. Is this proper?
Maxwell's equations also wouldn't be obeyed.
We don't have to
argue whether this alternate convention is proper, we can model it!
Consider a plasma of electrons and protons in a parallel magnetic and
gravitational field, and also consider a plasma of positrons and
anti-protons in the same set-up. The charge conjugated version then
obeys the proposed dynamics of the time-reversed system
I don't see why it's the same.
You have to reverse the sign of B. If E = f(t,x,y,z) and B = g(t,x,y,z)
solve Maxwell's equations then so do E' = f(-t,x,y,z), B' =
-g(-t,x,y,z) (if you also reverse the sign of the current J). However
your E' = f(-t,x,y,z), B' = g(-t,x,y,z) don't. If E,B satisfy Faraday's
law of induction:
curl E = -@B/@t
then your E',B' instead satisfy:
curl E' = @B'/@t
i.e. they violate Faraday (unless the B field is static).
Or to put it more simplistically (although not more simply), under time
reversal the electron current that generates your dipole moment reverses
direction while Coulomb's law is Coulomb's law regardless of the direction
of motion.
--
"Work hard, be curious and persistent, and you will prevail." -- Howard
Schilit, "Financial Shenanigans" 2nd ed.
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| User: "Edward Green" |
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| Title: Re: Yet another entropy paradox... |
26 Aug 2005 06:42:18 PM |
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michaeld wrote:
Edward Green wrote:
But I hope, a novel one.
We conventionally affect to be puzzled by the coexistence of microlaws
symmetric under time reversal and the noticably time reversal
asymmetric macrolaws which live with them. But what if the microlaws
were also asymmetric under time reversal -- would that make us feel any
better?
In considering a time reversal of the force law f = q v x B, the
convention is that B be flipped, so that the time reversed law has the
same form. Suppose we don't adopt this convention, so now the law has
lost its time reversal symmetry. Is this proper?
Maxwell's equations also wouldn't be obeyed.
We don't have to
argue whether this alternate convention is proper, we can model it!
Consider a plasma of electrons and protons in a parallel magnetic and
gravitational field, and also consider a plasma of positrons and
anti-protons in the same set-up. The charge conjugated version then
obeys the proposed dynamics of the time-reversed system
I don't see why it's the same.
You have to reverse the sign of B. If E = f(t,x,y,z) and B = g(t,x,y,z)
solve Maxwell's equations then so do E' = f(-t,x,y,z), B' =
-g(-t,x,y,z) (if you also reverse the sign of the current J). However
your E' = f(-t,x,y,z), B' = g(-t,x,y,z) don't. If E,B satisfy Faraday's
law of induction:
curl E = -@B/@t
then your E',B' instead satisfy:
curl E' = @B'/@t
i.e. they violate Faraday (unless the B field is static).
I had indeed worried about the internal fields generated by the charges
in motion in the plasma, and whether this spoiled my model of time
reversed systems, but I swept this under the rug. I _still_ think this
idea might be saved, but the point of my thought problem is being lost
under a possibly clumsy physical model. Let's back up a step.
You yourself just mentioned the lack of T symmetry in reactions
involving the electroweak force, along with the claim that this had
little to do with macroscopic physical irreversibility. Well, suppose
we extend this claim to a universe which had wider and more obvious
lack of T-symmetry in its physical laws -- not buried under some
sub-atomic force which requires heroic efforts to contact. I claim we
still would conclude that this assymetry had little to do with the
natural direction of physical evolution, and in fact if we constructed
_two_ such model universes with reversed versions of the microlaws,
starting them at an identical random point in phase space, both would
almost certainly evolve towards higher entropy.
If you accept this contention, it is perhaps the complement of the
standard observation concerning reversible microlaws and macroscopic
irreversibility.
Now, the model of the model, which is mainly for illustration and
motivation, might perhaps be saved as follows:
We break up the analogues of the electric and magnetic fields in our
model worlds into two components: E = E1 + E2, B = B1 + B2, and posit
the time reversal relations: E1,E2,B2 -> E1',E2',B2'; B1 -> -B1'
These are the fields in the mathematical model universe, and may behave
as we postulate. Now we map these fields to the physical model of the
model (our plasmas) as follows: E2,B2 are externally applied static
fields penetrating the region of the plasma, E1,B1 the local fields
generated by the moving charges: because of linearity, this
decomposition makes sense.
Now notice what happens if we "time reverse" the systems by charge
conjugation: the locally generated components of B flip obligingly,
whereas the externally applied B field does not -- just as required by
our rules of time reversal in the model universe. I _think_ this
works out, and that Maxwell's equations continue to be satisfied,
because the "wrong" component of B is static.
Well, I've failed to formulate a pithy paradox, that's sure: the
difficulty is the necessity of motivating the behavior of mathematical
systems by physical models. We don't have a pair of universes to hand
with strongly T-asymmetric and reversed microlaws, so that we may
verify they both evolve in the normal thermodynamic way by inspection.
Maybe you can think of a simpler example of real systems modeling
T-asymmetric pairs of microlaws?
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| User: "the softrat" |
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| Title: Re: Yet another entropy paradox... |
25 Aug 2005 01:14:40 AM |
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On 24 Aug 2005 18:38:49 -0700, "Edward Green"
<spamspamspam3@netzero.com> wrote:
So besides asking how symmetric microlaws fail to produce a symmetric
macroworld, we also may ask how reversed asymmetric microlaws fail to
produce asymmetric macroscopic results.
Yes, we may. We may also say, "Wubba, wubba, wubba." But most of us
don't.
the softrat
Sometimes I get so tired of the taste of my own toes.
mailto:softrat@pobox.com
--
"But why, my dear Crito, should we care about the opinion of the many?
Good men, and they are the only persons who are worth considering,
will think of these things truly as they happened."
-- Socrates to Crito, in "Crito"
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| User: "Autymn D. C." |
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| Title: Re: Yet another entropy paradox... |
24 Aug 2005 11:02:21 PM |
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The lawkins aren't time-summetric. The electron has a tiny electric
dipole moment.
We don't violate entropy because we never use black holes to rewind
everything. We should, so I can get some pigheaded and ignorant
scientists to shut up...
-Aut
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