Re: Yet another entropy paradox...

In article <1125063086.735678.16830@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
michaeld <michaeld@xxxxxxxxxx> 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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