Entropied Apples
Entropied Apples
Phy,
Could you reply to this from the 1 on 1:
Second, did Styer overstate his case when he said: "the entropy of any part of the universe can decrease with time, so long as that decrease is compensated by an even larger increase in some other part of the universe."
For example, can an entropy increase in ANY Location 1 really compensate for an entropy increase in Location 2, as in:
Location 1: outer space to one parsec around Alpha Centauri
Location 2: equipment operating on the Phoenix Mars Lander (NASA's has finally lost its signal by the way).
The "parts" of the universe that have the offsetting entropies must be adjacent. No? For example, a discrete amount of decreased entropy in Denver Colorado, say from an air conditioner cooling Denver Bible Church, cannot be accounted for by a slightly greater increase in entropy on Planet FFTE, a planet orbiting a star in a galaxy furthest from the earth. I realize the entire physical universe is "connected" (CMB light, etc.). But isn't it true that the offsetting entropy must occur contiguous to the decreasing entropy, in that the distances separating these must be close enough to physically allow for the transfer of entropy? Thus I'm asking if it is slightly misleading (and I'm not making a federal case out of this Johnny, just asking) to a college student reading AJP to say, "the entropy of any part of the universe can decrease [if] compensated by an even larger increase in some other part of the universe."
Phy, Styer's sixth reference (from his second inferred misconception
) is to the pages by John Patterson which include
this quote:
"According to the second law, the entropy decrease (ΔS2 < 0) may occur spontaneously as long as it is coupled to increases... that overcompensate the entropy inventory
nearby."
Just wondering what your thoughts are on this.
Thanks,
-Bob Enyart
KGOV.com
The Second Law mathematics used by Styer does not depend on the heat exchange being between adjacent objects. There is good reason for this.
One goal of expressing scientific laws is to “minimize the inputs”. In other words, do not include any preconditions that must be met unless the correctness of the law depends on them.
Example – Newton’ Law of Gravitation. The apocryphal apple bounced off Newton’s head, he looked up and saw the moon, and suddenly a realization that both the apple and the moon were being attracted by the earth’s gravity came to him. Had he written and published his Law of Gravity in the next few minutes, it may have said that the force of gravity was [ F = g * Me * Mo / (Re^2) ] where F is force, g is the gravitational constant, Me is the mass of the earth, Mo is the mass of the object (moon or apple or …), and Re is the distance from the center of the earth. Correct, but it is only a subset of the Law of Gravity he actually put forth. Why?
Being the insightful (fringe) Christian scientist that he was, Newton realized that the force of gravity was acting not only between the earth and moons and satellites and falling applies, but between any two objects that have mass. Bob’s computer (Al the 6th) in Denver is pulling on this computer (Alice the 7th) some 1000 miles away, with the force between them exactly described by the real Law of Gravity: [ F = g * Ma * Mb / (R^2) ] where Ma is now the mass of the first object, Mb is the mass of the second, and R is the distance between them. (I keep a small block of lead in my office near my wall opposite Denver, just to counter the pull of Al on Alice.)
So in the context of minimizing the restriction on the inputs, Newton made his law much more useful by deleting any need for one object to be the earth, or close by.
A similar rule holds on the SLoT. Use the minimum number of restrictions possible in developing the law. Nothing in the mathematical formulation of entropy stipulates locality. It deals only with energy budgets. (I use the word “budget” because of Johnny’s insightful response about money in the 1-on-1).
If we move away from the rigid formalism of the mathematical logic, isn’t it true that energy exchanges are always somewhat local? Yes, as far as we can tell right now. I think Styer was perhaps a bit extreme in his examples, but maybe he was trying to make a point. Even the energy budget on the earth is massively greater than required to come to his answer.
But to impose locality as a necessary limitation on the SLoT is not only to introduce extraneous non-value added complications, but in fact it can subtly involve the SLoT in decisions it has no part in. The structure of space-time is an active field of research, and saying SLoT can only be applied locally would define part of the structure of space-time. Let’s let General Relativity and Quantum (and String Theory?) do their jobs of finding restrictions on the need for locality, free of unwarranted restrictions imposed by the SLoT.
