A trip from Los Angeles to San Diego should not take more than 3 hours. Yet the congestion was such that for much of the trip we were traveling at no more than 20 miles per hour. For most of the trip we rarely went above 40. It was only upon entering the city limits that we were able to race along as far as the campus of San Diego State college. The time was 5:30: we'd spent over 5 hours on the road.
Using the Kirsh's cell phone I placed a call to Lee Conte, friend of a mutual friend, who'd agreed to put me up for the night and take me over to the conference the following morning. He checked out my location on a Yahoo map, and picked me up in less than half an hour.
Lee works as a telecommunications engineer for AT&T. He'd only recently come out to San Diego. Lee had already decided what we should do for the evening. After I'd cleaned up a taken a short nap, he drove us over to the San Diego Zoo. Lee is quite fond of animals and had been to the Zoo several times before. On this occasion he was hoping to catch some of the nocturnal animals coming out of their lairs. Lee asked me questions about Thermodynamics and Mathematics and I interrogated him on the lives of the denizens of the Zoo.
The artificially "natural" settings of the Zoo were impressive as models of construction, landscaping and art, but it didn't seem to me that the animals were terribly happy in them. One must agree that it's very dangerous for an animal to be out alone in the wild, say on the plains or in jungles, but they can't be very happy either, alone in a cage with no other creatures, ( even if they are enemies) , in sight.(See4 Nature Myths) Lee admitted that this problem had worried him also. He felt that, as zoos go, the one in San Diego did what it could to make its residents feel at home, but there was no way it could hope to reproduce the ambience of their natural habitat.
It led me to speculate on the strangeness of our world. Earth appear to be a place wherein creatures remove other creatures from their natural home, place them in contrived settings for their own amusement, then worry about their well-being.
After breakfast I amused myself working out an effective registration for playing Bach's Italian Concerto on Lee's large electronic Casio keyboard. My experiments culminated in an equilibrium state of strings in the right hand against trombones in the bass. At 11 Lee drove me over to the UCD campus.
The cost of maintaining so lavish an establishment must cost many millions of dollars . Given the costs the enrollment is remarkably small: around 5000 undergraduates . In a few words : USD is a private Catholic university endowed by billionaires, for a small student population consisting largely of with football jocks and valley girls. Athletics plays a large role here, as one could see from all the young people wandering around the campus, wearing the uniforms of their clubs, teams and summer institutes. The bookstore in the basement of Loma Hall contains little more than pulp detective fiction, a few best-sellers and textbooks.
(Comment by Daniel Sheehan: " Unfortunately, we're not endowed by billionaires here, merely by thousandaires and perhaps a few millionaires. Also, we do have a few scholars in addition to the jocks and valley girls.)"
Against this backdrop of vigorous health the delegation to QLSL2 appeared both seedy and eminent to a fault . It had been projected that no more than 40 delegates would show up. As it turned out, there were more than 120 of us, from 23 countries: Japan, the Czech Republic, Russia, Italy,Canada, Mexico, Germany, France, the UK, Holland, India, the United States and others. It must have been the great interest in the topics under discussion that brought the delegations , it being rather unlikely that they would have traveled such great distances just for the good eating and refreshing ocean breeze, although there were plenty of both.
Summarizing the 4 Laws of Thermodynamics:
One can of course argue at length about exactly what is meant by "contact": Proximity ?( How close?) ; Causal connectedness? Quantum Entanglement? Proximity by quantum entanglement was a recurring theme in many of the talks.
Several of these classical statements were critically examined during the conference. It was shown that, not only are there crucial differences between the statements of the 2nd Law, but that traditional connections between the 2nd Law, Entropy, Irreversibility and the Arrow of Time are over-simplifications.
At the level of daily experience and observation, the 2nd Law can be understood to mean that heat can never pass from a cold object to a warm one; equivalently, that mechanical work can not be extracted against the flow of heat from warm to cold. If, as in a steam engine, one tries to "recycle" the mechanism by alternating a state of steady temperature ( isothermal), with one of steady heat (adiabatic), a certain percentage of the heat will be unrecoverable from the cycle. This is called the Inefficiency. The measure of this inefficiency is called the Entropy.
Whereas everyone has had direct experience of the phenomenon of Heat, it is not well-defined scientifically unless certain variables are kept constant. Entropy on the other hand, a notion lying somewhere between an abstraction and a catalyst, is a well-defined quantity, if one means by quantity an observable whose states are independent of the way they are attained or measured.
In fact Classical Thermodynamics uses Entropy to quantify Heat and not the contrary. The basic equation is dS = dQ/T . Here Entropy (S) , and Temperature (T) , are total differentials, which means that their values in a given state ( Pressure, Volume) of a system, are independent of the way that state is reached. Heat (Q) is not a total differential; its value is a function of the amount of work needed to arrive at that state.
Even the notion of Temperature, however, is somewhat nebulous, in that there are disputes over its proper dimensions or units. One can say, roughly, that although temperature is spoken of as existing at an isolated point, ( say the tip of the thermometer) , the temperature is really a kind of mean energy averaged over the random motions of a huge number of particles, under the assumption of some kind of global homogeneity.
Succinctly , the 2nd Law turns out to be merely the collection of all the ways in which its been stated.
No other science uses thought experiments as much as theoretical physics: their role in physics may be compared to that of the "Magical If" in Stanislavski's Method for actors . Almost by definition, the situation in a thought experiment cannot be constructed in the real world : it would then be a real experiment. The fact that one cannot construct the situation described by the thought experiment may be itself an important statement about the physical world.
One can look upon thought experiments as realizations of the axioms for the purpose of clarifying the foundations of a subject. However Physics is notoriously resistant to axiomatization. All efforts to give an axiomatic formulation to Mechanics, Thermodynamics, Quantum Theory or Relativity have known only limited success
. To summarize, the Maxwell Demon is a thought experiment which calls into question the axiomatic foundations of a subject for which, to date, there are no axioms. Note that the 4 "Laws" of Thermodynamics are not axioms: no-one has ever shown that they are either independent, consistent or complete.
From his historical recapitulation of the restatements of the Maxwell Demon by von Clausius, Boltzmann, Landauer, Bennett, Szilard, and Feynman, Callender concluded that they all use the Second Law as a premise for deducing the Second Law. The Maxwell Demon thought experiment has led to the discovery of a close connection between Thermodynamics with Information Theory, through a common notion of Entropy. Nowadays, following Brillouin, most "explanations" of the paradox are based on Information Theory.
Following Callender's talk there was a reception on the outdoor terrace of the Kroc Center. I sat down at a table with the delegates from Charles University in Prague. Altogether there were 7 delegates from the Czech Republic at the conference . Among them was Mrs. Raji Hrovoska, from India but married to Mr. Hrovosky, who runs a research institute in Prague. She comes from a prominent family of scientists and is related to both Raman and Chandrasekhar.
We were told that if we stayed around until 9:45 we would be seeing fireworks from Seaworld, the neighboring whale and dolphin circus which has ties with USD . Most of us were tired, only a few remained to watch, and I did not stay around.
" ...thermodynamics was the mainspring of quantum theory. Some think the time is ripe for quantum mechanics to return the favor by challenging the foundations of thermodynamics...In a classical Carnot cycle engine the efficiency of converting heat to work is determined solely by the temperatures Th and Tc of the hot and cold reservoirs. However in quantum thermodynamics the quantum phase provides a new and interesting control parameter. For example, with properly chosen quantum phase, it is possible to extract work even when Th = Tc. However the second law of thermodynamics is not violated. The present photon-Carnot quantum heat engine provides a simple model for studying various quantum effects in thermodynamics. "
Scully is a tall, slender man, elderly but appears to be in his 50's, and in excellent condition . An international authority on quantum optics and a member of the National Academy of Sciences, his view of the subtleties of this subject is exceptionally lucid. In 1992 he coined the term "phaseonium" This is a new form of matter in which the quantum atomic phase is held fixed for long times compared with various relaxation processes. He is also associated with the development of the phaser, or phaseonium laser: a kind of laser without inversion (LWI) that creates quantum coherence via Electromagnetically Induced Transparency (EIT) .
On the blackboard Scully wrote down a list of 7 directions in which one ought to proceed in designing experiments to challenge the Second Law:
His interpretation of the Maxwell Demon paradox was well stated . Combining the Demon with the system itself to produce a hyper-system, he asked us to imagine that the actions involved in separating out the fast from the slow molecules has the effect of "disassociating" the demon itself , giving it two distinctive states, thereby greatly increasing the total entropy of the hyper-system.
According to Albert Liouville's Theorem ( Invariance of the phase-space volume of an ensemble under a Hamiltonian flow) is all that one really needs to show that Entropy cannot decrease. He admitted that this is insufficient to show why it must increase. Following that his delivery became so wrapped up in hypotheticals, vague meanderings, ifs, buts and maybes, that it was impossible to follow him further.
During the question period, V. Chapek ( Charles University, Prague) , gave his opinion that Caratheodory's Theorem refuted all of Albert's arguments. This is a Theorem of pure mathematics, ( theory of Integral Equations) , which can be used to show that inaccessible states exist in the neighborhood of any given state of a closed thermodynamic system. Chapek did not elaborate on how Caratheodory's beautiful result invalidated the assertions of David Albert. Nor did he specify which of his numerous assertions were being invalidated.
As a general rule, they avoid speaking of the direction of Causation itself because all of the other laws of physics are time reversible.
Schulman's talk was about the possible connections between (2) and (3) : what happens to the Second Law of Thermodynamics in cosmological models , in which there is a Big Bang at the beginning of universal time and a Big Crunch at the other end? If the direction of the Second Law is linked to the expansion of the universe, then it stands to reason that there will be a time-reversal of the Second Law after the expansion ceases, and the contraction leading to the Big Crunch begins. In other words, somewhere in between the beginning and the ending of the universe there is a period in which two arrows of time are simultaneously present.
The 1st Arrow, which we call the Second Law, goes from "order" to "disorder". The Second Arrow therefore goes from "disorder" to "order" . ( The pieces and contents of the broken glass of orange juice do pick themselves up and return to the table !)
Using a schematic and simplified model from the theory of Dynamical Systems, ( physicists call these "toy models") , Schulman elaborated a picture of what might happen if one lived in a world in which the two arrows of time were operative together. One then finds all the phenomena of Chaos Theory present in real physical systems: periodic cycles of transformation between work and heat ( perpetual motion engines of the second kind) , stationary "fixed point" systems, chaotic turbulence in which the concept of entropy no longer has any meaning. In his scheme all these phenomena emerge in a relatively short span of time.
If we are in fact poised between a Big Bang and a Big Crunch , there will come a time in which all of these phenomena will be visible in the world around us. If some of them are present in today's world, one might be able to use them to estimate how long the universe is destined to last.
"Heat", he said, merely means the sum total of all the inaccessible degrees of freedom in a system, whereas "Work" stands for the accessible degrees . The sum total of all degrees of freedom goes into the measurement of energy, which is invariant. By finding ways to access more degrees of freedom one can shift the balance between heat and work.
