It’s about time

Second Law of Thermodynamics, Part 2

The experience of time’s flow is woven so deeply into our experience of life that it is impossible to imagine what it would mean to exist outside of time, or for time to flow in reverse. The feeling that the past is causing the future and not vice versa is a precondition to our thinking. Physicists are human, and subject to this same condition of thinking. The equations that represent physical laws make no distinction between past and future, but we always solve the equations in the sensible direction, calculating how the past determines the future and never the other way around.

The science of Thermodynamics was developed in the 19th century, in the context of chemistry, expanding gases, and the steam engine. Two things which were not part of the theory were gravity and quantum mechanics. The Second Law has never fit comfortably with these other parts of physics. 

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Link to Part 1 last week.

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The Second Law and the Quantum 

When theorists attempted to re-formulate the Second Law in modern terms (1930s), they ran up against a property unique to quantum systems. Information loss is what the Second Law is all about. Information in QM plays a special role, associated with observations made on any system. In quantum mechanics, information from a measurement is never lost, even if the system mixes with other systems. How can the conservation of information in QM be squared with the loss of information in Thermodynamic theory? 

Add a dye to a viscous liquid. It makes a colored spot. Turn a crank and the dye mixes in so the whole cylinder is uniformly colored.

Now turn the crank backwards. What do you expect to happen? I first learned of this trick as an undergrad when it was demonstrated in class by one of the world’s great teachers. It’s called the Taylor-Couette effect, and you can see a modern version here.

What’s going on? The three colored dots represent a visible order in the system, a macroscopic order. After the crank is turned, there is still order in the system, but it is in small colored streaks that blend together so the eye can see them. Reversing the crank can reverse the flow back to the original colored blobs.

This works because the fluid is not water, but a viscous corn syrup. The dye is spread out by motion of the fluid, but the fluid is not diffusing. To the extent that the fluid diffuses,  the colored spots become fuzzy, and the demonstration doesn’t work as well.

To understand this amusing video, we note that the information present in the blobs of ink was never really lost — it was just spread out on a scale that our eyes couldn’t see. After a few turns of the crank, there was information coded in fine traces of color that stretched through the syrup. 

The usual reconciliation of the Second Law with QM is that information on the macroscopic scale becomes mixed into the atomic scale. This is much finer than the scale of the fine, colored lines in the Taylor-Couette demonstration above. In the case of the syrup, the information was easily recoverable. But in the case of ultra-microscopic quantum information, it can never be recovered. 

“What, never? No, never!” You can even ask Captain Corcoran.

Even if Captain Corcoran is correct, and the information always flows from macroscopic to atomic levels, never the other direction, we might ask, Why? This looks like an observation about the world rather than a rigorously-proven mathematical theorem. It is closely related to the other arbitrary rule about time that physicists must accept (discussed last week) — that causes propagate to effects, always forward in time and never backward.

At this point, we are in danger of drowning in many deep topics that I will mention, reference, and save for another day. 

1. What we mean by “forward in time” is confounded in the (special) theory of relativity. If two people are in relative motion close to the speed of light, they can observe two events and disagree about whether A came before B or B came before A. The classical resolution is that in such cases, A cannot cause B and B cannot cause A. This is exactly the famous rule that “information cannot travel faster than light.” All observers agree about which came first except when A and B are very close in time and very distant in space. 

2. Bell’s Theorem defies the “faster than light” rule. Two objects that are quantum entangled can affect one another regardless of which comes first in time. Bell’s Theorem is actually a proof that a measurement of one entangled object must affect the other entangled object, even if everyone agrees that the measurement took place a million years after the effect was observed— in other words, backwards in time by a million years. The classical resolution of this paradox is that even though we can prove the effect was felt, we can also prove that the effect is never observable (even statistically) because it is always hidden in the quantum noise, masked by the Uncertainty Principle.

3. Einstein was concerned all his career about logical consistency. If A can cause B and B can prevent A then you have a “grandfather paradox”. Today’s philosophers say that he needn’t have worried. There can be a single, logically coherent history that contains some future influence on the past. For example, it may be true that time travelers visited our past, and we can know this by studying history…and we will also know something about the future in this process.

I recommend Nick Herbert’s book, Faster than Light, for accessible but mind-expanding reading. For thought-provoking fantasy, try The Time Traveler’s Wife. 

Synchronicity 

This is a word given to us by Carl Jung. I like Charles Eisenstein’s take on the subject. Jung spoke loosely of coincidences that are more than coincidences, andt in recent years, Julia Mossbridge writes more explicitly about information from the future that can guide us in the present.

I was on a bicycle two years ago when a driver didn’t see me, pulled into my lane and hit me head-on. Somehow, I survived, and recovered after many months. I don’t call this an “accident”; I refer to it as “my date with destiny” because so much in my life changed from that event, much of it for the better.

Perhaps you, too, have had a brief, random encounter which became a turning point in your life. I came away from mine with an intuition that this was “meant to be.” We can dismiss such feelings as superstition, but there is enough scientific evidence to support us if we wish to take the phenomenon seriously. 

The scientific demonstration is that information flow backward in time is real. That the phenomenon is ubiquitous, and corresponds to a kind of Destiny — this is an idea with an ancient pedigree and a New Age-y ring to our ears. 

What I’m proposing is exactly the mirror image of the Second Law. Microscopic information that changes my thoughts about what I will do this afternoon, that controls the timing of “random” human encounters, that cascades through the Butterfly Effect to create a storm or a transportation delay — maybe all this information is coordinated toward creation of a particular future, one that has been chosen by some Consciousness with a capital C that subsumes yours and mine.

It gives a whole new meaning to “God doesn’t play dice.” It gives substance to Eisenstein’s miraculous transition into a More Beautiful World. 

What does your intuition say? 

Vitalism

In former times, it was universally believed — in all cultures, East and West, religious and tribal and scientific — that physical systems and living systems were governed by different laws. Then, in the middle of the 19th century, organic chemistry was discovered. Some of the tricks that bodies do could be reproduced in test tubes. From there, an ambitious extrapolation took place over a period of several decades. Scientists proposed that maybe there was no fundamental difference between living and non-living things. Living things obeyed the same laws of chemistry and physics as non-living things. Living things are more complex and highly organized, but they are still machines and they can be fully understood in terms of physics and chemistry.

By the end of the century, this became an article of faith among scientists, and the opposite idea — that living things invoked forces and tendencies and biological laws that were separate from chemistry and physics — this was called “vitalism” and it was derided as “unscientific”.

Of course, it was always an extrapolation to assume that the small part of biology that could be understood in terms of chemistry would someday grow to become all of it, and that no new scientific laws are needed to understand Life. The mechanical world-view that replaced vitalism was always a philosophical position more than a scientific position. Nevertheless, it is taken as gospel by the majority of scientists today that there is nothing fundamentally special about life. Living systems are complex machines.

There is, however, a side current in scientific thought that is associated with people who cannot easily be dismissed — Max Planck, Bernardo Kastrup, Amit Goswami, Rupert Sheldrake and many others. For these people, consciousness is at least as fundamental as space, time, and matter. Consciousness plays a fundamental role in all physical processes, and consciousness is an independent driver of every life form, the deus ex machina. 

There are paradoxes in quantum physics, associated with the “measurement problem”. Measurement plays a special role in the theory, and the paradoxes arise if you try to treat the “measurer” by the same rules as any other quantum system. John von Neumann took this as evidence that “measurement” is actually the mechanism by which consciousness impinges on physics. 80 years later, this is a controversial opinion, with supporters and detractors. Personally, I like the idea. I wrote about it last year in a post titled Schrödinger’s Cat and the Secret of Life.

Within this “new vitalism”, it is natural to think that the causality of physics pushes from behind, while the causality of consciousness pulls into a projected future. Order is destroyed by physical processes and order is created by processes of consciousness.

This paradigm appeals to me, though I readily admit that it falls far short of what we would rightly demand of a testable physical theory. 

Gravity

You may remember your high school chem teacher talking about “intensive” and “extensive” properties. If you have twice as much stuff, you have twice as much energy, twice as much mass, twice as much volume, twice as much entropy. Energy, mass, volume, and entropy are all “extensive” properties. But you don’t have twice as much temperature. You don’t have twice the pressure. You don’t have twice the density. Temperature, density, and pressure are “intensive” properties.

Chemical energy is an extensive property. Twice as much stuff means twice as much chemical energy. What about gravitational energy? Gravitational energy is so weak that you can forget about it. 

Except if you’re an astrophysicist. If you have twice as much stuff, you have four times as much gravitational energy.  Gravitational energy is “more extensive than extensive”. It’s “hyperextensive”, if you like the neologism. 

Even though gravity is forty orders of magnitude weaker than chemical energies, chemical energies are based on positive and negative charges that cancel each other out on a large scale. Gravity is based on mass, which is always positive. Gravity  increases quadratically with the amount of matter, while chemical energies increases linearly. So if you get enough matter together in one place, gravitational energy overwhelms chemical energy.

The transition between chemical energies being dominant and gravitational energy being dominant occurs for an object roughly the size of planet Earth. That is to say, matter that gravitated together to form the Earth dissipated enough energy as heat that the center became hot enough to dominate chemical energy, hot enough to melt rock, for example. 

Not hot enough to make nuclear reactions happen. For that, you need about a million times more mass than the Earth. This is the scale of the sun. 

What does this have to do with entropy and the Second Law?

Most of the matter in our galaxy (or any galaxy, or between galaxies) is not in the stars and planets — it is in tenuous gas clouds that spread over thousands of light years. We can look at a small interstellar cloud and say that it is in thermodynamic equilibrium. It is at its highest entropy state. But if the same gas cloud were a little larger, we would have to say it is not in its highest entropy state. A state of even higher entropy is available if the gas clumps together to make a star, and releases a huge amount of heat and light. A way to look at this is that, though there is great randomness in the spacing of all those atoms in the gas, there would be even more randomness if we were to turn some of the mass of the gas into photons of light, and allow the photons to spread out into an even larger space. The entropy is greater because for every atom of gas, you can create many photons of light. 

(This is another perspective from which to view the strange fact that the Big Bang started in a state of thermodynamic equilibrium (maximum entropy), but that entropy has been able to increase ever since.)

Black Hole Evaporation

All that gas collapsing into a star and ultimately into a black hole creates a huge amount of disorder in the form of light that spreads out through the vastness of space. But there’s a price to pay. The gas, which used to be spread out, is now in one very small place. (A black hole with the sun’s mass fills only about as much space as Mt Shasta.) So this represents a huge cost in the entropy equation. All information concentrated in one place can never be turned back to entropy.

“Really, never? Well, hardly ever.”

It was Stephen Hawking’s genius and persuasive power that changed the minds of the physics community on this question in 1974. He convinced us that black holes evaporate. Yes, in classical General Relativity, black holes are a one-way sink. But quantum mechanics means that “anything can happen” with a tiny probability. Hawking outlined an “anything” that would lead to turning a tiny bit of the mass of a black hole into a photon, a single photon. This happens ever so slowly. A black hole with the mass of one sun, will “evaporate” completely into photons, but the time required will be about 10^54 times the age of the universe. In other words, the process can be safely ignored even on the vast time scales of cosmology.

Information disappearing in a Black Hole? Wanna bet?

The vast time scale doesn’t stop physicists from speculating about the theory. Remember that quantum information can never be destroyed. What happens to the quantum information that is carried by gas falling into a black hole? Physicists answer this question by associating some quantity of entropy with a black hole of a certain size. The information is locked inside. 

But if the black hole evaporates, what then? Is the radiation that comes out ruled by quantum randomness? Or does the information come out again when the black hole evaporates?

This question was the subject of a famous wager between Hawking and John Preskill — an underdog with respect to his reputation in the astrophysics community. General Relativity says that the information cannot get out. Quantum mechanics says that the information must still be there no matter that you wait ten thousand trillion trillion trillion trillion times the age of the universe. How can we resolve these conflicting predictions? Well, we could just watch a black hole and wait and wait and wait — then we would have the answer. But Preskill and Hawking were not so patient.

Alternatively, we could try to answer the question theoretically. But that would require a physical theory that reconciles QM and GR. That theory doesn’t exist yet. 

Hawking was betting that GR would trump QM, maybe because GR is his main field of study. Preskill is a quantum physicist, and he was counting on QM to trump GR.

We still don’t know the answer, but Hawking conceded the bet in 2004. Kip Thorne, a GR luminary in his own right who took the wager alongside Hawking, is still alive, and continues to believe Preskill wrong, and that information is permanently destroyed in a black hole, even if “permanently” is stretched absurdly far into the future..

What would happen if the expansion of the universe turned around?

Twenty-five years ago, the expansion of the universe was discovered to be accelerating. Thus the latest interpretation of the Big Bang is that expansion will continue forever. But before 1998, people wondered if gravity would eventually turn around the expansion, leading to a contracting phase for the universe as a whole. This possibility is no longer considered likely; but we can still consider the hypothetical: what would be the experience of beings in a second phase of the Big Bang, in which the universe would be contracting toward a Big Crunch?

We considered last week a convincing argument that it is the expansion of the universe that makes room for entropy to increase, and thus the Second Law is conditioned on the expanding universe.

But just above, we saw that the Second Law is related to our experience of causality. Mathematical derivations of the Second Law are premised on the past causing the future.

So what would happen if we lived in a universe that had more gravitating mass and less dark energy, so that the expansion would someday turn around and distant galaxies would all start flowing back together toward a Big Crunch? What would be our local experience? 

Would we see entropy decreasing? Would we see shards of glass on the tile floor suddenly jump up and form a perfect glass vase? Would we see gas flow out from low pressure to high pressure and fried eggs uncooking themselves, then returning to a self-assembling eggshell?

Or would our experience of time be reversed along with the thermodynamic arrow of time, so that our experience would be backward, to match the reversal of the Second Law? In that case, would our experience of the contracting phase of the universe be identical to experience of the expanding phase, because our experience of time is backward?

My opinion

The direction of time will not (would not) reverse if the universe starts to contract. We would actually observe the universe contracting, and the Second Law would continue to appear true for us. The contracting phase of the universe would be perceived as a contracting phase. We would consider to see chemical systems change in the direction of greater disorder, and just as now, we would be able to expend energy to create a chosen order in the future.

This is common sense, and we may breathe a sigh of relief. But then we have lost the argument made last week about the increase in entropy coming from the expansion of the universe. We must give up the satisfaction that last week’s explanation provided, that the creation of more space controls the time direction of the Second Law.

Time is real, and the forward direction of time is a fundamental fact of the universe, as fundamental as any of the laws of physics, and independent of them. Time is unfolding. The past really is fixed and the future really is emerging from a range of possibilities. 

In relativity, time is part of space-time, so that one man’s time can be another man’s space. In this sense, there cannot be an absolute time so that everyone everywhere can set their clocks to agree. Nevertheless, within the conventional version of the Big Bang, there is a “co-moving frame” at each point in space, a natural velocity defined by the fact that distant galaxies will appear to be receding at the same rate no matter what direction you look in space. This is a time frame that can be defined such that everyone in the universe can agree about a universal “before” and “after”. I believe that things unfold over time, and that time has an absolute meaning, as Newton thought of time, and that Einstein’s discoveries about the relativity of time will not matter.

Time travel will never be discovered by our descendants, because if it will be discovered some time in the future, we would have evidence of it in our past. 

This is the end of Part 2. Next week, I plan to write about machines that purport to create energy from the vacuum, in defiance of the Second Law.