Last week, The Geogre brought an interesting article from Quanta Magazine to my attention, and I decided to devote a TC diary to describing the discoveries reported in this article. It deals with some of the biggest and oldest puzzles in physics, often based on assumptions most of us don’t even think about.
The ultimate issue has to do with time. What is it? How do we measure it? What are the physical consequences of measuring it?
Einstein’s theories of relativity are famous for regarding time as a fourth-dimensional direction equivalent to the three spatial directions (forward/back, left/right, and up/down). However, time can never be considered quite interchangeable with the spatial directions because our experience of them is very different from our experience with time. We can choose to go left or right, forward or back, up or down, but we can’t choose whether to go to the past or the future. We are propelled toward the future and away from the past regardless of what we might prefer. We can perceive what is to our right or to our left. We can only remember what we experienced in the past, and we can’t see into the future at all.
Most physical theories are said to be symmetric with respect to time reversal. This means that if you choose to run a calculation for a system backward in time (by just putting a minus sign in front of the time variable), the system would follow the same path backward that is followed in the forward direction. The only physical observation that is not symmetric to time reversal is the second law of thermodynamics, which states that the total entropy content of the universe increases as time passes. Note that there is nothing causal about this statement. We can observe that the entropy of the universe increases as time passes, but at this stage, it’s just a correlation—there’s no evidence that the passage of time causes the entropy to increase, or vice versa.
At this point, it’s helpful to have an idea of what entropy is. A common casual definition is that entropy is a measure of disorder in a system, but a better way to put it is that the entropy of a system reflects the number of different ways the components of a system can be rearranged without changing the state of the system. One common example given for entropy is a messy desk, but from a more formal standpoint, this is because there are many more ways to arrange the stuff on your desk in a disorderly manner than there are ways to arrange them neatly.
Pertinent to the subject of this diary is the entropy of energy content. Energy with low entropy is energy that is densely stored. A tightly wound spring or a can of gasoline are examples of energy with low entropy. It is possible to employ low-entropy energy to do work, such as lifting masses against gravity, or moving a car… or running a clock. Energy with high entropy, on the other hand, is widely dispersed in a system, such as molecules in a gas moving randomly. It’s very hard to get any work out of the energy in a system with high entropy. Furthermore, doing work transforms the low-entropy stored energy into high-entropy dispersed energy, so any machine that does work is increasing the entropy of the universe.
Clocks are machines that do the work of measuring constant time intervals in sequence, so it should come as no surprise that they produce entropy in the process. The scientists behind the study described in the Quanta article performed a quantum mechanical study of the simplest conceivable clock (a three-atom model), and from this study, determined that as a clock becomes more precise in its time measurement, its rate of entropy production increases. Further, this relationship is linear: the measure of clock precision is proportional to the amount of entropy produced. Indeed, a clock with perfect precision (a purely theoretical concept) would have to produce entropy at an infinite rate. Thus, there is a practical limit to clock precision.
Clocks have existed for centuries, and the concept of entropy is about 200 years old, but until now, nobody had ever considered the relationship between the running of clocks and the production of entropy before, even knowing entropy’s role as an arrow of time itself.
All of this is well and good, but, you might argue, “it’s just a theory.” But then somebody did an experiment. Anna Pearson at Oxford University was performing experiments on tiny vibrating membranes stimulated by white noise when she ran into Paul Erker, one of the theorists behind the work on clocks and entropy. A vibrating membrane is a clock, a real clock, not a quantum model for a clock, but an excellent model system for testing the theory. Further, it’s fairly straightforward to measure the entropy produced by the membrane, and Pearson did indeed find a linear relationship between the precision of the membrane vibration period and the entropy produced.
The implication here is that time (and its measurement) and entropy appear to be bound up much more intimately than the simple correlation suggested by the second law of thermodynamics. Maybe there is a causal relationship between the two, which would be mind-blowing. But the fact is, time as a dynamical variable is not understood at a basic level. This research may provide a key to a better understanding of time as we experience it.
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