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Whence the arrow of time?

[“Quantum foundations” series]

A physicist walks into a bar, and asks the bartender, “What time is it?” The bartender is about to reply but then recognizes the customer. “You’re a physicist, correct? So, it’s a trick question.”

So, what’s with time? A venerable philosophical question. A foundational question in physics.

We have electronic devices, extremely accurate so-called atomic clocks, which can be used to detect changes in the relative rate of time. GPS technology. And based on physics.

So, imagine you could sense time. No, that’s not what I mean — an ability to tell what time it is, some type of internal clock. Rather, imagine you could sense changes in the flow of time, sense when the “speed” of time changes – changes in the rate of that internal chronometer. For real.

Well, in his latest Forbes article, this is what science communicator Ethan Siegel says is not possible.

Forbes > No, Thermodynamics Does Not Explain Our Perceived Arrow Of Time by Ethan Siegel, Senior Contributor (November 22, 2019).

Siegel contrasts the thermodynamic arrow of time and the perceptive arrow of time. He concludes that “The thermodynamic arrow of time does not determine our perceptive arrow of time.”

Different observers [in different inertial reference frames] … will experience the flow of time differently from one another. Whether two events occur simultaneously or one-before-the-other depends entirely on the observer’s point of view. [1]

And yet, despite how ambiguous time is, there are some facts about it that all observers can agree on. Perhaps the most fundamental — and yet perhaps the most puzzling as well — is that everyone, in their own inertial reference frame, always sees time moving forward at the same [universal] rate: one second-per-second. This fact is known as the arrow of time, and while there are many ideas as to what causes it, we know it isn’t thermodynamics.

If you want to know why yesterday is in the immutable past, tomorrow will arrive in a day, and the present is what you’re experiencing right now, you’re in good company. But thermodynamics, interesting though it may be, won’t give you the answer. As of 2019, it’s still an unsolved mystery. [2]

Well, I find the start of his article confusing – opening with some references to Special Relativity. Special Relativity (SR) in fact says that two people moving in relative frames will experience the laws of physics and sense of time the same. For either frame considered at rest, clocks will “tick” the same. For either frame considered in relation to the other, there will be effects such as length contraction and time dilation.

Wiki > [Special Relativity] has, for example, replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. … Events that occur at the same time for one observer can occur at different times for another.

I do not think SR (the special case of physics for “flat” spacetime) says anything about the flow of time – in Siegel’s sense (later in his article) of moving forward, backward, or standing still. Other than whether two events are simultaneous, the order of events in each frame remains intact.

Physics does not describe how things evolve “in time” but how things evolve in their own times, and how “times” evolve relative to each other. – Rovelli, Carlo. The Order of Time (p. 17). Penguin Publishing Group. Kindle Edition. 

Also, he does not discuss time dilation in General Relativity, which seems to counter his claim that “time still runs forward … at the rate of one second-per-second.”

It is not just the clocks that slow down: lower down, all processes are slower. Two friends separate, with one of them living in the plains and the other going to live in the mountains. They meet up again years later: the one who has stayed down has lived less, aged less, the mechanism of his cuckoo clock has oscillated fewer times. – Ibid. (p. 10)

So, his argument that time always runs forward regardless of entropic conditions does not seem to depend on either of Einstein’s theories. Which leaves me with … reviewing what Sean Carroll and Carlo Rovelli say on the matter.

Carroll says that: “When the entropy of a system is as high as it can get, we say that the system is in equilibrium. In equilibrium, time has no arrow” (The Big Picture (pp. 57-58). Penguin Publishing Group. Kindle Edition.) Hmm …

In his chapter “Time Is Ignorance,” Rovelli introduces time as an emergent phenomenon and the notion of thermal time.

Time emerges from a world without time, in a way that has something in common with each of these examples. The reconstruction of time begins here, in two little chapters … that are brief and technical. – Rovelli, ibid (p. 134)

Thermal time is tied to thermodynamics, and hence to heat, but does not yet resemble time as we experience it, because it does not distinguish between the past and the future, has no direction, and lacks what we mean when we speak of its flow. We have not yet reached the time of our own experience. – Ibid. (p. 142)

In the following chapter, “Perspective,” Rovelli relates entropy (introduced in an early chapter) to our frame of reference – a framework for how we perceive time. [7]

In other words, if in the universe there is something like this – and it seems natural to me that there could be – then we belong to that something. Here, “we” refers to that collection of physical variables to which we commonly have access and by means of which we describe the universe. Perhaps, therefore, the flow of time is not a characteristic of the universe: like the rotation of the heavens, it is due to the particular perspective that we have from our corner of it. – Ibid. (p. 150)

Similarly, in the boundless variety of the universe, it may happen that there are physical systems that interact with the rest of the world through those particular variables that define an initial low entropy. With regard to these systems, entropy is constantly increasing. There, and not elsewhere, there are the typical phenomena associated with the flowing of time: life is possible, together with evolution, thought, and our awareness of time passing. – Ibid. (pp. 150-151)

Our being situated in the world is essential to understanding our experience of time. We must not, in short, confuse the temporal structures that belong to the world as “seen from the outside” with the aspects of the world that we observe and which depend on our being part of it, on our being situated within it. – Ibid. (p. 153)

In the final chapters, Rovelli references Augustine’s Confessions on the nature of time, that time might exist only in the mind.

Augustine’s exposition of the idea is quite beautiful. It is based on our experience of music. When we listen to a hymn, the meaning of a sound is given by the ones that come before and after it. Music can occur only in time, but if we are always in the present moment, how is it possible to hear it? It is possible, Augustine observes, because our consciousness is based on memory and on anticipation. A hymn, a song, is in some way present in our minds in a unified form, held together by something—by that which we take time to be. And hence this is what time is: it is entirely in the present, in our minds, as memory and as anticipation. – Ibid. (p. 182)

And he concludes: “This is time for us: a multilayered, complex concept with multiple, distinct properties deriving from various different approximations.” – Ibid. (p. 198)

It is with respect to that physical system to which we belong – due to the peculiar way in which it interacts with the rest of the world, thanks to the fact that it allows traces and because we, as physical entities, consist of memory and anticipation – that the perspective of time opens up for us, like our small, lit clearing. Time opens up our limited access to the world. Time, then, is the form in which we beings, whose brains are made up essentially of memory and foresight, interact with the world: it is the source of our identity. – Ibid. (pp. 189-190)

Does Rovelli’s final chapter “The Source of Time” resolve Siegel’s unsolved mystery? Even Rovelli says that, aside from getting beyond a naïve understanding of temporal structure, his story is “far from being confirmed or widely accepted.”

Notes and references

[1] How would you tell someone how old you are if you lived in places (moved between places) where (relative) time passed at significantly different rates?

cf. Wiki > Twin paradox

See also > MIT Technology Review > “How does time dilation affect aging during high-speed space travel?” by Neel V. Patel (Dec 7, 2019)

Unlike the Twin Paradox, time dilation isn’t a thought experiment or a hypothetical concept––it’s real. The 1971 Hafele-Keating experiments proved as much, when two atomic clocks were flown on planes traveling in opposite directions. The relative motion actually had a measurable impact and created a time difference between the two clocks. This has also been confirmed in other physics experiments (e.g., fast-moving muon particles take longer to decay).

… time dilation as a result of gravitational effects … is also real, and it’s because in Einstein’s theory of general relativity, gravity can bend spacetime, and therefore time itself. The closer the clock is to the source of gravitation, the slower time passes; the farther away the clock is from gravity, the faster time will pass.

[2] Other definitive statements in Siegel’s article include these:

… At no point, and under no circumstances, does time ever appear to either stand still or reverse.

… the equations that govern reality don’t have a preference for the flow of time. The behavior of any system can be described by equations that are just as valid in the forward direction as they are in the backward direction.

According to many, there might be a link between what we perceive as the arrow of time and a quantity called entropy.

In particular, the second law is of extreme relevance, stating that the entropy of a closed (self-contained) system can only increase or stay the same over time; it can never go down. In other words, over time, the entropy of the entire Universe must increase. It’s the only known law of physics that appears to have a preferred direction for time.

So, does that mean that we only experience time the way we do because of the second law of thermodynamics? That there’s a fundamentally deep connection between the arrow of time and entropy? While many in the philosophy community (including physicists who tread into philosophy) think there might be, the physical evidence strongly indicates otherwise.

[Common examples of so-called irreversible reactions in physics: scrambling and cooking an egg, pouring cream into coffee and stirring it, ice cubes melting in a drink.]

There’s a caveat that most people forget when it comes to the second law of thermodynamics and the inevitable, accompanying entropy increase: the law only holds when we apply it to a closed system.

But if we violate those conditions, we could violate the second law of thermodynamics after all. A way to reverse the “two halves of a box” reaction was first thought up by the great physicist James Clerk Maxwell way back in the 1870s. By positing an external entity that’s capable of quickly opening or closing a divide between the two sides of the room at an opportune moment, the “cold” molecules can be collected one side with the “hot” molecules collected on the other.

This idea is now known as Maxwell’s demon, and it enables you to decrease the entropy of the system after all, at the cost of expending the energy required to monitor the system and open-and-close the gate between the two sides.

Doing this doesn’t violate the second law of thermodynamics, as the total entropy of the box and the entropy of the demon (or the actions of the demon) must be added together, and that combined entropy always increases. Only if you look at a part of the system, like the box alone (and ignored the demon and its actions), would you perceive a decrease in entropy.

But this is exactly what we need to disprove the hypothetical connection betweenthe thermodynamic arrow of time and the perceptive arrow of time. Even if you lived in the box and the demon were undetectable — similar to if you lived in a pocket of the Universe that saw an entropy decrease — time would still run forward for you. The thermodynamic arrow of time does not determine our perceptive arrow of time.

… even if you make those reactions [previously labeled as irreversible] happen in a way that (locally) reverses entropy, your clocks still run forward. In natural systems where the entropy remains constant, such as an adiabatically expanding cloud of collisionless matter, time still runs forward. Moreover, it always does so at exactly the same rate for all observers, regardless of whether or how their entropy changes: at the rate of one second-per-second. [3]

As far as we can tell, the second law of thermodynamics is true: entropy never decreases for any closed system in the Universe, including for the entirety of the observable Universe itself. It’s also true that time always runs in one direction only, forward, for all observers. What many don’t appreciate is that these two types of arrows — the thermodynamic arrow of entropy and the perceptive arrow of time — are not interchangeable.

[3] Wiki > Time

Subatomic particles exist for a well known average fraction of a second in a lab relatively at rest, but when traveling close to the speed of light they are measured to travel farther and exist for much longer than when at rest. According to the special theory of relativity, in the high-speed particle’s frame of reference, it exists, on the average, for a standard amount of time known as its mean lifetime, and the distance it travels in that time is zero, because its velocity is zero. Relative to a frame of reference at rest, time seems to “slow down” for the particle. Relative to the high-speed particle, distances seem to shorten.

[4] Physics Central > GPS satellite clocks and relativity

The satellite clocks are moving at 14,000 km/hr in orbits that circle the Earth twice per day, much faster than clocks on the surface of the Earth, and Einstein’s theory of special relativity says that rapidly moving clocks tick more slowly, by about seven microseconds (millionths of a second) per day.

Also, the orbiting clocks are 20,000 km above the Earth, and experience gravity that is four times weaker than that on the ground. Einstein’s general relativity theory says that gravity curves space and time, resulting in a tendency for the orbiting clocks to tick slightly faster, by about 45 microseconds per day. The net result is that time on a GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day.

[5] Wiki > Gravitational time dilation

Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer the clock is from the source of gravitation), the slower time passes, speeding up as the gravitational potential increases (the clock getting away from the source of gravitation).

This has been demonstrated by noting that atomic clocks at differing altitudes (and thus different gravitational potential) will eventually show different times.

[6] In his book The Big Picture, Sean Carroll discusses the notion of everyday causality as linked to the arrow of time. A chronology of past and future events. Relationships between events. In physics, the arrow of time is linked to the increase in entropy over time – the “thermodynamic” arrow of time, which “literally brings the universe to life.”

As with memory, the emergence of everyday causality from the underlying rigid pattern of the laws of physics can be traced to the arrow of time. Think of an example very much like that of the broken egg: a glass of wine spilled on the carpet. – Carroll, Sean. The Big Picture (p. 64). Penguin Publishing Group. Kindle Edition. 

“Memories” and “causes” aren’t pieces of our fundamental ontology describing our world that we discover through careful research. They are concepts that we invent in order to provide useful descriptions of the macroscopic world. The arrow of time plays a crucial role in how those contexts relate to the underlying time-symmetric laws of physics. And the origin of that arrow is that we know something specific and informative about the past (it had a low entropy), but there is no corresponding statement we can make about the future. Our progress through time is pushed from behind, not pulled from ahead. – Ibid. (pp. 65-66)

The microscopic laws of physics don’t distinguish between past and future. So any tendency of things to behave differently in one direction in time as opposed to the other – whether it’s birth and death, biological evolution, or the appearance of complicated structures – must ultimately be traced to the arrow of time and therefore to the second law. The increase of entropy over time literally brings the universe to life. – Ibid. (p. 235)

With Boltzmann’s definition in hand, it makes perfect sense that entropy tends to increase over time. The reason is simple: there are far more states with high entropy than states with low entropy. If you start in a low-entropy configuration and simply evolve in almost any direction, your entropy is extraordinarily likely to increase. When the entropy of a system is as high as it can get, we say that the system is in equilibrium. In equilibrium, time has no arrow. – Ibid. (pp. 57-58)

Nobody knows exactly why the early universe had such a low entropy. It’s one of those features of our world that may have a deeper explanation we haven’t yet found, or may just be a true fact we need to learn to accept.

What we know is that this initially low entropy is responsible for the “thermodynamic” arrow of time, the one that says entropy was lower toward the past and higher toward the future. Amazingly, it seems that this property of entropy is responsible for all of the differences between past and future that we know about. – Ibid. (pp. 58-59)

[7] Rovelli >  “Loss of Direction”

In the elementary equations of the world, the arrow of time appears only where there is heat.*

The link between time and heat is therefore fundamental: every time a difference is manifested between the past and the future, heat is involved. In every sequence of events that becomes absurd if projected backward, there is something that is heating up. If I watch a film that shows a ball rolling, I cannot tell if the film is being projected correctly or in reverse. But if the ball stops, I know that it is being run properly; run backward, it would show an implausible event: a ball starting to move by itself. The ball’s slowing down and coming to rest are due to friction, and friction produces heat. Only where there is heat is there a distinction between past and future. Thoughts, for instance, unfold from the past to the future, not vice versa—and, in fact, thinking produces heat in our heads. . . . Clausius introduces a quantity that measures this irreversible progress of heat in only one direction and, since he was a cultivated German, he gives it a name taken from ancient Greek—entropy … – Rovelli, Carlo. The Order of Time (pp. 24-25). Penguin Publishing Group. Kindle Edition.

* Strictly speaking, the arrow of time can also manifest itself in phenomena that are not linked directly to heat but share crucial aspects with it – for instance, in the use of retarded potentials in electrodynamics. What follows applies also for these phenomena—in particular, the conclusions. I prefer here not to overload the discussion by breaking it down into all its different subcases. – Ibid. (p. 240)

[8] And regarding Special Relativity, these YouTube videos by Fermilab’s Don Lincoln provide useful background.

• “Is relativistic mass real?” (September 5, 2017)

One of the oddest features of special relativity is the inability to go faster than the speed of light and this is absolutely true. The most common explanation is that the mass of an object increases with speed, but this particular explanation simply isn’t true. In this video, Fermilab’s Dr. Don Lincoln explains the truth behind this.

• “Why can’t you go faster than light?” (October 3, 2017)

One of the most counterintuitive facts of our universe is that you can’t go faster than the speed of light. From this single observation arise all of the mind-bending behaviors of special relativity. But why is this so? In this in-depth video, Fermilab’s Dr. Don Lincoln explains the real reason that you can’t go faster than the speed of light. It will blow your mind.