“It is also necessary—may God grant it!—that in providing others with books to read I myself should make progress, and that in trying to answer their questions I myself should find what I am seeking. Therefore at the command of God our Lord and with his help, I have undertaken not so much to discourse with authority on matters known to me as to know them better by discoursing devoutly of them.” -St. Augustine of Hippo, “The Trinity” I, 8

“...The concept of time within present physical theories—by which we mean Newtonian physics, special relativity, and general relativity—is an approximation within a quite different conceptual framework that is associated with a quite different theory.” -J. Butterfield, C.J. Isham, “On the Emergence of Time in Quantum Gravity”

This is the fifth in a series of articles addressing the question “What is time?”

The first dealt with philosophical issues, the second with how we perceive time, the third with entropy as “the arrow of time,” and the fourth with relativistic time. In this post I’ll examine how time in quantum mechanics is strange, but of course, quantum mechanics (QM) in general is strange.(1)

The uncertainty of time in quantum mechanics  

You readers probably know about the Heisenberg Uncertainty Principle, particularly as it applies to position and momentum (mass times velocity). Let’s just refresh those ideas. The Uncertainty Principle says that you can’t measure simultaneously and precisely values for both position and momentum of a particle. The uncertainty principle also applies to another pair of variables—time, t, and energy, E:

ΔΕ times Δt not less than  [h/(4π)]

ΔΕ is the uncertainty in the measured value of the energy; Δt is the uncertainty in the time at which the measurement is made; h is Planck’s constant. (2)

Here’s an example: fundamental particles—pions and muons—are generated when cosmic rays penetrate the earth’s atmosphere (see here). These particles have very short lifetimes, ranging from less than 10-17s to 10-6s, after which they then decay into more stable particles.  During their extremely short lifetime, there will be a “significant uncertainty” in any measurement of mass/energy. This uncertainty relation between energy and lifetime has been verified in a number of experiments (see the link above and here).

Quantum mechanics measurement: past ---> future

Classical physics (that is to say, physics before quantum mechanics) used equations that were time symmetric.  That is to say, if time, “t” (as a parameter or coordinate) is replaced by “-t,” the fundamental equations of physics look the same. (3) The replacement of t by -t is equivalent to going backwards in time. The solutions to these equations that corresponded to going backwards in time were almost always discarded as being physically unrealistic (but see below).

This is not the case in conventional, “textbook,” quantum mechanics. If the quantum mechanical state is regarded as a superposition of possible states that could result from a measurement, then the measurement act “collapses” that superposition into one of those component states. (This is the so-called “measurement problem.”) There is past: the superposition of states before the measurement; and there is future: the one state of those possible picked out afterwards by the measurement. This measurement problem is pictorially summarized in the famous Schrodinger Cat paradox.  

Various QM theories to remove the “measurement problem” have been proposed (see here), but they aren’t universally accepted. Some of these alternatives posit a time symmetry such that events in the future cause events in the present, what is termed “retrocausality.” I’ll examine two of these interpretations below.

Back to the Future with quantum mechanics  

From H.G. Wells to Robert Heinlein (4), time travel has been a staple of science-fiction, with the “fiction” part more important than the science. But if some QM interpretations are valid, then time travel—future events influencing the past, retrocausality—is possible, at least for particles on the atomic scale. I’ll focus on one such theory in this section: the Transactional Interpretation of John Cramer. (5) 

Before doing that, I want to give one example of backwards time in “conventional” QM. Consider the collision of an electron with its antiparticle, a positron. When the particles meet they are annihilated, releasing two high energy gamma rays (two rays to conserve momentum). The process is summarized in the Feynman diagram shown below:

Note that the red arrow for the positron is drawn backwards, from present to previous time. This convention represents an “anti-symmetry:” a positron can be thought of as an electron going backwards in time.

The Transactional Interpretation of quantum mechanics: the handshake

“'There's no use trying,' she [Alice] said. 'One can't believe impossible things.' I daresay you haven't had much practice,' said the Queen. 'When I was your age, I always did it for half-an-hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.”  Lewis Carroll, “Alice through the Looking Glass”

Quantum Mechanics has several impossible features, but these can be made to seem reasonable by crediting John Cramer’s Transactional Interpretation of quantum mechanics.  Some might regard this as replacing several impossible things by one impossible thing, but I’ll let the reader decide that for himself/herself. (5)

Cramer built his Transactional Interpretation on the Feynman-Wheeler absorption theory for electromagnetic radiation (light). (6) He takes the wave-function, a solution to a modified Schrodinger equation, as being real, not just a mathematical device to describe what’s going on. He then takes two solutions to the modified Schrodinger equations, one a wave going forward in time (OW for “offer wave”) and one a wave going backwards in time. The waves, describing some particle or system, meet a measuring device, which then emits another backwards wave (CW for “confirm wave”). The offer and confirm waves engage, that is to say a handshake or transaction occurs, to yield the measurement. 

There’s much more to it than the simple description above, but I’ll leave it to the interested reader to follow up by going to the reference given in note 5 and here. This interpretation, like other interpretations of quantum mechanics, cannot be confirmed experimentally. It’s the math, common to all QM interpretations, that is verified empirically, and that has been done for many, many experiments down to 10 figure accuracy.

Quantum mysteries “explained” by the Transactional Interpretation

Here are three “quantum mysteries,” strange behaviors, that the Transactional Interpretation (TI) explains in a common sense way. (By the term “common sense,” I mean that the three strange quantum behaviors listed below are taken into account by one non-common sense hypothesis, interaction with future events.)

• Wheeler’s Delayed Choice Experiment—quantum systems know beforehand if they’re going to be measured;
• Schrodinger’s Cat—the superposition of states and collapse on measurement—a system exists simultaneously in two different states but only one is perceived on measurement;
• The Violation of the Bell Inequality—the nonlocality and instantaneous interaction of coupled particles—separated entangled particles seem to interact instantaneously even though separated by large distances.

Huw Price has given another account (7) of time symmetry and quantum time travel, reasonable on the face of it, which I’ll not discuss here because of space limitations.

Final thoughts 

I am not a quantum realist. I believe physics gives a mathematical framework to understand what our world is like, insofar as that may be possible. That is to say, the object of scientific inquiry is to “save the phenomena,” to make coherent and to relate the way things behave.   There is a deeper reality, veiled as the physicist/philosopher d’Espagnat would have it,  that science does not penetrate. Therefore, I regard theories which treat the future as ontologically real more as conceptual tools to help us picture what quantum mechanics is about, rather than as models for reality.

Now there is one other quantum feature that deals with time: quantum gravity.  Again, space limits a discussion of this, so I will just list references for the interested reader. (8,9)  Summing these up very briefly: they discuss whether time actually does exist as a fundamental variable, and, if it does, whether like other physical variables that extend over a finite range, it must be discrete, rather than continuous. Indeed, one three body black hole dynamics modeling project suggests that time’s arrow may result from chaotic behavior at the limit of very small discrete spacetime lengths.

What’s to come

In the final article of this series I’ll discuss God, outside of time, and why God created time. 

Notes

(1) Here’s one thing to keep in mind: there is a correspondence between a physics equation, as it would be given in “classical” physics and as it is given in quantum mechanics.  For example, a vibrating spring models the vibration of atoms in a molecule.   The classical differential equation describing such vibrations transforms into an equation with “operators,” the Schrodinger equation.   I’ll not go into this in detail, but note only  the following: in physics there are pairs of what are called canonical variables: position and momentum, rotation angle and angular momentum, components of angular momentum, time and energy.   Heisenberg showed that one could not measure simultaneously and exactly the values for both members of such pairs. This is the Heisenberg Uncertainty Principle. You can get a short, non-mathematical primer on quantum mechanics here. (Pardon the shameless self-promotion!)

(2) Please note that the value of h, Planck’s constant, is so small that uncertainty effects do not manifest themselves for macroscopic objects.

(3) This time symmetry is followed for conservative systems. For situations where there is transport (flow of matter or energy) or dissipation (e.g. friction) then time will have a direction. The time dependent Schrodinger equation (which includes a partial derivative of the wave-function with respect to t, time) is not symmetric in time.  

(4) Heinlein gave perhaps the most ingenious twist to time travel with the story, “—All You Zombies—” (WARNING: SPOILER!) in which a man became his own mother and father.

(5) Ruth Kastner has written a fine book for the non-scientist about Cramer’s Transactional Interpretation.   For those with a stronger physics background, Cramer’s review articles (here and here) give an excellent exposition of his arguments.

(6) In that theory both “advanced” and “retarded” waves are used as vehicles for radiation emission and absorption. The advanced waves go backwards in time;  the retarded waves go forward in time; both are solutions of the wave equation for electromagnetic radiation. Conventionally, advanced wave solutions are discarded as physically unrealistic.

(7) See here.

(8) Isham and Butterfield have written an interesting article on how time might emerge from a theory of quantum gravity.

(9) Carlo Rovelli discusses time in all its aspects--philosophical, relativistic, thermodynamic (“Time’s Arrow”), psychological, quantum gravity--in a fine book, “The Order of Time.”  He concludes  that time is an illusion, a psychological mechanism brought about by evolution.  It’s a fine book, even though I disagree strongly with his conclusion.

Read Also:

What is Time? Part I—Philosophy

What is Time? Part II—How We Perceive Time 

What is Time? Part III—Entropy, Time’s Arrow

“What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.” -St. Augustine of Hippo, Confessions, Chapter 11

At the turn of the last century, a little remembered but dramatic debate took place between prominent astronomers Harlow Shapely and Heber Curtis. The debate concerned essentially several key issues: the location of the sun in the Milky Way galaxy, the size of the universe, and whether spiral nebulae were other galaxies. 

If someone asked you who discovered DNA, what answer would you give?

Niels Bohr, a friend with whom Einstein had many spirited debates about the nature of quantum mechanics, is said to have quipped on one occasion: “Einstein, stop telling God what to do.”

“What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.” -St. Augustine of Hippo, Confessions, Chapter 11

This is the second of six in a series. In the first, I discussed how philosophers, Greek and contemporary, viewed time. I’ll recapitulate briefly: one can think of the present as real, and time flowing like a river (“presentism” or “A-theory”), or one can think of “now” as just another coordinate to be designated in an eternal time, as “here” is an index in space (“eternalism” or “B-theory”).

In this article, we’ll focus on three stories of how we perceive time: St. Augustine of Hippo’s thoughts in his “Confessions”; the insights of the American philosopher and psychologist, William James; and what Oliver Sacks, a renowned author and psychiatrist, has to say.

St. Augustine of Hippo: time as a melody

St. Augustine discourses at some length on the nature of time in Book XI of Confessions. Even though he doubts that he can explain what time is (opening quote above), his explanations are insightful—particularly those about the timeless nature of God and how we perceive the passage of time.

In Chapters XXVI and XXVII of Book XI, St. Augustine examines whether duration is a measure of time; he assigns memory as the tool which makes the past real and designates forethought as our way to visualize the future. His discussion focuses on hearing a psalm, and how this example shows how our minds perceive the passage. 

Let me summarize with an example. Suppose you’re listening to music, perhaps a hymn. Listening to one note by itself will not give you the melody. It’s the memory of the previous notes, in sequence, that does so; and it’s the anticipation of the note that is to come that makes the melody memorable.

If we look at the score of Amazing Grace, we see the repetitive AABA pattern (look at the sequence of uppermost notes under “Amazing...sound”  “That...me” and “was...see” differing only in the final note). Memory and repetition plays a part in how the melody strikes us. It is a sequence in time, and duration is used to emphasize. Can one imagine all these notes existing simultaneously?

St. Augustine made the point that our perception of time is determined by perception of events in sequence. As with other insights of the wise saint, this view is echoed in contemporary psychology and neurology, as I’ll try to demonstrate below.

William James: the stream of consciousness 

William James (1842-1910) was a great American philosopher and psychologist and one of the founders of the philosophical school of Pragmatism. In his seminal work, “The Principles of Psychology,” William James proposed a theory of how we perceive time (Chapter XV).

James dismissed the notion that time is perceived as a sequence of separated, isolated events.  This would be “like a glow-worm spark, illuminating the point it immediately covered, but leaving all beyond in total darkness. ” (Chapter XV, The Principles of Psychology.) He emphasized that consciousness of events in the present was linked to memory of events in the past and the expectation of future events:

“...all our concrete states of mind are representations of objects with some amount of complexity. Part of the complexity is the echo of the objects just past, and, in a less degree, perhaps, the foretaste of those just to arrive. Objects fade out of consciousness slowly. If the present thought is of ABCDEFG, the next one will be of BCDEFGH, and the one after that of CDEFGHI—the lingerings of the past dropping successively away, and the incomings of the future making up the loss. These lingerings of old objects, these incomings of new, are the germs of memory and expectation, the retrospective and the prospective sense of time. They give that continuity to consciousness without which it could not be called a stream.” -William James. “The Principles of Psychology, Volume 1, Chapter XV [emphasis added]

According to James, the perceived “present” is not a point in time, but an interval:

“...the practically cognized present is no knife-edge, but a saddle-back, with a certain breadth of its own on which we sit perched, and from which we look in two directions into time. The unit of composition of our perception of time is a duration, with a bow and a stern, as it were—a rearward- and a forward-looking end” -William James. “The Principles of Psychology, Volume 1, Chapter XV

What is the speed of time? James observed that the more events in a given day for us, the faster time passes. Accordingly, we can say that if there were 1000 events during a day, the speed of time would 10,000 times faster (in consciousness) than if there were 1 event in 10 days. (See this nice video about James’s work.) These ideas about the speed of time in consciousness have been developed further by Oliver Sacks, a contemporary psychiatrist.

Oliver Sacks: 'speed,' how slow, how fast we think

In his book, “The River of Consciousness,” Oliver Sacks discussed how fast or slow mental processes can go in normal activities and for disturbed mental states. There are extreme cases when time seems to slow down and when it speeds up. Some of these occur in life-threatening circumstances, some during activities requiring subconscious skills, and some are the result of neurological or psychological disorders. However, all are evidence that the brain sets its own clock.

A man jumps from a high building and his life passes before him. That’s a familiar image, and it’s also a true one. Sacks recounts several stories of how time slows down in such situations:  a race car driver thrown 30 feet into the air in a crash experiences his accident calmly, in slow motion:

“It seemed like the whole thing took forever. Everything was in slow motion, and it seemed to me like I was a player on a stage and could see myself tumbling over and over… as though I sat in the stands and saw it all happening… but I was not frightened.” -Oliver Sacks, “The River of Consciousness”  

Time also slows down for good athletes, according to Sacks: training takes over in the subconsciousness while the conscious mind slows down time:

“But at some point the basic skills and their neural representation become so ingrained in the nervous system as to be almost second nature, no longer in need of conscious effort or decision. One level of brain activity may be working automatically, while another, the conscious level, is fashioning a perception of time, a perception which is elastic and can be compressed or expanded.” -Oliver Sacks, “The River of Consciousness”  

A telling example is that of bicyclists in a race:

“In a bicycle race, cyclists may be moving at nearly forty miles per hour, separated only by inches. The situation, to an onlooker, looks precarious in the extreme, and, indeed, the cyclists may be mere milliseconds away from each other. The slightest error might lead to a multiple crash. But to the cyclists themselves, concentrating intensely, everything seems to be moving in relatively slow motion, and there is ample room and time, enough to allow improvisation and intricate maneuverings.” -Oliver Sacks, “The River of Consciousness” 

Neurological and psychological ailments can also affect an individual’s tempo. Tourette’s Syndrome greatly speeds up activity:

“Some people with Tourette’s are able to catch flies on the wing. When I asked one man how he managed this, he said that he had no sense of moving especially fast but rather that, to him, the flies moved slowly.” -Oliver Sacks, “The River of Consciousness” 

Slowing down of time and motion occur in some psychological disorders. A time lapse scan of what seems to be arbitrary, random movements turns out to be a purposeful ordered motion.  Sacks talks about a patient with postencephalitic parkinsonism who seemed to be making such motions while sitting outside his office:

“I took a series of twenty or so photographs and stapled them together to make a flick-book… With this, I could see that Miron actually was wiping his nose—but was doing so a thousand times more slowly than normal.” -Oliver Sacks, “The River of Consciousness” 

Psychoactive drugs also change time action and perception. L-dopa can raise the levels of dopamine in the brain and thus accelerate time perspectives that have been slowed down by disease. Sacks relates the story of one such patient, Hester Y, who suffered from postencephalitic parkinsonism, and was treated with L-dopa:

“If she had previously resembled a slow-motion film, or a persistent film frame stuck in the projector, she now gave the impression of a speeded-up film, so much so that my colleagues, looking at a film of Mrs. Y, which I took at the time, insisted that the projector was running too fast.” -Oliver Sacks, “The River of Consciousness” 

So we see the speed at which we act and perceive time is governed by our brain, by its memories and neurochemistry. Even so, there are lower and upper limits to this speed.   However, as Sacks observes, we can extend those limits by instruments: telescopes to observe over billions of light years from the Big Bang to the present and laser optics to act in nanoseconds.

To Come: 'entropy,' the arrow of time

The next article in this series will deal with entropy, “the arrow of time.” I’ll present, as a preliminary, a mini-tutorial on what thermodynamics is all about.

Read Also:

What is Time? Part One—Philosophy

A Point in Time: Not All Time is Linear

New Ebook Discusses How to Navigate the Weirdness of a Quantum Universe 

Why do people care what Einstein thought and believed about religion and about God?

This is to be a series of six articles that try to answer the question posed in the title. Necessarily, it will be a selective and brief survey of what has been written about time. I’ll summarize answers given by philosophy, psychology, and physics. The physics articles will deal with “entropy, the arrow of time,” with the physics of motion—classical and relativistic—and with how (or whether) time is manifested in quantum mechanics. I’ll try to explain the science in simple terms, minimizing mathematics and giving lots of links and references to videos.

“It is also necessary—may God grant it!—that in providing others with books to read I myself should make progress, and that in trying to answer their questions I myself should find what I am seeking. Therefore at the command of God our Lord and with his help, I have undertaken not so much to discourse with authority on matters known to me as to know them better by discoursing devoutly of them.” -St. Augustine of Hippo, "The Trinity" (I, 8)