quantum theory as demonstrated in
the Double Slit Experiment
A central tenet of the Copenhagen Interpretation, a term that embraces all of quantum physics from Heisenberg’s description of Bohr’s understanding up to and including the current consensus, is that the Arrow of Time points from the past to the future, whence Richard Feynman’s use of the phrase “Sum over Histories” to describe the Path Integral approach. This is in conflict with the view of Sir Arthur Stanley Eddington, inventor of the term “Time’s Arrow”:
“The existence of a thermodynamic arrow of time implies that the system is highly ordered in one time direction only, which would by definition be the ‘past’”.
He added later:
“It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.”
This prediction has been fully borne out in the subsequent development of quantum physics which is better known for its paradoxes than for the far more successful mathematics that supports it. Fortunately, a simple return to Eddington’s definition eliminates all such enigmas and provides a common sense description of the quantum realm. This is readily evident in the Double Slit Experiment.
On March 6th, 1998, at the Second Millennium Evening at The White House, Stephen Hawking said:
“What now appear as the paradoxes of quantum theory will seem as just common sense to our children’s children”.
Hawking made this statement a generation ago–our children’s children are already with us–yet the quantum world remains as counterintuitive as ever. As a result, instead of common sense, we have the Looking Glass generation, capable, like the White Queen, of believing six impossible things before breakfast, but without the ability to make sense of any of them.
To understand how this state of affairs came to be, while others far more qualified than I have investigated the physics, I have looked for conflict in the unquestioned assumptions that underlie both the common sense and the scientific positions. It turns out there is one crucial discrepancy between them which, once taken into account, renders the quantum realm, at least as it appears in the Double Slit Experiment, readily comprehensible; in fact, common sense.
I call this approach the Clapham Interpretation, after the man on the eponymous omnibus.
But first, a little background…
The Double Slit Experiment was first devised by Thomas Young in 1801 to determine whether light consisted of waves, or of particles, as Newton believed. The experiment involves shining a monochromatic light source through two slits in a barrier (to provide two coherent sources) onto a screen. Young’s experiments produced the interference patterns characteristic of waves, and appeared to settle that question. However, in the last century. versions capable of sending individual electrons and photons through the slits have produced an interference pattern made up of particles, implying what is now known as wave/particle duality. Currently, in laboratories that can transmit molecules as large as buckminsterfullerene–buckyballs to you–results have confirmed that this duality is not a property of electromagnetism alone, but of matter as well.
DOUBLE SLIT EXPERIMENT:
The current version consists of a transmission source, a barrier with two slits and a screen capable of registering the impact of whatever is transmitted. There is also a device (operated by a switch of some kind or capable of being plugged and unplugged) that is able to detect the passage of whatever is transmitted once it passes through the slits. With this detector switched off or unplugged, each photon/molecule will pass through the barrier in some way to arrive at the screen in a distribution according to probability. However, if the detector is switched on, then each will arrive at a location according to its linear trajectory.
There are no criteria for the switch; any ordinary power switch will do to turn the distributions off and on.
If the detector is replaced by a measuring device, the subsequent trajectory, if it continues, is similarly linear.
The best and clearest description of the Double Sit Experiment that I have seen lately is by Professor Jim Al Khalili on YouTube. His setup is essentially as I have described it, but with one important difference when it comes to discussing particle-like behaviour: where most people have simply turned down the intensity of the light source until it releases only one photon at a time, the Professor uses atoms from an atom gun. Atoms are indisputably particles, so can only go through one slit or the other; they should not be physically capable of interfering with each other.
At the same time, we now know that the wave form is a real wave, not purely statistical. This is nicely demonstrated in what is called the Afshar experiment where physical wires across the light path cannot be detected when they would coincide with troughs in the wave form, but clearly affect the light when there is no second slit to create interference.
The first time we see Al Khalili’s gun, he’s taped over the top slit, and we can plainly see particles hitting the screen behind, slightly scattered, but perhaps normal for atoms, as the Professor says. But the next time, when the second slit is also open, as with the electrons, we see the atoms build up in a wavelike interference pattern, even when they are sent through one at a time.
That is where the detector is brought in to see what is causing the interference. It is set to count the atoms that pass through the top slit, and we can assume the others go through the other one. Sure enough, all the atoms are accounted for, but this time there is no interference pattern. At this point, just to cover every possibility, the Professor disconnects the detector, leaving the apparatus in place, whereupon the waveform returns.
This sounds like a trick, I know, but there is none. You can use a perfectly ordinary domestic power switch or the most elaborate remote device, the result is the same: so long as you turn on the detector, there will be no waveform pattern. Turn it off, and the pattern returns. Similarly, the professor is not trying to confuse you. His description of the phenomena is accurate, and identical experiments have been performed many times around the world for over a hundred years now.
It is this last example that so shocks the scientific mind. The quantum world is Nature at her most fundamental; the idea that such a simple, even arbitrary, interaction as turning a piece of equipment on or off could even be noticed, let alone reacted to, seems to turn science on its head. It’s no wonder that even leaders in the field take it badly:
“Quantum physics describes a world in which nothing has a stable existence: an atom or an electron may be a wave or a particle, depending on how you look at it; cats are both alive and dead. This is great for popular culture, which has made ‘quantum’ a buzzword for cool, geek mystification. But it’s terrible for those of us who want to understand the world we live in, for there seems to be no easy answer to the simple question, ‘What is a rock?’”
Lee Smolin, “Einstein’s Unfinished Revolution”
AND CURRENT CONSENSUS
The Copenhagen Interpretation was originally formulated by Niels Bohr and Werner Heisenberg in Copenhagen, whence the name. There are a couple of givens: first, the Arrow of Time, in the sense of causation, points from Past to Future. However, as Hawking himself said in the next sentence to the earlier quote:
“In quantum theory things don’t have a single unique history as our present day common sense would suggest.”
That ‘single unique history’ is replaced by Richard Feynman’s ‘Sum over Histories’, i.e. all possible trajectories, now known as the Path Integral Formulation.
Secondly, all possible paths are in a composite state known as “superposition”.
As Wikipedia puts it: “The principle of quantum superposition states that if a physical system may be in one of many configurations—arrangements of particles or fields—then the most general state is a combination of all of these possibilities, where the amount in each configuration is specified by a complex number”. The resulting theory of quantum electro-dynamics (QED) produces calculations that are extraordinarily accurate, equivalent to calculating the distance from the Earth to the Moon to within the width of a human hair.
Thirdly, if a measurement takes place, only that value can be known, and all other probabilities disappear through what is called Wavefunction Collapse. Its causes are unknown:
“But if the wave function undergoes spontaneous collapse, as soon as that happens the game is up. If spontaneous collapse is right, no experimentalist will ever be able to superpose two wave functions of a large, complex system.”
Despite its computational power, this interpretation of quantum phenomena gives rise to a number of paradoxes, the best known being the Observer Effect, Quantum Leaps, Schrödinger’s Cat, Heisenberg’s Uncertainty Principle, the EPR Paradox, the Multiverse, Everett’s Many Worlds Theory, etc.
Now for the CLAPHAM INTERPRETATION:
One small point: the physics community has a huge human and intellectual investment in the Copenhagen Interpretation. It is almost a hundred years since it was first formulated by Bohr and consequently Heisenberg. Whole careers, not to mention whole lives, have since been devoted to formulating and calculating the paradoxical implications of their ideas. Any common sense, and thus realist, version is naturally bound to be dull by comparison. Nonetheless, it is that dullness that argues best for its likelihood, as Charles Peirce would agree.
“There is a reason, an interpretation, a logic, in the course of scientific advance, and this indisputably proves to him who has perceptions of rational or significant relations, that man’s mind must have been attuned to the truth of things in order to discover what he has discovered. It is the very bed-rock of logical truth.”
Charles Sanders Peirce
If we deny Peirce, we deny our ability to recognise truth in any form whatever. Perhaps the most damaging legacy of the Copenhagen Interpretation has been that it is no longer possible in any branch of science–or public discourse generally–to say: “But that makes no sense!”
The “crucial discrepancy” I mentioned at the beginning refers to a logical fallacy at the heart of the Copenhagen Interpretation; remove it, and the Double Slit Experiment becomes not a paradox, but a proof, and Hawking’s unwitting prediction comes true.
In the late ‘20s, when the foundations of quantum mechanics were beginning to be laid and the Copenhagen Interpretation to be formed, the soon-to-be knighted Arthur Stanley Eddington was working on the Nature of the Physical World, published in 1928, where he wrote the following:
“Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the state of the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. That is the only distinction known to physics. […] I shall use the phrase ‘time’s arrow’ to express this one-way property of time which has no analogue in space.”
Later he added:
“The existence of a thermodynamic arrow of time implies that the system is highly ordered in one time direction only, which would by definition be the ‘past’”.
This presents an interesting problem; the mathematics don’t show a preferred direction for Time. I’ll explain why in a moment, but for physicists Time is like a railway track; it has no inherent direction. Nowadays even the trains no longer have an engine at the front, so if you were to film a train and then play it in reverse, you would not be able to tell in which direction the train was originally travelling, to left or right. Both directions would look the same.
This is known as Reversibility, and is a crucial issue in physics. However, any passenger on the train can easily tell which way the train is going without even looking out of the window. To give a local example, if Falmer comes before Lewes, then you’re on your way to Eastbourne, but if Lewes comes before Falmer, you’re heading for Brighton. We can do the same with Time, as Sir Arthur points out: if we follow his arrow and the world becomes more and more random, or ‘probabilistic’ as we would say today, then the Arrow of Time is heading into the Future, but if it is becoming less so, it points towards the Past.
So, there is a second arrow, and what’s more, it is the Event Arrow. This is what Einstein meant when he spoke of Time as providing “the order of events by which we measure it”. An “event”, in this sense, is any temporally defined occurrence. This would include, for example, the 17th century, World War II, last Tuesday, even the Pleistocene,1 all of which are now in the Past, but also next Thursday or my granddaughter’s fourth birthday, which remain in the Future.
In this, all ‘events’ are the same–birthdays, wars, collisions in particle accelerators–all of them start out as a range of things that might happen, then they happen, and then they’re over. They start in the future, happen in the present, and end up in the past. Also, just like birthdays, they never go the other way. Events are “Irreversible”. Nothing ever comes out of the Past into the Present, acquires the probabilities it needs and becomes a Future possibility. Time itself only flows in one direction, and that is into the Past. Of course, you can have a sequence of events, just as you will go on having birthdays, but each individual birthday will follow the same sequence: future, then present, then past. The fact that an event can be causally related to another future event does not alter the inherent direction of Eddington’s Arrow. All we know from that is that we are travelling upstream. That is the Arrow of Us.
Unfortunately, as we’ve seen, the Copenhagen Interpretation’s Arrow of Time originates in the Past and leads to the Future, as physicists today generally equate the Arrow of Time with the Arrow of Causality. Even Lee Smolin, who argues convincingly for a universe where Time is fundamental and Space is emergent, adopts as his First Hypothesis that “Time, in the sense of causation, is fundamental” which contradicts Eddington and thus common sense.
The common sense view, as I hope you’ll agree, is that the Past consists entirely of what has already happened, while the Future consists solely of what might possibly happen, but hasn’t yet, if it ever does. The Present, of course, is reserved for what is happening “now”.
The Present is more interesting than the other two states, and somewhat less intuitive. Most people would consider the Present as lasting a reasonable amount of time, enough at least to get work done. However, at the quantum level, it can’t possibly be long enough for anything to happen during it, because then the past would start at that point, by definition. It has to be shorter than that.
In fact, and this is key, no change at all can take place during the quantum present if it’s to avoid instantly becoming the past. At the same time, it can’t simply be zero, as that would mean it does not exist, which it patently does. It has to be greater than zero, just enough to form a buffer between future and past, but in the course of which nothing can happen.2
In short, the present is binary.
But how short is it? Thanks again to Max Planck who reluctantly defined it for us, we know how short it is, and it’s very, very short: 5.39116(13)×10-44 seconds. He called it Planck Time, and defined it as “the time required for light to travel, in a vacuum, a distance of 1 Planck Length”, 1.616229(38)12×10−35 metres, or the length of what we now call a photon, i.e. a quantum of light. Most importantly, there is no interval between Planck Times; when change occurs, it is instantaneous, whence the Quantum Leap so distasteful to Bohr and, incidentally, Smolin.
If we accept the above, then it follows logically that the correct sequence for the Arrow of Time must be, as Eddington says, first the Future, where the probabilities of an event’s occurrence reside, followed by the Present, where those probabilities are replaced by what actually occurs, and finally the Past, when it becomes history.
These three temporal concepts–Future, Present, and Past–roughly correspond to the three quantum states: Potential/Probabilistic, Active/Actual, and Inertial/Deterministic. However, they all take place in what we would consider the Present, so when we look at the Double Slit Experiment, that is precisely what we see: initially the default Potential/Probabilistic state, a combination of uncommitted future possibilities and an uneventful Present. The probabilities are there in the form of Schrödinger’s Wavefunction, and it is in that form that they pass through the slits and are distributed according to Feynman’s Probability Amplitudes, creating the interference pattern. These are not histories, then, as Feynman called them, but futures, which eliminates the requirement for superpositioning, and thus a whole class of anomalies, including all causality paradoxes3. As to whether those probabilities are ‘real’ or not, Afshar notwithstanding, all we can say is that those really are the odds, just as they are at the bookmakers. However, they do follow the One Rule: “If nothing happens, nothing happens”. Until something, an event, actually occurs, we remain in the default Potential/Probabilistic state.4 Smolin actually says this:
“Naively, when we say that something is possible, such as that my son’s lizard might become pregnant in the next year, we mean it is among the things that might happen. When something possible happens it becomes part of the real; but till then it is not real.”
Lee Smolin, Einstein’s Unfinished Revolution
Eventually, the atoms hit the screen, at which point the probabilities all vanish, leaving only the actual fact of their extinction. At this point they become what I call Past Particles and are absorbed into the fabric of the universe, while their energy and momentum are conserved in the inheritor Present.
However, before that point, we meet the detector.
So long as the detector is on, each detection will constitute an event, i.e. something that happens, taking us directly into the Active Present. We know they constitute quantum events because the probabilities do, in fact, collapse to what is actually happening. Turn it off, and we are event-free again.
Parenthetically, between the detector and the screen, the quantum, now a particle, continues on its trajectory until it hits the screen, thus entering the residual past. That continuing motion is the Inertial/Deterministic state. It also answers one of Smolin’s major problems, which is that, among all the rest of the issues, it is very hard to see how the Copenhagen Interpretation can provide the necessary energy and momentum for causation to take place. Particles do that perfectly, whence the Determinism.
This is precisely the sequence that Eddington defined for his thermodynamic Arrow of Time.
To sum up:
Looking at the experimental set-up, what we have at one end is stuff that’s going to happen, and at the other stuff that will have happened. In the middle it happens. Falmer, Lewes, ergo Eastbourne.
What we start with is probabilistic, whence the wave form, and what we end up with is particles that strongly resemble the atoms we thought we were starting with, and so the cycle continues. This isn’t just common sense quantum theory; it’s also common sense ‘atom gun’. That’s how guns work; you pull the trigger and the bullet comes out. If you didn’t know about the first probabilistic stage, it would simply be pull the trigger and the atom comes out. After that, it’s just ballistics.
That is the world of classical mechanics, the world of Newton, Pascal, even Aristotle and everybody else until a hundred years ago. All I’m telling you is that it is also our world. On the other hand, there is an element of statistics. There seems to be a safety margin built in just to make sure that the expected result actually occurs. So even after the wave function has collapsed, we can still see what you might call entropic redundancy in the scattering. It is this vital superfluity at the quantum level that ensures predictability at the macro level, and incidentally gives us Eddington’s beloved Second Law.
It is now time for me to reveal the dull and, quite frankly, disappointing, albeit common sense, truth I promised you at the beginning: there is no Arrow of Time. Nothing actually goes into the Past or into the Future; everything is always in what we call the present, because that is all there is. Of course, we can remember the Past, so it feels real to us. I am never sure whether it is the Madagascans or the Maoris who describe us as walking backwards in Time, because we can see the Past but not the Future, which is endearing, but the truth is that we cannot see the Future because it does not exist. Sadly, that is also true of the Past, although we can see where it used to be, the traces that remain: in quantum terms, the residue of waveform collapse.
It follows that the Present has to provide all that the universe–and we–need.
John Archibald Wheeler once made the joke that Time was Nature’s way of avoiding everything happening at once, and physicists believe that. However, in reality, everything that happens must happen simultaneously with everything else that is happening. The Present is the same throughout the Universe. That is why, when we see a supernova, for instance, we can calculate how far away it was and precisely when the explosion took place. If the Present varied in different parts of the Universe, as it might in a Multiverse for example, we would not be able to make that calculation.
So that is my gift to you: the Present that keeps on giving!
Let’s hear it for Now!
Before I finish, I must tell you that Eddington had one more thing to say about his thermodynamic Arrow of Time:
“It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical,”
which brings us directly to:
Recognition of the quantum realm was a defining moment in science. From that point on, scientists have abandoned their traditional role of devising formulae that accurately reflect reality, choosing instead to devise realities that reflect the formulae. This brought us problems right from the start: Heisenberg’s Uncertainty Principle5, for example, and the EPR paradox; Schrödinger’s cat and the superposition of states, through ultimately to the Multiverse. Niels Bohr didn’t even like quantum leaps6.
In this interpretation, the two states are sequential, not simultaneous, so no “superposition” is required (See above)
When a race is to be run, whether of horses, people, cars or, famously, raindrops on a window pane, bets can be laid; there are probabilities. Even after the starting pistol has been fired and the bookmakers close their books, there are still probabilities as the fortunes of the track take over. However, at the point that the winner passes the post, or breasts the tape, the probabilities vanish, or collapse if you prefer. The important point is that no interaction is required for that to happen. It is purely a function of Time. The Present becomes the Past.
That is how it is in the quantum realm.
(See “One Rule” above)
Preserves the original particulate structure and translates the probabilities into spatial distribution in the form of the wave.
In the end all we can say about Schrödinger’s cat is that it was alive when it went into the box, and no one knew at what point it would die in the future. Pretty much the way I feel when I go to bed. Until it happens, it’s in the future, which is uncertain; when it happens, it goes into the past. The present is just where that transaction takes place.
The sad thing is that this was Schrödinger’s attempt to get to the central fallacy of the Copenhagen Interpretation, i.e. that the physicist’s Arrow of Time is pointing in the wrong direction. It didn’t help that his main opponent, Einstein, believed in a Block Universe, now known as Spacetime, where Time, specifically Past, Present and Future, exists as a single and unchanging entity where any arrow can point in any direction, even with conflicting results.
(See Upstream above)
The EPR Paradox/Entanglement
Imagine that somewhere in the plotline of The Godfather, Don Vito Corleone is betrayed by twin brothers. He determines that they must die, and he alone is to kill them. They head for the (widely separated) hills, where they live in fear (and anonymity). Eventually, Don Vito dies, and simultaneously their curse is lifted. No information travels anywhere, there is no “spooky action at a distance”. Nonetheless, the probability of either of them dying at the hands of Don Vito drops to nil.
Entanglement at the quantum level is an aspect of the universal present. Entangled quanta thus share a timeline. If nothing happens, nothing happens; the future probabilities of the two quanta remain unchanged, and therefore identical. Should something happen, e.g. one of them is measured in the dimensional universe, they both simultaneously “collapse” into past particles, regardless of wherever in that universe they may be. In other words, they are synchronised.
That’s about it, really. Same goes for Quantum Teleportation.
Heisenberg’s Uncertainty Principle
Any event must cause complementary properties, e.g. position and momentum, to collapse simultaneously.
The story goes that Hugh Everett was pondering the double slit experiment when it occurred to him that another way of viewing the photon’s appearing to pass through both slits at the same time would be if the universe itself split into two identical universes, with the photon passing through the left slit in one, and through the right slit in the other.
This has now gone from unthinkable nonsense to accepted mainstream thinking, championed by most, if not all, leading quantum theoreticians. Sadly, if he had only given it just a moment’s more thought, he would have realised that if the universe were to split into two different realities, then we would not see the interference pattern. We would only see one inheritor reality or the other. For the interference pattern to be visible requires that both realities be present, and thus the universe cannot have split.
Shame about that.
This is Schrödinger’s version of the above, and arose from the same basic fallacy that this article is about. His idea was that, rather than there being a single universe with a single coherent set of universal laws, quantum superpositions are actually multiple universes, each with its own laws. If you’ve read this far and still entertain these ideas, I can be of no more help to you, and must accept that I have failed.
The universe is binary, with a helluva flop rate. Furthermore, as I understand it, any well constructed formula only has one possible outcome, so the probabilities should resolve themselves. The drawback is what is called the Holevo Bound. To save you looking it up:
“In essence, the Holevo bound proves that given n qubits, although they can “carry” a larger amount of (classical) information (thanks to quantum superposition), the amount of classical information that can be retrieved, i.e. accessed, can be only up to n classical (non-quantum encoded) bits. This is surprising, for two reasons: (1) quantum computing is so often more powerful than classical computing, that results that show it to be only as good or inferior to conventional techniques are unusual, and (2) because it takes 2n − 1 complex numbers to encode the qubits that represent a mere n bits.” Wikipedia
In short, precisely what you would expect from qubit past particles.
Hawking Chronology Protection Hypothesis
This is it.
The sequential present provides Relativity with Einstein’s array of synchronised clocks. Nonetheless, so long as E=mc2 remains just a coincidence (see elsewhere on this site), the story is not over.
The c Paradox
In order for c to be the speed of light, light must travel at that speed; however, at that speed, light does not travel; it is already there, where it has always been7. Even as a schoolboy I knew that, if nothing can travel at the speed of light, then light must either not travel, or be nothing. It simply didn’t occur to me that both would be true. Nonetheless, a combination of time dilation, which they were so worried about when defining the second89, and length contraction, which is to speed as perspective is to distance10, if taken to its logical conclusion, means that, at the speed of light, all meaningful concepts of measurable existence cease to be. At that speed, and only electromagnetic radiation can actually “travel” at that speed, the entire universe is a dimensionless, timeless point in a non-existent void; essentially the initial conditions of the Big Bang, which is where this story started.
You can see why I say that the Clapham Interpretation has a nice GUT feel to it.
Getting back to the Hawking quote above, I have a three year old granddaughter (my child’s child) who is quite familiar with the definitions I have cited above. She knows when her birthday is due, for example, and as it draws near, she constantly discusses all the possibilities that involves, from bouncy castles to the types of cake she would prefer to have. She does not see these possibilities as “superposed” in any way, since she knows that we are discussing future possibilities of which only a subset will become reality.
When her birthday finally arrives, she is generally delighted with what is actually happening, and unfazed by the unrealised possibilities. Even if she would have liked jelly, she consumes the strawberries with gusto. She is a realist.
The next day she understands that the party’s over, and she must be content with her memories (and whatever is left in the fridge).
I should point out that I am not stating unequivocally that this version is the only possible one, although its simplicity and logic is appealing. I know that many people, including those with whom I have discussed this, much prefer the more intriguing version, and there may be something in that. I did say the common sense version would be dull. However, the fact that the central misunderstanding arises solely from conventional physics having the Arrow of Time pointing in the wrong direction at the quantum event level leads me to suppose that this approach will be useful. It explains everything about the Double Slit Experiment in terms that the average person will easily accept, and thus might well make a suitable version to be presented to Hawking’s future generations.