David L. Martin

in praise of science and technology

Revolution 3 – Quantum Mechanics

For centuries, physicists have debated about light.  What is it, exactly?  Does it consist of particles?  Or is it a wave?  It turns out, both, sort of.  Light has particle characteristics, and wave characteristics.  In everyday life, we see particles of various sizes.  Dust particles.  Baseballs.  Planets.  What makes a particle a particle is that it’s separate from other particles.  And we see waves.  Water waves particularly are very familiar.  What makes a wave a wave is that it’s continuous.  It’s spread out.  It’s part of a larger whole.

waves-circles-water-wave-circle-rings-arrangement-1

Waves do things that particles don’t.  A wave’s very existence depends on how it interacts with the waves around it.  If two waves collide, and one is as its crest while the other is at its trough, they will cancel each other out.  Think about that for a moment.  The two waves come together and the result is NO WAVE.  They just vanish.  This is called interference.  On the other hand, if they are both at their crests when they collide, the result will be an even bigger wave.

Imagine if particles acted this way – peanuts, baseballs, people – if sometimes, when they collided, they just vanished.  The universe would look very different, obviously.  Particles do not exhibit interference.  Or do they?

photons_iso

Photons, the so-called particles of light, unquestionably behave like particles.  In fact, we have devices that can shoot them, one at a time, like tiny bullets.  When we do this we can see the impacts on a screen, where each photon is absorbed.  Although we can’t see the photons in flight, each photon hits one and only one spot on the screen.  Particles.  No doubt about it.

Now suppose we start shooting photons toward a screen, one at a time.  Between the emitter and the screen we place an opaque barrier with 2 slits close together.  And we fire away.  As always, each photon that passes through hits the screen in only one spot.  But was we accumulate hits, we notice something strange.

fringe

What the hell is this?  Instead of 2 distinct clusters of hits, corresponding to the 2 slits, we get this fringe pattern.  Well, it turns out we know of something that exhibits a similar effect – water.  If we create water waves on one side of a barrier with 2 slits, as they pass through the slits they create new sets of waves, centered on each slit.  Waves do not simply strike each other.  They can interfere with each other.  When a crest encounters a trough, they cancel each other out.  When a crest encounters another crest, they reinforce each other.  The result, in a 2-slit situation, is a fringe pattern.

waterwaves

At this point you may well ask, “What are you saying Dave?  That somehow an individual photon can interfere with itself?”  That’s exactly what I’m saying.  Quantum mechanics dictates that the seemingly particulate photon goes through both slits.  Eventually it hits the screen in only one spot.  But where it hits is dictated by wave mechanics.  The photon in flight behaves like a wave.

Now you may notice that the water comparison doesn’t quite hold up.  With water waves, you don’t see bright lines with dark areas in between.   Along each path leading to each bright area, the water waves are still “waving.”  Up and down, up and down.  Along each path leading to each dark area, the water is flat.  How does this translate into photon behavior?

SchrodingersEquation

The mathematics of quantum mechanics can be very intimidating.  But it’s really not hard if it’s presented visually.  Suppose we have a series of waves like the blue waves below.  Let’s say that the “waviness” at any given position translates into the probability of finding a particle at that point.  This is represented by the red wavy line (and the intensity of the red dots).  Notice that there are places where we will never find the particle.  This is because of the underlying wave mechanics.

  qmplanewave

This is really the nuts and bolts of quantum mechanics.  If you understand this figure, you understand QM.  The position, momentum, energy, and other characteristics of particles are described by wave mechanics, and this is why we see a fringe pattern when we shoot photons at a screen.  But the strangeness has only begun.  What if there’s a way to distinguish the 2 paths?  What if we had some way of “marking” the photons passing through, so that we KNEW they went through one slit and not the other?  In fact, we can.  I won’t go into the details, suffice it to say that we can do this, without even actually knowing which slit a particular photon went through, only that it went through one or the other, not both.  What happens now?  When we accumulate lots of hits, we get the pattern at the top of this image:

doubleslitparticlewave

Instead of the fringe pattern (the bottom pattern), we get photon hits that accumulate in 2 distinct areas, corresponding to the 2 slits.  The photons now behave, in flight, like particles, simply because we have information that tells us each one had to go through one slit or the other, not both.  Notice that many of these photons strike the screen in areas that were pretty dark when the fringe pattern was produced.  It’s important to realize that we only have to place a “marker” in the path through ONE of the slits to eliminate the fringe pattern.  This marker tells us that either the photon went through that slit or it didn’t.  Since the only alternative is the other slit, we don’t have to do anything at all to any photons going through the other slit.

doubleslit2.jpg

What I’m saying is that the photons that go through the other slit are NOT EXAMINED DIRECTLY in any way, let alone altered.  Yet they fail to accumulate in a fringe pattern on the screen.  They stop “avoiding” some of the areas that are normally dark when the fringe pattern is produced.  It is only because we have information about their path that they change their impact pattern on the screen, not because they are examined or interacted with directly.  It’s as if they “know” what’s going on along the other path, which they never follow.

Think this is strange?  I’ve only just begun.  What if we could somehow “erase” the information about which path each photon went through?  It turns out we can do this too.  Instead of using a double slit, let’s really separate the two paths.  In the upper part of the figure below, we are shooting individual photons from the lower left through a beam splitter (the green object).  This is simply a half-silvered mirror.  An individual photon has a 50% chance of going straight through, and a 50% chance of bouncing off.  We have ordinary mirrors in each of these alternative paths, which cause the paths to cross at the upper right.  But if we put a screen in the red path, it can only be struck by photons following that path.  So we should see a particle-type pattern.  And we do.

quantumeraser

But what if we place a second beam splitter right at the point that the two paths cross, like in the lower part of the figure?  It shouldn’t make any difference at that point right?  The individual photons have supposedly already “committed” to one and only one path by then.  They can’t back up and retrace their paths, changing their behavior.  We still get the “particle” pattern on the screen, right?  Wrong.  If we place a screen in the path, we get the fringe pattern.  This is called a quantum eraser, and it has been observed many times.

entanglement

Obviously, water waves do not behave like this.  Saying that tiny particles have wave-like behavior doesn’t fully explain quantum phenomena.  The strangeness goes much deeper than that.  Another experiment illustrates just how deeply it goes.  What if we could somehow delay the acquisition of information about which path the photons took, until AFTER they had been detected at their destination?  Surprising as it may seem, we can do that too.  We can do it by splitting a photon into 2 new photons.  The way we do this is by sending it through a special crystal.  The photon strikes an electron within the crystal.  The electron absorbs the photon, causing the electron to jump to a higher energy level.  Very quickly it will drop back down to its previous energy level, but this time it does it in two steps.  Each step produces a new photon.

delayedchoiceab

Each of these new “daughter” photons is said to be entangled with the other.  That is, the characteristics of one must always complement the characteristics of the other, no matter how far they travel.  So here’s the experiment.  We send the “parent” photon through a barrier with a double slit.  Then we send it through our special crystal, splitting it into 2 entangled photons.  We then send these 2 photons through two separate experiments.  One photon (we’ll called it photon 1) simply goes to a screen.  The other (photon 2) is directed through a carefully positioned set of mirrors and beam splitters.  Depending on what path it takes, it will hit one of four detectors.  If it hits detector A, the “parent” photon must have gone through slit 1.  If it hits B, the “parent” photon must have gone through slit 2.  If it hits C or D, we don’t know which slit the “parent” went through.

But here’s an important point:  Photon 2 will only reach one of these detectors AFTER photon 1 hits the screen.  Thus the “marking” only occurs after photon 1 has completed its journey.  So what happens?  Do the original photons behave like particles or waves?  Answer:  It depends on whether one of their entangled “children” will eventually be marked.  “Wait a minute!” you might say.  “What do you see on the screen? Some of the photons behave like waves and some don’t?  You can’t have a fringe pattern AND at the same time, a particle pattern!”  Actually, you can.  Some of the photons go through slit 1.  Their “daughter” photons produce a particle pattern on the screen.  Others go through slit 2.  These “daughters” produce another particle pattern.  Still others go through both.  These produce a wave pattern, a fringe pattern.  But all of these patterns are superimposed on the screen.  Only by identifying which photons hitting the screen correspond to which photons hitting each of the other detectors can we tease apart these patterns

delayedchoicequantumeraser

In other words, it’s as if each photon “knows” whether one of its entangled “children” will or will not eventually be marked, and insists on behaving like a particle or wave, accordingly.  Even if we delay the acquisition of this “knowledge” until after one of its “daughters” has hit its screen, been absorbed, and is long gone, this still affects the behavior of the “parent.”  This is called a delayed choice quantum eraser.  In principle, we could delay the acquisition of the “which slit” information for a HUNDRED YEARS.  The “parent” photon would have to adjust its behavior according to actions taken a century later.

Quantum_Supe

It hardly needs to be said that explaining this requires something pretty strange.  And the standard quantum mechanical explanation is just that.  Here it is:  The photon doesn’t follow a particular path, UNTIL the experiment is complete and the fate of all of its entangled “daughters” is established. A physicist would say it’s in a superposition of states.  It is spread out, and it will stay spread out until the fate of its “offspring” is decided.  It is in more than one place at once.  The implication of this is astounding – the screen itself is in multiple states, until the fate of the entangled photon is known!

Don’t misunderstand me.  I’m not staying that if you look at the screen, you will see the same photon hit multiple spots.  I’m saying that the screen AND you, if you’re looking at it, are in a superposition of states.  There are other versions of “you,” looking at other screens which are in different states.  Any given version of you only sees one of them.  This seems to be the only way to account for what we observe in these experiments.

quantum_entanglement

The “daughter” photons discussed above, in the delayed choice quantum eraser experiment, are linked.  They are part of a combined system that is spread out in space.  The photons are said to be entangled.  When they interact with a larger system that has information about both of them, they will always be found to have complementary states.  Even if the system measures the 2 photons when they are miles apart, and measures them AT THE SAME MOMENT, they will always be found to have complementary states.  It’s almost as if they are in instantaneous contact with each other.  In quantum mechanics we call this non-locality.  Einstein called it “spooky action at a distance.”  The only way to explain it, seemingly, is to say that the 2 particles are not really separate – that they are parts of a combined system that is in multiple states until it is measured.  It means that we can’t speak of a particle as having an existence in isolation from the rest of the universe.

doubleslit

Now at this point, dear reader, you may interject, “Well, okay, this is pretty weird, but light is special.  It’s not matter, it’s energy.  Matter is made of particles, not “wave/particles.”

Matter is made of particles all right.  Subatomic particles.  Protons, neutrons, and electrons.  It turns out we can shoot individual electrons, one at a time, just like we can shoot individual photons.  What happens when we shoot some through a double slit apparatus?  This:

electronfringes

Electrons exhibit the same kind of behavior that photons do.  We see fringes when we don’t know which slit each electron goes through.  We don’t see them when we do.  All of the strange effects I have described apply to matter as well as light.  An electron isn’t actually a particle, until it interacts with a large system.  Until then, it’s a wave/particle.  And what it does is influenced not only by what you do to it directly, but what you do to any particles it’s entangled with, even in the future.

pilotwave

Some physicists have argued that actually, particles like electrons and photons always behave like particles.  It’s just that these particles are GUIDED by a “wave function” that gives them wave-like behavior, just like a ball in flight is guided by mathematical rules.  This is called the pilot wave theory.  The problem with this is that this pilot wave has to somehow take into account what the entangled “children” of the particle will encounter in the future, even after some of them are long gone.

freeparticle

The only way out of this conundrum, seemingly, is to assume that the wave/particle is actually doing all of these different things at once – in other words, that it is in superposition.  When it interacts with a larger system, that system becomes entangled with the wave/particle.  The system only “sees” one of these possibilities.  That’s what we call measurement.  But our measurements can be affected by what happens to other parts of the wave/particle that we don’t measure directly, even if those events are far away, or in the future.  In this sense, quantum mechanics does involve a kind of time travel to the past.

radioactiveatom

Because matter obeys the laws of quantum mechanics, we can get some very strange effects.  Let’s take radioactive material for example.  The reason some substances are radioactive is that their atoms are falling apart.  They are losing some of their subatomic particles, like electrons.  But whether a particular atom will lose an electron is only a probability, not a certainty.  Quantum mechanics dictates that as long as the atom is observed, it is “trapped” in a state of non-decay.  When it is not observed, it enters a state of superposition between being intact and having decayed.  When it is observed again, it will be seen to be in one state or the other.  But the atom will never show ANY SIGN that it’s about to fall apart.  It will always be either intact or decayed.  Nothing is “breaking.”  Nothing is “wearing out.”  It is all or nothing.

radioactivedecay

Let’s say the atom has a 50% chance of decaying within 1 hour.  Within 24 hours, it’s almost sure to fall apart.  But until this happens, the atom doesn’t degrade, decompose, wear down, or anything of the sort.  Quantum mechanics dictates that, as long as it is observed, it is “trapped” in a completely intact state.  What I’m saying is that as long as the atom is observed, IT WILL NEVER DECAY.

watchedpot

Yet at any time, we can stop our observation.  Within an hour, if we observe again, there’s a 50% chance that the atom will have decayed.  If we wait 2 hours, 75%, and if we wait 3 hours, almost 90%.  Simply because we didn’t look at it!  There’s an old expression:  A watched pot never boils.  It refers to the fact that it seems to take water longer to boil when you’re watching.  In everyday life this is simply due to the fact that our sense of time is subjective.  It doesn’t actually take longer.  But when you look at very small chunks of matter, like atoms, IT REALLY HAPPENS.  We can inhibit the decay of an atom simply by observing it frequently.  We can actually keep it from decaying by observing it continuously.  This is called the quantum Zeno effect.  It is not some wild theory.  It is a well-documented principle.

 I’m not done.  Because small chunks of matter obey the principles of quantum mechanics, rather than classical mechanics, they can do some unexpected things.  Let’s say an electron approaches a barrier.  If the electron were merely a particle, if would either bounce off, embed itself in the barrier, or rip through.  But an electron isn’t a particle, not most of the time.  It’s a wave/particle.  As it approaches the barrier, some of the wave/particle can actually appear on the opposite side.  At some point, the electron will “commit” to being on one side of the barrier or the other.  There’s a chance it will appear on the opposite side of the barrier.  And sometimes, it does.  This is called quantum tunneling.

quantumtunneling

It’s important to realize how different this “tunneling” is from what we normally think of as penetration.  The electron doesn’t necessarily pass through the barrier.  It can actually APPEAR on the opposite side.  It can do this because until it “collapses” into a particle state, it is actually in more than one place at once.  Furthermore, the parts of the wave/particle that are on opposite sides of the barrier can be completely disconnected from one another.  And this is one of the strangest things about quantum mechanics.

wavepackets

Let’s say you have two water waves, with a completely undisturbed, tranquil water surface in between.  The undisturbed area is literally wave-free.  No wave exists there.  But this doesn’t seem strange to us, because there is still a physical connection between the two waves.  In a sense, there IS a wave there – It’s just that its amplitude is zero.  The entire surface of the water is continuous, and this explains why waves behave the way they do – how a wave can split into two waves, with no wave in between, and how two waves, one at a trough and one at a crest, can destroy one another.

probabilitydensity

But imagine that the condition of the water waves will actually translate into the existence of a particle.  If there is no wave at a given location and time, a particle will not appear there.  That is what happens with quantum mechanical waves.  They determine the position and other characteristics of particles when they are observed.  The waves themselves are never directly observed.  We never actually see particles “spread out.”  What we see is that particles never appear where the mathematics tell us there is no quantum mechanical “waviness.”  And the “wavy” areas may be completely disconnected, with only “flatness” in between.  This is what quantum non-locality means.  In its superposed state, one part of a wave/particle can be on one side of a barrier, while another part is on the opposite side, WITH NO PART OF IT inside the barrier.  In many situations, the particle quite literally CAN’T EXIST within the barrier.  So it doesn’t rip through the barrier.  It is NEVER IN THERE.  It merely appears on the opposite side.  Classical mechanics allows nothing of this sort.  Only quantum mechanics explains such behavior, and it is routinely observed.

hydrogenatom

We can illustrate how truly strange this is by looking at a simple atom.  A hydrogen atom.  It consists of one proton and one electron.  Remember that the proton has a positive charge and the electron a negative charge.  So why doesn’t the electron simply fall toward the proton?  Answer:  Because it has angular momentum.  The reason the earth doesn’t fall into the sun is that it has angular momentum.  In the case of the earth, this is easy to understand.  The earth is in constant motion around the sun, traveling in an elliptical orbit.  The earth’s “sideways” momentum balances the sun’s pull.

But in the case of an electron, we have a problem.  Remember that in the absence of an external force, any object tends to continue moving in a straight line.  Any object that is changing direction is being accelerated.  Since orbital motion is a constant change in direction, an object in an orbit is constantly accelerating.  We know that if an electron is accelerated, it gives off a photon.  But an electron in a hydrogen atom doesn’t.  How can this be?

 The resolution of this problem is that an electron is not a particle in an orbit.  It is a wave/particle.  Its angular momentum is not like that of a planet in orbit.  It really can’t be understood in that way.  In a sense, the electron isn’t moving at all, because it is ALREADY IN MANY PLACES AT ONCE.  When observed, it will be found to have a specific location.  But when not observed, it is “spread out.”  This is why it doesn’t fall toward the proton.

hydrogenorbitals

Electrons can move to higher energy levels within an atom, called orbitals.  But this term is misleading.  In fact, the whole sentence is somewhat misleading, because an electron is NEVER OBSERVED to be in between energy levels.  It is either in one or the other.  It doesn’t “move” between levels in the way we normally think of movement.  It shifts from one level to the other.  And within these levels, these orbitals, it isn’t “orbiting.”  It is spread out within the orbital.  Notice that many orbitals have gaps – areas where the electron WILL NEVER BE FOUND.

electron1

Over short distances, an electron can appear to move faster than light.  It can do this because it ISN’T REALLY MOVING that distance.  Instead, it is spread out over the space in question when it is not observed.  When it is actually observed, it will be somewhere within that space.

As you can see, the quantum mechanical world is very different from our everyday world.  Some people are fond of arguing that quantum mechanics only applies at very small scales.  We don’t really have to worry about the strangeness of quantum mechanics, they say, because we never see it at large scales.  The problem with this argument is simple – it’s false.  This is illustrated by the quantum eraser experiment we looked at before.  Suppose the 2 mirrors in this experiment are 20 feet apart.

quantumeraser

This means that when the photon reaches these mirrors it is spread out over a distance of 20 feet.  And notice – the photon has no existence in the space between the 2 alternate paths.  In principle, we could spread this experiment out so that these 2 mirrors could be miles apart.  It shouldn’t change the outcome of the experiment.  This is the nature of quantum non-locality.  Quantum mechanics dictates that a photon isn’t a particle until it interacts with a larger system.  Until then it is spread out as a wave/particle, spread out over miles if conditions are right, with no “existence” in between.  Only when it interacts with a large system does it actually become a particle, with a particular location.  And I’ll say it again.  All matter is composed of particles that obey these same principles.  When these particles interact with larger systems, when they are measured, they behave like particles.  But the rest of the time they behave like wave/particles.

Schrodingers_cat.svg

Now suppose we take a particle, like an atom, and connect it to a large system, so that the fate of the large system is intimately tied to the fate of the atom.  One of the founders of quantum mechanics, Erwin Schrodinger, imagined doing just that, and his thought experiment is one of the most famous aspects of quantum mechanics.  It’s actually pretty simple.  We put a live cat in a box, which completely isolates it from the surrounding environment.  We also put a vial containing poison gas in the box.  Adjacent to the vial is a small hammer, connected to a switch.  When the switch is activated, the hammer will break the vial, releasing the gas and killing the cat.  The switch is activated by a detector, which sends a signal when it detects the radioactive decay of a single atom.

Schroedingers_cat_film.png

An important point here is that the detector is not monitoring the atom continuously.  It is merely “watching” for a decay product.  So the quantum Zeno effect doesn’t apply.  At some point, the atom will decay, and the cat will die.  But since the cat is isolated from any outside observer, quantum mechanics dictates that the ENTIRE SYSTEM – the atom, the detector, the switch, the hammer, and the cat – is in a state of superposition.  The cat is both alive and dead, until we open the box.  The experiment is called Schrodinger’s cat.  This actual experiment has not even been attempted, for all kinds of reasons.  But the principle is far from ridiculous.  In fact, superpositions of “large” objects have been achieved, and appropriately, they are called cat states.  One example is a resonator, consisting of about 10 trillion atoms, which vibrates and does not vibrate at the same time.

bohrquote

Notice that from the point of view of the cat, there is no superposition of the hammer and the vial, only of the atom itself, which is not being continuously monitored.  If the atom decays, the cat dies, period.  Only from a point of view outside the box is there a superposition of the cat.  As soon as a larger system interacts with the atom, it is entangled with it.  But superposition remains, from the point of view of other systems that remain isolated.

John-Archibald-Wheeler-in-order-to-more-fully-understand-this-114168

This brings up a very crucial question.  Suppose I have a device that is constantly monitoring a radioactive atom.  The quantum Zeno effect dictates that the atom will never decay, from the point of view of this device.  Now suppose I have a second device, isolated from the first, that also monitors the radioactive atom.  But this device only checks the atom after 24 hours.  If the substance in question has a half-life of 1 hour, after 24 hours it is almost certain that the atom will decay.  Yet the quantum Zeno effect dictates that it CANNOT have decayed, because the other device has been monitoring it continuously.  So what happens?

Answer:  BOTH RESULTS HAPPEN, as long as the two devices are isolated from one another.  The device that monitors the atom constantly will observe that it never decays.  The device that checks the atom after 24 hours will almost certainly see it decayed – as long as they don’t exchange information in the future.  But if information about the state of the atom is EVER exchanged between the two, even thousands or millions of years later, the atom will be found to have not decayed by BOTH devices.

quantum-information-header

This illustrates two critical points about quantum mechanics.  The first is that it is all about INFORMATION.  The flow of information between systems is what determines the behavior of particles.  And second, it does allow a kind of backwards in time effect, because what we see today is a function of what information will be exchanged in the future.

entanglement

Now you might think this leads to an inherent contradiction.  Suppose I store the 24-hour reading from the first device in a computer file (let’s say as a zero, meaning no decay) and the 24-hour reading from the second device in a different file (let’s say a zero for no decay or a one for decay).  Then I have someone examine the second file, someone who has no knowledge of the experiment.  It’s quite likely that the file contains a 1.  He tells me so.  Then I decide to examine the first file.  It MUST contain a zero, because of the quantum Zeno effect.  So the two results contradict each other!

But this doesn’t happen, and understanding why it doesn’t happen helps us understand the real strangeness of QM.  Remember that I have knowledge of the nature of the experiment.  So when my friend gives me the result from the second device, we are creating an informational connection between the two devices.  The two devices are now entangled, so the quantum Zeno effect applies to both.  My friend will invariably see a zero.  The behavior of the two devices MUST comport with their informational connections, even if those connections happen in the future.

quantum-teleportation-3-638

Notice something very crucial though.  The behavior of an atom could be said, in this scenario, to depend on nothing more than what knowledge a person has about the experiment.  Information, and information alone, determines the outcome.  This is the real revolution in physics that quantum mechanics represents.  The flow of information controls the behavior of physical systems.

quantummechanicsabsurd

I repeat – These are not wild speculations.  They are very much in line with mainstream physics.  Many theoreticians have tried to “save” quantum mechanics from its strangeness.  They have failed.  Quantum strangeness seems unavoidable.  The exchange of information, even in the future, affects the behavior of physical objects in the present.  Physical objects can pass “through” other physical objects without affecting them.  And there is no such thing as an observation that has no effect on what is being observed.   Quantum mechanics is so revolutionary that, decades after it was formulated, the most brilliant physicists are still trying to get their minds around it.  Our common sense is a very poor guide to the universe.  Understanding it requires us to stretch ourselves.  The universe is strange.  Very strange.

http://www.scientificamerican.com/article/quantum-microphone/

https://www.youtube.com/watch?v=8ORLN_KwAgs

https://en.wikipedia.org/wiki/Quantum_Zeno_effect

https://en.wikipedia.org/wiki/Quantum_eraser_experiment

https://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser

https://en.wikipedia.org/wiki/Quantum_tunnelling

https://en.wikipedia.org/wiki/Quantum_nonlocality

https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat

https://en.wikipedia.org/wiki/Cat_state

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One thought on “Revolution 3 – Quantum Mechanics

  1. Pingback: Quantum mechanics revisited – When does entanglement occur? | David L. Martin

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