David L. Martin

in praise of science and technology

Quantum mechanics revisited – When does entanglement occur?

In a previous post, I discussed quantum mechanics, one of the 3 great revolutions of physics in the 20th century.  QM has been very successful in predicting the outcomes of experiments, and the strangeness of QM is something that most people fail to appreciate.  In fact, QM is so strange that some physicists recommend not even trying to interpret what it means – thus the expression, “Shut up and calculate.”

To me, that’s a cop out.  In the first place, we have to have numbers to plug into the equations, and that means having some understanding of the processes involved.  And in the second place, the success of QM has profound implications for our understanding of the universe.

entanglement2

One of the most important principles in QM is what is called entanglement.  Entanglement, in a way, is actually a very simple concept.  If 2 systems share information, they are entangled.  Take 2 coins for example.  We can flip one coin and get a head or a tail.  Same with the second coin.  The 2 outcomes are independent.  The coins do not share information.  But if we glue the two coins together, the 2 outcomes are 100% correlated.  The coins are entangled.

The same is true if we look at a single coin and an observer.  If the observer doesn’t look at the outcome of the flip, no information is shared.  But if the observer looks, the coin is entangled with the observer.  In other words, measurement is entanglement between the system being measured and the system making the measurement.

collapse

Because measurements take place at specific times, this led the pioneers of QM to say that a quantum system “collapses” to a specific state when measured.  The problem is that there is nothing in the mathematics of QM about this so-called collapse.  We can illustrate this with the classic double-slit experiment.

doubleslit2

In the double-slit experiment, particles are fired at a screen.  Between the screen and the emitter is a barrier with 2 slits close together.  If there is nothing to tell us which slit each particle goes through, QM predicts that the particles will accumulate in a fringe pattern on the screen.  If, however, we introduce a detector which tells us which slit each particle goes through, we will not see a fringe pattern.  Instead we will see 2 clusters of hits on the screen, corresponding to the 2 slits.

delayedchoice2

The detector and the particles are entangled.  This is reflected in the mathematics of QM.  But here’s the problem.  The information about which slit each particle went through can be “erased” after it passes the detector.  A fringe pattern on the screen will result.  In order to make a QM prediction, we need to know what happens throughout the flight of each particle.  And it gets worse.  We can take each particle and split it into 2 entangled “daughter” particles.  Now, in order to make a prediction about how the particles behave, we will need to know the fate of these “daughter” particles.

Such problems blow the idea of “collapse” right out of the water.  When is this collapse supposed to occur?  We could extend the experiment for years.  In order to make a QM prediction about what some of the particles in some parts of the experiment will do, we must know the fate of the entangled particles in the future.

superfluid

A common misconception about QM is that it makes very different predictions, depending on whether a single particle is involved or whether a large system consisting of many particles is involved.  The mathematics make no such distinction.  A single particle can make a measurement, or a large system can make a measurement.

squids

Take the Schrodinger’s cat experiment for example.  Suppose that instead of the cat, the vial, and so on, we simply use a single particle as a detector.  The state of this single particle will either reflect that the radioactive atom decayed or didn’t.  This is no different than the detector in the original experiment, or the hammer it’s connected to, or the vial, or the cat.  There is no magical number of particles for a detector that suddenly causes the equations of QM to change.  A detector is simply a system that changes its state as the atom changes state.  It can be one particle or many.  Superposed “cat states” have been created using trillions of atoms.

baseball

Now just so there’s no confusion, there IS a difference in QM between the behavior of a single particle and that of a large, multi-particle system.  A single particle, or a small collection of particles, even after it is observed, can quickly return to a superposition of states, from the point of view of the observer.  A large system will not.  For example, an electron’s location can be pinpointed within an atom, but after that its location quickly becomes impossible to predict.  If we pinpoint its location, we lose information about its momentum.  It soon returns to a superposed state in which it is at many locations simultaneously.  This of course is not true of a baseball.  We can measure both its position and momentum and predict where it will be in the future.

HOWEVER, this is only true to the extent that the observable properties of large objects are not directly tied to the behavior of particles, or small groups of particles, as with the Schrodinger’s cat experiment.  If the position of a baseball is actually strongly influenced by the fate of a single radioactive atom, it will be just as superposed as that atom.  Nothing in the mathematics of QM says otherwise.

entangledphotons

Now to get back to entanglement.  When does entanglement occur?  The answer seems to be, no particular time.  If, at some point in the future, 2 systems will share information, their entire histories will have to reflect this.  What Einstein called “spooky action at a distance” applies to time as well as space.

quantumcoins

To illustrate how strange this is, let’s pretend that a coin is like a single photon.  Instead of being either heads or tails, let’s say that the coin is both at the same time, until we look at it.  Now let’s say that 2 such coins are entangled – let’s say that if one is heads, the other has to also be heads.  But both coins are still both heads and tails at the same time.  This in itself is strange.  Intuitively, we think, “If they are both heads and tails at the same time, how can we really say that one must be heads if the other is heads?”  Sorry, but that’s QM.  Deal with it.

superposedcoins

Now let’s say that you have a device that checks one of the coins.  The device looks at the state of the coin, and saves this information in a computer file.  The computer is connected to a printer, which prints the word “heads” or “tails” in big bold letters on a sheet of paper, according to the reading from the coin.  This sheet of paper stays inside the printer and no one looks at it.  Hours later, a second device looks at the state of the other coin, and saves this information in a computer file.  This computer sends a print command to a second printer, which prints out “heads” or “tails” in big bold letters on a sheet of paper, according to the reading on the second coin.  I walk up to this second printer, eject the sheet of paper, and examine it.  It says clearly, in big bold letters, “heads.”  I walk over to the first printer and eject its sheet.  Sure enough, the sheet from the first printer says “heads.”

superposedcoin

BUT, if I repeat this whole process with pairs of entangled coins, sometimes the 2 sheets will say tails.  If I never check the second printer, but merely keep presenting entangled coins to the first device, I will find that its printer generates a series of heads and tails messages randomly.  I will not be able to predict them.  But if I check the second printer, I will be able to predict the first result, every single time – even though the second reading occurs HOURS LATER.

nonlocality

Furthermore, it doesn’t matter how far apart the 2 coins are.  If one comes up heads, the other will come up heads.  It never fails.  This might seem like a psychic phenomenon.  If I can accurately predict what a printer HAS ALREADY PRINTED without having direct knowledge, isn’t that psychic?  Not really.  It’s important to realize that, while I can predict it, I can’t CHANGE it.  I can’t actually CONTROL it.  But it is strange to say the least, and it’s not controversial.  This kind of result is well-established in the QM world.

schrodingerscat

Obviously, coins do not behave like this.  Photons, however, do.  So do atoms, and even molecules.  Seemingly, the only way to account for it is to say that the printer itself is superposed – that it has printed both “heads” and “tails.”  It doesn’t matter in the least that we printed the result in big bold letters on a piece of paper.  This macroscopic event is entangled with the state of the coin, so it too is in superposition.  In fact, the whole experiment – the coin, the computers, the printers, and myself – would remain in superposition from the point of view of an isolated observer.

wheelerdelayedchoice

This is what the mathematics of quantum mechanics tells us – or to be more precise, DOESN’T tell us.  It says nothing about “collapse.”  It says nothing about “measurement,” as distinct from entanglement.  Measurement and entanglement are the same thing.  In fact, measurement/entanglement can be a matter of degree.  2 systems can have incomplete information about each other.  The equations of QM work just as well.  There is no “collapse.”  All that happens is that if 2 (or more) systems share information, they no do not have access to each other’s full range of superpositions.  From the point of view of another system, isolated from the 2, all of the superpositions are still there.

schrodingerscatfilm

To return to the analogy of coins.  If 2 coins are perfectly entangled, each coin “sees” only one state of the other.  Similarly, if I look at one of the coins, I will see either a head or a tail.  My state (either sees-head or sees-tail) is perfectly correlated with the state of the coin.  I won’t have access to both states.  But if I have 10 coins, and I only look at 5, the others can still be superposed.  The entire 10-coin “system” is partially entangled with me.

renningersneativeresult

In fact, so-called measurement, in quantum mechanics, doesn’t even require interaction between the system being measured and the system doing the measurement.  One example of this is what is called Renninger’s negative-result experiment.  Suppose we have an unstable atom that will soon give off a particle.  QM dictates that the particle will fly off in any direction with equal probability.  So we put a hemispherical “shell” on one side of the atom that will detect any particle flying off on that side.  On the other side of the atom, we put another hemispherical “shell” detector.  But this one is much larger in diameter.

Now any particle given off must strike one of the 2 shells and be detected.  But what about a particle that misses the smaller shell but has not yet reached the larger shell?  QM dictates that the particle’s wave function has shifted from being spherical to hemispherical.  But the particle hasn’t interacted with anything!  How does the wave function “know” to do this?

interactionfree

Another example that illustrates the same problem is the so-called non-interacting bomb tester.  We have a collection of bombs.  Some are duds, some are real bombs.  And suppose we know that the real bombs will absorb a photon and detonate, while the duds won’t.  So we take each bomb and put it in one of 2 photon paths, like this:

bombtester

A is the photon emitter.  It shoots the photon to a beam-splitter.  The photon has a 50-50 chance of bouncing off or passing through.  Obviously, if it passes through, it must pass through the bomb.  If the bomb is real, it will explode.  The 2 photon paths reunite at a second beam-splitter (in the upper right).  Two detectors (C and D) record photon hits.  The 2 detectors are cleverly positioned to take advantage of interference effects.  Any photon reaching detector C will constructively interfere with itself and be registered there.  Any photon in the path to detector D will destructively interfere with itself.  It will not register at that detector.

Notice that if the bomb is a dud, it does not affect a photon on that path.  The photon takes both paths, and either shows up at C or does not show up at all.  But if the bomb is real, the photon can complete only the upper left path.  It cannot interfere with itself.  It will show up at C or D with equal probability.  Remember that any photon taking both paths will interfere with itself, and never be detected at D.  SO, any photon that shows up at D reveals the bomb to be real – EVEN THOUGH THAT PHOTON NEVER INTERACTED WITH THE BOMB.

bombtesterbetter

In fact, by adding more mirrors and beam splitters to this experiment, we can test almost 100% of the bombs WITHOUT RISK OF DETONATION.  We avoid the detonations because the photons don’t interact with the bombs.  They simply “refuse” to take that path.  In QM, it’s called interaction-free measurement.  This is a striking example of quantum non-locality, and illustrates clearly that QM is all about information, not interaction in the way we normally think of it.  This is not wild theorizing.  It has been verified by experiment.

When, in this bomb tester, does measurement occur?  When the photon reaches the bomb?  But the photon we actually see at detector D NEVER REACHES THE BOMB.  The entire apparatus is entangled with the photon.  If we change any element in the apparatus, we change the result.  In order to predict that the photons will do, we have to know their entire history.

russellquote2

The point is that quantum non-locality applies to time as well as space.  Actions in the future enable us to make predictions about events that have already occurred, and not just microscopic events either.  Local realism – the idea that a particular thing is going on at a particular time and place – is dead.  Quantum strangeness requires us to abandon a lot of our intuitions about how the universe works.

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

https://www.youtube.com/watch?v=sFRdVj4rrAE

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

https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester

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

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