© 2019

63. Spooky Action at a Distance:

The EPR Paradox

The Question:

One of the most momentous events in the history of science occurred when an apple fell from a tree, near a young man who was lying there, pondering the world. The episode got the man thinking: there must be some force that pulls the apple towards the ground.

Such a revolutionary idea did not sit well with the man’s contemporaries. They could imagine using one’s muscle-force to pull a donkey by a rope. But to pull the donkey without a rope? Impossible! So what force could pull the apple towards the ground?

Nowadays, the force of gravity, as discovered by Isaac Newton in the seventeenth century, is well established. One can envision ‘action at a distance’ even in the absence of a rope between the puller and the pullee.

But can there be action at a distance not only without a rope but also in the absence of a force?

 

The Paradox:

Yes!

That’s really spooky. In fact, it is so spooky that even Albert Einstein could not believe it. He called it “spooky action at a distance”

It happens all the way down, at the level of quantum mechanics. To show this, two doctrines of post-Newtonian physics must be recalled. They are fundamental principles of nature, never to be questioned. First, neither matter nor information can travel faster than the speed of light. This is the central tenet of relativity theory. The second is the ‘uncertainty principle’, a supremely important notion of quantum mechanics.

Introduced by Werner Heisenberg in 1927, the uncertainty principle (UP), states that when one wants to establish, say, the position and momentum of a sub-atomic particle, one cannot determine both accurately. The more precise the position, the less precisely can its speed be determined, and vice versa. The reason for this phenomenon is that in order to determine a particle’s position, light needs to be shone onto it. But when light photons hit the particle, they disturb its path

Let me illustrate with an example of two opera singers, Dee and Dum. One is light-skinned, the other dark-skinned. They are very versatile, with vocal ranges between low pitch and high pitch. At the start of their careers, they decided that they would never compete against each other: whenever one sings high-pitched, the other sings low-pitched, and vice versa. Then they separated and travelled off in different directions; eventually, they were a light year apart.

You have have never seen Dee and Dum perform. One day, you attend Dee’s performance. The lights go on and you see that Dee is the light-skinned singer. At that moment, the opera’s audio equipment goes on the blink and the performance is cancelled. You never heard whether Dee was going to sing in a high-pich or low-pitch. But at least you now know for certain that Dum, a light year away, is dark-skinned.

Dee is in town again and this time the opera’s light-system goes on the blink. But you can hear him sing in low-pitch. Immediately, you know that dark-skinned Dum, a light year away, is – at that very instant – singing in high pitch. So, without ever seeing and hearing Dum, you know that he is dark-skinned and sings in high pitch.

What if Dee had decided to sing in low pitch? In that case you would have known for sure that Dum, a light year away, would at that very instant, be singing in high pitch. Just by changing his pitch, Dee induced Dum to sing in the other pitch.

Now, let’s take the virtual opera scenario to the realm of quantum mechanics. According to UP, you could not know both Dee’s skin-color and the pitch in which he sings. An opera-goer could either see the singer’s skin-color, or hear the pitch of his voice, but not both. So, how is it possible that at the very moment that Dee starts singing, one knows that Dum is singing in the opposite pitch? This contradicts UP.

So, it must be that Dee sent a message to Dum telling him in which pitch he would sing. But how did Dum get the message? Since nothing can travel faster than light, it would have taken a year for the message to reach him.

Something has to give: either Heisenberg’s UP does not hold, or messages can travel faster than the speed of light. Or does some hidden information exist?

Spooky!

 

Background:

According to the so-called Copenhagen Interpretation, a particle does not exist at all as long as its position is not precisely determined. But when its position is being determined then, by UP, its momentum is disturbed.

In 1935, Albert Einstein and two young collaborators, Boris Podolsky and Nathan Rosen (EPR), thought that something was amiss with quantum theory. They suspected that there must be variables hidden somewhere that would explain quantum theory. To demonstrate this, they devised a thought experiment about a sub-atomic particle that splits into two pieces; we’ll call them Twin and Twain. The particles then fly off in different directions.

EPR claim, quite reasonably, that since the speed and direction at which the particles fly apart is known, Twain’s position can be computed by determining the position of Twin. Hence, by the Copenhagen Interpretation, Twain’s position is determined, albeit without having measured it directly. Hence Twain exists.

 

Dénouement:

But there’s more. As EPR suggested in their thought experiment, by measuring Twin’s position, Twain’s position can be mathematically determined without disturbing its momentum. Therefore, at that very moment, one should be able to measure Twain’s unaffected momentum. As a result, one would obtain exact measurements of both Twain’s position and its momentum. But that cannot be: it would contradict Heisenberg’s uncertainty principle!

Hence, if EPR’s thought experiment were to be carried out in real life, Twain’s momentum would not remain unaffected. It would be fuzzied up, just like Twin’s momentum. Alternatively, if Twin’s momentum is measured, both its and Twain’s positions must become fuzzy.

Somehow, whenever a measurement is performed on Twin, Twain, a light year away, immediately ‘gets the message’ to fuzzy up either its positon or its momentum. But how does Twain, instantaneously ‘know’ which of the two characteristics needs fuzzying? Does Twin send a message faster than the speed of light? No, that cannot be either.

Enter Erwin Schrödinger, an Austrian physicist who shaped some of the key results in quantum mechanics. In 1935, he proposed the notion of ‘entanglement’ to describe the phenomenon. Two particles that interact and then separate remain correlated: instead of becoming two one-particle systems, they remain one two-particle system. Even light years apart, they maintain their correlation. Most surprisingly, any change that happens to one of the two particles immediately affects the other. There are no messages telling the other particle what to do. It just does it.

Yes, it sounds quite absurd, but that’s what happens on a quantum level. The simple act of measuring one particle’s position instantaneously influences the other particle in such a way that its momentum cannot be determined accurately.

* * *

The bewildered reader may be forgiven for thinking that the dénouement is no less puzzling than the paradox itself. But that’s the nature of quantum mechanics. After all, even Albert Einstein was stumped. And it made the news: on July 28, 1935, the New York Times devoted a full half-page to the EPR paradox.

 

Technical supplement:

In any case, several decades later, the Irish physicist John Stuart Bell proved mathematically that, contrary to EPR’s belief, hidden variables could not explain quantum entanglement. Furthermore, beginning in the 1960s, experiments showed that the predictions of quantum mechanics were correct and EPR’s suspicions were erroneous. “Spooky action at a distance” does occur.

* * *

Research is underway to utilize entangled particles to transmit signals that cannot be intercepted by an eavesdropper without leaving a trace.

 

© George Szpiro, 2019

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