Wednesday, 14 June 2017

Confronting Quantum Woo: Understanding Entanglement.

Last time we confronted some quantum woo, we tackled perhaps the most fundamentally misunderstood facet of quantum physics, and it's most exploited. The double slit experiment. In this post, we'll take away the most important point of that post and apply it to another element of the discipline that is almost as misunderstood and as misused- entanglement. Another facet of quantum physics that displays the discipline's deeply non-intuitive nature. As such it is prime fodder for woo-merchants to distort in order to appropriate an air of credibility and legitimacy for nonsense ideas and hypothesises. Just as the misrepresentation of the double slit experiment is used to support ideas of like after death, entanglement is commonly used to support ideas of new-age healing techniques such as distance healing and energy healing and "psychic" abilities and ESP.

As a starting point, let's see what the new age opinion is of entanglement, then we will assess those ideas using the formalism of quantum physics, in the process, we will get an idea of how physicists represent a system of entangled particles and importantly, why entanglement doesn't support ideas of "energy healing" and the like.

Some "woo" definitions of entanglement.

Underground Health Reporter States:
"...all types of particles can become linked and instantaneously influence one another regardless of distance.  When two particles are entangled, they stay that way, and no matter how far apart those two particles get, information passes between them instantaneously.Quantum entanglement explains those times when you were just thinking of your dear sister and your phone rings.  Not only are you not surprised, but you even know what she is calling about.  This happens most often with those you are closest to, because the more QI that’s entangled, the deeper and wider the effect.  In other words, when you think of that person with any emotional charge, the “message” reaches him or her instantaneously."
Pinnacle Healing, who offer "quantum healing workshops" for £180-£229 a pop go further:
"What this means – is simply speaking, that All Are One and that Everything Is Connected because everything has originated from the same source – the Divine – and therefore is bound by commonality, by the truth that we have all been created by the Divine." 
The Paranormal Analyst states:
Is it possible quantum entanglement connect all humans or living beings through sub-atomic particles? Maybe certain people have become attuned to interpreting these signals and have psychic powers.

All those statements highlight the most common misconceptions about entanglement.

1. Entanglement is permanent.

2. All things are entangled. (Many quotes regarding quantum physics with regards to psychic family members such as twins seem to imply that the particles in close family members will be as closely related. Utter nonsense of course. Birth is not a quantum event, nor is sharing a womb!)

3. Entanglement allows for the passage of meaningful information between entangled particles. Information that pertains to more than simply the relevant attributes which are entangled.

The truth is entanglement is extremely delicate. Any measurement causes the collapse of the entangled state and by any measurement, we reapply one of our main takeaways from our examination of the double-slit experiment, measurement is defined in quantum physics as an interaction between two quantum systems or a quantum system and a macroscopic system that causes an irreversible change in those systems.  The example I gave last time was of atomic decay in an isolated region of space- daughter particles are entangled due to the conservation of angular momentum. A measurement occurs when either of these particles collides with a dust particle or other object. Whilst it's conceivable that particles at opposite ends of the universe remain entangled -their mutual journeys must remain uneventful. Any collision or interaction destroys the entanglement. As for the second statement, obviously most particles in your body are not isolated and in accordance with the principles I've laid out above, they aren't going to be entangled. If that isn't detrimental enough, consider that not all particles are entangled only particles which are created in the same process or have some form of entanglement forced upon them (pairs or groups of photons, for example, can have entanglement induced upon them). The third statement requires us to go deeper into the formalism of entanglement.

So we've seen two examples of what new agers mean when say entangled, what do physicists mean?

Entangled States 
A wavefunction or state vector representing the state of two particles is said to represent an entangled state if it cannot be expressed as a product of terms each specifying the state of a single particle. (Quantum Mechanics and its intereptation, Bolton, Macintosh, 2007.)

As I've mentioned before in quantum mechanics the states of particles are described using a wavefunction, often referred to as a DeBroglie wave, a mathematical representation of the various qualities of the system. The wavefunction represents all it is possible to "know" about the state that a particle is in. Entangled particles are simply particles for which it is impossible to describe in isolation. To explore this more fully let's use a quality of particles known as spin. The specifics of spin don't particularly matter here but it's useful to state that spin isn't as many new agers present it, actual movement or rotation of a particle. In fact, it's more useful to describe spin as a magnetic quality. Electrons are particles of 1/2 spin. This means their spin has two possible values, +1/2 which we call spin up, and -1/2 which we predictably call spin down.

We can represent the spin states of a particle using a funky feature of a system known as Dirac notation as a "ket". So, ignoring for simplicity's sake the spatial state of a particle, for a single spin-up electron (which we will denote particle A) sat in isolation in space the wavefunction looks like this:
Pretty simple right? So let's also say we have another electron somewhere in space which is spin down. We'll label it particle B and thus denote its wavefunction:
So far so good. But what if we want to describe a quantum system comprised of these two particles. The system's wavefunction would be: 

Using the rule that particle A always comes first we can simplify this as:
It's clear to see this system isn't entangled. It can be described as a product of the state of particle A multiplied by the state of particle B. Explicitly:

It might be apparent to you that the reason this system isn't entangled because we know the spin states of particle A and B. What if we didn't, but we do know that the particles were created in the same process. We also know that if particle A is spin up, particle B must be spin down. If particle A is spin down, particle B must be spin up. This is a consequence of the Pauli exclusion principle which forbids particles like electrons having the same quantum numbers. Clearly, our wavefunction for the system must represent the two possible states of the system.

What would that look like?
Clearly, this is somewhat more complicated, but using the rules established thus far it should become apparent that the term underlined in red represents the state if particle A is measured spin up. The term underlined in blue represents the state if particle A is measured spin down. This wavefunction can't be described as a product of particle A and particle B wavefunctions, it's not separable. Thus this is truly an entangled state. 

You have also no doubt noticed our entangled wavefunction has picked up an extra complication. Namely C1 and C2. These are the probability amplitudes of the two outcomes. We square these to find the probability of a particular outcome. Their addition ensures the wavefunction is normalised. They are also the key to understanding the collapse of the wavefunction and how the measurement of a particular state destroys entanglement.

The wavefunction above has only two possible outcomes. When the spin of either measurement is made the total wavefunction must collapse to either the red state (A: up, B: down) or the blue state (A: down, B: up), thus the probability of returning one of these states is certain.

We therefore require:

As there's no reason to suspect that either the red state or the blue state is more likely than the other. So we can see:

Giving our full wavefunction:

This wavefunction applies as long is there is uncertainty which state the measurement will yield.

So we can see that if a measurement is taken on particle A and it is found to be spin up:

And our wavefunction becomes:

Which we can see reduces to our original non-collapsed state! Entaglement is destroyed.

So it's clear to see from this mathematically why the measurement of a quantum system causes it wavefuntion to collapse "onto" a particular state. To hold the woo postulates of entanglement to be true we have to believe that all particles were created in the same event. Also, we have to accept that the particles have interacted with not just any other forms of matter but even magnetic fields. What are the chances of a loose electron in your body existing there for a prolonged period without interacting with anything else? And then it's partner existing in your energy healer or psychic twin free from interactions too?

What's important to note here is that you may be tempted here to suppose that the system was in a particular state before measurement and that said interaction simply revealed what state the system was in. This is fundamentally incorrect. Observables (measurable quantities) in quantum physics have no values before measurement, there are no "hidden variables". They have a number of possible values but that is the most we can possibly say. Entanglement has another important consequence, measurement of a particular observable on one particle causes its partner to adopt a value for said quality immediately, no matter how great the separation between the two. These two factors deeply troubled Einstein, arguably the greatest mind of his time, and the inadvertent father of quantum physics. Einstein felt that this non-locality was in direct violation of special relativity.

This leads to the two most famous quotes about quantum physics:

"God does not play dice with the universe."
And Einstein's dismissal of entanglement as "spukhafte Fernwirkung" or "spooky action at a distance." We can thank Einstein for introducing the word "spooky" to the lexicon of physics, we can also thank him for the quote which I guarantee will appear in almost every article you ever read that connects quantum physics and any aspect of the paranormal.  In fact, the second of these two quotes is so ubiquitous that it deserves special attention in a separate post.

And for good reason that's where we head next.