Miscalibrated Internet Receptor Stalks
Miscalibrated Internet Receptor Stalks

# Corpore Metal's Delusions of Grandeur #1: Quantum Entanglement

Because Dave Goldberg and Flowergirl Physicist are never around when the Internet vomits up all kinds of misconceptions about physics and what it can do, I, as an aging, lowly, ex-physics major with delusions of grandeur, have elected to step up and build an FAQ to give succinct answers to questions that are endlessly repeated on this site.

First lesson:

## Quantum Entanglement and Why We Can't Make Magic FTL Radios With It

Okay this is going take a long and detailed explanation. Strap yourself in.

Notice that I'll be covering a lot things that don't seem to be related to the subject of entanglement but, when we start to dig into it, we'll see that it's all related. Be patient.

The first thing you have to do is put aside your intuition (Which physics has repeatedly shown to be wrong in many areas for centuries let alone in more recent stuff like quantum mechanics.) and instead let logic guide you.

## Wave Particle Duality

The next thing you have to accept is that quanta are a third kind of thing that can be particle-like or wave-like at the same time or one or the other depending on what context they are in. This is why the term "quantum" was invented, to label this other kind of thing beyond waves and particles. Quantum mechanics is the mathematical model that governs how these "other things" behave.

This "both/neither/either" wave or particle nature of quanta, called "wave particle duality" all by itself opens the door to counter-intuitive stuff like entanglement. For example, particle-wave duality gives us nonlocal, "action at a distance" stuff happening right in the famous double slit experiment.

## Exclusion

The other thing about quanta that allows for entanglement is the exclusion of measurements of position from measurements of velocity. You can know exactly where a quantum is but you are absolutely forbidden from knowing what the velocity of that quantum is. Or conversely, you can know exactly what a quantum's speed is but, you are absolutely forbidden from knowing what its position is.

Or you can accept an inaccurate position measurements along with an inaccurate velocity measurementsâ€”which is essentially what classical mechanics is. But as you increase the accuracy of one you lose accuracy on the other. This is called exclusion.

Exclusion crops up nearly everywhere in systems of quanta. Not merely in the exclusion of measuring position versus velocity. It also governs how electrons arrange themselves in the orbitals in atoms as well as the shapes of those orbitals. And it also governs quantized angular momentum, called "spin" in the jargon of quantum theory, as you'll see later on.

Exclusion isn't just a lack of knowledge we can somehow get around. It's fundamental to quanta and quantum systems that, at best, we can only say what states are not allowed rather than what states they are in until we take a measurement.

In fact you'll see in the paragraphs that follow that quanta don't have a definite state at all beyond excluded ones until we take a measurement. It's basic to the nature of systems involving quanta. Quantum mechanics literally places fundamental limits on what we can measure depending on the context we are in.

## Superposition

There is a third counter-intuitive fact about quanta that we have to accept if we are to proceed.

The two counter intuitive facts I mentioned before are facets of deeper concept called "superposition." In the jargon of quantum mechanics, superposition says that until you measure a quantum, it exists in an infinite number of states. Is it wave-like or particle-like? Do we know its position or speed? The quantum is all of those things at once but we can't say something definite about it's exact state until we measure it. The act of measuring the quantum or the quantum system collapses it into a definite state where it's a wave and in a certain position, it's a particle and moving at a specific velocity or so on.

Superposition gets us into other things like:

• uncertainty (Also partially related to wave-particle duality and exclusion and explained further below.)
• indeterminacy (The utter acausality of quantum systems where things happen with no causes and causes sometimes generate no effects.)

## Past Interactions

The fourth thing about quanta is they retain information about the other quanta or quantum systems they interact with.

This by itself is not remarkable. Even in the classical world, waves and particles retain information about their interactions. For example, looking at the waves in a still pond can tell you where those waves originated and what the shape of the pond is. Looking at the movement of two billiard balls on a pool table can tell you when they struck each other and where they the came from prior to the collision. The point is you can look at a billiard ball or a water wave and discover things about its past.

So assuming you accept this one intuitive fact and three counter-intuitive facts about the microscopic world, here is how entanglement works.

## Quantum Entanglement

Consider a quantum with a spin of zero. (Aside from what I said about exclusion above, what "spin" means is irrelevant to our discussion. For now just accept it as a feature that quanta have.) that decays into two new quanta. (Again why some quanta decay into other quanta is irrelevant to our purpose of understanding what entanglement is. Don't worry about it for now.) These new quanta, A and B, head off in opposite directions. However just like water waves or billiard balls they retain information about their past.

The original quantum has a spin of zero. Both of the new quanta have spin of plus one half and negative one half. This because the original quantum they came from had a spin of zero and, in the math of quantum mechanics, the addition or subtraction of spin is always conserved. One half plus negative one half equals zero, dig?

Anyway, right there we can see that these two new quanta retain information about their past and origin.

Now, here is another fact, a counter-intuitive fact, about quantum systems. Pay close attention: Thanks to exclusion, no two quanta in a quantum system can have the same spin state. This means that if these two quanta were the only quanta in the entire universe, one can't have the same spin number as the other one.

It doesn't matter how far apart they are. It doesn't matter what they're speeds are. The only thing that matters is they are two quanta alone in giant universe devoid of any other quanta and that they once interacted in the past.

So here's what happens. If I interact with quantum A to change its spin state to another number, quantum B must instantaneously and immediately change its spin state to an opposing number.

This relationship means that the two quanta are entangled. When you measure the spin of quantum A, that measurement has an immediate impact on the possible result you'd get when measuring the spin of quantum B.

This is is called "nonlocality" and it's precisely the acausal, action at a distance that creeped the hell out of Einstein nearly 90 years ago.

But it's true. We can contrive all kinds of quantum systems where entanglement happens all the time. This is fundamental aspect to nature on the microscopic scale. This is the only way things can work given what we know so far about nature.

So, knowing and accepting all that, here's why it can't be used for FTL communications.

## Uncertainty

It's all down to another counter-intuitive fact we must accept about quanta: uncertainty. Uncertainty lurks behind many of the things I've described earlier and it says that until we take a measurement, until we interact with that quantum, we are forbidden from knowing what state it's in. At best all we can say is what state it's not in as I'll explain a bit below.

Uncertainty says that even if a quantum never interacts with another quantum again it's still acausally jostling around in all the states it can be in. Uncertainty says that, if left alone, a quantum system is in superposition, rattling around all in all the states it's allowed to be in.

Let me explain that another way as it will make what say later make more sense.

The superposition of states is represented in the math of quantum mechanics as a coherent wave equation. This wave represents all the possible states that quantum or system is in before interactions with the outside world that take information in or out of the system.

This act of interacting with the quantum system to take information out of it is called "taking a measurement" and it leads to something called decoherence, or collapsing the state wave function.

## Decoherence

[This was major piece I left out when I wrote this essay a few days ago. In conversations with some friends, they reminded me of this. So I'm adding it here now to make things clearer. Sorry for any confusion this may have caused.]

Docoherence relates to what has been called the measurement problem or the observer effect. Simply, the moment you extract information from quanta or a quantum system, superposition ends and the quantum or system resolves into a single specific state.

This is called decoherence because it breaks the coherence of the state wave function and collapses the system to specific single, state.

The measurement problem or the observer effect has been a difficult matter in quantum mechanics from the beginning. This problem was summed up in the infamous ShrĂ¶dinger's Cat thought experiment. The measurement problem is rich enough that I will probably have to devote another rant just to it.

But never mind, we can narrow ourselves down to just how it ruins magic entanglement based FTL radios.

## Cry Me River or, Physics Has Nothing to Do With What You Want

Basically the fun ends when you attempt to jiggle one of the entangled particles. Doing this docoheres the system of entangled particles and brakes entanglement. The two particles are no longer in nonlocal synchrony.

It gets worse. Even if you don't jiggle either particle just checking the state of either one breaks coherence and entanglement. You get to look in the box once and the link is broken.

When uncertainty and decoherence get together, it utterly fucks up our dreams of magic FTL radios.

Uncertainty says that until we take a measurement, until we interact with the quantum in the box, we know nothing about what its state is. Its spin number could any of an infinite number of whole or half integer numbers. This happens regardless of entanglement. Any quantum sitting or bouncing around alone by itself has no specific state until we measure it.

Decoherence says that jiggling either quantum or even just checking its state breaks entanglement.

So suppose we take our two entangled quanta and put each in a box to prevent them from interacting with anything else. Then we zoom one of the boxes over to Tau Ceti as an experiment.

Until the gal at Tau Ceti looks in the box, she has no idea what state quantum A is in. All she knows for certain is that quantum B, back on Earth, because of entanglement, is always in the opposite state instantaneously. She looks in the box and finds that that quantum A is spin plus one. This means that quantum B at that very moment is spin negative one.

But here is where uncertainty and decoherence ruin it all. She has no way of knowing, except by classical means, if the state of quantum A is due to just the random, acausal jostling that all quanta exhibit or if it's due to deliberate manipulation by her friend back on Earth.

She has to point an ordinary message laser back to the Earth, which works at the speed of light, to ask, "Hey friend, did you jiggle quantum B at 12:36 PM, 2973 CE, local time?" and then wait about 25 years for an answer. And when she gets an answer all she can confirm is that entanglement works.

And it gets worse. She looks in the box once, or her friend on Earth jiggles the quantum once and entanglement is broken. End of story.

Because of this, no magic FTL radios are possible by entanglement. Physicists shorthand this complicated fact with the label, "the no-communication theorem."

Sorry to smash any dreams but these are the facts as we know them currently.

## References and Supplementary Material

If your interested, I can point you to many books and articles that explain entanglement in different ways if mine doesn't work for you.