Far beyond the speed of light: Spooky action at a distance

A casual conversation about Star Wars led to one of the most fascinating questions in modern physics - can quantum entanglement let us communicate faster than light?

A random conversation

I was chatting with a friend about Star Wars (ROTS is releasing again!) when our conversation took an unexpected turn into relativity and quantum mechanics. You know how it goes - one minute you're discussing lightsabers, the next you're deep into physics and existential crises.

His question was straightforward:

The Quantum Conundrum

This excellent question stumped physicists for years before they reached a consensus. It's confusing for several reasons, but primarily because quantum mechanics is just plain weird. It defies our intuition because we've evolved to understand the world through classical physics, while quantum mechanics operates by entirely different rules.

Another source of confusion comes from popular science books, movies, and news articles. They often make quantum physics sound like we're living in a Star Trek episode (which is admittedly fun)! While I appreciate how they spark interest in science, they sometimes simplify concepts to the point where even Einstein would scratch his head and say, "Wait, what?"

The question may seem simple, but it contains several fascinating concepts worth exploring. Let's unpack them step by step. I'll keep things as straightforward as possible, though I'll include some light mathematics here and there (Don't worry - I promise it won't be too complex).

Quantum 101: The Basics

In simple terms, when things get incredibly tiny—I mean subatomic-level tiny—our familiar rules of physics that Newton and other pre-20th century scientists developed simply fall apart. We can't make sense of what happens at that scale using our everyday intuition. Quantum mechanics is essentially the theory that helps us describe and understand these extremely small things that behave in ways that seem weird to us.

Spin: Not What You Think It Is

Let me dive straight into a quantum mechanics example. Talking about classical physics would only muddy the waters and wouldn't capture the true essence of quantum weirdness.

Consider a particle with various properties. For our discussion, we'll focus on just one property called "spin." Many explanations might lead you to visualize spin as a particle rotating around an axis, like a spinning top. But this visualization is actually the source of many misconceptions. So let's abandon that image entirely, we are dealing with things that are beyond the classical intuition and lie beyond what everyday language can describe. Instead, think of spin as simply an intrinsic property that has specific fixed values when measured, nothing more, nothing less. No actual spinning involved!

Particles in Quantum Mechanics

Now that we have established that, let's get back to our particle, we went off on a tangent. This special particle has two possible values for its spin, which we'll represent with numbers 1 and -1.

So we have two possible states of the particle, \( \vert 1 \rangle \) and \( \vert -1 \rangle \). These \( \vert \rangle \) brackets are just some fancy physics notation for denoting states in quantum mechanics (I might write a post about this notation later if you're curious).

Now, let's say we have two particles, and we measure the spin of both of them. We can get either an outcome of 1 or -1.

The Magic of Superposition

We can write this mathematically as:

Don't worry about the \( \frac{1}{\sqrt{2}} \) - it's just a normalization constant to keep our math tidy. The important takeaway is that before we measure the particle, it exists in a superposition of both states. Think about that for a moment - it's like the particle is saying "Why choose one state when I can be both until someone looks at me?"

Entanglement: One isn't enough, we need two

Now that we have a basic understanding of quantum states, let's move our conversation to entanglement - after all, that's what the original question was about. Before we dive in, let's clarify some notation.

Imagine we have two particles (not lonely anymore!) which we'll call A and B. Both have two possible states each: \( \vert 1 \rangle \) and \( \vert -1 \rangle \). We can write their individual states as:

where the subscript \( A \) and \( B \) indicate that these are the states of particle A and B respectively. Now we can write a combination of these two particles as:

where \( \otimes \) is formally called a tensor product. Think of it as a fancy multiplication of two states. Note that I have left out the normalization constant and coefficients for simplicity in the above equation.

Now that we know the notation, we can do some quantum magic with particles A and B (fear not, people regularly do this in their labs!) to create a state given by:

Now that we understand the basics of entanglement, you might be wondering: "What's all this fuss about faster-than-light communication? Where does the speed of light even enter this picture?"

I, Alice and Bob's Quantum Adventure

Let me walk you through a thought experiment. Picture this: I'm in my lab with my friends Alice and Bob (I know some of you are probably tired of these names, but physicists love these names - they're like the Romeo and Juliet of quantum mechanics). I prepare a pair of entangled particles, carefully entangling their quantum states. Then, I give one particle to Alice and one to Bob, and ask them to travel as far apart as they want - they could be on opposite sides of the galaxy if they wished (to be specific, spacelike separation).

Wait a second, what is communication?

First, let me break down what we mean by communication in this context. In our everyday world, when we want to send information (like through computers), everything boils down to sequences of 0s and 1s - this is what we call the binary system. For example, when you type the letter "A" on your computer, it's actually represented as 01000001 in binary. So if Alice wanted to send the letter "A" to Bob using our entangled particles, she would need to somehow transmit this specific sequence (where we could think of -1 as 0 and 1 as 1). Let's get back to the experiment.

The Spooky Action

After they go to their respective locations, let's say Alice measures her particle's spin. Alice has a 50% chance of getting \( 1 \) and \( -1 \). This time she gets a value of \( 1 \). Here's where things get interesting: because of entanglement, when Bob measures his particle, he will get \( -1 \). No matter how far apart they are.

But here's the crucial catch: every time Alice measures her particle, she has no control over the outcome. The result she gets is completely random - that's a fundamental feature of quantum mechanics! She has absolutely no way to predict whether she'll get a \( 1 \) or \( -1 \), and consequently, no way to control whether Bob will get \( -1 \) or \( 1 \).

From Bob's perspective, his results also appear completely random - he has a 50% chance of getting \( 1 \) and a 50% chance of getting \( -1 \). If he measures his particle without knowing Alice's result, he sees nothing unusual at all.

This randomness is the key reason why entanglement can't be used for faster-than-light communication. Alice cannot send a specific message like the letter "A" (01000001 in binary) to Bob because she cannot control or predict her measurement outcomes. What they have is perfectly correlated (or in this case, anti-correlated) randomness - fascinating, but not useful for transmitting information.

To actually observe these entanglement-induced correlations, Alice and Bob must come back together and compare their results - a process that respects causality (Oops, I slipped in a new word there, I mean nothing faster than speed of light). Only when they compare their results do they discover the perfect pattern: whenever Alice measured \( 1 \), Bob always measured \( -1 \), and vice versa. This correlation is far stronger than anything possible in classical physics, but it still can't be used to transmit information faster than light. To summarize:

• Neither Alice nor Bob can control what measurement result they get
• Each person's results look completely random on their own
• The correlation only becomes apparent when they compare results later, which requires classical communication bound by the speed of light

Is that all?

So, have we fully resolved the mystery of quantum entanglement? Not quite. While we now understand why we can't use entanglement for faster-than-light communication, there's still something profoundly puzzling about these quantum correlations between Alice and Bob's measurements.

This brings us to one of the most fascinating developments in quantum mechanics: Bell's inequality. John Stewart Bell, in 1964, found a brilliant way to test whether quantum entanglement could be explained by some "hidden variables" that we just couldn't see (Einstein's preferred interpretation), or if there was something fundamentally "spooky" going on.

I've been diving deep into Bell's inequality lately, and I'm still amazed by how such a simple mathematical statement can reveal such profound truths about our universe. In my next post, we'll explore how Bell's theorem and what it means for our understanding of reality.