Quantum Mechanics – Introduction

Quantum mechanics is even crazier than relativity. It’s one thing to be faced with a universal speed limit – a crazy idea if there ever was one – but how about some physics that messes with reality itself?

In the old days, to understand weird quantum behavior, you had to do a lot of statistics. But the physicists have managed to boil it down very nicely. Of course it was pretty simple all along, but it it took the physicists decades to get it all straight anyway, probably because they like it complicated.

Okay, enough physicist bashing and kudos to guys like Mermin who have worked very hard seeking simplicity. With a little help from the good professor Mermin (no relation to Merlin), let’s learn quantum mechanics.

All in a Day’s Work

You and two of your friends find yourselves confronted by the Devil and his minions. He wants your souls and even though you have all led lives of honor and integrity, the Devil took out an option on you and your two friends anyway and you will have to complete a series of tasks in order to keep your souls. The tasks are all possible – even the Devil has to play by some rules – but they will get progressively more difficult.

A young devil-in-training shows up to give you your first task. He tries to breathe fire but ends up burning himself and then he says, with an attempt at sounding sinister, “I will ask one of you whether the other two will give the Same or Different answers to a question and if whoever I ask is wrong, you all lose your souls, HAHAHAHAHA.”

So he asks you if your two friends will give the Same answer or Different answers and you say, “Same!” nice and loudly so your friends can hear. Then he asks one friend, “Do you enjoy strolling through cemeteries late at night?” Your friend, very loudly and clearly, says “Yes!”

Then the little devil-in-training turns to your other friend and says, “And how about you, my soon-to-be-slave, do you enjoy strolling through cemeteries at night?” Your second friend has of course heard the two previous answers: you said Same and your first friend said Yes, so of course your second friend loudly and carefully says, “Yes!”

The little devil tries to roar his disappointment but just makes sort of a grating whimper. He presses on however asking you if your friends will give the Same or Different answers and he forces you to say, “Different!” just to try to confuse your friends. But they are standing right there and can hear everything, so, when one answers, “No!” the other says, “Yes!” The little, kind-of-stupid devil tries asking the cemetery questions first, but the third person always hears the first two and always gives the correct answer. Then he asks the cemetery question, then the same-or-different question, and then the final cemetery question, but there is still no problem as long as you are all paying attention and, given the circumstances, neither you nor your friends allow attention to waver for an instant.

The devil-in-training shakes his pitchfork in frustration, injures himself, and vanishes in a puff of smoke and a shrill whine of pain.

Now a somewhat more experienced, but still youngish devil shows up. He casually lights your hair on fire and laughs as you shriek and squirm. He says in a loud, booming voice, “Time for a little rule change!” and the sound reverberates menacingly before dying away. “Same three questions but this time you’ll be locked in soundproofed rooms,” he says. “You have 10 seconds, HAHAHAHAHAHAHA.”

Moments later you find yourself in a soundproof room, alone and hoping your friends understood your hastily-delivered instructions. You don’t know who is going to get asked what but that doesn’t matter. Here is your plan.

You: Same, Yes

Friend 1: Same, Yes

Friend 2: Same, Yes

No matter how devil #2 asks the questions, he always gets Same-Yes-Yes and your souls are safe. Suddenly you are back with your friends and the second devil who says, “Very clever, but now the rule is if I decide to ask all three of you whether the other two will give the same or different answers, if you all say, ‘Same,’ you all lose your souls. HAHAHAHAHAHA! You have 5 seconds this time.” He smiles and you notice a tiny flame on each tooth and in each of his eyes.

Now you are in the soundproofed room again. Fortunately, you had anticipated this particular move and you were ready with your instructions for your friends. Here is your plan.

You: Same, Yes

Friend 1: Different, No

Friend 2: Different, No

Four things can happen and your souls are safe each time. Here’s the first scenario.

You: Same, Yes

Friend 1: Different, No

Friend 2: Different, No

And the second scenario . . .

You: Same, Yes

Friend 1: Different, No

Friend 2: Different, No

And the third scenario . . .

You: Same, Yes

Friend 1: Different, No

Friend 2: Different, No

Finally, the devil might check that you are not all saying, “Same,” but this will do him no good.

You: Same, Yes

Friend 1: Different, No

Friend 2: Different, No

You have vanquished the second devil. Even though you had only five seconds to tell your friends what to do, your foresight saved you. The second devil screams bloody murder, erupts in a sheet of flame, and vanishes. You know there will be a third devil and you are not sure if you are up to the task of defeating this one as that last one nearly finished you. Your friends are grateful to you for saving them so far, but both are now rather pale, almost in tears. You aren’t doing all that well yourself.  You pray for calm but praying seems quite a hollow thing to do so close to the gates of Hell.

Uh Oh

The third Devil arrives. He is older, MUCH older. “Yes, I see you have out-thought my two young assistants,” he says quietly.  “But don’t worry,” he says reassuringly, almost soothingly, “I won’t pull any of that nonsense about giving you only 5 seconds to think,. You can have all the time you want.” He smiles. There are no flames, just a gleam in his eye. In all of your life, nothing has ever unnerved you so much as this smoothly pleasant Devil.

“You can talk with each other and take notes if you like,” says the Devil (and this is the Devil, capitalized). Some paper and pencils appear and a writing table and chairs.

“We will ask the same questions as before and any one of you must correctly predict whether the other two will give the same or different answers. You will be locked in separate rooms again.  BUT” – and here the Devil allows a brief flicker of universal hatred to cross his face – “if we ask all three of you whether the others will give the same or different answers, you may NOT all say ‘Same’ AND I’m terribly, terribly sorry to inform that you may NOT give us one ‘Same’ and two ‘Different’ answers either.”

“It’s very simple really. We’ll do it 10 times and you’ll be able to meet before each round,” the Devil says calmly. “Take your time . . . or I will.” And he vanishes without fanfare.

One of your friends is shaking uncontrollably. “We can’t do it!” he screams. “I thought he wasn’t allowed to give us an impossible task! We can’t all three of us say Different. It just won’t work! Three yes or no answers CAN’T MAKE THREE DIFFERENT PAIRS . . . one pair will always, always, always be the same.” And he starts to cry. You reflect that you have never seen this particular friend cry.

He looks at the two of you pleading, wanting it all to be a dream. He grabs you and starts shaking you. “Don’t you see,” he yells, “yes-no-no or yes-yes-no or no-yes-no or whatever you want, at least one pair is always the same. WE CAN’T ALL SAY DIFFERENT!”

You scribble down a quick note for yourself just to make absolutely sure you and your friends are truly in big trouble.

You: Different, Yes

Friend 1: Different, No

Friend 2: Different, Uh-oh

Friend 2 will be right when he says “Different” as long as you and Friend 1 plan on saying “Yes” and “No.” But if Friend 2 chooses his yes-or-no answer ahead of time, either you or Friend 1 will be wrong when you say “Different” – damned wrong you might say.

Your crying friend looks at your paper, nods his head, and collapses into a fetal position; his skin is cold and clammy even with all the fire licking around the walls. He begins to mutter incoherently. Your other friend, wiping the sweat away from his face and making a Herculean effort to stay calm, says, “B-B-But wait, M-M-Mr. Devil said we could have two of us say, ‘Same’ and one say ‘D-D-Different.’ What about that?”

From his fetal position, your other friend just moans, “Noooooo! If two pairs are the same, they ALL have to be the same.” And he goes back to his muttering.

For the first time since all this started, you are deeply and terribly afraid. Using the paper and pencil so helpfully provided by the Devil, you write down the second option. You don’t like what you see. You don’t like it at all.

You: Same, Yes

Friend 1: Same, No

Friend 2: Different, Uh oh

Again, Friend 2’s “Different” answer is fine but the same cannot be said for your “Same” answer or Friend 1’s “Same” answer. The “Uh-oh” can’t be both “No” and “Yes” at the same time!!! And yet it has to be or your souls are in jeopardy.

You look at the flames leaping exuberantly from the walls. You could swear they are forming into the letters, “U-h o-h i-s r-i-g-h-t.” You look away.

There is no plan that will always work. You can’t all say “Different” because three yes-or-no answers can’t all be different. And you can’t have two saying “Same” and one saying “Different” either because if one pair is different, there is automatically another different pair. You are absolutely and totally stuck. Your souls might be safe for a round or two of questioning if you get a little bit lucky, but there is absolutely no way to give the right answers every time.

Maybe the fetal position isn’t such a bad idea . . . The paper and pencil is useless. You can write things down all you want but writing down, “answer yes or no depending on what who got asked what even though you have no idea but please give the right answer every time anyway by magic” doesn’t sound very safe to you. Your souls are as good as gone . . . You feel the black cloak of despair settling over you, a heavy smothering weight, unending darkness everlasting . . . In a way it’s comforting to just give up completely . . . no hope . . . no striving . . . just plain old suffering . . . It won’t be so bad . . .

But wait! With the pathetic young devil, you and your friends could hear each other’s answers. It’s only the insistence that you have to plan it out beforehand that is keeping you from solving the problem. “If only we had radio equipment,” you mutter to  yourself. And suddenly three radios appear! They work perfectly and you and your still-standing friend try them out and you can talk to each other.

“We can bring these with us!” exclaims your friend. “He never said we couldn’t and soundproofing won’t stop a radio transmission.”

One of the radios crackles to life: “Hi honey, it’s me.”

You are rather surprised to hear your wife’s voice and you feel a surge of comfort and hope. But the voice, still soft and feminine, says, “I’m afraid you’ll be placed on 3 different planets in the Solar System and the three questions will be asked simultaneously and you’ll have 3 seconds to answer. Oh, and by the way sweetie, if we don’t nail you the first time, we’ll get you by the tenth try. It’s such a shame – isn’t it? – that radio waves only travel at the speed of light. Love you. Bye.”

Waves after wave of rage ripple through your body penetrating to your bone marrow, enveloping your psyche, briefly rendering you mindless as every thought, every memory, and every feeling you’ve ever had transform into highly purified anger. But you can’t kill a Devil.

A little spark of memory from something you once read or heard fights its way to the surface. As you calm down, you think, “quantum mechanics.” Aloud, you say, “if only we had a quantum physicist.” A rumpled old man appears looking bemused. “Vat is dis?” he says. “I vas just writing de wave function for teleportation and den here I am.”

Beside yourself with excitement, you blurt out, talking a mile a minute, “There’s something in quantum physics about particles being connected and wave functions instantly collapsing. I just need a quick lesson and then you can go back to your lab. Will you help me?”

The rumpled old man gets a familiar gleam in his eye and somehow doesn’t look so rumpled anymore. He says, “Vat’s all the fuss about? You act like you are about to lose your soul! I’d love to help you of course because I am the type who likes to help people in need but I’m afraid any personal help from the outside is strictly – what is the word? – VERBOTEN. Yes, that’s it. VERBOTEN.” He SPITS out the word and a little bit of saliva gets on your skin and it burns you. “I certainly vouldn’t vant to break any rules, now vould I?!”

Mission Impossible

The “physicist” disappears before you can get your hands around his throat. Recovering your composure more quickly this time, you say, “If only we had a high-speed internet connection.” A computer appears and you roll up your sleeves and get to work. Your friends, both on their feet now, stand behind you hoping you find what you are looking for. “I forget the guy’s name,” you say. “All I can think of is John Ringer for some reason, but I’m not finding anything.”

Your previously-fetal friend is still not entirely coherent and just starts mumbling, “Ringer, dinger, danger, donger. I ring, he rings, she rings the bell . . . ”

“BELL!!!” You are smiling now as you type into the computer. “Thank God for that course in modern physics I ended up in when there was that computer glitch with my schedule sophomore year!” you say out loud to yourself.  “It’s John Stewart Bell, the discoverer of the Bell Inequality. Here it is. Three guys have upgraded it to involve three particles rather than two . . . ”

Equipment begins appearing but your friends are still skeptical. “How can this work?” the relatively coherent one says. “We’re going to be on different planets and they are going to ask the questions simultaneously and demand immediate answers. We can’t agree beforehand on what our answers are going to be because we have to fulfill these contradictory conditions.”

“The particles can do it,” you calmly say. “No one knows how.”

“But it’s impossible,” your friend says. “Are you telling me the three particles can all say Different and at the same time all three answers of Different are correct?”

“That’s right,” you say.

“I’m sorry, but there’s just no way to do that,” protests your friend. “There is no combination of three yes-or-no answers where all three pairs are Different.”

“True enough,” you say, “but we don’t have to produce such a combination. All we have to do is make sure three answers are always ‘Different-No-Yes’ or ‘Different-Yes-No’ or ‘Different-Different-Different.’

Your friend is never going to believe it. He says, “Are you trying to tell me that when you measure a particle and it says Different, it forces the other two far-away particles to give different answers? Because it has to be doing that, you know. The particles couldn’t have decided on their Yes or No answers beforehand because there would always be a pair that was the Same.”

You figure there’s some hope that he’s starting to get it. “You’re right of course. That’s why we can’t try this by writing our answers on paper before we get split up. If we tried it that way, we’d burn.”

“What about the ‘Same-Same-Different’ possibility? I suppose you’re going to tell me the particles can do that too,” says your still-skeptical friend.

“Yes,” you say, “some sets of three particles will give ‘Same-Same-Different’ or, if he asks the questions the other way, they’ll give ‘Same-Yes-Yes’ or ‘Same-No-No” or ‘Different-No-Yes’ or ‘Different-Yes-No’.

“But Same-Same-Different doesn’t make an ounce of sense,” protests your friend. “It’s impossible. Don’t you see? You can’t have two Sames and a Different. If one pair is the Same, maybe it’s Yes-Yes, and you want a second pair to be the Same, you have to have Yes-Yes-Yes, there’s no other way. But then you won’t have a Different pair AND YOU’LL BURN IN HELL FOREVER!”

“That’s only true,” you say, “if the particles have to decide what they are going to be beforehand.”

“It’s not going to work,” says your friend, crossing his arms and gnashing his teeth. “We’re going to be on separate planets for God’s sake and we’re going to be asked simultaneously! The particles aren’t going to have time to make the ‘right’ decision any more than we would with our radios. It takes way longer than 3 seconds for any signal to travel between planets.”

“It will work,” you say. “They’ve tested it. No one knows how the particles do it, but they do do it.”

Now Mr. Fetal Position has more or less recovered and he’s got some questions. “Okay,” he says, “you’ve got three particles on separate planets and I can find out about the third particle by measuring the other two. For example, I might get a ‘Same’ answer from one particle and a ‘Yes’ answer from another particle which means I am guaranteed to get a ‘Yes’ from the third particle. Also, I can decide to measure Yes-or-No for two particles and if I get ‘Yes’ and ‘No’ then I know for certain that the third particle will say, ‘Different.’ So I can determine the answer to any question for any particle without ever coming anywhere near it.”

“That’s right,” you say.

“But at the same time, the particles cannot have decided beforehand what they are going to be because there is no previous decision that will give the Devil his due and save our souls which is why I’ve been in the fetal position for the last few hours. Right?”

“Yes.”

“But when I measure two of the particles, the third particle that is on a different planet and that could not possibly have decided what it was beforehand now suddenly decides what it is going to be. Right?”

“Yes.”

“So the particles can communicate with each other instantly! That’s what you’re saying. Sorry, but that’s impossible. No way, no how, absolutely not,” insists your friend, his eyes starting to glisten again, the blood running out of his face. “It’s really, really hot in here,” he says, stumbling a bit even though he wasn’t trying to walk. “Have you noticed that?”

“Well,” you say, gripping your friend’s shoulders and staring into his eyes, “I guess the particles do appear to be communicating instantly. The physicists even have a name for this phenomenon – they say quantum mechanics is ‘weakly non-local’ which I guess means the particles act as if they are talking to each other but they don’t talk loud enough for us to hear. Anyway, I’ll make the apparatus and we’ll see what happens. I can get anything I ask for and I had a good teacher in that crazy class I took way back when so I don’t think it will be a problem to build the equipment. We can test it thoroughly, so we’ll know it works before we try it.”

More and more stuff appears and soon, with the help of the internet and the supernatural procurement abilities of the Devil himself, you are ready to give your friends their instructions: “If you are asked whether the answers will be the Same or Different, set your meter to “X” and press the red button to get the measurement. If the result says ‘Spin Up’ then answer ‘Same’ and if the result says ‘Spin Down,’ answer ‘Different.’ If you are asked whether or not you like to stroll in the cemetery at night, set your meter to ‘Y’ and press the red button. ‘Spin Up’ means ‘Yes’ and ‘Spin Down’ means ‘No.’ That’s all there is to it. As long as we can meet before each round, we can set up the equipment and we’ll be fine.”

“What exactly are we doing?” one friend asks.

“We have three particles that were produced together in a particular quantum state. If you measure the x-component of spin of one particle by shooting it through a magnetic field, that will determine whether the y-components of the other two particles are the same or different. So if the x-component of any of the three particles reads as up, the y-components of the other two particles will be the same – either both up or both down. If the x-component of any particle reads as down, the y-components of the other two particles will be different – either up and down or down and up. The best part is if you measure the x-components of each of the three particles, you will always get either three downs or two ups and a down even though this should be impossible. You can always find out what one particle is by measuring the other two, but if you try to write down what the particles might decide to be before any measurements are made, your written list will never give the results of these experiments.”

“Amazing,” one friend says. “You’d think you couldn’t get three downs for the x-components because that implies all three pairs of y-components are different which is absurd. And if you get two ups and a down for the x-components, that implies the y-components have two pairs the same and one pair different at the same time which is also impossible. Incredible.”

“Not if these particles have some sort of special magic web of communication between them that works instantly,” says your other friend, his words laced with an odd mixture of  skepticism and foreboding. “Has this little trick of yours ever been tried with the three particles on three different planets?” he asks.

“Well, no,” you say, “but it works in the lab with the measurements happening almost exactly simultaneously, so it should continue to work for us even if we are placed in rooms millions of miles apart and asked simultaneously. Many physicists are truly puzzled by this behavior of the particles so they’ve checked it many times. I know this will work.”

At that moment, the whole place erupts in white-hot flames. Your friends, terrified and bewildered, run as far from the flames as possible as all your equipment begins to bubble and smoke and melt into lava. You calmly walk through the flames untouched and unharmed smiling at your cowering friends. You scoop up some melting plastic and metal and glass and form it into a ball without burning your hands. Your voice is strong and clear, your confidence returned, your fear a thing of the past: “C’,mon HONEY,” you say rather loudly, “don’t you want to come play catch with me? What’s the matter – sore loser? Poor devil! Ha-ha. Get it? I feel so bad for you! Better luck next time, you dirty little outcast, you filthy bottom-dwelling worm, you disgusting . . . ”

Suddenly you are in your kitchen standing next to your wife at the very instant you were taken. This time you know it’s really her. “What’s for dinner?” she says.

“Anything you want, baby.”