Sunday, March 27, 2016

Batman v Superman: Dawn of Just a Minute...

The internet at large has already covered a lot of what's wrong with BvS, so rather than repeat what's already been said, I'm going to restrict myself to a couple of major things not much touched upon, specifically: the Act 3 climax is a huge mis-fire; and the post-climax codicil makes no sense whatsoever.

First, the climactic battle with Doomsday. The problem here is: who really cares? Comparisons to The Avengers are inevitable, and in that movie we've had all kinds of foreshadowing and build-up: the Avengers must stop Loki from using the Cube and opening the portal, failing every step along the way, until the emotional climax of Stark laying down his life... In BvS by contrast we get a rock-monster with arbitrary powers and an equally arbitrary weakness, that appears deus ex machina with no motivation nor character of any kind, and that is not set up in any emotionally meaningful way by preceding events or threats. And even ignoring the disconnect from the foregoing story, there's neither a logical reason that the Kryptonian spaceship even has the ability to create a Doomsday nor a narrative reason that Lex chooses to do so (compare Avengers, where opening a portal is Loki's motivation from the very beginning). 

Consequently, here there's no sense whatsoever that we're building towards this apocalyptic battle -- a problem highlighted by the fact that Wonder Woman decides to get involved in the fight for no adequately explored reason. (More generally, Wonder Woman is woefully underdeveloped -- and not in an intriguing, "show me more backstory!" kind of way, but in a frustrating "what does she want? why is she doing that?" way.) In fact, given that Luthor's main plot is all about manipulating Superman and Batman over many months into fighting each other, the whole Doomsday plot line feels like it was left over from an entirely different draft of the script. Having made the Batman v Superman conflict the core of their movie, the writers apparently had no idea what to give them to do once they had resolved that conflict.

Second, the post-battle State funeral. Why? In the Death of Superman comic book source material, this makes perfect sense. In the comics arc, Superman is a long-established hero, known and trusted, even loved; and the world watches as he fights Doomsday all the way across the country for days on end, other heroes falling by the wayside, until finally, battered into exhaustion in full view of friends and news cameras, he sacrifices his life to save the world. Of course the world mourns. But in BvS, (i) Superman is mysterious, distrusted, and even disliked; (ii) Doomsday appears out of nowhere and spends around twenty minutes in Metropolis, hardly enough time for everybody to decide that we've tried everything and the world is going to end unless Superman can stop it (frankly, anybody that was there for Zod is probably thinking "meh, I've seen worse"); and (iii) nobody witnesses Superman's self-sacrifice and death except Batman, Wonder Woman, and Lois Lane... but their word is good enough for the US government to throw a funeral fit for a president.

On reflection, the two best sequences in Dawn of Justice are (i) Batman rescuing Martha Kent, and (ii) Wonder Woman fighting Doomsday. The former is the one fight scene that is most true to the Batman character (I wouldn't be at all surprised to learn it was done entirely by the Second Unit); and the latter the only part of the movie where anybody seems to be having fun. Like Doomsday,Wonder Woman seems to have wandered in from the theater next door where she had been starring in a movie that was a lot more fun than the one I was sitting through.

And so it struck me: DC could in fact have made a far more interesting movie if Superman never appeared at all. Sure, he's out there in the world somewhere, motivating Lex and the others to their actions, but never actually seen. Edit out every scene with Kent or Superman (except maybe Bruce's nightmare sequences), give Wonder Woman some proper background and motivation, and you've probably got a pretty decent movie about how the rest of the world feels about Superman, and how it copes when he doesn't come flying to the rescue.

Saturday, December 05, 2015

Quantum entanglement does not work like that

Whenever the topic of quantum entanglement -- which Einstein decried as "spooky action at a distance" -- comes up in online conversation, somebody will always ask whether this phenomenon can be used for instantaneous communication. And this is a very reasonable question because although the answer is definitively No, it's far from intuitively obvious why this is so, not least because it depends on details of quantum behavior usually omitted from non-technical explanations -- details that are critical to understanding the phenomenon.

I originally wrote the explanation below in response to a post on Gizmodo. Several people said it was helpful, so I decided to preserve it online for when the question inevitably comes up again.

The Very, Very Short Version

Entanglement allows you to infer what result somebody else's experiment will get; but it doesn't allow you to influence what result they will get.

The long version:

First, entangle your electrons

Suppose you “entangle” two electrons (there are lots of ways to do this; we'll take it as given). What this means is that they are paired in such way that certain of their properties are reflections of each other. (In technical language we would say they have a "shared state".) In particular, we are interested in the so-called "spin". So you send me one electron and keep the other. Now you measure yours to see if it's spin is pointed up or down; if you find yours is up, you’ll know that if I do the same experiment, mine is pointed down; and vice versa. (The entangled electrons are always opposite, like two sides of a coin). 

Importantly, you won’t know whether you’ll get up or down until you do the experiment -- it’s a coin toss. The only way to tell which is the Up electron and which is the Down, by definition, is to do the measurement. 

Anyway: so far, so normal. Up to this point, it's really no more surprising than if you had split a coin down the middle and sent one half to me. It's no surprise that if you kept the heads side, I got the tails side.

But note the really important part here: I can't use this to send you a signal. The typical misunderstanding at this point is to think that since the electrons are always opposite, if I somehow force my electron into the Up position before measuring, yours will instantaneously be in the Down position, and from there with enough entangled electrons I can easily construct a binary code. And the simple fact is, entanglement does not work like that. Although the electrons are opposite to begin with, anything I do to change the state of my electron does not change the state of yours; instead it just breaks the entanglement. I can no more flip your electron by flipping mine than I can turn your half of the coin from heads to tails.

Let's get spooky

But now it gets quantum. Unlike a coin, there are lots of ways you can measure spin: in fact you can choose any axis you want to measure it along. You don’t have to measure whether your electron is pointing up or down like this: |. You could measure whether it is pointing left or right, like this --. Or along any in-between axis, like / or \. 

Now here's the critical part: electron spin is quantized. This means that whatever axis you measure spin on, the answer will always be precisely "+1" or "-1" units of spin (using the units that physicists typically choose), regardless of what state you thought the electron was previously in; in other words, either clockwise or counterclockwise. Yes, even if you think your equipment only generates up and down electrons, if you choose to measure it on the left-right axis, its spin will definitely be measured as either one unit of left or right spin. Oh, and of course if I measure mine on the same axis, it is pointing the other way. Or you could measure it on any orientation in between, and if I measure it on the same orientation, I get the opposite.

There is no analog in the macroscopic world for this behavior that I can think of. If you had, say, a spinning basketball and you measured it's spin as "+1" in the up/down axis, it's spin on the left/right axis would be 0, and its spin in the / or \ directions would be somewhere between 0 and 1. This is a crucial difference between the quantum world and the familiar classical world.

One of the things this tells us is that, unlike basketballs and other classical objects, electrons don't have a definite spin until you measure it (and even then, that spin is only good until you measure it again on a different axis).

It gets worse (or maybe better)

Now, we’re not done. Up to now we've always measured our electrons on the same axis. It gets even spookier if you and I choose to measure our electrons along different orientations. 

Suppose you measure on the | axis and, say, get Up; but I choose to measure on the -- axis. Now two things I said above seem to be in conflict: 
  • entangled spins are always opposite, so mine must be Down; but 
  • if I measure left/right I must get precisely left or right. 
So what happens? Well, in fact I get left or right, and with an equal chance of each. It’s as if my electron was pointing Down after your experiment, and randomly chose which of left or right to flip to when I measured it.

Notice, by the way, that when I do my measurement, nothing now happens to your electron. If you were to subsequently measure your electron on the -- axis, your result would be completely random. The moment you measured your electron the first time, the entanglement was over. So no amount of cleverness with repeated measurements will let me send a signal either.

The really hard part

Now I do something even more interesting: instead of measuring --, I set my equipment at an angle to yours, lets say at /. If we think of a clock face with Up/Down at 12 o’clock / 6 o’clock, I set mine at 1 o’clock / 7 o’clock. Now what happens? 

What I find is that when your result is Up (12), I’ll get 7 most of the time and 1 some of the time (the exact proportions can be predicted, and have been demonstrated experimentally literally billions of times). And if your result was Down (6), I get the opposite results; mostly 1, some 7. Somehow, my electron “knows” what axis you measured along and what result you got -- even though the orientation was not fixed at the beginning before the electrons separated. In fact, even the orientations of our measurements can be chosen long after the electrons have separated, yet the entanglement still occurs. 

So maybe there's something here that can be used to communicate? Maybe you can send a signal with the way you choose the axis you measure on, since that influences the distribution of my measurements on a different axis? 

Unfortunately, no. And the reason is this:

Remember that when you measure on your end, you always get a random result, either up or down. You can’t force your electron to Up, and thereby influence my distribution; you can only discover whether it is Up or Down (and then infer what I am seeing). You can choose the axis you measure on, but not the outcome you get. (You can't even "separate out" the Up electrons from the Down: the only way to know which is which is to measure them, which destroys the entanglement.) And since you are getting 12 or 6 at random, to me it looks like I'm getting 7 or 1 at random too.

One last throw of the dice?

So perhaps there is one last loophole. If being entangled affects the measurements I get, maybe there is some way I can tell whether our electrons are still entangled? Since entanglement breaking is also instantaneous, maybe that in itself can be used to send a message? But no. Even while our electrons are still entangled, your stream of results looks completely random to you. Similarly on the other end, whatever I measure looks completely random to me: 1 or 7, 7 or 1, with no pattern. It’s only when we bring our results together that we see that whenever you got 12 I was more likely to get 7, and whenever you got 6 I was more likely to get 1, thereby proving that our electrons were entangled.

This is what physicists mean when they say our results are correlated, and the degree of correlation (as mentioned above) is precisely predictable, and has been tested in the lab. But it's only by bringing our results together that we see the correlation -- in isolation, each of us appears to get a random series of results. And bringing our results together to compare requires conventional slower than light communication.

(By the way, this is the basis of quantum cryptography, but that's a long story for another time.)

So in summary...

A lot of the confusion here comes from non-technical explanations being loose in their language when they say that one electron "influences" the other. This is true in the sense explained above -- the result I measure is linked at a distance (yes OK, Albert, "spookily") to the result you measure. But it's not true in the sense that you could change your electron and instantaneously cause a change in my electron. Any change you make to your electron in an attempt to change mine simply breaks the entanglement, and our results are no longer connected in any way.