UPDATED BELOW

In principle, the equations of classical (~~or quantum**~~) mechanics completely determine the future of every particle in the universe given the present state of every particle. This has two implications: one, that the universe is deterministic (with attendant restrictions on what “free will” can mean); and two, that the physical law that entropy in the universe always increases requires serious explanation. I recently attended an interesting talk on the second of these by a philosopher of science. Even more recently, a chat with a friend turned to the determinism of the physical laws.

If you accept that the basic laws governing the motion (and therefore the time-evolution) are deterministic, does that mean, given that there was a definite beginning, that every one of us is unique? Can there be somebody else who is exactly like you? If that question seems leading, that’s because it probably was. In order to answer that question, however, you’d have to define what “exact” means. Now, it may seem like I’m splitting hairs here, but bear with me.

What’s a good definition of “exact”? Clearly, I know the universe exactly if I know where every molecule of the universe is and how fast it is moving. You might think this is an extreme demand and you’d be right. You would need a computer larger than the universe to keep track of all the data. (Why? The simplest “computer” that can do this is the universe itself. Any device with a more complicated process for tracking every molecule will have to have many times the number of molecules the universe has. And universes are hard to come by.) If this is your definition of “exact”, then, it is meaningless (and perhaps trivial) to ask if somebody else can be “exactly like” you.

Luckily, this level of detailed knowledge is not only impossible, but also unnecessary. I don’t need to know what every molecule on Earth is doing in order to predict that the Earth will go around the Sun in a slightly eccentric circle. This is the salvation of the scientific enterprise. Emergent phenomena can be studied without needing to know every detail of the underlying physics*.

Phrased slightly differently, it is indeed true that you are “unique”; both in the sense that there’s nobody else whose molecules are exactly like yours (i.e. we’re all snowflakes), but also in the more important sense that the arrangement of molecules that makes you could be no other way.

But even this more correct interpretation is meaningless for the reasons I’ve given above: what matters are some aggregate properties of the molecules that make up you and me. In general, whether or not these macroscopic properties are uniquely determined by initial conditions is not a question that has an answer. You might think the answer is what you choose it to be, the answer that lets you sleep at night.

UPDATES: When I say above that you can choose the answer you want, I mean you can’t get to the answer by pure rationalism. We don’t, of course, have to answer this question “rationally”; we can find the answer empirically.

*I say underlying* physics*, not in support of the sentiment that “it is all physics underneath.” In fact, this is not only wrongheaded, but also counterproductive. The wrongheaded bit is illustrated (as only Randall Munroe can do it) here. I know of at least two prominent examples of people taking “everything is numbers” to idiotic heights: Steven Levitt of *Freakonomics*, and now Nate Silver o*f Five Thirty-Eight.*

** Srikanth points out that since quantum mechanics is inherently probabilistic, what I say here may not hold. I think it still might, but I realise that it’ll take more than one blogpost to sort this out.

HT: Aanveeksha, who brought this topic up.

Well, so far as I know, what you said must be correct: QM is indeed deterministic. It’s just that the ‘magnification’ we do to measure things in it makes it run riot – introduces probability (Reduction of state vector – R procedure?). Which is sometimes called collapse of the wave function. <:-|

I have recently been told that the wavefunction in QM basically tells you all you need to know about stuff in the quantum scale as long as you are not measuring it; attempts at measurement leads to a collapse of the wavefunction. However, the description at quantum scale is in terms of the probability densities at all the possible states. So although your statement is technically correct, I wouldn’t know how one would realize it in practice. Besides, there’s always the sensitive dependence to initial conditions to add to the chaos.

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