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If I understand correctly, a principle of physics is that information is never created or destroyed. And, unless information is defined differently in physics, according to information theory there is information whenever an event, out of more than one possible events, occurs. The typical example is a coin flip, which would contain 1 bit of information because there are two possible events and one of them occurs, so we obtain information when we learn which of these possible outcomes actually occurred.

I understand that in a deterministic world, coin flips only seem to be probabilistic, but in reality, the probability of being heads or tails was already determined, so one of them really had a probability of 1 and the other had a probability of 0. So there was really no new information here; the information of whether it'd land heads or tails was already contained in the state of the system around the coin and we could've predicted the outcome if we knew enough about the coin's surroundings.

But in quantum physics, unless I'm dead wrong on my understanding of QM, the wave function collapse is pretty much an actual random coin flip. So then wouldn't running a quantum experiment and observing the result create new information?

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  • $\begingroup$ The probability distribution also contains information. When you make a measurement, you're approximating this distribution. As such, you're actually likely to lose information. $\endgroup$
    – probably_someone
    Commented Apr 25, 2018 at 19:07
  • $\begingroup$ Who told you that "information is never created/destroyed"? Information is a very complicated concept and nothing that figures in a formulation of fundamental physical laws. It's nothing like energy, momentum and the like. You talk as if information would be "somewhere in the world", which is often a misleading way to think. $\endgroup$
    – Luke
    Commented Apr 26, 2018 at 12:58
  • $\begingroup$ @Luke Isn't this why there's a black hole information paradox? I know information can be complicated but it doesn't seem so much if you think about it in terms of information theory and possible states of a system. But anyway, it seems to me now that this principle only holds for quantum systems but not necessarily for classical objects if they're not deterministic (which I guess there's no agreement about). $\endgroup$
    – Juan
    Commented Apr 26, 2018 at 17:29

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great question, I believe you are really asking if QM and its wave function, which shows the probability distribution is really random, or is there something in the microcosm that we do not understand and we handle it random, but it is really just that we do not have enough information about the system that builds up the microcosm, so we do not know how to calculate the outcome.

As per QM, the wavefunction of a particle is the probability distribution of the particle really in space. You have to make many measurements, to get the map of the outcomes. The example is the double slit experiment, where you really get to see the probability distribution as a map on the screen.

QM describes the outcomes with the wavefunction. If you make one measurement, it is random, which distribution you will get from the map. But if you make enough measurements, you will see the pattern.

Your question is really why QM does do it randomly. It is because although QM gives the best mathematical description for the outcome of the experiments about the microcosm, we still do not know exactly what is going on in the microcosm in classical (layman) terms. We do not know exactly if particles are really pointlike (they are pointlike in the current accepted views, but string theory gives another explanation) or what it means that an electron has rest mass but no spacial extension. We do not know what a quark really is, or what it looks like at the planck scale. We do not know why the Pauli principle really goes for one type of particle but not the other and how that looks in a classical view or our common sense.

Things just work differently at that size and QM still gives the best description. Our energy levels in our experiments do not allow us to check what goes on at Planck scale.

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    $\begingroup$ I guess what I'm really asking is, assuming it really is random (there are no hidden variables), wouldn't this imply that information is created? $\endgroup$
    – Juan
    Commented Apr 25, 2018 at 19:47
  • $\begingroup$ You are correct, information is created, but only on the macro scale, in the common sense. In the micro level there is no information created, since the probability distribution of the particle is already there. When you do the experiments, you just map the wavefunction, the probability distribution to see it. But you are not creating in the micro level no new information, since the information was still there, you just map that distribution with the experiments. $\endgroup$
    – Árpád Szendrei
    Commented Apr 25, 2018 at 19:51
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Your question can be resolved through understanding some terms better.

A coin flip does not 'contain information.' A coin flip is a stochastic process that generates a random outcome. A well-defined stochastic process is associated with a probability distribution that has a well-defined associated information-entropy. For the toss of a fair-coin, this is one bit.

When you measure the result of a coin-toss, you gain information about the state of the coin. If your previous information was, "The coin's value is determined by a coin toss," and your new information is, "Heads," your information about the coin's state has increased by 1 bit. This will be exactly the same as measuring the difference in entropy for your prior and posterior distributions.

Now that we have that background, we can really talk about information in fundamental physics. While a coin-flip, as we have considered it is a stochastic process, it is also a deterministic process. That is, if we took an accounting of the exact dynamics of the flip and the exact initial state of the coin before the toss, we could calculate (supposing we had enough computational power) the final state of the coin perfectly and we will have gained no information about the coins state from measuring it.

In fundamental physics, it is possible to treat ANY physical process in this way, as the dynamical evolution of some closed system. Hence the principle that 'information is never destroyed'. This is just (sloppy?) shorthand for: Any state is recoverable as long as we perfectly understand the exact state and dynamics of some large enough system (where large enough system might be the entire universe) and have unlimited computational power.

Hopefully this is enough to understand why it's strange to say that measurement collapse 'creates information.' Information is a property of a description (in our case a probability distribution over state). When we measure something (quantum mechanically or no), we are increasing the accuracy of our description.

You might wonder if wave-function collapse destroys information. If you understand paragraph 4 you will see that it does not. The trick is that the information is stored in some larger system, one that includes the quantum object and you the measurement-taker. Some exterior being could in principle reverse this larger system and somehow recover the original state of the quantum system. There are a lot of problems with this- quantum states cannot be measured to unlimited accuracy or reversed as easily as classical states, and again you would need nearly unlimited computational resources.

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    $\begingroup$ I understand your coin example because coins are macroscopic objects and given enough information we could in principle predict the outcome. So the information was already contained in the system. But in the case of QM (if we assume no hidden variables), AFAIK the information of whether the photon will hit some particular point doesn't exist at all until we observe it, so this is new information that couldn't have been deduced from looking at the state of the system before... $\endgroup$
    – Juan
    Commented Apr 25, 2018 at 23:53
  • $\begingroup$ I think, after reading these responses and checking the Wikipedia entry again, what happening is that the no information loss/gain principle is only a thing within the quantum system itself, but doesn't necessarily holds for macro-states. (For example this article states "A fundamental postulate of the Copenhagen interpretation of quantum mechanics is that complete information about a system is encoded in its wave function up to when the wave function collapses."). I'm I understanding this right? $\endgroup$
    – Juan
    Commented Apr 25, 2018 at 23:56
  • $\begingroup$ You're asking the right questions. I didn't go into it above, but there are a lot of caveats to my quantum example. To reaffirm: Any closed system in physics only evolves reversibly and this includes quantum systems. This is sometimes referred to as the principle of Unitarity since the quantum mechanical description of state evolution is through transformation by some unitary matrix operation. This only covers the evolution of the system's quantum state which may be a superposition state. It may not say whether a photon hits a point or not. There's no problem unless you enforce 'realism'. $\endgroup$
    – Eric Bahr
    Commented Apr 26, 2018 at 0:53
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Wavefunction collapse doesn't actually exist. It's only a feature of the Copenhagen interpretation of quantum mechanics. If it did exist, it would be destroying information, not creating it, since collapse is represented by a projection operator.

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  • $\begingroup$ A well-defined theory without fundamental collapse of the wave function is, for example, Bohmian mechanics (a.k.a. Pilot wave theory). $\endgroup$
    – Luke
    Commented Apr 27, 2018 at 12:37
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Wave function collapse is just an interpretation. No information created when you roll a dice and it turns out be a 6.

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