Remember when I asked for suggested topics for an upcoming Bloggingheads discussion with David Albert about quantum mechanics? The finished dialogue is up and available here:
I would estimate that we covered about, say, three percent of the suggested topics. Sorry about that. But perhaps it’s better to speak carefully about a small number of subject than to rush through a larger number.
And I think the dialogue came out pretty well, if I do say so myself. (And if not me, who?) We started out by laying out our respective definitions of what quantum mechanics “is,” in terms that should be accessible to non-experts. (One user-friendly answer to that question is here.) Happily, that didn’t take up the whole dialogue, and we had the chance to home in on the real sticky issue in the field: what really happens when we observe something? This is known as the “measurement problem” — it is unique to quantum mechanics, and there is no consensus as to what the right answer is.
In classical mechanics, there is no problem at all; you can observe anything you like, and if you are careful you can observe to any precision you wish. But in quantum mechanics there is no option of “being careful”; a physical system can exist in a state that you can never observe it to be in. The famous example is Schrodinger’s cat, trapped in a box with some quantum-mechanical killing device. (Someone must write a thesis on the ease with which scientists turn to bloodthirsty examples to illustrate their theories.) After a certain time has passed, the cat exists in a superposition of states: half alive, half dead. It’s not that we don’t know; it is really in a superposition of both possibilities at once. But when you open the box and take a look, you never see that superposition; you see the cat alive or dead. The wave function, we say, has collapsed.
This raises all sorts of questions, the most basic of which are: “What counts as `looking’ vs. `not looking’?” and “Do we really need a separate law of physics to describe the evolution of systems that are being looked at?”
In our dialogue, David does a good job at laying out the three major schools of thought. One, following Niels Bohr, says “Yes, you really do need a new law, the wave function really does collapse.” Another, following David Bohm, says “Actually, the wave function doesn’t tell the whole story; you need extra (`hidden’) variables.” And the final one, following Hugh Everett, says “You don’t need a new law, and in fact the wave function never really collapses; it just appears that way to you.” This last one is the “Many Worlds Interpretation.”
I want to actually talk about the pros and cons of the MWI, but reality intervenes, so hopefully some time soon. Enjoy the dialogue.
Comments
133 responses to “Quantum Diavlog”
Peter Shor wrote: On a related topic, I have never been able to make sense of the factoring algorithm in Bohm
Huh? How’s that going to work for, say, the three-slit experiment?
I had not thought of a 3-slit experiment. I suppose we could consider the Bohmian path as a set of three paths which are loops that pass through all possible pairs of loops. Maybe some sort of braid group or knot system can be formed from these loops.
Lawrence B. Crowell
Sounds hopelessly contrived to me. And I suspect that the result will depend strongly upon the choice of path, and it seems questionable that it would coincide with the predictions of quantum mechanics.
Jason wrote:
It still works in this scenario if I and my brother are identical twins, though.
Bohm’s interpretation is somewhat contrived as it is. There is this quantum potential
$latex
Q~=~-{hbar^2over{2m}}{{nabla^2 R}over R}
$
for R the polar amplitude, which is often computed by first finding solutions for a system by standard methods. So Bohm’s QM is weak or contrived to some degree. Also since it avoids Hilbert space and discrete states it also fails in the domain of relativistic QED where particles are produced. Yet, if one wanted to connect Bohm’s theory to quantum factorization what I suggest above might be one way of doing this.
Bohm’s QM is not the most convenient approach to working with quantum information issues — to say the least.
Lawrence B. Crowell
Jason, this statement in #98:
But I can still be firmly justified in expecting to see around 7 flips away from 50 heads because nearly all of these 2^100 future me
collin237,
(Sorry for the delay, I was away.)
I realize relationships at the quantum level are complex and inherently fuzzy, but in post 49 you asked a basic question; ” How does the universe knows which is the observing system and which is the observed?” To which I offered a simple answer.
Whether they change at the same time, or not energy(the observer) goes from past events to future ones, while information(the observed) goes from future potential to past circumstance.
Consider the light passing through the slits and striking the screen. The energy goes from one event, the slits, to the next, the screen. On the other hand, the information that is these events goes from potential to actual. So while the energy may be conserved and therefore not collapse, the information would seem to collapse, at least within the context of the observer’s particular world.
It would be hard to argue another world is formed, as this would require a duplication of the energy, as it means a duplicate observation. If energy and information were analogous, then information would also move from past circumstance to future potential and many worlds would result, but only energy does. That’s why the physical energy of your brain moves into the future, but the information of your mind recedes into the past.
The point is that before the measurement, the observer is one person. After the measurement, the observer becomes many different persons. Consider the situation where we’re talking about gambling, and let’s say you want to bet in such a manner that you maximize your winnings afterwards.
Now, in this situation, some of the observers after the experiment are guaranteed to win, while others are guaranteed to lose. But how do we maximize the overall win/loss ratio? It turns out that the way to do that is to understand the system as operating probabilistically under Born’s rule. Maximizing the probability of winning using the Born rule turns out to be the exact same thing as maximizing the winnings of the multiple selves after the experiment.
That’s probably because the more common terminology is “quantum measurement problem”.
John Merryman,
You’re misunderstanding what is going on in the many worlds interpretation. Energy is not duplicated. If the system splits into two after the observation, all that has happened is that the wavefunction of the system has been placed into a superposition of two states, and those two states are such that they don’t interfere strongly with one another. Because the observer is also quantum-mechanical, they exist in the same superposition of two states. But since the two states don’t interfere significantly, each component of the superposition isn’t capable of observing the other.
John Merryman —
As jason has pointed out, there are not ‘two universes’. The MWI is simply a statement that the unitary evolution of the wave function is mathematically equivalent to ‘many worlds’. There is no problem regarding energy conservation. And even if you misunderstand the idea and think that it is literally saying that universes are being created or destroyed, there is no physical law regarding the conservation of energy across multiple universes. All that physicists know is that energy is conserved in the world we can see around us.
Re Peter Shor #92
Is there an up to date review of BQP and its relation to various classical computational complexity classes (and any other quantum ones as well)?
(I don
Jason: “The basic Copenhagen interpretation simply fails to explain what
St, Jason,
So you want to constrain and condense the argument for an unconstrained and un-condensed view of reality?
Maybe a bipolar argument is necessary to support a bipolar reality.
@Jason & ohm
Hi,
I definitely think your last answer is correct according to MWI. I don’t understand, however, how one can consider it’s enough to solve the problem.
Yes the energy is conserved overall, but that’s not the same as “each world in MWI must have the same energy content”.
Energy conservation [I]as MWI predicts it[/I] corresponds to the former. Energy conservation [I]as we see it[/I] correspond to the latter. If it is a natural feature of MWI that both correspond… well then I just missed something, please let me know what.
In fact, MWI would offer a natural explanation if energy would prove to be [I]not[/I] conserved in our (partial) world, as one might imagine from this http://fr.arxiv.org/abs/0804.2178
PS: in my previous post please understand “each world in MWI must have the same energy content” as “in MWI each possible observer will experiment energy conservation”.
Q-CD,
I don’t think we’ll get non-conservation of energy in any interpretation of quantum mechanics, let alone with MWI. The basic problem is all of the interactions in quantum mechanics conserve energy, and since any change in the energy levels will involve an entanglement between some other particle that carries off or supplies the energy of the state, it seems to me that the most you’ll be able to do is have energy reshuffled differently in the different worlds of the MWI.
Here is, basically, what you would need for energy conservation to be violated:
1. Start with a single, discrete energy state.
2. Make a change to the system so that it is split into a two-level state with different energies, without transferring energy to/from the environment
3. Make a measurement of the energy level of the system: some of the worlds will measure an energy increase, some an energy decrease.
It’s the bolded point in step two that I don’t think is going to ever be possible.
As for the heat bath theory paper you mentioned, I think it’d be interesting to compare the entropy transfer of that setup with the entropy required to perform the measurements. Somehow I suspect that we’ll find that the measurement itself requires an entropy increase that makes up for the decrease in entropy of the system. If not, then this will be a method to obtain free energy (that’s why I strongly doubt that it’s going to be the case).
Jason,
Wouldn’t the scale be tipped in favor of the direction/world that received the most energy and that determines whether the cat is dead or alive? Once the scale has tipped, with that original quantum break, it has a cascading effect to the macro level, so that while at the quantum level there is inherent fuzziness, this doesn’t carry to the macro level, since valid worlds built around both events would require sufficient energy to manifest them. ?
>the most you
mathematician wrote on Aug 13th, 2008 at 4:56 am
Is there an up to date review of BQP and its relation to various classical computational complexity classes (and any other quantum ones as well)?
===========
I would suggest Lecture 10 in Scott Aaronson’s class (and maybe some previous lectures as well, depending on what your background is:
http://www.scottaaronson.com/democritus/
Thanks! Looks good!
Q-CD:
Those worlds are probabilistically-suppressed just as they are in any interpretation of quantum theory. We still don’t expect to see such violations because they’re going to be so rare.
As for quantum suicide/immortality, I think it ignores something crucial: death isn’t instantaneous. If, for example, the “me” in the current world is going to die in ten seconds, but the “me” in a different world from which I have already decohered will not, it is of no help whatsoever as far as my future is concerned. It also ignores the fact that the elimination of consciousness is going to be a gradual process, such that death itself is an inherently classical phenomenon.
@ Peter Shor: thanks for this interesting link
@ Jason Dick: that’s definitely a good point. Thanks for this discussion 😉
The discussion was very interesting but seemed to reach somewhat of an impasse relating to an amoeba