Sunday, March 16, 2008

Intro to the Quantum Measurement Problem

See the previous page: The double slit experiment

Intro to Quantum Weirdness

As previously explained, when we shoot a photon through a double slit, it creates an interference pattern. This interference pattern is only possible if some wave-like behavior is occurring, and if the wave goes through both slits simultaneously. And yet, when we watch where the photon hits the screen behind the double slits, the photon will always land in exactly one spot. Thus a photon has some properties of a wave, and some properties of a particle. I should also add that the exact same experiment works works with any kind of particles, not just photons. All "particles" have both particle-like and wave-like properties.

You may have wondered why this experiment must provide such indirect evidence. If we only need to show that the photon goes through both slits at once, couldn't we just put a measuring device on both slits? Yes, we can. But when we do so, we find that the photon goes through exactly one slit every time. Furthermore, the interference pattern on the wall disappears! It seems that when we try to gather more observations, the results change!

This is why Quantum mechanics is said to be counterintuitive. It defies common sense. Most everything we previously knew no longer applies. So on and so forth. Every time Quantum Mechanics is explained to popular audiences, I hear the same shtick over and over about how Quantum Mechanics is so weird. Personally, I get kind of annoyed that it's repeated to no end. So instead, I'd like to emphasize that while Quantum Mechanics is weird, not everything is up for grabs. It doesn't quite jive with intuition, but it does follow rules that can be studied and understood.

The Copenhagen Interpretation

To explain the basic gist of these rules, I will first consider what is called the Copenhagen Interpretation. According to this interpretation, particles can be described by their wavefunctions. Wavefunctions behave like waves. They propagate around walls, and can go through multiple slits simultaneously. They can diffract and interfere with themselves.

Unlike normal waves, we cannot observe wavefunctions directly. If we try to observe a wavefunction, something called "wavefunction collapse" occurs. When a wavefunction collapses, it suddenly becomes like a particle. It appears in exactly one location. If the wavefunction was originally spread out over a large area, the particle will appear randomly somewhere within this area. The probability that it will appear at any given location is based on the magnitude of the wavefunction at that location.

Let's apply the Copenhagen interpretation to the double slit experiment. First, we shoot a photon through the slits. At first, the photon is a wavefunction, and thus can go through both slits at once. The wavefunction diffracts, and interferes with itself, creating an interference pattern. But then the photon suddenly hits the screen, and collapses its wavefunction in a random location. Because of the wavefunction's original interference pattern, the photon is more likely to appear in some places than others. If we repeat the experiment many times, we can get a good idea of how the original wavefunction was shaped. And that's how we show that there was indeed an interference pattern.

If we put detectors on the slits, then these detectors will collapse the photon's wave function. The photon will become particle-like as it goes through exactly one of the slits. On the other side of the slits, the photon will spread out its wavefunction again, but since it has gone through only one slit, there is no opportunity for an interference pattern to form. If we repeat the experiment many times, we would find no interference pattern.

Observations and Observers

According to the Copenhagen interpretation, wavefunction collapse occurs when a particle is observed. But what constitutes an observation, and who is observing it? In popular imagination, the observer must be a conscious human. But that's not necessarily true. If we performed the double slit experiment with detectors on the slits, no interference pattern appears. This remains true whether we actually look at the data from the detectors. So do the detectors themselves count as observers? Further complicating matters are the experiments of quantum erasure. I will not cover the details, but it's possible to set up detectors such that the information from the detectors is erased after it has been measured. If the information is erased carefully enough, the interference pattern reappears. So sometimes a detector counts as an observer, and sometimes it doesn't?

At this point, I should clear up a common misconception about wavefunction collapse. Some people confuse wavefunction collapse with observer effect. Observer effect occurs because in order to observe the particle, we must knock it with another particle. Because we're hitting the particle, we change it when we measure it. This is not the same as wavefunction collapse. There are actually other ways to observe a particle without knocking it with another particle. Wavefunction collapse can occur whether you physically touch the particle or not. I should also add that the observer in no way "decides" where the particle will appear. Wavefunction collapse is entirely random, and does not depend on the state of mind of the observer.

Back to the detectors. It turns out that it does not matter whether we consider the detectors to be observers or not. Further research has developed a mechanism called "quantum decoherence". In a complicated system, wavefunctions become "decoherent," and no recognizable interference patterns can occur. Any such system will act like an observer and appear to be able to collapse wavefunctions. This is the idea behind the Many Worlds interpretation, an alternative to the Copenhagen interpretation. According to this interpretation, wavefunctions never actually collapse, but only appear to collapse through the mechanism of decoherence. The Many Worlds interpretation implies that our universe's wavefunction is equal to the sum of many non-interacting parallel worlds. In other words, all quantum possibilities are realities in a parallel universe. That may seem like a lot to swallow, but the advantage of the Many Worlds interpretation is that there are no awkward distinctions between observers and non-observers.

There are also other, less popular interpretations to quantum mechanics. Some interpretations say that the wavefunction is not real, but is a representation of what we know about a particle. I understand the philosophical appeal of such interpretations, but in practice they require other nonintuitive rules, and generally just make things harder. Note that the scientific results of every interpretation must agree with the Copenhagen and Many Worlds interpretations, otherwise we would quickly disprove one interpretation or the other.

The end. Questions? Corrections?
After this post, I think I will take a short break from quantum mechanics.

36 comments:

intrinsicallyknotted said...

Very cool stuff--I'd be interested to understand more what an "observer" means in this context, since it's obviously a very difficult thing to pin down. I don't have much of a problem with the wave/particle duality in general (I would call them both imperfect models for some of the behavior of photons, which seems to be what the "collapsing wavefunction" idea is getting at.
It's a lot harder to wrap my mind around the idea that the presence of an observer affects the behavior of the particle, but your description of the experiments makes sense.

miller said...

To distinguish observers and non-observers, you ultimately have to have an understanding of quantum decoherence. Unfortunately I only understand it well enough to do some handwaving. It has to do with a system's constant interaction and quantum entanglement with its environment. The arrow of time also fits in there somewhere. *waves hands around mysteriously*

But more seriously, you can look up quantum decoherence, and maybe you'll find stuff like this website.

Anonymous said...

Can you describe the experiment? Can you identify the single-photon source, the detector, and the geometry of the two slits?

miller said...

I sort of explained the geometry in the previous post. The source is a sort of laser that shoots one photon at a time. The photon goes through two very thin parallel slits, and hits a screen at the back of the room.

The details of the detectors are not particularly important for my purposes. But for quantum erasure to work, you usually use a complicated system of mirrors. To "erase" the information, you arrange the mirrors such that the path that the photon takes does not ultimately affect which detector sees it.

Anonymous said...

On the contrary, I think the detector is important. In the experiment you describe with a screen, the screen is the detector. If you see an interference pattern, it is a pattern defined by multiple photons, even if they are fired at the slit one at a time. The interference pattern merely describes the probability of where the photons will strike. It has been my experience that physicists have the disconcerting habit of failing to describe their experiments completely.

miller said...

You're expecting a lot from a fairly simple introduction to the quantum measurement problem. Perhaps the blogosphere is not your best source of information. Frankly, I'm not knowledgeable enough to give you all the details, nor am I sure why I need to know all the details. In principle, the experiment should work regardless of the type of detectors that are used.

Anonymous said...

This comment for señor Miller...
My question,as a layman,is that ,looking at the famous Heisenberg's statement:
"The conception of objective reality of the elementary particles has thus evaporated not into the cloud of some obscure new reality concept but into the transparent clarity of a mathematics that represents no longer the behaviour of particles but rather our knowledge of this behaviour",one has he feeling that "onjective reality" (the thing in itself)is out of our reach,period,and it seems that this is what gave rise to all kinds of rather philosophical speculations,to say the least.
So,from this I infer that what we oberve (perceive) is just "our picture" of an elusive reality.
What is your view of Heisenberg's
statement?

Regards

Alberto

Alwinder said...

Ok,I managed to make this Google account to work here,the above message is from me.
Thank you!

Alberto

miller said...

I wouldn't make too much of the "objective reality" which may or may not lie behind the mathematics. The mathematics, in principle, make exact predictions of the probabilities. Positing an underlying reality only ends up complicating the theory, and does not help to make new predictions.

In fact, since the time of that Heisenberg quote, it's been shown that there are problems with most hidden variable quantum theories. In other words, it's been shown that most theories which involve a "hidden reality" end up contradicting experimental results. See Bell's Theorem.

Anonymous said...

toffoli:
the rules of quantum mechanics tell us something of what one part of the world looks like to the other part; they don’t tell us what the whole world might look to an “outside observer”; they don’t even help us imagine such a view

Alwinder said...

"I wouldn't make too much of the "objective reality" which may or may not lie behind the mathematics."

Hi,can you elaborate a little on this?,it seems to me that you are not concerned (as a physicist) about the "reality" or "illusion" of an objective reality behind the mathematical formalism?,and perhaps it would not be a problem for physicists,but for philoshophers?

Thank you!

miller said...

If two theories cannot possibly be discerned through experiments, what difference does it make which theory is "real"? If it makes no difference, then it's best to simply use the theory which makes calculations easiest.

On the other hand, if it is possible to distinguish between two theories, then, yes, I would be concerned. For instance, the Many Worlds Interpretation is, in principle (though not in practice), possible to test through experiment. Therefore, I do in fact care about whether the Many Worlds interpretation is true.

Alwinder said...

Physicists sem to have conflicting views of the so called "reality" (the nature of),for some it is mind stuff,for others it is just "material",what would be your definition of "reality"?

miller said...

Well, I think that's a rather meaningless question unless we be more specific about what we even mean by "reality".

What you got to do first is create two competing hypotheses about what "reality" is. Then you have to determine whether there exists an experiment which can distinguish between the two theories. If there exists such an experiment, try it, and then base your conclusion on the results. If there doesn't exist such an experiment, then it doesn't matter which one is correct.

Which two hypotheses did you have in mind? Just saying hypothesis 1 is "mind stuff" and hypothesis 2 is "material stuff" is not clear enough to decide anything.

Alwinder said...

I just want to make sure that you do not think I am "interrogating" you señor Miller!,I have a genuine interest in finding out what is it that a modern physicist thinks about these subjects,thank you for your responses!

Now,there is this what the man on the street simply calls reality (our perceived reality),what our senses are interpreting as real,the seemingly solid world around us..

This reality opposes for example the Hinduism view of it,as they say that it is Maya,an illusion created by our senses.

Then,what I hear ,from Heisenberg,Bohr and others,is that physics has renounced to describe reality (an Ontology),in favor of describing just "our knowledge" of reality (epistemology).

Is this view still prevailing in the physics community,or there is an alternative view of it?

Regards

Alberto

miller said...

I'm not so sure that I'm a good representative of modern physicists. I'm only a physics student for one thing. And I have a blog about skepticism, so I'm probably very opinionated.

I think religious views of reality are basically devoid of useful scientific content. They are not clear enough to make sense. They are not even wrong.

I'm inclined to think of quantum physics as describing reality rather than just our knowledge of reality. Did you read what I said about Bell's theorem? If you assume that particles have definite, but unknowable positions, then you have to make some very counterintuitive conclusions, or the predictions will contradict experiments. If you decide to swallow the counterintuitive conclusions, then you have what's called the Bohmian Interpretation of Quantum Mechanics. The Bohmian Interpretation is not very popular among physicists (it's more just a proof of concept).

It's not impossible for there to be a "hidden reality" underlying the wavefunction, but there's just no reason to think so. It is at best, wrong, and at worst, not even wrong.

Alwinder said...

"I'm inclined to think of quantum physics as describing reality rather than just our knowledge of reality."

Let me to elaborate on this:It seems to me that there are "different levels of reality",according to our "measuring devices" (our five senses),for example,if we look at our hand with the naked eye,we see a "normal hand",but if we look at it with a microscope,we then have a "different view" of the same hand,with an increased resolution,this amounts to having multiples realities,and these depending on the observer's tools for "measuremement" (observation).

Does this make sense to you?

The Bell's theorem is another puzzle that I would like to tackle later on,but I am looking more at the implications rather than the mathematical formalism (....that is over my head)

Thank you

Alberto

miller said...

That doesn't amount to multiple realities, it just amounts to multiple resolutions.

The same thing happens in physics. For instance, we know that most everyday objects are made up of billions of billions of particles, all undergoing complex quantum mechanical interactions. But it's impossible to describe every single particle this way, so we use statistical mechanics and thermodynamics instead.

Another example: Newton's law of gravity is technically incorrect. In fact, Einstein's General Relativity is the correct theory--however, Newton's laws are a sufficiently good approximation most of the time.

And did I say that Einstein's General Relativity is correct? That's not true either. In principle, the theory must be replaced by some sort of quantum gravity theory (yet to be agreed upon).

And if I ever said quantum mechanics is exact, I lied about that too. In fact, quantum mechanics is only the non-relativistic approximation of quantum field theory. And quantum field theory may be an approximation of some deeper theory.

However, I think it is unlikely that there exists a deeper theory where particles have definite, but unknowable positions. On the largest resolution (ie everyday scales), objects appear to have definite position and momentum. On smaller scales, they do not. There is no reason to suppose that on an even smaller scale, the physics will again begin to resemble the largest resolution.

Alwinder said...

"That doesn't amount to multiple realities, it just amounts to multiple resolutions".

Sorry,what I was trying to say is rather that this amounts to "multiple perceptions of that one reality",that hand.

So,every observer actually has (and creates) his own perception of reality,according to the sophistication of his senses ,or his tools.

How does this sound to you?

Thank you

Alberto

miller said...

Yeah, sure. Everyone has their own perceptions.

Alwinder said...

Doesn't this validate the Heisenberg statement about "objective reality"?

miller said...

If Heisenberg only intended to say that everyone has their own perceptions, then yes. I think Heisenberg meant something deeper than that, and that you wanted to say something deeper than that as well.

Alwinder said...

You bet!,I am trying rather hard not to wander into philoshofy,but what I am getting at,is the "ultimate reality",the "thing in itself" of Kant.
It seems to me that there are "levels of reality",meaning different perception levels,yes,and we humans have for example,a different perception of "what is out there",than dogs (they seem to hear a wider or at least different range of sounds?)
The "ultimate reality" would be outside our reach due to "a limitation imposed on us by Nature" (Heisenberg)
In this respect,it looks to me that the statement of Heisenberg has to be taken literally,and it is not a "figure of speech".
I have been reading some of the Stapp papers,and there are lots of ideas coming from him and I can learn a lot from him.
I think Heisenberg meant to say (and really said it explicitally) that quantum physics supports the view that "reality" is just a term,a word,and we are forever banned from knowing it.
What would be your take on all this?

miller said...

I would think of the "ultimate reality" to be unknown in the completest sense. As in, we don't even know whether we know it already, whether there is anything to know, or if the idea even makes sense. We have no idea whether we will ever gain this knowledge in the future, or if we won't.

But as I said before, I don't think the answer really matters unless it turns out we can make testable predictions from it.

Alwinder said...

An interesting riddle that is well known (and relates to observers):"If a tree falls in the forest and nobody is there,is there any noise?"

I believe that some physicists have said No,what would you answer? (and my answer is No)

miller said...

The answer is yes. There is no reasonable interpretation of quantum mechanics which says no, and it's preposterous to claim that most physicists say no.

Alwinder said...

"The answer is yes. There is no reasonable interpretation of quantum mechanics which says no, and it's preposterous to claim that most physicists say no."

I am sorry you had the impression that I said:"Most physicists",in fact I said: "Some physicists" ( and I can mention a prominent one,Fred Allan Wolf),however I could agree easily with you in that "most physicists would answer Yes",at least that is what is suggested to me after seeing their comments on this matter.

In any ways,I thought to lighten up our dialogue with this rather funny,but thought provoking question.

As to my justification for answering No,here it is:What we call Sound is,as I understand it,first a disturbance of the air,in the form of waves,and when this air waves reach my ear,then they are processed by the timpanus first,and then transformed in an electrical signal that reaches the brain.Then ,and only then ,I can talk about Noise,so,basically,Noise is a response (creation?) of the brain.No brain present?....no sound.

How would you justify your Yes answer? (and I have not come accross any physicist giving an answer to this,probably I have not searched hard enough?)

Regards

Alberto

Alwinder said...

....and no,I did not claim that any interpretation of quantum mechanics would support this "No" answer.I think this has nothing to do with quantum mechanics but rather with classical physics.....

miller said...

I do not think highly of Wolf, since he appeared in What the Bleep!?, although the film easily could have misrepresented him.

Perhaps I was too quick to assume you were asking the question in the context of quantum mechanics. Frankly, there is a lot of BS which they tell you in popularizations of quantum mechanics, and I make a point to oppose it. I guess that means I'm incapable of lightening up. :)

Trivially, if you define "noise" to mean the brain signal which occurs when we hear a sound, then no, the tree produces no noise. Also, if you define "two" to mean three, then one plus two equals four. Perhaps if we defined our terms clearly from the beginning, we wouldn't end up disagreeing so much.

Alwinder said...

A question:Are you familiarized and/or interested in the ideas of Henry Stapp,related to the role of the observer in Quantum Mechanics?

miller said...

No, I don't keep close track of famous physicists.

Hey, listen. As fun as it is, I don't actually have the time for extended internet discussions over periods of weeks. Since we were about to change topics, I think this would be the best time to cut it short. Feel free to comment further, but don't expect too much back and forth. Thanks for stopping by.

Alwinder said...

I understand.Thanks for your responses and take care señor!

Regards

Alberto

Scott said...
This comment has been removed by the author.
Scott said...

Alwinder: I don't know for sure, but I would guess the answer to your falling tree question would be that, according to QM, the other trees "hear" it fall (as does the dirt, the air, etc.) As I understand it, the moment of decoherence is the moment at which something becomes capable of causation (in the intuitive sense). So the tree falling can cause our ears to register sound, or they can just cause the surrounding matter to vibrate and heat up a little -- same thing. Anyone who knows, correct me if I'm wrong.

Anonymous said...

This is a confused and mystical description of QM, which unfortunately reflects the way it is commonly taught to non-mathematicians.

The reality is that the underlying mathematical description (the time-dependent Schroedinger wave equation) is non-probabilistic and fully deterministic (like classical mechanics). The numerical approximations used for calculation introduce unreal artefacts such as "wave-function collapse", "superpostion" and "probabilistic wavefunctions" which less-numerate physicists reify (assume are "real") and then teach their students and put in popular articles and blogs. Innumeracy has perpetuated this quasi-religion for the last 100 years. It's about time physicists dropped the mysticism and learnt to do real maths.

miller said...

Anonymous, would you like to point out a specific instance where I reify wavefunction collapse? I generally try not to...