B Understanding The Conscious Observer: Young's Double Slit Experiment

[JaredMessenger]

How exactly does the mere act of observing collapse the wave function of, say, photons? I don't quite understand that one. And Richard Feynman's question related to Young's double slit experiment and the fact the electron went through both slits, as well as neither, and just one slit, and just the other, he challenged how you would calculate the probability of which slit it would go through, by saying "What if you cut a third slit, or a fourth, or fifth, or cut infinite slits, so there was no panel left, then added a second panel, but cut infinite slits in that panel. How would you calculate the probability then? I am only 15, so I'm not as smart as you guys, but I like to try to understand things.

 

[PeroK]

How exactly does the mere act of observing collapse the wave function of, say, photons? I don't quite understand that one.

What makes you say "mere" act? How do you observe a photon?

 

[JaredMessenger]

What makes you say "mere" act? How do you observe a photon?

You can use a photodiode connected to speakers to hear clicks when a photon is detected. But when I said “mere act” I just meant that it was strange that something that is easily done such as observing and detecting the photons could completely collapse the wave function.

 

[PeroK]

You can use a photodiode connected to speakers to hear clicks when a photon is detected. But when I said “mere act” I just meant that it was strange that something that is easily done such as observing and detecting the photons could completely collapse the wave function.

Two points. The photodiode absorbs the photon, so the photon is gone. That's not observing the photon in the way that you might observe a car or an electron, where the object or particle still exists.

That's more than "collapsing" a wavefunction.

If you turn your attention to a particle, then you can observe it by interacting with it in a non destructive way.

The term "collapse" can be misleading, as it suggests some catastrophe has happened to the wavefunction. But, in fact, the wavefunction has changed to an eigenfunction of the observable's operator.

It's not like the wavefunction no longer exists.

There is no physical "mechanism" for this as effectively this process is a mathematical one and the wavefunction can be seen as a mathematical object in the theory.

The mathematical process is essentially a postulate - an observation returns an eigenvalue of the observable and the state changes to the corresponding eigenfunction.

 

[stevendaryl]

How exactly does the mere act of observing collapse the wave function of, say, photons? I don't quite understand that one. And Richard Feynman's question related to Young's double slit experiment and the fact the electron went through both slits, as well as neither, and just one slit, and just the other, he challenged how you would calculate the probability of which slit it would go through, by saying "What if you cut a third slit, or a fourth, or fifth, or cut infinite slits, so there was no panel left, then added a second panel, but cut infinite slits in that panel. How would you calculate the probability then? I am only 15, so I'm not as smart as you guys, but I like to try to understand things.

Hi, Jared. I think the full story of what exactly goes on in a measurement or observation is complicated and there isn't universal agreement about it. However, I think that I can give you a feel for why observation makes a difference. It requires a little bit about the mathematics of quantum mechanics, though. This might be a little bit beyond a high-school student, but maybe it can give you a little more intuition about it.

Here's a typical quantum-mechanical problem, illustrated by Figure 1:

Figure 1: Two paths from state A that end at the same final state D.

• You have some system that starts off in state A.
• From there, it can make a transition to two possible states, B and C.
• Then we want to compute the probability that it ends up in state D.

Let P_{ABD} be the probability of ending up at D via the top path (through B), and let P_{ACD} be the probability of ending up at D via the bottom path (through C). Then using ordinary probability theory, you would just add these probabilities to get the total probability for ending up at D.

P_{AD} = P_{ABD} + P_{ACD}

For an example from real life, suppose I'm trying to catch a goat. I might try to use a net, or I might try to use a rope and lasso it. Suppose I just flip a coin to decide which to use. Then before flipping the coin, someone might figure my chances as follows:

• There is a 50% chance that I will choose a net, and if I do, there is a 30% chance that I will catch the goat. So the probability of using a net and catching the goat is 50% X 30% = 15%.
• There is a 50% chance that I will choose a rope, and if I do, there is only a 10% chance that I will catch the goat (because I'm not too good with lassoing). So the probability of using a rope and catching the goat is 50% X 10% = 5%
• The total probability that I will catch the goat is 15% + 5% = 20%

With quantum mechanics, things don't always work that way. Instead, there is an effect called "interference". If you have different paths to get to the same final state, then there is an additional "interference term" in the probability:

P_{AD} = P_{ABD} + P_{ACD} + 2 \sqrt{P_{ABD}P_{ACD}} cos(\theta)

where \theta is the "phase difference" between the two paths. This additional term, 2 \sqrt{P_{ABD}P_{ACD}} cos(\theta), is the interference term. It can be positive, making the probability higher, and so making the final state D more likely, or it can be negative, making the probability lower and so making state D less likely. But notice that it involves both paths. Because of interference, we can't just think "The system either went through B, or it went through C, we just don't know which", because there wouldn't be an interference term in that case.

Now, let me introduce a slightly different situation. Suppose that somehow the system "remembers" which path it took, because someone took a photograph of the intermediate state. (In that case, the complete system is the original system plus the camera). What that means is that the system ends up in two different states, as shown in Figure 2:

Figure 2: Two paths from A that end up in two different states.

The final state D_B is different from final state D_C, because part of the state remembers which path was taken. In this case, there is no interference term:

P_{AD_{either}} = P_{ABD_B} + P_{ACD_C}

There is only interference between alternatives that end up at the exact same final state. If the alternatives end up at different final states, there's no interference term.

So observing and recording the intermediate state destroys the interference term and makes the probabilities work out the way they would in ordinary probability theory. So it becomes possible to interpret the probabilities to mean: It really went one way or the other. The "wave function collapsed". Note that even if you destroy the record of which path was taken, by burning the photograph, there will (unless you're very, very careful) generally be some difference in final states depending on which path was taken.

What all of this shows isn't that consciousness collapses the wave function, or that it doesn't collapse the wave function. It just shows why observation and measurement make probabilities work out the way they would classically---as if the wave function collapsed.

 

[Enk]

Hello there, i stumbled on this forum out of curiosity, and have a few question on the concept of conscious observer. I come from litterary studies so my questions won't be technical, but rather methaphysical.

Again, I'm a profane, i don't know which simplifications have been used to introduce quantum physics mechanics to the masses and therefore might end up making a few technical understanding mistakes, feel free to correct me if so.

The first question that comes to my mind is this: how can conciousness influence the state of matter? What's so special about life, which given a high enough level of complexity and acuity of senses, becomes capable of interacting with the fabric of our world? Woulden't this suggest that counciousness is a primal force of this universe, on the same level as gravity and nuclear and electromagnetic forces? Moreover, I'm not the religious kind, but if to exist in a state of certainty, matter needs to be observed, how has life even come to be, how did our universe even come to exist, how can the big bang be a fixed event without an observer to allow our universe to exist in a state of certainty? Basically it's back to the old "if a tree falls in the forest without no one earing it, did it really fall?", if possibilities are all that exist until they're observed or recorded, doesen't it suggest that some form(s) of conciousness have been arround ever since the dawn of our universe? Or at the very least that this chain of events has been recorded in some form of data to be accessible at some point in time and space to an outside form of counciousness to access?

 

[DrChinese]

The first question that comes to my mind is this: how can conciousness influence the state of matter? What's so special about life, which given a high enough level of complexity and acuity of senses, becomes capable of interacting with the fabric of our world? Woulden't this suggest that counciousness is a primal force of this universe, on the same level as gravity and nuclear and electromagnetic forces?

The short answer is that there is nothing special about the role of life or a conscious observer - from the perspective of physics - to consider. Outside of that, it's purely philosophical.

The role of the "act of observation" in quantum physics has to do with the NATURE of the observation, not who is doing it. Generally, there are pairs of physical attributes that cannot be simultaneously determined with complete certainty. This is a critical variable in measuring quantum state.

 

[Enk]

First, Thanks for you welcome, and your answer :)
​

The short answer is that there is nothing special about the role of life or a conscious observer - from the perspective of physics - to consider. Outside of that, it's purely philosophical.

The role of the "act of observation" in quantum physics has to do with the NATURE of the observation, not who is doing it.

I will admit that i am having a bit of trouble understanding what you mean exactly, (Not being a native english speaker might be the reason, that or my complete ignorance of this field), do you mean by this that conciousness does not play a part in those changes, that only the act of observation, be it by a mechanism without any form of outside monitoring, is provoking them?

 

[DrChinese]

...do you mean by this that conciousness does not play a part in those changes, that only the act of observation, be it by a mechanism without any form of outside monitoring, is provoking them?

Of course, there is no ABSOLUTE proof that consciousness is not a factor in quantum events. Just as there could no absolute disproof of the existence of god. (Which is why I made reference to philosophy.)

Within the physics community itself: the idea that consciousness plays a preferred role in quantum events is (essentially) rejected. There is certainly no proof (or hint of proof) that it does play any role. And there is experimental proof it does not. For example, there are experiments (such as double slit with polarizers) in which a conscious observer "could" obtain certain information, but doesn't. The experiment acts as if the observer did obtain the information. So in that case, the variables are strictly mechanical; and the results are as predicted by quantum theory.

Of course, what is proof to one person may not be proof to another.

 

[bhobba]

I will admit that i am having a bit of trouble understanding what you mean exactly,

Its that QM uses observer in a way different to your literary studies.

In QM an observation is anything that leaves a, for want of a better word, 'mark' here is an assumed common-sense classical world.

Consciousness is not involved in any way.

Now that does leave an issue - but I will let you think about that yourself - hint - shouldn't QM explain the classical world - but what is an observation?

As a literary type person you might find the attached file interesting on the history of such ideas. It's from a peer reviewed physics journal so is an OK reference here, but is generally not the sort of thing physicists worry about - its just an an interesting note on the history of such things and why some of it still hangs around even today, especially in popularization's you find on TV, in books etc, even by famous scientists like Brian Green and Roger Penrose. Its simply they are trying to grope in literary terms with what is best expressed mathematically.

Thanks
Bill

 

[OCR]

Brian Green

Brian Greene ?

 

[Urs Schreiber]

How exactly does the mere act of observing collapse the wave function

From the perspective of quantum probability, which is the basis for the inner workings of quantum observables and states in perturbative quantum field theory (prop. 14.15 in the PF QFT notes) the "collapse of the wave function" after observing a given observable is nothing but the formula for the conditional expectation (e.g. Kuperberg 05, section 1.2, or Yuan 12):

Let $(\mathcal{A},\langle -\rangle)$ be a quantum probability space, hence a complex star algebra $\mathcal{A}$ of quantum observables, and a state on the star-algebra $\langle -\rangle \;\colon\; \mathcal{A} \to \mathbb{C}$ (as in the section States of the PF QFT notes).

This means that for $A \in \mathcal{A}$ any observable, its expectation value in the state is

$$
\mathbb{E}(A) \;:=\; \langle A \rangle \in \mathbb{C}
\,.
$$

More generally, if $P \in \mathcal{A}$ is a real idempotent/projector

$$
P^\ast = P
\,,
\phantom{AAA}
P P = P
$$

thought of as an event (i.e the observable which takes value "1" when that even has occured, and "0" otherwise), then for any observable $A \in \mathcal{A}$ the conditional expectation value of $A$, conditioned on the observation of $P$, is (e.g. Redei-Summers 06, section 7.3)

$$
\mathbb{E}(A \vert P) \;:=\;
\frac{ \left \langle P A P \right\rangle}{
\left\langle P \right\rangle}\,.
$$

Now assume a star-representation $\rho \;\colon\; \mathcal{A} \to End(\mathcal{H})$ of the algebra of observables by linear operators on a Hilbert space $\mathcal{H}$ is given, and that the state $\langle -\rangle$ is a pure state, hence given by a vector $\psi \in \mathcal{H}$ ("wave function") via the Hilbert space inner product $\langle (-), (-)\rangle \;\colon\; \mathcal{H} \otimes \mathcal{H} \to \mathbb{C}$ as

$$
\begin{aligned}
\langle A \rangle
& :=
\left\langle\psi
\vert A \vert \psi
\right\rangle
\\
& :=
\left\langle\psi,
A \psi
\right\rangle
\end{aligned}
\,.
$$

In this case the above expression for the conditional expectation value of an observable $A$ conditioned on an idempotent observable $P$ becomes (notationally suppressing the representation $\rho$)

$$
\begin{aligned}
\mathbb{E}(A\vert P)
& =
\frac{
\left\langle
\psi \vert P A P\vert \psi
\right\rangle
}{
\left\langle
\psi \vert P \vert \psi
\right\rangle
}
\\
& =
\frac{
\left\langle
P \psi \vert A \vert P \psi
\right\rangle
}{
\left\langle
P \psi \vert P \psi
\right\rangle
}
\,.
\end{aligned}
$$

This says that assuming that $P$ has been observed in the pure state $\vert \psi\rangle$, then the corresponding conditional expectation values are the same as actual expectation values but for the new pure state $\vert P \psi \rangle$.

This is the statement of "wave function collapse": The original wave function is $\psi \in \mathcal{H}$, and after observing $P$ it "collapses" to $P \psi \in \mathcal{H}$ (up to normalization).

 

[bhobba]

Brian Greene ?

Of course

Thanks
Bill

 

[bhobba]

This is the statement of "wave function collapse": The original wave function is $\psi \in \mathcal{H}$, and after observing $P$ it "collapses" to $P \psi \in \mathcal{H}$ (up to normalization).

As I said the precise answer is quite mathematical. Don't worry if you don't understand it - just absorb the idea it does have a solution, but it, like a lot of physics, is written in the language of math.

We know a lot more these days than the early pioneers that had to grope with something completely new. It took us a while to resolve it and express the ideas correctly.

Some would say issues remain, I am not one of those, but there is no consensus on the matter. What Uris gave is an elaboration of a more modern take on the whole thing. Here is something on it at a less sophisticated mathematical level - but may be even a bit advanced for your background:
https://www.scottaaronson.com/democritus/lec9.html

Thanks
Bill

 

[Urs Schreiber]

Possibly a good historical example for how proper mathematical formulation may make superficial problems evaporate is the initial puzzlement over the "hole paradox" at Einstein's times. With the modern formulation of differential geometry in terms of manifolds general relativity becomes very easy, and what becomes difficult to understand is instead what the people back then were actually puzzled about!

 

[Urs Schreiber]

Here is something on it at a less sophisticated mathematical level - but may be even a bit advanced for your background: https://www.scottaaronson.com/democritus/lec9.html

On about the same level as Aaronson's account, but (to my mind) more useful is

Jonathan Gleason,
"The formalism of quantum mechanics"
2009, 21 pages
(pdf)

(In fact I learned of the existence of this nice introductory text here. Maybe even from you, or maybe it was from @dextericoby.)

 

[bhobba]

(In fact I learned of the existence of this nice introductory text here. Maybe even from you, or maybe it was from @dextericoby.)

It was me.

But even it is too advanced for a beginner thread. The one I gave may just get by - maybe.

Still as I often say even if you can't follow the math you may get a gist.

A note to Enc, if its beyond you don't worry - Urs is often way beyond me as well - which is why I really like his stuff - it makes me think. Hopefully it makes you think as well - just don't get discouraged - it not really meant for a beginner.

Thanks
Bill

 

[dextercioby]

On about the same level as Aaronson's account, but (to my mind) more useful is

Jonathan Gleason,
"The formalism of quantum mechanics"
2009, 21 pages
(pdf)

(In fact I learned of the existence of this nice introductory text here. Maybe even from you, or maybe it was from @dextercioby )

I do not know about last part. I checked my computer after I saw your message and this PDF has been in the appropriate folder since May 6th, 2013.

 

[bhobba]

Possibly a good historical example for how proper mathematical formulation may make superficial problems evaporate is the initial puzzlement over the "hole paradox" at Einstein's times. With the modern formulation of differential geometry in terms of manifolds, which by definition are independent from their choice of coordinate charts, general relativity becomes very easy, and what becomes difficult to understand is instead what the people back then were actually puzzled about!

Indeed. Looking at things the right way makes what once seems hard trivial. If you look at my info page I say - My favorite interest is exactly how can we view the world so what science tells us is intuitive. Much work in that direction has been accomplished and I really enjoy explaining it to others. Some like Jackson of Classical Electrodynamics fame thinks such things are silly - physics takes its lead from experiment - each to their own I suppose - but for me the sublime beauty of physics viewed correctly is like Erdos's description of the proofs from God's book - when you see them you know it and can just shake your head and smile.

Thanks
Bill

 

[Lord Jestocost]

The first question that comes to my mind is this: how can conciousness influence the state of matter?

Astonishing that the term “consciousness” is so often associated with strange magical effects when discussing quantum mechanics. When quantum mechanics was coming up, some physicists immediately realized that “physical theories” of an "out there" or of an „objective, physical reality“ are – so to speak – built upon our mental impressions/images of “observed phenomena” which must not be identical with the objective, intrinsic nature of phenomena. Mental impressions like temporal or spatial patterns of “clicks” or “spots” do not mean that there must be “particles” at some place and at some time. Confusion arises in case one mixes up the "projections of observed phenomena on the inner screen of our consciousness" with the "objective, intrinsic nature of phenomena". Conciousness does not influence the state of matter, the "states of matter" are pictures in our mind. Here is a passage from the book “THE NATURE OF THE PHYSICAL WORLD” by Arthur Stanley Eddington:

“Besides the direct knowledge contained in each self-knowing unit, there is inferential knowledge. The latter includes our knowledge of the physical world. It is necessary to keep reminding ourselves that all knowledge of our environment from which the world of physics is constructed, has entered in the form of messages transmitted along the nerves to the seat of consciousness. Obviously the messages travel in code. When messages relating to a table are traveling in the nerves, the nerve-disturbance does not in the least resemble either the external table that originates the mental impression or the conception of the table that arises in consciousness.* In the central clearing station the incoming messages are sorted and decoded, partly by instinctive image-building inherited from the experience of our ancestors, partly by scientific comparison and reasoning. By this very indirect and hypothetical inference all our supposed acquaintance with and our theories of a world outside us have been built up. We are acquainted with an external world because its fibers run into our consciousness; it is only our own ends of the fibers that we know; from those ends we more or less successfully reconstruct the rest, as a paleontologist reconstructs an extinct monster from its footprint.


* I mean, resemble in intrinsic nature. It is true (as Bertrand Russell has emphasized) that the symbolic description of structure will be identical for the table in the external world and for the conception of the table in consciousness if the conception is scientifically correct. If the physicist does not attempt to penetrate beneath the structure he is indifferent as to which of the two we imagine ourselves to be discussing.”

 

[OCR]

Of course

Uh-huh....

 

[Quandry]

How exactly does the mere act of observing collapse the wave function of, say, photons? I don't quite understand that O’Neill .

The wave function is not a real thing. It is a mathematical representation of the probability of the photon being somewhere based on uncertainty. When you observe it (ie determine exactly where it is) there is no uncertainty and all the probable positions “collapse” to a single known position.

 

[stevendaryl]

The wave function is not a real thing. It is a mathematical representation of the probability of the photon being somewhere based on uncertainty. When you observe it (ie determine exactly where it is) there is no uncertainty and all the probable positions “collapse” to a single known position.

That might be a little misleading. What it suggests is that the particle had a definite position all along, and the observation only served to let the observer know what that value is. But quantum uncertainty isn't simply a matter of lack of information. There is a distinction in quantum mechanics between:

1. The particle is either in state A or state B, but we don't know which.
2. The particle is in some superposition of states A and B.

Your description blurs the distinction between the two.

 

[Quandry]

For the purposes of answering the original post (or at least that part of it) I made no effort to define uncertainty, just to point out that if the wave function is a representation of uncertainty then certainty "collapses" the wave function.

 

[PeroK]

For the purposes of answering the original post (or at least that part of it) I made no effort to define uncertainty, just to point out that if the wave function is a representation of uncertainty then certainty "collapses" the wave function.

That's equally misleading. A wave function is not really a representation of uncertainty: it's a (position-space) representation of the state of a particle. A measurement of an observable does not represent "certainty", it represents the measurement of an observable. And, a "collapsed" wave function is essentially no different from any wave-function: to be precise, it is an eigenstate of the measured observable.

 

[Kely]

A wave function is not really a representation of uncertainty: it's a (position-space) representation of the state of a particle

Can we say instead that a wave function is a representation of an underlying group?

 

[PeroK]

Can we say instead that a wave function is a representation of an underlying group?

I don't understand what you mean by that.

 

[Kely]

I don't understand what you mean by that.

My fault. I meant because basis states are linearly independent functions, maybe they can always provide a basis for a representation of a given group.

 

[DarMM]

The wave function is not a real thing.

Depends on the interpretation. The current options are:

1. It is literally physically real
2. It's a probabilistic description of the quantum system's underlying behaviour, i.e. it's like a macrostate in statistical mechanics, due to our ignorance
3. It's a probabilistic assignment of what devices might measure (not directly connected with the actual properties of the quantum system)
4. It's a method of organising an agent's beliefs about measurements (same)
   
5. It's a statement about the statistics of an ensemble of measurements on quantum systems (same)

The last three are anti-realist (about the measurements, not the system itself) and only really differ in how they view probability theory (Objective Bayesian, Subjective Bayesian or Frequentist)

 

[Stephen Tashi]

Depends on the interpretation. The current options are:

1. It is literally physically real
2. It's a probabilistic description of the quantum system's underlying behaviour, i.e. it's like a macrostate in statistical mechanics, due to our ignorance
3. It's a probabilistic assignment of what devices might measure (not directly connected with the actual properties of the quantum system)
4. It's a method of organising an agents beliefs about a measurements (same)
   
5. It's a statement about the statistics of an ensemble of measurements on quantum systems (same)

It's worth noting that that 2 and 4 involve consciousness - insofar as an "agent" is conscious of a belief or conscious of assigning a probability.

It makes sense (I think) to speak of a measurement that I am conscious of, but Bob is not. Or we can speak of a measurement that took place at 12 PM that Bob was not conscious of at 12 PM, but was informed about at 12:05 PM. So it seems safe to say that the predictions of QM vis-a-vis measurements do not depend on whether the Bob is a conscious observer of the measurment. However, from the viewpoint of 2 or 4, it risks some sort of logical contradiction if we say that the predictions of QM do not depend on the existence of someone who is conscious of the measurement. How can the predictions be made (by someone) if nobody is conscious of the measurement?

 

[Nugatory]

It's worth noting that that 2 and 4 involve consciousness - insofar as an "agent" is conscious of a belief or conscious of assigning a probability.

Indeed it is (there might be some dispute about #2, but "insofar" leaves much room for general agreement with your point).

However, this is involving consciousness in a different and much less pop-woo sense than in the question that started this thread.

 

[DarMM]

It's worth noting that that 2 and 4 involve consciousness - insofar as an "agent" is conscious of a belief or conscious of assigning a probability.

2 involves consciousness as much as Statistical Mechanics does, so I guess it depends on how much one thinks Statistical Mechanics involves a conscious agent.

4 does involve a reasoning agent, but it could be a non-conscious computer. It just depicts a large part of QM, especially the Born Rule, as normative rules for how such an agent should "mesh" their probabilities for different observations.

Note that it is still open whether experiments or measurements in QM have single objective outcomes. They may have multiple, e.g. Many Worlds, or they may only exist relative to the observer, e.g. QBism (though here it would be relative to all observers who share the same environmental context). So it might not make sense to speak of the objective "out there in the world" results of a measurement.

 

[strangerep]

Can we say instead that a wave function is a representation of an underlying group?

[...] I meant because basis states are linearly independent functions, maybe they can always provide a basis for a representation of a given group.

Advanced quantization is essentially a procedure of finding a unitary representation space (Hilbert space) for the dynamical group applicable to the (class of) systems being modeled. The group elements are represented by unitary operators acting on the Hilbert space.

The wave function by itself is not a "representation", rather the particular Hilbert space is chosen (constructed) such that it "carries" a unitary representation of the relevant dynamical group.