Understanding the Uncertainty Principle

[nanobug]

The "thing", as you put it, cannot, under any circumstances, be in two places at the same time.That's why we use probability -- maybe it's here, maybe it's there. But we don't know until we measure. And by the nature of the measurement, we'll always find one electron in one place at one time; never in two or more places.

Well, for this type of thinking you wouldn't need quantum theory, classical probabilities would be fine. What happens, however, is that things such as interference and superposition, which don't have a classical interpretation, manifest themselves both theoretical and practically. They are a property of quantum mechanics and states in which 'cats' are both alive and dead at the same time are very much a possibility. What you described above are 'mixed states'. But 'pure states' also exist.

And, how in the world can a dead cat observe? Please tell us how.

The dead cat 'observes' the same way that a lump of coal does, by being a macroscopic system.

 

[sgoodrow]

Ah, you may have misunderstood me Zapperz. I was not saying that the principle was not well defined; in fact I attributed immense care that I did not say that. Rather, I said that it is not being properly taught, or properly explained, or what have you, as there is clearly a lot of confusion about what it means, what it implies, and most importantly what it does not imply, as you clearly stated.

 

[Fra]

Be it external or internal, it remains within the confounds of reasonably logical thought; does that alone make it scientific? No; but it does make it rational, and I think many of us agree that you can apply the rules of formal argument to rational ideas, though perhaps not as strictly, and perhaps it does not yield a precise conclusion, but it does have value in the context of a discussion.

That said, your internal subjectivity should be rationalized, as you are a rational being and would not agree to something irrational; yet I ask: since it is just as well to not make a decision, why do you specifically make one? I don't mean to question the validity of your ideas, but I do mean to address the certainty about it. Though of course, I could be misinterpreting that certainty, as it is quite difficult to communicate to another human being (in person, let alone on a message board), but I feel this is a problem of post-modernity in Science and is something we should not turn a blind eye to.

I am not entirely sure I understood your follow up question here, and you're probably right that communications issues is always a problem.
But I think you are asking something like:

Given that I can't make a formal deduction of something, how can I still make a decision? Couldn't I as well play safe and choose to make no decision?

That's a really good question IMO! and it also connects to the point.

Again, my comment here is no formal deduction. And to try to explain ALL of my own internal "reasoning" to someone I don't know much about would be extremely resource consuming so it's still a simple expression.

Each time a decision is made, or not made(!), all the options must be subjectively rated. And even though we do not know what will later turn out to be the best move, our actions are based on the best possible odds, as found by a constrained processing. This means that sometimes the co choice of "playing safe" may be more risks than make one of a set of uncertain choices! This is how I even imagine how time generated. Why does anything change at all? Why isn't the status quo just preserved?

My choices are based on to the limit of my incomplete knowledge and experience, my estimated rating of the options. I am not formally certain of what I write, but I do not need that to make a decision. To chose not to answer the question is also a decision. And for me, that is sometimes less promising.

But I still am not sure if you were talking about something particular in this case. Like why can we know x and p at the same time? You can see this in different ways. For this question to make sense x and p must first be defined. And in the way they are defined in QM, by means of the operator, the uncertainty follows from the definition and axioms of QM.

The other part of the question is to question these definitions, or ask WHY does these definition seem to be so useful? THAT is another question, that I find useful, and this question I didn't comment above. I commented more generally. I have ideas on this too, but nothing that is mature enough for me to convince to you I think.

But, in short I think the relation between x and p can be understood in such a way that in a context of a real observer measuring x, the QUESTION or OPERATOR p can MAYBE be understood to emerge as an answer to improving the observers selfpreservation. But I'm still working on these ideas for myself, and I have no definite opinon. And in THIS case, I do not find estimate it to be favourable to jump into a choice... my other choice is trying to reformulate the very question I am asking, so that answering it beceoms easier.

So I found two subissues in this topic. And until this last post, I only touched the first one.

/Fredrik

 

[Fra]

But, in short I think the relation between x and p can be understood in such a way that...

Since you asked before about certainty of subjective reasoning, I might want to note here that with "I think" I do not mean "I know" or "I am certain", it rather expresses the direction in which I am searching for further information. Thta's I think the most accurate way of thinking of it. But "I think" is much easier to write.

/Fredrik

 

[Fra]

But, in short I think the relation between x and p can be understood in such a way that in a context of a real observer measuring x, the QUESTION or OPERATOR p can MAYBE be understood to emerge as an answer to improving the observers selfpreservation. But I'm still working on these ideas for myself, and I have no definite opinon. And in THIS case, I do not find estimate it to be favourable to jump into a choice... my other choice is trying to reformulate the very question I am asking, so that answering it beceoms easier.

The questions I'm asking here is something like a scheme for inducing new questions, as a respons to a prior question. IE. before you can answer a question, you need to formulate a question - before you can make a measurement you need to build the measurement device! This process should IMO not be underestimated. The feedback between past experments, certainly affects our CHOICE of what measurement devices to build, and what questions to ask next. This is I think tricky and lot to think about.

Edit: This problem is ignored in ordinary QM, except for decoherence - but that is only a partial answer. The measurementdevice is just there. But I think, asking how it got there and how it is beeing deformed remains.

/Fredrik

 

[ZapperZ]

Ah, you may have misunderstood me Zapperz. I was not saying that the principle was not well defined; in fact I attributed immense care that I did not say that. Rather, I said that it is not being properly taught, or properly explained, or what have you, as there is clearly a lot of confusion about what it means, what it implies, and most importantly what it does not imply, as you clearly stated.

There are two different aspects of having something "properly explained". The first is among physicists or people who are experts in the field. I don't see much confusion here. There may be arguments about different interpretations and subtle details, but there are no "confusion" of any sort. We tend to know what we are measuring and the issues surrounding those measurements.

It is the second aspect, the explanation given to the general public, that often is the source of confusion. Here, the "blame" is on both side - physicsts either not giving a clear explanation, or going beyond or sensationalizing certain concepts in physics (Michio Kaku, did you hear that?) to an audience that isn't grounded in knowing the "scale" of things. The other "blame" goes on the receiving end (the general public), where the lack of knowledge certainly can cause outrageous understanding of something.

A case in point here is the often-brought-up question about "relativistic mass". Such issues very seldom comes up in hard-core physics papers. Think of a subject area that deals with particles traveling at close to c - high energy physics. You very seldom encounter any issues about "relativistic mass". Yet, nailing down the mass of an elementary particle is a BIG part of high energy physics experiments! How come there are no confusion of any kind in that field of study? Yet, if you just wait for a few days, the question about "mass" or "relativistic mass" will creep its ugly head again in the Relativity forum. It seems that it is such a big issue among those who don't understand it well, yet it is almost a non-issue to those who have to deal with it almost daily.

To be able to "understand" something, the "explainer" and the "explainee" must be on the same page. The explainer must understand the level of knowledge of the explainee, and not go beyond that, or else the explainee will start to extrapolate things beyond his or her capabilities. The explainee, on the other hand, must put some effort into gaining enough knowledge to know when things simply are beyond what he/she knows, so as not to make silly deductions. It is why, in college, there are prerequisites before one can take a more advance class. There must already be a set of knowledge that is already known before one can build on top of it.

Zz.

 

[PhysicsMaster]

i agree with Fra, it is misleading.

 

[reilly]

ZapperZ -- I was going to write a post on the same topic, particularly in regard to experience. But, you have provided an excellent touch of reality, and a very good discussion of practical explanation and understanding and experience. In fact, I'll go so far as to say that your post should be the second post in all threads. Thanks
Regards,
Reilly

There are two different aspects of having something "properly explained". The first is among physicists or people who are experts in the field. I don't see much confusion here. There may be arguments about different interpretations and subtle details, but there are no "confusion" of any sort. We tend to know what we are measuring and the issues surrounding those measurements.

It is the second aspect, the explanation given to the general public, that often is the source of confusion. Here, the "blame" is on both side - physicsts either not giving a clear explanation, or going beyond or sensationalizing certain concepts in physics (Michio Kaku, did you hear that?) to an audience that isn't grounded in knowing the "scale" of things. The other "blame" goes on the receiving end (the general public), where the lack of knowledge certainly can cause outrageous understanding of something.

A case in point here is the often-brought-up question about "relativistic mass". Such issues very seldom comes up in hard-core physics papers. Think of a subject area that deals with particles traveling at close to c - high energy physics. You very seldom encounter any issues about "relativistic mass". Yet, nailing down the mass of an elementary particle is a BIG part of high energy physics experiments! How come there are no confusion of any kind in that field of study? Yet, if you just wait for a few days, the question about "mass" or "relativistic mass" will creep its ugly head again in the Relativity forum. It seems that it is such a big issue among those who don't understand it well, yet it is almost a non-issue to those who have to deal with it almost daily.

To be able to "understand" something, the "explainer" and the "explainee" must be on the same page. The explainer must understand the level of knowledge of the explainee, and not go beyond that, or else the explainee will start to extrapolate things beyond his or her capabilities. The explainee, on the other hand, must put some effort into gaining enough knowledge to know when things simply are beyond what he/she knows, so as not to make silly deductions. It is why, in college, there are prerequisites before one can take a more advance class. There must already be a set of knowledge that is already known before one can build on top of it.

Zz.

 

[Fra]

I'm not sure if it's just me that found this confusing, but I feel an urge to add this for clarity...

i agree with Fra, it is misleading.

I guess(?) "it" alludes to my post #15 on page 1?

I'm all with you on that physics, like Bohr said, is about what we can say about nature, not what nature us is.

IMO, this does not imply an objective absolute reality. In fact I can't figure out how we can DEFINE an objective reality? The best definition is the collective one, ie, the agreement among a local set of subjective reality views, as communicated between them.

In the everyday sense of science, it is supposedly objective - ie results must be repeatable by others etc. However this has more do to with the science in the sociologicla context. I personally think taking some kind of objectivity idea to it's extreme is misleading.

All I can speak of is MY subjective view of reality. I communicate with others and we compare our views, and most of the time it makses sense. But I can not make the conclusion that there is some absolute objective reality out there because of that. The locally objective reality lies in our communicated, partial, agreements. But this is subject to ongoing change IMO.

This seems to be somewhat "loosely" (all analogies are flawed) analogous to Einsteins search for absolute reference frames where his conclusion was that it doesn't exists, and instead the only reference we have is the local gravitational field.

What the correspondence to the local gravitational field of the analogy in this case? :)

I just wanted to say that nothing of this suggest is in favour of restoring a larger degree of determinism or realism. It's rather the opposite. I am not critisising the lack of determinism in QM, I'm more likely to critisize the determinism we do have in QM! Namely the deterministic evolution of information.

This is only remotely connected to the uncertainty principle, which is why I found post #42 to come out as a little confusing and I wasn't sure if physicsmaster really agree with what I meant to say or if there was a confusion somewhere.

/Fredrik

 

[lightarrow]

From the lecture (and other reading I've done), I am seeing that the math for determining the momentum and position of a particle are directly linked and, together, have a "lower bound". This is my understanding of the premise for the Uncertainty Principle.
Given that, I wanted to ask something to make sure I understand it properly. The principle is saying that it is impossible for us to know, fully, the momentum and position of a particle. However, and here is my question, the particle has a specific momentum and position, it is simply unknowable. Is this correct, or am I misunderstanding? Does the fact that we cannot know both its position and momentum imply it has no specific position and momentum?

You have to understand the difference between physics and philosophy (not that it's an easy task, in QM). First answer to yourself that question, then ask yourself what does in physics mean "that system has that specific property". If you succeed to answer those questions you will understand something very interesting.

 

[lightarrow]

To chose not to answer the question is also a decision.

How true is this!

 

[vanesch]

Given that, I wanted to ask something to make sure I understand it properly. The principle is saying that it is impossible for us to know, fully, the momentum and position of a particle. However, and here is my question, the particle has a specific momentum and position, it is simply unknowable.

There are already many interesting responses, but I just wanted to point out one thing, over which there is no interpretational dispute (or not much, in any case).

If it were true that a particle HAD at each moment a definite momentum and a definite position, but that we simply don't KNOW it, then the particle's momentum and position would behave as a statistical ensemble: that is, we would be able to specify the *probability* for it to have a specific momentum and position, but as we cannot KNOW it, this probability would just not be a 1 or a 0, but a distribution over a certain domain of position and momentum values.

Well, it turns out that this doesn't work out, and the simplest illustration is the double-slit experiment. In the double-slit experiment we "don't know" through which the particle came. If it DID come through either the left or the right slit, but we didn't KNOW it, then we could assign a probability for it to come through the left slit, and a probability for it to come through the right slit. Maybe some obscure god is making it impossible for us to know this, but at least it DOES pass through one or the other slit, right ?

Well, this doesn't work, for the simple reason that if we close one slit, then we only ELIMINATE those particles that came through that slit, and it would be impossible that the probability of arrival at a certain spot RISES when we CUT AWAY a certain number of particles. And nevertheless, that happens! In the "lows" of the interference pattern, with both slits open, there are NO particles, and if we eliminate those that come through one slit, then suddenly there ARE particles.

Or is it ?
Not quite so simple. It might be that closing the distant slit might influence the dynamics of the particles coming through the other slit. People worked that out, and they found such a way of seeing things: Bohmian mechanics. But the price to pay is instantaneous non-local action. Incompatibility with the principles of relativity.

In the 2-slit experiment, the slits are not far away, but you can have variations of the two-slit experiment where one "slit" is miles away from the other. It would mean that a modification of one slit immediately modifies the dynamics of the particle that is a few miles further, at the other slit.

But one thing is sure: unless you introduce these kinds of things, you cannot give a "statistical distribution" to your particles, consider that they HAVE momentum and position, but that you are simply ignoring it.

 

[reilly]

vanesch We've tangled on this issue before, but let us continue. Given Babinet's
Principle, the two slit problem can be replaced by a two strip problem -- like the hole in a donut -- with the same dimensions and location of the slits. I do this because it's much easier to see that the problem is equivalent to scattering from two potentials, the theory of which is highly developed. These strips provide infinite barriers, and absorb or reflect incoming photons, or electrons, or whatever. (Absorption means inelastic scattering.) Now, let's put very tiny detectors on the back of the strips. So, we can determine the blocked "current", the negative of the current passed by the slits. All we'll do is confirm the symmetry argument that says the both targets, over time, block equal numbers of electrons. or photons. And, of course, this is exactly what the Schrodinger Eq. + Born tells us...

This is a totally different experiment than the two-slit non-detecting system -- provided we look for the interference pattern at a reasonable distance from the slit. You really can't compare two open slits and one open slit -- just as you can't easily compare any form of multiple scattering to one-potential scattering.

The probability about which you are concerned is quite well defined; a classical or quantum approach says, for a symmetrical beam, the chances of going through one or the other slit are equal. Measurements will confirm this. When we say "go through" we are using an ordinary-language description -- like, intuition tells us..I don't see any problems with using probability for the two slits

Regards,
Reilly

There are already many interesting responses, but I just wanted to point out one thing, over which there is no interpretational dispute (or not much, in any case).

If it were true that a particle HAD at each moment a definite momentum and a definite position, but that we simply don't KNOW it, then the particle's momentum and position would behave as a statistical ensemble: that is, we would be able to specify the *probability* for it to have a specific momentum and position, but as we cannot KNOW it, this probability would just not be a 1 or a 0, but a distribution over a certain domain of position and momentum values.

Well, it turns out that this doesn't work out, and the simplest illustration is the double-slit experiment. In the double-slit experiment we "don't know" through which the particle came. If it DID come through either the left or the right slit, but we didn't KNOW it, then we could assign a probability for it to come through the left slit, and a probability for it to come through the right slit. Maybe some obscure god is making it impossible for us to know this, but at least it DOES pass through one or the other slit, right ?

Well, this doesn't work, for the simple reason that if we close one slit, then we only ELIMINATE those particles that came through that slit, and it would be impossible that the probability of arrival at a certain spot RISES when we CUT AWAY a certain number of particles. And nevertheless, that happens! In the "lows" of the interference pattern, with both slits open, there are NO particles, and if we eliminate those that come through one slit, then suddenly there ARE particles.

Or is it ?
Not quite so simple. It might be that closing the distant slit might influence the dynamics of the particles coming through the other slit. People worked that out, and they found such a way of seeing things: Bohmian mechanics. But the price to pay is instantaneous non-local action. Incompatibility with the principles of relativity.

In the 2-slit experiment, the slits are not far away, but you can have variations of the two-slit experiment where one "slit" is miles away from the other. It would mean that a modification of one slit immediately modifies the dynamics of the particle that is a few miles further, at the other slit.

But one thing is sure: unless you introduce these kinds of things, you cannot give a "statistical distribution" to your particles, consider that they HAVE momentum and position, but that you are simply ignoring it.

 

[ZapperZ]

vanesh: you might want to read this paper:

T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008).

especially in the last section of it where they did something interesting with their Mach-zehnder interferometer:

The demonstration, whose result is astonishing for students, is realized in the following way. First the fringe pattern is locked to a photodiode as explained in Sec. IV B, and the photomultiplier is moved to a fringe minimum, as characterized by a low photon count rate which can also be displayed acoustically. If now path A of beam 1 is blocked inside the interferometer, it is possible to hear (and see) a distinct increase of the click rate. This result demonstrates that if we give each photon the choice of taking either path A or path B, it has a low probability to appear at the detector. In contrast, if we force the photon to follow a specific path by blocking the other path, then the probability to arrive at the detector is much higher. The puzzling fact that a two-path alternative for each photon prevents it from reaching the detector, while blocking one of the paths leads to a revival of the clicks, is most intriguing for beginning students. This experiment is well suited for illustrating this remarkable quantum mechanical effect, which can be explained only if we assume that each photon simultaneously takes both paths A and B; that is, each photon, in the phrasing of Dirac, "interferes with itself."

Zz.

 

[nanobug]

vanesh: you might want to read this paper:

T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008).

especially in the last section of it where they did something interesting with their Mach-zehnder interferometer:

Actually, I would first recommend this paper to reilly.

 

[ZapperZ]

Actually, I would first recommend this paper to reilly.

Maybe, but I thought it fits in roughly with what vanesh had described. So this would be the "experimental verification".

Zz.

 

[reilly]

Originally Posted by reilly View Post

The "thing", as you put it, cannot, under any circumstances, be in two places at the same time.That's why we use probability -- maybe it's here, maybe it's there. But we don't know until we measure. And by the nature of the measurement, we'll always find one electron in one place at one time; never in two or more places.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
nanobug
Well, for this type of thinking you wouldn't need quantum theory, classical probabilities would be fine. What happens, however, is that things such as interference and superposition, which don't have a classical interpretation, manifest themselves both theoretical and practically. They are a property of quantum mechanics and states in which 'cats' are both alive and dead at the same time are very much a possibility. What you described above are 'mixed states'. But 'pure states' also exist.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>.

As I'm sure you know, standard probability theory says the only difference between classical and quantum probability structures is in the determination thereof. And, by the way, in classical probability systems involving waves you can find interference phenomena. Think about dealing with weak reflected radar signals -- noise can result in much interference;and you measure the incoming energy, power if you will, , hence amplitudes squared, hence interference; hence interference playing a role in probabilities, including those related to decoding, dependent on the received signal, the state of the system, and ...

Note that cats are quite familiar to all of us. And, like all living creatures, cats are either dead or alive, at least that's the conclusion of thousands of years of human experience. Let's assume you are right about being alive and dead at the same time. So, first, how would I determine such a state? Then what are the circumstances in which we might see such a cat, and why haven't any of us never experienced such a curiosity?



Originally Posted by reilly View Post

And, how in the world can a dead cat observe? Please tell us how.

nanobug
The dead cat 'observes' the same way that a lump of coal does, by being a macroscopic system.
>>>>>>>>>>>>>>>>>>>
And exactly how does a macroscopic system observe? What is it that a lump of coal observes -- are you suggesting that a lump of coal has a brain, albeit a very primitive one?
Regards,
Reilly Atkinson

 

[nanobug]

standard probability theory says the only difference between classical and quantum probability structures is in the determination thereof.

Could you please explain the result of the double-slit experiment using classical probabilities and particles with precise but unknown positions and momenta?

 

[reilly]

Could you please explain the result of the double-slit experiment using classical probabilities and particles with precise but unknown positions and momenta?

Can't be done. I said a bit ago that to get the right probabilities for a quantum experiment, you need to follow the prescriptions of QM to find the probabilities. After that, the prescriptions for applying the probabilities in any probabilistic situation are identical -- true for market research, signal detection, horse race and short term stock market betting schemes, line broadening, transmission of light through an absorbing non-equilibrium gas, economic forecasting, ..

How you ever thought that I considered "classical-like" objects for QM in my post above is totally beyond me -- I said no such thing, nor do I subscribe to any such view.

I've answered your question. So how about at least one answer -- cat state or lump of coal, take your pick.

Regards,
Reilly

 

[nanobug]

And exactly how does a macroscopic system observe? What is it that a lump of coal observes -- are you suggesting that a lump of coal has a brain, albeit a very primitive one?

'Observation', within the context of QM is simply a synonym of decoherence. As decoherence relies on the entangling of quantum systems with a macroscopic environment, a cat is as good as a lump of coal. No brains are necessary, just lots and lots of entanglements with the corresponding tracing-out of the density matrix.

By the way, the situation is somewhat similar to the use of 'observer' in special relativity, in which one is really talking about a specific setup of rods and clocks and not about awareness.

 

[vanesch]

Can't be done. I said a bit ago that to get the right probabilities for a quantum experiment, you need to follow the prescriptions of QM to find the probabilities. After that, the prescriptions for applying the probabilities in any probabilistic situation are identical

This is true! But only when using it for observations. The probabilities you obtain for a set of outcomes (in a definite observation basis) are 'normal' probabilities, which can be dealt with in the usual way, as you describe.

The error is to assume that we can use this rule also for non-observed quantum states. Indeed, how do you link the 50% chance of going to the left slit and 50% chance of going to the right slit to the interference pattern ?

As I said, it CAN be done, in Bohmian mechanics, where you can have a modification of the dynamics instantaneously, at a distance. This is maybe what you mean with "a setup with 1 slit is not the same as with 2 slits" (implicitly implying that the dynamics of the 50% of the particles that came through the left slit is now modified by the closing of the right slit - as in Bohmian mechanics).

But if you stick to "local" explanations, it is not clear what the 50% through the left slit means, given that these 50% are going to behave differently, than a particle that goes for sure through the left slit. If 50% was just our *ignorance*, then a particle which went through the left slit (but we weren't sure) should do the same thing as a particle that went through the left slit (but we knew it for sure).

 

[reilly]

vanesh: you might want to read this paper:

T.L. Dimitrova and A. Weis, Am. J. Phys. v.76, p.137 (2008).

especially in the last section of it where they did something interesting with their Mach-zehnder interferometer:



Zz.

How can I get to the paper; AJP won't let me do a download\
Thanks, Reilly

 

[reilly]

'Observation', within the context of QM is simply a synonym of decoherence. As decoherence relies on the entangling of quantum systems with a macroscopic environment, a cat is as good as a lump of coal. No brains are necessary, just lots and lots of entanglements with the corresponding tracing-out of the density matrix.

By the way, the situation is somewhat similar to the use of 'observer' in special relativity, in which one is really talking about a specific setup of rods and clocks and not about awareness.

Really? So, what exactly does a lump of coal observe? How do we know the coal actually observes? Could we decode coal to describe an experiment's results?

Consider a double slit experiment, one that is fully automated so that the experimenter can be thousands of miles away. Let's suppose that the photon pattern is transmitted to the experimenter over a noisy line. Does decoherence get rid of the noise? Would there be any difference between communicating with lasers(quantum), vs. AM radio(Classical)?

Re observers and relativity. Perhaps, you have forgotten, but Einstein was quite anthropormorphic with respect to observers in his more popular writings. In his classic book, Relativity, Einstein always refers to human observers. If there is a specific setup at issue, Einstein's observers will construct it. And, not infrequently, Einstein suggests how the setup is to be done.

I would suggest, with all due respect, that your take on relativistic observers is somewhat at variance with the common practice of the last 100 years.

Regards,
Reilly Atkinson

 

[jsc314159]

The rabbit hole gets deeper.

Besides x and p, t and E also have an associated uncertainty in QM.

$$\Delta t * \Delta E \geq \hbar/2$$.

From what I understand about this, it means that there is a finite limit on how well we can know the energy of a particle that has existed for a finite time $$\Delta t$$ .

In addition, when we use dynamical variables like position and momentum, we are applying classical concepts to the quantum world. One of the postulates of QM is that independent dynamical variables are represented by Hermitian operators. These operators are the observables and they act on wavefunctions when we measure a dynamical variable. The wavefunctions themselves represent the state of a particle and can be thought of as vectors (in the broader sense than lines in a Cartesian coordinate system) in Hilbert space.

Therefore, the way I interpret this is that until we measure position or momentum of a particle, the particle does not have a specific position or momentum. When we take a measurement, the values that we measure are limited to being the eigenvalues of the observable we are measuring. The wavefunction helps us to determine the probability of measuring one of these eigenvalues. Once measure, the state of the particle is known and will now be the eigenvector of the observable that corresponds to the measured eigenvalue (ignoring degeneracies).

jsc

 

[Fra]

Philosophical reflections

I partly share a generalized view of the observer, although perhaps not identical to nanobug. To be an observer is something that makes observations by interactions. I think this connect to the other thread.

How do we know the coal actually observes?

IMHO we don't - at least I don't (that way I have not said too much). But by the same reason I don't know of anyone but me observes anything. How do we KNOW anything at all?

It still seems highly *plausible* that other systems around me are similarly constructed, because the opposite seems less plausible.

So if we ask, if it's plausible that a lump of coal observes? I think it is.

Can I prove it? No. But if my rating systems which suggest it's plausible, serves me well, that alone is indirect support.

Could we decode coal to describe an experiment's results?

Possibly to a certain extent at least - isn't that what we do, when we analyse the state ad composition of matter? But certainly the information encoded in a piece of coal would not come anywhere near the information stored in the human brain if we talk about complex human level things.

But decoding a lump of coal would mean not just chemistry, it would mean decoding the matter in the coal. Which takes us right down to quark level. So maybe a piece of coal can even tell us a few things about nature? But decoding it is a process of learning.

/Fredrik

 

[kenewbie]

I just wanted to jump in with a simple question about the double slit experiment:

Has this ever been done in an environment where care has been taken to remove everything (including things which are not considered to act on a particle) else? By everything I mean doing the experiment in a vacuum at 0 kelvin in a led box blocking out gamma rays, removing magnetic fields, preferably at 0 g, and so on.

If this has been done, did it affect the result at all?

I can't stop looking the unknown variable in this experiment, because I don't understand the math / underlying physics of it (yet).

k

 

[ZapperZ]

I just wanted to jump in with a simple question about the double slit experiment:

Has this ever been done in an environment where care has been taken to remove everything (including things which are not considered to act on a particle) else? By everything I mean doing the experiment in a vacuum at 0 kelvin in a led box blocking out gamma rays, removing magnetic fields, preferably at 0 g, and so on.

Can you show an argument or derivation on why this would matter?

Please also note that the double-slit experiment is testing a more general principle of QM, which is the principle of superposition of orthogonal states. The experiments that tests this principle come in many different types, not just the double slit. I've mentioned the Delft/Stony Brook experiments many times on here which illustrates this principle even MORE dramatically than the double-slit. Those are done on a "robust" system at very low temperature (0 Kelvin is unrealistic especially when no one has achieve it) that was "immune" to such external factors that you described (superconductivity is a "quantum protectorate" state).

So doing what you wanted would not change anything.

Zz.

 

[kenewbie]

I certainly cannot show or make it logically follow that any of the criteria I mentioned has any impact. My only argument would be that historically there has been cases where "obvious" non-relevant factors turned out to have an impact after all, once they were removed.

So, if I where to do a follow-up to the original experiment (which had a result which seemed counter-intuitive at least at that point) I would go the extra mile and remove as much as possible.

I will take a look at the Delft/Stony Brook experiments, thanks a lot for the pointer.

k