Heisenberg and quantum mechanics

[superweirdo]

Heisenberg showed that, even in theory with a hypothetical infinitely precise instrument, no measurement could be made to arbitrary accuracy of both the position and the momentum of a physical object.

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

 

[selfAdjoint]

Heisenberg showed that, even in theory with a hypothetical infinitely precise instrument, no measurement could be made to arbitrary accuracy of both the position and the momentum of a physical object.

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

Actually the way Heisenberg did it is this: In quantum mechanics each of position and momentum come out as probabilities when you perform a measurement. And the quantum math says that these two probability distributions are Fourier Transforms of each other. Well there is an old theorem about Fourier transforms of each other that says the product of their standard deviations is constant. So the sharper one is, the more diffuse the other one is, in a seesaw relationship. Hence the smaller a variance in position your measurement produces, the bigger a variance in momentum it entails, and vice versa.

 

[Locrian]

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

The HUP is hardly the biggest hurdle in predicting everything! In fact, the HUP is unimportant in predicting almost anything.

 

[ZapperZ]

Heisenberg showed that, even in theory with a hypothetical infinitely precise instrument, no measurement could be made to arbitrary accuracy of both the position and the momentum of a physical object.

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

There is a again a misconception here. Let's see if you might be surprised by this:

The HUP says nothing about how precise a measurement you can make in a single measurement. I can make as precise a measurement as I want of a particle's position, and after that, I can make as precise a measurement of its momentum as I want, limited only to my technical limitation. There's nothing in the measurement accuracy in here that is limited by the HUP.

Look again at the HUP and look at the statistical nature of the observable that is being measured to arrive the the \Delta(x) value, for example.

Zz.

 

[MeJennifer]

The HUP says nothing about how precise a measurement you can make in a single measurement. I can make as precise a measurement as I want of a particle's position, and after that, I can make as precise a measurement of its momentum as I want, limited only to my technical limitation. There's nothing in the measurement accuracy in here that is limited by the HUP.

In your example you are making two measurements not one.

 

[ZapperZ]

In your example you are making two measurements not one.

Which is what is contained in the HUP.. the relationship between two pairs of non-commuting operators. If you make a measurement of A, then your knowledge of what B would be IF you were to measure it NEXT would depend on how well you know about A. It doesn't say you make just ONE measurement.

Zz.

 

[selfAdjoint]

In your example you are making two measurements not one.

Kind of missing the point aren't you MeJennifer? The point is that you can know the position accurately as long as you don't ask about momentum, or momentum accurately as long as you don't ask about position, and if you like you can do these two measurements successively on the same particle, and this is all in accord with the uncertainty principle. If you don't like seeing both measurements discussed, just read one.

 

[moving finger]

Heisenberg showed that, even in theory with a hypothetical infinitely precise instrument, no measurement could be made to arbitrary accuracy of both the position and the momentum of a physical object.

The HUP says nothing about how precise a measurement you can make in a single measurement. I can make as precise a measurement as I want of a particle's position, and after that, I can make as precise a measurement of its momentum as I want, limited only to my technical limitation. There's nothing in the measurement accuracy in here that is limited by the HUP.

To be fair to superweirdo, what he should have said is “we cannot simultaneously know to arbitrary precision both the position and the momentum”

Best Regards

 

[-Job-]

Can we get arbitrarily close to the values of position and momentum of a particle at a time T by measuring these quantities separately & successively with an arbitrarily small interval between measurements?

Or maybe by measuring momentum at time T1, and measuring position at time T3 and using this information to estimate the quantities at time T2, then again measuring momentum at time T5 and position at time T7, using these values to estimate position and momentum at time T6, then using T2 and T6 to estimate the quantities at time T4 and so on. Through a process of eliminating error little by little can't we catch up to the actual values for momentum and position at a given T?

 

[moving finger]

Can we get arbitrarily close to the values of position and momentum of a particle at a time T by measuring these quantities separately & successively with an arbitrarily small interval between measurements?

No, because if you measure position to absolute precision (ie with zero uncertainty), that automatically makes momentum completely unknown. If you then subesequently measure the momentum to absolute precision, your earlier position measurement becomes invalid for making any predictions - measure the position a second time (after the momentum measurement) and it will be different to what you thought it was going to be based on your earlier measurment.

There is an analogous (but perhaps easier to visualise) problem with "vertical spin" versus "horizontal spin". If you measure the vertical spin of a spin-1/2 quantum object (eg an electron) then you will find that it is either spin-up or spin-down. But having done this, the horizontal spin is now completely unknown. If you subsequently measure the horizontal spin then you will find that it is either spin-left or spin-right, but having done this the vertical spin is now completely unknown! You cannot "know" both the horizontal and vertical spin directions of a spin-1/2 object at the same time, because the question has no meaning. In the same way, you cannot know the position and momentum (with arbitrary position) at the same time, because the question has no meaning.

Best Regards

 

[Rach3]

Can we get arbitrarily close to the values of position and momentum of a particle at a time T by measuring these quantities separately & successively with an arbitrarily small interval between measurements?

Or maybe by measuring momentum at time T1, and measuring position at time T3 and using this information to estimate the quantities at time T2, then again measuring momentum at time T5 and position at time T7, using these values to estimate position and momentum at time T6, then using T2 and T6 to estimate the quantities at time T4 and so on. Through a process of eliminating error little by little can't we catch up to the actual values for momentum and position at a given T?

Problem is, there really does not exist such a thing at given time T! Think of a wave packet; a very narrow wave packet involves plane waves of a wide spread of momentum (and v.v.), in its Fourier representation. Is there a wave packet well-localized in both space and momentum? It's quite absurd. In QM this is essential to measurements; if you make a precise position measurement, the wavefunction is very narrow in position space in consistency with that measurment, so the momentumspace wavefunction is very wide and has little information. You could measure momentum here, but that would collapse the wavefunction into something very wide in position space, thus erasing information about your earlier position measurement.

 

[Rach3]

There is an analogous (but perhaps easier to visualise) problem with "vertical spin" versus "horizontal spin". If you measure the vertical spin of a spin-1/2 quantum object (eg an electron) then you will find that it is either spin-up or spin-down. But having done this, the horizontal spin is now completely unknown. If you subsequently measure the horizontal spin then you will find that it is either spin-left or spin-right, but having done this the vertical spin is now completely unknown! You cannot "know" both the horizontal and vertical spin directions of a spin-1/2 object at the same time, because the question has no meaning. In the same way, you cannot know the position and momentum (with arbitrary position) at the same time, because the question has no meaning.

The essential feature here is that the "spin up" and "spin left" states are not orthogonal as you'd expect, but at a 45deg angle. The basis state for a spin-1/2 object is quite non-intuitive; it's a two-dimensional space, spanned by {spin-up, spin-down} basis states, or equally well by {spin-left, spin-right} basis states, at 45deg and 135deg angles to the previous two.

Thus, "spin up" is equally well described as a superposition of "spin left" and "spin right".

 

[-Job-]

In other words, is it as if any process measuring the momentum at a given time can change the position and vice-versa?
In macroscopic objects this problem doesn't seem to exist. At what point in the scale of matter does accurate knowledge of both position and momentum become impossible to gain? Can we at least use the values obtained at the smallest "allowed" scale to bound the values at the "prohibited" scale?

Is it also impossible to purposedly give a particle exact values for position and momentum at the same time?

 

[Rach3]

At what point in the scale of matter does accurate knowledge of both position and momentum become impossible to gain?

At the scale where \Delta x \Delta p are on the order of Planck's constant. As far as we're dealing with coherent systems, there's no abrupt boundrary, but a gradual transition - large systems involve large X's and P's, and so the HUP becomes much less important, till it becomes negligble at macroscopic scales. The intermediate region is known as the "mesoscopic" region, ('meso' for 'middle'), and quantum effects at this scale are an active area of research. (by which I mean - there's much we don't know!)

 

[moving finger]

The essential feature here is that the "spin up" and "spin left" states are not orthogonal as you'd expect, but at a 45deg angle. The basis state for a spin-1/2 object is quite non-intuitive; it's a two-dimensional space, spanned by {spin-up, spin-down} basis states, or equally well by {spin-left, spin-right} basis states, at 45deg and 135deg angles to the previous two.

when one makes the measurement of horizontal spin (for a spin-1/2 object) the physical configuration of the system is orthogonal to the configuration one uses for vertical spin - see http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html

Thus, "spin up" is equally well described as a superposition of "spin left" and "spin right".

This is another way of saying that if we measure vertical spin, horizontal spin is unknown.

Best Regards

 

[Rach3]

when one makes the measurement of horizontal spin the physical configuration of the system is orthogonal to the configuration one uses for vertical spin - see http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html

The physical system yes, but the physical quantum states, in the Hilbert space, are not orthogonal. That's exactly the common source of confusion; orthogonal states are emphatically not the ones corresponding to measurements orthogonal in physical position.

Apologies for any confusion.

 

[moving finger]

In other words, is it as if any process measuring the momentum at a given time can change the position and vice-versa?
In macroscopic objects this problem doesn't seem to exist.

It doesn't "seem" to exist because the uncertainty is normally so very small in the macroscopic world - so we can usually ignore it.

The process of measuring momentum doesn't exactly change the position - but there is no easy way of understanding what is going on.

Explaining exactly what is going on in the apparently simple Stern-Gerlach case of spin-measurement is not easy - it does not matter which "direction" you measure the spin of a spin-1/2 particle to be, you will always find the spin is quantised in one of two ways - +1/2 or -1/2 relative to the orientation of the measurement system.

Best Regards

 

[moving finger]

The physical system yes, but the physical quantum states, in the Hilbert space, are not orthogonal. That's exactly the common source of confusion; orthogonal states are emphatically not the ones corresponding to measurements orthogonal in physical position.

Apologies for any confusion.

OK, agreed. To avoid confusion one obviously needs to be careful to specify whether one is talking about Hilbert space or physical space when referring to orthogonality in measurements.

Best Regards

 

[lalbatros]

Posted by Locrian
The HUP is hardly the biggest hurdle in predicting everything!
In fact, the HUP is unimportant in predicting almost anything.

That's right the uncertainty principle doesn't allow you much predictions.
It is merely the root of quantum mechanics.
Further, it explains the most fundamental predictions.

Like the size of the atoms.
Quantum tunneling, nuclear decay.
Vacuum quantum noise.
Electron diffraction.
Line width.
Resolution of electron microscope.
Quantum cryptography.

... any more ?

Let's start a big list ...


Michel

 

[ZapperZ]

To be fair to superweirdo, what he should have said is “we cannot simultaneously know to arbitrary precision both the position and the momentum”

Best Regards

Yes we can!

The precision of a SINGLE MEASUREMENT of position and momentum is limited only via our technology. Furthermore, the more precise I measure momentum is INDEPENDENT of how precise I can measure momentum. This does not follow the HUP! For example, in my avatar, would you be surprise to know that the horizontal axis is in fact, a measure of the momentum of a bunch of photoelectrons, and that how precise I can measure it depends only on the pixel size of my CCD? Yet, I haven't told you anything about what happened before, i.e. did I pass it through a slit?

People forget that the HUP is a STATISTICS of measurement, not just ONE single measurement. The average of a measurement makes no sense when you have just one measurement to play with. No, what the HUP says here is that if you have a pair of non-commuting observables A and B, then if you make a measurement of A, then your knowledge of the outcome of a measurement on B depends on how well you knew A. This is contradictory to classical physics, where the more you know A, then you will have a better prediction of B for identically-prepared system.

Zz.

 

[moving finger]

Yes we can!

The precision of a SINGLE MEASUREMENT of position and momentum is limited only via our technology.

Do you literally mean measuring position AND momentum simultaneously? If so, this would seem to be in conflict with the HUP. Can you provide any published information to support this claim?

Furthermore, the more precise I measure momentum is INDEPENDENT of how precise I can measure momentum. This does not follow the HUP!

Is this a typo? Did you mean to say that momentum measurement precision is independent of momentum measurement precision? If yes, what on Earth does it mean?

For example, in my avatar, would you be surprise to know that the horizontal axis is in fact, a measure of the momentum of a bunch of photoelectrons, and that how precise I can measure it depends only on the pixel size of my CCD? Yet, I haven't told you anything about what happened before, i.e. did I pass it through a slit?

OK - but how does measuring momentum alone have any bearing on the question of measuring momentum and position simultaneously?

what the HUP says here is that if you have a pair of non-commuting observables A and B, then if you make a measurement of A, then your knowledge of the outcome of a measurement on B depends on how well you knew A.

That's just what I said. Position and momentum are non-commuting variables. This means that we cannot know both simultaneously to arbitrary precision - the precision to which we can know both simultaneously is limited by the HUP.

Best Regards

 

[ZapperZ]

Do you literally mean measuring position AND momentum simultaneously? If so, this would seem to be in conflict with the HUP. Can you provide any published information to support this claim?


Is this a typo? Did you mean to say that momentum measurement precision is independent of momentum measurement precision? If yes, what on Earth does it mean?


OK - but how does measuring momentum alone have any bearing on the question of measuring momentum and position simultaneously?


That's just what I said. Position and momentum are non-commuting variables. This means that we cannot know both simultaneously to arbitrary precision - the precision to which we can know both simultaneously is limited by the HUP.

Best Regards

Again, let's go back to the single slit example that I've used numerous times.

As I make the slit narrower and narrower (let's say the width is along x), then the uncertainty in position of the photon or electron that pased through the slit \Delta(x) is getting smaller.

After it passed through the slit, I want to know its x-component momentum. What do I do? I let it hit a detector behind the slit. How do I measure p_x? I measure how far it has deviated from the center line, because this tells me how much momentum in the x-direction it has picked up after it passed through the slit. Now, how well can I measure this momentum? It depends on how FINE of a detector I have! If I have a very fine CCD, I can measure where the particle hit the detector to very high accuracy! This accuracy has nothing to do with how fine I measure \Delta (x)! This is why I said that my ability to finely measure this momentum is INDEPENDENT of how well I determine the position. In a single measurement, the HUP has no role!

However, and this is where the HUP kicks in, if I were to perform the IDENTICAL experiment again, even if \Delta (x) is the same as before, the value that I would obtain for p_x may NOT be the same. In fact, the smaller \Delta (x) is, the MORE VARIED p_x can get as I do this experiment many times. I will see the spread in momentum that I measure getting larger and larger as I know more precisely where it passed by making the slit smaller.

What does this mean? The smaller the slit and the better I know where the particle was when it passed through the slit, the poorer is my knowledge of what momentum value the particle will have after it passed through the slit. This is a reflection of the STATISTICAL spread of the momentum values, NOT from the accuracy from a single measurement!

This is the one aspect of the HUP that many people do not get.

Zz.

 

[selfAdjoint]

This is the one aspect of the HUP that many people do not get.

What I hear you saying is that the Born rule associating a probability with the squared amplitude has only a frequentist interpretation at the phenomenal level. You can't really see the probabilistic aspect of one particle; you have to use the collective statistics of many particles.

Is that a correct interpretation of what you wrote?

 

[ZapperZ]

What I hear you saying is that the Born rule associating a probability with the squared amplitude has only a frequentist interpretation at the phenomenal level. You can't really see the probabilistic aspect of one particle; you have to use the collective statistics of many particles.

Is that a correct interpretation of what you wrote?

Probably. :)

The "statistics" here isn't any different than classical statistics. You make a measurement of something repeatedly, and only after a "sufficient" number of sampling are you able to deduce what the "actual" value is supposed to be. Typically, you get a Lorentzian or Gaussian distribution centered at the "actual" value. But how is one to know that when one only made ONE measurement. The sampling domain is not sufficient to convey any degree of confidence.

What makes a QM system different than a classical system in this case is that the "widths" of such distributions (more commonly known as the standard deviation in statistics) between a pair of non-commuting observables are related to each other via the HUP. This is where the HUP kicks in, in the spread of values of each of the observable, but NOT in the value of each individual measurement itself. The latter is determined by the ability of the instrumentation.

Zz.

 

[moving finger]

Again, let's go back to the single slit example that I've used numerous times.

As I make the slit narrower and narrower (let's say the width is along x), then the uncertainty in position of the photon or electron that pased through the slit \Delta(x) is getting smaller.

After it passed through the slit, I want to know its x-component momentum. What do I do? I let it hit a detector behind the slit. How do I measure p_x? I measure how far it has deviated from the center line, because this tells me how much momentum in the x-direction it has picked up after it passed through the slit. Now, how well can I measure this momentum? It depends on how FINE of a detector I have! If I have a very fine CCD, I can measure where the particle hit the detector to very high accuracy! This accuracy has nothing to do with how fine I measure \Delta (x)! This is why I said that my ability to finely measure this momentum is INDEPENDENT of how well I determine the position. In a single measurement, the HUP has no role!

Zz.

You're not measuring position and momentum simultaneously in your experiment, you are measuring them sequentially, via two separate measurements (the "slit" measures position, and a certain time later your CCD detector measures another position, from which you infer a momentum). But you can only correctly infer momentum from this second measurement if you assume that the electron has behaved like a classical macroscopic object between the two measurements. The measurements are separated in time, thus not simultaneous. Check any good text on QM, they all say the same thing - one cannot measure position and momentum simultaneously to arbitrary precision.

Best Regards

 

[selfAdjoint]

Probably. :)

The "statistics" here isn't any different than classical statistics. You make a measurement of something repeatedly, and only after a "sufficient" number of sampling are you able to deduce what the "actual" value is supposed to be. Typically, you get a Lorentzian or Gaussian distribution centered at the "actual" value. But how is one to know that when one only made ONE measurement. The sampling domain is not sufficient to convey any degree of confidence.

What makes a QM system different than a classical system in this case is that the "widths" of such distributions (more commonly known as the standard deviation in statistics) between a pair of non-commuting observables are related to each other via the HUP. This is where the HUP kicks in, in the spread of values of each of the observable, but NOT in the value of each individual measurement itself. The latter is determined by the ability of the instrumentation.

Zz.

This then would strongly affect the interpretaion of the delayed choice quantum eraser, which we've been discussing on another thread. The experimental choice of whether to observe path is delayed relative to a notional single photon (as figured by calculated flight time), but "delay" doesn't seem to be a well-defined concept relative to a large population.

 

[MeJennifer]

I can make as precise a measurement as I want of a particle's position, and after that, I can make as precise a measurement of its momentum as I want, limited only to my technical limitation. There's nothing in the measurement accuracy in here that is limited by the HUP.

But if you measure the position of a particle, don't you disturb the momentum of particle? So that when you shortly after this measure the momentum, you would have to take into account the amount of disturbance the initial measurement gave. And since we don't know that we can only use statistics?

 

[DrChinese]

But if you measure the position of a particle, don't you disturb the momentum of particle? So that when you shortly after this measure the momentum, you would have to take into account the amount of disturbance the initial measurement gave. And since we don't know that we can only use statistics?

No, that isn't actually case. As ZapperZ points out, the HUP (Heisenberg Uncertainty Principle) really has nothing to do with experimental uncertainty (as the source of the uncertainty) and also has nothing really to do with an experiment causing a disturbance to the particle being observed. It is a statement about the statistics of observables, true, but it is also a statement that goes deeper (a la the formalism). Here's why:

In the 1935 EPR paper, they addressed the issue brought on by the OP, who doubts that the HUP is anything more than an experimental issue. The idea was to separately measure 2 particles that had interacted in the past, so that you could measure each to arbitrary precision and "beat" the HUP. But Bell's Theorem shows that you cannot do this AND get results consistent with the predictions of QM if you assume there are no causes propagating faster than c. Experiments (Aspect and many others) support QM in this. The results are always consistent with the HUP.

 

[Dr.Brain]

Heisenberg showed that, even in theory with a hypothetical infinitely precise instrument, no measurement could be made to arbitrary accuracy of both the position and the momentum of a physical object.

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

As truly put , infact , Heisenberg never quoted anything about the role of instruments in analyzing the variables connected to the motion of quantum world particles.
Infact the uncertainity in depicting the position/momentum of a particle doesnot arise due to lack of high-precision instruments but due to inner-fluctuations of the particle.The Heisenberg Principle has principally arised due to the wave-particle duality as proposed by DeBroglie , in quantum world , a particle moving from one point to another proposed point maynot always travel in a line , or a firm trajectory , due to which a probability arises which we study in form of standard deviations and wavefuctions.

 

[MeJennifer]

No, that isn't actually case. As ZapperZ points out, the HUP (Heisenberg Uncertainty Principle) really has nothing to do with experimental uncertainty (as the source of the uncertainty) and also has nothing really to do with an experiment causing a disturbance to the particle being observed. It is a statement about the statistics of observables, true, but it is also a statement that goes deeper (a la the formalism). Here's why:

In the 1935 EPR paper, they addressed the issue brought on by the OP, who doubts that the HUP is anything more than an experimental issue. The idea was to separately measure 2 particles that had interacted in the past, so that you could measure each to arbitrary precision and "beat" the HUP. But Bell's Theorem shows that you cannot do this AND get results consistent with the predictions of QM if you assume there are no causes propagating faster than c. Experiments (Aspect and many others) support QM in this. The results are always consistent with the HUP.

I really don't see how this EPR experiments disproves experimental uncertainty. How do we know for sure that even after the two particles are separated there is not some connection between them?

 

[ZapperZ]

You're not measuring position and momentum simultaneously in your experiment, you are measuring them sequentially, via two separate measurements (the "slit" measures position, and a certain time later your CCD detector measures another position, from which you infer a momentum). But you can only correctly infer momentum from this second measurement if you assume that the electron has behaved like a classical macroscopic object between the two measurements. The measurements are separated in time, thus not simultaneous. Check any good text on QM, they all say the same thing - one cannot measure position and momentum simultaneously to arbitrary precision.

Best Regards

I don't understand this "measuring position and momentum simultaneously" stuff. You will note that the very fact that non-commuting operators, by definition, do not commute, means there is an ORDER in the measurement of the observables. You get one result when you measure A first, and then B, versus measuring B first, and then A. Where is this "simultaneous" measurement? Since when does the HUP requires such a thing? As long as the system remains isolated and does not lose coherence, the HUP kicks in. In the example I mentioned, there is no "simultaneous" measurement, yet you STILL have a demonstration of the HUP.

Can you point to me a "simultaneous" measurement that demonstrates the HUP? If you say one cannot make such a measurement, then you are implying that the HUP doesn't exist.

and take note that the original argument I was trying to correct was the fallacy surrounding the accuracy of a SINGLE measurement of position and a SINGLE measurement of momentum of a SINGLE particle. The accuracy of a single measurement of observable A and B are NOT goverened by the HUP. Have we settled this yet before migrating to this "simultaneous" issue?Zz.

 

[ZapperZ]

But if you measure the position of a particle, don't you disturb the momentum of particle? So that when you shortly after this measure the momentum, you would have to take into account the amount of disturbance the initial measurement gave. And since we don't know that we can only use statistics?

There's two kinds of "disturbance". One is spurious intrusion, the other is inherent. Spurious intrusion is when an electron, let's say, passes though a slit and it sees its own image and causes a self-interaction. This is NOT taken into account in the ideal situation and is not what we are talking about. What we are dealing here is the inherent effect that is built in into our physics (and our universe).

So what kind of a disturbance would there be when photons passed through a single slit? Note that in such a case, all you are doing is to cause only photons that happen to pass within the opening to get through. So even when you ignore all the other spurious intrusions, by simply confining the x-position of the photons to such a narrow size already can cause a change in the expected momentum of the outgoing photons.

So OF COURSE, there is an effect due to the slit. The very fact that there is now a transverse component of the particle where there wasn't any before is obvious. But this is right out of the HUP and the QM formulation.

Zz.

 

[MeJennifer]

So what kind of a disturbance would there be when photons passed through a single slit? Note that in such a case, all you are doing is to cause only photons that happen to pass within the opening to get through.

Well as long as the particle does not bounce against the wall it seems that there would be no disturbance. But of course a particle is more than just an object at a specific location, it also can carry and interact with forces from other particles.
I suppose that it can interact with forces from other particles (e.g. the endges of the slit) even when its position is not at the edge.

 

[ZapperZ]

I suppose that it can interact with forces from other particles (e.g. the endges of the slit) even when its position is not at the edge.

But is this particle-particle interaction built in in the HUP and QM formulation?

We know what particle-particle interaction entails - I do this as a condensed matter physicist. But turn it off and you STILL get the HUP. We can see this already since there's nothing to prevent us at sending each of these particles through the slit one at a time. There's no particle-particle interactions here.

Zz.

 

[jtbell]

I suppose that it can interact with forces from other particles (e.g. the endges of the slit) even when its position is not at the edge.

Has anyone produced a model of the "non-Heisenberg" interactions between a particle and the edge of a slit that it passes through, that accurately describes diffraction phenomena that have been observed? I've never seen or heard of such a model. If such a model existed, and were widely accepted, it would surely be mentioned in many textbooks when particle diffraction is introduced.

 

[DrChinese]

I really don't see how this EPR experiments disproves experimental uncertainty. How do we know for sure that even after the two particles are separated there is not some connection between them?

Well, there is, sort of - they are part in superposition of the same wave function. But are they mediated by a physical non-local force? That is certainly a possibility that cannot be absolutely ruled out. If you accept Bohmian Mechanics, then that is indeed the case... and now the HUP can be explained in different terms. I would say that many scientists do postulate that there is some sort of non-local physical mechanism (for lack of a better term) involved. But I would not say it is generally accepted as such.

 

[Locrian]

That's right the uncertainty principle doesn't allow you much predictions.
It is merely the root of quantum mechanics.
Further, it explains the most fundamental predictions.

Like the [blah blah blah]

... any more ?

Let's start a big list ...


Michel

Congratulations on misrepresenting what I wrote, confusing what the "root" of quantum mechanics is, and - best of all - missing the forest for the trees.

I'll say again: The uncertainty principle is not the primary barrier in "predicting everything," as the opening post suggests. On the contrary, we're more than capable of predicting many things even beyond the necessary precision and accuracy necessary, and yet are completely stumped at predicting other things (weather, turbulent fluid flow, economic shifts) within an order of magnitude of the precision we would prefer.

 

[MeJennifer]

But are they mediated by a physical non-local force?

Well to me it seems that all forces work non-local.
Locality seems only relevant when there is some sort of scattering, which I see as a space-time event where two (or more) particles happens to interact. The other forces kind of "hover" above space-time directing the probability of the location of the particle.

 

[ZapperZ]

Well to me it seems that all forces work non-local.

OK, could you point out to me an example of a "non-local" EM force at work?

Zz.

 

[MeJennifer]

OK, could you point out to me an example of a "non-local" EM force at work?

I would say pretty much every force that require some sort of wave function.

Could you point out to me an example of a force that is local?

 

[Locrian]

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

So what situation does the HUP actually prevent us from predicting something? The most obvious (and probably only) situation is one that fits the following criteria:

1) The prediction involves a system exhibiting quantum mechanical phenomena. More precisely, the system must require quantum mechanics to make predictions. I've had individuals in this forum try to argue that large objects (such as tennis balls) must be described as a wavefunction, but anyone with sense or a grasp of physics knows that most massive objects shouldn't be - at least if you plan to actually predict what will happen in the system.

2) The prediction involves taking two consecutive measurements whose operators don't commute. The HUP only affects something multiple consecutive measurments that are in some special way related. The addage about position and momentum isn't even entirely accurate: for instance, you can know the position in one direction and the momentum in an orthogonal one without violating the HUP at all.

3) The prediciton must require precision for multiple noncommuting measurables that is less than the HUP would allow. This alone removes just about any measurement ever made to predict some result. We don't need precision that low for most military, economic, physical or social issues that we would like to predict. The universe is one of many scales, and almost none require us to measure things to that small a degree.

It should be plainly obvious that the HUP doesn't prevent us from predicting what will happen in any but a select set of arenas.

 

[ZapperZ]

I would say pretty much every force that require some sort of wave function.

Could you point out to me an example of a force that is local?

You'll notice that I made no assertion one way or the other. You did. And your answer is very vague. Show me exactly one concrete example which clearly illustrates what you mean by a force that is "non-local".

Zz.

 

[MeJennifer]

You'll notice that I made no assertion one way or the other. You did. And your answer is very vague. Show me exactly one concrete example which clearly illustrates what you mean by a force that is "non-local".

Zz.

Well EM waves in the EPR experiment for instance.

 

[jbusc]

So what situation does the HUP actually prevent us from predicting something? The most obvious (and probably only) situation is one that fits the following criteria:
*snip*
It should be plainly obvious that the HUP doesn't prevent us from predicting what will happen in any but a select set of arenas.

In fact, the uncertainty principle allows us insight and predictions into fundamental questions which were proposed at the beginning of the 20th century - like why electrons are not found in atomic nuclei.

I think it was from Beiser's Modern Physics, he stated that the HUP was not a limitation of our knowledge, but a useful tool unto itself.

 

[ZapperZ]

Well EM waves in the EPR experiment for instance.

Er... what EM waves? The EPR experiment in which there is entanglement has no transfer of any kind of interaction when a measurement on one of the pair is made! There's no EM wave, no "strong" wave, no "weak" wave, no gravity wave of any kind going from one to another. Even the QM description shows no kind of EM "wave".

So how did EM wave became non-local here? You do know that the QM wavefunction is not the same as the EM wave, don't you?

Zz.

 

[moving finger]

I don't understand this "measuring position and momentum simultaneously" stuff.

Perhaps you should have said so earlier, when it was first mentioned in post #8, which you responded to but obviously ignored the reference to “simultaneously”.

You will note that the very fact that non-commuting operators, by definition, do not commute, means there is an ORDER in the measurement of the observables. You get one result when you measure A first, and then B, versus measuring B first, and then A. Where is this "simultaneous" measurement?

See the following for a paper on the Simultaneous Measurement of Noncommuting Observables :

http://prola.aps.org/abstract/PR/v152/i4/p1103_1

Since when does the HUP requires such a thing?

It has never been claimed that the HUP “requires” such a thing – but the HUP places limits on the precision with which such simultaneous measurements can be made.

As long as the system remains isolated and does not lose coherence, the HUP kicks in. In the example I mentioned, there is no "simultaneous" measurement, yet you STILL have a demonstration of the HUP.

The HUP applies all the way through, it does not mysteriously “kick in” just when you are about to make another measurement.

Can you point to me a "simultaneous" measurement that demonstrates the HUP? If you say one cannot make such a measurement, then you are implying that the HUP doesn't exist.

I have never said that a simultaneous measurement “demonstrates the HUP”, and I have never said that such measurements are impossible – you seem to misunderstand.

and take note that the original argument I was trying to correct was the fallacy surrounding the accuracy of a SINGLE measurement of position and a SINGLE measurement of momentum of a SINGLE particle. The accuracy of a single measurement of observable A and B are NOT goverened by the HUP. Have we settled this yet before migrating to this "simultaneous" issue?

I understand that you believe the OP was referring to sequential measurements – and I have no problem agreeing that two sequential measurements can provide you with information as precise as you would like – but I do not believe such was the intent of the OP.

Best regards

 

[ZapperZ]

Perhaps you should have said so earlier, when it was first mentioned in post #8, which you responded to but obviously ignored the reference to “simultaneously”.


See the following for a paper on the Simultaneous Measurement of Noncommuting Observables :

http://prola.aps.org/abstract/PR/v152/i4/p1103_1


It has never been claimed that the HUP “requires” such a thing – but the HUP places limits on the precision with which such simultaneous measurements can be made.


The HUP applies all the way through, it does not mysteriously “kick in” just when you are about to make another measurement.


I have never said that a simultaneous measurement “demonstrates the HUP”, and I have never said that such measurements are impossible – you seem to misunderstand.


I understand that you believe the OP was referring to sequential measurements – and I have no problem agreeing that two sequential measurements can provide you with information as precise as you would like – but I do not believe such was the intent of the OP.

Best regards

This is the OP:

Heisenberg showed that, even in theory with a hypothetical infinitely precise instrument, no measurement could be made to arbitrary accuracy of both the position and the momentum of a physical object.

What I want to know is how? How did he show it coz that conters my belief of predictability. I believed that w/ infinite knowledge and tools, we could see the future coz we would have the ability to predict everything.

And this was your response to me in post #8

To be fair to superweirdo, what he should have said is “we cannot simultaneously know to arbitrary precision both the position and the momentum”

Best Regards

I "ignored" the "simultaneous" aspect of it because QM and the HUP never require such a constrained in the first place. So I do not see the point of discussing a "special case" when the GENERAL case is equally valid. I don't have to make a "simultaneous" measurement of the non-commuting observable to detect the HUP. In other word, I don't have to go through all that difficult contortions to detect this. An ordinary one, such as from a single slit, will do just fine. This is why I said I do not understand why such a thing needs to be brought up in first place.

Secondly, recall what I am trying to do here. There is a very common fallacy that one cannot determine (be it simultaneous or not) the position and momentum with arbitrary precision of a particle. This is wrong. The HUP never says such a thing. The single measurement of a position is limited in accuracy only by the instrument. The same can be said of the position. The HUP is not about the value of p and x after a single measurement of each, but rather the spread in p and x and consequently, our ability to predict their values. This applies be it a simultaneous or non-simultaneous measurement.

And oh, aren't you curious that in the paper you cited, their definition of a "simultaneous" measurement is actually the same as my single-slit example? See Fig. 1.

Zz.

 

[MeJennifer]

Er... what EM waves? The EPR experiment in which there is entanglement has no transfer of any kind of interaction when a measurement on one of the pair is made! There's no EM wave, no "strong" wave, no "weak" wave, no gravity wave of any kind going from one to another. Even the QM description shows no kind of EM "wave".

So how did EM wave became non-local here? You do know that the QM wavefunction is not the same as the EM wave, don't you?

Zz.

So photons are not EM waves?

 

[ZapperZ]

So photons are not EM waves?

The EM waves are NOT the "wavefunction" of QM. You don't solve the Schrodinger equation for photons and get EM waves that you get out of Maxwell equations as the solution.

So again, where is the non-local interaction of EM?

Zz.

 

[MeJennifer]

The EM waves are NOT the "wavefunction" of QM. You don't solve the Schrodinger equation for photons and get EM waves that you get out of Maxwell equations as the solution.

So again, where is the non-local interaction of EM?

Zz.

Where did I say that the EM waves and the wave fuction are the same?

You were asking me about forces, electro-magnetism is a force.