Is Uncertainty intrinsic property or a consequence of measurement ?

[physics_jest]

Hello friends,

Most people that I heard put uncertainty as an intrinsic property of the universe which is evident when we make a measurement. But to me it seems that intrinsic property and making a measurement are two entirely different things.

If uncertainty were to be just(purely) intrinsic property, then I suppose the uncertainty would stack with the passing of time. But it doesn't.

At the same time the uncertainty can be an effect of just measurement itself, because of the definition, the uncertainty is only defined for the simultaneous measurement of canonically conjugate variables.

So the question why do we think/believe that uncertainty is intrinsic to the universe, when it seems its just a measurement aspect for conjugate variables.

Thanks

 

[phinds]

The HUP is emphatically NOT an artifact of measurement but an intrinsic property of quantum objects. This is proven conclusively by the single slit experiment, among a number of ways in which it has been verified.

There are numerous threads on this forum about this.

 

[ShayanJ]

If uncertainty were to be just(purely) intrinsic property, then I suppose the uncertainty would stack with the passing of time. But it doesn't.

This is a very naive reasoning.The formulation of QM answers the question.Its just waiting for you to go and learn it!

At the same time the uncertainty can be an effect of just measurement itself, because of the definition, the uncertainty is only defined for the simultaneous measurement of canonically conjugate variables.

So the question why do we think/believe that uncertainty is intrinsic to the universe, when it seems its just a measurement aspect for conjugate variables.

Well,of course if you don't observe a system,you can't see its features!
The point is that obtaining more accuracy than what HUP allows is impossible even in principle.

 

[physics_jest]

This is a very naive reasoning.The formulation of QM answers the question.Its just waiting for you to go and learn it!

I think a good example of stacking of uncertainty can be seen by looking at the random walk problem. The dispersion of the steps(variance) is proportional to the number of steps taken(= N.p.q) since there is intrinsic uncertainty(probability) of taking steps in right or left.

Well,of course if you don't observe a system,you can't see its features!
The point is that obtaining more accuracy than what HUP allows is impossible even in principle.

Is it "even in the principle according to the mathematical formulation of QM",

This is what I know so far about HUP, I think HUP is nothing but the generalization of the statistical nature of Quantum Mechanics via canonical conjugate variables, which is to say there is nothing that stops you from getting a value for momentum and position simultaneously but these values we get are not going to predict where the particle will be without some uncertainty(No matter how fast you make the subsequent measurement or if we make simultaneous measurements on large number of identical systems).

From classical mechanics(on which most of the QM formulation relies), value of canonical conjugate variables at one instant are enough to describe a system(Lagrangian, Hamiltonian mechanics) for any other instant, but the values of these same variables in QM are not enough to predict what is going to happen next. Instead if we repeat the measurement of these variables again and again(even on a stationary energy state) we will get a dispersion of values (let's say $\Delta p_x$ and $\Delta x$) of conjugate variables. And it is the product of the statistical dispersion/variance ($\sqrt{\left\langle p_x^2 \right\rangle - (\left\langle p_x \right\rangle)^2 }$) and ($\sqrt{\left\langle x^2 \right\rangle - (\left\langle x \right\rangle)^2 }$) which cannot be lower than the limit.

Edit: In other words, momentum and position in a particular direction cannot have simultaneous Eigenstates(according to the formulation of QM)

 

[phinds]

I think a good example of stacking of uncertainty can be seen by looking at the random walk problem. The dispersion of the steps(variance) is proportional to the number of steps taken(= N.p.q) since there is intrinsic uncertainty(probability) of taking steps in right or left.

This has NOTHING to do with the HUP.

 

[atyy]

So the question why do we think/believe that uncertainty is intrinsic to the universe, when it seems its just a measurement aspect for conjugate variables

The commutation relations lead to both types of uncertainties.

There is intrinsic uncertainty of the state, as well as measurement uncertainty.

The intrinsic uncertainty of the state says if we have a state, and we perform separate precise measurements of position and separate precise measurements of momentum, the standard deviations of the distributions of the results will obey an uncertainty principle. Here since the measurements are separate, they can be precise. Since the measurements are precise, we say the uncertainty is intrinsic to the state.

Examples of measurement uncertainty (several different definitions exist, so it depends on which definition one uses) are found in:
http://physicsworld.com/cws/article...y-reigns-over-heisenbergs-measurement-analogy
http://arxiv.org/abs/1304.2071
http://arxiv.org/abs/1306.1565

 

[physics_jest]

This has NOTHING to do with the HUP.

It would have if HUP were to be a purely intrinsic property, that was my point in the later part of the quoted post.

 

[phinds]

It would have if HUP were to be a purely intrinsic property, that was my point in the later part of the quoted post.

I don't follow you here at all. The HUP IS an intrinsic property and the random walk is totally unrelated to it.

 

[physics_jest]

The commutation relations lead to both types of uncertainties.

There is intrinsic uncertainty of the state, as well as measurement uncertainty.

The intrinsic uncertainty of the state says if we have a state, and we perform separate precise measurements of position and separate precise measurements of momentum, the standard deviations of the distributions of the results will obey an uncertainty principle. Here since the measurements are separate, they can be precise. Since the measurements are precise, we say the uncertainty is intrinsic to the state.

Nice reply, thanks.

But how does one conclude that measurements were precise, just because one can have a value for the measurements does not conclusively validate the measurement is precise. Because one can always assume that the dispersion of the different measurements is a consequence of measurement itself, just like one would get the dispersion in measurement results in classical sense.

 

[atyy]

But how does one conclude that measurements were precise, just because one can have a value for the measurements does not conclusively validate the measurement is precise. Because one can always assume that the dispersion of the different measurements is a consequence of measurement itself, just like one would get the dispersion in measurement results in classical sense.

The idea behind the definition of a precise measurement is one that if the state is ψ(x), then the distribution of measured positions if ψ(x)ψ*(x) (and similarly for other quantities) if the measurement is precise. I don't know if this is quite right for a quantity like position in an infinite dimensional Hilbert space, but that's the basic idea. You can look at the other papers I linked to on joint uncertain measurements for more precise definitions of what a precise measurement is.

 

[physics_jest]

I don't follow you here at all. The HUP IS an intrinsic property and the random walk is totally unrelated to it.

OK, What I'm trying to convey is, random walk problem has intrinsic uncertainty(probability) in it(the step taken at any particular point is independent of every variable i.e. intrinsic).

And therefore the dispersion(N.p.q) of the steps is proportional to the number of steps taken, whereas in QM momentum dispersion in a particular direction is not proportional to the number of measurements(in other words not proportional to the elapsed time), and for stationary states of the bound systems the dispersion is constant.

Whereas, HUP is the product of the dispersion of canonical conjugate variables, which one can easily formulate from commutation relation and Schwarz inequality.

It seems the uncertainty principle only shows the statistical nature of quantum mechanics, and that there is very thin line between the precise measurement and the intrinsic nature of the measured property.

 

[Nugatory]

But how does one conclude that measurements were precise, just because one can have a value for the measurements does not conclusively validate the measurement is precise. Because one can always assume that the dispersion of the different measurements is a consequence of measurement itself, just like one would get the dispersion in measurement results in classical sense.

You can assume that, but if you do you're not using quantum mechanics, you're using some other theory. The formalism of QM works as atyy describes ("The commutation relations lead to both types of uncertainties") with no wiggle room in this area.

Note that this does not mean that QM is "right" or "true", just that if you use it you are committed to intrinsic uncertainty in some pairs of measurements. Of course, if you don't use QM, you have to use something else, and so far no one has found a remotely plausible alternative that matches experimental results with equal success - and a lot of people have been trying for more than a century now.

 

[Nugatory]

OK, What I'm trying to convey is, random walk problem has intrinsic uncertainty(probability) in it(the step taken at any particular point is independent of every variable i.e. intrinsic).

That's true, but random walks are Markovian and the evolution of the state function according to the Schrodinger equation is not. That's why the uncertainties don't "stack" in the same way.

 

[TrickyDicky]

That's true, but random walks are Markovian and the evolution of the state function according to the Schrodinger equation is not. That's why the uncertainties don't "stack" in the same way.

I don't get this, I thought Markovian evolution was "memoryless" and therefore uncertainties don't stack, as happens with Schrodinger evolution(they don't stack either).

 

[bhobba]

I don't get this, I thought Markovian evolution was "memoryless" and therefore uncertainties don't stack, as happens with Schrodinger evolution(they don't stack either).

Markovian assumptions applied to a particle leads to the basic Wiener process. One has to do something utterly unintuitive and physically not particularly clear without a careful analysis, to derive QM from that, and go over to complex numbers.

Thanks
Bill

 

[bhobba]

OK, What I'm trying to convey is, random walk problem has intrinsic uncertainty(probability) in it(the step taken at any particular point is independent of every variable i.e. intrinsic).

The random walk leads to a Wiener process. It is an interesting fact that QM can be derived from that by going over to complex numbers - this is the path integral formulation of Feynman.

Its physical basis is entirely different though, and sorting out exactly why the introduction of complex numbers accomplishes this feat requires careful analysis. Some say its the central mystery of QM - why complex numbers.

To understand the uncertainly relations you need to delve into the math - its an intrinsic property of QM associated with the non-commutativeity of observables.

Thanks
Bill

 

[bhobba]

But how does one conclude that measurements were precise

Its to do with the probabilistic nature of QM. Measurement outcomes are precise, but done under exactly the same conditions different outcomes will result. Why that is is the very essence of QM.

Here is a modern take since I suspect you know a bit about probability models:
http://arxiv.org/abs/quant-ph/0101012

The modern view is QM is one of the two most reasonable generalized probability models that can be used to model physical systems - the other being bog standard probability theory. However, as in the case of the random walk, things do not quite work out if you use that to model say particle position. The deep reason, as the paper above points out, is there is no continuous transformation between pure states in probability theory - that's why you need to over to complex numbers to get it to work and why you in fact get QM.

Thanks
Bill

 

[forcefield]

Since the measurements are precise, we say the uncertainty is intrinsic to the state.

the step taken at any particular point is independent of every variable i.e. intrinsic

It looks like you have different definitions of "intrinsic". The latter is "independent" whereas in the former the uncertainty follows naturally from QM formulation.

 

[billschnieder]

Measurement outcomes are precise, but done under exactly the same conditions different outcomes will result.

Isn't the latter part of your statement the meaning of "imprecise"? Looks like a contradiction.

 

[dextercioby]

Isn't the latter part of your statement the meaning of "imprecise"? Looks like a contradiction.

That's meant in the sense that the precision is basically getting one and only number/reading shown by an apparatus out of the multitude of possible measurement outcomes.

 

[bhobba]

Isn't the latter part of your statement the meaning of "imprecise"? Looks like a contradiction.

No.

If you conduct an experiment with highly accurate equipment, and under exactly the same conditions you get different answers, then the situation is that its fundamentally probabilistic, not a problem with the precision of your equipment. This is the exact situation in QM.

Take the double slit experiment as an example. When you get a flash it flashes at an exact position, and if you had a detector there it would register a whole photon with a definite position at that point. This measurement is precise. The fact that you can't predict, except probabilistically, where that photon will be detected is not an issue with imprecision in the detector - its that nature is fundamentally probabilistic.

Thanks
Bill

 

[bhobba]

That's meant in the sense that the precision is basically getting one and only number/reading shown by an apparatus out of the multitude of possible measurement outcomes.

True.

And also that it's not an issue with imprecision in the measuring equipment.

As far as anyone can tell in QM you can't find the cause of the differing outcomes done under the same conditions. Its not an imprecision in the measuring device. Its not like flipping a coin where the imprecision is lack of knowledge about how it was flipped, and if you knew that you could predict it. It just seems fundamental.

And there is this marvelous theorem, Gleason's Theorem, that shows, from the nature of observables in QM, if you require things to be basis independent, it must be probabilistic:
http://en.wikipedia.org/wiki/Gleason's_theorem
http://kof.physto.se/theses/helena-master.pdf
'Gleason's theorem highlights a number of fundamental issues in quantum measurement theory. The fact that the logical structure of quantum events dictates the probability measure of the formalism is taken by some to demonstrate an inherent stochasticity in the very fabric of the world. To some researchers, such as Pitowski, the result is convincing enough to conclude that quantum mechanics represents a new theory of probability. Alternatively, such approaches as relational quantum mechanics make use of Gleason's theorem as an essential step in deriving the quantum formalism from information-theoretic postulates.'

Thanks
Bill

 

[billschnieder]

No.
If you conduct an experiment with highly accurate equipment, and under exactly the same conditions you get different answers,

A measurement can be accurate but not precise, and a measurement can be precise but not accurate. If your measurement is precise, you expect repeated measurements to give you the same value. But that value could be the wrong one if the device is not accurate.

then the situation is that its fundamentally probabilistic, not a problem with the precision of your equipment.

But how do you know that the measurement is precise if you get different values every time? This is the question.

Take the double slit experiment as an example. When you get a flash it flashes at an exact position, and if you had a detector there it would register a whole photon with a definite position at that point. This measurement is precise.

Sorry, that's not what it means for a measurement to be precise. Look it up.

 

[bhobba]

If your measurement is precise, you expect repeated measurements to give you the same value.

If you are trying to imply such is true a-priori then your reasoning for that assertion escapes me. But I certainly agree its what one would reasonably expect - its just nature doesn't seem to oblige.

Take the double slit experiment again. It gives a precise measurement of the photons position - but if you repeat the experiment under exactly the same conditions many times you get different positions. The position of the photon is different. This directly contradicts your assertion. I agree that's not what you expect, and that lies right at the foundation of quantum weirdness - nevertheless, as far as we can tell today, its how nature behaves. However if you do the same observation immediately after you get the same result (provided what you are measuring like the photon has not been destroyed by the first measurement). This is quite reasonable by physical continuity - but of course nature doesn't have to be like that - it just is. But if it wasn't QM would be in a real mess because you would reasonably say it has that property as a result of measurement and that property shouldn't really change wildly in a very short amount of time. Fortunately nature conforms to our intuition on that count.

But I may be misunderstanding something so I am all ears.

But how do you know that the measurement is precise if you get different values every time? This is the question.

Because if you do the the same measurement immediately after you get the same result. That's not what you expect if the measuring device was at fault.

When QM makes assertions that nature is inherently probabilistic its not based on one experiment - its based on a myriad of different ones and this is the only reasonable interpretation.

But feel free to come up with another theory if you like where its a problem with the measuring device and have it explain all the experimental evidence we have.

Sorry, that's not what it means for a measurement to be precise. Look it up.

Hmmmm. I am not sure you quite understand what's being said here. But ok - take it to mean when we know it has that property it gives that result.

Thanks
Bill

 

[billschnieder]

If you are trying to imply such is true a-priori then your reasoning for that assertion escapes me.

In physics the word "precision" has a very specific meaning. Your use of the term does not conform to the accepted meaning, that's all I'm saying. Maybe you intended a different meaning, then use a different word because precision does not cut it. This is not my idea, this is pretty standard stuff you can found in any reputable reference.

 

[bhobba]

In physics the word "precision" has a very specific meaning. Your use of the term does not conform to the accepted meaning, that's all I'm saying. Maybe you intended a different meaning, then use a different word because precision does not cut it. This is not my idea, this is pretty standard stuff you can found in any reputable reference.

I am aware of what you are talking about eg:
http://en.wikipedia.org/wiki/Accuracy_and_precision

But I also want to point out, as the article says:
'Although the two words precision and accuracy can be synonymous in colloquial use, they are deliberately contrasted in the context of the scientific method.'

In discussions like this where it's a bit chatty it more along the lines of colloquial use.

However, I want to point out, if exactitude is the aim here, then QM really does pose problems in following that definition exactly.

Thanks
Bill

 

[atyy]

Here is an explanation for the definition of an ideal measurement in quantum theory:
http://arxiv.org/abs/0910.4222
"Among the features of an ideal measurement, one tends to request that the device correctly identifies the state. In quantum physics, this cannot be enforced for all states because of the Born’s rule; but at least, one can request the following: if the input system is in state |φ_j >, the measurement should produce the outcome associated to that state with certainty (for non-destructive measurements, this implies that the measurement outcome is reproducible). Therefore, given Born’s rule, an ideal measurement is defined by an orthonormal basis, i.e. a set of orthogonal vectors."

 

[physics_jest]

Its to do with the probabilistic nature of QM. Measurement outcomes are precise, but done under exactly the same conditions different outcomes will result. Why that is is the very essence of QM.

Here is a modern take since I suspect you know a bit about probability models:
http://arxiv.org/abs/quant-ph/0101012

The modern view is QM is one of the two most reasonable generalized probability models that can be used to model physical systems - the other being bog standard probability theory. However, as in the case of the random walk, things do not quite work out if you use that to model say particle position. The deep reason, as the paper above points out, is there is no continuous transformation between pure states in probability theory - that's why you need to over to complex numbers to get it to work and why you in fact get QM.

Thanks
Bill

OK, but different outcomes can be understood easily if we understand that quantum mechanics is statistical, just like classical statistical mechanics. But no body says that nature is probabilistic/indeterministic classically, it is understood that due to high degrees of freedom we cannot solve for the motion of particles and that is why we work through statistical mechanics because it can be handled.

So what is so different in QM statistics and classical statistics, that former makes nature itself probabilistic and later is used because it is the only simple way to handle large number of degrees of freedom but considers nature to be non-probabilistic.

 

[physics_jest]

No.

If you conduct an experiment with highly accurate equipment, and under exactly the same conditions you get different answers, then the situation is that its fundamentally probabilistic, not a problem with the precision of your equipment. This is the exact situation in QM.

Take the double slit experiment as an example. When you get a flash it flashes at an exact position, and if you had a detector there it would register a whole photon with a definite position at that point. This measurement is precise. The fact that you can't predict, except probabilistically, where that photon will be detected is not an issue with imprecision in the detector - its that nature is fundamentally probabilistic.

Thanks
Bill

What do you mean by highly accurate equipment, since it can only be made of atoms and if we are going to measure the properties of another type of atoms with the equipment we can only expect a limited accuracy. Just like if we were to measure the diameter of a ball by using other similar balls, the accuracy we should expect is in the terms of the diameter of one ball itself and not more than that. Why is this not the case in QM?

 

[bhobba]

What do you mean by highly accurate equipment, since it can only be made of atoms and if we are going to measure the properties of another type of atoms with the equipment we can only expect a limited accuracy. Just like if we were to measure the diameter of a ball by using other similar balls, the accuracy we should expect is in the terms of the diameter of one ball itself and not more than that. Why is this not the case in QM?

How does that not allow accurate and precise equipment to be made? Do you deny when a photon hits a screen in the double slit experiment it gives an actual position it hit the screen? No one is claiming that position is revealed with 100% accuracy. Its made of atoms, but reveals an actual position because of the interaction the photon has with atoms of the screen. The positions of those atoms can not be known with 100% accuracy. So?

You may be getting a bit 'confused' because I used the term 'highly accurate'. Obviously such is only applicable within the context of a given situation. I don't know, for example, if experimenters would say in the double slit experiment a photographic plate when developed gives a highly accurate position of a photon as that is purely context dependent . But a position it most certainly does give as can be checked by placing it behind a screen with a small hole in it. You can make the hole smaller and smaller and in that way check on the accuracy and precision of the photographic plate as a detector of the position of a photon.

In general filtering type preparations/observations allow checking of the accuracy/precision of measuring devices in a QM setting.

Thanks
Bill

 

[bhobba]

I think in this regard its also important to understand exactly the axiomatic basis of QM, as well as a way of looking at them that brings out clearly what they are saying. I will base the following on the two axioms in Ballentine - QM - A Modern development. Its a very interesting fact that it really rests on just two axioms. There is a bit more to it, but they are more or less along the lines of reasonableness assumptions such as the probability of outcomes should not dependent on coordinate systems ie symmetry.

Imagine we have a system and some observational apparatus that has n possible outcomes associated with values yi. Note we are assuming such observational apparatus exists. It is a fact they do. Their accuracy and precision is a matter for experimental guys to investigate - it is simply assumed they exist and have some accuracy and precision.

This immediately suggests a vector and to bring this out I will write it as Ʃ yi |bi>. Now we have a problem - the |bi> are freely chosen - they are simply man made things that follow from a theorem on vector spaces - fundamental physics can not depend on that. To get around it QM replaces the |bi> by |bi><bi| to give the operator Ʃ yi |bi><bi| - which is basis independent. In this way observations are associated with Hermitian operators. This is the first axiom in Ballentine, and heuristically why its reasonable.

Next we have this wonderful theorem Gleason's theorem that I alluded to previously, which, basically, follows from the above axiom:
http://kof.physto.se/theses/helena-master.pdf

This is the second axioms in Ballentine's treatment.

This means a state is simply a mathematical requirement to allow us to calculate expected values in QM. It may or may not be real - there is no way to tell. Its very similar to the role probabilities play in probability theory. In fact in QM you can also calculate probabilities. Most people would say probabilities don't exist in a real sense and why I personally don't think the state is real - but that's just my view - as far as we can tell today its an open question.

Basically QM is a theory about the probabilities of outcomes of observation, if we were to observe it. The fundamental assumption is devices capable of observing quantum systems exist, and they will give an actual outcome. There accuracy and precision is a characteristic of the device and its up experimentation to determine what that is.

Thanks
Bill

 

[bhobba]

So what is so different in QM statistics and classical statistics, that former makes nature itself probabilistic and later is used because it is the only simple way to handle large number of degrees of freedom but considers nature to be non-probabilistic.

Well if you read the paper I linked to on QM from 5 reasonable axioms you see at a mathematical level QM allows a continuous transformation between so called pure states. Classical probability doesn't do that. That is the key difference mathematically.

In fact further work has been done that shows entanglement is the fundamental difference:
http://arxiv.org/abs/0911.0695

Basically only two reasonable theories exist to model physical systems as generalized probability models - standard probability theory and QM. But of those two QM is the only one that allows entanglement, which has been experimentally demonstrated innumerable times eg bell type experiments.

Why is nature probabilistic? That's just the way she is. But as mentioned previously Gleason's theorem shows if you want to model observations by Hermitian operators that's something that's forced on us. Why Hermitian operators? Well as I mentioned above we want basis independence. But in explaining anything some assumptions must be made - these are the assumptions QM makes and it's been verified to an extremely high degree of accuracy.

Thanks
Bill