Quantum mechanics is random in nature?

[bhobba]

Yes, but gravitational field is metaphysics.

Come again - space time curvature is as real as you can get.

Thanks
Bill

 

[bhobba]

I don't think that most physicists think that QM requires an observer (as opposed von Neumann). The usual axioms don't require it. What do you think?

It doesn't, as interpretations such as MW and BM that do not have it prove.

Thanks
Bill

 

[bhobba]

The usual axioms require it. It may be stated in slightly different language (eg. a classical measuring apparatus), but it is required. See also bhobba's post #58 for yet another way of stating this.

I said observation was a primitive of the theory. What it means, and if it requires an observer, or even an observation in a more limited sense of being the outcome of an interaction, is very interpretation dependent. For example in BM the mixed state after decoherence is actually in that state independent of an observer or observation (ie decoherence outcome - it has actual values at all times).

Thanks
Bill

 

[bhobba]

OK, how does mass make the changes?

This is not the place to discuss it, the relativity forum is, but GR is very very elegant. Pretty much the assumption of no prior geometry all by itself leads to the Einstein Field equations. Mathematically this means the geometry is a dynamical variable ie obeys a least action principle - see for example section 4 of the following:
http://www.if.nu.ac.th/sites/default/files/bin/BS_chakkrit.pdf

Of course it solves nothing in a fundamental sense because you have simply changed the question to - why is there no prior geometry. Its just no prior geometry seems pretty intuitive - why should nature single out one geometry over another.

Thanks
Bill

 

[atyy]

I said observation was a primitive of the theory. What it means, and if it requires an observer, or even an observation in a more limited sense of being the outcome of an interaction, is very interpretation dependent. For example in BM the mixed state after decoherence is actually in that state independent of an observer or observation (ie decoherence outcome - it has actual values at all times).

Thanks
Bill

Observation is not a primitive in BM.

 

[zonde]

Come again - space time curvature is as real as you can get.

GR took gravity to a new level of course.
But I would change the wording of your statement: space time deformation is physical. I understand that "curvature" is the standard word but as I see it implies 5th dimension and that is metaphysics.

 

[Mentz114]

GR took gravity to a new level of course.
But I would change the wording of your statement: space time deformation is physical. I understand that "curvature" is the standard word but as I see it implies 5th dimension and that is metaphysics.

Spacetime curvature does not require a fifth dimension. It is intrinsic in the metric.

 

[Stephen Tashi]

What began as discussion of randomness has turned into debates about things that sound (to me) rather deterministic. Is there a line of reasoning that leads down this path? - or is it just a digression?

 

[atyy]

What began as discussion of randomness has turned into debates about things that sound (to me) rather deterministic. Is there a line of reasoning that leads down this path? - or is it just a digression?

Probability according to Kolmogorov can always be interpreted as ignorance of a deterministic process. In this sense, Kolmogorov probability is not truly random. In contrast, QM does not obey the pure Kolmogorov axioms. In contrast to Kolmogorovian probability, the QM state space is not a simplex, and may be "truly random" because it is not due to ignorance of a deterministic process.

The question is whether QM can be embedded in a larger theory whose state space is a simplex.

 

[Zafa Pi]

Probability according to Kolmogorov can always be interpreted as ignorance of a deterministic process. In this sense, Kolmogorov probability is not truly random. In contrast, QM does not obey the pure Kolmogorov axioms. In contrast to Kolmogorovian probability, the QM state space is not a simplex, and may be "truly random" because it is not due to ignorance of a deterministic process.

The question is whether QM can be embedded in a larger theory whose state space is a simplex.

But it doesn't have to be interpreted as ignorance of a deterministic process, though the BM interpretation does. The Kolmogorov axioms (the usual ones we now think of) are silent on such issues. And as I have pointed out in previous posts "random" or "truly random" are not defined in probability theory. They are intuitive ideas, usually connoting, "having no cause", what ever that means.

Could you please give a concrete where probabilistic notions in QM don't obey the Kolmogorov axioms.

 

[atyy]

But it doesn't have to be interpreted as ignorance of a deterministic process, though the BM interpretation does. The Kolmogorov axioms (the usual ones we now think of) are silent on such issues. And as I have pointed out in previous posts "random" or "truly random" are not defined in probability theory. They are intuitive ideas, usually connoting, "having no cause", what ever that means.

Could you please give a concrete where probabilistic notions in QM don't obey the Kolmogorov axioms.

Yes, however, Kolmogorov probability does allow notions such as a particle having a trajectory at all times.

So fundamentally, classical probability has a state space that is a simplex. That is the difference between QM and Kolmogorov.

 

[Zafa Pi]

Yes, however, Kolmogorov probability does allow notions such as a particle having a trajectory at all times.

So fundamentally, classical probability has a state space that is a simplex. That is the difference between QM and Kolmogorov.

Kolmogorov probability, which I now merely call probability theory, as given in chapter 1 of Feller also allows notions such as red eyed dragons. It doesn't say anything about dragons or particle trajectories. Within probability theory there is a probability space or sample space, but I can't find a state space within the theory. I know what a state space is in QM.

 

[bhobba]

Observation is not a primitive in BM.

Exactly.

Observation is a primitive in the standard formalism with no or very minimal interpretation. In interpretations that use decoherence it has morphed to why do we get outcomes at all which is its status in my ignorance ensemble. Although it could be reasonably argued that since decherence applies to any interpretation even just the formalism it has morphed in every interpretation, but I would not argue that since its really, IMHO just semantics on what interpretation means. In still others it is explained by other things. In the very formal mathematical approach such as the found in Varadarajan it is reduced to the logic of QM - here logic means in the formal mathematical sense of a lattice. But like Hilbert's axioms of Euclidean geometry is generally not used in applications where a slightly looser development is better.

Thanks
Bill

 

[bhobba]

Yes, however, Kolmogorov probability does allow notions such as a particle having a trajectory at all times.

Yes of course. Just to elaborate, the use of probability anywhere can result from a number reasons. Its truly random being one, inherent lack of knowledge is another, and there are probably other ways although I can't think of them off the top of my head.

BM is an example of a deterministic theory where because of inherent lack of knowledge (to be specific as implied by the indeterminacy relations) you don't know enough, and the theory forbids you from finding it, to predict outcomes so you must use probability theory. Another is the use of decision theory in MW which, while not the same as the Kolmogorov axioms, does imply them as professions like actuarial science that also make use of it know quite well.

Thanks
Bill

 

[bhobba]

Within probability theory there is a probability space or sample space, but I can't find a state space within the theory. I know what a state space is in QM.

Of course you are correct.

But to elaborate a bit one can define a measure over the state space (eg via Gleason) and relate that measure to events - which of course is what Gleason also does. In that way the Kolmogorov axioms are recovered.

Thanks
Bill

 

[Zafa Pi]

Of course you are correct.

But to elaborate a bit one can define a measure over the state space (eg via Gleason) and relate that measure to events - which of course is what Gleason also does. In that way the Kolmogorov axioms are recovered.

Thanks
Bill

And you are correct. Given any set whatsoever one can define a countably additive probability measure on some sigma-algebra of subsets.

 

[mikeyork]

Sorry to join this thread so late, but I need to point out that you can't talk about randomness without specifying what variable is random. In QM, you can have a particle with an exactly deterministic momentum, but then the position is completely (uniformly, infinitely) random. In Hilbert space any state vector that is a superposition in one basis can be an eigenstate in another.

 

[vanhees71]

You can NOT have a particle with precisely determined momentum. An observable can never have a determined value that's in the continuous part of the corresponding operator. For momentum it's immediately clear, because the generalized eigenfunction in position representation is a plane wave, which is not square integrable. That's the true meaning of the famous uncertainty principle $\Delta x \Delta p \geq \hbar/2$, which tells you that neither position (which has only continuous eigenvalues) and momentum (which as well has only continuous eigenvalues) can have 0 variance in any pure or mixed state possible!

 

[Stephen Tashi]

That's the true meaning of the famous uncertainty principle $\Delta x \Delta p \geq \hbar/2$, which tells you that neither position (which has only continuous eigenvalues) and momentum (which as well has only continuous eigenvalues) can have 0 variance in any pure or mixed state possible!

Are you interpreting $\Delta x$ and $\Delta p$ as standard deviations of random variables ? Does the fact that a random variable has a non-zero standard deviation preclude us from doing an experiment where one specific value of the random variable is realized?

As I said in a previous post, the (Kolmogorov) theory of probability doesn't say anything (pro or con) about whether random variables can take on "actual" values or whether we can do experiments that cause these actual values to occur. So demonstrating that a physical quantity cannot be precisely measured can't be done by a purely mathematical argument. I'd like to understand what physical argument is used to reach your conclusion.

 

[vanhees71]

What do you mean by "realized". Quantum theory tells you that you cannot prepare a particle such that it has a precisely determined momentum. You can prepare it at any precision (standard deviation) $\Delta p>0$ but never make $\Delta p=0$. It doesn't say that you cannot measure momentum at any accuracy. This only depends on your measurement apparatus. In principle you can always construct a device that measures momentum more precise than the $\Delta p$ of the prepared state of the particle. Then you'll find fluctuations around the mean value given by the corresponding probability distribution according to this standard deviation, when measuring the momentum at this higher accuracy, on a large set of equally prepared partices (an ensemble).

The physical argument is the overwhelming accuracy of quantum theory in describing all observations we have collected about nature today. There's not a single reproducible contradiction between quantum theory and observations, and quantum theory has been tested to extreme accuracy in some cases. So we have good reason to believe that quantum theory describes nature very accurately. Of course, as with all scientific knowledge, it's always possible that one day one discovers a phenomenon that cannot be described by quantum theory. This would be a real progress, because then we'd have learned something completely new about nature and we would have to adjust our theories leading to an even more comprehensive view about nature. In some sense you can say that finding discrepancies between the theories we have today and experiment is the true goals of scientific research in order to find even better theories.

 

[Delta Kilo]

In QM, you can have a particle with an exactly deterministic momentum, but then the position is completely (uniformly, infinitely) random.

The particle does not "have" a random position. Instead, the result of a position measurement, should we choose to perform one, is random. Before the measurement the particle is in well defined state. Randomness only appears as a result of measurement process, which necessarily involves interaction with large number of particles in unknown state.

I don't get why so much fuss is made about randomness in QM. Everyone seems to be OK with classical Brownian motion of a speck of dust being random. But, they say, unlike QM, it is not a "true" randomness, they could predict it if it they knew the positions and velocities of all air molecules in a volume at time t0. But is it really so? Penrose gave this argument in "Road to Reality": moving 1kg by 1 meter somewhere in the vicinity of Alpha Centauri causes enough change in gravitation here on Earth to completely scramble the trajectories of molecules in 1m^3 volume of air within 1 minute. Given that gravitation travels at c and cannot be screened, we'd need to know the state of the entire universe all the way back to Big Bang. So for all intents and purposes the motion of individual molecules of air is truly random.

I feel it is exactly the same way with QM, I don't see much conceptual difference between QM spin measured 50/50 up or down and a classical problem of a ball on a knife's edge falling 50/50 left or right. In theory in the absence of external influences the ball stays on the edge forever and the detector remains in Schrodinger cat state of superposition. In real life the ball eventually falls down and the detector reports a single outcome.

 

[mikeyork]

Vanhees, you say "An observable can never have a determined value that's in the continuous part of the corresponding operator." in response to me. But I said deterministic (meaning in a definite eigenstate) not determined (i.e.observed).

 

[Stephen Tashi]

What do you mean by "realized".

It doesn't say that you cannot measure momentum at any accuracy.

I don't understand the distinction that you are apparently making between knowing a particles momentum was precisely measured to be a specific value at time t and concluding the particle "had" that precise momentum at time t. By a "realized" value , I mean that the value was measured and thus that the random physical quantity is thus know to have taken that specific value. Perhaps erroneously, I think of a theoretical measurement of momentum as a "realization" of a specific value of momentum.

I agree that any practical apparatus does not produce infinitely precise measurements. The conceptual question is whether the thing being measured "had" a exact value when an imperfect measuring apparatus measured it. is the argument that no particle ever had an exact momentum because all practical measuring equipment has limited precision ?[/QUOTE]

 

[Zafa Pi]

Vanhees, you say "An observable can never have a determined value that's in the continuous part of the corresponding operator." in response to me. But I said deterministic (meaning in a definite eigenstate) not determined (i.e.observed).

Confusion regularly results when people blur the lines between theory and reality. QM is a mathematical theory and in that theory a measurement by an obsversable (Hermitian operator) of a state (unit vector in a Hilbret space, or ray, or L² "wave" function) is a random variable (see Feller and Nielsen & Chuang). If the variance of that r.v. is 0 then the state is an eigenvector of the operator. What vanhees71 is saying (my interpretation) is that the momentum operator has no eigenvector in the state (Hilbert) space (same for the position operator). Thus Δp (of a state) is > 0 (Δp is the s.d. = sqrt of the variance)

Now in reality the experimental physicist selects a momentum measuring apparatus (hopefully modeled by QM) and prepares a large number of entities in the same state and procedes to measure them. The resulting measurements are not all the same in spite of the fact that each individual measurement is a single precise value. Thus the collection of all the measurements has a non-zero (statistical) variance. And as vanhees71 says QM and reality agree.

 

[DrChinese]

The particle does not "have" a random position. Instead, the result of a position measurement, should we choose to perform one, is random. Before the measurement the particle is in well defined state. Randomness only appears as a result of measurement process, which necessarily involves interaction with large number of particles in unknown state.

I don't get why so much fuss is made about randomness in QM. Everyone seems to be OK with classical Brownian motion of a speck of dust being random. But, they say, unlike QM, it is not a "true" randomness, they could predict it if it they knew the positions and velocities of all air molecules in a volume at time t0. But is it really so? Penrose gave this argument in "Road to Reality": moving 1kg by 1 meter somewhere in the vicinity of Alpha Centauri causes enough change in gravitation here on Earth to completely scramble the trajectories of molecules in 1m^3 volume of air within 1 minute. Given that gravitation travels at c and cannot be screened, we'd need to know the state of the entire universe all the way back to Big Bang. So for all intents and purposes the motion of individual molecules of air is truly random.

I feel it is exactly the same way with QM, I don't see much conceptual difference between QM spin measured 50/50 up or down and a classical problem of a ball on a knife's edge falling 50/50 left or right. In theory in the absence of external influences the ball stays on the edge forever and the detector remains in Schrodinger cat state of superposition. In real life the ball eventually falls down and the detector reports a single outcome.

Clearly, there are tremendous differences between the classical examples you give and the quantum ones. Classical systems do not feature non-commuting observables. Non-commuting observables not only have specific limits in their precision, those limits can be seen in experiments on entangled pairs. So if you don't see the conceptual difference between these, you need to consider more experiments.

 

[David Lewis]

Given that gravitation travels at c and cannot be screened, we'd need to know the state of the entire universe all the way back to Big Bang. So for all intents and purposes the motion of individual molecules of air is truly random.

My understanding of classical mechanics there are no hypothetically random processes, even if we can't collect enough information to make a prediction.

 

[drschools]

Would not truly random fit the Aristotelian definition of God i.e. the "unmoved mover" ? We might therefore attribute all genuinely random or uncaused phenomenon to God. We would therefore be following a similar argument as the "God of the Gaps". It might be argued also that while "Newtonian phenomenon" increasingly shrinks the unexplained gaps and therefore evidence of God in the universe, "Quantum phenomenon" re-expands the mysterious unexplainable gaps of science and therefore evidence of God (of the gaps).

 

[DrChinese]

Would not truly random fit the Aristotelian definition of God i.e. the "unmoved mover" ? We might therefore attribute all genuinely random or uncaused phenomenon to God. We would therefore be following a similar argument as the "God of the Gaps". It might be argued also that while "Newtonian phenomenon" increasingly shrinks the unexplained gaps and therefore evidence of God in the universe, "Quantum phenomenon" re-expands the mysterious unexplainable gaps of science and therefore evidence of God (of the gaps).

Sure. Although it does beg the question: why are there any physical laws at all if god is reserving her efforts only to fill in those gaps?

 

[Zafa Pi]

The particle does not "have" a random position. Instead, the result of a position measurement, should we choose to perform one, is random. Before the measurement the particle is in well defined state. Randomness only appears as a result of measurement process, which necessarily involves interaction with large number of particles in unknown state.

I don't get why so much fuss is made about randomness in QM. Everyone seems to be OK with classical Brownian motion of a speck of dust being random. But, they say, unlike QM, it is not a "true" randomness, they could predict it if it they knew the positions and velocities of all air molecules in a volume at time t0. But is it really so? Penrose gave this argument in "Road to Reality": moving 1kg by 1 meter somewhere in the vicinity of Alpha Centauri causes enough change in gravitation here on Earth to completely scramble the trajectories of molecules in 1m^3 volume of air within 1 minute. Given that gravitation travels at c and cannot be screened, we'd need to know the state of the entire universe all the way back to Big Bang. So for all intents and purposes the motion of individual molecules of air is truly random.

I feel it is exactly the same way with QM, I don't see much conceptual difference between QM spin measured 50/50 up or down and a classical problem of a ball on a knife's edge falling 50/50 left or right. In theory in the absence of external influences the ball stays on the edge forever and the detector remains in Schrodinger cat state of superposition. In real life the ball eventually falls down and the detector reports a single outcome.

I believe yours' is the valid answer to the original question of this thread. The key is in the 2nd line of your 2nd paragraph : "if they knew the positions ... " But they don't know and cannot give any reasonable way to go about knowing. Those which want to make a distinction between random due to lack of knowledge and "pure random" will come down to events that have a cause and those that don't. A philosophical quagmire of the 1st order in which I have squandered my youth.

In knowing the state of the universe all the way back to the Big Bang is also the ultimate loop hole in the disproving of realism using the measurements of entangled entities (super-determinism). And nobody cares, nor should they.

 

[Zafa Pi]

Sure. Although it does beg the question: why are there any physical laws at all if god is reserving her efforts only to fill in those gaps?

God moves in mysterious ways just like Simone Biles.

 

[drschools]

I'm glad you made that point as the physical laws are in fact also uncaused or truly unexplainable phenomenon... the speed of light for instance . Another argument for God -in this light (no pun intended)- would be the "Fine-tuned" or "Goldilocks principle" of many universal constants and phenomenon.

 

[Zafa Pi]

Clearly, there are tremendous differences between the classical examples you give and the quantum ones. Classical systems do not feature non-commuting observables. Non-commuting observables not only have specific limits in their precision, those limits can be seen in experiments on entangled pairs. So if you don't see the conceptual difference between these, you need to consider more experiments.

This is an example of what I consider the blurring of lines between theory and reality. There is no question that classical and quantum theories are different, as you and David Lewis (post #96) point out. The experiments on entangled pairs show that classical determinism (= realism) is wrong (assuming locality). But in reality if I flip a coin in a wind tunnel I'll get different and random looking results. The classicist says the initial conditions changed, but is incapable of measuring or controlling them.

Delta Kilo says that "in reality" one can't tell the difference between quantum randomness and the hypothetical classical (lack of knowledge) randomness.

 

[Delta Kilo]

Clearly, there are tremendous differences between the classical examples you give and the quantum ones.

Of course they are hugely different. But they are both examples of spontaneous symmetry breaking and I was only referring to the conceptual source of randomness in both cases. I just don't see the need to look any further than the unknown state of the environment. So the fact that some measurement are inherently random does not surprise me at all. It it actually the other way around: it is surprising that some measurements are less random than they should have been according to classical view.

 

[vanhees71]

Vanhees, you say "An observable can never have a determined value that's in the continuous part of the corresponding operator." in response to me. But I said deterministic (meaning in a definite eigenstate) not determined (i.e.observed).

Quantum theory is not determinstic. Some observables may be determined by preparation the system in a corresponding state. This is possible only for true eigenvalues of the self-adjoint operator, i.e., such eigenvalues for which normalizable eigenvectors exist, and these eigenvectors are in the discrete part of the spectrum.

 

[bhobba]

I'm glad you made that point as the physical laws are in fact also uncaused or truly unexplainable phenomenon... the speed of light for instance .

Hmmmm.

See the following:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

My view is symmetry. Its almost, but not quite magic.

If this is your first exposure I highly recommend Landau:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20
'If physicists could weep, they would weep over this book. The book is devastingly brief whilst deriving, in its few pages, all the great results of classical mechanics. Results that in other books take take up many more pages. I first came across Landau's mechanics many years ago as a brash undergrad. My prof at the time had given me this book but warned me that it's the kind of book that ages like wine. I've read this book several times since and I have found that indeed, each time is more rewarding than the last. The reason for the brevity is that, as pointed out by previous reviewers, Landau derives mechanics from symmetry. Historically, it was long after the main bulk of mechanics was developed that Emmy Noether proved that symmetries underly every important quantity in physics. So instead of starting from concrete mechanical case-studies and generalising to the formal machinery of the Hamilton equations, Landau starts out from the most generic symmetry and dervies the mechanics. The 2nd laws of mechanics, for example, is derived as a consequence of the uniqueness of trajectories in the Lagragian. For some, this may seem too "mathematical" but in reality, it is a sign of sophisitication in physics if one can identify the underlying symmetries in a mechanical system. Thus this book represents the height of theoretical sophistication in that symmetries are used to derive so many physical results.'

Magic - no - like I said it seems like it but isn't. However sorting out the real physical assumptions is both rewarding and illuminating.

Start a new thread if interested.

Thanks
Bill