QM and Determinism: Can We Predict the Future?

[Johan0001]

"Determinism often is taken to mean causal determinism, which in physics is known as cause-and-effect. It is the concept that events within a given paradigm are bound by causality in such a way that any state (of an object or event) is completely determined by prior states" -- from wiki

Does it follow that the next state of a system is already mapped out by the history built up of prior states.
Thus without observation or interference we can determine the next state to happen, if we had all the information of prior states?

Can an event occur without any observation/measurement thereof?
This question seems nonsensical , but when one talks of observation/measurement / events in QM they
are crucial in understanding their definitions WRT determinism.

How does QM relate to determinism , if everything can be predicted given that we have collected all the information available to us in the universe.

I'm quite confused on how it fits together? I.E. QM and determinism..

 

[atyy]

A deterministic theory is one in which it is possible to say, given full knowledge of the state at one point in time, it is possible in principle to know the state at all other points in time.

Quantum mechanics is not a deterministic theory. In quantum mechanics, only future "expectation values" or "average values over many repetitions of the same experiment" can be known given full knowledge of the state at an initial time.

 

[naima]

And the same is true for the past. Given the result of a measure, one cannot know exactly how the state of the incoming particle was prepared

 

[Johan0001]

Quantum mechanics is not a deterministic theory. In quantum mechanics, only future "expectation values" or "average values over many repetitions of the same experiment" can be known given full knowledge of the state at an initial time.

Then which theory would describe what we observe most accurately, Determinism or QM , because they have radically different fundamentals , which seem to contradict each other.

 

[naima]

QM is a theory and determinism is a philosophical notion.

 

[atyy]

Then which theory would describe what we observe most accurately, Determinism or QM , because they have radically different fundamentals , which seem to contradict each other.

At present, QM, which is a non-deterministic theory, is our most fundamental theory, in the sense that all observations to date are consistent with QM. However, determinism and QM do not contradict each other.

This is because a non-deterministic theory can be an approximation to a deterministic theory. It could be that we don't have enough experimental control, so that what we consider a "state" is actually a different state each time we do "the same" experiment. So it is conceivable that there is a non-deterministic theory that underlies QM. If this is the case, then by improving our experimental finesse, we may one day observe phenomena that cannot be well described by QM.

It is also possible for a deterministic theory to be an approximation to a non-deterministic theory. For example, deterministic classical mechanics is a good approximation to quantum theory over some regime.

So at this stage, we cannot say whether determinism or non-determinism is more fundamental, since each can arise from the other.

 

[microsansfil]

QM is a theory and determinism is a philosophical notion.

Indeed, there is a philosophical definition of determinism:

From Stanford Encyclopedia of Philosophy:

Determinism: The world is governed by (or is under the sway of) determinism if and only if, given a specified way things are at a time t, the way things go thereafter is fixed as a matter of natural law.

A theoretical model can not be qualified "deterministic" related to the notion of causality ?

Patrick

 

[Neandethal00]

QM is a theory and determinism is a philosophical notion.

May we label determinism as Observation?
Unfortunate thing is physicists are content with nondeterministic nature of QM.
Very few are bothered by why QM is nondeterministic.

 

[the_pulp]

QM is not deterministic in the sense that, given the full information of a state, you cannot predict the output of a an experiment over this state. Nevertheless, there are a lot of interpretations of "why" this happens, and these interpretations vary in wether they are:
Deterministic or Stochastic
Local or Nonlocal
If there are hidden variables or not in the instrument of the experiment or in the state itself
...
The problem is that there are nice characteristics and not nice characteristics (in terms of what is the average man intuition) and there is no interpretation that has all of the nice characteristics and none of the not nice ones.

The interpretation that I like the most is very similar to the interpretation called "Time Symmetric Interpretation" (for a quick review of the different interpretations, see http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics ) and it is deterministic. In a word, in this terms, we cannot say that QM is deterministic or not.

Nevertheless, two comments:
this does not abolish the general notion that given the full knowledge of a state, we can not know for certain the result of a experiment
the practical interpretation applied in real life (and what I see in the forum) is "Shut up and calculate", meaning that all this discussion is irrelevant to the actual state of science and that perhaps will never be of any use

Im just an amateur reader of QM and such so take my comments as just a little of information that should be validated or corrected by professionals.

 

[bhobba]

The Pulp had it right.

If QM is deterministic or not is purely a matter of interpretation eg BM is completely deterministic, probabilities appear due to lack of knowledge of initial conditions.

That being the case it's meaningless to talk about determinism in QM without reference to a specific interpretation.

Looking just at the formalism Gleasons theroem shows you can't have a probability measure of just 0 or 1, ie determinism, if you have non-contextuality which is its rock bottom essence - in this sense Gleason is a stronger version of Kochen-Specker which anyone interested in this should look into.

With our modern understanding of decoherence the real issue is the so called problem of definite outcomes. We end up with an improper mixed state after decoherence, but exactly how is a particular outcome singled out.

Thanks
Bill

 

[bhobba]

Can an event occur without any observation/measurement thereof? This question seems nonsensical , but when one talks of observation/measurement / events in QM they are crucial in understanding their definitions WRT determinism.

In modern times observations and decoherence are usually taken to be the same thing. The rock bottom question is the definite outcomes issue I mentioned above.

Thanks
Bill

 

[vanhees71]

It's indeed a question of definition, what you mean by "deterministic". In my definition, which I think is the most common definition among physicists, a physical model is deterministic, if the complete knowledge of the state of the system implies the knowledge of the values of all possible observables of the system, and it is (at least in principle) possible to gain complete knowledge about the state of any system. All of classical physics is deterministic (i.e., Newtonian and relativistic discrete and continuum mechanics, classical electromagnetism).

Quantum theory is not deterministic, because the complete knowledge about the state of the system does not imply the knowledge about the values of all observables. This is the content of the general Heisenberg-Robertson uncertainty relation in the minimal statistical interpretation, which in my opinion is the only one justified by physics, i.e., without additional metaphysical elements reflecting the personal view of the followers of any representation going beyond that. According to quantum theory in the minimal representation the indeterminacy of observables according to the preparation of the system in a certain state is objective, i.e., these observables really do not take any determined value, but you can predict the probability of finding a certain value of any observable.

All of today's physics is, however, causal. This means that the complete knowledge about the state of a system in the past implies its evolution in the future, i.e., the state at later times is given by dynamical laws. On a fundamental level this causality is even local in time, i.e., it is sufficient to know the state of the system at one instant of time, t_0 to calculate the state of the system at any later time, t>t_0.

For a very detailed and careful analysis of this, see the introductory chapter of

Schwinger, Julian: Quantum Mechanics, Symbolism of Atomic Measurements, Springer, 2001

 

[moriheru]

In a deterministic theory, given some information, one can predict the future of a state. In QM one only has probabilityamplitudes or expectation-values of the nth state of say some particle.

 

[Johan0001]

bhobba wrote -

probabilities appear due to lack of knowledge of initial conditions

With HUP we would never really know the initial conditions precisely in the microscopic world, but is it really necessary to know ?Is it not accurate enough to say that , the most probable future state is the one with the highest probability.
"The most probable macro state is the one with the highest number of micro states"

If we can only absorb/bounce photons off particles then , what do we bounce
off photons.

atyv wrote -

It could be that we don't have enough experimental control, so that what we consider a "state" is actually a different state each time we do "the same" experiment. So it is conceivable that there is a non-deterministic theory that underlies QM. If this is the case, then by improving our experimental finesse, we may one day observe phenomena that cannot be well described by QM.

I tend to believe that there is no 2 states that can be exactly the same when repeating the experiment over and over, no matter how strict our repeated experiment is done.
If something has changed in the universe , between the 2 repeated experiments , then another state has evolved in the second attempt of the "same experiment" around which is a result of previous states of the universe.

My question is , how practical is this approach , does it matter if we cannot define each state exactly. Why can't we just say :
The next state is exactly what the highest probability predicts.
"The most probable macro state is the one with the highest number of micro states"
What could change this prediction?

 

[bhobba]

If we can only absorb/bounce photons off particles then , what do we bounce off photons.

Why do you think we can only know about 'things' by bouncing photons off them?

Indeed QFT tells us photons 'bouncing' is way off the mark.

Is it not accurate enough to say that , the most probable future state is the one with the highest probability.

Do you know what a tautology is?

Thanks
Bill

 

[aleazk]

The Pulp had it right.

If QM is deterministic or not is purely a matter of interpretation eg BM is completely deterministic, probabilities appear due to lack of knowledge of initial conditions.

That being the case it's meaningless to talk about determinism in QM without reference to a specific interpretation.

Looking just at the formalism Gleasons theroem shows you can't have a probability measure of just 0 or 1, ie determinism, if you have non-contextuality which is its rock bottom essence - in this sense Gleason is a stronger version of Kochen-Specker which anyone interested in this should look into.

With our modern understanding of decoherence the real issue is the so called problem of definite outcomes. We end up with an improper mixed state after decoherence, but exactly how is a particular outcome singled out.

Thanks
Bill

Do you know references in which I can read a little more about the physical implications of contextuality? I mean, if nature is non-contextual, then Gleason's theorem provides a quite strong case in favor of indeterminism in QM, and from the very core of its mathematical foundation.

 

[atyy]

I tend to believe that there is no 2 states that can be exactly the same when repeating the experiment over and over, no matter how strict our repeated experiment is done.
If something has changed in the universe , between the 2 repeated experiments , then another state has evolved in the second attempt of the "same experiment" around which is a result of previous states of the universe.

My question is , how practical is this approach , does it matter if we cannot define each state exactly. Why can't we just say :
The next state is exactly what the highest probability predicts.
"The most probable macro state is the one with the highest number of micro states"
What could change this prediction?

No one is suggesting that present observations be modeled by a deterministic theory. It is impractical, and given that no violation of QM has been observed, we should stick to it.

However, QM is not a completely stochastic theory. It has deterministic time evolution as well as stochastic time evolution. The time evolution between measurements is deterministic. When a measurement is made, the time evolution is stochastic.

 

[bhobba]

Do you know references in which I can read a little more about the physical implications of contextuality? I mean, if nature is non-contextual, then Gleason's theorem provides a quite strong case in favor of indeterminism in QM, and from the very core of its mathematical foundation.

http://en.wikipedia.org/wiki/Quantum_contextuality

Thanks
Bill

 

[atyy]

Do you know references in which I can read a little more about the physical implications of contextuality? I mean, if nature is non-contextual, then Gleason's theorem provides a quite strong case in favor of indeterminism in QM, and from the very core of its mathematical foundation.

That would not be the right interpretation. The interpretation is that if we want a formalism that is non-contextual, and uses rays in Hilbert space to label measurement outcomes, then the Born rule of QM is unique.

Why would we want such a formalism? Well, it works! Also, there are indications that QM is "easier to handle" than other alternatives with the same "expressive" power.
http://arxiv.org/abs/quant-ph/0604155
http://arxiv.org/abs/0711.4770

Another intriguing approach is the Piron approach, with a recent result by Soler, that bhobba can tell you about :)

 

[the_pulp]

What I will say is just philosophy, but I don't see that it will be much more philosophy than some other posts.

We can say that nature is not only deterministic between measurements but also deterministic during measurements but also it is deterministic during measurement. We could say that what really happens is that the instrument used to measure has a lot of degrees of freedom (lets say, just to be graphical, the exact positions of each and every atom of the instrument) inaccesible to humans and if we knew all of them, we could really know the exact result of the experiment. Then we will have other problems (Nature will be no local -perhaps this can be saved with retrocausality but I don't want to miss the point-) but nature could really be deterministic and QM (and its born rule) is just the aproximation that should be used when dealing with instruments with a lot of degrees of freedom.

I am not saying that this is the truth. I just say that up to now (and up to what I understood -much of it with a lot of your help-) we cannot say that QM says that nature is deterministic o stochastic. Here, when I say nature, I mean "what 'really' is behind QM, if there 'really' is something behind QM".

 

[Nugatory]

What I will say is just philosophy, but I don't see that it will be much more philosophy than some other posts.

We accept much more philosophy in the QM forum than anywhere else, so you're OK.

I just say that up to now (and up to what I understood -much of it with a lot of your help-) we cannot say that QM says that nature is deterministic o stochastic. Here, when I say nature, I mean "what 'really' is behind QM, if there 'really' is something behind QM".

To repeat Bhobba: "the_pulp has it right"
- T'Hooft has given us a proof by example that a completely deterministic interpretation can be consistent with QM.
- There are already too many is no shortage of stochastic interpretations.
- No experiment can distinguish them (although Bell has pushed the local determinists back into their final unassailable redoubt - superdeterminism - and it's not a place where I'd want to live).

 

[Jano L.]

All of today's physics is, however, causal. This means that the complete knowledge about the state of a system in the past implies its evolution in the future, i.e., the state at later times is given by dynamical laws. On a fundamental level this causality is even local in time, i.e., it is sufficient to know the state of the system at one instant of time, t_0 to calculate the state of the system at any later time, t>t_0.

Do you mean also quantum theory is causal? I do not understand how that can be. Consider the following example from quantum theory.

Let a silver atom (initially with the spin state $|x+\rangle$ - eigenket of the $\hat s_x$ operator associated with the eigenvalue $+\hbar/2$) move along the axis $y$ and let it pass through the Stern-Gerlach magnets oriented in such a way that the silver atoms are separated into two groups with different $z$ while their $x$ coordinates stay the same. Let us denote the two $z$ values $z_+,z_-$.

When the $z$ coordinate of the silver atom is measured after passing the Stern-Gerlach magnet to be $z_+$, the spin state of the atom before the measurement of atom's position is believed to have changed into $|z+\rangle$. This new state cannot be calculated from the Schroedinger-Pauli equation for the spin wave function and the initial spin state $|x+\rangle$; books on quantum theory only talk about calculating that there is 50% probability the state will change into $|z+\rangle$ and 50% probability it will change into $|z-\rangle$... Have I missed something?

 

[bhobba]

books on quantum theory only talk about calculating that there is 50% probability the state will change into $|z+\rangle$ and 50% probability it will change into $|z-\rangle$... Have I missed something?

Taking into account decoherernce everything is causal up until you get the improper mixed state. What it doesn't say is which element of the mixed state is selected by observation to go into which beam in your example - that is the point causality breaks down - maybe.

The maybe is we have interpretations such as BM where a specific element of the mixed state is there prior to observation - it all depends on how you look at it. And BM is not the only one - there is Nelson stochastics, primary state diffusion and probably others.

Thanks
Bill

 

[microsansfil]

Hello,

What is the falsification scientific method for probabilistic ? Is there a relationship beetween causality and probabilistic in the frame of QM ?

The classical physical concept of causality have to be revisited in light of the QM ?

Patrick

 

[vanhees71]

Do you mean also quantum theory is causal? I do not understand how that can be. Consider the following example from quantum theory.

Let a silver atom (initially with the spin state $|x+\rangle$ - eigenket of the $\hat s_x$ operator associated with the eigenvalue $+\hbar/2$) move along the axis $y$ and let it pass through the Stern-Gerlach magnets oriented in such a way that the silver atoms are separated into two groups with different $z$ while their $x$ coordinates stay the same. Let us denote the two $z$ values $z_+,z_-$.

When the $z$ coordinate of the silver atom is measured after passing the Stern-Gerlach magnet to be $z_+$, the spin state of the atom before the measurement of atom's position is believed to have changed into $|z+\rangle$. This new state cannot be calculated from the Schroedinger-Pauli equation for the spin wave function and the initial spin state $|x+\rangle$; books on quantum theory only talk about calculating that there is 50% probability the state will change into $|z+\rangle$ and 50% probability it will change into $|z-\rangle$... Have I missed something?

Of course, everything in physics is (asssumed to be) causal. Your example is not too difficult. You have a classical initial-value problem for the Schrödinger equation. The initial state is a wave packet of particles with determinate spin-x component, running along the y-axis through a inhomogeneous magnetic field adjusted to measure the spin-z component. What happens is that the wave gets split into two wave packets, leading to a (nearly perfect) entanglement between position and spin-z component. You'll find 50% of the particles in the one wave packet having (nearly) 100% spin-z up and 50% of the particles in the other wave packet having (nearly) 100% spin-z down.

Of course, the spin-z component is not determined before filtering out one beam, but the state evolution is causal. The Schrödinger equation is a causal differential equation, as it must be, because it describes a physical dynamical process.

For details of a correct quantum mechanical treatment, taking into account the correct magnetostatic field, fulfilling the constraint \vec{\nabla} \cdot \vec{B}=0, including the "spin-flip probabilities", see

PHYSICAL REVIEW A 71, 052106 (2005)
Quantum mechanical description of Stern-Gerlach experiments
G. Potel, F. Barranco, S. Cruz-Barrios, and J. Gómez-Camacho
http://dx.doi.org/10.1103/PhysRevA.71.052106
http://arxiv.org/pdf/quant-ph/0409206

Most textbooks are pretty sloppy in this. You can, however treat the problem correctly analytically to a high accuracy in an advanced quantum-mechanics lecture.

 

[bhobba]

What is the falsification scientific method for probabilistic ? Is there a relationship beetween causality and probabilistic in the frame of QM ? The classical physical concept of causality have to be revisited in light of the QM?

Hi Patrick

There is no way to tell if any data is fundamentally random or is deterministic.

That's because our most powerful tests for randomness are fooled by sufficiently complex pseudo random number generators - at least as far as we can tell today.

Purely classical interpretations of QM exist, such as BM, that conform to our usual idea of causality ie are deterministic.

Thanks
Bill

 

[aleazk]

...
The problem is that there are nice characteristics and not nice characteristics (in terms of what is the average man intuition) and there is no interpretation that has all of the nice characteristics and none of the not nice ones

That's a nice way of putting it. So, I second, 'the pulp has it right'!

 

[BruceW]

Of course, the spin-z component is not determined before filtering out one beam, but the state evolution is causal. The Schrödinger equation is a causal differential equation, as it must be, because it describes a physical dynamical process.

So, in this context, causal means that we are able to calculate probabilities of possible experimental outcomes? It seems to be a bit different from the layman's idea of the word 'causal'.

 

[vanhees71]

As I pointed out earlier, you should distinguish between causality and determinism. A large part of science is to refine the language to describe nature accurately, including giving words a clear definition, probably modifying the less sharp meaning it has in everyday language.

 

[BruceW]

yes, that is very true. In physics, the definitions should be precise enough that someone can potentially use those definitions to empirically prove or disprove certain statements. So, just out of curiosity, what are your preferred physics definitions of causality and determinism? I have not actually seen any physics definitions of these things. But, I'm still a student, so my knowledge is not so wide.

Having said that, I know of causality being used in the sense that two spacetime events are causally connected if one event lies within the light cone of the other event. But this is really the only instance where I have heard of causality or determinism used in physics.

 

[DrChinese]

yes, that is very true. In physics, the definitions should be precise enough that someone can potentially use those definitions to empirically prove or disprove certain statements. So, just out of curiosity, what are your preferred physics definitions of causality and determinism? I have not actually seen any physics definitions of these things. But, I'm still a student, so my knowledge is not so wide.

Having said that, I know of causality being used in the sense that two spacetime events are causally connected if one event lies within the light cone of the other event. But this is really the only instance where I have heard of causality or determinism used in physics.

You may walk away with an incorrect conclusion depending on how you interpret some of the statements above.

1. Classical causality has been soundly refuted and there are no standing interpretations generally accepted otherwise.

2. Deterministic interpretations today are all non-local.

3. There are NO interpretations capable of providing a more "complete" prediction than QM does, including Bohmian Mechanics. It is fundamental to BM that initial conditions are unknown.

4. Although physicists often debate the "true" meaning of determinism, causality, etc. there are no generally accepted definitions that provide a *useful* difference. They are most often used interchangeably, and when given different definitions, it is usually for a specific purpose and not something accepted all around.

5. It is not generally accepted that physics is deterministic. The non-local interpretations have this feature, but most do not.

 

[atyy]

yes, that is very true. In physics, the definitions should be precise enough that someone can potentially use those definitions to empirically prove or disprove certain statements. So, just out of curiosity, what are your preferred physics definitions of causality and determinism? I have not actually seen any physics definitions of these things. But, I'm still a student, so my knowledge is not so wide.

Having said that, I know of causality being used in the sense that two spacetime events are causally connected if one event lies within the light cone of the other event. But this is really the only instance where I have heard of causality or determinism used in physics.

There's no standard terminology, but one of the ideas is indeed that causality has to do with no faster than light transfer of information, due to the light cone structure of spacetime.

Classically, one would think that correlations between distant events would be due to correlations prepared in the common past light cone of these events. This is often called local causality, or EPR-Bell locality. But quantum mechanics has wave function collapse, and violates local causality. Surprisingly, we still cannot use it to send information faster than light, and quantum mechanics is consistent with relativity. So there are at least two notions of causality - classical local causality, and the wider notion of relativistic causality, as discussed eg. by http://arxiv.org/abs/quant-ph/9508009.

 

[bhobba]

1. Classical causality has been soundly refuted and there are no standing interpretations generally accepted otherwise.

2. Deterministic interpretations today are all non-local.

That's a good point I wasn't clear about in my reply.

There is a bit of confusion in the use of classical. Non relativistic classical mechanics is non local as well - although that isn't usually stressed - an exception is Landau - Mechanics:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Here Landau explains it is a crucial and critical assumption.

Thanks
Bill

 

[bhobba]

So, in this context, causal means that we are able to calculate probabilities of possible experimental outcomes? It seems to be a bit different from the layman's idea of the word 'causal'.

Here casual means its deterministic up until you get an improper mixed state from decoherence.

After that its a matter of interpretation if it remains deterministic.

To further explain take BM. Here everything is deterministic (but non local) and particles have a definite momentum and position. This means after decoherence the mixed state is a proper mixed state with a definite outcome that was determined by the initial state and interaction with the observing apparatus. The reason probabilities enter into it is lack of knowledge about initial conditions.

Note - I am not an expert on BM. More detail can be had from Dymystifyer who is the expert on it around here.

Thanks
Bill

 

[microsansfil]

Hello,

In an "instrumentalist" approach to science who is having a "minimal interpretation", the goal is the prediction.

As expressed very well DaleSpam

https://www.physicsforums.com/threads/what-is-the-pfs-policy-on-lorentz-ether-theory-and-block-universe.772224/

The core of a scientific theory is a mathematical model which can be used to predict the outcome of experiments, i.e. in addition to the model there is a mapping between elements of the model and outcomes of experiments. This mapping is sometimes called the "minimal interpretation". Scientifically, theories are judged on how complicated their mathematical models are and on how well they predict the outcomes of experiments, with the best models being both simple and applying to a wide variety of phenomena.

In this frame, the predictive power of classical mechanics (Non relativistic and relativistic) stems from laws ( For example the conservation laws ) that appear as consistency rules that any description of the past must meet.

The Quantum Mechanics seem to be different about prediction. The predictions are not as a description of the past, it is the substance of the problem of measurement in QM.

Patrick

 

[Jano L.]

Of course, everything in physics is (asssumed to be) causal...
...
the state evolution is causal. The Schrödinger equation is a causal differential equation, as it must be, because it describes a physical dynamical process.

Initial value problem with the Schroedinger equation may have unique solution. As I understand, you call that "causal".
When we calculate the spin wave function this way, we obtain unique result $\boldsymbol \psi_1$ giving probability density in space symmetrical in $z$.

But this calculated $\boldsymbol\psi_1$ is appropriate only before the measurement of the z coordinate takes place; after the measurement, we know the appropriate pair of wave functions in space is no longer that calculated in the above way. Based on the result of the measurement, the best choice is asymmetric pair where one component carries most of the probability and its density is localized asymmetrically in z.

This new pair of wave functions $\boldsymbol \psi_2$ cannot be obtained from the Schroedinger equation in a "causal" way. It is chosen based on the result of the measurement, which is random, not causal in quantum theory.

Another theory (not quantum theory in the usual sense of this name) may explain this change of the wave functions in a "causal" way (as a result of some evolution equation), but I do not think that is what you meant.

 

[BruceW]

You may walk away with an incorrect conclusion depending on how you interpret some of the statements above.

1. Classical causality has been soundly refuted and there are no standing interpretations generally accepted otherwise.

2. Deterministic interpretations today are all non-local.
...

This looks very interesting, thanks for replying. But still I don't understand what is meant by several things. "Classical Causality" - no idea. "Deterministic interpretations are non-local" - This is Bell's theorem, right? We can't have a local theory of hidden variables. So now I'm guessing that "Classical Causality" means "local and deterministic", which is not allowed because of Bell's theorem.

Classically, one would think that correlations between distant events would be due to correlations prepared in the common past light cone of these events. This is often called local causality, or EPR-Bell locality. But quantum mechanics has wave function collapse, and violates local causality. Surprisingly, we still cannot use it to send information faster than light, and quantum mechanics is consistent with relativity. So there are at least two notions of causality - classical local causality, and the wider notion of relativistic causality, as discussed eg. by http://arxiv.org/abs/quant-ph/9508009.

Right, so the classical local causality is what Bell refers to as "local causality". And the standard QM is not locally causal. And what is the other idea of causality you mention? Is it just the idea that "QM does not give us a method for faster-than-light communication" ? I've skim-read a couple of papers that describe why this is true, given that the classical phenomena itself travels at the speed of light or less. Still, it does seem quite surprising. I would hope (someday) that there will be some overarching principle which automatically explains both ideas.

 

[vanhees71]

Initial value problem with the Schroedinger equation may have unique solution. As I understand, you call that "causal".
When we calculate the spin wave function this way, we obtain unique result $\boldsymbol \psi_1$ giving probability density in space symmetrical in $z$.

But this calculated $\boldsymbol\psi_1$ is appropriate only before the measurement of the z coordinate takes place; after the measurement, we know the appropriate pair of wave functions in space is no longer that calculated in the above way. Based on the result of the measurement, the best choice is asymmetric pair where one component carries most of the probability and its density is localized asymmetrically in z.

This new pair of wave functions $\boldsymbol \psi_2$ cannot be obtained from the Schroedinger equation in a "causal" way. It is chosen based on the result of the measurement, which is random, not causal in quantum theory.

Another theory (not quantum theory in the usual sense of this name) may explain this change of the wave functions in a "causal" way (as a result of some evolution equation), but I do not think that is what you meant.

Sure, the "measurement" here is done by filtering out one beam (it's the paradigmatic example for what's called an ideal von Neumann filter measurement which is at the same time a preparation procedure to produce a beam with determined spin-z component). Of course, this is not described by the simple Schrödinger equation, because I didn't inclue the filter. If you'd include the whole apparatus, you'd have to solve a complicated many-body quantum problem, but in principle then the entire dynamics is described by causal equations.

Analogously, even in a classical description, you wouldn't describe the measurement, if you wouldn't include the interaction of the particle with the measurement apparatus or filter in this case.

There's nothing mysterious about measurement apparati. In contrast to Bohr, I don't think that a cut between a quantum dynamics and classical dynamics makes sense. Anything is quantum, according to our understanding today, and the classical behavior of macroscopic systems (including measurement apparati) is emergent and can be understood by decoherence.

The main difference between quantum theory and classical theory is that the complete possible knowledge about a system (encoded in the quantum theoretical formalism as a ray in an appropriate Hilbert space) is only probabilistic, i.e., not all observables can have determined values (according to the Heisenberg-Robertson uncertainty relation). That's why I call quantum theory causal but indeterministic. Again, I recommend to read the introductory part of

J. Schwinger, Quantum Mechanics, Symbolism for Atomistic Measurements, Springer (2001)

It's the best introduction to a quantum-mechanics text I've ever read, although it's without math, which after that is introduced in a marvelous way. It's an unusual but very illuminating approach to quantum theory. I'd recommend it as a very good read for advanced students who have learned QT from a more conventional approach. The best thing about this book is that it does start with the representation-free formulation. The same approach is followed in Sakurai's textbook, which I'd recommend as a first book on quantum theory.

 

[DrChinese]

This looks very interesting, thanks for replying. But still I don't understand what is meant by several things. "Classical Causality" - no idea. "Deterministic interpretations are non-local" - This is Bell's theorem, right? We can't have a local theory of hidden variables. So now I'm guessing that "Classical Causality" means "local and deterministic", which is not allowed because of Bell's theorem.

All good. "Classical" can mean a variety of things according to context, as it is always a reference to an earlier perspective. In this case, the view in 1935 (when EPR was written) was that nothing could exceed the speed of light. So classical meant local in this context.

The easiest thing is to realize that 2 people must agree on some definition of locality/separability/hidden variables/determinism/causality/whatever you want to call it etc. in order to have Bell's Theorem make sense. The beauty of EPR and Bell is that despite the somewhat arcane language, the argument comes through regardless. Since, many alternate definitions have been floated and many "improved" versions of the arguments have been presented. And yet, in the end, none are accepted over the originals.

 

[naima]

I often read that local theories cannot describe reality.
Could you tell me if Haag's local theory could be disproofed
http://en.wikipedia.org/wiki/Local_quantum_field_theory

 

[bhobba]

I often read that local theories cannot describe reality.

Where do you get that from.

QFT is based on the cluster decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

But as the link shows its subtle.

Thanks
Bill

 

[atyy]

I often read that local theories cannot describe reality.
Could you tell me if Haag's local theory could be disproofed
http://en.wikipedia.org/wiki/Local_quantum_field_theory

I'll eat my hat if Haag's theory is disproved :D

The sense of local in Haag is the observables at spacelike separation should commute, eg. http://arxiv.org/abs/1303.2849 (footnote 1). This notion of locality can violate the Bell inequalities, so it is nonlocal in that sense.

However, QM has two notions of nonlocality. The first is the typical tensor product idea, and from there we get that the maximum CHSH is $2\sqrt{2}$, which is the Tsirelson bound http://en.wikipedia.org/wiki/Tsirelson's_bound. However, it is not known whether the bound is the same if we define it using the notion of spacelike commutation, which is called Tsirelson's problem http://www.tau.ac.il/~tsirel/Research/bellopalg/main.html.

 

[atyy]

Right, so the classical local causality is what Bell refers to as "local causality". And the standard QM is not locally causal. And what is the other idea of causality you mention? Is it just the idea that "QM does not give us a method for faster-than-light communication" ?

Yes. This is also known as "no signalling".

I've skim-read a couple of papers that describe why this is true, given that the classical phenomena itself travels at the speed of light or less. Still, it does seem quite surprising. I would hope (someday) that there will be some overarching principle which automatically explains both ideas.

Even more surprising to me is that a theory that is even more nonlocal than QM can be consistent with no signalling. This was discovered by Popescu and Rohrlich.

 

[DrChinese]

I often read that local theories cannot describe reality.
Could you tell me if Haag's local theory could be disproofed
http://en.wikipedia.org/wiki/Local_quantum_field_theory

I have never heard of Haag. It originated pre-Bell. Assuming it is also intended to be realistic, Bell would be all you need to disprove it. Keep in mind that we have an excellent standard model, so any alternative model is going to need something spectacular to gain any attention.

 

[atyy]

I have never heard of Haag. It originated pre-Bell. Assuming it is also intended to be realistic, Bell would be all you need to disprove it. Keep in mind that we have an excellent standard model, so any alternative model is going to need something spectacular to gain any attention.

Haag is one of the axiomatic formulations of QFT. So it is not realistic, because it is just quantum theory. The sense of locality in Haag is that spacelike observables commute, which is different from the local realism addressed by Bell. So Haag is local quantum theory in the sense of relativistic quantum theory, which is non-local in the sense of Bell.

http://ncatlab.org/nlab/show/Haag-Kastler axioms
"Therefore this translates into the axiom: quantum fields on a spacetime form an isotonic copresheaf of algebras such that the algebras assigned to any two spacelike separated regions commute with each other inside the algebra assigned to any larger region containing these two regions."

A remaining open issue is that when we say QM maximally violates CHSH with $2\sqrt{2}$ (Tsirelson's bound), this is proved using tensor products and finite dimensional Hilbert spaces. However, the Hilbert space of interacting QFT is infinite dimensional, and it is not known whether the QM bound is still $2\sqrt{2}$. This is Tsirelson's problem http://www.tau.ac.il/~tsirel/Research/bellopalg/main.html.

 

[Jano L.]

Of course, this is not described by the simple Schrödinger equation, because I didn't inclue the filter. If you'd include the whole apparatus, you'd have to solve a complicated many-body quantum problem, but in principle then the entire dynamics is described by causal equations.

Describing the apparatus and the atom by one wave function only makes the description more removed from experimental physics. Some dynamics would be described by such complicated differential equations. But it is not very clear that the result would be that the atom actually gets definite spin state and gets deflected towards one of the two z coordinates. The result of such computation would most probably be that the whole system atom + apparatus has wave function where there is some superposition of exclusive possibilities which is never observed. This is not physics. The fact that we get definite result for the z coordinate still needs to be put by hand.

Anything is quantum, according to our understanding today, and the classical behavior of macroscopic systems (including measurement apparati) is emergent and can be understood by decoherence.

I do not think this has ever been accomplished. But I could be wrong - can you suggest a paper that does that?

complete possible knowledge about a system (encoded in the quantum theoretical formalism as a ray in an appropriate Hilbert space) is only probabilistic, i.e., not all observables can have determined values (according to the Heisenberg-Robertson uncertainty relation).

It seems you are contradicting yourself here. Above you said that everything, even the apparatus, can be described by causal equations. Now you imply some states of the apparatus do not have determined values...?

 

[vanhees71]

Well, the deduction of the classical laws for many-body systems is standard. A very good introduction to this is Landau+Lifshitz vol. X, where the kinetic (Botlzmann) equation is derived from (non-relativistic) quantum-field theory. In our community (theory relativistic heavy-ion collisions) everybody learns this from the excellent paper

Danielewicz, P.: Quantum Theory of Nonequilibrium Processes I, Ann. Phys. 152, 239 (1984)

 

[Johan0001]

"Chaos: When the present determines the future, but the approximate present does not approximately determine the future"

When observing the properties of microscopic "particles" we currently have no practical way of completely defining the initial conditions of the closed system. This is inevitable.

It follows that we could never say (with 100 % certainty) that the state of the system in an experiment , is exactly the same state, as the same experiment done many times over previously.

Would I be correct in saying that this is a direct result of decoherence with the environment at the time of observation?

In fact would this not apply to all Theories whether QM or Classical. All theories are just an approximation of repeated observations.
Yet QM still defines the notion of mixed states before observation. How does this improve/advance science as we know it.

If we do not know whether the cat is dead or alive before actually observing. Why does it make sense to say it is in a mixed superposition of states i.e. alive and dead , until we look?

.

 

[vanhees71]

According to quantum theory a completely determined state is something else than an exact point in phase space. That's why it is so important to distinguish causality and determinism.

 

[BruceW]

There's nothing mysterious about measurement apparati. In contrast to Bohr, I don't think that a cut between a quantum dynamics and classical dynamics makes sense. Anything is quantum, according to our understanding today, and the classical behavior of macroscopic systems (including measurement apparati) is emergent and can be understood by decoherence.

There must be a cut, or we would not be able to assign a certain probability to our measurement apparatus giving one answer or another. If we had decoherence only, and no cut, then there would be no probabilities in quantum mechanics. (Unless we made some other changes to the standard QM, like using hidden variables, or many-worlds, e.t.c.)