Quantum state: Reality or mere probability?

In summary: If we can measure something at any moment we wish, and we always obtain the same result, why would we think those properties do not actually exist until we intrude with our measuring apparatus?"This is why I advocate a more relaxed view of the theorem in that the assumption of preparation independence is not necessary for the theorem to apply. In fact, the theorem is simply a re-statement of Gleasons Theorem, as noted in the OP, which does not require preparation independence.I'm not a fan of the preparation independence assumption, but the theorem itself is great.ThanksBillIn summary, the recent PBR theorem provides a strong argument that the quantum state is real and not just a mathematical tool for making predictions. This elev
  • #1
Demystifier
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There is an old controversy in quantum mechanics, with arguments on the borderline between science and philosophy, on the question whether the quantum state describes an objective reality associated with a single system, or mere probability describing properties of a large ensemble of equally prepared systems. The recent PBR theorem* provides the strongest argument so far that the quantum state is real, which elevates the controversy to a higher scientific level.

Here I attach the presentation of a recently presented talk, in which these things are explained at a level suitable for a general physicist audience.

*M.F. Pusey, J. Barrett, T. Rudolph, Nature Phys. 8, 476 (2012); arXiv:1111.3328 (v3)
 

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  • #2
Can it be said that the Bohmian answer to this question is reality and mere probability?
 
  • #3
Demystifier:

On page 18, I see that the 4 outcomes 00, 0+, +0, and ++ should be consistent with any initial preparation of 0/+ for the 2 similar systems. The choice of how to measure these 2 should not rule those out.

I see that the 4 phi options consistent with QM's predictions rule each rule out 1 of those outcomes. All 4 are rules out by an phi option.

What I don't understand is how the 4 phi options are constructed in some kind of setup. The first and forth, phi 1 and 4, looks like a traditional entangled state description.

What do the other 2 map to? Can you enlighten me in any way? And it seems as it the 2 systems are prepared in a known state that they couldn't be entangled. If they are separate, they seem classical. Help! :smile:
 
  • #4
Demystifier said:
The recent PBR theorem* provides the strongest argument so far that the quantum state is real, which elevates the controversy to a higher scientific level.

What definition of "real" are we using here? In any case, I don't see why any equation that describes something probabilistically would necessarily imply the thing it describes is not precisely defined both spatially and temporally. We can describe rain probabilistically, but that doesn't mean every drop of water doesn't actually have a unique position and standard properties at every point in time, until it hits the ground.
 
  • #5
Jabbu said:
What definition of "real" are we using here?

Good point.

To fully understand the theorem and its implications you need to go back to the original paper:
http://arxiv.org/pdf/1111.3328v2.pdf

'Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a 'real physical state' not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes. The other main assumption is that systems that are prepared independently have independent physical states.'

Also we have a very beautiful theorem, called Gleason's Theorem, that shows the state is really a requirement of what observations in QM are - see post 137:
https://www.physicsforums.com/showthread.php?t=763139&page=8

The foundational principle is:
An observation/measurement with possible outcomes i = 1, 2, 3 ... is described by a POVM Ei such that the probability of outcome i is determined by Ei, and only by Ei, in particular it does not depend on what POVM it is part of.

That completely bypasses the real physical state assumption of the theorem. The state is simply a mathematical device that helps us calculate those probabilities.

Its the view of the Copenhagen-information interpretation mentioned in Dymystifyers paper - although my view is not Copenhagen which associates a state with subjective knowledge - I associate it with an ensemble view as in the ensemble interpretation. It not a biggie though IMHO - its basically the same as frequentest and Bayesian type interpretations of Kolmogorov's probability axioms.

That said, its still a very important theorem worthy of the praise it received.

And guys like Schlosshauer have extended it in an interesting way elucidating the kind of interpretations that it applies to and those that evade it:
http://arxiv.org/pdf/1306.5805v3.pdf

Thanks
Bill
 
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  • #6
atyy said:
Can it be said that the Bohmian answer to this question is reality and mere probability?

I would say BM is real, and completely deterministic. Probabilities simply result from lack of knowledge of initial conditions.

Thanks
Bill
 
  • #7
bhobba said:
'Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on few assumptions. One is that a system has a 'real physical state' not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes. The other main assumption is that systems that are prepared independently have independent physical states.'

If "non-locality" is the same thing as "action at distance", then everything can still be uniquely defined at every point in time.

If we can measure something at any moment we wish, and we always obtain the same result, why would we think those properties do not actually exist until we intrude with our measuring apparatus? It's like saying there are no rain drops in the rain until they hit the ground.
 
  • #9
Jabbu said:
If "non-locality" is the same thing as "action at distance", then everything can still be uniquely defined at every point in time.

Non locality in QM is much more subtle than that. Its exact expression is the so called cluster decomposition property:
https://www.physicsforums.com/showthread.php?t=547574

Classically though you are correct, as for example the early pages of Landau's beautiful book - Mechanics - explains - instantaneous action at a distance is encoded into the foundations of classical mechanics.

You really need to go to relativity for it to be an issue - and when you do that - that's when you come face to face with the Cluster Decomposition Property. BUT that only applies to uncorrelated systems. And correlation in QM is much more subtle than classically - as shown by Bells Theorem.

Jabbu said:
If we can measure something at any moment we wish, and we always obtain the same result

But QM says you don't always obtain the same result except in very simple situations eg in EPR type situations where if you measure it's spin as up for example and conduct the same measurement again it will always be spin up. Most of the time however the state changes eg for a free particle if you measure its position exactly, the wave-function spreads so you can't say anything about its later position.

Thanks
Bill
 
  • #10
bhobba said:
Non locality in QM is much more subtle than that.

Isn't Bohmian mechanics direct contradiction to that? And if Bohmian mechanics is possible answer, then classical QM can't really exclude the possibility things do actually exist even if no one is looking.


But QM says you don't always obtain the same result except in very simple situations eg in EPR type situations where if you measure it's spin as up for example and conduct the same measurement again it will always be spin up. Most of the time however the state changes eg for a free particle if you measure its position exactly, the wave-function spreads so you can't say anything about its later position.

Yeah, but if photons are supposed to always move at c, that means their path from point of interaction to another point of interaction must always be a precisely defined straight line, the shortest distance or geodesic. I don't see how we can define our unit of distance with the speed of light and then say photons really travel over many possible paths, at once, or something among those lines.
 
  • #11
Jabbu said:
If we can measure something at any moment we wish, and we always obtain the same result, why would we think those properties do not actually exist until we intrude with our measuring apparatus? It's like saying there are no rain drops in the rain until they hit the ground.

In quantum mechanics, we can measure position and momentum, but we can also show that position and momentum are not uniquely defined at all times. For this reason, position and momentum are not "real" until they are measured.

However, this does not mean that the system is not fully and uniquely defined by "true properties" that exist at all times. It's just that those true properties are not position and momentum. Let X represent the true properties of the system, and let ψ represent the wave function.

In the definition of reality used in this paper, ψ is real if knowing X uniquely specifies ψ. On the other hand, ψ is at least partly a matter of belief if knowing X does not uniquely specify ψ.
 
  • #12
atyy said:
In quantum mechanics, we can measure position and momentum, but we can also show that position and momentum are not uniquely defined at all times. For this reason, position and momentum are not "real" until they are measured.

That would be good enough reason, but how can we show position and momentum are not uniquely defined at all times?
 
  • #13
Jabbu said:
That would be good enough reason, but how can we show position and momentum are not uniquely defined at all times?

If we have a state and we measure position x we get some distribution F(x). If we have the same state and we measure momentum p we get another distribution G(p). If the particles in the state have simultaneous position and momentum, then we should be able to write a joint distribution W(x,p), such that F(x) = ∫W(x,p)dp and G(p) = ∫W(x,p)dx. But we cannot. We can find a W(x,p), but we find that W is not always positive, and so cannot be a probability density. This W is called the Wigner function.
http://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution
http://dspace.mit.edu/bitstream/handle/1721.1/49800/50586846.pdf [Broken]
 
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  • #14
atyy said:
If we have a state and we measure position x we get some distribution F(x). If we have the same state and we measure momentum p we get another distribution G(p). If the particles in the state have simultaneous position and momentum, then we should be able to write a joint distribution W(x,p), such that F(x) = ∫W(x,p)dp and G(p) = ∫W(x,p)dx. But we cannot.

If we catch an electron or photon with a sensor, don't we measure both their position and momentum, and isn't it their momentum always equally proportional to electron speed and photon wavelength?
 
  • #15
Jabbu said:
Isn't Bohmian mechanics direct contradiction to that?

Why would you think that?

Thanks
Bill
 
  • #16
Jabbu said:
Yeah, but if photons are supposed to always move at c, that means their path from point of interaction to another point of interaction must always be a precisely defined straight line, the shortest distance or geodesic. I don't see how we can define our unit of distance with the speed of light and then say photons really travel over many possible paths, at once, or something among those lines.

Photons are problematical in basic QM because there is no frame where they are at rest.

We define our unit of distance via classical EM without QM issues.

Thanks
Bill
 
  • #17
DrChinese said:
What I don't understand is how the 4 phi options are constructed in some kind of setup. The first and forth, phi 1 and 4, looks like a traditional entangled state description.

What do the other 2 map to? Can you enlighten me in any way?
If you ask me how to do it in the laboratory, then I don't know. Perhaps the PBR guys who invented this thought experiment know better. At the botton of page 4 you will also see a reference to an experimental realization of this.

DrChinese said:
And it seems as it the 2 systems are prepared in a known state that they couldn't be entangled. If they are separate, they seem classical. Help! :smile:
The two systems are initially prepared in a classical non-entangled state, but the meassurement is performed in a non-classical entangled basis. In other words, the measurement makes them entangled. This should not be surprising, because measurement in a specific basis can often be viewed as a preparation.
 
  • #18
Jabbu said:
That would be good enough reason, but how can we show position and momentum are not uniquely defined at all times?

We can't show a negative like that.

All we know is no one has ever been able to figure out how measure the position of a photon.

Intuitively such would seem rather difficult for a particle that always, regardless of frame, travels at c. But you are most welcome to give it a try. The bugbear is while photons can be made to interact at a point, it is always destroyed by such, so you can't say it had such and such position.

Thanks
Bill
 
  • #19
bhobba said:
Why would you think that?

Thanks
Bill

Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing. The guiding wave thing looks more like "hidden variable" type of thing, something unknown rather than non-local.
 
  • #20
Jabbu said:
Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing.

Again I can't follow your concern.

I said that non locality is subtle in QM.

BM has this inherently unobservable pilot wave that's non local - sounds rather subtle to me.

But - yes BM and the cluster decomposition property requires a bit of analysis - I am not an expert on that - best to ask Dymystifyer about it.

Thanks
Bill
 
  • #21
Jabbu said:
Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing. The guiding wave thing looks more like "hidden variable" type of thing, something unknown rather than non-local.
This was brought up previously in Demystefier's blog, but are bohmian trajectories any more "hidden" than the wave function?

Bohmian trajectories are no longer "hidden variables"
https://www.physicsforums.com/blog.php?b=3622&goto=prev [Broken]

Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer
http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf [Broken]
 
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  • #22
Jabbu said:
If we catch an electron or photon with a sensor, don't we measure both their position and momentum, and isn't it their momentum always equally proportional to electron speed and photon wavelength?

Let's stick with electrons here, because talking about photon position is tricky. If you wish to think of an electron as a wave, and momentum as proportional to wavelength, then one way to see it is that a wave with a well defined wavelength cannot be precisely localized in space. The position-momentum uncertainty principle in quantum mechanics is mathematically exactly the same as time-frequency uncertainty in classical signal processing.
 
  • #23
Jabbu said:
Because of deterministic causality and continuous trajectories, which I think imply whatever it is moving along those paths is defined and existing.

If you assume deterministic causality, continuous trajectories make sense. If you assume continuous trajectories, then determinism is your likely conclusion. Circular reasoning, although a common viewpoint.

However, a lot of analyses question both of these assumptions/conclusions. The most obvious thing about determinism is that every quantum outcome appears completely random (and has no known cause). So the data is against you. If you could demonstrate a violation of the HUP, you might have something. Barring that, it is just your faith and nothing else.
 
  • #24
Several authors like Fuchs say that "there is no quantum states" only probabilities.
They argue that (according to Gleason Bush) a state is only a set of probabilities.

I read in scientific american (Fuchs june 2013): Quantum states are only tools used to calculate our personal confidence in outputs
The problem is that in interferometry, you cannot get probabilities without adding those quantum states.
I never found someone hereagreeing with Fuch's opinion. Could anyone be the devil's advocate?
 
  • #25
naima said:
Several authors like Fuchs say that "there is no quantum states" only probabilities.
They argue that (according to Gleason Bush) a state is only a set of probabilities.

I read in scientific american (Fuchs june 2013): Quantum states are only tools used to calculate our personal confidence in outputs
The problem is that in interferometry, you cannot get probabilities without adding those quantum states.
I never found someone hereagreeing with Fuch's opinion. Could anyone be the devil's advocate?

As a Bohmian, I agree fully with Fuchs! If degrees of freedom can be emergent, then so can ontology:)

Maybe a more serious question to which I don't know the answer - can we take the Bohmian quantum equilibrium distribution in the sense of subjective probability, say de Finetti? If so, then can we make Bohmian mechanics subjective too?

Actually, Wiseman had some comments on subjective probability in Bohmian mechanics, but I think along somehwat different lines: http://arxiv.org/abs/0706.2522.
 
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  • #26
What I don't understand is the no crossing rule obeyed in Bohmian trajectories. Since the non-crossing is with respect to configuration space why do some authors (e.g. Sanz) argue that the no-crossing offers insights that the more orthodox interpration does not. This appears to suggest that, in some ways, the bohemian trajectories are less "hidden" than the wave function:
In that sense, even though the trajectories reconstructed from the experiment cannot be associated with the paths followed by individual photons, but with electromagnetic energy streamlines, the experiment constitutes an important milestone in modern physics. The fact that the trajectories do not cross means that, at the level of the average electromagnetic field (or the wave function, in the case of material particles, in general), full which-way information can still be inferred without destroying the interference pattern. That is, rather than complementarity, the experiment seem to suggest that superposition has a tangible (measurable) physical reality [14], in agreement with a recent theorem on the realistic nature of the wave function [15].
How does light move? - Determining the flow of light without destroying interference
http://www.europhysicsnews.org/articles/epn/pdf/2013/06/epn2013446p33.pdf

A trajectory-based understanding of quantum interference
http://arxiv.org/pdf/0806.2105v2.pdf

Particles, waves and trajectories: 210 years after Young's experiment
http://arxiv.org/pdf/1402.3877.pdf

Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf

Quantumness beyond quantum mechanics
http://arxiv.org/pdf/1202.5181.pdf

Any insights would be appreciated as I might be misinterpreting this.
 
  • #27
bohm2 said:
What I don't understand is the no crossing rule obeyed in Bohmian trajectories. Since the non-crossing is with respect to configuration space why do some authors (e.g. Sanz) argue that the no-crossing offers insights that the more orthodox interpration does not. This appears to suggest that, in some ways, the bohemian trajectories are less "hidden" than the wave function:

How does light move? - Determining the flow of light without destroying interference
http://www.europhysicsnews.org/articles/epn/pdf/2013/06/epn2013446p33.pdf

A trajectory-based understanding of quantum interference
http://arxiv.org/pdf/0806.2105v2.pdf

Particles, waves and trajectories: 210 years after Young's experiment
http://arxiv.org/pdf/1402.3877.pdf

Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf

Quantumness beyond quantum mechanics
http://arxiv.org/pdf/1202.5181.pdf

Any insights would be appreciated as I might be misinterpreting this.

In this view, Bohmian trajectories are not any more real than virtual particles, which are just intermediate steps in a calculation. Just as the virtual particles picture made things easier for Feynman, the Bohmian trajectories make things easier for some people. Everything calculated by Bohmian trajectories can be calculated by standard Copenhagen quantum mechanics. (This is completely tangential to the real problem solved by Bohm - that there is at least one interpretation of quantum mechanics without observers.)

Also, the first link asks http://www.europhysicsnews.org/articles/epn/pdf/2013/06/epn2013446p33.pdf "According to the complementarity principle, complementary aspects of quantum systems cannot be measured at the same time by the same experiment. This has been a long debate in quantum mechanics since its inception. But is this a true constraint?" The answer to that is yes, it is a true constraint: http://arxiv.org/abs/1304.2071.
 
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  • #28
Thanks, atyy. That was what I understood but why does A. S. Sanz et al. claim the following (and note the hi-lited part (e.g. from a theoretical point of view" on p. 7. I didn't understand how they can make that claim. Are their arguments just plainly wrong?
As seen above, quantum coherence and its Bohmian effect, namely the non-crossing property, allow us to discern the slit traversed by a particle without disturbing it in two-slit experiments, at least from a theoretical point of view.
Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf
 
  • #29
Demystifier said:
The two systems are initially prepared in a classical non-entangled state, but the meassurement is performed in a non-classical entangled basis. In other words, the measurement makes them entangled. This should not be surprising, because measurement in a specific basis can often be viewed as a preparation.

How is "entangled" state accounted for in cos^2(theta), wouldn't that equation predict the same coincidence rate for both entangled and non-entangled systems?
 
  • #30
bohm2 said:
Thanks, atyy. That was what I understood but why does A. S. Sanz et al. claim the following (and note the hi-lited part (e.g. from a theoretical point of view" on p. 7. I didn't understand how they can make that claim. Are their arguments just plainly wrong?

Quantum phase analysis with quantum trajectories: A step towards the creation of a Bohmian thinking
http://arxiv.org/pdf/1104.1296.pdf

I think they just mean that because the trajectories are non-crossing, particles detected in the left side of the screen must come from the left slit, and particle detected from the right side of the screen must come from the right slit, which seems to me correct if non-crossing in ordinary space holds.
 
  • #31
This quote from Einstein presents his views on the issue more clearly than the presetation attempts to:
Einstein said:
Consider a mechanical system consisting of two partial systems A and B which interact with each other only during a limited time. ψ is the wavefunction before their interaction. One performs measurements on A and determines A's state. Then B's ψ function of the partial system B is determined from the measurement made, and from the ψ function of the total system. This determination gives a result which depends upon which of the observables of A have been measured (coordinates or momenta). That is, depending upon the choice of observables of A to be measured, according to quantum mechanics we have to assign different quantum states ψB and ψB' to B. These quantum states are different from one another. After the collision, the real state of (AB) consists precisely of the real state A and the real state of B, which two states have nothing to do with one another. The real state of B thus cannot depend upon the kind of measurement I carry out on A. But then for the same state of B there are two (in general arbitrarily many) equally justified ψB, which contradicts the hypothesis of a one-to-one or complete description of the real state.
Since there can be only one physical state of B after the interaction which cannot reasonably be considered to depend on the particular measurement we perform on the system A separated from B it may be concluded that the ψ function is not unambiguously coordinated to the physical state.
This coordination of several ψ functions to the same physical state of system B shows again that the ψ function cannot be interpreted as a (complete) description of a physical state of a single system. Here also the coordination of the ψ function to an ensemble of systems eliminates every difficulty.
 
  • #32
atyy said:
I think they just mean that because the trajectories are non-crossing, particles detected in the left side of the screen must come from the left slit, and particle detected from the right side of the screen must come from the right slit, which seems to me correct if non-crossing in ordinary space holds.
But, if that is the case, then it appears to provide us with more information than the orthodox view. In the orthodox view we cannot have such information, because the diffraction is lost if we look. So in a sense (if their arguments are correct) this appears to suggest that, in some ways, the bohmian trajectories are less "hidden" than the wave function. But I don't see how no-crossing over on configuration space allows one to claim that in fact, there is no-crossing over in ordinary space and infer "which slit" the particle went through without looking. I would think that this would be a pretty major finding.
 
  • #33
bhobba said:
The bugbear is while photons can be made to interact at a point, it is always destroyed by such, so you can't say it had such and such position.
I won't even say it has to do with the longevity of photons after they are measured. I think we sometimes mystify the situation more than is necessary. Momentum, like velocity is a vector. It is mathematically undefined at a single point, let alone being able to measure it at a single point. It's like trying to determine a person's behavior from a photograph.

But coming back to PBR, the two possibilities given in the presentation, are:
1- knowledge of lambda determines p(head) and p(tail) uniquely (ontic)
2- knowledge of lambda not enough to determine p(head) and p(tail) uniquely (epistemic)
appear to be criteria for completeness rather than definitions ontic/epistemic. In the second case, lambda is incomplete as far as the prediction of p(head) and p(tail). In the first p(head)/p(tail) is limited to the coin only, in second p(head)/p(tail) is describing the coin and the tossing mechanism.
 
  • #34
bohm2 said:
But, if that is the case, then it appears to provide us with more information than the orthodox view. In the orthodox view we cannot have such information, because the diffraction is lost if we look. So in a sense (if their arguments are correct) this appears to suggest that, in some ways, the bohmian trajectories are less "hidden" than the wave function. But I don't see how no-crossing over on configuration space allows one to claim that in fact, there is no-crossing over in ordinary space and infer "which slit" the particle went through without looking. I would think that this would be a pretty major finding.

I think ordinary space is a type of configuration space, where the dimensions are just labelled by coordinates. In contrast, phase space or state space in classical mechanics has dimensions labelled by positions and momenta.

I looked at the trajectories in http://scienceblogs.com/principles/2011/06/03/watching-photons-interfere-obs/ and it seems correct that one can get an interference pattern, and from the interference pattern know which slit a particle has come from.

To be honest, I have never understood the traditional formulation in which obtaining "which way" information prevents the interference pattern from forming. Is it a heuristic, or is there an equation that one can actually derive from quantum mechanics to show it? To me, when you do a different experiment and place a detector in front of one slit, then you block the slit, so it becomes a single slit interference. We had a long discussion in https://www.physicsforums.com/showthread.php?t=762601, and I don't think anyone pointed me to an exact mathematical formulation of the principle. Here is an interesting related thread started by RUTA https://www.physicsforums.com/showthread.php?t=765772.
 
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  • #35
billschnieder said:
1- knowledge of lambda determines p(head) and p(tail) uniquely (ontic)
2- knowledge of lambda not enough to determine p(head) and p(tail) uniquely (epistemic)

Why are we unable to experimentally confirm whether knowledge of lambda determines p(head) and p(tail) uniquely, or not?
 
<h2>1. What is a quantum state?</h2><p>A quantum state is a mathematical description of a quantum system, which includes all the possible states that the system can be in. It is represented by a vector in a complex vector space and contains information about the system's physical properties such as position, momentum, and spin.</p><h2>2. Is a quantum state a physical reality?</h2><p>This is a highly debated question in the field of quantum mechanics. Some scientists argue that the quantum state is a physical reality, meaning that it represents the true state of the system. Others argue that it is merely a mathematical representation of our knowledge and understanding of the system, and does not necessarily reflect its true physical state.</p><h2>3. Can a quantum state exist in multiple states at once?</h2><p>According to the principle of superposition in quantum mechanics, a quantum state can exist in multiple states simultaneously. This means that until a measurement is made, the system can exist in a combination of all the possible states it can be in.</p><h2>4. What is the role of probability in quantum states?</h2><p>Probability plays a crucial role in quantum states as it determines the likelihood of a particular state being observed when a measurement is made. The probability of a state is represented by the square of its amplitude in the quantum state vector.</p><h2>5. How do we determine the quantum state of a system?</h2><p>The quantum state of a system can be determined through various methods, such as performing measurements and observations, using mathematical equations and models, and conducting experiments. However, due to the probabilistic nature of quantum mechanics, it is impossible to determine the exact state of a system at any given time.</p>

1. What is a quantum state?

A quantum state is a mathematical description of a quantum system, which includes all the possible states that the system can be in. It is represented by a vector in a complex vector space and contains information about the system's physical properties such as position, momentum, and spin.

2. Is a quantum state a physical reality?

This is a highly debated question in the field of quantum mechanics. Some scientists argue that the quantum state is a physical reality, meaning that it represents the true state of the system. Others argue that it is merely a mathematical representation of our knowledge and understanding of the system, and does not necessarily reflect its true physical state.

3. Can a quantum state exist in multiple states at once?

According to the principle of superposition in quantum mechanics, a quantum state can exist in multiple states simultaneously. This means that until a measurement is made, the system can exist in a combination of all the possible states it can be in.

4. What is the role of probability in quantum states?

Probability plays a crucial role in quantum states as it determines the likelihood of a particular state being observed when a measurement is made. The probability of a state is represented by the square of its amplitude in the quantum state vector.

5. How do we determine the quantum state of a system?

The quantum state of a system can be determined through various methods, such as performing measurements and observations, using mathematical equations and models, and conducting experiments. However, due to the probabilistic nature of quantum mechanics, it is impossible to determine the exact state of a system at any given time.

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