Is uncertainty inherent in QM?

In summary: The summary of the content suggests that the uncertainty principle is not due to lack of knowledge but because it is impossible to have a particle with well defined position and momentum at the same time. The uncertainty principle states that it is impossible for a particle to have a specific position and also a specific velocity.
  • #1
San K
911
1
For example let's look at a single particle, double slit experiment:

we know that the particle (photon/electron) will land up on one of the fringes. however it is commonly understood that we cannot predict which of the fringes will it land up on.

one could argue that since there was uncertainty in the initial conditions of the photon its that same uncertainty that is being projected on the screen, thus there is no inherent uncertainty because we did not know the exact position of the photon to being with.

we just knew that it has a probability distribution and that same distribution is being projected on the screen after "interaction" with the slits.

The question is:

if we knew the exact starting position (co-ordinates) and state (spin, direction of velocity etc)

could we predict the particle's location (co-ordinates) on the screen?The question is:

is uncertainty inherent in QM

or

is it because of our lack of knowledge (and inability of the current state of art) of the exact "starting/initial" position of the photon prior to leaving on its journey towards the slit?
 
Last edited:
Physics news on Phys.org
  • #2
First of all, there's nothing in QM that says that particles have positions at all times. So it probably doesn't even make sense to say that the particle has a position, known or unknown, at the start of the experiment.

What we can do is to prepare a particle such that the probability that it will be detected outside of some small region immediately after the preparation is very close to zero. The problem is that as we make that region smaller, it will actually be harder to predict where the particle will eventually be detected. This is precisely the sort of thing that the uncertainty relations describe quantitatively.

Regarding the lack of knowledge/technology...there is clearly no technology that can invalidate a mathematical proof, and the uncertainty relations are theorems in QM. (That's why I never use the term "principle" in this context). If someone invents technology that enables us to violate an uncertainty relation, it would mean that we have found a type of experiment where QM is useless, like how Newton's theory of gravity is useless when we want to calculate time dilation or the orbital decay of a binary pulsar. This could happen, but there's no reason to think that the new theory that we would have to invent to replace QM would be more intuitive than QM. I would bet that it's less intuitive.
 
Last edited:
  • #3
San K said:
if we knew the exact starting position (co-ordinates) and state (spin, direction of velocity etc)

The problem is that photons, and particles generally, cannot have well-defined values for all these properties at once. This is the uncertainty principle. It isn't possible for a particle to have a specific position and also a specific velocity.

This isn't due to lack of knowledge but because there does not exist a state for the particle in which it has both well defined position and well-defined momentum.
 
  • #4
Fredrik said:
First of all, there's nothing in QM that says that particles have positions at all times. So it probably doesn't even make sense to say that the particle has a position, known or unknown, at the start of the experiment.

What we can do is to prepare a particle such that the probability that it will be detected outside of some small region immediately after the preparation is very close to zero. The problem is that as we make that region smaller, it will actually be harder to predict where the particle will eventually be detected. This is precisely the sort of thing that the uncertainty relations describe quantitatively.

Regarding the lack of knowledge/technology...there is clearly no technology that can invalidate a mathematical proof, and the uncertainty relations are theorems in QM. (That's why I never use the term "principle" in this context). If someone invents technology that enables us to violate an uncertainty relation, it would mean that we have found a type of experiment where QM is useless, like how Newton's theory of gravity is useless when we want to calculate time dilation or the orbital decay of a binary pulsar. This could happen, but there's no reason to think that the new theory that we would have to invent to replace QM would be more intuitive than QM. I would bet that it's less intuitive.

Thanks Fredrick and the duck...well said, and i agree.

the hypothesis that I am trying to test is that:

the interference pattern that is showing up on the screen is a simply an expression/result of the initial (uncertainty or whatever) state of the photon and does not need...

(the hypothesis of) a wave going through both slits and interfering to explain the pattern i.e. it is fully explainable without physical/real waves...(though of course the mathematical construct probability waves are need to carry the uncertainty from the initial state to the screen)
 
Last edited:
  • #5
No mate its not due to a lack of knowledge about initial conditions. QM is an inherently statistical theory. Basically there are two types of stochastic theories ie theories that are fundamentally probabilistic, one like standard probability theory where the so called pure states (they are the possible outcomes of experiments such as the 6 possible outcomes of throwing a dice) that are countable, and one where they are continuous - that is Quantum Mechanics. Nature chose the second one for how the world works at small scales.

Check out:
http://arxiv.org/pdf/quant-ph/0111068v1.pdf

Thanks
Bill
 
  • #6
Here's another way to see that uncertainty is quantum mechanics is fundamental to how it works (and hence should be called indeterminacy rather than uncertainty)-- the "quantum Zeno effect." This effect says that if you continuously monitor some observable (by establishing a definite value for that observable at all times), then the value of that observable can never change. Definiteness = unchangingness, whereas all change in any observable requires that the observable enter a state of indefiniteness in order to be different when it later becomes definite. That's what I'd call an inherent indeterminacy in how observables function, not just our own uncertainty in its ongoing value!
 
  • #7
Ken G said:
Here's another way to see that uncertainty is quantum mechanics is fundamental to how it works (and hence should be called indeterminacy rather than uncertainty)-- the "quantum Zeno effect." This effect says that if you continuously monitor some observable (by establishing a definite value for that observable at all times), then the value of that observable can never change. Definiteness = unchangingness, whereas all change in any observable requires that the observable enter a state of indefiniteness in order to be different when it later becomes definite. That's what I'd call an inherent indeterminacy in how observables function, not just our own uncertainty in its ongoing value!

good example Ken G, thanks. will explore zeno effect further
 
  • #8
The_Duck said:
The problem is that photons, and particles generally, cannot have well-defined values for all these properties at once. This is the uncertainty principle. It isn't possible for a particle to have a specific position and also a specific velocity.

This isn't due to lack of knowledge but because there does not exist a state for the particle in which it has both well defined position and well-defined momentum.

In my opinion the sentence in red is a profound statement, even though this is generally accepted by QM people as normal.

My problem is with the basic definition of velocity or momentum. According to our definition, for a particle to have a velocity it must change its position. Our velocity measurement at a point can never be exact, it can only be probabilistic or approximation, but it is not uncertainty.

This strangeness in velocity may be spilling over into special relativity.

Am I missing something here?
 
  • #9
Neandethal00 said:
In my opinion the sentence in red is a profound statement, even though this is generally accepted by QM people as normal.

My problem is with the basic definition of velocity or momentum. According to our definition, for a particle to have a velocity it must change its position. Our velocity measurement at a point can never be exact, it can only be probabilistic or approximation, but it is not uncertainty.

This strangeness in velocity may be spilling over into special relativity.

Am I missing something here?
You make it sound like it's an obvious fact that velocity "can never be exact." First of all, there are perfectly good theories like classical mechanics, special relativity, and general relativity where position and velocity are both defined exactly for all times. Second of all, in quantum mechanics it's possible to have a totally exact velocity for a particle, all that leads to it position being totally uncertain.
 
  • #10
lugita15 said:
First of all, there are perfectly good theories like classical mechanics, special relativity, and general relativity where position and velocity are both defined exactly for all times.
Actually, I would claim that is something of a myth about those theories. It involves mistaking how physics borrows from mathematics, for physics itself. Those theories only borrow from mathematics the concepts of exact positions and velocities, to take advantage of the rigor so afforded in math, but the physics theories themselves never required any of those things to be exact, were never tested on the basis of them being exact, and really never had access to any kind of empirically supported language in which those concepts were exact. The difference between what is exact and what is uncertain is pretty much the difference between math theorems and physics theories, and the way the latter borrow from the former is often mistaken for an actual attribute of the latter, but it really isn't. That is because physics is empirical in nature, and mathematics is not. Physics tests, math proves, and the testing of no theory ever required that the theory manipulate exact entities. That was always just the math component, and should never have been taken seriously as part of the physics.

If anyone doubts that, just note how easily all three of those theories could be replaced with precisely identical versions in practice that referred to uncertainties in x and p, centered on some x and p, and how those evolve in time. Such a version would be completely indistinguishable from those theories, would be tested in exactly the same way, and indeed would be much closer to what those theories always actually were-- without ever referring to exact positions and velocities. The theories would simply be left vague about how small those uncertainties could get before something breaks down, and it is perfectly routine for physics theories to not tell you when they break down.
 
Last edited:
  • #11
Ken G said:
Actually, I would claim that is something of a myth about those theories.
I interpret lugita15's statement as saying only that classical theories of point particles say that each particle has a position and a velocity at the same time. This is of course correct. He didn't suggest that such theories are exact representations of reality.
 
  • #12
Fredrik said:
I interpret lugita15's statement as saying only that classical theories of point particles say that each particle has a position and a velocity at the same time. This is of course correct. He didn't suggest that such theories are exact representations of reality.
You interpret me correctly.
 
  • #13
Fredrik said:
I interpret lugita15's statement as saying only that classical theories of point particles say that each particle has a position and a velocity at the same time. This is of course correct. He didn't suggest that such theories are exact representations of reality.
But what I am disputing is that the theories ever said that at all, not that they are exact representations of reality. We can probably accept that no theory is an exact representation of reality ("exact representation" is an oxymoron). My point is about what it is that theories actually assert about themselves, not about reality. I'm saying that a physics theory is not a mathematical structure, a physics theory borrows from a mathematical structure. (The distinction is in the approach to evidence-- a mathematical structure uses proofs, a physical theory uses observational tests, to establish its validity.) A physics theory is a claim on some testable outcome, and as such, no theory ever says that it is anything other than what it can be used to test, regardless of what mathematical structure that physics theory borrows from in order to be able to manipulate proofs.

My evidence is that there is no mathematical proof required by classical mechanics that cannot also be carried out perfectly well in a mathematical structure that refers only to intervals in x and v and maps them into other intervals in x and v, with no claims on any exact values of x and v. The mathematical proofs are all the same, and the theory is much more honest about the ways we actually test physical theories. The only wrinkle in such an approach is that no limit on how small the intervals can be is given in the theory, but that's perfectly normal, because many theories of physics do not come with instructions on when they break down. What's more, the sole reason that classical physics normally refers to x and v, instead of the uncertain intervals in x and v that we actually test to justify the theory, is that the former is more convenient than the latter, not because the former is any more fundamental to the spirit of classical mechanics. I'm arguing, in fact, that the latter approach is more fundamental to classical mechanics (being a branch of the empirical investigation of nature), it's just less convenient.
 
Last edited:
  • #14
Ken G said:
("exact representation" is an oxymoron).
I don't think I agree. An oxymoron is a contradiction. If someone would say that a theory is an exact representation of reality, he's not contradicting himself, he's just making a statement that's forever unfalsifiable, and therefore unscientific.

Ken G said:
My point is about what it is that theories actually assert about themselves, not about reality. I'm saying that a physics theory is not a mathematical structure, a physics theory borrows from a mathematical structure.
By my terminology, a theory consists of a purely mathematical part, and a set of "correspondence rules" that tells us how to interpret the mathematics as predictions about the results of experiments. Terms like "position" are defined in the purely mathematical part. So by my definitions, it's self-evidently true that point particles have positions and velocities in classical point-particle theories.
 

1. What is uncertainty in quantum mechanics (QM)?

Uncertainty in QM refers to the principle that it is impossible to know the exact position and momentum of a particle simultaneously. This is known as Heisenberg's uncertainty principle.

2. Why is uncertainty inherent in QM?

Uncertainty is inherent in QM because particles at the quantum level behave in a probabilistic manner, rather than following deterministic laws. This means that their exact position and momentum cannot be known with certainty.

3. How does uncertainty affect our understanding of reality?

Uncertainty in QM challenges our understanding of reality because it suggests that at the quantum level, the world is fundamentally unpredictable. This goes against our everyday experience and the classical laws of physics.

4. Can uncertainty be overcome in QM?

No, uncertainty is a fundamental aspect of QM and cannot be overcome. However, its effects can be minimized through advanced mathematical techniques and experimental design.

5. How does uncertainty impact technology and everyday life?

Uncertainty in QM has led to the development of technologies such as quantum computing and cryptography, which have the potential to greatly advance fields like data encryption and artificial intelligence. In everyday life, uncertainty has been harnessed in technologies like GPS and MRI machines.

Similar threads

Replies
28
Views
355
Replies
8
Views
2K
Replies
4
Views
785
Replies
10
Views
1K
  • Quantum Physics
2
Replies
48
Views
3K
Replies
16
Views
1K
Replies
14
Views
1K
Replies
32
Views
2K
Replies
7
Views
1K
Replies
2
Views
1K
Back
Top