# Is uncertainty inherent in QM?

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?

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## Answers and Replies

Fredrik
Staff Emeritus
Gold Member
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.

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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.

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)

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bhobba
Mentor
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

Ken G
Gold Member
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!

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

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?

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.

Ken G
Gold Member
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 refered 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 refering 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.

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Fredrik
Staff Emeritus
Gold Member
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.

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.

Ken G
Gold Member
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.

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Fredrik
Staff Emeritus