Heisenberg's indeterminacy principle with non-point particles ?

[Standard]

Hi.
I was just wondering.

Why does Heisenberg's principle of indeterminacy say that we can't know the position and velocity (momentum) of a particle with any precision, when a particle isn't point-like anyway? It's like the position of a car, it's arbitrary and all we can say about its position is that it occupies a space in which we can eventually interact with it.
So why don't we add within the principle the fact that the particle occupies a 3D space ... twice ?

I suppose i understand how we came to this principle because i have read about the tought experimentations that lead to the interpretation.
But i dont understand why when we talk about the position of a particle we do as if a particule would only have one position.
A non point-like particle occupy a space, so there are an infinity of position within continuous space (or at least because the quantum therory is right, there is a finite number of possible positions).

Did i missed some point ?

Thank you for your enlightenment.

 

[Drakkith]

Why does Heisenberg's principle of indeterminacy say that we can't know the position and velocity (momentum) of a particle with any precision, when a particle isn't point-like anyway?

But they are point-like. At least as far as we can tell. Whether they truly are point particles or not, we model them as such and I don't think I've heard of an experiment that ever gave a definite non-zero size for an elementary particle.

 

[Standard]

Ok, but then how do we explain that particles of null size can interact with particles of null size ?
This seems very unlikely.

 

[PeroK]

Ok, but then how do we explain that particles of null size can interact with particles of null size ?
This seems very unlikely.

Within QM, infinitely precise position states are not physically viable. Instead, a particle is described by a wave-packet, which implies a range of possible position measurements and a range of possible momenta. The Heisenberg Uncertainty Principle (HUP) applies to these wave-packets. You can construct any possible wave-packet and check that the HUP is satisfied. There is, in fact, a minimal uncertainty wave-packet, which is the closest you can have to a classical point-particle.

For more details, for example:

https://www.lancaster.ac.uk/staff/schomeru/lecturenotes/Quantum Mechanics/S7.html

 

[Standard]

Within QM, infinitely precise position states are not physically viable. Instead, a particle is described by a wave-packet, which implies a range of possible position measurements and a range of possible momenta.

If the wave packed IS the particle, i understand it has some extension in the space, like a car or any other usual object.

Therefore... what is the position of this particle ?
We can not say it has only one position, like the car it occupy space, and we can consider any position within the space it occupies to potentially be THE position of the particle.
Physically speaking, we say something have some position because when we have interacted with it, it is the place where some energy exchange took place.

Therefore, when we talk about the incertainty of THE position of some particle, in reality we talk about the incertainty of ONE OF THE position within all the possible positions of the particle.
Here with the wave packet, we can consider the wave occupy some concrete space, and the Heisenberg principle would need to apply to SOME of the possible position within this space.

But instead, we consider the particle like a point-like particle... and this lead us to consider it has some extension, like a wave.
BUT... we know it already, this (or part of this) is not the result of the Heisenberg principle.
The point-like particle is probably not a real representation of the particle (or it apply only to photons, i dont know).

Or perhaps the point particle representation lead to the wave particle representation and we would need to loop the principle again and again and again with every point like position within the new space generated at each generation of the wave...

Therefore I cant understand why the Heisenberg uncertainty principe work (or perhaps there are some flaws coming from this (mis ?)conception ?)
Why using some wrong conception of the particle (because it can't physically be one-point) can result in some good conception of the particle occupying some space ?
That's a mystery for me.

 

[PeroK]

If the wave packed IS the particle, i understand it has some extension in the space, like a car or any other usual object.

A particle is defined by its (mathematical) description. There is no alternative underlying reality. This is the lesson of QM. A car is not a good analogy for an electron.

Therefore... what is the position of this particle ?

There is no underlying position that is more fundamental than what QM describes. In the early days of QM, there were many debates about this (Einstein-Bohr). Ultimately, you cannot ask for more than what QM tells you.

We can not say it has only one position, like the car it occupy space, and we can consider any position within the space it occupies to potentially be THE position of the particle.
Physically speaking, we say something have some position because when we have interacted with it, it is the place where some energy exchange took place.

Therefore, when we talk about the incertainty of THE position of some particle, in reality we talk about the incertainty of ONE OF THE position within all the possible positions of the particle.
Here with the wave packet, we can consider the wave occupy some concrete space, and the Heisenberg principle would need to apply to SOME of the possible position within this space.

But instead, we consider the particle like a point-like particle... and this lead us to consider it has some extension, like a wave.
BUT... we know it already, this (or part of this) is not the result of the Heisenberg principle.
The point-like particle is probably not a real representation of the particle (or it apply only to photons, i dont know).

Or perhaps the point particle representation lead to the wave particle representation and we would need to loop the principle again and again and again with every point like position within the new space generated at each generation of the wave...

Therefore I cant understand why the Heisenberg uncertainty principe work (or perhaps there are some flaws coming from this (mis ?)conception ?)
Why using some wrong conception of the particle (because it can't physically be one-point) can result in some good conception of the particle occupying some space ?
That's a mystery for me.

This is a good example of why modern physics is mathematical and empirical and not philosophical. You are tying yourself in philosophical and linguistic knots. Modern physics cuts through that by giving a mathematical description.

Note that, IMO, even in classical physics that is the case. Classical physics, however, is more intuitive, so people fool themselves into equating the mathematical model with a "reality". But, you are still left with the same fundamental questions, such as if an electron has a real physical extent, then what is the electron made of? And you are back to square one.

 

[cianfa72]

wave-packet and check that the HUP is satisfied. There is, in fact, a minimal uncertainty wave-packet, which is the closest you can have to a classical point-particle.

Ah ok, such wave-packets are states satisfying exactly $$\Delta x \Delta p = \frac {\hbar} {2}$$

 

[PeroK]

Ah ok, such wave-packets are states satisfying exactly $$\Delta x \Delta p = \frac {\hbar} {2}$$

Yes, see the above notes from Lancaster University, section VII.5.

 

[Mister T]

Ok, but then how do we explain that particles of null size can interact with particles of null size ?

They exert forces on each other.

 

[Nugatory]

Why does Heisenberg's principle of indeterminacy say that we can't know the position and velocity (momentum) of a particle with any precision, when a particle isn't point-like anyway?

Are you sure they aren't pointlike? We can, in principle, measure either the position or the momentum with arbitrarily high precision (the uncertainty principle only limits measuring both at the same time) and so far we haven't found any behavior that isn't consistent with pointlike behavior.

 

[PeterDonis]

what is the position of this particle ?

If the particle's state is a wave packet in position space, then our knowledge of its position is only probabilistic: we can't say the particle has this position or that position, all we can give is the probability of it having position $x$, as a function of $x$. That doesn't mean the particle itself has more than one position, or is "smeared out" in space instead of being pointlike, or can't decide what its position is. All it means is that our ability to describe its position, or predict what the result will be of a measurement of its position, is only probabilistic, not completely definite.

 

[Standard]

If the particle's state is a wave packet in position space, then our knowledge of its position is only probabilistic: we can't say the particle has this position or that position, all we can give is the probability of it having position $x$, as a function of $x$. That doesn't mean the particle itself has more than one position, or is "smeared out" in space instead of being pointlike, or can't decide what its position is. All it means is that our ability to describe its position, or predict what the result will be of a measurement of its position, is only probabilistic, not completely definite.

This is one of the possible interpretation, but why should we prefer this ?

In reality, the only thing we know is : There is a probability for the particle (whatever it looks like) to interact at position x.
There is no need to assume there is some point-like particle.
Furthermore, if we say that the object "particle" has some property "position" and is infinite small, how do we explain that it is smaller than the Plancks length ? (a point diameter because it is of null length is smaller than the Plancks length).
Do the Heisenberg principle (who make use of point-like particles, because if not... how could the particle have only one position) contradict the principle of minimal Plancks length ?

 

[PeterDonis]

This is one of the possible interpretation

No, it's just describing what the basic math of QM does and does not tell us.

In reality, the only thing we know is : There is a probability for the particle (whatever it looks like) to interact at position x.

Not "to interact", to be measured. "Measurement" is a narrower category than "interaction".

There is no need to assume there is some point-like particle.

There is also no need to assume that it is not. The basic math of QM tells us nothing either way. Nor is it the reason why we treat fundamental particles as point-like.

We treat fundamental particles as point-like because, as others have already said in this thread, we have no evidence that they're not. That evidence is of course incomplete: the smallest distance scales we can probe, about one-tenth the size of an atomic nucleus, are still finite. It could be that fundamental particles have some kind of spatial extension on smaller scales than that. Or it might not be. We can't tell. All we can say is that, down to the smallest distance scales we can probe, we have found no evidence that fundamental particles are not point-like. But that is not just based on "position measurements". There are a lot of other experiments we can do and observations we can make besides just measuring position.

if we say that the object "particle" has some property "position"

Basic QM does not say this. So you are arguing against a straw man.

the principle of minimal Plancks length ?

There is no such "principle". There are speculations that, if we could probe distance scales as small as the Planck length, we would find that everything, including spacetime itself, had further internal structure on that scale. But those are speculations. They are not a "principle". They are not a law of physics. They are just speculations that could turn out to be wrong.

 

[PeterDonis]

the Heisenberg principle (who make use of point-like particles, because if not... how could the particle have only one position)

The Heisenberg principle does not say this. Your arguments are based on false premises.

 

[Standard]

Are you sure they aren't pointlike? We can, in principle, measure either the position or the momentum with arbitrarily high precision (the uncertainty principle only limits measuring both at the same time) and so far we haven't found any behavior that isn't consistent with pointlike behavior.

In fact it has nothing to do with the ability to measure with high precision and we can even mesure position AND mometum TOGETHER with arbitrary high precision.
The only thing is that the result (and it is a true result that we can measure with high efficiency) will we random.
There is very good explaination (at least i assume it is good) of that at this link :
https://physics.stackexchange.com/q...ition-and-momentum-at-the-same-time-with-arbi

 

[PeterDonis]

we can even mesure position AND mometum TOGETHER with arbitrary high precision.
The only thing is that the result (and it is a true result that we can measure with high efficiency) will we random.
There is very good explaination (at least i assume it is good) of that at this link :
https://physics.stackexchange.com/q...ition-and-momentum-at-the-same-time-with-arbi

The bolded statement in the quote above should have been a huge red flag to you.

The short answer is, no, the "explanation" you reference does not support the claim you are making. The fact that it seems to say the same thing as your claim is an illusion, a combination of poorly chosen phrasing by whoever wrote it and poor understanding of the underlying physics on your part.

 

[Nugatory]

This entire thread is based on misconceptions about the quantum descriptions of position and size, so has been closed.