Is the concept of a point particle in quantum mechanics ultimately untenable?

[Ran out of sp]

Quantum mechanics is a very powerful and accurate method of describing the actions of small particles in space but it has its limits.
On the large scale, QM cannot explain relativistic effects.
On the smallest of scales, the theory starts to become nonsensical. QM is based on events whch are partly explicable as waves and partly as independent particles. The trend over the years has been towards an exclusive interpretation using point particles.
The mathematics of Newtonian mechanics uses the idea of a centre of mass at a particular point in space but this does not prove that the Sun, Moon and Earth are dimensionless points. Yet the concept of centres of mass and charge is applied unquestionly at the quantum scale.
How can a dimensionless entity have a spin or a magnetic moment?
If a particle is confined to a single point, its mass density and charge density must be infinite.
And if everything is restricted to dimensionless points, space must be 100% empty.
There is an even greater problem in seeing protons and neutrons as point particles when they are made up from smaller point particles called quarks.
While the mathematical accuracy of QM has been well established, its interpretation in terms of point particles is ultimately untenable and tends toward the dogmatic.
I'd like to hear what other people think about this.
...ace

 

[Dr Lots-o'watts]

...the theory starts to become nonsensical...

Common sense is based on common macroscopic events which are familiar.

The trend over the years has been towards an exclusive interpretation using point particles...

Source?

The mathematics of Newtonian mechanics uses the idea of a centre of mass at a particular point in space but this does not prove that the Sun, Moon and Earth are dimensionless points...If a particle is confined to a single point...is restricted to dimensionless points...

Restriction? Confinement? In many calculations, the volume is simply irrelevant. Points just make calculations practical. When calculating the trajectory of a bouncing basketball, is it relevant to define the shape of its surface at each moment? It's perhaps doable, but getting results with the least amount of calculations is better, thus the equivalent single point.

its interpretation in terms of point particles is ultimately untenable and tends toward the dogmatic.

Perhaps QM should be abandoned?

 

[Ran out of sp]

Thank you for replying, Dr Lots-o'watts.
Taking your points in order,

1. 'Common sense' is a conventional description which is often hard to distinguish from common ignorance. What I meant by 'nonsensical' is that at the limit of dimensionless particles the theory becomes strained and inconsistent.

2. My impression of science reporting in the media is that point particles have received increasing coverage at the expense of wave based descriptions. Is it necessary to provide a full survey and methodology to prove this? Are you arguing the opposite case?

3. Yes. 'Points make calculations practical.' The calculations are accurate enough for most purposes but these points can mark the centre of distributed phenomena and not exclusively dimensionless concentrations of mass, charge and so on.

4. No of course we shouldn't abandon QM. I already said how powerful and accurate it is. My reservations are confined to the literal interpretation of centres af mass and charge as actual dimensionless particles.

 

[Dr Lots-o'watts]

1. Perhaps, but nowhere have I seen that particles are necessarily dimensionless. In the standard physics curriculum, their dimensions are simply not taken into account. When considering a solid, the atoms are dimensionless points, when considering an atom, the nucleus is a point, when considering a nucleus, the baryons are points, and so on. In each realm, points are approximations.

2. I suppose it depends on which media. Waves are still very essential for my purposes.

3. I think we agree. A point is usually an approximation to a distribution.

4. Again, a point is most often a mathematical approximation to a distribution, not anything physical, so I wouldn't personally spend too much time trying to interpret them.

Of course consider that in my own day to day activity, standard QM is largely sufficient. Others here may be more concerned about literal interpretations. I always keep in mind that all these equations are mere man-made mathematical models, not the real thing.

 

[ZapperZ]

1. Perhaps, but nowhere have I seen that particles are necessarily dimensionless. In the standard physics curriculum, their dimensions are simply not taken into account. When considering a solid, the atoms are dimensionless points, when considering an atom, the nucleus is a point, when considering a nucleus, the baryons are points, and so on. In each realm, points are approximations.

I'm not sure this is accurate. For example, in solid state physics, there is such a thing as "packing factor". This takes into account the atoms sizes at each of the lattice points. So they do have volumes. In fact, the location of the lattice points and the existence of lattice constants are strong indications that these atoms have volumes.

Zz.

 

[dxun]

4. No of course we shouldn't abandon QM. I already said how powerful and accurate it is. My reservations are confined to the literal interpretation of centres af mass and charge as actual dimensionless particles.

Actually, your objection to point-particle-like approximations in QM is one of the prime reasons why String Theory abandoned such approximations and used string-like Planck-sized fundamental objects instead.

While it did provide the means to circumvent a number of mathematical problems in efforts to harmonize GR with QM (e.g. singularities are avoided since nothing reaches zero size but Planck size instead), it also produced a number other difficulties (e.g., there are *five* equally valid theories, the exact vector space in which string resonates is not precisely determined).

Despite a host of problems, it still remains our best shot at GR+QM unification.

 

[Ran out of sp]

Dr Lots-o'watts,
Thamk you for getting back to me. I don't see any major disagreement between us.

Zapper Z,
Thank you too for your contribution.

dxun,
Again, thank you for replying. Personally, I remain to be convinced by string theories but I'm prepared to wait and see.

But I'm still concerned that some people appear to be promoting a world full of point-particle singularities. Am I worrying about nothing? What do the rest of you out there think?

 

[ZapperZ]

But I'm still concerned that some people appear to be promoting a world full of point-particle singularities. Am I worrying about nothing? What do the rest of you out there think?

You are worrying about nothing.

Until you learn about the physics and the mathematics, all you understand right now are superficial ideas of these things. That's like worrying about the animal based on a brief description of what it looks like from 2nd hand sources. It is seldom accurate.

Zz.

 

[Dr Lots-o'watts]

I'm not sure this is accurate. For example, in solid state physics, there is such a thing as "packing factor". This takes into account the atoms sizes at each of the lattice points. So they do have volumes. In fact, the location of the lattice points and the existence of lattice constants are strong indications that these atoms have volumes.

Zz.

Corrected, I should have said nuclei.

 

[dxun]

Until you learn about the physics and the mathematics, all you understand right now are superficial ideas of these things.

I agree completely.

 

[alxm]

Corrected, I should have said nuclei.

Nuclei aren't always treated as point particles. If you're doing solid-state or quantum chemistry they usually are, because the effect of the nuclei's finite size is both well within the experimental error of most properties being calculated, and within theoretical error of most methods used to calculate the properties.

But when it comes to extremely accurate calculations of very subtle properties, such as the Lamb shift, then the effect of a finite nucleus is indeed taken into account. It was in that way this quite recent result that protons may not have the same size (charge radius) as previously thought came about.

 

[Dr Lots-o'watts]

Nuclei aren't always treated as point particles. If you're doing solid-state or quantum chemistry they usually are, because the effect of the nuclei's finite size is both well within the experimental error of most properties being calculated, and within theoretical error of most methods used to calculate the properties.

But when it comes to extremely accurate calculations of very subtle properties, such as the Lamb shift, then the effect of a finite nucleus is indeed taken into account. It was in that way this quite recent result that protons may not have the same size (charge radius) as previously thought came about.

Sure, look, it depends on what your trying to calculate. Sometimes, a solid is seen as a periodic arrangement of ions, in which flow the free electrons, so part of the atom is a point (nucleus + valence electrons) defining the potential, and part is free electrons. So when I said atoms could be considered as points in solid state, it wasn't inaccurate. Atoms of a gas can also be approximated as point particles.

My point is that when I'm counting sheep, I don't care what their shape is, and in the same mindset, when physical things are approximated as points, it's not a fundamental statement on the nature of matter, it's just a useful approximation that allows doable calculations.

As far as I know, no one is stopping anyone to zoom in on a "point" to see what it looks like from up close. Either it has structure, either it doesn't, either you're not there yet. The question remains open.

 

[Dr Lots-o'watts]

Look, this may be relevant to some:

http://www.youtube.com/watch?v=ofp-OHIq6Wo&feature=related

Interesting anyway.

 

[dxun]

Look, this may be relevant to some:

http://www.youtube.com/watch?v=ofp-OHIq6Wo&feature=related

Interesting anyway.

Excellent vid, thanks!

It's probably not the actual electron orbits that are we're seeing as interference-like aliasing in the vid, but I am interested to know where produces that effect?

 

[alxm]

My point is that when I'm counting sheep, I don't care what their shape is, and in the same mindset, when physical things are approximated as points, it's not a fundamental statement on the nature of matter, it's just a useful approximation that allows doable calculations.

Well I can't let this pass without an obligatory reference to the http://en.wikipedia.org/wiki/Spherical_cow"

 

[alxm]

It's probably not the actual electron orbits that are we're seeing as interference-like aliasing in the vid, but I am interested to know where produces that effect?

You're seeing the interference pattern from the momentum distribution of the wave-packets of the two electrons from an ionized helium atom. http://www.atto.fysik.lth.se/publications/papers/RemetterNP2006.pdf" from the group's page.

 

[Ran out of sp]

Oh dear, I have unwittingly set up a straw man, based on oversimplefied summaries.
I suppose the same arguments apply to black holes. It is often stated that matter within a black hole will collapse to a single point.
If your basic unit of measurement is a parsec, the size of a black hole is virtually zero.
At the heart of the phenomenon, however, the protons and neutrons have a finite size and distance apart, so that the interior of the black hole will have a minimum density.
At the singularity itself, nothing can be properly defined.
Is this a fair summary?

 

[JDługosz]

How can a dimensionless entity have a spin or a magnetic moment?

How can it not?
If you combine special relativity (symmetry of spacetime) with the concept of a smallest scale to nature (quantum and uncertainty), spin just falls out. It's not common sense because it's not in your experience. But it just shows up for the party on its own.

If a particle is confined to a single point, its mass density and charge density must be infinite.

"renormalization".
Don't get that close, and don't worry about it.