Seeking Point Particle Explanation

[AndyDufresne]

Seeking "Point Particle" Explanation

Ahoy,

For some time I've been reading through various topics in theses Forums as a Guest, but decided to move beyond that. I'm unfortunately not adept with Science or Mathematics (I'm more adept in Langauge and in Words), but I've always found them fascinating to me nonetheless and try my best understand them as well as I can. So I thought I would preface my question with the hope respondents keep my general inexperience and lack of knowledge in mind.

I'd like some explanation on the concept of Point Particles--- dimensions, size, the lack-thereof, etc (analogies would be splendid---as I mention, language and words are more my forte).

Thanks ahead of time to those who respond and take the time to explain!


--Andy

 

[jnorman]

andy - wikipedia is often a good place to start with this kind of question. a point particle has no spatial dimensions, ie, it occupies no volume. electrons and quarks are considered to be point particles, thus everything which we perceive as matter is composed of particles which have no volume - very fun, huh?

 

[denisv]

I'm not sure if thinking of particles as points is very useful in quantum mechanics.

 

[WaveJumper]

The apparent volume of matter comes from the interaction of the electromagnetic, strong nuclear and weak nuclear force through mediating force carrier bosons. Not from purported zero dimensional point particles.

 

[ZapperZ]

I'm not sure if thinking of particles as points is very useful in quantum mechanics.

So what is the volume of, say, the free particle when you start solving the free particle Schrodinger equation at the beginning of a QM course?

Zz.

 

[wittgenstein]

http://en.wikipedia.org/wiki/Point_particle
I'd like an explanation too. How can anything that has no volume be said to exist?

 

[DrChinese]

http://en.wikipedia.org/wiki/Point_particle
I'd like an explanation too. How can anything that has no volume be said to exist?

Please remember that the Heisenberg Uncertainty Principle (HUP) is at play with quantum particles. A fundamental particle (say an electron) has no constituent structure and behaves "as if" it is a point particle. (Theory gives us that as well.)

You could say it has no volume (because you can confine it to any arbitrarily small volume of space). Or you could say it has a large volume (because it has a precise momentum). But quantum particles most definitely exist, by the usual meaning of the word.

 

[ZapperZ]

http://en.wikipedia.org/wiki/Point_particle
I'd like an explanation too. How can anything that has no volume be said to exist?

Maybe you should turn things around and ask yourself "what do I mean when something has a volume?"

Do you think in classical ways in which an object has definite boundary of occupation in space? Think about it! It certainly looks that way with your eyes, but what if you look at it using an electron microscope? Or what about using an atomic force microscope? Do those "definite boundaries" look definite anymore? So what "volume" are we talking about then?

You are trying to force a square object through the round hole. Rather than looking at the square object, you are complaining about the round hole. Same thing here. Maybe your concept of a "volume" really has no meaning at that scale. So trying to force it down to where it doesn't belong can easily be the problem!

Zz.

 

[wittgenstein]

"Do you think in classical ways in which an object has definite boundary of occupation in space? Think about it! It certainly looks that way with your eyes, but what if you look at it using an electron microscope? Or what about using an atomic force microscope? Do those "definite boundaries" look definite anymore? So what "volume" are we talking about then?"
ZapperZ
But isn't that indefiniteness a result of our technical inability rather than an objective trait of the object? If an object has an actual indefinite boundary would that not mean... well.. suppose I draw a line and have a particle that we call A. Then A would be on one side of the line and also the other. I realize that this has similarities to QM but that still leaves QM as something that cannot be understood. By understood I mean this; if I create a geometry based on the principle of a square circle and am able to make predictive computations with that geometry can I really be said to know what a square circle is?

 

[ZapperZ]

So you think an atom has a definite boundary, and that the "fuzziness" is simply due to our technical inability?

Zz.

 

[wittgenstein]

Or is QM not about "whats out there" but how we can get what we want from reality? We want to be able to make predictions and if we do, it does not matter if the model violates logic . I am asking a question about QM that has bothered me for quite some time. Does QM tell us anything about reality or is it only about making predictions. I realize that "making predictions" says something about reality (future reality) . But to me its like knowing how to do math without knowing why the math works.

 

[ZapperZ]

Or is QM not about "whats out there" but how we can get what we want from reality? We want to be able to make predictions and if we do, it does not matter if the model violates logic . I am asking a question about QM that has bothered me for quite some time. Does QM tell us anything about reality or is it only about making predictions. I realize that "making predictions" says something about reality (future reality) . But to me its like knowing how to do math without knowing why the math works.

Aren't you in the wrong thread to ask these questions? Did you forget where you were? Thread hijacking isn't exactly allowed.

Zz.

 

[wittgenstein]

On a personal level I'd love to understand something that violates normal logic. I have even heard about paraconsistent logic. But I have also heard what to me are contradictory claims. 1. There is nothing fantastic* about QM and 2. That A does not necessarily = A.
* By fantastic I mean anything beyond human understanding.

 

[wittgenstein]

You don't have to get angry. So you are saying that asking if QM describes reality or is only a system for predicting results belongs in the philosophy section? This is directly related to the point particle concept.

 

[ZapperZ]

You don't have to get angry. So you are saying that asking if QM describes reality or is only a system for predicting results belongs in the philosophy section?

I said "wrong thread", not wrong sub-forum.

This thread has a specific topic. You are trying to derail it with a different topic.

Zz.

 

[wittgenstein]

I think that "trying to derail it" is a bit strong. I was trying to respond to your question," So you think an atom has a definite boundary, and that the "fuzziness" is simply due to our technical inability?" Basically, I was asking is the 'fuzziness' actually there or only a useful model that aids calculations.

 

[ZapperZ]

I think that "trying to derail it" is a bit strong. I was trying to respond to your question," So you think an atom has a definite boundary, and that the "fuzziness" is simply due to our technical inability?" Basically, I was asking is the 'fuzziness' actually there or only a useful model that aids calculations.

You did not answer my question. Do you think an atom has definite boundary or not the way you see the volume of a block of wood?

Zz.

 

[wittgenstein]

I would say that if an atom does not have any clear boundaries then in that "fuzziness" area one could say that yes this area is part of the atom and not part of the atom. A is A and not A. Of course I am not saying that that is not the way it is. I am only saying that if a lack of boundaries is an objective fact ( and not the result of our technical inadequacies) then it is something that we humans cannot conceive of.

 

[ZapperZ]

I would say that if an atom does not have any clear boundaries then in that "fuzziness" area one could say that yes this area is part of the atom and not part of the atom. A is A and not A. Of course I am not saying that that is not the way it is. I am only saying that if a lack of boundaries is an objective fact ( and not the result of our technical inadequacies) then it is something that we humans cannot conceive of.

Er... You HAVE seen the wavefunction for, say, the hydrogen atom before you wrote this, haven't you?

For example, look at the s-orbital. Where do you think it "ends"? And where do you think the "boundary" of that atom is? And where is the "technical inadequacies" here?

And in case you missed it the first time around, here is our https://www.physicsforums.com/showthread.php?t=5374". Pay particular attention to our policy on speculative post.

Zz.

 

[wittgenstein]

So, if an object does not have a clear boundary then there are parts of it that are part of the object and not part of the object? So you are saying in the example you gave "there are parts of the wavefunction that are part of the wave function and at the same time not part of the wave function? "If you say "NO" to that then you are saying," at every point in the area under viewing it is clear that that point is part of the object or is not a part of the object. That is a clear boundary. Yes, even when looking at a photo I have difficulties telling if the photo is blurred ( technical difficulties) or that the object does not have clear boundaries. But that is a red herring or at least I do not know why you mentioned it. As for speculation, so no new ideas or new questions allowed?

 

[DrChinese]

I would say that if an atom does not have any clear boundaries then in that "fuzziness" area one could say that yes this area is part of the atom and not part of the atom. A is A and not A. Of course I am not saying that that is not the way it is. I am only saying that if a lack of boundaries is an objective fact ( and not the result of our technical inadequacies) then it is something that we humans cannot conceive of.

As I mentioned to one of your posts in another thread, you should be careful when mixing "normal" words and the language of QM. As ZapperZ is pointing out, the formulae are the true formalism. And they really don't have problems! It is only when you try to fit them into our everyday meaning that the issues arise.

So you can debate certain semantics without making much progress because the HUP is still the HUP regardless of how you choose to color it. Etc. for the other equations. Is it a point? Or does it encompass the entire universe? These questions are debated endlessly and Zz correctly wants to keep this thread on track. Obviously this has been a problem in the past, where a thread about A morphs into a thread about B. Don't hesitate to start your own thread, hey it's free!

 

[ZapperZ]

So, if an object does not have a clear boundary then there are parts of it that are part of the object and not part of the object? So you are saying in the example you gave "there are parts of the wavefunction that are part of the wave function and at the same time not part of the wave function? "If you say "NO" to that then you are saying," at every point in the area under viewing it is clear that that point is part of the object or is not a part of the object. That is a clear boundary. Yes, even when looking at a photo I have difficulties telling if the photo is blurred ( technical difficulties) or that the object does not have clear boundaries. But that is a red herring or at least I do not know why you mentioned it. As for speculation, so no new ideas or new questions allowed?

I have no idea what you just said here. All I asked is if you've looked at the wavefunction of a hydrogen atom that has been solved in any undergraduate QM class. You didn't answer, which leads me to presume that you haven't. Yet, you've made all of these guesses based on ... on ... what?

It appears that practically all of your "arguments" have been based not on established physics, but based on a matter of TASTES! Look back at all of your posts here. Not one of them are actually based on physics. That is why I kept asking you questions based on not only physics, but on empirical observations, trying to get you to think not only analytically, but also to try to ground this on at least something that we know to be VALID. Unlike philosophy, physics discussion, at least at this level, can't be based on that, especially when there are already well-established, documented evidence that can be used in this case.

My argument that this is really you trying to force a square object through a round hole has plenty of support. My examples of trying to look objects using more precise and finer instruments (SEM, AFM, etc) are the empirical evidence. I can even point to you arguments that provide a conclusion that it is the CLASSICAL world that you observe with your eyes that is not quite right. If you study a quantum phenomenon with "coarse-grained" observation, you can https://www.physicsforums.com/showpost.php?p=1520644&postcount=58"! So if anything, it is the classical world that has the "technical inadequacies", not the quantum level. The appearance of definite boundary to allow you to talk about volume is an illusion as the result of poor, coarse observation!

In other words, I just didn't spew all of this out based on simply a matter of my tastes. It is based on things that I've personally have looked at (SEM, AFM), and also based on published papers. We simply can't make things up as we go along in this forum, and certainly not in the physics subforums.

As for making speculation of "new ideas", which part of the guideline here which you had agreed to that you didn't understand?

Overly Speculative Posts:
One of the main goals of PF is to help students learn the current status of physics as practiced by the scientific community; accordingly, Physicsforums.com strives to maintain high standards of academic integrity. There are many open questions in physics, and we welcome discussion on those subjects provided the discussion remains intellectually sound. It is against our Posting Guidelines to discuss, in most of the PF forums or in blogs, new or non-mainstream theories or ideas that have not been published in professional peer-reviewed journals or are not part of current professional mainstream scientific discussion. Personal theories/Independent Research may be submitted to our Independent Research Forum, provided they meet our Independent Research Guidelines; Personal theories posted elsewhere will be deleted. Poorly formulated personal theories, unfounded challenges of mainstream science, and overt crackpottery will not be tolerated anywhere on the site. Linking to obviously "crank" or "crackpot" sites is prohibited.

Zz.

 

[Vanadium 50]

As for speculation, so no new ideas or new questions allowed?

Merely that we hope you have the integrity to follow the rules you agreed to on overly speculative posts.

 

[Demystifier]

I'm not sure if thinking of particles as points is very useful in quantum mechanics.

It depends on what one means by "useful".

If you only want to efficiently calculate the probabilities of different measurement outcomes, then particles as points are usually not very useful. (See however
http://prola.aps.org/abstract/PRL/v82/i26/p5190_1
for an exception.)

If, on the other hand, you want to have an intuitive visual picture of the stuff you are calculating, then a picture of particles as points may be very useful. However, one must be very careful with such a picture because it may lead some to a wrong conclusion. A consistent way of thinking about particles as points is provided by the Bohmian formulation of quantum mechanics. If used according to the well defined prescriptions, it cannot yield a result that is not consistent with statistical predictions of standard QM. Even if Bohmian interpretation is wrong in the sense that particles are not really points having trajectories, the Bohmian formulation is still useful in the sense of providing a useful intuitive picture.

 

[yossell]

I'm not sure I know what's meant when one's asked if one has seen the wavefunction of a hydrogen atom. Are we talking about the abstract mathematical wavefunction that assigns complex numbers to various base states? Or are we talking about the plots of probability distributions derived from the wavefunction such as those found here:
http://sevencolors.org/tag/atom%20orbitals

In either case, I'm not sure what conclusions I'm supposed to draw as a matter of pure physics about the boundary of an atom. If the probabilities are interpreted as corresponding to a genuine fuzziness in the positions of the quantum objects themselves then I think I see the argument, but this is partly an interpretational matter - not all interpretations of QM hold the eigenvalue-eigenvector link, that an object *only* has a sharp value when it is in an eigenstate of the relevant operator.

yossell.

 

[RUTA]

I'm not sure I know what's meant when one's asked if one has seen the wavefunction of a hydrogen atom. Are we talking about the abstract mathematical wavefunction that assigns complex numbers to various base states? Or are we talking about the plots of probability distributions derived from the wavefunction such as those found here:
http://sevencolors.org/tag/atom%20orbitals

In either case, I'm not sure what conclusions I'm supposed to draw as a matter of pure physics about the boundary of an atom. If the probabilities are interpreted as corresponding to a genuine fuzziness in the positions of the quantum objects themselves then I think I see the argument, but this is partly an interpretational matter - not all interpretations of QM hold the eigenvalue-eigenvector link, that an object *only* has a sharp value when it is in an eigenstate of the relevant operator.

“Indeed, atoms and particles as things are phantasms (things imagined).”

A. Bohr, O. Ulfbeck & B. Mottelson, “The Principle Underlying Quantum Mechanics,” Found. Phys. 34, Mar 2004, p. 405.

 

[bm0p700f]

Of course a point particle with mass has infinite density and is therefore a singularity, which a nonsense in reality. I suppose that's where string theory come's into give these point particle size in one dimension. The problem with our theory of matter is that while it describe the reality we live in very well and make verifiable predictions, it is not the whole story as there various issues like the one above which require mathematical trickery to get around. That is at least my understanding.

As to the point about fuzziness this "real" in the sense that HUP says it is, without quantum tunnelling would not be possible and so therefore the alpha decay would not happen nor would the scanning tunnelling microscope be possible.

All word based models have their limitations, and the limitations cause the confusion. As for the fuzziness it persist even when you measure the position of the electron, as doing that makes the momentum uncertain. Fuzziness is ingrained in QM you cannot get away from it.

 

[yossell]

As to the point about fuzziness this "real" in the sense that HUP says it is, without quantum tunnelling would not be possible and so therefore the alpha decay would not happen nor would the scanning tunnelling microscope be possible.

All word based models have their limitations, and the limitations cause the confusion. As for the fuzziness it persist even when you measure the position of the electron, as doing that makes the momentum uncertain. Fuzziness is ingrained in QM you cannot get away from it.

Does HUP say anything about the 'reality' of fuzziness? In many texts, it is presented as a relation between functions of expectation values of certain operators. (I thought Heisenberg himself seemed originally to treat it as a matter of ignorance, and it was only under the pressure of Bohr that he stated it represented some kind of fuzzy value). As for the HUP itself, we can all agree that, in the long run, we can expect a certain distribution of values to occur. And no doubt, QM gives incredibly accurate results here. But there are interpretational questions about how this uncertainty is to be interpreted.

What I'm not sure about is how to get from agreement that QM is right about the expectation values and probabilities and the fact of quantum tunelling and the statistical results of the two-slit experiment and the pictures of probability densities of atomic orbitals to the conclusion that objects themselves lack precise values. And, since there are several interpretations of QM other than the Bohr interpretation that seem to avoid this conclusion, I suspect it's not an obviously empirically confirmed fact, but rests upon some delicate interpretational/Philosophical issues.

yossell

 

[bm0p700f]

Does HUP say anything about the 'reality' of fuzziness? In many texts, it is presented as a relation between functions of expectation values of certain operators. (I thought Heisenberg himself seemed originally to treat it as a matter of ignorance, and it was only under the pressure of Bohr that he stated it represented some kind of fuzzy value). As for the HUP itself, we can all agree that, in the long run, we can expect a certain distribution of values to occur. And no doubt, QM gives incredibly accurate results here. But there are interpretational questions about how this uncertainty is to be interpreted.

What I'm not sure about is how to get from agreement that QM is right about the expectation values and probabilities and the fact of quantum tunelling and the statistical results of the two-slit experiment and the pictures of probability densities of atomic orbitals to the conclusion that objects themselves lack precise values. And, since there are several interpretations of QM other than the Bohr interpretation that seem to avoid this conclusion, I suspect it's not an obviously empirically confirmed fact, but rests upon some delicate interpretational/Philosophical issues.

yossell

I am not to sure anyone really understands it in a way that you asking. After all our concepts that can be described in words are based on the way we observe the macroscopic world. As the world on a small scale defies expectation QM logic has to apply and these weird results pop out. The maths does not lie and I accept that beyond that is philosophy for example which is right the many worlds interpreation or the idea of superposition? I have the same problem when teaching my physics class this, words don't seem to do these ideas justice.

As for fuzziness this makes a lot of sense in a strange sort of way. Take an electron it has an electric field. With in that field, particles pop out of the vacuum; a photon for example. These particles will interact with their other real particles, maybe, before they disappear. They would not exist if it where not for the field they where created in, briefly. So where does the real particle begin? The interaction is not with solid mater like we perceive but with a field or more to the point the virtual bosons within the field. In fact all contact forces fundimentally are the result of the interaction of the electromagnetic force between electron in the atoms of the two surface in "contact". With this view their is no contact but a close approach. Hence fuzziness on top of not being able to define the position and momentum of a particle or the amount of energy it has over a time makes for a fuzzy world. So all you really have is a field and virtual exchange bosons created by a real particle with no size which you cannot pinpoint. Daft isn't it but it works.

Also the point particle idea is necessary consequence of QM (QED). The theory as already stated says that point particles interact through exchange of virtual bosons that are created as the result of a field. If these particles had size, well then what would that surface and interior be composed of? As that in itself would be more fundamental than the electron, quark or neutrino. Also they would have another mechanism of interaction which would be the physical bumping into of other particles which they do not appear to do they nearly approach exchange a virtual boson and go about their merry way. The results of such a physical interaction would depend on the properties of the surface and its internal structure such as we see in our macroscopic world. So having point particles really simplifies matters.

I don't think I am wrong in the way I have described this.

 

[AndyDufresne]

andy - wikipedia is often a good place to start with this kind of question. a point particle has no spatial dimensions, ie, it occupies no volume. electrons and quarks are considered to be point particles, thus everything which we perceive as matter is composed of particles which have no volume - very fun, huh?

The apparent volume of matter comes from the interaction of the electromagnetic, strong nuclear and weak nuclear force through mediating force carrier bosons. Not from purported zero dimensional point particles.

Please remember that the Heisenberg Uncertainty Principle (HUP) is at play with quantum particles. A fundamental particle (say an electron) has no constituent structure and behaves "as if" it is a point particle. (Theory gives us that as well.)

You could say it has no volume (because you can confine it to any arbitrarily small volume of space). Or you could say it has a large volume (because it has a precise momentum). But quantum particles most definitely exist, by the usual meaning of the word.

I think these posts were the most helpful, but I still feel strangely in the dark. I suppose I will continue trying to my best to understand.