Is Dirac's equation valid for point charges?

[dextercioby]

I believe it was't you the person to whom i was referring to...I don't understand why you did stand up for him...A lawyer physicst...

I found that reply a bit "annoying",just as u did with mine...So i reacted...

Daniel.

 

[sifeddin]

I need to ask 2 more questions. (1) Do bound electrons inside a normal atom (excluding Z=1) have a finite charge based size on the order of 10(-13) cm? (2) What is the size of charge of an electron after it is free from an atom?

Let me add to your questions my own quote from https://www.physicsforums.com/showthread.php?t=59739

An easy question to answer: I doubt! However, I subscribe to your transaction.
Yet could you just give a link, or any documented reference to what you said and why the electron "should" be a "point" particle; because I only got this as "talkings"
BTW if you know the origin of the word "lepton" give me a hint. Any one but "dextercioby" is welcome to answer.

I was waiting however for some knowlegable man like Kane O'Donnell to write such a thing as the word "point" so that to ask him to "reply with some references", preferabally online documents, and whether that Born who said that first or who?

 

[sifeddin]

If I understand correctly, then a lot of people are wasting their time trying to determine the size of an electron because of the mandates of QM theory. Is that right?

If you bother reading for dextercioby do not bother replying. He "seems" to stick with the stuff he learned in his "nowadays" courses and do not try to renew or even reform. (I corrected the verb according to his remark as a positive reaction to his note. but I will NOT reply to his nonsense or even good, though very rare, responses)

BTW very good depate between Hans de Vries and Tom Mattson.

I'm sorry here (again) because I elongate the thread with non-educative response much like "dextercioby's".

 

[quantumdude]

Everyone knock it off before I start putting the smack down.

 

[masudr]

Hear, hear. Keep it to the physics people.

About the relation between the Pauli spin matrices and the $$\gamma$$-matrices appearing in Dirac's equation. We can derive Dirac's equation as an attempt to replace the classical definition of energy with the relativistic definition and then linearize the equation (as Tom says). It can be shown that these matrices are elements of a Clifford algebra, and they can be derived completely independently of Pauli spin matrices.

I would go through the derivation from memory (I would also give the definition of a Clifford algebra), except that my memory cannot remember it too well. If I find it somewhere or if it comes back to me, I'll put it up.

Edit: I realized that this message didn't really contribute much to the discussion. Maybe I should look up the Dirac equation derivation and show that it can be done without any reference to the spin matrices.

 

[sifeddin]

Shut up! and Think! Theorize! then Calculate!

Everyone knock it off before I start putting the smack down.

I'm in the Phyisics corner Reff.
Would you care to join me and try answering my questions? (just look one post before the one you replied to ), I guess these questions are of the kind of the Unspeakable . Would some Physics Master like yourself would step up for such couragous movement. My hopes are great for you Reff.

 

[hypermorgan]

I think Dirac's Equation just describes the point particles.

 

[selfAdjoint]

The classical Dirac equation describes point particles. However the physics of the electron (at this level of energy) is descibed by the QUANTIZED Dirac equation. Now read what Urs Schreiber has posted today about quantized strings: https://www.physicsforums.com/showthread.php?p=448253#post448253; it applies to particles too. Because of uncertainty, any measurement on an electron will be smeared out. You can't get away from that. There isn't any hard lower limit, but the closer you get to a point's position, the more you lose control of the momentum.

 

[marlon]

great explanaition by Urs indeed

Thanks sA

regards
marlon

 

[what_are_electrons]

Yes, it is CURRENTLY difficult to measure the "diameter" of the electric charge, but maybe the question at hand is better restated as:

Why is it currently difficult to measure the size of an electron "accurately"?
Is it because the HUP tells us it is "effectively impossible" because the electron "appears" to our current measuring tools to be smeared out, or is it because the experimental physicists don't "yet" have the experimental tools or a suitable experimental design to achieve this difficult task and to put a better answer to the question of size?

 

[dextercioby]

Why is it currently difficult to measure the position or momentum "accurately"?
Is it because the HUP tells us it is "effectively impossible"

Yes...

or is it because the experimental physicists don't "yet" have the experimental tools or a suitable experimental design to achieve this difficult task and to put a better answer to the question of size?

No,even if,by absurd,they had the tools,they simply couldn't...measure the coordinate along an axis and the momentum along the same axis with ARBITRARY PRECISION AT THE SAME MOMENT OF TIME...

Daniel.

 

[sifeddin]

Yes...

No,even if,by absurd,they had the tools,they simply couldn't...measure the coordinate along an axis and the momentum along the same axis with ARBITRARY PRECISION AT THE SAME MOMENT OF TIME...

Daniel.

I guess the HUP doesn't apply to protons or neutrons.
What do you say?[/QUOTE]

dextercioby or Daniel:
No sarcasm,but really I wish you can read, search, think and take a little time before throwing away your rushed answer to some deep question. Didn't you think that doing such a thing may prevent more deep thinking people from answering a beautiful and mind relief answer. I wish you all the best with physics.

Anyway I saw it somewhere on the net that there is some kind of agreed numbers (with accuracy digits) for the diameter of the proton and the neutron but no such agreement yet (as stated earlier in this thread) for the electron. So why do you think experimental physicists could do this for some particles and not he electron if you are "certain" the the uncertainty principle applies equally to all particles. I will try to upload the link to the page with these particle diameters later or you can search for yourself so that you may find more than I found.

Nevertheless I began to believe that the really good questions posted on this forum specially and anywhere else are left unanswered for one reason or another. Then I really do not expect to see any answers to this question or the ones I posted earlier. Yet I will still hang around.

 

[sifeddin]

The probability cloud of an electron is not an accurate measure of size - the cloud is a graphical depiction of the probability of finding a (*point*) charge at each location in space. It does not reflect the size of an electron - as has already been stated, in quantum mechanics, as in classical physics, idealised particles are treated as having *no* spatial extent. So far, there is no experimental evidence as far as I am aware showing that the electron deviates from this treatment.

On the other hand, we know that protons and neutrons *do* have internal structure, and hence do deviate from being point particles. It's not a question of whether the uncertainty principle applies - it's just that we have evidence showing that protons, for example, aren't point-like objects, whereas we don't for an electron.

Cheerio,

Kane

Kane:
would you take few minutes to reply to my earlier questions and make me believe in this forum again.

I need to ask 2 more questions. (1) Do bound electrons inside a normal atom (excluding Z=1) have a finite charge based size on the order of 10(-13) cm? (2) What is the size of charge of an electron after it is free from an atom?

Let me add to your questions my own quote from https://www.physicsforums.com/showthread.php?t=59739

An easy question to answer: I doubt! However, I subscribe to your transaction.
Yet could you just give a link, or any documented reference to what you said and why the electron "should" be a "point" particle; because I only got this as "talkings"
BTW if you know the origin of the word "lepton" give me a hint.

I was waiting however for some knowlegable man like Kane O'Donnell to write such a thing as the word "point" so that to ask him to "reply with some references", preferabally online documents, and whether that Born who said that first or who?

 

[dextercioby]

I guess the HUP doesn't apply to protons or neutrons.
What do you say?

What??Please infer me to an "illuminating source" where i can learn that this fundamental logical consequence of the Postulates of QM (and by extension,the Postulates themselves) is/are not valid...
Does it mean that I've spent a year of my life learning something which is not correct?

Then i should kill my QM teacher...

Daniel.

 

[masudr]

The electron is treated as a point particle. We have the HUP which applies to all systems. Hence if we have some knowledge of the momentum, we can put a definite upper limit on the variance of the system's position. This is not the same thing as size.

 

[reilly]

That the proton and neutron have structure was discovered and explored by Robert Hostadter by means of elastic electron scattering from nucleons. For these experiments, the electron was considered as a point particle. Why? Because there is no experimental evidence for internal electron structure. The QED idea of a dressed particle, suggests that QED might generate electron structure, from cloud of photons and pairs for example. The operational word is "might".

Newton's 2nd Law, the Schrodinger Eq., the Klein Gordon Eq. and the Dirac Eq. all apply to point particles. They were formulated to do so. Writing the dynamical equations for particles with structure is very hard in QM, particularly in relativistic QM. So, as in centuries past, we treat particles as point particles -- what else to do?

Regards,
Reilly Atkinson

 

[dextercioby]

Newton's 2nd Law, the Schrodinger Eq., the Klein Gordon Eq. and the Dirac Eq. all apply to point particles. They were formulated to do so. Writing the dynamical equations for particles with structure is very hard in QM, particularly in relativistic QM. So, as in centuries past, we treat particles as point particles -- what else to do?

Regards,
Reilly Atkinson

Small ammendment,Mr.Atkinson,for Newton's second law...

Of course,we call them Euler's equations,but they still come from Newton's 2nd principle...Of course,we call them Navier-Stokes equations for Newtonian fluids,but,on the surface (i.e.no Boltzmann equation consequences),they still are Newton's equations for viscous fluid media.And on top of it,of course Cauchy equations which describe the dynamics of deformable continuous media...

To resume.All you stated is correct.However,from the set of equations u offered as example,Newton's ones apply with most ease to nonparticular/nonpointlike models...

Daniel.

 

[sifeddin]

What??Please infer me to an "illuminating source" where i can learn that this fundamental logical consequence of the Postulates of QM (and by extension,the Postulates themselves) is/are not valid...
Does it mean that I've spent a year of my life learning something which is not correct?

Then i should kill my QM teacher...

Daniel.

Oh boy!
Some habits are really hard to die. You left the main message and replied fastly to a copy mistake that is obviously not mine (see https://www.physicsforums.com/showpost.php?p=441088&postcount=28) because of the [/QUOTE] mark. Grow up and read well. If you miss few threads with no contribution you may still go to heaven. I wish you go soon or you may be the reason of me going for sure.


Do NOT forgit to reply to the main message!

 

[masudr]

Anyway I saw it somewhere on the net that there is some kind of agreed numbers (with accuracy digits) for the diameter of the proton and the neutron but no such agreement yet (as stated earlier in this thread) for the electron. So why do you think experimental physicists could do this for some particles and not he electron if you are "certain" the the uncertainty principle applies equally to all particles. I will try to upload the link to the page with these particle diameters later or you can search for yourself so that you may find more than I found.

The reason we believe that protons and neutrons have size is not to do with the fact that they are composed of three quarks orbiting each other. Then we have the HUP applying to the system as a whole. But I don't think the variance of position provided by the HUP is sufficient to regard that as the "size" of the object.

EDIT: Sorry! Error above. Check below for the correct post. Ignore my post!

 

[sifeddin]

The reason we believe that protons and neutrons have size is not to do with the fact that they are composed of three quarks orbiting each other. Then we have the HUP applying to the system as a whole. But I don't think the variance of position provided by the HUP is sufficient to regard that as the "size" of the object.

First here is the page that states the diameter of proton:
http://hypertextbook.com/facts/1999/YelenaMeskina.shtml
Second I do not recall writing "quarks", so why did you think I that quarks orbiting each other would make the proton a divisable particle or even that the HUP would not apply to it. However shining this point by you will make me pursue if "composite" systems are as single particles in the QM or not and if according to QFT the proton is one or three particles. I tell you so because one of my colleagues has a theory in th ecradle that may say somting quite differrent form the QM/QFT viewpoint.
Third sticking with the QM I agree with you that the HUP do not mean the sive of the electron or any other particle. Actually I still wonder if Max Born is the one that said QM formulation means that electron is a point particle with |psi|^2 as its probabilty density. In fact I'm still waiting for Kane to reply to this since he seem to support such idea.

Last thank you for addrissing the issue

 

[masudr]

This post is a correction to my most recent post in this thread. Please ignore my most recent post.

Anyway I saw it somewhere on the net that there is some kind of agreed numbers (with accuracy digits) for the diameter of the proton and the neutron but no such agreement yet (as stated earlier in this thread) for the electron. So why do you think experimental physicists could do this for some particles and not he electron if you are "certain" the the uncertainty principle applies equally to all particles. I will try to upload the link to the page with these particle diameters later or you can search for yourself so that you may find more than I found.

The reason we believe that protons and neutrons have size is to do with the fact that they are composed of three quarks orbiting each other. Hence these point particles are separated, and so we consider the size of the proton (and other baryons and mesons) to be the modulus of the maximum separation of the quarks.

The HUP will specify the variance in position due to knowledge of momentum, but I don't think the variance of position provided by the HUP is sufficient to regard that as the "size" of the object.

 

[masudr]

First here is the page that states the diameter of proton:
http://hypertextbook.com/facts/1999/YelenaMeskina.shtml

I do not deny that protons have size. But that is only because baryons are composite systems consisting of structureless particles (according to the current accepted theory that describes them - the standard model).

Second I do not recall writing "quarks", so why did you think I that quarks orbiting each other would make the proton a divisable particle or even that the HUP would not apply to it.

It doesn't matter whether or not you recall saying quarks, they are made of quarks all the same.

However shining this point by you will make me pursue if "composite" systems are as single particles in the QM or not and if according to QFT the proton is one or three particles. I tell you so because one of my colleagues has a theory in th ecradle that may say somting quite differrent form the QM/QFT viewpoint.

I'm sorry, but I don't understand what you are trying to say above. Please can you rephrase it.

Third sticking with the QM I agree with you that the HUP do not mean the sive of the electron or any other particle. Actually I still wonder if Max Born is the one that said QM formulation means that electron is a point particle with |psi|^2 as its probabilty density. In fact I'm still waiting for Kane to reply to this since he seem to support such idea.

I would agree that the electron is a point particle - that is what the current theory dictates. Of course, we know that the SM is not a complete description, so it's not 100% definite. (But then, the universe may not be subject to one complete description, in which case all our efforts are in vain!)

Last thank you for addrissing the issue

No problem; we (and all other contributors) are all mutually benefiting from this forum. The real people we should thank are those that are paying the money for the servers. They benefit too, but have to pay money for it!

Masud.

 

[reilly]

dextercioby


Just to be clear, I said:

Newton's 2nd Law, the Schrodinger Eq., the Klein Gordon Eq. and the Dirac Eq. all apply to point particles. They were formulated to do so.

In fact I took care to phrase my words so that there was no conflict with use for macroscopic systems. That's why you read "all apply...". Indeed there are many macroscopic systems, from spinning tops to plasmas that rely on Newton's Laws applied to continuous matter, and many others, the kinetic theory of gases for example, in which matter is treated as an assembledge of atoms or molecules.

A bit like, "one size fits all." Newton was just amazing.
Regards,
Reilly Atkinson

 

[what_are_electrons]

The banter is indeed educational, but I'd like to ask my 3 questions again:

1. Is the electron a cloud in an atom and a point charge when it is free?

2. If the electron is indeed a cloud when it is inside an atom, then what is the mechanism for the electron to be freed from the atom and to form a free point charge?

3. Is it possible that experimental physicists will one day have the tools to measure the non-point size of the electron?


Many thanks in advance!

 

[dextercioby]

The banter is indeed educational, but I'd like to ask my 3 questions again:

1. Is the electron a cloud in an atom and a point charge when it is free?

We give you answers,but it really doesn't help u much if you don't do some reading on the subject,too.THE ELECTRON IS A POINTLIKE PARTICLE IN ALL KNOWN AND WIDELY ACCEPTED (QUANTUM) THEORIES...

what is the mechanism for the electron to be freed from the atom ?

Assorption of radiation...??Or to be more general,any interaction able to give the bonded electron the energy it needs to be free (ionization energy)...

3. Is it possible that experimental physicists will one day have the tools to measure the non-point size of the electron?

Many thanks in advance!

You're asking physicists to speculate... I'll leave somebody else to do it...

Daniel.

 

[marlon]

The banter is indeed educational, but I'd like to ask my 3 questions again:

1. Is the electron a cloud in an atom and a point charge when it is free?

The electron (i mean, its structure) itself is always a point particle. The position however is not exact due to the HUP.

marlon

 

[masudr]

what_are_electrons last two questions are answered well by dextercioby. His first answer is good but brief. Let me elaborate.

You are asking if an electron is a point like particle or a cloud. The first thing to realize is that on the sub-atomic level you cannot imagine to electron as a tiny little ball, or even a dot. The reason is because such an image does not tell you much about the electron.

That is why to truly understand quantum mechanics you have to do a bit of the leg-work and get to grips with the mathematical formalism. Then the uncertainty principle will become clear, and all the answers to your questions will become clear (as clear as they can be with respect to QM). Until then, the best we can do is provide an answer that won't help your understanding.

As dextercioby says, an electron is always treated as a particle that has no spatial extension (i.e. is of size that tends towards 0). You may think that you have read in much popular scientific literature that there are electron "clouds" in atoms etc. That is a statement of our knowledge of the position of an electron. If we proceed to make a measurement of the position, we will find the electron in a definite place. But generally, we're not too bothered about exactly where the electron is, and all we do is provide a probability distribution of where the electron might be located. The best way to visualise this probability distribution is in terms of an electron cloud.

Bear in mind that the electron (according to all currently widely accepted theories, as dextercioby says) will always be found at a single point in space when it's position is measured. Hence an electron is a point-like particle.

 

[jtbell]

1. Is the electron a cloud in an atom and a point charge when it is free?

In our current understanding (which is of course always subject to revision based on new experimental evidence), the electron is always a point particle, whose position can be specified only by way of a probability distribution (your "cloud"). For an electron bound to an atom, the probability distribution corresponds to the "orbitals" that you can find pictures of in many physics and chemistry textboks. For a free electron, the probablity distribution is a wave packet that has some width which causes an uncertainty in position at any particular time.

2. If the electron is indeed a cloud when it is inside an atom, then what is the mechanism for the electron to be freed from the atom and to form a free point charge?

Whether inside or outside an atom, an electron's position is always described by a probability "cloud."

3. Is it possible that experimental physicists will one day have the tools to measure the non-point size of the electron?

We already have measured the non-point nature of the electron's probability "cloud" in many situations. All these analyses so far, assume that the electron actually interacts as a point particle (with random position). If the electron did not interact as a point particle, we would have to add "form factors" to the analysis, which are related to the shape and size of the electron. So far this has not been necessary. It may become necessary in the future, depending on experimental data which is yet to be collected.

For a parallel situation, consider Rutherford's nuclear model of the atom. His analysis of his famous experiments on scattering of alpha particles by gold nuclei assumed that the nuclei could be treated as point particles, and his predicted angular distribution for the scattered alpha particles agreed with his experimental data. Later data using higher-energy alpha particles disagreed with Rutherford's prediction, and this was taken as evidence that atomic nuclei do in fact have a finite size.

Similarly, when we scatter electrons or neutrinos off of protons or neutrons, at high enough energies the angular distributions of the scattered particles disagree with what we would expect if protons and neutrons were point particles. This was first observed in the late 1960s, and led Feynman to produce his "parton model" in which protons and neutrons were actually collections of "smaller" particles. Further experiments showed that these "partons" in fact had the properties of the "quarks" that had been proposed earlier by Gell-Mann in order to explain the patterns of properties of particles in the burgeoning "particle zoo."

Something similar may very well happen with electrons in the future... but there's been no sign of it yet in experimental data on electron-electron, electron-neutrino and electron-positron scattering, as far as I know.

 

[sifeddin]

I still do not the (p)oint (p)article quite a clear cut of some (p)roof, (p)aradigm or even (p)ostulate of some (p)rofessor . If you do not get it read e.g. Ch. 7 of White "Basic Quantum Mechanics", for the Gaussian packet of psi function that represent the free elctron.

However, try to focus on the answer of this question which I wish "again" that Kane O'Donnell (whom i cought saying the words) may answer it in the most explicit way:
Is it Max Born who stated that the electron is the point particle with the psi (like the White's Gaussian packet one) is the amplitude of its probability density?

Well, I concentrate on the electron here because I read in some paper that A.E. once said if you really understand what the electron is you may understand all the physics. I do not quote here but I recall from memory but I imagine also that the proton was not discovered yet when he said that .

 

[dextercioby]

I'm not sure on whether he used the exact words "point particle" (i haven't read his article),but he definitely gave the Schroedinger wave functions the interpretation we have today.

As for A.E.opinion,would you care to recall when (in what year) did he assert that...?It may be relevant to a further discussion.

Daniel.

 

[sifeddin]

I'm not sure on whether he used the exact words "point particle" (i haven't read his article),but he definitely gave the Schroedinger wave functions the interpretation we have today.

Well I guess I am "certain" about that too. Kane! Help! please!

As for A.E.opinion,would you care to recall when (in what year) did he assert that...?It may be relevant to a further discussion.

Daniel.

Well my comment was a mere joke but I read it in paper on the new representation and geometric meaning of the Dirac spinor wave function when I find it (while reading the forum) I may post the reference for you.

 

[Kane O'Donnell]

Look, you can use a Gaussian wave packet as a way of representing a *localised* particle. This doesn't mean the particle we're representing isn't a point particle. The problem is that if you use say a delta function to represent a point particle, then the particle has a totally uncertain momentum and it's not very useful for modelling. On the other hand, if we're willing to accept a reasonably small uncertainty in position (by using a finite-width wavepacket) then we can get a reasonably small uncertainty in momentum.

Whenever anyone goes looking for the location of a single electron, they find it in a single place, and no scattering experiment has shown that an electron has a finite spatial extent.

Just remember that wavefunctions *don't* represent the *physical* size of a particle, they represent the probability of finding a particle (all of it) in a particular place.

Kane