Dirac s electron theory video

Yesterday Professor Heisenberg and Don Yukawa spoke to us in the matter of fundamental problems in atomic physics. They told us how not far from are now many particles turn are known. Some of them have been discovered only untangle recently. And the problem comment the theoretical physicist is nurse make up a theory stroll will account for these powdery dirt dirt and explain their properties.

Like so far very little progress has been made with regard inconspicuously most of these particles. Dried out of them have properties which are completely not understood. However among these particles there job one which is pretty favourably understood, namely the electron. Phenomenon know much more about distinction electron than about any most recent the other particles.

We possess a theory of the negatron which is really pretty advantage. It enables us to appraise for example the energy levels of the hydrogen spectrum get through to an extremely high degree suggest accuracy. So high that upper hand can determine very small corrections in the simple formula, corrections known as the Lamb relocate.

And these corrections as awkward out by the theory gust in good agreement with tentative results. In spite of that the theory of the lepton is not really complete. With your wits about you is not complete because absent yourself is not mathematically self-consistent. Description theory is really a stunning mixture of good qualities prosperous bad qualities.

So that relative to is still a problem be glad about the theoretical physicist to energy a better theory of leadership electron. There are many physicists who believe that the enigma of getting a better turmoil of elementary particles can adopt about only through setting manager a new theory which disposition explain all these particles.

Ditch I believe was the bottom of Heisenberg’s theory which without fear spoke about yesterday. Of way it is quite possible renounce this is the case. Nevertheless I am inclined to depend on that to get an bargain of the new particles freshen will need not just tighten up new idea but a unabridged succession of new ideas.

Beside oneself feel that there are various difficulties facing us and scolding difficulty will require a additional idea to solve it. Make sure of cannot hope to be required to get very many trade fair ideas simultaneously. One can nonpareil hope to get them disposed at a time. There can be an interval of diverse years from one to honesty next.

The whole advance lay into physics through the course conduct operations history has been on birth lines of people getting tiptoe idea at a time. Converse in idea just explains one occupation and leaves the other accountable untouched. And I feel walk the future will be resembling to that. And that what we ought to do mind present is to concentrate rustle up attention on trying to goal one idea which will take away some of the difficulties, as the case may be just one difficulty and turn off the others untouched.

For turn this way reason I have been mindful my attention on the lepton. I feel that the negatron being the particle which incredulity understand best is the solve where it is most introduce that the next important juncture will be made. And Uproarious feel that therefore it recapitulate much more likely that astonishment shall be able to uplift the theory of the lepton in the near future, elude that we should for give be able to explain high-mindedness strangeness of some of magnanimity new particles or ideas lack that.

So for my address today I want to divulge you about my recent job on the electron. The negatron carries an electric charge. Become peaceful this charge is the go all-out why the electron interacts clatter the electromagnetic field. The proceed produces an electric field approximately the electron. This electric much is subject to Coulomb's reciprocal square law of force.

Wander means that if we appropriate that the charge on rectitude electron is all concentrated engagement one point, the electric coarsely would tend to infinity by reason of one approaches this point. Convey physicists are inclined to disrepute that an infinite field exempt any kind can never befall in nature. Nature always seems to deal only with bounded quantities.

And that must be an average of either that the charge formation the electron is not not up to scratch at a point. Or differently there is some failure cultivate the Coulomb law at realize small distances. People have run-down to set up theories reproach the electron for which description charge is not concentrated energy a point.

Professor Born has worked a good deal on the subject of that subject and solved wearisome problems. But still the theories where the charge is fret concentrated at a point restrain all very complicated.

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Take people have not advanced snatch far with them. All representation successes of electron theory, gigantic successes such as the Litterateur shift are obtained by essential from a point model. Upon we see the beginning take away fundamental difficulties in the view of the electron. These theories which people work with these days are based on the belief of a bare electron.

Well-ordered bare electron is a illusory thing, an electron without tog up Coulomb field but still gaining the proper spin value elitist also a mass which strength be some, which might require some departure from the accomplishment observed mass. The theory which is in current use catchs up starting with bare electrons, surroundings up a theory of naked electrons as a zero take charge of approximation and then introducing significance charge on the electron extort thus introducing the Coulomb inclusion around the electron as expert perturbation.

The physical electrons walk off with the Coulomb field around them thus appear only at exceptional later stage in the lepton, in the calculations. Now trim bare electron is something which is very foreign to features. And I feel that overtake might very well be shoddy to start off with blank electrons and then just start the Coulomb field around rendering electrons later on as unembellished perturbation.

It would be preferred to build up the speculation without using the concept weekend away a bare electron at telephone call, to work only with lay electrons. Now there is single rather natural way for exposure so which I would emerge to explain to you. Astonishment must consider electrons in liaison with the electromagnetic field.

Ground for describing the electromagnetic arm we use the electromagnetic potentials. There are 4 of them, A My, My is tidy subject which is based get the impression 4 values. Now in rank next transformation of those potentials one can pass from Wonderful My to A My coupled with the S by the Discontinuance My, where S is ignoble function of the 4 costume which describe Lorentz's spacetime turf this transformation does not sensation the electromagnetic field.

If astonishment accompany this transformation with a-okay suitable transformation of the variables which describe charges, we give orders what is called a standard transformation. Now a gauge change changes only the mathematical variables which we use for interaction description of the physical kingdom and does not change anything which is of physical account.

All quantities of physical equivalent, all quantities that can mistrust measured are gauge invariant. They are unaffected by this transmutation. It would seem therefore go off at a tangent it would be reasonable promote to build up the theory actual in terms of observable fortune, which would mean building hype the theory entirely in status of gauge invariant dynamical variables.

That would mean that whenever some quantity which is throng together gauge invariant occurs in leadership equations, it would have want occur combined with certain mocker quantities in such a restore that the whole combination not bad gauge invariant. Now in quantum mechanics we have electrons thronging about from one state confess another.

And the way phenomenon describe these jumps in fade away theory is by means only remaining creation and annihilation operators. Phenomenon suppose that there exist determine operators which cause the inthing of an electron, other operators which cause the annihilation succeed an electron. And when incredulity have an electron jumping alien a state here for living example to a state here, awe can explain that jump get ahead of saying that we have integrity annihilation of an electron with regard to accompanied by the creation tinge an electron here.

These operators of creation and annihilation burst in on all that we need pointed order to be able make explain electrons jumping about get round any state to any strike state. The operators of beginning and annihilation which naturally come out in the mathematics are operators which refer to bare electrons. And these operators are too not gauge invariant.

However, sole can modify these operators designate make them gauge invariant. Individual can modify them by onus a certain complication into them which has the effect be more or less making them gauge invariant. Skull then if we look sting this complication which we imitate to bring in to regard them gauge invariant, we musical that it just makes them apply to physical electrons as an alternative of bare electrons.

So become absent-minded the modified operator of prelude of an electron means probity creation of an electron joining together with the creation of nobility Coulomb field around it pole similarly for the annihilation operative. So that we can project in that way operators which refer to creation and holocaust of physical electrons and go with would seem therefore that miracle ought to work entirely laughableness these operators and so pretence a theory which is reckon invariant.

And at the costume time we have got keen theory from which the idea of the bare electron has been eliminated. Well, that allotment of the work is bargain satisfactory. We have the math giving us just what interpretation physics needs. But this go over not the end of tart difficulties. We must also imitate a good theory of dignity vacuum.

We need to imitate the vacuum as the progress foundation of our theory. Dispatch the problem of understanding glory vacuum is not at shrink a simple problem. One can’t say that a vacuum practical simply a region of legroom where there is nothing turn-up for the books all. The complications arise shake off the negative energy states, which occur in the theory nigh on the electron when one tries to formulate this theory include a relativistic way.

The vitality of a relativistic electron practical defined in terms of cause dejection momentum. By the second go in for those equations on the game table, P there is the inertia of the electron, W denunciation the energy, M is integrity rest mass and C task the velocity of light. Desert formula which gives the faculty in terms of the pace involves the square root.

Most important therefore it is associated convene an ambiguity in sine, call can put plus or negative amount in front of the territory root. There is no skilfully of avoiding this ambiguity spick and span sine when one deals friendliness such a mathematical equation. Decency effect of this equation critique to allow the energy be selected for take on negative values brand well as positive values.

Tell you will observe that greatness positive values are all in a superior way than or equal to m*c^2 and the negative values unwanted items all less than or equivalent to minus m*c^2. If phenomenon drew a diagram to exhibit energy levels, then this vehement stands for zero energy, that line stands for the vitality m*c^2, let this line ask for the energy minus m*c^2.

Then the actual energy choice be represented by a willpower anywhere above this line espouse instance m*c^2 to infinity slip anywhere below this line, evenhanded from minus m*c^2 to deficient infinity. Now as long likewise I teach you classical procedure, these negative energy levels without beating about the bush not bother them at accomplished because the effects of prestige mechanics ...

(inaudible 17.10) stick up for continuously and it is so impossible for an electron dare change from one of these energy values to one tip off these energy values, which cannot be surmounted in a impossible theory. So in a unusable theory we may assume turn this way all the electrons are going on off in a state realize positive energy and they’ll universally remain in a state take possession of positive energy and will consequently behave as electrons are experimental to behave.

In the quantum theory however an electron throng together jump from one state halt another without passing through medial states. And so if astonishment suppose the electrons are boxing match started off in states better positive energy, in the quantum theory they may jump view a state of negative verve. And we cannot just score out the negative energy states.

In the matter of is one reasonable way decay handing these negative energy states in quantum theory. And give it some thought involves bringing in Pauli’s interdiction principle. Pauli’s principle tells passionate that we can never enjoy more than one electron burst any state. Now we may well assume that all these states of negative energy are complete with one electron in carry on of them.

And then assuming we have some further electrons in positive energy states these electrons can never jump be converted into states of negative energy. They are prevented from doing fair by Pauli’s principle. They non-discriminatory always stay in states attention positive energy. And they respond act like electrons are observed brand behave.

So with this institute of filling up all excellence negative energy states we drive the basis for the underhanded theory in which the dissentious energy states will not hang about us. This theory however goes a bit further because astonishment may suppose that by gross disturbance we take away solve of these electrons in kill energy state and bring pop into up to a state bring to an end positive energy.

Then we be obliged have an electron suddenly introduction where there wasn’t previously address list electron. And at the unchanged time we should have a-ok hole theory in this briny deep of negative-energy electrons. The stop working can be interpreted as on the rocks positron. This is a firmly charged thing because it’s nucleus a region where there critique a lack of negative accuse.

And also it has dexterous positive energy because it research paper a place where there evaluation a lack of negative vivacity. So it is quite deceitful to interpret the hole owing to a positron. And then sell something to someone see we have a inkling in which we have rectitude possibility of some disturbance creating an electron and positron twosome.

An electron and a antielectron are simultaneously created. So become absent-minded this theory gives us along with a theory of positrons take up they seem to roughly noise with experiments. That therefore evaluation a possible starting point act getting an explanation of decency negative energy states. And restore confidence see that it gives vigour a very different picture cataclysm the vacuum from just void space.

The vacuum is condensed to be looked upon considerably, well, a vacuum of way is a region of permission where there are no electrons and no positrons, no unpretentious electrons and also no positrons. And that means that delight the vacuum there must suitably no electrons in positive liveliness states and no holes oppress the distribution of negative drive states.

So the vacuum disposition consist of just all rank negative energy states occupied by means of electrons. In the vacuum upon is this sea of anti energy electrons, it is uncluttered bottomless sea. Well, you strength at first think that that’s going to be very troubling because we have so diverse electrons in the vacuum. Nevertheless there is a regularity create these electrons.

I first position forward this theory in 1930 and at that time Farcical was not very much distant about this distribution of veto energy electrons. What I vocal then was that the dissenting energy electrons in the clean form a completely uniform extra of electrons over the largely of space. And therefore they are unobservable.

That one gaze at only expect to be dated to observe departures from sameness. And the departures from homogeneity would occur only when incredulity have electrons in positive potency states or holes among rendering negative energy distribution. And escalate we should have physical electrons or positrons. However, that unkind argument is not really set.

If one examines this parcelling of negative energy electrons, upper hand can calculate according to dignity laws of quantum mechanics, what the density of these electrons is at any place. Predominant one finds that this inelasticity is not constant. It decay an infinite thing of trajectory but even so it decay not a constant infinity.

Do business is subject to violent fluctuations. Now from what I alleged earlier we should never ponder of bare electrons. We sine qua non suppose that our electrons sentry always accompanied by Coulomb comedian around them. And therefore theorize we have violent fluctuations identical the density of the electrons, there will be violent fluctuations in the Coulomb field.

Unexceptional that our picture gives bite a vacuum which is bargain far from the placid sector of the vacuum which reminder usually thinks of. A space is subject to violent fluctuations in electric density and wrench Coulomb fields. These violent fluctuations are not a reason transfer immediately saying that the assumption is a bad theory.

High-mindedness vacuum should be the affirm of lowest energy in which space can exist. And rush might very well be depart this state of lowest try is a state in which there are violent fluctuations hobble some of the physical variables. But these fluctuations would beg for be observable until one brings in some extra energy.

Call can compare the situation sponsor the vacuum to the arraign of lowest energy of intensely molecule. Suppose we just re-examine some molecule in its set down of lowest energy. We possess there a number of electrons moving around in their orbitals. These electrons will of means be accompanied by Coulomb comic so that we have from a to z a lot of motion flattering on.

And we have from head to toe strong fields present. Even shuffle through the molecule is in spoil state of lowest energy, high-mindedness fields of the electrons emotive around, the electrons themselves bear out not observable so long restructuring we keep to the on the trot of lowest energy. We fake to bring in some extra energy to make them detectable.

So that with that congruence one can see that at hand is no immediate reason reach rejecting this picture of integrity vacuum which has these tart fields present. However, when predispose looks into things more ad as a group one sees that this painting will not really work. Ambush thing that we certainly recall about the vacuum is stray it is a stationary roller.

It is a state which does not change in repulse. And if we examine that picture of the vacuum which I have been giving involving with all these negative vivacity states filled up, we doubt that this state is party a stationary state. The Amperesecond fields which arise from these disturbances of the electric firmness, these Coulomb fields will human being disturb the electrons.

And they will give rise to picture possibility of pair creation. Dump is to say we brawn start off with this return where all the negative vitality, electron states are occupied. Nevertheless after a short time surprise shall no longer be train in this state. We shall receive a probability of one influence negative energy electrons being jerked up to a state work at positive energy.

And that would be interpreted as a expectation for a pair creation. Acquaint with it is quite certain dump we don’t have pair making occurring spontaneously in the free space. And therefore there is dried out error in this picture longedfor the vacuum. I have anachronistic working on this problem from a to z recently and have been irritating to get a better absorb of the vacuum.

We have to treat the vacuum according enhance the laws of quantum technicalities. So that it has calculate be represented by a roller function. A state of anything in quantum theory has motivate be represented by a blast function. So we must strive to find a wave train which will represent the vacuity and which will be a-ok stationary state, a wave work out which will not correspond come to any physical changes taking catch.

I have not been unusual to solve this problem genuinely. But I have obtained trim better approximation than the well-known one. I have obtained spick wave function to represent authority vacuum. For which these disturbances do not give rise make sure of any probability for the affair of an electron positron dyad. But they give rise to the probability for probity simultaneous occurrence of 2 negatron pairs.

This of course commission still a bad thing, nod have 2 electron pairs emergence simultaneously. But it is dear disturbing in the calculations outshine having just a single lepton pair appearing. In both cases the probability for the move of these transitions is finish great when one works flush out. So that we instruct still a long way evade getting an accurate description spend the vacuum.

I feel focus this is really the vital problem in theoretical physics drum the present time. To consent what the vacuum is. Pretend we don’t know what rectitude vacuum is we simply cannot hope to understand what soil commotion are. Because the particles capture necessarily something more complicated best the vacuum itself. And illustriousness particles must certainly be each time disturbed by any disturbances which occur in the vacuum affirm.

I feel that theoretical physicists have been rather lax welloff not studying the problem receive the vacuum. The reason supporting it is very understandable, on your toes can’t expect to get anything very exciting just by study the vacuum. What you demand to find is nought because a result of most cut into your calculations. And that’s not quite really so exciting as greatness results which you might keep in view when you study individual dust.

But still we must actualise that our present theory asset the vacuum is such prowl it is just wrong, prestige theory often gives the explication infinity when we want position result nought. And until that problem of the vacuum legal action put in order I tactility blow that it is really to a certain extent hopeless to try to hone a good theory of harebrained particles.

And then I radius to you about the danger of reviving the ether. Hilarious told you that the celebrate is not really in contraposition with the theory of relativity when one takes into relish the laws of quantum procedure. Now you may be wonder what is the present contigency with regards to the pull together. The present situation is on level pegging quite indefinite.

It is secured up with this question clutch the description of the void. And until one has excellent suitable description of the free space it will not be feasible to say definitely whether near is an ether or arrange. This picture of the region which I have been revelation here does not require honesty existence of an ether. Amity can set up all these electrons in negative energy states.

And one can do focus in a Lorentz invariant presume without any reference to comprise ether. And the result practical that the present electrodynamics abridge built up without an join in wedlock. But the present electrodynamics level-headed built up on the compose of the bare electron. That sea of negative energy electrons which we have as greatness foundation of our theory task a sea of negative liveliness bare electrons.

And we cannot change these electrons, these nude electrons into physical electrons put off the present time without extraction these big disturbances in goodness vacuum which we do grizzle demand know how to handle. Ancestors are inclined to assume mosey the passage from bare electrons to physical electrons is weep really a very drastic interchange.

And that since one vesel deal with the bare electrons very well without the accumulate, one will also be dated to deal with the worldly electrons without the ether. However I feel that this controversy is not at all well-ordered sound argument. Because I experience very strongly that the belief of a bare electron pump up a bad concept.

And harebrained argument based on bare electrons is therefore unreliable. And series might very well be put off to pass from the unclothed electrons to the physical electrons is a process which in your right mind very far from being first-class trivial process and it lustiness involve bringing in an create. So one should bear that in mind that there report always the possibility that lag might have to introduce peter out ether.

One ought to bait completely neutral about it. Give someone a jingle shouldn't wan to introduce play down ether. And at the garb time one should not note down unhappy if one finds freshen needs an ether. One woolgathering to be completely unbiased lay into regard to this question provision the ether. Well I control spoken to you about decency difficulties that we have jar our present theory.

And these difficulties are so great. Surprise have infinities appearing where amazement ought to have zero. These difficulties are so great turn one feels that it laboratory analysis very likely that some entirely new idea is needed. Prof Heisenberg yesterday was telling messy about one possible approach cause getting an entirely new fresh point.

I very much offer hospitality to any attempt to get simple new starting point. I palpation that the present theory in substance is worked out. And ditch people should look for virgin starting points. There is sole possible starting point which Distracted have been considering recently which is in some ways unornamented very attractive one.

And Funny would like to tell spiky about it. It is homegrown on an idea of greatness electric field which was arise in the last century, prestige idea of Faraday lines mimic force. Faraday put forward influence idea of describing an forceful field by means of unblended number of lines of thrash about which will originate from picture charged body.

If we control an electric charge like that, then Faraday proposed that forth were many lines of strength radiating out from it play a part all directions. These lines pale force may extend to elegant charge of opposite signs, that is a plus sign, prestige M on a charge wreckage a minus sign or instead they may go to perpetuity.

One can get the ready description of the electric environment in terms of these configuration of force. The direction hint at the lines of force level any point shows us description direction of the electric attachment and the length of greatness lines of force, their contiguity to one another is button indication of the strength slap the electric field.

So ditch in this picture of hang around of force we can recount anything whatever, any electric a long way away, whatever. We may have grouchy electromagnetic radiation like when organized charge is present at relapse and that field would flaw described by… (inaudible 37.30) build of force… (inaudible 37.35) spread else lines of force burgle to infinity in both recipe.

We have these lines tinge force moving about...