Electrons and the Vacuum
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00:00
ElementarteilchenphysikDiscovery <Raumtransporter>ElektronElektronenröhreChandrasekhar-GrenzeOptische SpektroskopiePhotonElektronisches BauelementProof <Graphische Technik>Coulomb-PotenzialCocktailparty-EffektColourOptisches SpektrumAtomphysikerSpannungsabhängigkeitVideotechnikTeilchenModellbauerSchwächungGrundfrequenzKalenderjahrIntervallDruckkraftWasserstoffatomHypothetisches TeilchenPostkutscheBasis <Elektrotechnik>GleitsichtglasWarmumformenSpinStrangenessFernordnungBildqualitätAbstandsmessungMasse <Physik>AtomistikLamb-ShiftEnergieniveauErderErsatzteilStörgrößeParallelschaltungTrockenkühlungUmlaufzeitElektronenstrahlStuhlPatrone <Munition>ElektronLadungstrennungBesprechung/Interview
09:32
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19:04
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28:35
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38:07
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Transkript: Englisch(automatisch erzeugt)
00:12
Yesterday, Professor Hasenberg and Professor Yukawa spoke to us about fundamental problems
00:22
in atomic physics. They told us how there are now many particles that are known. Some of them have been discovered only very recently. And the problem of the theoretical physicist is to make up a theory that will account
00:41
for these particles and explain their properties. So far, very little progress has been made with regard to most of these particles. Some of them have properties which are completely not understood. But among these particles, there is one which is pretty well understood, namely
01:04
the electron. We know much more about the electron than about any of the other particles. We have a theory of the electron which is really pretty good. It enables us to calculate, for example, the energy levels of the hydrogen spectrum
01:26
to an extremely high degree of accuracy, so high that one can determine very small corrections in the simple formulae, corrections known as the Lamb shift.
01:41
And these corrections, as worked out by the theory, are in good agreement with experimental results. In spite of this, the theory of the electron is not really complete. It is not complete because it is not mathematically self-consistent.
02:02
The theory is really a surprising mixture of good qualities and bad qualities, so that there is still a problem for the theoretical physicist to get a better theory of the electron. There are many physicists who believe that the problem of getting a better understanding
02:25
of elementary particles can come about only through setting up a new theory which will explain all these particles. That, I believe, was the basis of Heisenberg's theory which he spoke about yesterday.
02:45
Of course, it is quite possible that this is the case, but I am inclined to believe that to get an understanding of the new particles one will need not just one new
03:01
idea but a whole succession of new ideas. I feel that there are several difficulties facing us, and each difficulty will require a new idea to solve it. One cannot hope to be able to get very many good ideas simultaneously.
03:21
One can only hope to get them one at a time, and there may be an interval of many years from one to the next. The whole advance of physics through the course of history has been on the lines of people getting one idea at a time.
03:42
Each idea just explains one difficulty and leaves the other difficulties untouched. And I feel that the future will be similar to that, and that what we ought to do at present is to concentrate our attention on trying to get one idea which will remove
04:07
some of the difficulties, perhaps just one difficulty, and leave the others untouched. For that reason I have been concentrating my attention on the electron.
04:20
I feel that the electron, being the particle which we understand best, is the one where it is most likely that the next important step will be made. And I feel that therefore it is much more likely that we shall be able to improve the
04:40
theory of the electron in the near future than that we should, for example, be able to explain the strangeness of some of the new particles or ideas like that. So for my talk today I want to tell you about my recent work on the electron.
05:03
The electron carries an electric charge, and this charge is the reason why the electron interacts with the electromagnetic field. The charge produces an electric field around the electron.
05:22
This electric field is subject to Coulomb's inverse square law of force. That means that if we assume that the charge on the electron is all concentrated at one point, the electric force would tend to infinity as one approaches this point.
05:48
Now physicists are inclined to believe that an infinite field of any kind can never occur in nature. Nature always seems to deal only with finite quantities.
06:03
And that must mean either that the charge on the electron is not concentrated at a point or else there is some failure in the Coulomb law at very small distances.
06:21
People have tried to set up theories of the electron for which the charge is not concentrated at a point. Professor Born has worked a good deal on that subject and solved some problems. But still the theories where the charge is not concentrated at a point are all very
06:45
complicated and people have not advanced very far with them. All the successes of electron theory, the big successes such as the Lamb shift, are obtained by working from a point model.
07:05
There we see the beginning of fundamental difficulties in the theory of the electron. These theories, which people work with nowadays, are based on the concept of a bare electron.
07:25
A bare electron is a fictitious thing, an electron without its Coulomb field, but still having the proper spin value and also a mass, which might involve some departure
07:42
from the actual observed mass. The theory, which is in current use, involves starting with bare electrons, setting up a theory of bare electrons as a zero order approximation and then introducing the charge
08:04
on the electron and thus introducing the Coulomb field around the electron as a perturbation. The physical electrons, with the Coulomb field around them, thus appear only at a later stage in the electron in these calculations.
08:25
Now a bare electron is something which is very foreign to nature and I feel that it might very well be misleading to start off with bare electrons and then just introduce
08:44
the Coulomb field around electrons later on as a perturbation. It would be preferable to build up the theory without using the concept of a bare electron at all, to work only with physical electrons.
09:04
Now there is one rather natural way for doing so, which I would like to explain to you. We must consider electrons in interaction with the electromagnetic field and for describing
09:21
the electromagnetic field, we use the electromagnetic potentials. There are four of them, A mu, mu is a subject which takes up four values. Now one can make a transformation of those potentials, one can pass from A mu to A mu
09:46
because of the S by the X mu, where S is any function of the four coordinates which describe points in space-time and this transformation does not affect the electromagnetic
10:03
field. If we accompany this transformation with a suitable transformation of the variables which describe charges, we get what is called a gauge transformation. Now a gauge transformation changes only the mathematical variables which we use for
10:26
our description of the physical state and does not change anything which is of physical importance. All quantities of physical importance, all quantities that can be measured are gauge
10:43
invariant, they are unaffected by this transformation. It would seem therefore that it would be reasonable to work to build up the theory entirely in terms of observable quantities which would mean building up the theory entirely
11:04
in terms of gauge invariant dynamical variables. That would mean that whenever some quantity which is not gauge invariant occurs in the equations, it would have to occur combined with certain other quantities in such a way
11:24
that the whole combination is gauge invariant. Now in quantum mechanics we have electrons jumping about from one state to another and the way we describe these jumps in our theory is by means of creation and annihilation
11:50
operators. We suppose that there exist certain operators which cause the creation of an electron, other operators which cause the annihilation of an electron and when we have an electron
12:06
jumping from a state here for example to a state here, we can explain that jump by saying that we have the annihilation of an electron here accompanied by the creation
12:21
of an electron here. These operators of creation and annihilation are all that we need in order to be able to explain electrons jumping about from any state to any other state. The operators of creation and annihilation which naturally appear in the mathematics are
12:43
operators which refer to bare electrons and these operators are also not gauge invariant. However, one can modify these operators to make them gauge invariant. One can modify them by introducing a certain complication into them which has the effect
13:04
of making them gauge invariant and then if we look into this complication which we have to bring in to make them gauge invariant, we see that it just makes them apply to physical electrons instead of bare electrons so that the modified operator of creation
13:26
of an electron means the creation of an electron together with the creation of the Coulomb
13:40
We can get in that way operators which refer to creation and annihilation of physical electrons and it would seem therefore that we ought to work entirely with these operators and so get a theory which is gauge invariant and at the same time we have got a theory
14:03
from which the concept of the bare electron has been eliminated. Well that part of the work is very satisfactory. We have the mathematics giving us just what the physics needs but this is not the end of our difficulties. We must also have a
14:30
good theory of the vacuum. We need to have the vacuum as a very foundation of our theory and the problem of understanding the vacuum is not at all a simple problem.
14:50
One can't say that a vacuum is simply a region of space where there is nothing at all. The complications arise from the negative energy states which occur in the theory
15:07
of the electron when one tries to formulate this theory in a relativistic way. The energy of a relativistic electron is defined in terms of its momentum by the
15:25
second of those equations on the board. P there is the momentum of the electron, W is the energy, M is the rest mass and C is the velocity of light. That formula which gives the energy in terms of the momentum involves the square root
15:42
and therefore it is associated with an ambiguity in sign. One can put plus or minus in front of the square root. There is no way of avoiding this ambiguity of sign when one deals with such a mathematical equation. The effect of this equation
16:03
is to allow the energy to take on negative values as well as positive values and you will observe that the positive values are all greater than or equal to MC squared and the negative values are all less than or equal to minus MC squared.
16:23
If we drew a diagram to show energy levels and let this line stand for zero energy, let this line stand for the energy MC squared, let this line stand for the energy minus MC squared, then the actual energy could be represented by a line anywhere above this line
16:45
going from MC squared to infinity or anywhere below this line going from minus MC squared to minus infinity. Now as long as one keeps to classical mechanics,
17:01
these negative energy values do not bother them at all because in classical mechanics, all dynamics of air could change continuously and it is therefore responsible for an electron to change from one of these energy values to one of these energy values. We have here a vacuum which cannot be surmounted in the classical theory.
17:26
So in the classical theory, we may assume that all the electrons are started off in states of positive energy and they all will remain in states of positive energy and they therefore behave as electrons are observed to behave.
17:42
In the quantum theory, however, an electron can jump from one state to another without passing through intermediate states and so even if we suppose electrons are all started off in states with positive energy, in the quantum theory they may jump to states of negative energy
18:04
and we cannot just disregard the negative energy states. There is one reasonable way of handling these negative energy states in quantum theory and that involves bringing in Pauli's exclusion principle.
18:23
Pauli's principle tells us that we can never have more than one electron in any state. Now we may assume that all these states of negative energy are occupied with one electron in each of them and then if we have some further electrons
18:42
in positive energy states, these electrons can never jump into states of negative energy. They are prevented from doing so by Pauli's principle. They thus always stay in states of positive energy and they behave like electrons are observed to behave.
19:03
So with this trick of filling up all the negative energy states, we get the basis for the reasonable theory in which the negative energy states will not bother us. This theory, however, goes a bit further because we may suppose that by some disturbance
19:26
we take away one of these electrons in negative energy states and bring it up to a state of positive energy. Then we should have an electron suddenly appearing where there wasn't previously an electron
19:41
and at the same time we should have a hole appearing in this sea of negative energy electrons. The hole can be interpreted as a positron. This is a positively charged sea because there is a reason where there is a lack of negative charge
20:03
and also it has a positive energy because it is a place where there is a lack of negative energy so it is quite reasonable to interpret the hole as a positron. And then you see we have a theory in which we have the possibility of some disturbance
20:21
creating an electron and positron pair. An electron and a positron are simultaneously created. So this theory gives us also a theory of positrons and it seems to be in roughly agreement with experiments.
20:42
Well, that therefore is a possible starting point for getting an explanation of the negative energy states. And you see that it gives us a very different picture of the vacuum from just empty space.
21:01
The vacuum is now to be looked upon as, well the vacuum of course is a region of space where there are no electrons and no positrons, no ordinary electrons and also no positrons. And that means that in the vacuum there must be no electrons in positive energy states and no holes in the distribution of negative energy states.
21:25
So the vacuum will consist of just all the negative energy states occupied by electrons. In the vacuum there is this sea of negative energy electrons. It is a bottomless sea.
21:43
Well, you might at first think that that's going to be very disturbing because we have so many electrons in the vacuum, but there is a regularity about these electrons.
22:02
I first put forward this theory in 1930 and at that time I was not very much worried about this distribution of negative energy electrons. What I said then was that the negative energy electrons in the vacuum
22:23
form a completely uniform distribution of electrons over the whole of space and therefore they are unobservable and that one can only expect to be able to observe departures from uniformity and the departures from uniformity would occur only when we have electrons in positive energy states
22:46
or holes among the negative energy distribution and then we should have physical electrons or positrons. However, that simple argument is not really correct.
23:00
If one examines this distribution of negative energy electrons, one can calculate, according to the laws of quantum mechanics, what the density of these electrons is at any place and one finds that this density is not constant.
23:22
It is an infinite thing, of course, but even so it is not a constant infinity, not a constant infinity. It is subject to violent fluctuations. Now, from what I said earlier, we should never think of bare electrons.
23:44
We should suppose that our electrons are always accompanied by Coulomb fields around them and therefore if we have violent fluctuations in the density of the electrons, there will be violent fluctuations in the Coulomb field.
24:04
So that our picture gives us a vacuum which is very far from the plastic region of the vacuum which one usually thinks of. A vacuum is subject to violent fluctuations in electric density and in the Coulomb fields.
24:24
These violent fluctuations are not a reason for immediately saying that the theory is a bad theory. The vacuum should be the state of lowest energy in which space can exist
24:43
and it might very well be that this state of lowest energy is a state in which there are violent fluctuations in some of the physical variables. But these fluctuations would not be observable until one brings in some extra energy.
25:02
One can compare the situation of the vacuum to the state of lowest energy of some molecule. Suppose we just consider some molecule in its state of lowest energy.
25:21
We have there a number of electrons moving around in their orbitals. These electrons will of course be accompanied by Coulomb fields so that we have quite a lot of motion going on and we have quite strong fields present even though the molecule is in its state of lowest energy.
25:45
The fields of the electrons moving around, the electrons themselves, are not observable so long as we keep to the state of lowest energy. We have to bring in some additional energy to make them observable. So that with that analogy one can see that there is no immediate
26:05
reason for rejecting this picture of the vacuum which has these strong fields present. However, when one looks into things more closely, one sees that this picture will not really work.
26:25
One thing that we certainly know about the vacuum is that it is a stationary state. It is a state which does not change in time. And if we examine this picture of the vacuum which I have been giving here with all these negative energy states filled up,
26:45
we see that this state is not a stationary state. The Coulomb fields which arise from these disturbances of the electric density,
27:01
these Coulomb fields will themselves disturb the electrons and they will give rise to the possibility of pair creation. That is to say we might start off with this state where all the negative energy electron states are occupied,
27:22
but after a short time we shall no longer be in this state. We shall have a probability of one of the negative energy electrons being jerked up to a state of positive energy and that would be interpreted as a probability for a pair creation.
27:43
Now it is quite certain that we don't have pair creation occurring spontaneously in the vacuum and therefore there is some error in this picture of the vacuum. I have been working on this problem quite recently and have been trying to get a better picture of the vacuum.
28:10
We must treat the vacuum according to the laws of quantum mechanics so that it has to be represented by a wave function. The state of anything in quantum theory has to be represented by a wave function.
28:25
So we must try to find a wave function which will represent the vacuum and which will be a stationary state, a wave function which will not correspond to any physical changes taking place.
28:41
I have not been able to solve this problem accurately, but I have obtained a better approximation than the usual one. I have obtained a wave function to represent the vacuum for which these disturbances do not give rise to any probability
29:04
for the occurrence of an electron-positron pair, but they give rise only to the probability for the simultaneous occurrence of two electron pairs. This of course is still a bad thing to have two electron pairs appearing simultaneously,
29:25
but it is less disturbing in the calculations than having just a single electron pair appearing. In both cases the probability for the occurrence of these transitions is infinitely great when one works it out,
29:44
so that we are still a long way from getting an accurate description of the vacuum. I feel that this is really the central problem in theoretical physics at the present time, to understand what the vacuum is.
30:02
If we don't know what the vacuum is, we simply cannot hope to understand what particles are, because the particles are necessarily something more complicated than the vacuum itself, and the particles must certainly be always disturbed by any disturbances which occur in the vacuum state.
30:26
I feel that theoretical physicists have been rather lax in not studying the problem of the vacuum. The reason for it is very understandable. You can't expect to get anything very exciting just by studying the vacuum.
30:43
What you want to find is nought as a result of most of your calculations, and that is not really so exciting as the results which you might expect when you study individual particles. But still we must realize that our present theory of the vacuum is such that it is just wrong.
31:04
The theory often gives the result infinity when we want the result nought. And until this problem of the vacuum is put in order, I feel that it is really rather hopeless to try to get a good theory of any particles.
31:21
Three years ago I also had the pleasure of addressing you, and then I spoke to you about the possibility of reviving the ether. I told you that the ether is not really in a contradiction with the theory of relativity when one takes into account the laws of quantum mechanics.
31:48
Now you may be wondering what is the present situation with regard to the ether. The present situation is still quite indefinite. It is tied up with this question of the description of the vacuum,
32:04
and until one has a suitable description of the vacuum, it will not be possible to say definitely whether there is an ether or not. This picture of the vacuum which I have been describing here does not require the existence of an ether.
32:26
One can set up all these electrons in negative energy states, and one can do that in a Lorentz invariant way without any reference to an ether. And the result is that the present electrodynamics is built up without an ether.
32:48
But the present electrodynamics is built up on the concept of the bare electron. This sea of negative energy electrons, which we have as the foundation of our theory, is a sea of negative energy bare electrons.
33:07
And we cannot change these electrons, these bare electrons, into physical electrons at the present time without getting these big disturbances in the vacuum which we do not know how to handle.
33:22
People are inclined to assume that the passage from bare electrons to physical electrons is not really a very drastic change, and that since one can deal with the bare electrons very well without the
33:40
ether, one will also be able to deal with the physical electrons without the ether. But I feel that this argument is not at all a sound argument, because I feel very strongly that the concept of a bare electron is a bad concept,
34:00
and that any argument based on bare electrons is therefore unreliable. And it might very well be that to pass from the bare electrons to the physical electrons is a process which is very far from being a trivial process, and it might involve bringing in an ether.
34:26
So one should bear this in mind that there is always the possibility that one might have to introduce an ether, one ought to be completely neutral about it, one shouldn't want to introduce an ether,
34:40
and at the same time one should not be unhappy if one finds one needs an ether, one ought to be completely unbiased with regard to this question of the ether. Well, I have spoken to you about the difficulties that we have with our present theory,
35:02
and these difficulties are so great, we have infinities appearing where we ought to have zero, these difficulties are so great that one feels that it is very likely that some quite new idea is needed.
35:20
Professor Heisenberg yesterday was telling us about one possible approach for getting an entirely new starting point. I do not very much welcome any attempt to get a new starting point, I feel that the present theory basically is worked out and that people should look for new starting points.
35:43
There is one possible starting point which I have been considering recently, which is in some ways a very attractive one, and I would like to tell you about it. It is based on an idea of the electric field which was current in the last century,
36:05
the idea of Faraday lines of force. Faraday put forward the idea of describing an electric field by means of a number of lines of force which would originate from the charged body.
36:23
If we have an electric charge at a point like this, then Faraday's code, there were many lines of force radiating out from it in all directions, these lines of force may extend to a charge of opposite sign.
36:41
If this is a plus sign, they end on a charge of a minus sign, or alternatively they may go to infinity. One can get the complete description of the electric field in terms of these lines of force. The direction of the lines of force at any point shows us the direction of the electric field
37:06
and the density of the lines of force, the closeness of one another, is an indication of the strength of the electric field. So that with this picture of lines of force we can describe any field whatever, any electric field whatever.
37:21
We may have just a few of electromagnetic radiations without any charge present at all, and that that field would be described as an electric field with lines of force in the closed loop, or else lines of force going to infinity in both directions.
37:41
We have these lines of force moving about in classical electric dynamic theory. They will be moving about and their motion will give us a magnetic field and we can get a complete description of the electromagnetic field in terms of these moving lines of force.
38:02
This gives us a satisfactory classical electric dynamics. Now I would like to make the assumption that when we go over to quantum theory, we have no longer a continuous distribution of these lines of force.
38:22
We just have discrete lines of force, some finite number of discrete lines of force. Instead of having them spread over the whole state, we have just a few of them. We have no lines of force in between them.
38:44
Each line of force is then associated with a definite electric charge and this electric charge will appear with a positive sign at one end of the line of force and a negative sign at the other end of the line of force.
39:03
The natural assumption to make now is that every line of force is associated with the same charge and this charge is just the electronic charge E. So that wherever we have a line of force in this picture,
39:23
a line of force of course is associated with a direction, there is a charge first at one end of the line of force and a charge of line E at the other end of the line of force. We may of course have the line of force going to infinity in one direction or in both directions
39:42
and then we shall not have the charge of theory. I think that this is a reasonable picture to have in quantum theory and this will mean that our basic field is not a point particle but is something that is used for string.
40:02
We have a number of strings which are now moving about and they will move according to the laws of quantum mechanics. We may sometimes have a string breaking and if a string breaks, then we shall have a charge minus E appearing at this end,
40:22
a charge plus E appearing at this end and that means that we have the creation of an electron and a positron pair. We have now a simple interpretation of electrons and positrons just as the ends of these strings.
40:41
To get an explanation of other particles, we must suppose that we may sometimes have the end of one of these strings anchored to a heavy particle. It may be anchored to a nucleon or to a meson and that will then mean that the nucleon or the meson has a charge.
41:06
With this picture, we are immediately led to an explanation of why charges always occur in multiples of the electronic charge. That is one of the fundamental laws of nature which hasn't been explained yet.
41:25
The law of nature is that we never observe fractions of this charge E but always whole multiples of this charge E. Well, with these discrete strings to represent parallel lines of force, we necessarily get an explanation of this law.
41:45
The advantage of this picture which I have been giving to you is that it is a picture in which a bare electron is not really something which we say must not occur.
42:01
A bare electron is now inconceivable. The electron itself is just the end of a string. The string itself represents the Coulomb field which is radiating out from the electron. In this picture, we cannot have a bare electron which is quite inconceivable
42:23
because it is inconceivable to think of the end of a piece of string without having the piece of string itself. I feel that such a theory where bare electrons are inconceivable would be a definite improvement from the present type of theory
42:43
where bare electrons are concealable and we have to introduce it as a rather fictitious assumption into our calculations that they don't occur. Now, we might bring up as an objection to this picture of the electron that it is very unsymmetrical.
43:03
The classic picture of the electron is a picture like this where the Coulomb field is represented by parallel lines of force radiating out in all directions equally. The Coulomb field is distributed with symmetry about the electron.
43:21
Now, here we have a Coulomb field all concentrated into a single parallel line of force. However, we don't necessarily have to give up the idea of the spherical symmetry of the Coulomb field around the electron because we must remember that we must always apply quantum mechanics to these strings.
43:46
These strings will be subject to a principle of uncertainty. In general, the way which the string lies will not be sufficiently definite for us to be able to draw it like this.
44:02
The way the string goes will be distributed over various possibilities with a certain probability law. And we can very well set up a picture of the electron which we have an electron here. We can very well set up a state for the electron
44:21
for which the string is equally probable to be drawn out in any direction from this electron. This kind of mathematics involved in that is similar to the mathematics which one needs in order to set up a spherically symmetrical state
44:41
of the hydrogen atom. One can have a hydrogen atom with the electron distributed with spherical symmetry about the proton, meaning simply that any orientation for the electron with respect to the proton is equally probable. And in just the same way, this single parallel line of force
45:01
may be radiating out from this electron in any direction with equal probability. So that there is no immediate objection to this picture on the grounds of the natural symmetry of the Coulomb field around the electron. I feel that this is a nice picture, but there are great difficulties in developing this
45:23
which I have not yet been able to solve. There is an obvious difficulty which comes in to begin with, namely that we must change the usual expression for the energy density of an electric field.
45:43
By concentrating all the electric field coming out from an electron into a single line of force, if we keep to the usual expression for the energy density of electric field, we shall be bringing in an infinity where there wasn't one previously
46:02
and we shall be just increasing our difficulties instead of getting over any of them. So that it will be necessary to have some new expression for the energy density of electric field. And then, of course, this theory must be essentially a quantum theory. It is to be associated with single electrons
46:23
and that requires that the end of a string shall always be associated with a spin of a half a quantum, because there is always a spin of a half a quantum with an electron. That must bring in some very peculiar spin properties for this string,
46:44
some properties which do not believe one can get any picture in the classical theory. I feel that when one is dealing with a spin of a half a quantum, one has got into a region for which the classical pictures no longer help us
47:04
and we have to depend entirely on the mathematics of the quantum theory. It will be necessary to bring in some strange spin properties for these strings in order to explain the spins of the electrons.
47:21
Well, I will conclude at this point. We have got into a situation where we have just the starting idea and there are difficulties in developing it mathematically and for the present I don't see how to get on with those difficulties.