Elementary Particles
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Lindau Nobel Laureate Meetings22 / 340
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00:00
Yukawa, HidekiParticle physicsForceNuclear powerMesonParticleRadioactive decayPauli, WolfgangAngeregter ZustandProzessleittechnikQuantum numberElementary particleLambda baryonIsospinNeutrinoQuantumStrangenessWeak interactionSpin (physics)LightColor chargeRulerSteckverbinderOrder and disorder (physics)Alcohol proofYearNeutronPionNuclear powerSpare partBird vocalizationMeasurementGroup delay and phase delayPower (physics)Roll formingTARGET2Cartridge (firearms)IceRoman calendarTransmission towerGreen politicsProgressive lens
08:13
Radioactive decayPauli, WolfgangParticle physicsQuantum numberStrangenessElementary particleQuantumMitsubishi A6M ZeroNegationMaxwellsche TheorieQuantization (physics)PhotonicsWeak interactionOrder and disorder (physics)MesonSpare partAtomic form factorSingle (music)Linear motorTypesettingCocktail party effectCartridge (firearms)Composite materialVideoForceNeutronRoll formingWoodturningSunriseEffects unitLambda baryonCosmic distance ladderMassSteckverbinderShort circuitProgressive lensAngeregter ZustandAutumnKopfstützeWind waveSchwache LokalisationPair productionHose couplingSpantGroup delay and phase delayDayBallpoint penDirect currentGreyPower (physics)Catadioptric systemNeutronenaktivierungWatercraft rowingAerodynamicsCurrent densitySpin (physics)Bending (metalworking)Nuclear physicsEngineGentlemanMeeting/Interview
16:27
Particle physicsRadioactive decayLightGround stationSpare partKraftfahrzeugzulieferindustrieGround (electricity)TypesettingRoll formingYearElectronic mediaElementary particleMaser, VenetoOrbital periodMinuteMorningGlättung <Elektrotechnik>MassCogenerationPhotodissoziationMusical developmentOrder and disorder (physics)RulerSchwache LokalisationCapacitanceWoodturningSeparation processMaxwellsche TheorieWind waveCartridge (firearms)StrahldivergenzQuantization (physics)SharpeningSunriseMeeting/Interview
24:40
Pauli, WolfgangParticle physicsRadioactive decaySteckverbinderCrystal structureProgressive lensSpare partRail transport operationsFACTS (newspaper)QuantumMaxwellsche TheorieStrangenessElementary particlePair productionIsospinTypesettingOrder and disorder (physics)AnnihilationLungenautomatSpeckle imagingNorthrop Grumman B-2 SpiritCurrent densityWind waveElectric power distributionEuropean Train Control SystemTrajectoryCosmic microwave background radiationScale (map)DrehmasseQuantum numberNetztransformatorElectronic mediaStationeryFinger protocolPhase (matter)Narrow gauge railwayGround stationAmplitudeRulerInkFormation flyingYearGroup delay and phase delayMassCommitteeAngeregter ZustandColor chargeBiasingClassical mechanicsGeokoronaOptical cavityTurningMeeting/Interview
32:53
VideoMaterialElectric power distributionNanotechnologyVery low frequencyComputer animation
Transcript: English(auto-generated)
00:12
What I'm going to talk was already spoken greatly by Professor Heidenberg.
00:21
But fortunately, I couldn't follow exactly what he had spoken in German. So please excuse me if there's too much over-wrapping in what I'm going to say, which was spoken already by Professor Heidenberg.
00:42
Now, three years ago, I had the opportunity to talk to you here on a little attempt at the unified theory of elementary particles. Since then, it has become more likely that the new quantum numbers
01:05
or new degrees of freedom, which were introduced in order to distinguish between various kinds of new and old particles, could hardly be reconciled with the notion of quantum mechanical motion
01:30
of a particle which was confined within three-dimensional ordinary space or four-dimensional spacetime of spatial relativity.
01:47
In fact, those theories which have been successful in classifying new and old particles and in deriving a number of selection rules related to elementary processes
02:10
have the following general assumptions in common. In addition to orbital and spin quantum numbers,
02:23
there are extra quantum numbers which characterize the properties and the interactions of common as well as strange particles, you may say, old and new particles.
02:44
For instance, the concept of isospin, which was already discussed by Professor Heidenberg and Professor Pauli and Professor Bohn, the concept of isospin, which had been convenient for distinguishing
03:06
between different charge states of pi meson, pi plus, pi zero, pi minus one,
03:20
as well as between the neutron and the proton. This concept of isospin was extended by pi so as to include the newly discovered unstable particles
03:43
such as lambda particle, theta meson, and so on. Thus, the isospin quantum number was connected with the state of motion in a space which was called omega space,
04:05
a new space which has apparently no connection with the ordinary three-dimensional space. And the distinction between strong and weak interactions
04:22
was attributed to the even-odd rule for the parity of states of particles in this space. According to a further refinement due to Gherman and Nishijima, it is necessary to introduce another quantum number which is called the strangeness,
04:48
which again does not have any relation as yet to the ordinary space. In any case, the point is as follows.
05:01
Whereas the old quantum numbers were directly connected with the state of motion in ordinary space, the new quantum numbers are introduced apparently at least with no such connection. Granted that such theories have something essentially correct in it,
05:26
which reveals a new aspect of the world of elementary particles. Our further step is to have a deeper insight into the significance of new degrees of freedom
05:43
so that we would be able to approach nearer to a unified theory of elementary particles. At this point, one is tempted to raise an old question once more. Are these common and strange particles all elementary?
06:06
One may well be expecting the answer. Namely, only very few of them are really elementary, all others being composite.
06:22
In fact, there have been various attempts at reducing the number of really elementary particles. The earliest of such attempts was perhaps the neutrino theory of light by de Broglie.
06:44
More recently, there appeared the nuclear pair theory of pi meson by Fermi and Yang. However, now that we are informed of the existence of a variety of new particles,
07:03
which seems to necessitate the introduction of such a concept as strangeness, we have to count among really elementary particles some of the strange particles for the following reason.
07:24
We expect that the strangeness quantum number of a composite particle is the sum of strangeness quantum numbers of the constituent elementary particles.
07:42
Now, all the common particles, such as the nucleon, anti-nucleon, and pi meson, are assumed to have the strangeness quantum number zero, while the new unstable particles, such as the lambda particle or theta meson,
08:07
are assumed to have the strangeness quantum number, which are positive or negative integers different from zero. Thus, we have to count among elementary particles
08:23
at least two kinds of strange particles with the strangeness quantum number plus one and minus one, respectively. For instance, according to recent proposal by Markov and Sakata,
08:47
the lambda particle and the anti-lambda particle with the strangeness quantum number minus one and plus one, respectively, are on the list of really elementary particles,
09:03
in addition to the neutron, proton, anti-neutron, and anti-proton, all of which have the strangeness zero. Obviously, such an answer immediately gives rise to another question,
09:23
what would be the primary interaction between these really elementary particles? It is clear that a very strong attraction between a neutron and an anti-nucleon
09:46
must exist at very short distances in order that they form a composite particle of mass as small as that of the pi meson.
10:03
In such a case, the effect of the interaction might be drastically different from what we could infer from the usual quantum theory of fields, which, after all, is based on the assumption of weak interaction.
10:23
Thus, the formulation of quantum theory of non-linear fields becomes a matter of more urgent needs, as emphasized by Professor Heidenberg in the preceding lecture.
10:42
Now, the properties of the stationary solutions of classical non-linear field equations have been investigated by a number of authors in spite of the formidable mathematical complications.
11:01
In particular, just take the case which Finkelstein has been dealing with. He concentrated his attention to the so-called particle-like solutions, whereas a linear field equation, which is associated with free particles,
11:25
has plane-wave solutions extending over the whole space. Non-linear field equations, which correspond to particles with self or mutual interaction, turn out to have, in certain cases, stationary solutions that are concentrated in a small region of space.
11:51
Each of such solutions could be regarded as representing a particular form of the elementary particle
12:03
with a definite mass, spin, charge, etc. However, it depends on the procedure of quantization of non-linear fields, whether such interpretation in the framework of classical field theory
12:26
survived all changes from classical to quantum theory. Now, the relativistically invariant method of quantization of fields has been greatly refined
12:42
and developed in connection with quantum electrodynamics and meson theory during the last decade, as to which Professor Heidenberg already discussed in detail. Although the method was inseparably connected with the assumption of recoupling between linear fields,
13:09
one may well expect that some part of it could be taken over by non-linear field theories. Actually, Professor Heidenberg recently developed an ingenious method of quantization
13:26
on this line. Thus, he tried to deduce various types of particles as stationary solutions of quantized non-linear equations for a single spinor field or maybe two such fields.
13:46
This is a further step along the lines of de Broglie, Fermion, and others above mentioned. However, in his formulation, usual Hilbert space with a positive definite metric
14:04
was to be so generalized that the metric was no longer positive definite. This means that the concept of probability in quantum mechanics cannot be applied straightforwardly, but the introduction of the strange concept of negative probability is necessitated.
14:29
Thus, it is still an open question whether a mathematically consistent theory could be constructed in this way as discussed by Professor Pauli.
14:41
In this connection, one may look for another formulation in which the particle-like solutions of classical field equations would remain after quantization as something which characterizes the shape of the particles.
15:01
There is some attempt on this line, although it is still far from being accomplished. In any case, such a method would be intimately related to field theories with so-called non-local interactions.
15:20
By a non-local interaction, we mean an interaction which is related to the simultaneous appearance and disappearance of particles not at the same point, but at nearby points in the four dimensional world.
15:42
This is because the form factor in the case of non-local interaction could be determined from the particle-like solutions if you quantize non-linear field equations. It should be noticed further that these two methods may not be entirely different from each other,
16:08
but the negative probability and non-locality may turn out to be two sides of the same thing. We know of a very simple and peculiar example in quantum electrodynamics,
16:26
namely the elimination of time-like photons with which the notion of negative probability could be associated results in Coulomb interaction between charged particles,
16:45
which is a kind of non-local interaction. However, we do not know exactly what would be the situation in non-linear field theories. Now let us turn to the problem of non-locality of interaction or a field itself.
17:05
When I talked to you three years ago, I discussed the possibility of introducing extra degrees of freedom of motion of an elementary particle in relation to the non-locality of the wave field which is associated with the particle.
17:31
Namely, the concept of the field which had been represented by a function of a set of space-time coordinates
17:41
was extended so as to include the non-local field which was represented by a function of two sets of space-time coordinates, the ordinary local field being a limiting case where the dependence on the relative coordinates tend to be a delta function.
18:11
The particle associated with such a field has the degrees of freedom of internal motion in addition to those of the motion of its center of mass.
18:24
Obviously, the internal motion as well as the motion of the center of mass takes place in the same space-time world of spatial relativity, namely Minkowski space. This is an unavoidable restriction which has its own disadvantage as well as advantage for the following reason.
18:55
On the one hand, the inherent divergence difficulties of the relativistic field theories
19:02
could be dealt with precisely because the internal and external motions are correlated with each other in the same space in such a way that the internal motion may serve for smoothing out the divergences attached to the external motion.
19:25
On the other hand, however, this gives rise in turn to a disadvantage. Namely, in the world of spatial relativity, an invariant space-time region
19:41
cannot be confined to a small volume around the origin but extends always to infinity along the light cone. We could overcome the difficulty by considering the internal motion
20:01
as something attached rigidly to the motion of the center of mass, provided that the mass was different from zero. However, the situation is very complicated when the non-local field in question interacts with other fields.
20:27
The internal motion as well as the external motion would be influenced by the interaction or in other words, the particle would be deformed in a complicated manner.
20:42
We do not know yet how to deal with such a deformability adequately. The problem of causality is closely connected with that of non-locality as discussed already by Professor Heidenberg.
21:01
In order to describe the causal relationship between two events in spatial theory of relativity, one is obliged to accept the sharp separation of past, present and future from each other by the light cone in Minkowski space.
21:26
The introduction of non-locality somewhere in the theory, however, tends to obscure this sharp distinction. Thus, it is difficult in general for a non-local theory
21:43
to reconcile the requirement of causality with that of spatial relativity, although it may not be impossible but certainly it's very difficult in general. On the other hand, these requirements are both satisfied in local field theories
22:03
at the cost of regularity of functions such as propagators on the light cone. There are another point which one has to keep in mind when one speaks of causality in field theory.
22:22
Namely, one must ask himself at the outset, to what phenomena are the causal laws to be applied? Such a question has become more significant since the development of field theory
22:42
in recent years by which the procedure of renormalization turned out to be indispensable. Generally speaking, the causal relationship is not to be applied directly to the primary quantities in terms of which the fundamental natural laws are formulated,
23:07
but to those secondary quantities which are so modified from primary quantities as to be more directly connected with observable phenomena.
23:22
One may imagine, for example, that one would start from an overall space-time picture in future theory of elementary particles and then derive causal relationships between phenomena which are more or less localized.
23:44
Under these circumstances, it would not be useless to reconsider the whole subject from an entirely different standpoint. These are two theories of elementary particles started from certain types of classical fields
24:06
which were subject to quantization afterwards. In other words, we took up the wave aspect of the elementary particles first and the particle aspect subsequently.
24:24
Now one may ask the question, is it at all possible to reverse the order? It is certainly not easy to do so because we have thus to leave the firm ground
24:40
of well-established space-time structure of spatial relativity, at least for a moment, and start anew from the bare fact of appearance and disappearance of multifarious particles in nature. One may be inclined to think that this is too far departed from the familiar quantum theory of fields
25:07
to expect to result in anything fruitful. However, such an approach does not seem very strange if we recall the spirit of Einstein's theory of general relativity,
25:24
namely, in the large-scale world, the space-time framework is not predetermined independently of the distribution of matter and energy in it.
25:40
But they are related to each other intimately. One may well suspect that such a mutual regulation of framework and content would exist also in the small-scale world, though in a way very much different
26:06
from the one in the large-scale world. In the usual field theories, the regulation is one-sided because the space-time structure is fixed before we consider the wave field.
26:28
The opposite side of the mutual regulation would be the influence of the behavior of elementary particles on the, so to speak, fine structure of the space-time world,
26:43
or the small-scale world in a more general sense. I mean the world including the omega space or some other space which may have some relation to the strangeness quantum number.
27:01
Such a world may be decomposed asymptotically into the Minkowski space and the space corresponding to extra degrees of freedom such as isospin and strangeness. In order to give a little more definite image to this idea,
27:21
let us consider the appearance and disappearance of particles as such. The structure of space-time world in the background being purposely left aside. These particles can exist in a great variety of different ways.
27:46
They can be different from each other either for the reason of having different masses, spins, charges, etc., or merely for the reason of existing at different places
28:02
or having different values of energy and momentum. Let us forget for the moment that such worlds as spin, energy, momentum, etc., are already closely connected with the structure of the space-time world.
28:21
And let us say in broader terms that the particles can exist in a great number of different ways which can be distinguished between each other by means of a set of certain quantum numbers.
28:42
Some of these quantum numbers may be discrete and others may be continuous, but let us for brevity denote the set of quantum numbers simply by j which can be 0 or any integer. Then the appearance and disappearance of a particle of type j
29:02
could be represented by the creation operator and the annihilation operator which satisfy the familiar commutation relation. There should be some direct or indirect connection between any two creation and annihilation operators
29:24
with different values of j. Otherwise, the appearance and disappearance of a great variety of particles could be entirely chaotic to say nothing of their ordered behavior in the space-time world.
29:43
Now, there are two kinds of ordered behavior of particles according to our customary way of thinking. One is the ordered motion of particles in the narrow sense. In classical mechanics, this was represented by a trajectory in space
30:06
or a world line in space-time world. In modern formulation of classical mechanics, the corresponding terms appear as the kinetic energy part or free part of the Lagrangian.
30:29
The second kind of ordered behavior is the possibility of transformation between different types of particles.
30:41
Such a possibility can be dealt with only in quantum mechanics and is represented by appropriate terms in the interaction part of the Lagrangian. Keeping this in mind, we may hope to give order to the chaotic assembly of creation and annihilation operators.
31:07
Namely, we may assume the existence of a certain function of these operators which plays a role similar to the Lagrangian in classical and quantum theory of fields.
31:21
The invariance or symmetry properties of this function with respect to the linear transformations of infinitely many operators would be connected with the more familiar symmetry properties in current field theories of elementary particles.
31:43
All this is certainly a wishful thinking. I do not at all expect an easy success of such an approach. I suggest merely that such an approach may not be entirely useless
32:00
since we do not know yet as to what extent the structure of world of very small scale would be different from that of the world more easily accessible to us. It seems to me that the approach from the wave picture
32:22
which starts from the classical wave field and then quantizes has been so much developed and so widely investigated that we are reaching close to the point where a complementary approach to the same goal
32:41
would be of some help for further progress.