Space, Mass, and QuarksSpace, Mass, and Quarks

P. ŻenczykowskiP. ŻenczykowskiInstitute of Nuclear PhysicsPolish Academy of Sciences

Kraków, Poland

May 11, 2006

Physics provides

DESCRIPTION of phenomena

In order to describe phenomena we use language

Over centuries we have found that a very useful description is provided by the language of mathematics

Consequently, some people think that mathematics may lead us in our attempts to describe Nature

This is erroneousMathematics does not lead anywhere

It just provides a tool which facilitatesand quantifies the description and the idea behind it

In reality we are almost totally blind, we have no maps of new territory - it was, it is, it always will be like that

Perfect figurePerfect figure

r2

Pythagoras - the most perfect figure is a Pythagoras - the most perfect figure is a sphere

rmmF 2

21

SphericallySphericallysymmetricsymmetric

rmmF 2

21

rr2 - 2 - SO(3) scalarSO(3) scalar

Vision, intuition,aesthetics

Macroscopic classical space and elementary particlesMacroscopic classical space and elementary particles

At least some of the attributes of observed particles are closely connected with the properties of macroscopic space

Examples:Spin – rotationSpin – rotationParity, chirality – space reflection PParity, chirality – space reflection PExistence of particles and antiparticles – C – CPT Existence of particles and antiparticles – C – CPT – – (Antiparticles as particles moving backward in time) (Antiparticles as particles moving backward in time)

Other quantum numbers – internal symmetries? Flavour, colour?There were attempts – no connection seen so farNO GO theorems

However: such NO GO theorems are valid only EXACTLY in the form they were provenHowever: such NO GO theorems are valid only EXACTLY in the form they were proven

In fact: there exists an enormous space of untried concepts, ways, and possibilites

HYPOTHESIS: All attributes of elementary particles are connected with the properties of macroscopic classical arena on which physical processes are deemed to occur

Roger Penrose:Roger Penrose:(„Structure of spacetime”, 1968)

Other physicists of similar opinions:Other physicists of similar opinions:Wheeler: „How could one believe any account of the foundation for the central structure „How could one believe any account of the foundation for the central structure of physics, spacetime, which proceeded without reference to the quantum,..?”of physics, spacetime, which proceeded without reference to the quantum,..?”Finkelstein: „inherent spacetime illusion”: „inherent spacetime illusion”Einstein: „Time and space are modes by which we think, …”: „Time and space are modes by which we think, …”

I do not believe that a real understanding of the nature of elementary particles can ever be achieved without a simultaneous deeper understanding of the nature of spacetime

TWISTORS ?

Nonrelativistic or relativistic description ?Nonrelativistic or relativistic description ?

Spin – rotation - nonrelativisticSpin – rotation - nonrelativistic

Parity – reflection - nonrelativisticParity – reflection - nonrelativistic

Existence of left and right does not have much to do

with Lorentz transformationsand different transformations of

L and R

For example one may linearize Schrödinger equation 2mE=p2

Invariance under reflections requires thatp2 p 1 = 0 3

p –p 1 1 – 1

Left and Right, Dirac matrices -- no relativity needed

Somebody may say: but relativistic Dirac equation

not only yieldsproper gyromagnetic ratio g=2

[e (L + 2 S)B/m]but also leads to ANTIPARTICLES

This is true.But it does NOT follow from relativity!

Gyromagnetic:Levy-Leblond 1971

Particles to antiparticles?Particles to antiparticles?Nonrelativistic description is enough: (Horzela, Kapuścik; P.Ż)

In words: no relativity is needed in the idea of antiparticles as particles moving „backwards in time”

In formulas: in linearized Schrödinger equation we must obtain the term (p – e A) 1 (p – e A)

As for Dirac case: complex conjugation yields (p* – e A) *

But p* = – p, and C * C-1 = hence – (p + e A) ( C = – i 2 2 ) change of relative sign at „e”

This suggests that NONRELATIVISTICNONRELATIVISTIC description should be sufficient (at least at the beginning) when

trying to extend our understanding of quantum numbers of elementary particles in terms of space concepts

MassMass

Higgs mechanism:Higgs mechanism:

(+) renormalizability with massive gauge bosons

(() THEORY: ) THEORY: just shifting the problem

constant term in energy density of constant term in energy density of vacuumvacuum

55 orders of magnitude too large55 orders of magnitude too large

EXPERIMENT: EXPERIMENT: not observed (?)

PHILOSOPHY: PHILOSOPHY: tendency to „explain” phenomena in terms of material objects rather than abstract concepts („heat fluid”, …)

Particle and quark massesParticle and quark masses

F = e v x BF = ma

e/m, m

theory used to extract mass

Free particlesFree particles THEORETICALTHEORETICALCALCULATIONSCALCULATIONS

LQCD(mq)mp, mn, m

mp= fp,theory(mq,…)

i.e. again: theory used to extract mass

Conceptually identical

method actually used method NOT usedPROBLEM

Constituent, current quark massesConstituent, current quark massesconstituent – current with interactionconstituent – current with interaction

251 qqA current:current:

25121252112 qqmmqppqAm

mmmmmm sdduK ,, 22

external quarks

Free Dirac equation usedQuarks on mass shellPlane, infinite waves

No confinement

Nothing in common withmp = fp,theory(mq,…)

Constituent – e.g. magnetic momentsFree Dirac quarks again

CONCEPTUALNONSENSE

Quark mass – internal quarksQuark mass – internal quarksTreesTrees

LoopsLoopsWRHD

s uu

No quark model pole

No: ZweigYes: Gell-Mann SU(3)L SU(3)R

charmed quark mass

Gaillard, Lee (1974) 1.5-2.0 GeV

ds

sd

Quark mass through propagator

meson formfactors

(Schwinger – magnetic moments)

DEEPLYDISSATISFYING:

1) Conceptual problems & internal inconsistencies2) Point 1 either unnoticed or „swept under the carpet”

Mass problemMass problem

Quark mass - no standard propagators (trees)

- some meaning in loops?

- extension of concept ? detach concept of mass from concept of standard propagator broader structure needed

One basic constant needed: e.g. m0

– other masses from (unknown) theory through dimensional mass ratios

If (c), ħ added – the basic constant may be of dimension GeV/cm( Fundamental length, momentum)

M. Born -1949 – „Reciprocity theory of elementary particles”

„I think that the assumption of the observability of the 4-dimensional

distance of two events inside atomic dimensions (no clocks or

measuring rods) is an extrapolation…

…I am inclined to interpret the difficulties which QM encounters in

describing elementary particles and their interactions as indicating

the failure of that assumption

There is of course a quantity analogous to R=t2-x2, namely P=E2-p2 , not continuous (square of rest mass). A determination of P is not a real measurement, but a choice between a number of values corresponding to the particles…

It looks, therefore, as if the distance P in momentum space is capableof an infinite number of discrete values which can be roughly determined,while the distance R in coordinate space is not an observable quantity at all

This LACK OF SYMMETRYLACK OF SYMMETRY seems to me very strange and rather improbable.”

Born’s principle of reciprocityBorn’s principle of reciprocity(„odwzajemnianie, wzajemność”)(„odwzajemnianie, wzajemność”)

Laws of nature are invariant under reciprocity transformation:

xk pk, pk -xk

kkkk x

H

p

H px

,

kllk ipx ,

kllkkl pxpxL

Arena of PhysicsArena of Physics

Usually adopted description: arena = spacetime

Macroscopic space on which (classical) processes are described

Hamiltonian formalism: independent position and momentum coordinates

CONJECTURE:

use NONRELATIVISTIC PHASE SPACENONRELATIVISTIC PHASE SPACE as the arena on which processes are to be described

introduce constant [GeV/cm] to permit SYMMETRICSYMMETRIC treatment of momentum and position

Further arguments (nonrelativistic)Further arguments (nonrelativistic)In classical Hamiltonian formalism – time occupies a distinguished

position – it is a parameter upon which p and x depend

In quantum mechanics p and x are operators, while time is still a c-number parameter

Relativistic field theory unites relativity and quantum physics,but does this in a formal way, argued by many to be unsatisfactory(Wigner, Dirac, Chew, Finkelstein, Penrose)

Instantaneous reduction of a nonlocal state does not seemto be in accord with the spirit of relativity (instantaneous in which Lorentz frame?)

This highlights essential difference between time and space,In spite ot these notions being united in the concept of Minkowskian spacetime (description!)

Local Lorentz-equivalent frames are not fully equivalent physically(background radiation defines a preferred frame)

Further physical arguments (GeV/cm)Further physical arguments (GeV/cm)

1) Description in terms of spacetime followed from the observation that Maxwell equations are form-invariant under Lorentz transformations, which transform time space,

with [c]=cm/s being the dimensional constant

permitting these transformations to be effected

2) String-like properties of hadrons (with energy proportional to the length of the string)

suggests introduction of []=GeV/cm;

whether is related to 1/’ 1 GeV2 or m2Planck 10 38 GeV2

is irrelevant at the moment

Constants (phase space, GeV/cm) and ħ (quantum, GeVcm) suffice to set mass scale.

Thus, the problem of mass may be addresssed.

dual string model of 60’s-70’s: relevant constant is [’] = GeV - 2 (slope of Regge trajectories) (add [ħc] = GeV cm);

nowadays: string-like properties of hadrons - confined flux tubes, here: more fundamental in origin

„„Perfect figure” in phase spacePerfect figure” in phase spaceGeneralization: beyond Born reciprocity

beyond sphere in 3 dimensions

22xp O(6)

Require Poisson brackets (commutators)

to be form-invariant

U(1) SU(3) „global”

local?local? Perhaps, but:further conceptual shifts needed

GeneratorsGenerators

...

...

...

8

31135

12212

21211

F

pxpxF

pxpxF

xxppF

SU(3) U(1)

Standard rotations + …

R = …R = …

Reciprocity transformations,Standard reflections

p -x - px p - x

So far p and x treated completely symmetrically:One cannot really say what is momentum and what is position

Standard mass: Standard mass: momentum-position distinctionmomentum-position distinction

For individual objects separated by large distances:

energy of observed FREE objects (elem. particles) is defined by their

mass and momenta (either via relativistic or nonrelativistic formula)

THE STANDARD CONCEPT OF MASSmay be said to be directly ASSOCIATED with the concept of momentum (p),NOT position (x)

Recall: BornRecall: Born

The six-dimensional vector (p1,p2,p3,x1,x2,x3)is divided into two triplets of canonically conjugated variablesin such a way that ONE of the triplets is ASSOCIATED with the concept of „mass”

Generalization of the concept of massGeneralization of the concept of mass

Is such a division into (p1,p2,p3) and (x1,x2,x3) unique?

Gen.momentum gen.position

(p1,p2,p3) (x1,x2,x3)

(p1,x2,-x3) (x1,-p2,p3)(-x1,p2,x3) (p1,x2,-p3)(x1,-x2,p3) (-p1,p2,x3)

SU(3)SU(3)

U(1)U(1)

Generalizarion through SU(3), not U(1)

Odd # of p’s Even # of p’s

SO(3)

SO(3)

Concept of mass may be ASSOCIATED with these 1 + 3 possibilities

Rotational (translational) invariance ?Rotational (translational) invariance ?Since each of three new choices violates rotational invariance –

- an object with mass associated with any one of these choices

CANNOT belong as individual object to our rotationally invariant

macroworld

However, these objects could belong to macroworld as unseparable components of composite objects,provided the latter are constructed in such a way, that all appropriate invariance conditions are satisfied

CONJECTURE: QUARKSCONJECTURE: QUARKSArgument that strong interactions are rotationally etc. invariant is NOT a valid one:

What we ALWAYS see is the interaction of external probes (photons, W,Z bosons) with colour-singlet currents. Colour-singlet current has quantum numbers of a colourless meson, and from the point of photon, etc. behaves like a hadron – not an individual quark (e.g. VMD)

In other words quarks have to conspire in such a way that the resulting composite object – hadron - behaves in a „normal” way

Toy modelToy modelApply SU(3) to Dirac equationApply SU(3) to Dirac equation

(simpler than non-rel. Schródinger)

(linearize p2+x2+m2)

kk

kkk

B

B

A

20

0300

010

..........

1

0,,,

2,,

BB

BBBABA

BBAA

kklk

kllklk BmpAH kkD

BmxBxBpAH

BmxBpAxBH

BmxBxBpAH

B

G

R

332211

332211

332211

H = HR+HG+HB

Rotational invariance restored

Charge conjugationCharge conjugation

HD=Ak(pk- e A k)+Bm+e A 0Explicit particles

Antiparticles through reinterpretation

c.c.: i - i, x x, t t, H - H, p - p, Ak A*k, B B*, A A, m m, e e,

-H’D= A*k(-pk- eA k)+B*m+e A 0C=-i 222

CB*C-1=-BCA*kC-1=A k

CB*kC-1=B kHD=Ak(pk+ eA k)+Bm-e A 0

HR=A1(p1- e A 1)+B2x2+B3x3+Bmquark

HR=A1(p1+e A 1)-B2x2-B3x3+Bmantiquark

When particle goes into antiparticle,physical quantities change as follows:

E E, , ,p p, x - x, e - e, m m, (and i - i)

Simple quark-antiquark systemSimple quark-antiquark systemmBxxBxxBppAHH RR 2)()()( 333222111

Translation and rotation invariant after summation over quarks, antiquarks of all three types Translation and rotation invariant after summation over quarks, antiquarks of all three types

Spin 0 and 1 (tensor product Spin 0 and 1 (tensor product kl0))

Comments:* additivity of quark charges* additivity of quark masses* appearance of a „string”* intrinsic angular momentum of a quark: p1 x2 etc.* objects exhibiting well-defined properties of one kind

do not have well-defined properties of another kind* vague similarity to RISHON scheme of Harari (1979)

Two rishons (charge): T(+1/3), V(0)

e+ T T T u T T V T V T V T T V V V d V V T V T V T V V

Last transparencyLast transparency

Mirage only? I believe not…

CONCEPTS OF PHYSICS:CONCEPTS OF PHYSICS:

„Physics is based on well-founded concepts, and its progress relies heavily on the creation of new concepts.

Our understanding of Physics deepens as we gain new perspectives on already existing notions.

Therefore, Physics continuously requires both new concepts and new perceptions of the old ones.”