Gerard ’t HooftGerard ’t Hooft ENS Paris, October 2008

Utrecht University

What is an

A scientific day in memory of Philippe MEYER (1925 - 2007)

Particles in experimentsElementary vs Composite Unstable particlesPole in propagatorDressed and bare particlesParticles in GRParticles at HorizonsGravitonsThe disputes about QMOntological objectsProtons, Photons and Phonons

Particles in experiments

Elementary vs Composite

In Effective Quantum Field Theory, this distinctiongradually disappears. Particles are elementary at one scale, composite at another. Use Ren. Group.

Is a black hole a composite particle ?Is a black hole a particle ?Is a particle a black hole ?

Is technicolor a viable theory ?The Higgs as a shifted particle:

Unstable particles

2 2

2 2

1

( ) ( )

k m i

k k m

2 2

2 2 2

1( )

( )( )| ( ) |

k m i k

kkk m i k

†stable stableS S I † end end

product productS S I

Dressed and Bare Particles

x x x x

x x

+ + ...

+

+ ...x xx

General Relativity:Particles in curved space-time

0

†

20

( , ) ( ) ( )d k i t ik x i t ik xk

x t d e a k e a k

( , )t t x t

†1 2( ) ( ) ( )a a a

Particles and horizons, the hybrid picture

Is the graviton an elementary particle?

Gauge dependence: not a problem,as in Yang-Mills ...

Is graviton distinct from matter ?gravity – matter unification ...

In “crystalline gravity”, space-time is a crystal where“defects” play the role of matter and gravitons.

gravitons are as photons.

A particle is an energy quantum.Can this yet be a tangible, “ontological”,physical object?

This leads to the disputes concerning theinterpretation of quantum mechanics.

The Bohr – Einsteindispute.

Today’s historiansof science contend

that the dispute wassettled in favour of Niels Bohr: Quantum Mechanicsis non-deterministic.J.S. Bell is said to havesettled the issue withthe Bell Inequalities.

A new variety of the same idea: theConway – Kochen Free Will Theorem

Consider two entangled massive spin 1particles, with total spin S = 0 :

( ) ( ) ( )

( )2 ( )2

(1) (2)

[ , ]

2

( ) 0

i j i j ia b abc c

i ia

a

a a

S S i S

S S

S S

2 2 2 2 2 2

2 2 2

2 2 2

or or

[ , ] [ , ] [ , ] 0

2

, ,

(1,1,0) (1,0,1) (0,1,1)

x z y z x y

x y z

x y z

S S S S S S

S S S

S S S

In case of spin 2 :1 1

2 22 2

1 12 2

10 , 1

1z xS S

1

10

The 4 cubes of Conway & Kochen

It is impossible to attach 0’s and 1’s to all axes at the positions of the dots, such that all orthogonaltriples of axes have exactly the (1,1,0) combination.

Source

(1) (2) 0S S

1 2

Conclude:Free Will Theorem:

If observers on the two differentsites have the free will to choose

which axes to pick, the spin valuesof the two particles cannot be

pre-determined. No “hidden variables ”

This proves (once again) that particles are NOTaccompanied by “hidden variables” that dictate:

< if you choose this axis, then you measure this value for the spin >

But it does not disprove hidden variable modelsof a more delicate nature:

There could be field variables at ultra short distance scales, that evolve deterministically,while non-commuting quantum operators are still needed to handle the statistics at intermediate scales.

In such theories, what we call elementaryparticles today, are not exactly eigenstates ofthe “ontological” observables (beables).They are eigenstates of non-commutingoperators,even though the evolution of the system maybe deterministic: a large class of commuting operators evolve into operators that stillcommute with them – the beables.

Compare:

protonsphotonsphonons

An elementary particle is a calculationalunit. Its appearance may vary, dependingon cicumstances. Under some conditionsit may appear to be very real, being something that can be detected in apiece of apparatus.But in other cases its ontological statusis much more vague.