Transcript Big Questions – some answers?

Einstein and the big
questions – some answers?
Morelia, MEXICO 2006
R. Delbourgo, November
What big questions?










What is the fate of the universe?
How did the universe begin?
What is the universe made of?
Where is the antimatter in the universe?
Why are there only 3 “generations” of particles?
Why are there no magnetic charges?
Is there another basic unit besides h & c? GN?
Can one predict the 20 or so SM parameters?
Are relativity & CPT conservation correct?
Can one unify gravity with quantum theory?
Current ideas on the universe’s fate

The universe is expanding at an ever increasing
rate (based on assumptions about supernovas)!
So is there a cosmological constant?
Einstein and the early universe
There was NOTHING before the big bang,
no space, no time, zilch, i.e. it had zero
dimensions.
Einstein on the early universe: “One may
not assume the validity of the equations
for very high density of field and matter,
and one may not conclude that the
beginning of expansion must mean a
singularity in the mathematical sense”
What is the universe made of?



75% vacuum energy
20% dark matter (non-baryonic = machos, wimps, neutrinos,
axions,..)
5% mostly visible matter (baryonic = known particles, atoms)
etc.
Fate of the universe
Supernova data => accelerating expansion
corresponds to a -ve pressure or an Einstein
“cosmological constant” of Λ = 10-52 m-2.
Compare with known scales:
Nuclear size ~ 10-15 m
Human size ~ 1 m
Milky Way galaxy ~ 1022 m
Size of visible universe ~ 1026 m
Einstein on the size of the universe: “Only two
things are infinite: the universe and human
stupidity. And I’m not sure about the former.”
The scale of things
Einstein and Research
Einstein on research: “If we knew what we were
doing, it would not be called research, would it?”
Einstein and Relativity

Overturned our notions of space and especially
time, through the special theory of relativity.
Einstein on the 4-dimensional Minkowskian
description: “Since the mathematicians have
invaded the theory of relativity, I do not
understand it myself any more.”

Connected curvature of spacetime with the presence of
matter-energy through his
general theory of relativity, e.g.
the bending of light.
Einstein on the happiest thought
of his life, namely discovering
the equivalence principle: “I was
sitting in a chair in the patent
office when all of a sudden a
thought occurred to me: If a
person falls freely he will not feel
his own weight. I was startled
and this simple thought made a
deep impression on me. It
impelled me towards a theory of
gravitation.”
Einstein and astronomy
Started off the science of cosmology, introducing
the cosmological constant (his “biggest blunder”).
Einstein to Weyl: “If there is no quasistatic world,
then away with the cosmological term.”
“Anyone who has never made a mistake has never
tried anything new.”

Predicted gravitational lensing, seen for some
galaxies and now used (as “microlensing”) to
detect stellar planets.

Predicted the existence of gravitational radiation
from changing non-spherical systems (Einstein’s
quadrupole formula).
Detected indirectly from orbiting pulsars and
most recently the double-pulsar J0737-3039.
Einstein, Antimatter & the Big Bang
Einstein on the Big Bang Theory: “For
every billion particles of antimatter there
were one billion and one particles of
matter. And when the annihilation was
complete one billionth remained – and
that’s our present universe.”
The difference is ascribed to CP violation
as seen in elementary particle physics.
Einstein and quantum mechanics




Postulated the existence of the photon
(his most revolutionary idea -> Nobel
prize)
Described the heat capacity of bodies at
low temperatures using quantum theory
Developed the statistics of integer spin
systems and predicted the existence of a
“Bose-Einstein” condensate (recently
discovered at 10 μK)
Predicted stimulated light emission from
metastable states (leading to lasers)
Einstein and Unified Field Theory
Einstein on Maxwell: “Imagine his feelings when
the differential equations he had formulated
proved to him that electromagnetic fields spread
in the form of polarized waves and with the speed
of light!”


Tried to unify electromagnetism and gravity
(oblivious of other forces)
Based much on his work on the 5-dimensional
extension of space-time by Kaluza & Klein
Higher Dimensional Schemes
Quantum Field theory




To every system (or
particle) is associated a
quantized field.
Particles are subdivided
into source-fields (usually
spin ½) and force-fields
(usually spin 1).
Fundamental sources are
“quarks” and “leptons’.
Force fields include
photons, weak bosons,
gluons and gravitons.
Source (and some force) fields interact with one
another by exchanging force fields.
Particle Generations and the SM
3 (light) generations discovered so far:
(ne, e, u, d, u, d, u, d)
(nm, m, c, s, c, s, c, s)
(nt, t, t, b, t, b, t, b)
Interacting via force (gauge) fields:
g (graviton), g (photon), W & Z (-bosons),
G (gluons in 8 mixed colours) but
masses widely different: Mt >350000 Me and
Mn <100000 Me.
How come?
Magnetic monopoles - where?
Maxwell’s equations:
 Electric charge ~ spread of electric field
 Electric current ~ twist of magnetic field &
change of electric field
 0 = spread of magnetic field
 0 = twist of electric field & change of
magnetic field
i.e. there are no free magnetic monopoles!
Searches have never revealed them.
The fundamental scale constants


Planck’s h sets the scale of action
Light-speed c sets the scale of velocity
Is there another basic independent scale?
Newton’s gravitational constant GN?
Einstein’s cosmological constant Λ ?
NB: There are many ill-understood scale
free constants of nature, e.g.
fine structure constant α ~ 1/137,
Me/Mp ~ 1/2000, etc.
Two sorts of numbers?







Bose (commuting)
x y = +y x
A(x)B(y) = +B(y)A(x)
Associate with integer
spin fields
Symmetric states
Obey BE statistics
Increase dimension
c-numbers
Fermi (anticommuting)

ξη=-ηξ

ψ(x)χ(y) = -χ(y)ψ(x)

Associate with ½
integer spin fields

Antisymmetric states

Obey FD statistics

Decrease dimension

a-numbers
Property coordinates?
Introduce 5 (complex) a-coordinates ξ0 to ξ4
represent property and attach to the four real ccoordinates x0 to x3 for space-time:
X = (xm, ξμ)
which can potentially reduce the total effective
dimensions of the universe to 0.
Property tells us what things (quantum nos.) are
involved in an interaction, so any event is
characterized by
WHERE, WHEN and WHAT
Composite properties




As the ξ anticommute
there are only a finite
number of properties.
Bose fields have even
ξ powers, Fermi fields
have odd ξ powers.
e.g. e ~ ξ4 , n = ξ0
u ~ ξ0ξ1ξ2, d ~ ξ3ξ2ξ4.
Can accommodate 3
particle generations
(with 4 extra D and
one extra l – nl pair)
Geometrizing gravity





Einstein tied gravity to
curvature of space-time
Curvature R ~ matter-energy T
Curvature associated with a
space-time Riemann metric
squared distance ds2
ds2 = dxm gmn dxn where gmn is
the (10 component tensor)
gravitational field
R = R(g) & T = T(energy)
Geometrizing forces




Forces tied to extended
metric connecting space
to property (e.g. charge
due an electron there).
ds2 includes contribution
dxm gmµ dξµ where
gmµ = λ2 Am ξµ and Am
are the gauge fields.
Space-property curvature
is the electroweak or
chromomagnetic field.
λ is a scaling constant.
Geometrizing property

rage

cry
cry


rage
The state of a system is a
linear combination of
properties.
Metric distance includes
term dξµ gµndξn where gµn
is the (scalar) Higgs field.
Changes of property
depend on order of
operation in general.
Property curvature ~
variation in strength of
the forces.
The various curvatures



Rspace-space ~ gravity and matter
Rspace-property ~ charges and force
Rproperty-property ~ sources and strengths
The total curvature is the sum of all R-terms:
it describes gravitational interactions, forces
between material sources and includes a
cosmological term (its value depends on the
constant λ tying property to length in the
“metric distance”).
Another theory that bites the dust?
Some advice from Einstein
“Any intelligent fool can
make things bigger and
more complex. It takes …
a lot of courage to move
in the opposite direction.”
“If A is success in life,
then A equals X plus Y
plus Z. Work is X, Y is
play and Z is keeping your
mouth shut.”
In conclusion:
There is a time (t)
and a place (x)
for every thing (ξ)