On The Coming Revolution
in Fundamental Physics
What is String Theory?
The Dewey B. Larson
Memorial Research Center
Copyright 2008
Beginning of Fundamental Physics
Newton’s program of research: Focus on the forces
F = Gmm’
r2
Nature can be described as a few interactions among a
few particles using the calculus and the idea of the limit
Force
Velocity
Position
Acceleration
F = ma
Mass
Momentum
Energy
More than 200 Years Later
19th Century Optimism
Lord Kelvin stated:
"There is nothing new to be discovered in
physics now, All that remains is more and more
precise measurement."
…Not!!
Surprise!
Space and time are not absolute
Energy is not continuous
Maxwell  electromagnetic equations
Planck  discrete energy
Michelson|Morley  constant light speed
Einstein  photo electric effect
Heisenberg  uncertainty principle
Pauli  exclusion principle
th
20
Century Revolutions in
Fundamental Physics
G
+
c
=
Einstein
h
Planck
+
c
Dirac
general relativity
Theory of gravity
=
quantum field theory
Standard model
theory of matter and radiation
Trouble with Fundamental
Physics
• GR and SM are “deeply schizophrenic” theories
• General relativity: idealizes reality without ‘h.’
– Dynamic background, or background free, theory
– A non-quantum geometric concept (‘G’ + ‘c’)
• Standard model: idealizes reality without ‘G.’
– Fixed background theory
– A non-geometric quantum concept (‘h’ + ‘c’)
How Do We Unify the Theories?
Combine the Fundamental Constants!
G
+
h
+
Planck
+
Plank mass
c
=
SM forces
& gravity
converge
?
Einstein
+
Plank length
mp, lp, tp
= natural units
Plank time
Assume Vibrations at
Fundamental length
Is String Theory the Next Revolution?
G
+
c
+
= mp, lp, tp
h
?
Planck
Einstein
Gravitational
constant
Newton’s theory
10-33 cm

Velocity constant

Energy constant

“God constant”

Relativity theory

Quantum theory

String theory?
Unification of Forces
Unification
Supersymmetry
The Basic Idea of Tiny Vibrations
Perplexing Dilemma
What is the Natural Phenomena?
G = Gravitation
c = Speed of light
}
h = Energy quantum
lp = ?
Ad Hoc Invention
Edward Witten
“Unraveling String Theory”
“Einstein understood the central concepts of general
relativity years before he developed the detailed equations.
By contrast, string theory has been discovered in bits and
pieces — over a period that has stretched for nearly four
decades — without anyone really understanding what is
behind it. As a result, every bit that is unearthed comes as
a surprise. We still don’t know where all these ideas are
coming from — or heading to.”
Essay in Nature, 2005
David Gross:
What Recommends It?
• Principle feature is elimination of infinities
– If particles are actually 2D vibrations, paradox of point
particles and point interactions is eliminated
• Quantum gravity is an extra bonus
– Particles, as strings, include graviton
– Thus, quantum gravity emerges automatically
• It is what it is
– Does not have free parameters
– Cannot be modified
QFT Standard Model of Particles
GR “Standard Model” of Cosmology
Not Quite So Successful
Equations breakdown
Strings Eliminate Infinities
Black Hole Information Loss
In QM, information seemed to be lost…
Origin of the Universe
“One of the most important open questions.”
Strength of String Theory
• It’s an extension of traditional physics
• Replaces enigmatic 0D with intuitive 1D
• Promises unification of physical theories
Extension of Traditional Physics
–
–
–
–
–
–
First, Newton’s observation of ‘G’
Then, Einstein’s use of ‘c’ to modify ‘G’ theory
Second, Planck’s discovery of ‘h’
Then, Dirac’s use of ‘c’ to deal with ‘h’
These efforts led to two most successful theories ever
The next logical step is to hypothesize that these
constants define a fundamental length
Intuitive 1D Strings
– Leads to consistent, finite, concept of gravitons (quantum
gravity)
– Hints at structure with all the elements of standard model
– Replaces general relativity at small scales with graviton
– Eliminates black hole violation of quantum theory
– Promises eventual explanation of big bang singularity
Hoping for Supersymmetry
– Helps to unify the fundamental forces
– Helps explain the mass hierarchy
– Offers candidate for dark matter
Popularity of String Theory Soars
• Started for physicists when embraced by Ed
Witten
• Stephen Hawking’s expectations
contributed to media attention
• Brian Green’s book and Nova program
Elegant Universe fired public imagination
th
20
Century Optimism
David Politzer, 2004 Nobel Lecture:
“…many leading physicists were inclined to conclude in the
late 1970's that the task of basic physics was nearly complete,
and we'd soon be out of jobs….Hawking titled his lecture, "Is
the End in Sight for Theoretical Physics?" And he argued
strongly for ``Yes.“
…Not!!
Surprise!
So far, no Supersymmetry
String theory is not unique
Galactic expansion is accelerating
String Theory Problems
• Requires more physical dimensions than are observed
– Started with 26 dimensions
– Supersymmetry concept reduces to 10 (6 extra dimensions
of space), but it hasn’t been observed
• Non-unique theory and non-predictable (so far)
– There is practically an infinite number of ways to
conceptualize the required extra dimensions
– Leads to landscape of multiverse (10500 possibilities!)
• Strings are not observable
– Planck scale is beyond human reach
– Energy required to probe at this scale is just enormous
Supersymmetry Reduces
Dimensional Requirement
1
2
3
4
5
6
7
8
}
}
= 10 dimensional fermionic theories
as aspects of one theory (M theory*)
Add supersymmetry
= 26 dimensional bosonic theory
*Five incompatible superstring theories in 10 dimensions turn
out to be aspects of one superstring theory (M theory), through
the principle of duality and supergravity
Huge LHC at CERN to Search
Look for Supersymmetry
Fundamental forces unified
at very, very high energy,
very short distances
Comes online this year
Calabi-Yau Manifold
10500 possibilities!
Show Stopper
Discovery of Non-Zero ZPE
ZPE = 10-8
1998 discovery: Universe
expansion is accelerating
implying non-zero ZPE!
Properties of the Vacuum
Heisenberg’s uncertainty principle leads to
theoretical conclusion that the force between two
particles, which depends upon the distance between
them, is due to the dynamics of the fluctuating field
in the quantum vacuum.
Zero Point Energy (ZPE)
of Quantum Mechanics
ZPE Calculation was Big Problem
• Non-string calculation of ZPE is infinite
– Obviously wrong –has to be zero
– Must be zeroed by unknown mechanism
• String theory only reduces calculation
– With unbroken supersymmetry ZPE = 0
– With broken supersymmetry: ZPE = 1060
What to Think?
• “Anthropic” principle
– Argues that the existence of non-unique string theory
“solutions,” eternal inflation, and non-zero ZPE implies
a multi-verse of physical universes
• “Not Even Wrong” principle
– Argues that the landscape of non-unique “solutions” and
lack of predictive power implies a non-scientific theory;
i.e. string theory “Landscape” is un-testable
• “In Progress” principle
– Argues that the achievements of string theory, while
purely academic, at this point, are nevertheless
substantial, implying that a breakthrough is looming;
i. e. the revolution is coming
Attacking the Small
Cosmological Constant Problem
• Assume non-zero ZPE is a ratio of scales like
Dirac’s “Large Number” problem
– QCD solves logarithmically from unified Planck scale
– As energy drops, quarks become bound, fixing the size
(mass) of the proton
– QCD can calculate it within an order of magnitude, and
similar scale ratios appear solvable as well
• Hence, the real problem
– Is not calculating the small value of CC
– It’s finding the physical mechanism to account for it
• Dirac postulated that fundamental constants vary over time,
which was disproved, but the hypothesis was testable
Small ZPE Can Be Calculated
Within an Order of Magnitude
Work backwards, logarithmically
But What is the Physical Principle?
• This is the great unknown
– String theory can be constructed many ways
– But without a core physical principle
• The different constructions have no meaning
• String theory can even be constructed without strings!
• Something is still missing after 40 years
– Maybe it’s not a theory, but a framework, like QFT
– Yet, with no adjustable parameters, how can this be?
– Conclusion: The missing principle is very fundamental
• The missing physical law must have universal scope
– Einstein first pointed this out
– Physics only just now addresses these cosmological questions
– The ultimate cosmological question: “What is the nature of space
and time?”
“What is the Nature of Space and Time?”
“What is the Nature of Space?”
Implications of Emergent Space
• If initially no space, then initially no spacetime gravity (dynamics of space)
• If space-time is emergent, then time must be
also
• But how do we do physics without time?
• Gross: “This is the great, perplexing,
obstacle, the conceptual block, to our
progress with string theory.”
Physics Without Time?
Conclusion
• The coming revolution will constitute a
major change in our understanding of the
nature of space and time.
• “[It] probably requires a young Heisenberg
sitting somewhere to fiddle with something
totally off in left field that will lead to these
new concepts.”
– David Gross
Heisenberg’s Discovery was
Based on Observable Quantities
“The present paper seeks to establish a basis for
theoretical quantum mechanics founded exclusively
upon relationships between quantities which are in
principle observable.”
Heisenberg’s Rock?
"... it had become clear to me what precisely had to take the place of the Bohr-Sommerfeld
quantum conditions.....I was far too excited to sleep and so as a new day dawned, I made
for the southern tip of the island, where I had been longing to climb a rock jutting out into
the sea. I now did so without too much trouble and I waited for the sun to rise."
Fundamental Units?
“Measurement is Backbone of Science.”
SI System
7 Base Units
1) Kilograms
2) Meters
3) Seconds
4) Ampere
5) Kelvin
6) Mole
7) Candela
A Simple Observation
SI Units
ST Units
Dimensional analysis shows that any two of the seven historical SI
units may be regarded as independent, but since space and time units
are the most fundamental, we should use them for theoretical research.
- Xavier Borg
Space and Time as Two
Fundamental Units of Measure
Fiddling in Left Field
Question:
If the dimensions of gravitational constant,
G, as well as the quantum action, h, and the
speed of light, c, are units of space and
time, then what’s the physical implication?
Answer:
The only known physical relationship between
space and time is motion:
v = ds/dt
A change in the quantity of space for a quantity of time
Critical Observations
Observed expansion of space = 3D pseudoscalar increase
(Space has 23 = 8 directions of expansion)
Observed march of Time = 0D scalar increase
(Time has 20 = 1 direction of expansion)
New Idea
Start with
And then add the concept of vibration!
How Can We Do That?
By using observed constant ‘c’ for space/time expansion:
By using observed constant ‘R’ for space/time vibration:
Then vibration time scale is:
And vibration space scale is:
1D (ds/dt) Vibration
“String Theory”
Einstein Meets Hendrix
3D (ds3/dt0)Vibration
“Ball Theory”
ds3/dt0 = 1/2
ds0/dt3 = 2/1
ds0/dt0 = 2/2
-1
1/2 =.5
Fundamental
1
Two octaves
1st Harmonic
1|2 + 1|1 +2|1 = 4|4
2/1 = 2
2st Harmonic
Crucial Calculations
&
from
&
=
= 6.6743e-8
=
= 6.6260e-34
No success yet…
Mass, Energy, Gravitation
Notice that, dimensionally, energy of mass and radiation is
just the inverse of velocity:
mc2 = t3/s3 * s2/t2 = t/s
hv = t2/s * 1/t = t/s
And Newton’s constant is time divided by mass squared:
G = t 2 = s6/t5
m
So, dimensionally, mass is the square root of quantity time
divided by G:
m = ( t )1/2 = t3/s3
G
Thus, inverse mass is the square root of quantity G per unit time:
1/m = ( G )1/2 = s3/t3
t
Dimensions of Space & Time
Clearly, there are more than three dimensions of
space and time in the equations of gravitational force:
6/t5 t6/s6
2
s
F = G m’m’’
=
=
t/s
2
s
s2
1/G = m’m’’
Fs2
2
Fs
G=
= t/(t6/s6) = s6/t5
m’m’’
So, it seems very prudent to seek a natural unit of
space and time.
Whatever these units may be, we know that their
quotient, s/t, is the constant c, the speed of light.
Conclusion
Physicists to study 3D, non-linear,
vibrations, or “ball theory”
Upcoming Topics in
LRC Lecture Series
1) Unification of geometry and algebra: The Bott
Periodicity theorem and the Greek Tetraktys
2) On the foundations of quantum mechanics: the origin
of spin, uncertainty, and wave/particle duality
3) Combinations of 3D scalar vibrations as preons of
standard model particles
4) Energy, momentum and the periodic table of elements
5) Gravity and the zero-point vacuum energy dilemma
6) The big bang and the big rip - Revisiting the
implications of dark matter and dark energy