On The Coming Revolution in Fundamental Physics

What is String Theory?

The Dewey B. Larson

Memorial Research CenterCopyright 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

F = maPosition

Momentum

Velocity Acceleration

MassEnergy

Force

More than 200 Years Later19th 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

Planck discrete energy

Einstein photo electric effect

Heisenberg uncertainty principle

Michelson|Morley constant light speed

Maxwell electromagnetic equations

Pauli exclusion principle

20th Century Revolutions inFundamental Physics

+G c = general relativity

+h c = quantum field theory

Planck Dirac

Standard modeltheory of matter and radiation

Theory of gravityEinstein

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 c =+

+ + = natural units

Plank mass Plank length Plank time

SM forces & gravity converge

?Planck

mp, lp, tp

Einstein

+G c h =+

“God constant”Energy constantGravitational

constantVelocity constant

Newton’s theory Relativity theory Quantum theory String theory?

Assume Vibrations at Fundamental length

Is String Theory the Next Revolution?

?

10-33 cmPlanck

mp, lp, tp

Einstein

Unification of Forces

Unification

Supersymmetry

The Basic Idea of Tiny Vibrations

Perplexing DilemmaWhat 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 SuccessfulEquations 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

20th Century Optimism

“…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!!

David Politzer, 2004 Nobel Lecture:

Surprise!

String theory is not unique

Galactic expansion is accelerating

So far, no Supersymmetry

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

} = 26 dimensional bosonic theory

} = 10 dimensional fermionic theoriesas aspects of one theory (M theory*)

12345678

*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

Add supersymmetry

Huge LHC at CERN to Search

Fundamental forces unified at very, very high energy, very short distances

Look for Supersymmetry

Comes online this year

Calabi-Yau Manifold

10500 possibilities!

Show Stopper Discovery of Non-Zero ZPE

1998 discovery: Universe expansion is accelerating implying non-zero ZPE!

ZPE = 10-8

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 space-time 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.”

7 Base Units

1) Kilograms2) Meters3) Seconds4) Ampere5) Kelvin6) Mole7) Candela

SI System

A Simple Observation

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

SI Units ST Units

Space and Time as Two Fundamental Units of Measure

Fiddling in Left Field

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?

Question:

The only knownknown physical relationship between space and time is motion:

v = ds/dtA change in the quantity of space for a quantity of time

Answer:

Critical Observations

Observed march of Time = 0D scalar increase

Observed expansion of space = 3D pseudoscalar increase

(Time has 20 = 1 direction of expansion)

(Space has 23 = 8 directions 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 = 2/1ds0/dt0 = 2/2

-1 1

Two octaves1/2 =.5 2/1 = 2

Fundamental 1st Harmonic 2st Harmonic

1|2 + 1|1 +2|1 = 4|4

Crucial Calculations

& from &

= = 6.6743e-8

= = 6.6260e-34

No success yet…

G ( )1/2

Mass, Energy, Gravitation

Notice that, dimensionally, energy of mass and radiation is just the inverse of velocity:

mc2 = t3/s3 * s2/t2 = t/shv = t2/s * 1/t = t/s

And Newton’s constant is time divided by mass squared: t = s6/t5

m2G =

So, dimensionally, mass is the square root of quantity time divided by G: t = t3/s3

G

m = ( )1/2

Thus, inverse mass is the square root of quantity G per unit time:= s3/t3

t1/m =

Fs2 = s6/t5

G m’m’’ s2 F =

m’m’’ Fs2 1/G =

m’m’’ G =

Dimensions of Space & TimeClearly, there are more than three dimensions of space and time in the equations of gravitational force:

= t/(t6/s6)

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.

s6/t5 t6/s6 s2

= t/s2 =

Conclusion

Physicists to study 3D, non-linear, vibrations, or “ball theory”

Upcoming Topics inLRC 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