String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point
but as a little loop of vibrating string. Ed Witten (1951-)
Unification: Consistency is required. Actual high-energy unification is not.
In order of appearance :
Steven Weinberg,
Michael Green,
Jim Gates,
Peter Galison,
Marcia Bartusiak,
Joseph Polchinski,
Walter Lewin,
Amanda Peet,
Nima Arkani-Hamed,
Edward Farhi,
Michael Duff,
Ed Witten,
Joe Lykken,
Sheldon Glashow,
Gabriele Veneziano,
Lenny Susskind,
John Schwarz,
Cumrun Vafa,
David Gross,
Savas Dimopoulos,
Burt Ovrut,
Nathan Seiberg,
Gary Horowitz,
Alan Guth,
Paul Steinhardt,
Maria Spiropulu.
The current epistemological status of String Theory is probably best grasped by
comparing it with another theory devised in simpler times:
The Dirac equation was a clever example of a theory
consistent with the axioms of both quantum mechanics and special relativity.
Some of the concepts involved in its interpretation may not have survived
the test of time but it was instrumental in predicting the existence
of antimatter and it helped demonstrate that any quantum theory consistent
with special relativity would likewise involve antimatter (which was duly
observed, by Carl Anderson, a couple of years after
P.A.M. Dirac predicted it).
Similarly, String Theory is a quantum theory consistent with General Relativity.
Unlike the Dirac equation, however, it has failed to make any definite physical
prediction so far.
Therefore, it's currently a legitimate target for critics who call it
"nonphysical" or "unscientific"
(arguably, a theory must have falsifiable consequences
to be call "scientific" outside of the realm of pure mathematics).
Over the years, this state of affairs has slowly transformed "String Theory"
into a general study of all possible quantum theories compatible with
General Relativity. It's not just a theory of "strings" anymore.
It is hoped that, sooner or later, String Theory will achieve at least the
same philosophical status as either Newtonian mechanics or Dirac's equation.
It may or may not turn out to be the advertised "theory of everything"
but its logical structure would at least reveal some testable features
of our physical universe.
The social impact of String Theory among the "community" of
theoretical physicists can hardly be overstated...
An entire generation of many of the brightest theoretical physicists
have been lured by its mathematical appeal away from other pursuits.
Yet, nobody knows how relevant to physics the resulting body of knowledge
really is. So far,
this has been a gamble of unprecedented magnitude without any definite payoff
in sight.
The Large Hadron Collider (LHC) is touted as bringing new hope for fresh
experimental data in particle physics. It should soon provide proof
of the existence of the long-awaited Higgs Boson
and determine its mass
(which will round up the structure of the
standard model).
However, the LHC cannot provide a test of String Theory, for two reasons:
The experimental consequences of String Theory are not yet clear
(they are not ready to be compared with observation) and, anyway, such
direct consequences would be in a range of energy far beyond what's
accessible to the LHC (or any other particle accelerator like it).
Of course, there might well be indirect consequences
which could take center stage and bring new excitement in the world
of particle physics...
On the day LHC was supposed to starts operations
(2008-09-10)
Google
flaunted the above version of their logo worldwide.
The discovery of the Higgs boson was announced 4 years later (2012-07-04).
The 2012 Nobel prize was then widely expected to go to Peter Higgs
(it went to Serge Haroche and David Wineland instead, for unrelated work).
Peter Higgs and François Englert
were duly awarded the
2013 Nobel prize for physics.
(2008-07-23) Unification of Physical Concepts
Why use the same units for all kinds of distances, large and small?
The ancient Egyptians measured large
horizontal distances by rolling a wheel whose diameter was measured in
the units they used for small vertical distances...
The countless appearances of the number
p (the ratio of the circumference
of a circle to its diameter) in the Egyptian
pyramids can be puzzling to whoever has been exposed to unified
Euclidean space since childhood.
To Egyptian architects, the relevant dimensions were integers!
Robert
Grosseteste (1168-1253) is credited with the idea that the homogeneous and
isotropic space of Euclidean geometry can be a backdrop for
light and matter
(De Luce =
About Light, c. 1235).
Blurring the distinction between horizontal and vertical
distances is philosophically pleasing, although this does not
make practical differences go away...
There's very little difference between right and left but
there's a huge difference between up and down (just try falling up).
The distinction between the horizontal and
vertical directions (near the surface of the Earth)
seems to vanish at high energies : If you shoot a gun
indoors, the bullet always moves in a straight line and at
the same speed no matter where you aim. Outdoors,
distances are larger and there's enough time for the pull of gravity
to influence the bullet noticeably.
Very fast "bullets" (photons or particles moving at
nearly the speed of light) are not noticeably influenced by gravity,
except over astronomical distances.
"Unifying" two physical concepts is not at all a denial of their differences,
it's the creation of a common consistent framework
where those differences can be charted and where their interplay becomes clear.
If you have a rigid stick with one fixed
end, our "unified" notion of Euclidean distance will tell you
how the vertical position of the moving end varies
when its horizontal position changes.
Similarly, the unification of space and time in the context of
Special Relativity does not equate
the two notions but it describes circumstances
(motion of the observer) where one is traded for the other.
Loosely speaking, the speed of light
(Einstein's constant c)
is built into relativistic spacetime in very much the same way
p was built into the architecture
of the ancient Egyptians...
The numerical value of c
is merely a consequence of our traditional ways to measure spatial
distances, on one hand, and time intervals, on the other. Rulers and clocks.
Historically, unifying separate physical concepts has always resulted in
a deeper understanding of Nature.
Arguably, the most satisfying such event was the unification of electricity
and magnetism by Maxwell (1861) as
he found a simple way to amend
the law of Ampère into a
consistent picture of electromagnetism which
demanded the existence of electromagnetic waves propagating
at a constant speed c.
The fact that this ought to be so for all observers in uniform motion
with respect to each other directly led to
special relativity.
Unifying quests are so appealing that many mathematical
physicist share a blind faith: The forces of nature must
ultimately be unified;
at high enough energies all interactions ought to look
alike (just like the aforementioned great speed of bullets blurs the distinction
between horizontal and vertical directions).
Some evidence indicates that it may well be so.
However, the greatest goal of physics will be achieved if we have
consistent descriptions of all physical
phenomena, not necessarily unified ones.
(2008-07-09) Kaluza-Klein Theory
A universe with 5 dimensions to unify gravity and electromagnetism.
When Oskar Klein told of his ideas which would not only unify the Maxwell with the Einstein
equations but also bring in the quantum theory, I felt a kind of ecstasy:
Now, one understands the world ! George
Uhlenbeck (1900-1988) Summer of 1926.
Theodor Kaluza
Classical relativistic spacetime has 4 dimensions;
one dimension of time and 3 dimensions of space.
In 1919, the German physicist
Theodor Kaluza (1885-1954)
suggested that one extra geometrical dimension could be added to account for
electromagnetic phenomena and describe them in
purely geometrical terms, in much the same way Einstein's
General Relativity describes gravity.
In the summer of 1926,
Paul Ehrenfest (1880-1933)
invited to Leiden the Swedish physicist
Oskar Klein (1894-1977)
to present his refinement of the Kaluza theory
and the idea that extra spatial dimensions
might be a good way of unifying Relativity
with Quantum Theory.
Klein envisioned that a topologically curled extra dimension
wouldn't be perceived as a spatial dimension
on a normal scale, pretty much like the two-dimensional surface of a garden hose
may look like a single-dimensional wire, if observed from a large enough distance.
For a while, this stirred the enthusiasm of
Albert Einstein (1879-1955) himself
and caused the special type of ecstasy
described in the above quote by
George Uhlenbeck (who was Ehrenfest's assistant at Leiden in 1926).
However,
the excitement over this 5-dimensional physical universe of 1926
(the so-called Kaluza-Klein Universe)
was short-lived, since some consequences of
Oskar Klein's proposal turn out to be entirely off-base.
What's still with us today is Klein's fundamental ideas about how extra dimensions
might provide a quantum theory compatible with
General Relativity.
The concept was revived in the 1970s and in the 1980s,
as extra geometrical dimensions are a prerequisite for
what's now called String Theory.
Such dimensions are still visualized as rolled up,
although they need not have a compact topology.
(2007-08-17) The Magic of Euler's Beta and Gamma Functions
Veneziano's 4-particle amplitude (1968). Dual resonance model.
In 1968,
Gabriele Veneziano (1942-)
took a boat trip from Israel to Italy en route to his
first postdoctoral job at CERN.
At the time, Veneziano had already been working for about a year
(with M. Ademollo, H. Rubinstein and M. Virasono)
on the complementary duality of the
Regge
and resonance description
of pion-nucleon exchange, which had been proposed by R. Dolen, D. Horn
and C. Schmid.
Veneziano and his three colleagues had been putting together a model
of the relevant scattering amplitude in the process.
On the boat, Veneziano realized that the essential features of that
scattering amplitude would be captured by a simple expression
involving Euler's Beta function and Gamma function,
namely:
A ( s , t ) »
B ( 1 - a(s) ,
1 - a(t) ) =
G( 1 - a(s) )
G( 1 - a(t) )
G( 2 - a(s)
- a(t) )
The attractive closed form of the Veneziano amplitude contrasted
sharply with the usual intractability which physicists had to deal with for
strong nuclear interactions. The formula created a widespread stir.
(2007-08-17) The Idea of a Fundamental String (1969)
Leonard Susskind (1940-) Nielsen and Nambu.
Lenny Susskind has been
at Stanford since 1979
(Felix Bloch Professor of Theoretical Physics, since 2000).
In 1969, Susskind pondered Veneziano's formula for months,
trying to make some clear physical sense out of it.
He finally came to the conclusion
that an entity was described which could stretch and vibrate just like
an open-ended elastic string.
(I'm told that the expression is now interpreted as
the scattering amplitude for four open-string tachyons).
Yoichiro Nambu
Holger Bech Nielsen
Two other physicists working on the same premises arrived independently
at similar conclusions shortly thereafter:
Holger Nielsen (1941-)
at the Niels Bohr Institute, and
Yoichiro Nambu (1921-2005)
the inventor of the color charge (University of Chicago).
In 2008,
Nambu was awarded the Nobel prize in Physics for his introduction (in 1960) of mass-producing
spontaneous symmetry breaking in particle physics
(he had been inspired by an analogy with the theory of superconductivity).
(2007-08-17) Could that be a... graviton ? (1974)
Joël Scherk (1946-1979) & John H. Schwarz (1941-).
As they were trying to use the newly minted string theory to describe
the strong nuclear force, Joël Scherk and John Schwarz
kept bumping into a massless elementary particle of spin 2 which did not
fit whatever was known about strong interactions.
After failing to conjure up ways to get rid of this nuisance,
they came to the conclusion that this unavoidable entity could very well be the
graviton itself
(that same idea is also credited to the Japanese physicist
Tamiaki Yoneya, b. 1947)...
Thus, string theory had to encompass gravity
and seemed destined to describe fundamental
strings with a much smaller size and a much greater tension than
previously thought (in the restricted context of strong interactions).
Working with
Eugène Cremmer
and Bernard Julia, Scherk devised
an 11-dimensional theory of
supergravity
and proposed (with Cremmer) the
mechanism of spontaneous compactification in quantum field theory.
Scherk was a diabetic and he died in tragic circumstances, as he passed out when
nobody was around to give him a shot of insulin.
After the death of Scherk, Schwartz found only one person willing to help with
the work they had started together:
Michael Green...
(2007-08-17) A
Theory of Everything ? (1984)
Michael B. Green (1946-) & John H. Schwarz (1941-).
Arguably, Superstring Theory was born in the Summer of 1984,
when Michael Green and John Schwarz
finally established the consistency of a theory rich enough to encompass
all known forces of nature.
This was the first credible candidate for a Theory of Everything (TOE).
At the time, it appeared that the ultimate puzzle was being solved for good.
At Princeton, Ed Witten
built immediately on the breakthrough of Green & Schwarz.
On Monday, November 12, 1984, for the annual Marston
Morse Memorial lecture, Witten delivered a fast-paced speech entitled
"Index Theorems and Superstrings" at the Institute for Advanced Study.
Witten was speaking for the record, not for the immediate
benefit of the 200 top-level scientists who were attending
(there were no questions from them).
When Stephen Hawking (1942-2018)
stepped down as Lucasian Professor of Mathematics in Cambridge
(on 2009-09-30) Michael B. Green was appointed
(on 2009-10-19, as of 2009-11-01) to the
prestigious chair, once held by
Newton,
Airy,
Babbage,
Stokes,
Larmor and
Dirac.
With effect from 2015-07-01, Green's successor is
Michael Cates (b. 1961).
(2017-08-07) Two Kinds of Heterotic Strings (1985)
Hybrids of a closed superstring and a bosonic string.
Heterotic string theory was first developed in 1985,
by the so-called Princeton String Quartet composed of:
(2008-08-29) String Quintet
Too much of a good thing: 5 consistent
string theories.
No fewer than five consistent string theories
have been devised:
Type I :
The earliest theory. It allows both open and closed strings
(the other theories allow only closed strings).
Type II A : The only nonchiral
string theory.
Type II B : The chiral
version of the previous one. Both of them feature
two supersymmetries between fermions and bosons
(the other three superstring theories have only one such supersymmetry).
SO(32)
Heterotic Strings : The term "heterotic" means that
the two directions along a string represent two different particles.
E8 x E8 Heterotic Strings : Based on two copies of the largest
exceptional Lie group (E8).
(2007-08-17) Ed Witten's M-Theory (1995)
Is "M"
magic, mystery, matrix, murky or membrane ?
In 1995,
Edward Witten (1951-)
combined into a single 11-dimensional framework the 5 competing 10-dimensional string theories
and the 11-dimensional theory of supergravity which had been devised in 1978 by
Joël Scherk (1946-1979)
Eugène Cremmer (1942-2019)
and Bernard Julia (1952-).
Even before that tour de force,
Ed Witten was widely recognized as the dominant string theorist
of that era. (He became a
Fields Medalist in 1990.)
(2023-08-42) The most fumdamental contribution of String Theory
It proves that General Relativity and Quantum principles are not incompatible.
At the very least, the existence of string theory proves that General Relativity and the
quantum principles on which our standard model is based can coexist logically.
Unification is thus not impossible a priori.
