The no-hair theorem (which is a hypothesis) states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent externally observable classical parameters: mass, electric charge, and angular momentum.
Other characteristics (such as geometry and magnetic moment) are
uniquely determined by these three parameters, and all other information
(for which "hair" is a metaphor) about the matter that formed a black hole or is falling into it "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers after the black hole "settles down" (by emitting gravitational and electromagnetic waves). Physicist John Archibald Wheeler expressed this idea with the phrase "black holes have no hair", which was the origin of the name.
In a later interview, Wheeler said that Jacob Bekenstein coined this phrase.
Richard Feynman
objected to the phrase that seemed to me to best symbolize the finding
of one of the graduate students: graduate student Jacob Bekenstein had
shown that a black hole reveals nothing outside it of what went in, in
the way of spinning electric particles. It might show electric charge,
yes; mass, yes; but no other features – or as he put it, "A black hole
has no hair". Richard Feynman thought that was an obscene phrase and he
didn't want to use it. But that is a phrase now often used to state this
feature of black holes, that they don't indicate any other properties
other than a charge and angular momentum and mass.
The first version of the no-hair theorem for the simplified case of the uniqueness of the Schwarzschild metric was shown by Werner Israel in 1967. The result was quickly generalized to the cases of charged or spinning black holes. There is still no rigorous mathematical proof of a general no-hair theorem, and mathematicians refer to it as the no-hair conjecture. Even in the case of gravity alone (i.e., zero electric fields), the conjecture has only been partially resolved by results of Stephen Hawking, Brandon Carter,
and David C. Robinson, under the additional hypothesis of
non-degenerate event horizons and the technical, restrictive and
difficult-to-justify assumption of real analyticity of the space-time continuum.
Example
Suppose
two black holes have the same masses, electrical charges, and angular
momenta, but the first black hole was made by collapsing ordinary matter whereas the second was made out of antimatter; nevertheless, then the conjecture states they will be completely indistinguishable to an observer outside the event horizon. None of the special particle physics pseudo-charges (i.e., the global charges baryonic number, leptonic
number, etc., all of which would be different for the originating
masses of matter that created the black holes) are conserved in the
black hole, or if they are conserved somehow then their values would be
unobservable from the outside.
Changing the reference frame
Every
isolated unstable black hole decays rapidly to a stable black hole; and
(excepting quantum fluctuations) stable black holes can be completely
described (in a Cartesian coordinate system) at any moment in time by
these eleven numbers:
These numbers represent the conserved attributes of an object which
can be determined from a distance by examining its gravitational and
electromagnetic fields. All other variations in the black hole will
either escape to infinity or be swallowed up by the black hole.
By changing the reference frame one can set the linear momentum
and position to zero and orient the spin angular momentum along the
positive z axis. This eliminates eight of the eleven numbers,
leaving three which are independent of the reference frame: mass,
angular momentum magnitude, and electric charge. Thus any black hole
that has been isolated for a significant period of time can be described
by the Kerr–Newman metric in an appropriately chosen reference frame.
It has since been extended to include the case where the cosmological constant is positive (which recent observations are tending to support).
Magnetic charge, if detected as predicted by some theories, would form the fourth parameter possessed by a classical black hole.
Counterexamples
Counterexamples in which the theorem fails are known in spacetime dimensions higher than four; in the presence of non-abelianYang–Mills fields, non-abelian Proca fields, some non-minimally coupledscalar fields, or skyrmions;
or in some theories of gravity other than Einstein's general
relativity. However, these exceptions are often unstable solutions
and/or do not lead to conserved quantum numbers so that "The 'spirit' of
the no-hair conjecture, however, seems to be maintained". It has been proposed that "hairy" black holes may be considered to be bound states of hairless black holes and solitons.
In 2004, the exact analytical solution of a (3+1)-dimensional
spherically symmetric black hole with minimally coupled self-interacting
scalar field was derived. This showed that, apart from mass, electrical charge and angular momentum, black holes can carry a finite scalar charge which might be a result of interaction with cosmological scalar fields such as the inflaton.
The solution is stable and does not possess any unphysical properties;
however, the existence of a scalar field with the desired properties is
only speculative.
Observational results
The results from the first observation of gravitational waves in 2015 provide some experimental evidence consistent with the uniqueness of the no-hair theorem. This observation is consistent with Stephen Hawking's theoretical work on black holes in the 1970s.
Soft hair
A study by Sasha Haco, Stephen Hawking, Malcolm Perry and Andrew Strominger postulates that black holes might contain "soft hair", giving the black hole more degrees of freedom than previously thought.
This hair permeates at a very low-energy state, which is why it didn't
come up in previous calculations that postulated the no-hair theorem. This was the subject of Hawking's final paper which was published posthumously.
Spacelike singularities: The singularity lies in the future or
past of all events within a certain region. The Big Bang singularity and
the typical singularity inside a non-rotating, uncharged Schwarzschild black hole are spacelike.
Timelike singularities: These are singularities that can be avoided
by an observer because they are not necessarily in the future of all
events. An observer might be able to move around a timelike singularity.
These are less common in known solutions of the Einstein field equations.
Null singularities: These singularities occur on light-like or null
surfaces. An example might be found in certain types of black hole
interiors, such as the Cauchy horizon of a charged (Reissner-Nordström) or rotating (Kerr) black hole.
A singularity can be either strong or weak:
- Weak singularities: A weak singularity is one where the tidal forces (which are responsible for the spaghettification
in black holes) are not necessarily infinite. An observer falling into a
weak singularity might not be torn apart before reaching the
singularity, although the laws of physics would still break down there.
The Cauchy horizon inside a charged or rotating black hole might be an
example of a weak singularity.
Strong singularities: A strong singularity is one where tidal forces
become infinite. In a strong singularity, any object would be destroyed
by infinite tidal forces as it approaches the singularity. The
singularity at the center of a Schwarzschild black hole is an example of
a strong singularity.
Space-like singularities are a feature of non-rotating uncharged black holes as described by the Schwarzschild metric,
while time-like singularities are those that occur in charged or
rotating black hole exact solutions. Both of them have the property of geodesic incompleteness,
in which either some light-path or some particle-path cannot be
extended beyond a certain proper time or affine parameter (affine
parameter being the null analog of proper time).
The Penrose theorem guarantees that some sort of geodesic incompleteness occurs inside any black hole whenever matter satisfies reasonable energy conditions.
The energy condition required for the black-hole singularity theorem is
weak: it says that light rays are always focused together by gravity,
never drawn apart, and this holds whenever the energy of matter is
non-negative.
Hawking's singularity theorem is for the whole universe, and works backwards in time: it guarantees that the (classical) Big Bang has infinite density. This theorem is more restricted and only holds when matter obeys a stronger energy condition, called the strong energy condition, in which the energy is larger than the pressure. All ordinary matter, with the exception of a vacuum expectation value of a scalar field, obeys this condition. During inflation, the universe violates the dominant energy condition, and it was initially argued (e.g. by Starobinsky)
that inflationary cosmologies could avoid the initial big-bang
singularity. However, it has since been shown that inflationary
cosmologies are still past-incomplete, and thus require physics other than inflation to describe the past boundary of the inflating region of spacetime.
It is still an open question whether (classical) general
relativity predicts spacelike singularities in the interior of realistic
charged or rotating black holes, or whether these are artefacts of
high-symmetry solutions and turn into null or timelike singularities
when perturbations are added.
Interpretation and significance
In general relativity,
a singularity is a place that objects or light rays can reach in a
finite time where the curvature becomes infinite, or spacetime stops
being a manifold. Singularities can be found in all the black-hole spacetimes, the Schwarzschild metric, the Reissner–Nordström metric, the Kerr metric and the Kerr–Newman metric, and in all cosmological solutions that do not have a scalar field energy or a cosmological constant.
One cannot predict what might come "out" of a big-bang
singularity in our past, or what happens to an observer that falls "in"
to a black-hole singularity in the future, so they require a
modification of physical law. Before Penrose, it was conceivable that
singularities only form in contrived situations. For example, in the
collapse of a star to form a black hole, if the star is spinning and thus possesses some angular momentum, maybe the centrifugal force
partly counteracts gravity and keeps a singularity from forming. The
singularity theorems prove that this cannot happen, and that a
singularity will always form once an event horizon forms.
In the collapsing star example, since all matter and energy is a
source of gravitational attraction in general relativity, the additional
angular momentum only pulls the star together more strongly as it
contracts: the part outside the event horizon eventually settles down to
a Kerr black hole (see No-hair theorem).
The part inside the event horizon necessarily has a singularity
somewhere. The proof is somewhat constructive – it shows that the
singularity can be found by following light-rays from a surface just
inside the horizon. But the proof does not say what type of singularity
occurs, spacelike, timelike, null, orbifold,
jump discontinuity in the metric. It only guarantees that if one
follows the time-like geodesics into the future, it is impossible for
the boundary of the region they form to be generated by the null
geodesics from the surface. This means that the boundary must either
come from nowhere or the whole future ends at some finite extension.
An interesting "philosophical" feature of general relativity is
revealed by the singularity theorems. Because general relativity
predicts the inevitable occurrence of singularities, the theory is not
complete without a specification for what happens to matter that hits
the singularity. One can extend general relativity
to a unified field theory, such as the Einstein–Maxwell–Dirac system,
where no such singularities occur.
Elements of the theorems
In history, there is a deep connection between the curvature of a manifold and its topology. The Bonnet–Myers theorem states that a complete Riemannian manifold that has Ricci curvature everywhere greater than a certain positive constant must be compact.
The condition of positive Ricci curvature is most conveniently stated
in the following way: for every geodesic there is a nearby initially
parallel geodesic that will bend toward it when extended, and the two
will intersect at some finite length.
When two nearby parallel geodesics intersect (see conjugate point),
the extension of either one is no longer the shortest path between the
endpoints. The reason is that two parallel geodesic paths necessarily
collide after an extension of equal length, and if one path is followed
to the intersection then the other, you are connecting the endpoints by a
non-geodesic path of equal length. This means that for a geodesic to be
a shortest length path, it must never intersect neighboring parallel
geodesics.
Starting with a small sphere and sending out parallel geodesics from the boundary, assuming that the manifold has a Ricci curvature
bounded below by a positive constant, none of the geodesics are
shortest paths after a while, since they all collide with a neighbor.
This means that after a certain amount of extension, all potentially new
points have been reached. If all points in a connected manifold are at a
finite geodesic distance from a small sphere, the manifold must be
compact.
Roger Penrose argued analogously in relativity. If null geodesics, the paths of light rays,
are followed into the future, points in the future of the region are
generated. If a point is on the boundary of the future of the region, it
can only be reached by going at the speed of light, no slower, so null
geodesics include the entire boundary of the proper future of a region.
When the null geodesics intersect, they are no longer on the boundary
of the future, they are in the interior of the future. So, if all the
null geodesics collide, there is no boundary to the future.
In relativity, the Ricci curvature, which determines the collision properties of geodesics, is determined by the energy tensor,
and its projection on light rays is equal to the null-projection of the
energy–momentum tensor and is always non-negative. This implies that
the volume of a congruence
of parallel null geodesics once it starts decreasing, will reach zero
in a finite time. Once the volume is zero, there is a collapse in some
direction, so every geodesic intersects some neighbor.
Penrose concluded that whenever there is a sphere where all the
outgoing (and ingoing) light rays are initially converging, the boundary
of the future of that region will end after a finite extension, because
all the null geodesics will converge. This is significant, because the outgoing light rays for any sphere inside the horizon of a black hole
solution are all converging, so the boundary of the future of this
region is either compact or comes from nowhere. The future of the
interior either ends after a finite extension, or has a boundary that is
eventually generated by new light rays that cannot be traced back to
the original sphere.
Nature of a singularity
The
singularity theorems use the notion of geodesic incompleteness as a
stand-in for the presence of infinite curvatures. Geodesic
incompleteness is the notion that there are geodesics,
paths of observers through spacetime, that can only be extended for a
finite time as measured by an observer traveling along one. Presumably,
at the end of the geodesic the observer has fallen into a singularity or
encountered some other pathology at which the laws of general
relativity break down.
Assumptions of the theorems
Typically a singularity theorem has three ingredients:
Gravity is strong enough (somewhere) to trap a region.
There are various possibilities for each ingredient, and each leads to different singularity theorems.
Tools employed
A key tool used in the formulation and proof of the singularity theorems is the Raychaudhuri equation, which describes the divergence of a congruence (family) of geodesics. The divergence of a congruence is defined
as the derivative of the log of the determinant of the congruence volume. The Raychaudhuri
equation is
where is the shear tensor of the congruence and is also known as the Raychaudhuri scalar (see the congruence page for details). The key point is that will be non-negative provided that the Einstein field equations hold and
When these hold, the divergence becomes infinite at some finite value
of the affine parameter. Thus all geodesics leaving a point will
eventually reconverge after a finite time, provided the appropriate
energy condition holds, a result also known as the focusing theorem.
This is relevant for singularities thanks to the following argument:
Suppose we have a spacetime that is globally hyperbolic, and two points and that can be connected by a timelike or null curve. Then there exists a geodesic of maximal length connecting and . Call this geodesic .
The geodesic can be varied to a longer curve if another geodesic from intersects at another point, called a conjugate point.
From the focusing theorem, we know that all geodesics from
have conjugate points at finite values of the affine parameter. In
particular, this is true for the geodesic of maximal length. But this is
a contradiction – one can therefore conclude that the spacetime is
geodesically incomplete.
In general relativity, there are several versions of the Penrose–Hawking singularity theorem. Most versions state, roughly, that if there is a trapped null surface and the energy density is nonnegative, then there exist geodesics of finite length that cannot be extended.
These theorems, strictly speaking, prove that there is at least
one non-spacelike geodesic that is only finitely extendible into the
past but there are cases in which the conditions of these theorems
obtain in such a way that all past-directed spacetime paths terminate at
a singularity.
Versions
There are many versions; below is the null version:
Sketch of proof: Proof by contradiction. The boundary of the future of , is generated by null geodesic segments originating from with tangent vectors orthogonal to it. Being a trapped null surface, by the null Raychaudhuri equation, both families of null rays emanating from
will encounter caustics. (A caustic by itself is unproblematic. For
instance, the boundary of the future of two spacelike separated points
is the union of two future light cones with the interior parts of the
intersection removed. Caustics occur where the light cones intersect,
but no singularity lies there.) The null geodesics generating
have to terminate, however, i.e. reach their future endpoints at or
before the caustics. Otherwise, we can take two null geodesic segments –
changing at the caustic – and then deform them slightly to get a
timelike curve connecting a point on the boundary to a point on , a contradiction. But as
is compact, given a continuous affine parameterization of the geodesic
generators, there exists a lower bound to the absolute value of the
expansion parameter. So, we know caustics will develop for every
generator before a uniform bound in the affine parameter has elapsed. As
a result,
has to be compact. Either we have closed timelike curves, or we can
construct a congruence by timelike curves, and every single one of them
has to intersect the noncompact Cauchy surface exactly once. Consider
all such timelike curves passing through and look at their image on the Cauchy surface. Being a continuous map, the image also has to be compact. Being a timelike congruence, the timelike curves can't intersect, and so, the map is injective.
If the Cauchy surface were noncompact, then the image has a boundary.
We're assuming spacetime comes in one connected piece. But
is compact and boundariless because the boundary of a boundary is
empty. A continuous injective map can't create a boundary, giving us our
contradiction.
Loopholes: If closed timelike curves exist, then timelike curves don't have to intersect the partial
Cauchy surface. If the Cauchy surface were compact, i.e. space is
compact, the null geodesic generators of the boundary can intersect
everywhere because they can intersect on the other side of space.
Other versions of the theorem involving the weak or strong energy condition also exist.
Modified gravity
In
modified gravity, the Einstein field equations do not hold and so these
singularities do not necessarily arise. For example, in Infinite Derivative Gravity, it is possible for to be negative even if the Null Energy Condition holds.
Penrose has contributed to the mathematical physics of general relativity and cosmology. He has received several prizes and awards, including the 1988 Wolf Prize in Physics, which he shared with Stephen Hawking for the Penrose–Hawking singularity theorems, and the 2020 Nobel Prize in Physics "for the discovery that black hole formation is a robust prediction of the general theory of relativity".
He is regarded as one of the greatest living physicists, mathematicians
and scientists, and is particularly noted for the breadth and depth of
his work in both natural and formal sciences.
In 1955, while a student, Penrose reintroduced the E. H. Moore generalised matrix inverse, also known as the Moore–Penrose inverse, after it had been reinvented by Arne Bjerhammar in 1951. Having started research under the professor of geometry and astronomy, Sir W. V. D. Hodge, Penrose finished his PhD at St John's College, Cambridge, in 1958, with a thesis on tensor methods in algebraic geometry supervised by algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle
in the 1950s in collaboration with his father, describing it as
"impossibility in its purest form", and exchanged material with the
artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. Escher's Waterfall, and Ascending and Descending were in turn inspired by Penrose.
As reviewer Manjit Kumar puts it:
As a student in 1954, Penrose was
attending a conference in Amsterdam when by chance he came across an
exhibition of Escher's work. Soon he was trying to conjure up impossible
figures of his own and discovered the tribar – a triangle that looks
like a real, solid three-dimensional object, but isn't. Together with
his father, a physicist and mathematician, Penrose went on to design a staircase
that simultaneously loops up and down. An article followed and a copy
was sent to Escher. Completing a cyclical flow of creativity, the Dutch
master of geometrical illusions was inspired to produce his two
masterpieces.
Research and career
Penrose spent the academic year 1956–57 as an assistant lecturer at Bedford College, London and was then a research fellow at St John's College, Cambridge. During that three-year post, he married Joan Isabel Wedge, in 1959. Before the fellowship ended Penrose won a NATO Research Fellowship for 1959–61, first at Princeton and then at Syracuse University. Returning to the University of London, Penrose spent two years, 1961–63, as a researcher at King's College, London, before returning to the United States to spend the year 1963–64 as a visiting associate professor at the University of Texas at Austin. He later held visiting positions at Yeshiva, Princeton, and Cornell during 1966–67 and 1969.
In 1964, while a reader at Birkbeck College, London, (and having had his attention drawn from pure mathematics to astrophysics by the cosmologist Dennis Sciama, then at Cambridge) in the words of Kip Thorne of Caltech, "Roger Penrose revolutionised the mathematical tools that we use to analyse the properties of spacetime".
Until then, work on the curved geometry of general relativity had been
confined to configurations with sufficiently high symmetry for
Einstein's equations to be solvable explicitly, and there was doubt
about whether such cases were typical. One approach to this issue was by
the use of perturbation theory, as developed under the leadership of John Archibald Wheeler at Princeton.
The other, and more radically innovative, approach initiated by Penrose
was to overlook the detailed geometrical structure of spacetime and
instead concentrate attention just on the topology of the space, or at
most its conformal structure,
since it is the latter – as determined by the lay of the lightcones –
that determines the trajectories of lightlike geodesics, and hence their
causal relationships. The importance of Penrose's epoch-making paper
"Gravitational Collapse and Space-Time Singularities"
was not its only result, summarised roughly as that if an object such
as a dying star implodes beyond a certain point, then nothing can
prevent the gravitational field getting so strong as to form some kind
of singularity. It also showed a way to obtain similarly general
conclusions in other contexts, notably that of the cosmological Big Bang, which he dealt with in collaboration with Dennis Sciama's most famous student, Stephen Hawking.
It was in the local context of gravitational collapse that the
contribution of Penrose was most decisive, starting with his 1969 cosmic
censorship conjecture, to the effect that any ensuing singularities would be confined within a well-behaved event horizon surrounding a hidden space-time region for which Wheeler coined the term black hole,
leaving a visible exterior region with strong but finite curvature,
from which some of the gravitational energy may be extractable by what
is known as the Penrose process, while accretion of surrounding matter may release further energy that can account for astrophysical phenomena such as quasars.
Following up his "weak cosmic censorship hypothesis", Penrose went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". Together with the Belinski–Khalatnikov–Lifshitz conjecture and issues of nonlinear stability, settling the censorship conjectures is one of the most important outstanding problems in general relativity. Also from 1979, dates Penrose's influential Weyl curvature hypothesis on the initial conditions of the observable part of the universe and the origin of the second law of thermodynamics.
Penrose and James Terrell independently realised that objects
travelling near the speed of light will appear to undergo a peculiar
skewing or rotation. This effect has come to be called the Terrell rotation or Penrose–Terrell rotation.
In 1967, Penrose invented the twistor theory, which maps geometric objects in Minkowski space into the 4-dimensional complex space with the metric signature (2,2).
Penrose is well known for his 1974 discovery of Penrose tilings, which are formed from two tiles that can only tile
the plane nonperiodically, and are the first tilings to exhibit
fivefold rotational symmetry. In 1984, such patterns were observed in
the arrangement of atoms in quasicrystals. Another noteworthy contribution is his 1971 invention of spin networks, which later came to form the geometry of spacetime in loop quantum gravity. He was influential in popularizing what are commonly known as Penrose diagrams (causal diagrams).
Penrose is the Francis and Helen Pentz Distinguished Visiting Professor of Physics and Mathematics at Pennsylvania State University.
An earlier universe
In 2010, Penrose reported possible evidence, based on concentric circles found in Wilkinson Microwave Anisotropy Probe data of the cosmic microwave background sky, of an earlier universe existing before the Big Bang of our own present universe. He mentions this evidence in the epilogue of his 2010 book Cycles of Time, a book in which he presents his reasons, to do with Einstein's field equations, the Weyl curvature C, and the Weyl curvature hypothesis (WCH), that the transition at the Big Bang could have been smooth enough for a previous universe to survive it. He made several conjectures about C and the WCH, some of which were subsequently proved by others, and he also popularized his conformal cyclic cosmology (CCC) theory.
In this theory, Penrose postulates that at the end of the universe all
matter is eventually contained within black holes, which subsequently
evaporate via Hawking radiation. At this point, everything contained within the universe consists of photons,
which "experience" neither time nor space. There is essentially no
difference between an infinitely large universe consisting only of
photons and an infinitely small universe consisting only of photons.
Therefore, a singularity for a Big Bang and an infinitely expanded universe are equivalent.
In simple terms, Penrose believes that the singularity in Einstein's field equation at the Big Bang is only an apparent singularity, similar to the well-known apparent singularity at the event horizon of a black hole. The latter singularity can be removed by a change of coordinate system, and Penrose proposes a different change of coordinate system that will remove the singularity at the big bang.
One implication of this is that the major events at the Big Bang can be
understood without unifying general relativity and quantum mechanics,
and therefore we are not necessarily constrained by the Wheeler–DeWitt equation, which disrupts time. Alternatively, one can use the Einstein–Maxwell–Dirac equations.
Consciousness
Penrose has written books on the connection between fundamental physics and human (or animal) consciousness. In The Emperor's New Mind (1989), he argues that known laws of physics are inadequate to explain the phenomenon of consciousness.
Penrose proposes the characteristics this new physics may have and
specifies the requirements for a bridge between classical and quantum
mechanics (what he calls correct quantum gravity). Penrose uses a variant of Turing's halting theorem to demonstrate that a system can be deterministic without being algorithmic. (For example, imagine a system with only two states, ON and OFF. If the system's state is ON when a given Turing machine
halts and OFF when the Turing machine does not halt, then the system's
state is completely determined by the machine; nevertheless, there is no
algorithmic way to determine whether the Turing machine stops.)
Penrose believes that such deterministic yet non-algorithmic processes may come into play in the quantum mechanical wave function reduction,
and may be harnessed by the brain. He argues that computers today are
unable to have intelligence because they are algorithmically
deterministic systems. He argues against the viewpoint that the rational
processes of the mind are completely algorithmic and can thus be
duplicated by a sufficiently complex computer. This contrasts with supporters of strong artificial intelligence, who contend that thought can be simulated algorithmically. He bases this on claims that consciousness transcends formal logic because factors such as the insolubility of the halting problem and Gödel's incompleteness theorem prevent an algorithmically based system of logic from reproducing such traits of human intelligence as mathematical insight. These claims were originally espoused by the philosopher John Lucas of Merton College, Oxford.
The Penrose–Lucas argument
about the implications of Gödel's incompleteness theorem for
computational theories of human intelligence has been criticised by
mathematicians, computer scientists and philosophers. Many experts in
these fields assert that Penrose's argument fails, though different
authors may choose different aspects of the argument to attack. Marvin Minsky,
a leading proponent of artificial intelligence, was particularly
critical, stating that Penrose "tries to show, in chapter after chapter,
that human thought cannot be based on any known scientific principle."
Minsky's position is exactly the opposite – he believed that humans are,
in fact, machines, whose functioning, although complex, is fully
explainable by current physics. Minsky maintained that "one can carry
that quest [for scientific explanation] too far by only seeking new
basic principles instead of attacking the real detail. This is what I
see in Penrose's quest for a new basic principle of physics that will
account for consciousness."
Penrose and Hameroff have argued that consciousness is the result of quantum gravity effects in microtubules, which they dubbed Orch-OR (orchestrated objective reduction). Max Tegmark, in a paper in Physical Review E, calculated that the time scale of neuron firing and excitations in microtubules is slower than the decoherence
time by a factor of at least 10,000,000,000. The reception of the paper
is summed up by this statement in Tegmark's support: "Physicists
outside the fray, such as IBM's John A. Smolin,
say the calculations confirm what they had suspected all along. 'We're
not working with a brain that's near absolute zero. It's reasonably
unlikely that the brain evolved quantum behavior'". Tegmark's paper has been widely cited by critics of the Penrose–Hameroff position.
In their reply to Tegmark's paper, also published in Physical Review E, the physicists Scott Hagan, Jack Tuszyński and Hameroff
claimed that Tegmark did not address the Orch-OR model, but instead a
model of his own construction. This involved superpositions of quanta
separated by 24 nm rather than the much smaller separations stipulated
for Orch-OR. As a result, Hameroff's group claimed a decoherence time
seven orders of magnitude greater than Tegmark's, but still well short
of the 25 ms required if the quantum processing in the theory was to be
linked to the 40 Hz gamma synchrony, as Orch-OR suggested. To bridge
this gap, the group made a series of proposals. They supposed that the interiors of neurons could alternate between liquid and gel
states. In the gel state, it was further hypothesized that the water
electrical dipoles are oriented in the same direction, along the outer
edge of the microtubule tubulin subunits.
Hameroff et al. proposed that this ordered water could screen any
quantum coherence within the tubulin of the microtubules from the
environment of the rest of the brain. Each tubulin also has a tail
extending out from the microtubules, which is negatively charged, and
therefore attracts positively charged ions. It is suggested that this
could provide further screening. Further to this, there was a suggestion
that the microtubules could be pumped into a coherent state by
biochemical energy.
Finally, he suggested that the configuration of the microtubule lattice
might be suitable for quantum error correction, a means of holding
together quantum coherence in the face of environmental interaction.
Hameroff, in a lecture in part of a Google Tech talks series exploring quantum biology, gave an overview of current research in the area, and responded to subsequent criticisms of the Orch-OR model. In addition to this, a 2011 paper by Roger Penrose and Stuart Hameroff published in the Journal of Cosmology
gives an updated model of their Orch-OR theory, in light of criticisms,
and discusses the place of consciousness within the universe.
Phillip Tetlow, although himself supportive of Penrose's views,
acknowledges that Penrose's ideas about the human thought process are at
present a minority view in scientific circles, citing Minsky's
criticisms and quoting science journalist Charles Seife's
description of Penrose as "one of a handful of scientists" who believe
that the nature of consciousness suggests a quantum process.
In January 2014, Hameroff and Penrose ventured that a discovery
of quantum vibrations in microtubules by Anirban Bandyopadhyay of the
National Institute for Materials Science in Japan supports the hypothesis of Orch-OR theory.
A reviewed and updated version of the theory was published along with
critical commentary and debate in the March 2014 issue of Physics of Life Reviews.
White Mars: The Mind Set Free (with Brian Aldiss) (1999)
His academic books include:
Techniques of Differential Topology in Relativity (1972, ISBN0-89871-005-7)
Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with Wolfgang Rindler, 1987) ISBN0-521-33707-0 (paperback)
Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint), ISBN0-521-34786-6 (paperback)
In 2004, he was awarded the De Morgan Medal for his wide and original contributions to mathematical physics. To quote the citation from the London Mathematical Society:
His deep work on General Relativity has been a major factor in our understanding of black holes. His development of Twistor Theory
has produced a beautiful and productive approach to the classical
equations of mathematical physics. His tilings of the plane underlie the
newly discovered quasi-crystals.
In 2012, Penrose was awarded the Richard R. Ernst Medal by ETH Zürich
for his contributions to science and strengthening the connection
between science and society. In 2015 Penrose was awarded an honorary
doctorate by CINVESTAV-IPN (Mexico).
In 2017, he was awarded the Commandino Medal at the Urbino University for his contributions to the history of science.
Penrose's first marriage was to American Joan Isabel Penrose (née Wedge), whom he married in 1959. They had three sons. Penrose is now married to Vanessa Thomas, director of Academic Development at Cokethorpe School and former head of mathematics at Abingdon School.They had one son.
Religious views
During
an interview with BBC Radio 4 on 25 September 2010, Penrose stated,
"I'm not a believer myself. I don't believe in established religions of
any kind." He regards himself as an agnostic. In the 1991 film A Brief History of Time,
he also said, "I think I would say that the universe has a purpose,
it's not somehow just there by chance … some people, I think, take the
view that the universe is just there and it runs along—it's a bit like
it just sort of computes, and we happen somehow by accident to find
ourselves in this thing. But I don't think that's a very fruitful or
helpful way of looking at the universe, I think that there is something
much deeper about it."