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Two-dimensional analogy of spacetime distortion. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.

In physics, spacetime (or space-time, space time, space-time continuum) is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. From a Euclidean space perspective, the universe has three dimensions of space and one dimension of time. By combining space and time into a single manifold, physicists have significantly simplified a large number of physical theories, as well as described in a more uniform way the workings of the universe at both the supergalactic and subatomic levels.

In non-relativistic classical mechanics, the use of Euclidean space instead of spacetime is appropriate, as time is treated as universal and constant, being independent of the state of motion of an observer. In relativistic contexts, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer and also on the strength of gravitational fields, which can slow the passage of time.

In cosmology, the concept of spacetime combines space and time to a single abstract universe. Mathematically it is a manifold consisting of "events" which are described by some type of coordinate system. Typically three spatial dimensions (length, width, height), and one temporal dimension (time) are required. Dimensions are independent components of a coordinate grid needed to locate a point in a certain defined "space". For example, on the globe the latitude and longitude are two independent coordinates which together uniquely determine a location. In spacetime, a coordinate grid that spans the 3+1 dimensions locates events (rather than just points in space), i.e. time is added as another dimension to the coordinate grid. This way the coordinates specify where and when events occur. However, the unified nature of spacetime and the freedom of coordinate choice it allows imply that to express the temporal coordinate in one coordinate system requires both temporal and spatial coordinates in another coordinate system. Unlike in normal spatial coordinates, there are still restrictions for how measurements can be made spatially and temporally (see Spacetime intervals). These restrictions correspond roughly to a particular mathematical model which differs from Euclidean space in its manifest symmetry.

Until the beginning of the 20th century, time was believed to be independent of motion, progressing at a fixed rate in all reference frames; however, later experiments revealed that time slowed down at higher speeds of the reference frame relative to another reference frame (with such slowing called "time dilation" explained in the theory of "special relativity"). Many experiments have confirmed time dilation, such as atomic clocks onboard a Space Shuttle running slower than synchronized Earth-bound inertial clocks and the relativistic decay of muons from cosmic ray showers. The duration of time can therefore vary for various events and various reference frames.

When dimensions are understood as mere components of the grid system, rather than physical attributes of space, it is easier to understand the alternate dimensional views as being simply the result of coordinate transformations.

The term spacetime has taken on a generalized meaning beyond treating spacetime events with the normal 3+1 dimensions. It is really the combination of space and time. Other proposed spacetime theories include additional dimensions—normally spatial but there exist some speculative theories that include additional temporal dimensions and even some that include dimensions that are neither temporal nor spatial. How many dimensions are needed to describe the universe is still an open question. Speculative theories such as string theory predict 10 or 26 dimensions (with M-theory predicting 11 dimensions: 10 spatial and 1 temporal), but the existence of more than four dimensions would only appear to make a difference at the subatomic level.

Spacetime in literature[link]

Incas regarded space and time as a single concept, named pacha (Quechua: pacha, Aymara: pacha).^[1][2] The peoples of the Andes have kept this understanding until now.^[3]

Arthur Schopenhauer wrote in §18 of On the Fourfold Root of the Principle of Sufficient Reason (1813): "...the representation of coexistence is impossible in Time alone; it depends, for its completion, upon the representation of Space; because, in mere Time, all things follow one another, and in mere Space all things are side by side; it is accordingly only by the combination of Time and Space that the representation of coexistence arises."

The idea of a unified spacetime is stated by Edgar Allan Poe in his essay on cosmology titled Eureka (1848) that "Space and duration are one." In 1895, in his novel The Time Machine, H.G. Wells wrote, "There is no difference between time and any of the three dimensions of space except that our consciousness moves along it", and that "any real body must have extension in four directions: it must have Length, Breadth, Thickness, and Duration."

Mathematical concept[link]

The first reference to spacetime as a mathematical concept was in 1754 by Jean le Rond d'Alembert in the article Dimension in Encyclopedie. Another early venture was by Joseph Louis Lagrange in his Theory of Analytic Functions (1797, 1813). He said, "One may view mechanics as a geometry of four dimensions, and mechanical analysis as an extension of geometric analysis".^[4]

After discovering quaternions,^[5] William Rowan Hamilton commented, "Time is said to have only one dimension, and space to have three dimensions. ... The mathematical quaternion partakes of both these elements; in technical language it may be said to be 'time plus space', or 'space plus time': and in this sense it has, or at least involves a reference to, four dimensions. And how the One of Time, of Space the Three, Might in the Chain of Symbols girdled be." Hamilton's biquaternions, which have algebraic properties sufficient to model spacetime and its symmetry, were in play for more than a half-century before formal relativity. For instance, William Kingdon Clifford noted their relevance.

Another important antecedent to spacetime was the work of James Clerk Maxwell as he used partial differential equations to develop electrodynamics with the four parameters. Lorentz discovered some invariances of Maxwell's equations late in the 19th century which were to become the basis of Einstein's theory of special relativity. Fiction authors were also involved, as mentioned above. It has always been the case that time and space are measured using real numbers, and the suggestion that the dimensions of space and time are comparable could have been raised by the first people to have formalized physics, but ultimately, the contradictions between Maxwell's laws and Galilean relativity had to come to a head with the realization of the import of finitude of the speed of light.

While spacetime can be viewed as a consequence of Albert Einstein's 1905 theory of special relativity, it was first explicitly proposed mathematically by one of his teachers, the mathematician Hermann Minkowski, in a 1908 essay^[6] building on and extending Einstein's work. His concept of Minkowski space is the earliest treatment of space and time as two aspects of a unified whole, the essence of special relativity. The idea of Minkowski space also led to special relativity being viewed in a more geometrical way, this geometric viewpoint of spacetime being important in general relativity too. (For an English translation of Minkowski's article, see Lorentz et al. 1952.) The 1926 thirteenth edition of the Encyclopædia Britannica included an article by Einstein titled "Space-Time".^[7]

Basic concepts[link]

Spacetimes are the arenas in which all physical events take place—an event is a point in spacetime specified by its time and place. For example, the motion of planets around the sun may be described in a particular type of spacetime, or the motion of light around a rotating star may be described in another type of spacetime. The basic elements of spacetime are events. In any given spacetime, an event is a unique position at a unique time. Because events are spacetime points, an example of an event in classical relativistic physics is Failed to parse (Missing texvc executable; please see math/README to configure.): (x,y,z,t) , the location of an elementary (point-like) particle at a particular time. A spacetime itself can be viewed as the union of all events in the same way that a line is the union of all of its points, formally organized into a manifold, a space which can be described at small scales using coordinates systems.

A spacetime is independent of any observer.^[8] However, in describing physical phenomena (which occur at certain moments of time in a given region of space), each observer chooses a convenient metrical coordinate system. Events are specified by four real numbers in any such coordinate system. The trajectories of elementary (point-like) particles through space and time are thus a continuum of events called the world line of the particle. Extended or composite objects (consisting of many elementary particles) are thus a union of many world lines twisted together by virtue of their interactions through spacetime into a "world-braid".

However, in physics, it is common to treat an extended object as a "particle" or "field" with its own unique (e.g. center of mass) position at any given time, so that the world line of a particle or light beam is the path that this particle or beam takes in the spacetime and represents the history of the particle or beam. The world line of the orbit of the Earth (in such a description) is depicted in two spatial dimensions x and y (the plane of the Earth's orbit) and a time dimension orthogonal to x and y. The orbit of the Earth is an ellipse in space alone, but its world line is a helix in spacetime.^[9]

The unification of space and time is exemplified by the common practice of selecting a metric (the measure that specifies the interval between two events in spacetime) such that all four dimensions are measured in terms of units of distance: representing an event as Failed to parse (Missing texvc executable; please see math/README to configure.): (x_0,x_1,x_2,x_3) = (ct,x,y,z)

(in the Lorentz metric) or Failed to parse (Missing texvc executable; please see math/README to configure.): (x_1,x_2,x_3,x_4) = (x,y,z,ict)
(in the original Minkowski metric)[10] where Failed to parse (Missing texvc executable; please see math/README to configure.): c
is the speed of light. The metrical descriptions of Minkowski Space and spacelike, lightlike, and timelike intervals given below follow this convention, as do the conventional formulations of the Lorentz transformation.

Spacetime intervals[link]

In a Euclidean space, the separation between two points is measured by the distance between the two points. A distance is purely spatial, and is always positive. In spacetime, the separation between two events is measured by the invariant interval between the two events, which takes into account not only the spatial separation between the events, but also their temporal separation. The interval between two events is defined as:

where c is the speed of light, and Δr and Δt denote differences of the space and time coordinates, respectively, between the events.

(Note that the choice of signs for Failed to parse (Missing texvc executable; please see math/README to configure.): s^2

above follows the space-like convention (-+++). Other treatments reverse the sign of Failed to parse (Missing texvc executable; please see math/README to configure.): s^2

.)

Spacetime intervals may be classified into three distinct types based on whether the temporal separation (Failed to parse (Missing texvc executable; please see math/README to configure.): c^2 \Delta t^2 ) or the spatial separation (Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta r^2 ) of the two events is greater.

Certain types of world lines (called geodesics of the spacetime) are the shortest paths between any two events, with distance being defined in terms of spacetime intervals. The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as "pure motion" (inertial motion) in spacetime, that is, free from any external influences.

Time-like interval[link]

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} \\ c^2\Delta t^2 &> \Delta r^2 \\ s^2 &< 0 \\ \end{align}

For two events separated by a time-like interval, enough time passes between them for there to be a cause-effect relationship between the two events. For a particle traveling through space at less than the speed of light, any two events which occur to or by the particle must be separated by a time-like interval. Event pairs with time-like separation define a negative squared spacetime interval (Failed to parse (Missing texvc executable; please see math/README to configure.): s^2 < 0 ) and may be said to occur in each other's future or past. There exists a reference frame such that the two events are observed to occur in the same spatial location, but there is no reference frame in which the two events can occur at the same time.

The measure of a time-like spacetime interval is described by the proper time:

The proper time interval would be measured by an observer with a clock traveling between the two events in an inertial reference frame, when the observer's path intersects each event as that event occurs. (The proper time defines a real number, since the interior of the square root is positive.)

Light-like interval[link]

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} c^2\Delta t^2 &= \Delta r^2 \\ s^2 &= 0 \\ \end{align}

In a light-like interval, the spatial distance between two events is exactly balanced by the time between the two events. The events define a squared spacetime interval of zero (Failed to parse (Missing texvc executable; please see math/README to configure.): s^2 = 0 ). Light-like intervals are also known as "null" intervals.

Events which occur to or are initiated by a photon along its path (i.e., while traveling at Failed to parse (Missing texvc executable; please see math/README to configure.): c , the speed of light) all have light-like separation. Given one event, all those events which follow at light-like intervals define the propagation of a light cone, and all the events which preceded from a light-like interval define a second (graphically inverted, which is to say "pastward") light cone.

Space-like interval[link]

Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{align} \\ c^2\Delta t^2 &< \Delta r^2 \\ s^2 &> 0 \\ \end{align}

When a space-like interval separates two events, not enough time passes between their occurrences for there to exist a causal relationship crossing the spatial distance between the two events at the speed of light or slower. Generally, the events are considered not to occur in each other's future or past. There exists a reference frame such that the two events are observed to occur at the same time, but there is no reference frame in which the two events can occur in the same spatial location.

For these space-like event pairs with a positive squared spacetime interval (Failed to parse (Missing texvc executable; please see math/README to configure.): s^2 > 0 ), the measurement of space-like separation is the proper distance:

Like the proper time of time-like intervals, the proper distance (Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta\sigma ) of space-like spacetime intervals is a real number value.

Mathematics of spacetimes[link]

For physical reasons, a spacetime continuum is mathematically defined as a four-dimensional, smooth, connected Lorentzian manifold Failed to parse (Missing texvc executable; please see math/README to configure.): (M,g) . This means the smooth Lorentz metric Failed to parse (Missing texvc executable; please see math/README to configure.): g

has signature Failed to parse (Missing texvc executable; please see math/README to configure.): (3,1)

. The metric determines the geometry of spacetime, as well as determining the geodesics of particles and light beams. About each point (event) on this manifold, coordinate charts are used to represent observers in reference frames. Usually, Cartesian coordinates Failed to parse (Missing texvc executable; please see math/README to configure.): (x, y, z, t)

are used. Moreover, for simplicity's sake, the speed of light Failed to parse (Missing texvc executable; please see math/README to configure.): c
is usually assumed to be unity.

A reference frame (observer) can be identified with one of these coordinate charts; any such observer can describe any event Failed to parse (Missing texvc executable; please see math/README to configure.): p . Another reference frame may be identified by a second coordinate chart about Failed to parse (Missing texvc executable; please see math/README to configure.): p . Two observers (one in each reference frame) may describe the same event Failed to parse (Missing texvc executable; please see math/README to configure.): p

but obtain different descriptions.

Usually, many overlapping coordinate charts are needed to cover a manifold. Given two coordinate charts, one containing Failed to parse (Missing texvc executable; please see math/README to configure.): p

(representing an observer) and another containing Failed to parse (Missing texvc executable; please see math/README to configure.): q
(representing another observer), the intersection of the charts represents the region of spacetime in which both observers can measure physical quantities and hence compare results. The relation between the two sets of measurements is given by a non-singular coordinate transformation on this intersection. The idea of coordinate charts as local observers who can perform measurements in their vicinity also makes good physical sense, as this is how one actually collects physical data—locally.

For example, two observers, one of whom is on Earth, but the other one who is on a fast rocket to Jupiter, may observe a comet crashing into Jupiter (this is the event Failed to parse (Missing texvc executable; please see math/README to configure.): p ). In general, they will disagree about the exact location and timing of this impact, i.e., they will have different 4-tuples Failed to parse (Missing texvc executable; please see math/README to configure.): (x, y, z, t)

(as they are using different coordinate systems). Although their kinematic descriptions will differ, dynamical (physical) laws, such as momentum conservation and the first law of thermodynamics, will still hold. In fact, relativity theory requires more than this in the sense that it stipulates these (and all other physical) laws must take the same form in all coordinate systems. This introduces tensors into relativity, by which all physical quantities are represented.

Geodesics are said to be time-like, null, or space-like if the tangent vector to one point of the geodesic is of this nature. Paths of particles and light beams in spacetime are represented by time-like and null (light-like) geodesics, respectively.

Topology[link]

The assumptions contained in the definition of a spacetime are usually justified by the following considerations.

The connectedness assumption serves two main purposes. First, different observers making measurements (represented by coordinate charts) should be able to compare their observations on the non-empty intersection of the charts. If the connectedness assumption were dropped, this would not be possible. Second, for a manifold, the properties of connectedness and path-connectedness are equivalent, and one requires the existence of paths (in particular, geodesics) in the spacetime to represent the motion of particles and radiation.

Every spacetime is paracompact. This property, allied with the smoothness of the spacetime, gives rise to a smooth linear connection, an important structure in general relativity. Some important theorems on constructing spacetimes from compact and non-compact manifolds include the following:^{[citation needed]}

• A compact manifold can be turned into a spacetime if, and only if, its Euler characteristic is 0. (Proof idea: the existence of a Lorentzian metric is shown to be equivalent to the existence of a nonvanishing vector field.)
• Any non-compact 4-manifold can be turned into a spacetime.

Spacetime symmetries[link]

Often in relativity, spacetimes that have some form of symmetry are studied. As well as helping to classify spacetimes, these symmetries usually serve as a simplifying assumption in specialized work. Some of the most popular ones include:

• Axisymmetric spacetimes
• Spherically symmetric spacetimes
• Static spacetimes
• Stationary spacetimes.

Causal structure[link]

The causal structure of a spacetime describes causal relationships between pairs of points in the spacetime based on the existence of certain types of curves joining the points.

Spacetime in special relativity[link]

The geometry of spacetime in special relativity is described by the Minkowski metric on R⁴. This spacetime is called Minkowski space. The Minkowski metric is usually denoted by Failed to parse (Missing texvc executable; please see math/README to configure.): \eta

and can be written as a four-by-four matrix:

Failed to parse (Missing texvc executable; please see math/README to configure.): \eta_{ab} \, = \operatorname{diag}(1, -1, -1, -1)

where the Landau–Lifshitz space-like convention is being used. A basic assumption of relativity is that coordinate transformations must leave spacetime intervals invariant. Intervals are invariant under Lorentz transformations. This invariance property leads to the use of four-vectors (and other tensors) in describing physics.

Strictly speaking, one can also consider events in Newtonian physics as a single spacetime. This is Galilean-Newtonian relativity, and the coordinate systems are related by Galilean transformations. However, since these preserve spatial and temporal distances independently, such a spacetime can be decomposed into spatial coordinates plus temporal coordinates, which is not possible in the general case.

Spacetime in general relativity[link]

In general relativity, it is assumed that spacetime is curved by the presence of matter (energy), this curvature being represented by the Riemann tensor. In special relativity, the Riemann tensor is identically zero, and so this concept of "non-curvedness" is sometimes expressed by the statement Minkowski spacetime is flat.

The earlier discussed notions of time-like, light-like and space-like intervals in special relativity can similarly be used to classify one-dimensional curves through curved spacetime. A time-like curve can be understood as one where the interval between any two infinitesimally close events on the curve is time-like, and likewise for light-like and space-like curves. Technically the three types of curves are usually defined in terms of whether the tangent vector at each point on the curve is time-like, light-like or space-like. The world line of a slower-than-light object will always be a time-like curve, the world line of a massless particle such as a photon will be a light-like curve, and a space-like curve could be the world line of a hypothetical tachyon. In the local neighborhood of any event, time-like curves that pass through the event will remain inside that event's past and future light cones, light-like curves that pass through the event will be on the surface of the light cones, and space-like curves that pass through the event will be outside the light cones. One can also define the notion of a 3-dimensional "spacelike hypersurface", a continuous 3-dimensional "slice" through the 4-dimensional property with the property that every curve that is contained entirely within this hypersurface is a space-like curve.^[11]

Many spacetime continua have physical interpretations which most physicists would consider bizarre or unsettling. For example, a compact spacetime has closed timelike curves, which violate our usual ideas of causality (that is, future events could affect past ones). For this reason, mathematical physicists usually consider only restricted subsets of all the possible spacetimes. One way to do this is to study "realistic" solutions of the equations of general relativity. Another way is to add some additional "physically reasonable" but still fairly general geometric restrictions and try to prove interesting things about the resulting spacetimes. The latter approach has led to some important results, most notably the Penrose–Hawking singularity theorems.

Quantized spacetime[link]

In general relativity, spacetime is assumed to be smooth and continuous—and not just in the mathematical sense. In the theory of quantum mechanics, there is an inherent discreteness present in physics. In attempting to reconcile these two theories, it is sometimes postulated that spacetime should be quantized at the very smallest scales. Current theory is focused on the nature of spacetime at the Planck scale. Causal sets, loop quantum gravity, string theory, and black hole thermodynamics all predict a quantized spacetime with agreement on the order of magnitude. Loop quantum gravity makes precise predictions about the geometry of spacetime at the Planck scale.

Privileged character of 3+1 spacetime[link]

There are two kinds of dimensions, spatial (bidirectional) and temporal (unidirectional). Let the number of spatial dimensions be N and the number of temporal dimensions be T. That N = 3 and T = 1, setting aside the compactified dimensions invoked by string theory and undetectable to date, can be explained by appealing to the physical consequences of letting N differ from 3 and T differ from 1. The argument is often of an anthropic character.

Immanuel Kant argued that 3-dimensional space was a consequence of the inverse square law of universal gravitation. While Kant's argument is historically important, John D. Barrow says that it "...gets the punch-line back to front: it is the three-dimensionality of space that explains why we see inverse-square force laws in Nature, not vice-versa." (Barrow 2002: 204). This is because the law of gravitation (or any other inverse-square law) follows from the concept of flux and the proportional relationship of flux density and the strength of field. If N = 3, then 3-dimensional solid objects have surface areas proportional to the square of their size in any selected spatial dimension. In particular, a sphere of radius r has area of 4πr ². More generally, in a space of N dimensions, the strength of the gravitational attraction between two bodies separated by a distance of r would be inversely proportional to r^N−1.

In 1920, Paul Ehrenfest showed that if we fix T = 1 and let N > 3, the orbit of a planet about its sun cannot remain stable. The same is true of a star's orbit around the center of its galaxy.^[12] Ehrenfest also showed that if N is even, then the different parts of a wave impulse will travel at different speeds. If N > 3 and odd, then wave impulses become distorted. Only when N = 3 or 1 are both problems avoided. In 1922, Hermann Weyl showed that Maxwell's theory of electromagnetism works only when N = 3 and T = 1, writing that this fact "...not only leads to a deeper understanding of Maxwell's theory, but also of the fact that the world is four dimensional, which has hitherto always been accepted as merely 'accidental,' become intelligible through it."^[13] Finally, Tangherlini^[14] showed in 1963 that when N > 3, electron orbitals around nuclei cannot be stable; electrons would either fall into the nucleus or disperse.

Properties of n+m-dimensional spacetimes

Max Tegmark^[15] expands on the preceding argument in the following anthropic manner. If T differs from 1, the behavior of physical systems could not be predicted reliably from knowledge of the relevant partial differential equations. In such a universe, intelligent life capable of manipulating technology could not emerge. Moreover, if T > 1, Tegmark maintains that protons and electrons would be unstable and could decay into particles having greater mass than themselves.^[why?] (This is not a problem if the particles have a sufficiently low temperature.) If N > 3, Ehrenfest's argument above holds; atoms as we know them (and probably more complex structures as well) could not exist. If N < 3, gravitation of any kind becomes problematic, and the universe is probably too simple to contain observers. For example, when N < 3, nerves cannot cross without intersecting.

In general, it is not clear how physical law could function if T differed from 1. If T > 1, subatomic particles which decay after a fixed period would not behave predictably, because time-like geodesics would not be necessarily maximal.^[16] N = 1 and T = 3 has the peculiar property that the speed of light in a vacuum is a lower bound on the velocity of matter; all matter consists of tachyons.^[15]

Hence anthropic and other arguments rule out all cases except N = 3 and T = 1—which happens to describe the world about us. Curiously, the cases N = 3 or 4 have the richest and most difficult geometry and topology. There are, for example, geometric statements whose truth or falsity is known for all N except one or both of 3 and 4.^{[citation needed]} N = 3 was the last case of the Poincaré conjecture to be proved.

For an elementary treatment of the privileged status of N = 3 and T = 1, see chpt. 10 (esp. Fig. 10.12) of Barrow;^[17] for deeper treatments, see §4.8 of Barrow and Tipler (1986) and Tegmark.^[15] Barrow has repeatedly cited the work of Whitrow.^[18]

String theory hypothesizes that matter and energy are composed of tiny vibrating strings of various types, most of which are embedded in dimensions that exist only on a scale no larger than the Planck length. Hence N = 3 and T = 1 do not characterize string theory, which embeds vibrating strings in coordinate grids having 10, or even 26, dimensions.

The Causal dynamical triangulation (CDT) theory is a background independent theory which derives the observed 3+1 spacetime from a minimal set of assumptions, and needs no adjusting factors. It does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. It shows spacetime to be 2-d near the Planck scale, and reveals a fractal structure on slices of constant time, but spacetime becomes 3+1-d in scales significantly larger than Planck. So, CDT may become the first theory which doesn't postulate but really explains observed number of spacetime dimensions.^[19]

See also[link]

	Time portal
	Space portal

Notes[link]

References[link]

• ^{[Edit this reference]}
  Barrow, John D.; Tipler, Frank J. (19 May 1988). The Anthropic Cosmological Principle. foreword by John A. Wheeler. Oxford: Oxford University Press. ISBN 9780192821478. LC 87-28148. http://books.google.com/books?id=uSykSbXklWEC&printsec=frontcover. Retrieved 31 December 2009. 
• Ehrenfest, Paul (1920) "How do the fundamental laws of physics make manifest that Space has 3 dimensions?" Annalen der Physik 61: 440.
• George F. Ellis and Ruth M. Williams (1992) Flat and curved space-times. Oxford Univ. Press. ISBN 0-19-851164-7
• Isenberg, J. A. (1981). "Wheeler-Einstein-Mach spacetimes". Phys. Rev. D 24 (2): 251–256. Bibcode 1981PhRvD..24..251I. DOI:10.1103/PhysRevD.24.251. 
• Kant, Immanuel (1929) "Thoughts on the true estimation of living forces" in J. Handyside, trans., Kant's Inaugural Dissertation and Early Writings on Space. Univ. of Chicago Press.
• Lorentz, H. A., Einstein, Albert, Minkowski, Hermann, and Weyl, Hermann (1952) The Principle of Relativity: A Collection of Original Memoirs. Dover.
• Lucas, John Randolph (1973) A Treatise on Time and Space. London: Methuen.
• Penrose, Roger (2004). The Road to Reality. Oxford: Oxford University Press. ISBN 0-679-45443-8.  Chpts. 17–18.
• Poe, Edgar A. (1848). Eureka; An Essay on the Material and Spiritual Universe. Hesperus Press Limited. ISBN 1-84391-009-8. 
• Robb, A. A. (1936). Geometry of Time and Space. University Press. 
• Erwin Schrödinger (1950) Space-time structure. Cambridge Univ. Press.
• Schutz, J. W. (1997). Independent axioms for Minkowski Space-time. Addison-Wesley Longman. ISBN 0-582-31760-6. 
• Tangherlini, F. R. (1963). "Atoms in Higher Dimensions". Nuovo Cimento 14 (27): 636. 
• Taylor, E. F.; Wheeler, John A. (1963). Spacetime Physics. W. H. Freeman. ISBN 0-7167-2327-1. 
• Wells, H.G. (2004). The Time Machine. New York: Pocket Books. ISBN 0-671-57554-6.  (pp. 5–6)

External links[link]

Wikibooks has a book on the topic of Special Relativity

• Stanford Encyclopedia of Philosophy: "Space and Time: Inertial Frames" by Robert DiSalle.

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The topic of this article may not meet Wikipedia's general notability guideline. Please help to establish notability by adding reliable, secondary sources about the topic. If notability cannot be established, the article is likely to be merged, redirected, or deleted. (December 2010)

Helen Fay Dowker (born 1965 in Manchester, Lancashire) is a British Theoretical Physicist at Imperial College London.

As a student, she was interested in wormholes and quantum cosmology. Having studied at the University of Cambridge, Dowker was awarded the Tyson Medal in 1987 and completed her Doctor of Philosophy under the supervision of Stephen Hawking^[1] in 1990.

Fay Dowker was later a Postdoctoral Researcher at the Fermi National Accelerator Laboratory, at the University of California at Santa Barbara and also the California Institute of Technology.^[2][3]

She is currently a Professor of Theoretical Physics and a member of the Theoretical Physics Group at Imperial College London and an Affiliate of the Institute for Quantum Computing. She conducts research in a number of areas of theoretical physics including quantum gravity and causal set theory.

Dowker was previously a Lecturer at Queen Mary, University of London.

References[link]

External links[link]

• Theoretical Physics Group at Imperial College London

This article about a physicist of the United Kingdom is a stub. You can help Wikipedia by expanding it. v t e

Kip Thorne
Born	(1940-06-01) June 1, 1940 (age 72) Logan, Utah
Residence	United States
Nationality	American
Fields	Physics
Institutions	Caltech
Alma mater	Caltech, Princeton University
Doctoral advisor	John Archibald Wheeler
Doctoral students	Saul Teukolsky Alan Lightman William H. Press Carlton M. Caves Clifford M. Will Richard H. Price Lee Samuel Finn William L. Burke Bernard F. Schutz Teviet Creighton
Known for	Relativity and Cosmology

Kip Stephen Thorne (born June 1, 1940) is an American theoretical physicist, known for his prolific contributions in gravitation physics and astrophysics and for having trained a generation of scientists. A longtime friend and colleague of Stephen Hawking and Carl Sagan, he was the Feynman Professor of Theoretical Physics at the California Institute of Technology (Caltech) until 2009^[1] and one of the world’s leading experts on the astrophysical implications of Einstein’s general theory of relativity. He continues to do scientific research and is also writing a film.

Biography[link]

Discussion in the main lecture hall at the École de Physique des Houches (Les Houches Physics School), 1972. From left, Yuval Ne'eman, Bryce DeWitt, Kip Thorne.

Thorne was born in Logan, Utah, the son of Utah State University professors D. Wynne Thorne and Alison C. Thorne, a soil chemist and an economist, respectively. Raised in an academic environment, two of his four siblings are also professors. He became interested in science at the age of eight, after attending a lecture about the solar system. Thorne and his mother then worked out calculations for their own model of the solar system.

Thorne rapidly excelled at academics early in life, becoming one of the youngest full professors in the history of the California Institute of Technology. He received his B.S. from Caltech in 1962, and Ph.D. from Princeton University in 1965. He wrote his Ph.D. thesis, Geometrodynamics of Cylindrical Systems, under the supervision of relativist John Wheeler. Thorne returned to Caltech as an associate professor in 1967 and became a professor of theoretical physics in 1970, the William R. Kenan, Jr. Professor in 1981, and the Feynman Professor of Theoretical Physics in 1991. In June 2009 he resigned his Feynman Professorship (he is now the Feynman Professor of Theoretical Physics, Emeritus) to pursue a career of writing and movie making. His first film project will team him with Steven Spielberg.^[1]

Throughout the years, Thorne has served as a mentor and thesis advisor for many leading theorists who now work on observational, experimental, or astrophysical aspects of general relativity. Approximately 50 physicists have received Ph.D.s at Caltech under Thorne's personal mentorship.

Thorne is known for his ability to convey the excitement and significance of discoveries in gravitation and astrophysics to both professional and lay audiences. In 1999, Thorne made some speculations on what the 21st century will find as the answers to the following questions:

• Is there a "dark side of the universe" populated by objects such as black holes?
• Can we observe the birth of the universe and its dark side using radiation made from space-time warpage, or so-called "gravitational waves"?
• Will 21st century technology reveal quantum behavior in the realm of human-size objects?

His presentations on subjects such as black holes, gravitational radiation, relativity, time travel, and wormholes have been included in PBS shows in the U.S. and in the United Kingdom on the BBC.

Thorne and Linda Jean Peterson married in 1960. Their children are Kares Anne and Bret Carter, an architect. Thorne and Peterson divorced in 1977. Thorne and his second wife, Carolee Joyce Winstein, a professor of biokinesiology and physical therapy at USC, married in 1984.

Research[link]

Thorne in 1972.

Thorne's research has principally focused on relativistic astrophysics and gravitation physics, with emphasis on relativistic stars, black holes and especially gravitational waves. He is perhaps best known to the public for his controversial theory that wormholes can conceivably be used for time travel. However, Thorne's scientific contributions, which center on the general nature of space, time, and gravity, span the full range of topics in general relativity.

Gravitational waves and LIGO[link]

Among a handful of physicists, Thorne is considered one of the world’s authorities on gravitational waves. In part, his work has dealt with the prediction of gravity-wave strengths and their temporal signatures as observed on Earth. These “signatures” are of great relevance to LIGO (Laser Interferometer Gravitational Wave Observatory), a multi-institution gravity-wave experiment for which Thorne has been a leading proponent — in 1984, he cofounded the LIGO Project (the largest project ever funded by the NSF) to discern and measure any fluctuations between two or more 'static' points; such fluctuations would be evidence of gravitational waves, as calculations describe. A significant aspect of his research is developing the mathematics necessary to analyze these objects.[1] Thorne also carries out engineering design analyses for features of the LIGO that cannot be developed on the basis of experiment and he gives advice on data analysis algorithms by which the waves will be sought. He has provided theoretical support for LIGO, including identifying gravitational wave sources that LIGO should target, designing the baffles to control scattered light in the LIGO beam tubes, and — in collaboration with Vladimir Braginsky's (Moscow, Russia) research group — inventing quantum nondemolition designs for advanced gravity-wave detectors and ways to reduce the most serious kind of noise in advanced detectors: thermoelastic noise. With Carlton M. Caves, Thorne invented the back-action-evasion approach to quantum nondemolition measurements of the quadrature amplitudes of harmonic oscillators — a technique applicable both in gravitational wave detection and quantum optics.

Black hole cosmology[link]

Thorne has made prolific contributions to black hole cosmology. Thorne proposed his Hoop Conjecture that cast aside the thought of a naked singularity. The Hoop Conjecture describes an imploding star turning into a black hole when the critical circumference of the designed hoop can be placed around it and set into rotation. [2] That is, any object of mass M around which a hoop of circumference Failed to parse (Missing texvc executable; please see math/README to configure.): \begin{matrix} \frac{4 \pi GM}{c^2} \end{matrix}

can be spun must be a black hole. As a tool to be used in both enterprises, astrophysics and theoretical physics, Thorne has developed an unusual approach, called the "Membrane Paradigm", to the theory of black holes and used it to clarify the "Blandford-Znajek" mechanism by which black holes may power some quasars and active galactic nuclei. Thorne has investigated the quantum statistical mechanical origin of the entropy of a black hole and the entropy of a cosmological horizon in an inflationary model of the universe. With Wojciech Zurek he showed that the entropy of a black hole of known mass, angular momentum, and electric charge is the logarithm of the number of ways that the hole could have been made. With Igor Novikov and Don Page he developed the general relativistic theory of thin accretion disks around black holes, and using this theory he deduced that with a doubling of its mass by such accretion a black hole will be spun up to 0.998 of the maximum spin allowed by general relativity, but never any farther; this is probably the maximum black-hole spin allowed in Nature. He, along with his mentor John Wheeler, additionally proved that it was impossible for cylindrical magnetic field lines to implode. Both Hawking and Thorne have theorized that a singularity exists in the interior of a black hole.

Wormholes and time travel[link]

Thorne was one of the first people to conduct scientific research on whether the laws of physics permit space and time to be multiply connected (can there exist classical, traversable wormholes and "time machines"?). With Sung-Won Kim, Thorne identified a universal physical mechanism (the explosive growth of vacuum polarization of quantum fields), that may always prevent spacetime from developing closed timelike curves (i.e., prevent "backward time travel"). With Mike Morris and Ulvi Yurtsever he showed that traversable Lorentzian wormholes can exist in the structure of spacetime only if they are threaded by quantum fields in quantum states that violate the averaged null energy condition (i.e. have negative renormalized energy spread over a sufficiently large region). This has triggered research to explore the ability of quantum fields to possess such extended negative energy. Recent calculations by Thorne indicate that simple masses passing through traversable wormholes could never engender paradoxes — there are no initial conditions that lead to paradox once time travel is introduced. If his results can be generalised, they would suggest that none of the supposed paradoxes formulated in time travel stories can actually be formulated at a precise physical level: that is, that any situation in a time travel story turns out to permit many consistent solutions.

Relativistic stars, multipole moments, & other endeavors[link]

With Anna Żytkow, Thorne predicted the existence of red supergiant stars with neutron-star cores (Thorne-Żytkow objects). Most importantly, he laid the foundations for the theory of pulsations of relativistic stars and the gravitational radiation they emit. With James Hartle, Thorne derived from general relativity the laws of motion and precession of black holes and other relativistic bodies, including the influence of the coupling of their multipole moments to the spacetime curvature of nearby objects. Thorne has also theoretically predicted the existence of universally antigravitating "exotic matter" — the element needed to accelerate the expansion rate of the universe, keep traversable wormhole "Star Gates" open and keep timelike geodesic free float "warp drives" working. With Clifford Will and others of his students, he laid foundations for the theoretical interpretation of experimental tests of relativistic theories of gravity — foundations on which Will and others then built. Thorne is currently interested in the origin of classical space and time from the quantum foam of quantum gravity theory.

Publications[link]

Thorne has written and edited books on topics in gravitational theory and high-energy astrophysics. In 1973, he co-authored the classic textbook Gravitation with Charles Misner and John Wheeler;^[2] from which most of the present generation of scientists have learned general relativity theory. In 1994, he published Black Holes and Time Warps: Einstein's Outrageous Legacy, a landmark book for non-scientists for which he received numerous awards. This book has been published in six languages, and editions in Chinese, Italian, Czech, and Polish are in press.

Thorne's work has appeared in magazines and encyclopedias such as:

• Scientific American,
• McGraw-Hill Yearbook of Science and Technology, and
• Collier's Encyclopedia among many others.

Thorne has published more than 150 articles in scholarly journals.

Some references[link]

• Thorne, K. S., in 300 Years of Gravitation, (Eds.) S. W. Hawking and W. Israel, 1987, (Chicago: Univ. of Chicago Press), Gravitational Radiation.

• Thorne, K. S., Price, R. H. and Macdonald, D. M., Black Holes, The Membrane Paradigm, 1986, (New Haven: Yale Univ. Press).

• Friedman, J., Morris, M. S., Novikov, I. D., Echeverria, F., Klinkhammer, G., Thorne, K. S. and Yurtsever, U., Physical Review D., 1990, (in press), Cauchy Problem in Spacetimes with Closed Timelike Curves.

Honors and awards[link]

Thorne has been elected to:

• the American Academy of Arts and Sciences, (1972)^[3]
• the National Academy of Sciences,
• the Russian Academy of Sciences, and
• the American Philosophical Society.

He has been recognized by numerous awards including:

• the American Institute of Physics Science Writing Award in Physics and Astronomy,
• the Phi Beta Kappa Science Writing Award,
• the American Physical Society's Lilienfeld Prize,
• the German Astronomical Society's Karl Schwarzschild Medal,
• the Robinson Prize in Cosmology from the University of Newcastle, England,
• the Albert Einstein Medal in 2009 from the Albert Einstein Society, Bern, Switzerland,
• the Sigma Xi: The Scientific Research Society's Common Wealth Awards for Science and Invention, and
• the California Science Center's California Scientist of the Year Award (2003).

He has been a Woodrow Wilson Fellow, Danforth Fellow, Guggenheim Fellow, and Fulbright Fellow. He has also received the honorary degree of doctor of humane letters from Claremont Graduate University.

He has been elected to hold Lorentz chair for the year 2009 Leiden University, the Netherlands.

Thorne has served on:

• the International Committee on General Relativity and Gravitation,
• the Committee on US-USSR Cooperation in Physics, and
• the National Academy of Sciences' Space Science Board, which has advised NASA and Congress on space science policy.

Films[link]

Carl Sagan once asked Thorne to examine the time travel section of the manuscript for Contact. Thorne immediately dismissed Sagan's hypothesis; however, he later had an epiphany — wormholes may be used as time machines. His subsequent work, Wormholes, Time Machines and the Weak Energy Condition, along with other papers, has made him popular with science fiction fans. He did not care that it was highly speculative work, and he put as much energy into it as he did other subjects.

In June 2006, Steven Spielberg announced he would direct a scientifically accurate film about "a group of explorers who travel through a worm hole and into another dimension",^[4] from a treatment by Kip Thorne and producer Lynda Obst.^[5] In January 2007, screenwriter Jonathan Nolan met with the studio to discuss adapting Obst and Thorne's treatment into a narrative screenplay. The screenwriter suggested the addition of a "time element" to the treatment's basic idea, which was welcomed by Obst and Thorne.^[5] In March, Paramount hired Nolan as well as scientists from Caltech, forming a workshop who will begin adapting the treatment after completing the script for Warner Bros.' The Chicago Fire.^[6] The following July, Kip Thorne said there was a push by people for him to portray himself in the film Interstellar.^[7]

The film, jointly financed by Paramount Pictures and Spielberg's DreamWorks, will be released in North America by DreamWorks through Touchstone Pictures on November 21, 2014. Paramount will handle the international distribution.

See also[link]

• Hoop Conjecture
• Membrane Paradigm
• LIGO
• Time travel
• Thorne-Zytkow object
• Thorne-Hawking-Preskill bet
• Stephen Hawking
• John Wheeler

References[link]

External links[link]

• Kip Thorne at the Internet Movie Database
• Home Page
• Crunch Time
• Founding Fathers of Relativity

Sir Roger Penrose OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the Mathematical Institute, University of Oxford and Emeritus Fellow of Wadham College. He has received a number of prizes and awards, including the 1988 Wolf Prize for physics which he shared with Stephen Hawking for their contribution to our understanding of the universe.^[1] He is renowned for his work in mathematical physics, in particular his contributions to general relativity and cosmology. He is also a recreational mathematician and philosopher.

Career[link]

He was born in Colchester, Essex, England, Roger Penrose is a son of Lionel S. Penrose and Margaret Leathes.^[2] Penrose is the brother of mathematician Oliver Penrose and of chess Grandmaster Jonathan Penrose. Penrose attended University College School and University College, London, where he graduated with a first class degree in mathematics. In 1955, while still a student, Penrose reintroduced the E. H. Moore generalized matrix inverse, also known as the Moore–Penrose inverse^[3], after it had been reinvented by Arne Bjerhammar (1951). Penrose earned his Ph.D. at Cambridge (St John's College) in 1958, writing a thesis on "tensor methods in algebraic geometry" under algebraist and geometer John A. Todd. He devised and popularised the Penrose triangle in the 1950s, 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 tri-bar – 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.^[4]

In 1965, at Cambridge, Penrose proved that singularities (such as black holes) could be formed from the gravitational collapse of immense, dying stars.^[5] This work was extended by Hawking to prove the Penrose–Hawking singularity theorems.

Oil painting by Urs Schmid (1995) of a Penrose tiling using fat and thin rhombi.

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). In 1969, he conjectured the cosmic censorship hypothesis. This proposes (rather informally) that the universe protects us from the inherent unpredictability of singularities (such as the one in the centre of a black hole) by hiding them from our view behind an event horizon. This form is now known as the "weak censorship hypothesis"; in 1979, Penrose formulated a stronger version called the "strong censorship hypothesis". Together with the BKL 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.^[6] Penrose and James Terrell independently realized 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.^[7][8]

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. Penrose developed these ideas based on the article Deux types fondamentaux de distribution statistique^[9] (1938; an English translation Two Basic Types of Statistical Distribution) by Czech geographer, demographer and statistician Jaromír Korčák. In 1984, such patterns were observed in the arrangement of atoms in quasicrystals.^[10] 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). In 2004 Penrose released The Road to Reality: A Complete Guide to the Laws of the Universe, a 1,099-page book aimed at giving a comprehensive guide to the laws of physics. He has proposed a novel interpretation of quantum mechanics.^[11] In 2010, Penrose reported possible evidence, based on concentric circles found in WMAP data of the CMB sky, of an earlier universe existing before the Big Bang of our own present universe.^[12]

Penrose is the Francis and Helen Pentz Distinguished (visiting) Professor of Physics and Mathematics at Pennsylvania State University.^[13] Penrose is married to Vanessa Thomas, head of mathematics at Abingdon School,^[14][15] with whom he has one son.^[14] He has three sons from a previous marriage to American Joan Isabel Wedge, whom he married in 1959.

Physics and consciousness[link]

At a conference in 2005

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. (E.g., imagine a system with only two states, ON and OFF. The system's state is ON if a given Turing machine halts, and OFF if the Turing machine does not halt, then the system's state is completely determined by the Turing machine, however there is no algorithmic way to determine whether the Turing machine stops.) Penrose believes that such deterministic non-algorithmic processes may come in play in the quantum mechanical wave function reduction, and may be harnessed by the brain. He argues that the present computer is unable to have intelligence because it is an algorithmically deterministic system. 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 things 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 widely criticized by mathematicians, computer scientists and philosophers, and the consensus among experts in these fields seems to be that the argument fails, though different authors may choose different aspects of the argument to attack.^[16] 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 believes that humans are, in fact, machines, whose functioning, although complex, is fully explainable by current physics. Minsky maintains 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."^[17]

Penrose responded to criticism of The Emperor's New Mind with his follow up 1994 book Shadows of the Mind, and in 1997 with The Large, the Small and the Human Mind. In those works, he also combined his observations with that of anesthesiologist Stuart Hameroff.

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,^[18] 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'".^[19] 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 Tuszynski and Hameroff^[20][21] 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. It was 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.

Roger Penrose in the University of Santiago de Compostela to pick up the Fonseca prize.

Finally, it is 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. In the last decade, some researchers who are sympathetic to Penrose's ideas have proposed an alternative scheme for quantum processing in microtubules based on the interaction of tubulin tails with microtubule-associated proteins, motor proteins and presynaptic scaffold proteins. These proposed alternative processes have the advantage of taking place within Tegmark's time to decoherence.

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.^[22] In addition to this, a recent 2011 paper by Roger Penrose and Stuart Hameroff gives an updated model of their Orch-OR theory, in light of criticisms, and discusses the place of consciousness within the universe.^[23]

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.^[19]

Religious views[link]

Penrose does not hold to any religious doctrine,^[24] and refers to himself as an atheist.^[25] In the film A Brief History of Time, he 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."^[26] Penrose is a Distinguished Supporter of the British Humanist Association.

Awards and honours[link]

Roger Penrose during a lecture

Penrose has been awarded many prizes for his contributions to science. He was elected a Fellow of the Royal Society of London in 1972. In 1975, Stephen Hawking and Penrose were jointly awarded the Eddington Medal of the Royal Astronomical Society. In 1985, he was awarded the Royal Society Royal Medal. Along with Stephen Hawking, he was awarded the prestigious Wolf Foundation Prize for Physics in 1988. In 1989 he was awarded the Dirac Medal and Prize of the British Institute of Physics. In 1990 Penrose was awarded the Albert Einstein Medal for outstanding work related to the work of Albert Einstein by the Albert Einstein Society. In 1991, he was awarded the Naylor Prize of the London Mathematical Society. From 1992 to 1995 he served as President of the International Society on General Relativity and Gravitation. In 1994, Penrose was knighted for services to science.^[27] In the same year he was also awarded an Honorary Degree (Doctor of Science) by the University of Bath.^[28] In 1998, he was elected Foreign Associate of the United States National Academy of Sciences. In 2000 he was appointed to the Order of Merit. 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 2005 Penrose was awarded an honorary doctorate (Honoris Causa) by Warsaw University and Katholieke Universiteit Leuven (Belgium), and in 2006 by the University of York. In 2008 Penrose was awarded the Copley Medal. He is also a Distinguished Supporter of the British Humanist Association and one of the patrons of the Oxford University Scientific Society. In 2011, Penrose was awarded the Fonseca prize by the University of Santiago de Compostela. In 2012 Penrose was awarded the Richard R. Ernst Medal by ETHZ for his contributions to science and strengthening the connection between science and society.

Works[link]

• Techniques of Differential Topology in Relativity (1972, ISBN 0-89871-005-7)
• Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (with Wolfgang Rindler, 1987) ISBN 0-521-33707-0 (paperback)
• Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (with Wolfgang Rindler, 1988) (reprint), ISBN 0-521-34786-6 (paperback)
• The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics (1989, ISBN 0-14-014534-6 (paperback); it received the Rhone-Poulenc science book prize in 1990)
• Shadows of the Mind: A Search for the Missing Science of Consciousness (1994, ISBN 0-19-853978-9 (hardback))
• The Nature of Space and Time (with Stephen Hawking, 1996, ISBN 0-691-03791-4 (hardback), ISBN 0-691-05084-8 (paperback))
• The Large, the Small, and the Human Mind (with Abner Shimony, Nancy Cartwright, and Stephen Hawking, 1997, ISBN 0-521-56330-5 (hardback), ISBN 0-521-65538-2 (paperback), Canto edition: ISBN 0-521-78572-3)
• White Mars or, The Mind Set Free (with Brian W. Aldiss, 1999, ISBN 978-0-316-85243-2 (hardback))
• The Road to Reality: A Complete Guide to the Laws of the Universe (2004, ISBN 0-224-04447-8 (hardcover), ISBN 0-09-944068-7 (paperback))
• Cycles of Time: An Extraordinary New View of the Universe (Bodley Head (23 Sep 2010) ISBN 978-0-224-08036-1)

Penrose also wrote forewords to Quantum Aspects of Life and Zee's book Fearful Symmetry.

See also[link]

• Conformal Cyclic Cosmology
• Orch-OR
• Quantum mind
• Multiverse
• Quantum Aspects of Life (book)
• Illumination problem

References[link]