“The idea of having an ambient space-time of some specific dimension seems to play less of a role of string theory than in conventional physics, and certainly less than the kind of role that I would myself feel comfortable with. It is particularly difficult to assess the functional freedom that is involved in a physical theory unless one has a clear idea of its actual space-time dimensionality.”

— Roger Penrose, book Fashion, Faith, and Fantasy in the New Physics of the Universe

Ch. 1, Mathematical Elegance as a Driving Force, p. 62 https://books.google.com/books?id=T09kCwAAQBAJ&pg=PA62. <br class="br">Fashion, Faith, and Fantasy in the New Physics of the Universe (2016)

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English mathematical physicist, recreational mathematician … 1931

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“I want to emphasize the necessity for a sound mathematical basis for any fundamental physical theory. Any philosophical ideas that one may have play only a subordinate role. Unless such ideas have a mathematical basis they will be ineffective.”

Paul Dirac (1902–1984) theoretical physicist

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“In classical Newtonian physics there was a clear understanding of 'what reality is'. Indeed in this classical view, reality at a certain time is the collection of all what is actual at this time, and this is contained in 'the present'. Often it is stated that three dimensional space and one dimensional time have been substituted by four dimensional space-time in relativity theory, and as a consequence the classical concept of reality, as that what is 'present', cannot be retained. Is reality then the four dimensional manifold of relativity theory? And if so, what is then the meaning of 'change in time?”

Diederik Aerts (1953) Belgian theoretical physicist

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“Fundamental ideas play the most essential role in forming a physical theory. Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory. The ideas must later take the mathematical form of a quantitative theory, to make possible the comparison with experiment.”

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“Why is space-time doomed? There are many reasons, among which: In string theory we can change the dimension of space-time by changing the strength of the string force. Thus, the so-called II-A string theory, which semi-classically describes closed strings moving in ten-dimensional flat space for very weak coupling is dual for strong coupling to a theory, called M-theory, that at low energies is described by eleven-dimensional supergravity. By increasing the string coupling we can grow an extra dimension. How can the spatial continuum be fundamental if the number of spatial dimensions can be so changed?”

David Gross (1941) American particle physicist and string theorist

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“In the realm of physics it is perhaps only the theory of relativity which has made it quite clear that the two essences, space and time, entering into our intuition, have no place in the world constructed by mathematical physics. Colours are thus "really" not even æther-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time.”

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“If supersymmetry plays the role in physics that we suspect it does, then it is very likely to be discovered by the next generation of particle accelerators, either at Fermilab… or at CERN… Discovery of supersymmetry would be one of the real milestones in physics, made even more exciting by its close links to still more ambitious theoretical ideas. Indeed, supersymmetry is one of the basic requirements of "string theory," which is the framework in which theoretical physicists have had some success in unifying gravity with the rest of the elementary particle forces. Discovery of supersymmetry would would certainly give string theory an enormous boost.”

Edward Witten (1951) American theoretical physicist

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“Some philosophers have believed that a philosophical clarification of space also provided a solution of the problem of time. Kant presented space and time as analogous forms of visualization and treated them in a common chapter in his major epistemological work. Time therefore seems to be much less problematic since it has none of the difficulties resulting from multidimensionality. Time does not have the problem of mirror-image congruence, i. e., the problem of equal and similarly shaped figures that cannot be superimposed, a problem that has played some role in Kant's philosophy. Furthermore, time has no problem analogous to non-Euclidean geometry. In a one-dimensional schema it is impossible to distinguish between straightness and curvature. …A line may have external curvature but never an internal one, since this possibility exists only for a two-dimensional or higher continuum. Thus time lacks, because of its one-dimensionality, all those problems which have led to philosophical analysis of the problems of space.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“By his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. ...Physical space and time are found to be closely bound... with... motion of the observer; and only an amorphous combination of the two is left... It is my aim to give an account of this work without introducing anything very technical in... mathematics, physics, or philosophy. ...[T]he task is one of interpreting a clear-cut theory... although perhaps not everyone would accept the author's views of its meaning.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Space, Time and Gravitation (1920)

“The last two years have seen the emergence of a beautiful new subject in mathematical physics. It manages to combine a most exotic range of disciplines: two-dimensional quantum field theory, intersection theory on the moduli space of Riemann surfaces, integrable hierarchies, matrix integrals, random surfaces, and many more. The common denominator of all these fields is two-dimensional quantum gravity or, more general, low-dimensional string theory.”

Robbert Dijkgraaf (1960) Dutch mathematical physicist and string theorist

[1992, Intersection Theory, Integrable Hierarchies and Topological Field Theory by Robbert Dijkgraaf, Fröhlich J., ’t Hooft G., Jaffe A., Mack G., Mitter P.K., Stora R. (eds.), New Symmetry Principles in Quantum Field Theory, NATO ASI Series (Series B: Physics), vol. 295, 95–158, Springer, Boston, MA, 10.1007/978-1-4615-3472-3_4]

“It is very possible that a proper understanding of string theory will make the space-time continuum melt away…. String theory is a miracle through and through.”

Edward Witten (1951) American theoretical physicist

as quoted by K.C. Cole, "A Theory of Everything" New York Times Magazine (1987) Oct.18

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