Epstein Secrets

Magueijo, Shahn Majid, Seth Major, Chanda Prescod-Weinstein and especially Giovanni Arnelino- Camelia for rel

rdinates are to be understood as coordinate ambiguities rather than physical non-localities. In section 4 this view is supported by an anal- ysis of Einstein's procedure for the synchronization of moving clocks, applied to sc-Minkowksi spacetime. This section closes with some general remarks about the phy

oks in commuting coordinates, (T, x`)(21, 26]. We can mention that one reason to suppose this is the physical choice is that there is a basis in the Hilbert space for a free relativistic particle in which x' and T are both sharply defined, while is there is no basis that simultaneously diagonalizes t an

el, Joao Magueijo, Seth Major and Chanda Prescod-Weinstein have also been very helpful. I am also grate- ful

icular local event in spacetime appears to be observer dependent. This challenges the basic operational definition of a spacetime event proposed by Einstein, according to which an event is defined by the coincide of several particles in space and time. From the point of view just mentioned, it is not su

rse length contraction and relativity 12 3.4 A classical locality paradox 12 4 Quantum theory of a free relativistic particle 13 4.1 Bases in Hilbert space 13 4.2 Dynamics in momentum space 14 4.3 Dynamics in position space 14 4.3.1 Propagation and spreading of a wavepacket 14 4.3.2 Wa

Newton was an extraordinary man. He discovered many of the physical principles we use today, and his view of the Universe reigned unchallenged until Einstein’s discovery of relativity. He was also, by many accounts, a nasty piece of work. Not only was he a famous academic, he also head of the Royal Mint. H

k. Who cares why? In 1964, John Bell, an Irish physicist working at the Conseil Européen pour la Recherche Nucléaire (“CERN’), devised a way to test Einstein’s hidden variable theory. He pointed out that if photons possess hidden variables and we randomly measure them with a detector set at three angles, w

disproof of P =NP @ 1.5 The Poincaré Conjecture @ —- Solved 1.6 Riemann Hypothesis °° 1.7 Yang-Mills Theory @ 1.8 Can we understand and solve all 23 Hilbert Problems ™** 1.9 Goldbach Conjecture ™ 1.10 Is mathematics fundamental to or simply a good model of our Universe? "° 1.11 Is mathematics an emergent

sed at the Institute of Advanced Mathematics in the USA on the Princeton University campus, next door to the Institute for Advanced Study that housed Einstein. Turing travelled to America in 1937 and completed his doctoral thesis at Princeton. He might have stayed, but Europe was heating up and war seemed i

r the occupants of the bus is larger than infinity. Real Numbers What about the real world we live in? Is the larger infinity we failed to fit into Hilbert’s Hotel present, or was it just a mathematical fiction? Hold up your thumb and index finger for a moment. The gap between them is a distance. Most li

quantum craziness of reality was taken by an unlikely explorer, Paul Adrien Maurice Dirac. In one sense, Dirac was the perfect man for the job. As Einstein is re- puted to have later said of him, "This balancing on the dizzying path between genius and madness is awful! When I think of Dirac, an old jok

return to the university and find that they are required to learn at the feet of a woman?" In a retort that eternally reinforced my admiration for Hilbert, beyond that for his remarkable talent as a mathematician, he replied, 1 do not see that the sex of the candidate is an argument against her ad- mi