Why Quantum Theory? Lucien Hardy November 13, 2001 Centre for Quantum Computation,
... of quantum theory. It is rather striking that the difference between classical probability theory and quantum theory is just one word. A few comments on these axioms are appropriate here. We can think of any probability theory as a structure. This structure, however, has no physical meaning unless ...
... of quantum theory. It is rather striking that the difference between classical probability theory and quantum theory is just one word. A few comments on these axioms are appropriate here. We can think of any probability theory as a structure. This structure, however, has no physical meaning unless ...
Another version - Scott Aaronson
... The Information Loss Problem: Calculations suggest that Hawking radiation is thermal—uncorrelated with whatever fell in. So, is infalling information lost forever? Would seem to violate the unitarity / reversibility of QM OK then, assume the information somehow gets out! The Xeroxing Problem: How co ...
... The Information Loss Problem: Calculations suggest that Hawking radiation is thermal—uncorrelated with whatever fell in. So, is infalling information lost forever? Would seem to violate the unitarity / reversibility of QM OK then, assume the information somehow gets out! The Xeroxing Problem: How co ...
I. Waves & Particles
... shines on the metal Hmm… (For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum – why did light have to be of a minimum frequency?) ...
... shines on the metal Hmm… (For a given metal, no electrons were emitted if the light’s frequency was below a certain minimum – why did light have to be of a minimum frequency?) ...
Celestial Mechanics V
... presence of close encounters • It is used to classify cometary orbits • T relates to the speed of the encounter • TP may be defined for other planets too, but they are less stable in case the orbits cross that of Jupiter ...
... presence of close encounters • It is used to classify cometary orbits • T relates to the speed of the encounter • TP may be defined for other planets too, but they are less stable in case the orbits cross that of Jupiter ...
The Future of Computer Science
... functions f,g:{0,1}n{0,1}p(n). Promised that Range(f) and Range(g) are either equal or disjoint. Decide which. In the “black-box” setting, this problem takes exp(n) time even with a quantum computer (a main result from my 2004 PhD thesis, the “collision lower bound”). Even in non-blackbox setting, ...
... functions f,g:{0,1}n{0,1}p(n). Promised that Range(f) and Range(g) are either equal or disjoint. Decide which. In the “black-box” setting, this problem takes exp(n) time even with a quantum computer (a main result from my 2004 PhD thesis, the “collision lower bound”). Even in non-blackbox setting, ...
The importance of the Empty Set and
... First one needs to understand the role of Bijection which is essential for a rigorous counting and constitutes the beginning of set theory and the work of G. Cantor [2,3]. Second we need to understand and appreciate the method of complete induction. It is due to Pascal but if one goes back in histor ...
... First one needs to understand the role of Bijection which is essential for a rigorous counting and constitutes the beginning of set theory and the work of G. Cantor [2,3]. Second we need to understand and appreciate the method of complete induction. It is due to Pascal but if one goes back in histor ...
Gauss` law - spherical symmetry
... 2. For infinite layer of the width h (0 < z < h), if z > h or z < 0 the solution is identical to the one for the infinite plane. In the case 0 < z < h we construct a shell of area S symmetrical relatively to the middle of the layer - its its bottom plate is at z, the top plate is at h − z and the he ...
... 2. For infinite layer of the width h (0 < z < h), if z > h or z < 0 the solution is identical to the one for the infinite plane. In the case 0 < z < h we construct a shell of area S symmetrical relatively to the middle of the layer - its its bottom plate is at z, the top plate is at h − z and the he ...
Gauge-Gravity Duality and the Black Hole Interior
... For small t t0 this expectation value is Oð1Þ in terms of the density of states eS , and can be calculated geometrically in terms of the two-sided black hole [34,37]. However, at times greater than the Page time OðSÞ, its exponentially falling geometrical value is less than its long-time average m ...
... For small t t0 this expectation value is Oð1Þ in terms of the density of states eS , and can be calculated geometrically in terms of the two-sided black hole [34,37]. However, at times greater than the Page time OðSÞ, its exponentially falling geometrical value is less than its long-time average m ...
text - Physics Department, Princeton University
... The weak nuclear force causes the splitting of atomic nuclei, and is, despite its name, responsible for enormous destructive force of nuclear weapons. The strong nuclear force, on the other hand, is responsible for holding the nucleons tightly together. It is described by the theory known as quantum ...
... The weak nuclear force causes the splitting of atomic nuclei, and is, despite its name, responsible for enormous destructive force of nuclear weapons. The strong nuclear force, on the other hand, is responsible for holding the nucleons tightly together. It is described by the theory known as quantum ...
The Learnability of Quantum States
... Proof Idea: The classical advice to the HeurQMA/poly verifier will consist of “training inputs” x1,…,xm where m=poly(n), as well as whether xiL for all i Given a purported quantum advice state |, the verifier first checks that | yields the right answers on the training inputs, and only then us ...
... Proof Idea: The classical advice to the HeurQMA/poly verifier will consist of “training inputs” x1,…,xm where m=poly(n), as well as whether xiL for all i Given a purported quantum advice state |, the verifier first checks that | yields the right answers on the training inputs, and only then us ...
May 2003
... Write the wave equation for small fluctuations p1 (~x, t) of the pressure field. State the relation between fluctuations ρ1 in the density and fluctuations p1 in the pressure (it involves the velocity of sound cs ). What is the equation that would allow one to infer the local velocity ~v of the air ...
... Write the wave equation for small fluctuations p1 (~x, t) of the pressure field. State the relation between fluctuations ρ1 in the density and fluctuations p1 in the pressure (it involves the velocity of sound cs ). What is the equation that would allow one to infer the local velocity ~v of the air ...
Strings as hadrons
... For the 2 years that followed, string theory was the theory of hadrons. One of the spectacular discoveries made in this early period was that the mathematical infinities that occur in Quantum Field Theory are completely absent in string theory. However, from the very beginning, there were big proble ...
... For the 2 years that followed, string theory was the theory of hadrons. One of the spectacular discoveries made in this early period was that the mathematical infinities that occur in Quantum Field Theory are completely absent in string theory. However, from the very beginning, there were big proble ...
A Quantum Version of Wigner`s Transition State Theory
... detail (see, e.g., the review paper [1]). A reaction can often be viewed as a transition across a saddle point of the potential energy surface which describes the interaction between the constituent atoms. In the 1930s Eyring, Polanyi and Wigner developed transition state theory (TST) which is a com ...
... detail (see, e.g., the review paper [1]). A reaction can often be viewed as a transition across a saddle point of the potential energy surface which describes the interaction between the constituent atoms. In the 1930s Eyring, Polanyi and Wigner developed transition state theory (TST) which is a com ...
Acrobat PDF - Electronic Journal of Theoretical Physics
... In general, the Feynman rules are large and the tensor algebra immense. Much of the calculational simplicity should be restored by submitting this part of the complexity to the computer. However, the intermediate results can be so extensive that even a supercomputer can choke without help. For examp ...
... In general, the Feynman rules are large and the tensor algebra immense. Much of the calculational simplicity should be restored by submitting this part of the complexity to the computer. However, the intermediate results can be so extensive that even a supercomputer can choke without help. For examp ...