174 research outputs found
The (Elusive) Theory of Everything
Stephen Hawking's work on black holes and the origin of the universe is arguably the most concrete progress theoretical physicists have made toward reconciling Einstein's gravitation and quantum physics into one final theory of everything.
Physicists have a favorite candidate for such a theory, string theory, but it comes in five different formulations, each covering a restricted range of situations.
A network of mathematical connections, however, links the different string theories into one overarching system, enigmatically called M-theory: perhaps the network is itself the final theory.
In a new book, The Grand Design, Hawking and Caltech physicist Leonard Mlodinow argue that the quest to discover a final theory may in fact never lead to a unique set of equations. Every scientific theory, they write, comes with its own model of reality, and it may not make sense to talk of what reality actually is. This essay is based on that book
Solving the Schrödinger equation with use of 1/N perturbation theory
The large N expansion provides a powerful new tool for solving the Schrödinger equation. In this
paper, we present simple recursion formulas which facilitate the calculation. We do some numerical calculations which illustrate the speed and accuracy of the technique
Abelian scalar theory at large global charge
We elaborate on Abelian complex scalar models, which are dictated by natural
actions (all couplings are of order one), at fixed and large global
charge in an arbitrary number of dimensions. The ground state is coherently constructed by the zero modes and the appearance
of a centrifugal potential is quantum mechanically verified. Using the path
integral formulation we systematically analyze the quantum fluctuations around
in order to derive an effective action for the Goldstone
mode, which becomes perturbatively meaningful when the charge is large. In this
regime we explicitly show that the whole construction is stable against quantum
corrections, in the sense that any higher derivative couplings to Goldstone's
tree-level action are suppressed by appropriate powers of the large charge.Comment: 24+1 pages, 2 figure
Relation between the psychological and thermodynamic arrows of time
In this paper we lay out an argument that generically the psychological arrow of time should align with the thermodynamic arrow of time where that arrow is well defined. This argument applies to any physical system that can act as a memory, in the sense of preserving a record of the state of some other system. This result follows from two principles: the robustness of the thermodynamic arrow of time to small perturbations in the state, and the principle that a memory should not have to be fine-tuned to match the state of the system being recorded. This argument applies even if the memory system itself is completely reversible and nondissipative. We make the argument with a paradigmatic system, and then formulate it more broadly for any system that can be considered a memory. We illustrate these principles for a few other example systems and compare our criteria to earlier treatments of this problem
Quantum interference with molecules: The role of internal states
Recent experiments have shown that fullerene and fluorofullerene molecules
can produce interference patterns. These molecules have both rotational and
vibrational degrees of freedom. This leads one to ask whether these internal
motions can play a role in degrading the interference pattern. We study this by
means of a simple model. Our molecule consists of two masses a fixed distance
apart. It scatters from a potential with two or several peaks, thereby
mimicking two or several slit interference. We find that in some parameter
regimes the entanglement between the internal states and the translational
degrees of freedom produced by the potential can decrease the visibility of the
interference pattern. In particular, different internal states correspond to
different outgoing wave vectors, so that if several internal states are
excited, the total interference pattern will be the sum of a number of
patterns, each with a different periodicity. The overall pattern is
consequently smeared out. In the case of two different peaks, the scattering
from the different peaks will excite different internal states so that the path
the molecule takes become entangled with its internal state. This will also
lead to degradation of the interference pattern. How these mechanisms might
lead to the emergence of classical behavior is discussed.Comment: 12 pages, 4 eps figures, quality of figures reduced because of size
restriction
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