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vincent

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Everything posted by vincent

  1. Right. It is a direct result of the basic principles of quantum mechanics that the narrower the probability distribution of one obervable is, the broader that of it’s conjugate will be. However the time-energy inequality is not on the same footing as the position-momentum uncertainty principle since there is no Hermitian operator corresponding to time. Yes, time is a dynamical quantity in that it varies with time, but in a trivial self-referential way and is really just a parameter on which other quantities depend. The actual meaning of ΔE and Δt in the time-energy inequality are respectively the spread in the energy distribution and the amount of time it takes for the wavefunction to changed appreciably. …therefore contradicting the tenets of quantum mechanics. Fine. But I would apply the term “on a much deeper level” instead to the relation between the uncertainty principle and the principle of complementarity. When due to the basic principles of quantum mechanics the use of one classical concept excludes the use of another, they are said to be complementary. The principle of complementarity says that the experimental arrangements that measure complementary properties are mutually exclusive and are both needed to demonstrate all of the physics of quantum mechanical systems. For example, consider wave-particle duality as applied to an electron which is the first form in which one usually encounters the concept of complementarity. Wave-particle duality is often erroneously described as meaning that the electron is simultaneously wave and particle. But this is impossible since particle and wavelike characteristics are strictly incompatible. What saves us is the uncertainty principle which says that there are no experiments one can perform in which the position of the electron, this being the particle aspect, and the momentum of the electron, this being the wave aspect, can be simultaneously measured to arbitrarly high precision. Thus the deeper meaning of the uncertainty principle is that it is the condition that ensures the logical consistency of quantum mechanics. A unitary quantum theory is one in which probability is conserved. Though they're pathological, one can imagine nonunitary theories in which the uncertainty principle formally still holds.
  2. Well thank you very much Martin!
  3. Yes, this is just as good as the way I put it.
  4. You'll be interested in knowing that in string theory the soft asymptotic behaviour means there are generically no singularities, including gravitational one's. However this does not mean we know what the true degrees of freedom of black holes actually are, which is true in all current approaches to black hole physics. So it shouldn’t be surprising that researchers tend to be quite circumspect in their attitudes towards this issue.
  5. Hi Wormwood, What’s required here is a fundamental shift in your understanding of how meaning is attributed to ideas in physics. In a nutshell, in physics you have to follow the math. The question we ask as physicists is not how we feel about the idea of a string, but whether such a theory can describe our universe. The consensus among researchers continues to be that it probably can and quite probably does, though it may take a while before we fully understand how this happens. As an example, string theory emerged from an attempt to describe the strong force using so-called dual resonance models. Gabrielle Veneziano discovered in a table of mathematical functions an expression which seemed to have the properties required for it to serve as the relevant scattering amplitudes. However nobody really understood what physical objects these amplitudes actually described. Eventually Leonard Susskind, by following the math, figured out that they describe objects having finite spatial extension in precisely one direction - i.e., they described strings. Leonard was very happy about this, and you can be too (unless you can find a better theory whose properties reflect your own personal world view).
  6. I believe! I believe! Okay, I think you’re referring to the way that one can obtain from string scattering amplitudes the low-energy effective field theory. In this case, since it is a graviton scattering amplitude, one would obtain the usual Hilbert action. But this is not what is usually meant by the remark that string theory implies General Relativity. As you know, different particles in string theory are represented by strings with different sets of internal modes of oscillations excited. Then assuming that strings represent a unified model of all interactions, every field with which strings can interact must be contained in the spectrum of states associated with the quantization of a string’s free oscillations. The point is that it’s the requirement that the dynamics of all background fields , even at the classical level, must be determind so as to be consistent with the results of string quantization that requires all background fields satisfy the Einstein equations. The demonstration of how this works begins with so-called nonlinear sigma models which describe how the world-sheet theory is embedded in spacetime. It’s terms represent the interactions of strings with all of the background fields. General Relativity is a result of requiring the two-dimensional conformal invariance of the world-sheet theory present in all string models and which is crucial for obtaining the quantum spectrum in which the background fields themselves are included not be destroyed by any of these interactions. The condition that there be no conformal anomaly is just the condition that the beta functions vanish. What is suprising is that the expressions for the beta functions turn out to be nothing but the Einstein equations for the background fields.
  7. There are also the following four more recent texts: String Theory and M-Theory: A Modern Introduction String Theory in a Nutshell Supersymmetry and String Theory: Beyond the Standard Model D-branes
  8. Hi BenTheMan, Strings are really wrapped M2-branes. Also, what did you mean by GR pops out of an S-matrix calculation?
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