Fwd: Negative Energy Problem in the Klein Gordon Equation

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Subject: Fwd: Negative Energy Problem in the Klein Gordon Equation
Date: Mon, 6 Apr 2009 10:52:49 EDT

Many thanks, as an undergraduate I was confused three years before you were confused! MAnsel told me he never understood it.

This is a very important and key piece of work in my view Myron. Hopefully it will clear up a lot of the uncertainty and confusion that has existed.

Best, Gareth

Date: Sun, 5 Apr 2009 05:10:39 -0400
Subject: Negative Energy Problem in the Klein Gordon Equation

This is discussed by L. H. Ryder, “Quantum Field Theory” (Cambridge, 1996, 2nd ed,.), on page 29. In his eqn. (22.4) he writes E as being plus or minus, so the negative energy problem is introduced by accepting that E, the total energy from the Einstein energy equation, can be negative on the classical level, before quantization even begins. So no wonder that there is a negative energy problem, it is inputted from the classical level and is not a problem introduced by quantization. I do not think that Einstein himself ever considered a negative E as being part of physics, and I think now that it is much better to adapt this eminently sensible point of view, based on the experimental fact that negative energy has never been observed. The negative energy problem disappears form both the Klein Gordon and Dirac equations, and there is no need for the tremendous obscurity of the Dirac sea and Feynman’s virtual particles that can by definition never be observed. This was compounded in the now obsolete QED by acausality and tremendous complexity. The problem with negative probability, however, remains in the Klein Gordon equation, and I will deal with these matters in the next note for paper 129. The standard claim is that negative probability is cleared up by the Dirac equation, and I will check this claim in full detail. Probability is at the very root of quantum mechanics, and its expectation values.

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