Don't believe me, huh?
No one believed or believes me about the non existence of event horizons.
No one believed me long ago that GR is incomplete.
No one believes me that gravity is repulsive, as well as attractive.
No one believes me that gravity can operate on gravity to translate a distortion that travels at v > c.
No one believes me about the non existence of the Higgs field.
No one believes me about a hundred other concepts in physics.
But they will.
By the way, that guy Incandela is a slug.
What you should understand is this. A physical paradigm lasts only so long. Then it's replaced by something else. Usually, something else builds on what went before, but sometimes the change is radical. As far as I can tell from my sources which are exotic sine qua non, there is no end to this process.
Applying this philosophy of science to our current situation we come to a severe conclusion. QFT has no completely sound theory under it. In Peskin's book, "Intro to QFT", Peskin & Schroeder, which is a standard and good, if old, graduate text, he gets to a point in the development where he runs into Feynman's "rest of the universe" problem:
Picking up the discussion (I have used # to represent "transpose" so that e.g., a# is left moving modes of a)
The simple harmonic oscillator is a system whose spectrum we already know how to find.We write the Hamiltonian as
H = (p^2 + omega^2*phi^2)/2 ....................... 2.22
To find the eigenvalues of H we write phi and p in terms of ladders operators,
phi = (a + a#)/sqrt(2*omega) p = i*sqrt(omega/2)*(a - a*) ..................... 2.23
The canonical commutation relation [p,phi] = i is equivalent to
[a, a#] = 1
The Hamiltonian can now be rewritten,
H = omega*( a# * a + 1/2)
The state |0> such that a |0> = 0 is an eigenstate of H with an eigenvalue omega/2, the zero point energy.
Furthermore, the commutators
[H, a#] = omega*a# [H, a] = -omega*a
make it easy to verify that states
|n> = a#^n |0>
are eigenstates of H with eigenvalues, (n + 1/2)*omega. These states exhaust the spectrum.
Skipping some equations I'll go to his conclusion,
H = integral( d^3p/(2*pi)^3 * omega * ((a# * a) - [a, a#]/2) ) ......................... 2.31
The second term is proportional to deltafunction(0), an infinite c-number. It is simply the sum over all modes of the zero point energies, omega/2, so its presence is completely expected, if somewhat disturbing. Fortunately, this infinite energy shift cannot be detected experimentally. since experiments only measure energy differences from the ground state of H. We will therefore ignore this infinite term in all our calculations. It is possible that this energy shift of the ground state.could create a problem at a deeper level.in the theory; we will discuss this matter in the epilogue.
In the epilogue he says "we ignore the anomalies because the theory works by giving us accurate calculations".
QFT has a lot of critics, but aside from explicit holes in the theory, it does have its charm. The above is a core point. All formulations of QFT flounder there. The problem goes back to Dirac's sea and the notions of "unbounded below" "unbounded above", and their complements. We can't tolerate a theory that's unbounded below. |
