island said:e−iHT=1→H=2πn/T=ωn ; n=0, ±1, ±2, . . . .
I'd like to set the vacuum energy at 1/2ω, while requiring e-iHT=−1, and that the negative energy states be filled, as well, although, this may require further explanation.
Can somebody please help me?
island said:This is the spectrum of a quantum harmonic oscillator, except for the emergence of negative energy states, with n<0. A "Vacuum energy" of 1/2ω arises if we require that e-iHT=−1 and just realized that I've answered my own question, thanks!
island said:Okay, my knowledge of this is too specific if not limited, but...
The "extra" 1/2 in the eigenvalues of the harmonic oscillator Hamiltonian can be thought of as having a phase factor of -1, which *can* represent vacuum energy as rarefied mass-energy that has a negative pressure, (-0.5*rho(matter)*c^2), in the cosmological model that I am thinking about.
The vacuum energy problem is the discrepancy between the theoretically predicted value of the vacuum energy density and the observed value, which is essentially zero. This discrepancy arises in quantum field theory, where the vacuum is considered to be a state of lowest energy.
This equation, known as the Euclidean path integral, is used to calculate the vacuum energy density. It is a mathematical tool used in quantum field theory to account for all possible paths of a particle in space and time.
The equation helps to solve the vacuum energy problem by accounting for the contribution of all possible particle paths, including negative energy states, in the calculation of the vacuum energy density. This allows for a more accurate prediction of the vacuum energy.
The value of -1, 1/2ω represents the contribution of the negative energy states to the vacuum energy density. This term is crucial in solving the vacuum energy problem as it accounts for the negative energy states that are typically ignored in calculations.
Yes, there are several challenges associated with using this equation. One major challenge is the difficulty in accurately calculating the negative energy contributions, which requires advanced mathematical techniques. Additionally, there is ongoing debate and research on the validity and applicability of this equation in different theoretical frameworks.