LOG#207. Beck, Zeldovich and maximal acceleration: the vacuum.

Some time ago, Zeldovich derived the following expression for the vacuum energy density:

(1)   \begin{equation*} \rho_{V}=\dfrac{Gm^6c^2}{\hbar^4} \end{equation*}

or equivalently, with a link to Caianiello’s maximal acceleration formula,

(2)   \begin{equation*} \rho_V=G_N\left(\dfrac{mc^3}{\hbar}\right)^6\left(\dfrac{\hbar}{c^8}\right)^2 \end{equation*}

Remark: the above vacuum energy density is related to the cosmological constant via the mathematical formula

(3)   \begin{equation*} \rho_V=\dfrac{\Lambda c^4}{8\pi G}=\rho_{CC} \end{equation*}

Now to far away, Christian Beck also proposed a formula for the measured cosmological constant and he derived it from pure informational axioms. It reads:

(4)   \begin{equation*} \rho_{CC}^{Beck}=\left(\dfrac{c}{\hbar}\right)^4\left(\dfrac{G_N}{8\pi}\right)\left(\dfrac{m_e}{\alpha_{em}}\right)^6 \end{equation*}

and where \alpha_{em}=K_Ce^2/\hbar c is the known fine structure constant. Why the cosmological constant is so small when our current theories based on standard Quantum Field Theories predice it should be HUGE is a mystery. We have some ideas based on supersymmetry and non-perturbative damping due to Schwinger effects that could work, but no one has managed a clear explanation. Some people believe we need a better theory. I agree partly, we need also experiments. Are the Beck formula or Zeldovich proposal right? Can we test them somehow? It is the work of future physicists to enlighten the dark issue of the vacuum energy and its radical mismatch between microscales and macroscales. What is vacuum or vacuum energy after all?


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