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As I understand it, the famous 120 orders of magnitude discrepancy between the observed cosmological constant and the calculated QFT vacuum energy density relies on the vacuum Einstein field equations

$$G_{\mu\nu} + \Lambda g_{\mu\nu} = \left< 0 |T_{\mu\nu}| 0 \right>.$$

The QFT vacuum energy expectation value $\left<\rho_{vac}\right>$ is formally infinite, but some natural cutoff is taken.

The quantum expectation value is the average value over many measurements. So why can we say that the vacuum is being measured? And if we can't say that there is wavefunction collapse, why should GR, a classical theory, care?

Of course this brings up the measurement problem. It is true that virtual particles can be realized, like for example in Hawking radiation, but this relies on some sort of wavefunction collapse due to interaction with the black hole. Since most of the universe is nearly empty, can we really say that vacuum fluctuations have an effect away from regions of appreciable matter and gravity?

For reference, I am coming at this from a mathematics background and the physics level of, say, a first graduate course in GR and QFT.

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It is expected that a future theory of everything will solve this discrepancy which depends, as you observe , in mathematically comparing classical with quantum values .

At the moment the only theories that can quantize gravity and at the same time embed the standard model of particle physics, which is expressed in quantum field theory terms, are string theories.

The question Can/has string theory solved cosmological constant problem? addresses this. A good answer exist by dr Motl, a known string theorist.

The gist as far as your question goes is that, yes, to mix classical with quantum and to consider it a big problem when there are discrepancies is not correct. There are possible solutions once gravity is quantized.

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  • $\begingroup$ Has anyone calculated something like the distribution of gravitational strength in the universe based on the distribution of matter? Not saying this is correct, but if some minimum curvature is required for wavefunction collapse of the vacuum, it would be interesting to know what that theoretical gravitational strength is to match the cosmological constant (I suppose assuming relatively homogeneous/isotropic distribution of gravity). $\endgroup$
    – John K.
    Apr 22, 2020 at 0:58
  • $\begingroup$ Again you are mixing two mathematical frameworks. There is no "wavefunction collapse of vacuum due to curvature connection", unless one goes to see what string theories,which have both QFT vacua and GR quantized, and I do not research has reached that level of detail $\endgroup$
    – anna v
    Apr 22, 2020 at 4:01

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