The disagreement between predicted and measured energy density of the vacuum is one of the great unsolved problems of science.

According to this book the predicted energy density was obtained as follows:

...we can adopt the Planck energy as a cutoff. This is the energy at which the gravitational force becomes as strong as the other three fundamental forces of nature (i.e. the scale at which we expect the current theory to break down). This energy is about $10^{19}GeV$.

My questions are:

  1. Why say that gravity becomes as strong as the other forces at the Planck scale? My understanding is that the Planck scale is characterised by our not being able to make meaningful statements about the laws of physics any more. Isn't this a bit like taking conditions at a singularity and applying them everywhere?

  2. Do the magnitudes of all forces approach equality as we approach $10^{19}GeV$? Electromagnetism and the weak force unify at $100GeV$, where does $10^{19}GeV$ come from?

  3. Come to think of it, what does $10^{19}GeV$ have to do with the Planck scale at all?

  4. Why use a cutoff? Shouldn't the theory apply at above-Planck scales?

I only have an armchair understanding of physics at this level, but the approach described above doesn't pass the smell test. I'd appreciate a better explanation.


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