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We often say that QFT describes the nature on a fundamental level. However this is indeed a very complicated theory for which the calculations related to the interaction of just a few particles simply blow up.

So it is in principle an accurate and consistent theory but when applied in large scales e.g. large number of particles it will not be useful in practice to give us values about the variables such as energy.

Suppose we use the standard model of elementary particles to write the Hamiltonian or the Lagrangian density of the universe, then find the equation of motion, and compare the result of operating on the vacuum state with the standard model of cosmology.

In principle we write the Lagrangian involving strong and electroweak sections and the scalar section describing the curvature of spacetime. Now if we operate the Hamiltonian on the vacuum state of the universe we have the energy.

And then we can compare the result with the energy density of the universe obtained from the classical GR theory.

But given the huge number of the particles we can never compute the energy density of the whole universe in practice using QFT of all interacting fileds including gravity, strong, and electroweak and test the final value against the observation or the result from GR in cosmology.

So the questions are:

  1. Am I correct in the above summary? If not which part is wrong?

  2. If computations based on QFT are only possible for just a few number of particles then in what sense we say that the quantum theory is useful to describe the whole cosmos? It only describes the universe in principle but not in a practical useful and "falsifiable" sense.

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  • $\begingroup$ -1 Not useful. Who is claiming that QFT is useful to describe the whole cosmos? You are either asking for a discussion of an idea which you are proposing, or setting up a Straw Man argument to knock down. $\endgroup$ – sammy gerbil Nov 23 '17 at 10:44
  • $\begingroup$ Useful in the sense that can we calculate based on QFT and compare with the classical result. $\endgroup$ – user56963 Nov 23 '17 at 10:49
  • $\begingroup$ Sorry for being ambiguous. I am saying that I think your question is "not useful" for this site. $\endgroup$ – sammy gerbil Nov 23 '17 at 10:54
  • $\begingroup$ In the light of answer below it will be useful to know what are the emergent properties from QFT. $\endgroup$ – user56963 Nov 23 '17 at 11:03
  • $\begingroup$ Related: physics.stackexchange.com/q/203654/50583 $\endgroup$ – ACuriousMind Nov 23 '17 at 16:44
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In our everyday life we are affected by temperature and pressure and a number of other thermodynamic quantities which very successfuly model observations mathematically.

Thermodynamics though can be derived as an emergent theory, from the classical and quantum statistical mechanics of atoms and molecules. One does not have to describe the thermodynamic behavior mathematically using statistical mechanics. Engineers build machines and cities based on thermodynamic calculations.

In an analogous manner it is not useful to use quantum field theory to describe the electricity web that feeds our cities. It can be shown that the classical electromagnetic fields emerge from the quantum mechanical, and this is enough for the continuity of the calculational systems.

Now special relativity and general relativity are a parallel development which redefines the coordinate systems of classical physics, the coordinates which describe obsrvations. Quantum field theory incorporates special relativity in its mathematical description. General Relativity has not been definitively quantized and the continuity between a quantum field theory and GR depends on effective theories used in the cosmological models , as the big bang mode.

Thus physics models are hierarchical, it makes no sense to use the quantum field theoretical model of the density matrix formalism for many particles when discussing macroscopic, human range observations, more so cosmological ones. It is enough to prove that at each dimensional range from the microscopic to the macroscopic to the cosmological there is mathematical continuity in the overlap regions of the theoretical models.

Appropriate mathematical tools have been developed. One does not use a needle to dig a ditch.

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  • $\begingroup$ Could you mention and share a few of "emergent properties" from QFT? $\endgroup$ – user56963 Nov 23 '17 at 10:43
  • $\begingroup$ motl's article ( first link) shows how the classical electric field emerges from the QFT one. Have a look here for the density matrix formulations physics.stackexchange.com/questions/98703/… . this if you have access is an example . generally taking h-->0 will give the classical limit. $\endgroup$ – anna v Nov 23 '17 at 11:36
  • $\begingroup$ Very helpful feedback. Really appreciate it! $\endgroup$ – user56963 Nov 23 '17 at 14:01
  • $\begingroup$ Victor, one area of interest among some cosmologists is how to write down the wavefunction for the entire universe (at some early time in its evolution, when such things might be possible). In one sense this means trying to derive a quantum mechanical description of the whole universe. You might try searching on "wave function of universe" and seeing if anything useful to you comes up. $\endgroup$ – niels nielsen Nov 24 '17 at 5:17