How do we know quantum fields exist?

Excellent explanation by Barak Shoshany, Graduate Student at Perimeter Institute for Theoretical Physics

Fields are a central component in the mathematical formulation of the most successful theories in physics, from electromagnetism to general relativity and quantum field theory. However, scientists have not proven and will never be able to prove that fields, or any other components of our mathematical model, actually "exist" in the same way that tables and chairs "exist".

Quantum field theory is a mathematical framework based on the mathematical concept of a field (a function that has some value at each point in spacetime), together with the mathematical tools of quantum mechanics.

Using this framework we may construct a model of Nature by choosing the types of fields we would like to have and their various properties and interactions. Then we use this model to derive predictions for experimental results.

When we perform these experiments in order to test out theory, we find that the results agree with our predictions to a very high accuracy. Therefore, one can say that scientists have shown that quantum field theory provides a very accurate description of Nature.

In fact, quantum field theory is regarded as one of the most accurate theories of Nature we currently have. So, is it "true"? Do quantum fields actually "exist"? No one knows. Some will tell you that the question itself is meaningless.

Why is that? Well, we wrote some equations and did some calculations, and they turned out to be correct to a certain degree of accuracy. We based our equations and calculations on the premise that fields "exist". However, tomorrow someone else might invent a totally different model, with no fields at all, whose predictions agree with experiment to an even higher accuracy. If we believe that fields exist now, will they suddenly stop existing after that more successful theory is published?

Indeed, many physicists believe that quantum field theory is merely a special case of another, more fundamental theory, that should presumably also include gravity. That theory, which is currently unknown, might or might not include fields as fundamental entities; however, it would have to reduce to quantum field theory at low energies.