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Suppose there’s a scalar field that permeates the universe.

Do quantum fluctuations really cause the field value ϕ to fluctuate, making the field value higher at some points in space and lower at some other points in space?

Some scientists argued that the quantum field is not fluctuating. The value of a field at a point is not precisely determined but it has nothing to do with fluctuations. $~$While some states that the value of a field at a point in space is constantly fluctuating.

Forge
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  • Can you provide reference for the first statement - "Some scientists argued ... with fluctuations."? – Avantgarde Oct 16 '18 at 07:13
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    Fluctuating Here $~$;$~$ Not Fluctuating Here – Forge Oct 16 '18 at 07:55
  • Hi Forge. The question I've linked references vacuum fluctuations, but the same principle applies. The fluctuation is in the measurement of the field not in the field itself. – John Rennie Oct 16 '18 at 07:57
  • @JohnRennie “Do quantum fluctuations cause the field value to fluctuate at each point in space?” So from your comment, the answer to this question is No? – Forge Oct 16 '18 at 08:08
  • @Forge Correct. Quantum fields do not fluctuate. – John Rennie Oct 16 '18 at 08:46
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    @Forge you need to read my answer to the linked question. If you make repeated measurements of some property of the field, energy or whatever, then you will in general measure a fluctuating value. But this fluctuation arises from the measurement process not from the field. The quantum field does not fluctuate. – John Rennie Oct 16 '18 at 14:01
  • @JohnRennie. A field in QFT is described by an operator with some similarities to the quantum harmonic oscillator. The lowest energy state (vacuum) should then have an uncertainty of field value, just like the lowest state of the quantum harmonic oscillator is not described by a Dirac function but a spread out function (a Gaussian). Correct? Isn't this what is referred to as "fluctuations" of the field? – md2perpe Oct 16 '18 at 14:10
  • @JohnRennie It’s been years and I’m still very confused. You explained that quantum fields do not fluctuate. Does that mean eternal inflation is not valid because it relies on quantum fluctuations making the field’s value fluctuates? – Forge Jun 22 '21 at 06:58
  • @Forge this would be best discussed in the physics chat room – John Rennie Jun 22 '21 at 07:09

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