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Nature of Microscopic space-time

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I am going through the introductory chapter's of Schwinger's Source theory. He writes,

It [Source Theory] is a phenomenological theory, designed to describe the observed particles. No speculations about the inner structure of the particles are introduced. No abstract definition of particle is devised. The theory is thereby firmly grounded in space-time, where the experimenter manipulates his tools, but the question of ultimate limitation to microscopic space-time description is left open, with the decision reserved to experiments. Correspondingly, no Operator-fields are used.

Now in this regard, I would want to know how operator fields answer the question of ultimate limitations to microscopic space-time (If they are related to each other)?

EDIT 1 : It just struck me that the limitation could be due to canonical commutation between field operators and their conjugates. However, I don't see how to formalize a restriction using this commutation.

This post imported from StackExchange Physics at 2014-04-13 14:38 (UCT), posted by SE-user user35952
asked Apr 8, 2014 in Theoretical Physics by user35952 (155 points) [ no revision ]

1 Answer

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The question of ultimate limitation to microscopic space-time description is the question about the inner structure of the particles, mentioned in the above quote.

As long as the inner structure is ignored, a particle can be treated as ''pointlike''. This is appropriate at a resolution larger than a few diameters of the particle (where the approximate diameter is determined by its scattering cross sections). But at a more microscopic resolution, the nner structure cannot be ignored without distorting the behavior of the particle, and a more precise description is needed.

Thus if the particle is an atom, the limitation of the pointlike description is due to the existence of electrons and nuclei. If the particle is a nucleus, the limitation is due to the existence of protons and neutrons; and If the particle is a proton or neutron, the limitation is due to the existence of quarks, etc..

answered Apr 13, 2014 by Arnold Neumaier (12,425 points) [ no revision ]

+1 Thanks !! So how do operator fields come into this whole discussion ? Do the somehow restrict or describe the inner structure of the particles ? If yes, typically what are the scales involved ?

This has not really anything to do with operator fields. The latter are constructed from the creation and annihilation operators of whatever happen to be the elementary (i.e., pointlike) particles of the theory. A more microscopic point of view simply means that what is considered to be elementary changes, and with it the interactions responsible for forming the composite particles that look elementary on a less detailed level.

@Arnold : Thanks for the answer, It would be better if you could post the same answer here, so that the bounty can be offered. The bounty is ending in a short while !! Thank you.

@user35952: I don't care much about my account on SE. Most of my reputation there is from before December 2012, when I announced to leave the site: http://meta.physics.stackexchange.com/q/2746

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