From Wikipedia: Casimir Effect

The typical example is of the two uncharged conductive plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force—either an attraction or a repulsion depending on the specific arrangement of the two plates.

This claim of force detection is confirmed on Matt Strassler's Blog so I guess it's generally accepted.

This is the point where I wander into the minefield of my ignorance of string theory and a reliance on popular science books on string theory, so my apologies for what follows.

As far as I remember, 1-D strings require vacuum fluctuations for their stabilisation. I tried to find a source to confirm this, but all I get are references to cosmic strings.

My questions are, if the Casimir force has been confirmed, does it conform to predictions based around 4-D spacetime? If so, then how does this fit with the need for 11 dimensions in string theory? In other words, should the energy related to vacuum fluctuations not be spread across 11 dimensions and therefore be weaker than predicted?

Or does string theory postulate another smaller scale class of vacuum fluctuations, as virtual photons, electrons etc, are the postulated vibration modes of fundamental, many order of magnitudes smaller, 1-D strings and currently we have no chance of detecting these fluctuations, if ever.

My apologies if this question is based on an incorrect understanding of a badly written book and I will withdraw it if that's the case.

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    $\begingroup$ There would be a thermal field even in the classical description. I can't see the connection to strings, though, unless you are squeezing them between branes? I also don't understand the point about vacuum fluctuations. Without boundary conditions those only exist in perturbation theory where they are really just a side effect of the approximation of the field by poorly chosen base functions. I don't see any reason why the non-perturbative theory should have them (which the string theorists don't seem to have...). Truthfully, I think the "wobbly" picture people have about the vacuum is false. $\endgroup$ – CuriousOne May 24 '16 at 9:28
  • $\begingroup$ @CuriousOne The best thing I can do is keep reading and ask a better version of this question, (in about oh, 10 years time). Thanks for the reply. $\endgroup$ – user108787 May 24 '16 at 13:06
  • $\begingroup$ One doesn't need string theory to understand the Casimir effect, but your next to last paragraph may nevertheless be correct. $\endgroup$ – Lewis Miller May 24 '16 at 15:03
  • $\begingroup$ Thanks @LewisMiller I saw a reference to this "smaller fluctuations for strings" on the web but then lost it. My Casimir effect paragraph does not hold up, (and thinking about it, it is stupidly wrong), as any of the proposed extra dimensions are far too small to detect in experiments involving the Casimir effect. $\endgroup$ – user108787 May 24 '16 at 17:30
  • $\begingroup$ Sounds like you are thinking of the quantum fluctuations of the string worldsheet, and how they determine the critical dimension. $\endgroup$ – Mitchell Porter Nov 30 '17 at 12:28

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