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A quantum correction to the Brans-Dicke theory due to interactions among matter fields is calculated, resulting in violation of WEP, hence giving a constraint on the parameter ω far more stringent than accepted so far. The tentative estimate gives the lower bounds ≳106 and ≳108 for the assumed force-range ≳1 m and ≳1 AU , respectively.
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Yasunori Fujii (1994) studied this question.
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