Summary
Gell-Mann and Low have emphasized that, as first pointed out by Uehling and Serber, vacuum polarization effects produce a logarithmic modification to the Coulomb potential at small distances. I point out here that, if these same considerations are applied to gravitation, the logarithmic term will have a sign opposite to that in the Coulomb case and in agreement with recent laboratory results on the gravitational «constant». Of considerable importance is the fact that such vacuum polarization effects cannot be observed in null experiments to test the gravitational inverse square law because the polarizing field is absent. It is a striking circumstance that the coefficient of the logarithm in QED is nearly the same as that found in gravitational experiments.
Riassunto
Gell-Mann e Low hanno messo in evidenza che, come predecentemente indicato da Uehling e Serber, effetti di polarizzazione nel vuoto producono una modificazione logaritmica al potenziale di Coulomb a piccole distanze. Si mette qui in evidenza che, se queste stesse considerazioni sono applicate alla gravitazione, il termine logaritmico avrà un segno opposto rispetto al caso di Coulomb e in accordo con recenti risultati di laboratorio sulla «costante» gravitazionale. Di considerevole importanza è il fatto che tali effetti di polarizzazione nel vuoto non possono essere osservati in esperimenti nulli per controllare la legge gravitazionale quadratica inversa perchè il campo polarizzante è assente. È una circostanza interessante che il coefficiente del logaritmo in QED sia quasi lo stesso che quello trovato negli esperimenti gravitazionali.
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References
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Long, D.R. Vacuum polarization and non-Newtonian gravitation. Nuov Cim B 55, 252–256 (1980). https://doi.org/10.1007/BF02739157
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DOI: https://doi.org/10.1007/BF02739157