Symmetry, Empirical Equivalence, and Identity

Abstract

Abstract:The paper proposes a novel approach to the much discussed question of which symmetries have direct empirical significance and which do not. The approach is based on a development of a recently proposed framework by Hilary Greaves and David Wallace, who claim that, contrary to the standard folklore among philosophers of physics, local symmetries may have direct empirical significance no less than global ones. Partly vindicating the standard folklore, a result is derived here from a number of quite plausible assumptions, which states that local symmetries can indeed have no direct empirical significance. Ways to interpret the result are considered and possible morals are outlined.

Symmetries and the Identity of Physical States

“…Namely, as I will show, one obtains a result according to which all (subsystem-restricted) gauge transformations in local gauge theories are without any direct empirical significance, whether or not they reduce to the identity transformation on the subsystem boundary and whether or not they connect topologically inequivalent configurations. Essentially the same result was already obtained in an earlier article (Friederich 2015), but the present article adds to the earlier considerations by showing that one of the assumptions used there-the assumption "Ext"-is not needed for the derivation of the result and by further motivating the other assumptions used there and here.…”

“…(See the appendix for a brief review.) Without appealing to the additional assumption "Ext" used in (Friederich 2015) I show that, by DES, SUL, and MAH, the local gauge symmetries in these theories do not have any direct empirical significance. The decisive feature of local gauge symmetries that is needed to derive the result is that, when restricted to operating on a proper subgregion of the universe, they can always be extended to a symmetry operating on a more encompassing ("embracing") proper subregion in such a way that this extension reduces to the identity transformation on the boundary of the embracing region.…”

“…In other words, s and s designate the same physical state if they are empirically equivalent both from within the subsystem and from the perspectives of arbitrary external observers. In (Friederich 2015), I used this idea to spell out what it means for a subsystem symmetry to have direct empirical significance in terms of physical identity for subsystem states. Using the symbol "∼" to denote the relation of designating the same physical state between subsystem ontic variables, the criterion in question "DES" (which stands for "direct empirical significance") reads:…”

“…In (Friederich 2015), where this assumption was first introduced, it was characterized as a "modest anti-holism"-hence "MAH"-since it rejects the apparently holistic idea that one and the same physical state of affairs of a subsystem S = S 1 ∪ S 2 (where "∪" should be thought of as the mereological sum) can be "reduced" in various different ways, i.e. MAH rejects the "holistic" idea that the state of the whole can be decomposed in more than one way into physically distinct states of the parts.…”

“…In this section, I will re-derive a result concerning the direct empirical significance of so-called local gauge symmetries in gauge theories (Friederich 2015). Among these theories are the important Yang-Mills gauge theories, which are the backbone of contemporary elementary particle physics.…”