But this is loose, formal but physically meaningless talk, since it is a gauge dependent quantity and gauge fixing is an arbitrary, unphysical procedure. Only gauge invariant quantities have a physical meaning.Demystifier said:Maybe in classical electrodynamics. But in QED it is certainly common to say that ##A^{\mu}## is a vector field with spin-1.
A. Neumaier said:the borderline where one switsches from one language to the other is fluent.
It is very important to say that it is a massless vector field, which together with locality implies that it must be a U(1) gauge field. See, e.g., Weinberg, Quantum Theory of Fields, vol. 1.Demystifier said:Maybe in classical electrodynamics. But in QED it is certainly common to say that ##A^{\mu}## is a vector field with spin-1.
True, but these quantities are measurable in principle. It's only not within our technical possibilities to do so.A. Neumaier said:I just asserted that this is the meaning with which the term is used by those who use it, by extrapolation form the interpretation that is valid for larger objects.
In the macroscopic and nonrelativistic limit it becomes the mass density which defines very obviously the shape, and since it can be defined for all objects no matter how large it is a meaningful physical concent, even though one can measure it only for sufficently robust objects such as single atoms on a surface or in a cavity, or mesoscopic or even macroscopic objects. (There is lots of nonmeasurable stuff that has a clear physical meaning, for example the detailed mass distribution in the interior of the sun or in the Andromeda galaxy.)
This is a misconception you find astonishingly often. Of course, for a system with non-zero mass there's a preferred frame of reference, the center-momentum frame, and this frame is used to define intrinsic quantities of this system. If you want you can call the energy-density distribution in this frame the "shape" of the object, although I've never seen this anywhere in the literature. You can define this quantity in a frame-independent way as a scalar density. For a fluid it's given by $$\epsilon=u_{\mu} u_{\nu} \Theta^{\mu \nu},$$ where ##u^{\mu}## is the four-velocity field of the fluid (normalized such that ##u_{\mu} u^{\mu}=1##) and ##\Theta^{\mu \nu}## is the energy-momentum tensor of the fluid.That shape is frame-dependent is already well-known form classical relativity (length contraction). It has to be so.
This doesn't work for a photon, whereas the energy-density distribution in the lab frame always exists. This is the one of interest to the experimenter. http://arxiv.org/abs/1605.00023, http://arxiv.org/abs/1601.07142, http://arxiv.org/abs/1512.08213, http://link.aps.org/abs/10.1103/PhysRevAccelBeams.19.021304 are some recent references to photon shape.vanhees71 said:If you want you can call the energy-density distribution in this frame the "shape" of the object,