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Dear Questioner,

that's a very good question. The spin of a particle is related to the
equation that "defines" the particle. In case of the photon, it is
described by the Maxwell equations. These equations are for a spin 1
particle, i.e. a vector particle.

If the spin of the photon was different, physics and the behaviour of
the particle would really change a lot, since the equations would
change. The spin is an essential property of a particle. Let me try to
explain in a few words why this is so.

In more mathematical terms (see e.g. the following wikipedia article
(and try to find some other useful links starting from there):
representation theory of the lorentz group,relativistic wave equations, particle physics and representation theory):

Symmetries are basic ingredients in physics. Symmetry means that an
object looks the same when you act on it with the corresponding
symmetry transformation, e.g. if you rotate the object by a certain
angle. Particles obey some symmetries. The probably most fundamental is
the so-called Lorentz symmetry. It's the symmetry of space-time
(vacuum). For the particle to satisfy or obey this symmetry, means in
mathematical terms that the particle needs to be in a certain
representation of the symmetry. The symmetry imposes mathematical
restrictions for the particles. The number of representations is also
restricted. Each representation corresponds to certain kind of
particles and to certain equations which the corresponding particles
has to satisfy. The parameter, which characterizes the different
representations, is the spin. Now, which particle observed in nature
belongs to which representation has to be determined by experiments.

I hope this helps.

Best regards, Michael

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