polarization of a photon

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Polarization can be defined for each photon, right? And the energy of a single photon is dependent on the wavelength. Now let's take a polarizer filter with the polarization in the X axis (i.e. X polarized light is transmitted, Y polarization is absorbed). Now take a single photon polarized 45 degrees from the X axis. Shoot this photon at the polarizer. What happens? Normally, one would say that the Y component of the electrical field is absorbed, and what passes through is X-polarized light with half the original intensity. However, if a single photon lost half its energy, its wavelength would change, which contradicts observations. So where am I making an invalid assumption?