Being full of doubts I have some questions of the equivalence principle. 1. In the presence of gravitational fields the Einstein Equivalence Principle (EEP) is a necessary and sufficient condition for the Principle of Relativity, (PR). Here I summarise PR as the doctrine of no preferred frames of reference. In the absence of such fields the EEP becomes meaningless, although then the PR does come into its own and is appropriate in Special Relativity (SR), which was formulated for such an idealised case. However, if we now re- introduce gravitational fields, i.e. gravitating masses, do we not then find that the PR collapses? For in that case is it not possible to identify preferred frames of reference? Such frames being those of the Centre of Mass (CoM) of the system in question and the universe as a whole, (that in which the Cosmic Microwave Background is globally isotropic.) The CoM is preferred in the sense that only in that frame of reference, that is the centroid measured in the frame co-moving with the massive system, is energy conserved as well as energy-momentum. But if the PR is not valid in the presence of gravitational masses then surely the EEP cannot be either? 2. Should not gravitational time dilation apply equally both to photons and the atoms they interact with? If so whence gravitational red shift? 3. Should not the total relativistic energy, measured in the system's CoM, of a freely falling body, be conserved as no work is being done on or by it? 4. In order for a gravitational theory to be consistent with SR should not the rest mass of a body include its gravitational potential energy? In which case questions 2 & 3 are resolved; gravitational red shift is not caused by the photon losing energy but by the measuring apparatus gaining it. Yet the EEP forbids it to do so, for according to the EEP rest mass is invariant. 5. According to the EEP a stationary electron on a laboratory bench is accelerating w.r.t. the local Lorentzian freely falling inertial frame of reference. According to Maxwell's theory of electromagnetism an accelerating electric charge, such as an electron, radiates. So why doesn't it? Or, if it is thought that such an electron actually does radiate, what is the source of such radiated energy? However, note that in the preferred CoM frame of reference the electron is not accelerating. 6. In the normal expanding cosmological solution of General Relativity (GR) what exactly is expanding? If it is space-time itself, as demanded by the theory, then what expands with it? As the Schwarzschild solution for gravitational orbits is embedded in that space-time should not its solutions co-expand? Also as the Bohr/Schrödinger/Dirac equations of atomic physics are also so embedded then should not their solutions expand? If, as a consequence, gravitational orbits and atoms together with the physical rulers constructed of those atoms so co-expand with the universe, then surely there would be no detectable expansion? Therefore cosmological red shift cannot be caused by recession, but, in a similar way to the case of gravitational red shift, it must be caused by the measuring apparatus, that is all fundamental particles, secularly gaining inertial mass.