First, a simple scenario to set our expectations: Consider a "stationary" massless non-relativistic test particle in empty space. We'll call the particle "P". At a very large proper distance to the cosmological "west" of P there is a neutron star, at proper rest relative to P. Let's call it Star West. At the same proper distance to the "east" of P there is another identical neutron star, also at proper rest. We'll call it Star East. Now we give a shove to both stars, radially inward toward P. Eventually their gravitational acceleration toward each other will become significant, and they will continue gaining velocity until they smash into each other and crush poor P between them. An observer on Star West considers Star West to be stationary, P to be accelerating toward Star West, and Star East to be accelerating at an even higher rate toward Star West. (An observer on Star East sees the reverse occurring). From the Star West observer's local perspective, P is gaining kinetic energy as it freefalls toward Star West, and Star East is gaining twice as much kinetic energy. The Star West observer concludes that the presence of Star East has no effect on how much local kinetic energy P gains. In other words, P's kinetic energy relative to Star West is not reduced by the fact that P is also accelerating toward, and gaining kinetic energy locally relative to, Star East. This happens because the two stars are in freefall toward each other. . . . . . . . . . . Now let's consider what happens when P is replaced with a relativistic photon: Instead of having P start in the center, let's have Star East fire a single photon radially toward Star West at some point in time while the two stars are gravitationally accelerating toward each other. When the photon arrives at Star West (let's say it arrives long before the two Stars crash together), the observer there will measure the photon to be gravitationally blueshifted. (For this discussion, we will divide out the component of SR Doppler blueshift so as to ignore it, and focus only on the component of gravitational blueshift). The photon is gravitationally blueshifted because, as observed in Star West's local frame, the photon experienced gravitational acceleration toward Star West all along its worldline. It didn't gain proper velocity from the acceleration, instead it became gravitationally blueshifted. And based on the prior experience with the nonrelativistic particle P, we know that any gravitational acceleration the photon experiences in the direction of Star East will not reduce the kinetic energy the photon gains toward Star West. This is an interesting outcome. Normally, a photon that travels from the surface of one star and is observed on the surface of another identical star will not experience ANY net gravitational blueshift. It will become gravitationally redshifted as it climbs out of the gravitational well of the source star, and then will become gravitationally blueshifted by exactly the same amount as it falls into the gravitational well on the observer star. Yet the blueshift occurs in our scenario because the two stars are in freefall toward each other. At the same time, there can be no gravitational time dilation as between Star East and Star West, because their masses are identical. So we have gravitational blueshift without any accompanying gravitational time dilation. Yes?