Two entangled particles. Particle A is in the pocket of a man who is 10 billion light years away from Earth, and he walking away from Earth (so according to Lorentz transformation in his time it is 150 years into the past on earth). He measures the particle spin. Would we have seen the entangled particle on earth with the same spin 150 years ago? Is it that simple? And if we had seen that particle 150 years ago, we could predict the spin of the far away particle.
Based on the discussions and chats, my original supposition was incorrect. The correct interpretation is that in the Earth time frame for me, it is January 6, 2020. In the spaceman's time frame on the far away planet, for him, it is January 6, 2020. But in the spaceman's time frame, once he starts walking he would consider that, on Earth, it is 150 years ago in 1870. Regardless of this, when we both open our box on January 6, 2020 in our own time frames, the particles would be in sync.