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**Physics, Astronomy & Cosmology / Re: What breaks the symmetry in this thought time dilation experiment?**

« **on:**05/05/2018 03:24:42 »

The fact that both an Earth observer and the ship observer locally measure 1g is a red herring. Gravitational time dilation is due to potential difference. Think of potential difference as the energy per unit mass needed to lift something from a lower height to a higher height. For the Earth observer, the difference in gravitational potential and thus the time dilation between the ship and himself is due to a gravitational field that decreases with strength as you move away from the center of the Earth.

For the ship observer to claim that he is "at rest" he has to assume that the 1 g acceleration he feels is also due to a gravitational field, In his case, however it is a uniform field that does not diminish in magnitude with height ( if his ship was really long and he traveled from tail to nose, he would not measure and weakening in " gravity"). This means that "his" gravity field extends at a constant 1g all the way from him to the Earth. Now it would take an lot more energy to lift a mass that distance against 1g the whole way, than it does against a gravity field that weakens as you get higher. Thus for the ship observer there is a much greater potential difference and thus time dilation between the Earth and himself than the Earth observer would measure between the ship and himself. Therein is the break in symmetry between the two observers.

For the ship observer to claim that he is "at rest" he has to assume that the 1 g acceleration he feels is also due to a gravitational field, In his case, however it is a uniform field that does not diminish in magnitude with height ( if his ship was really long and he traveled from tail to nose, he would not measure and weakening in " gravity"). This means that "his" gravity field extends at a constant 1g all the way from him to the Earth. Now it would take an lot more energy to lift a mass that distance against 1g the whole way, than it does against a gravity field that weakens as you get higher. Thus for the ship observer there is a much greater potential difference and thus time dilation between the Earth and himself than the Earth observer would measure between the ship and himself. Therein is the break in symmetry between the two observers.