Why I Cannot Accept Time Travel

Does time flow like a river or expand like a growing sphere? In either case there is mass moving down the river, or expanding infinitely.

Is there differentiation between layers of mass? Each layer following the one before, going in the same direction? Are there other directions?

Conservation of mass and energy would indicate each mass is finite as it moves through time. Why would there be copies of each layer of mass moving down the river? Are they possibly alternates following one another, each progressing down the river?

Even if you do go back in time you would end up in another mass. Not only has earth moved on in space but in time as well. What if the segment following is empty? Would you end up no where? What could be the measurement between each segment? Millisecond or smaller?

It is said they proved that time travel is possible. They have not proven that it is bidirectional. My mental processes are unable to process this data.