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I read this sometime in the last 3 years or so, but I believe it was older than that, and was included in a collection of time travel stories.
The main thing that I remember from the story is that there is a guy inside of some kind of box or chamber. It is either transparent, or has a window. There are some scientists gathered around who observe him and try to figure out why he is there. He writes messages for them to read, I think, and when viewed from the outside, he appears to be travelling backward in time.
I don't clearly remember how it ends, but I have this vague recollection that one of the scientists eventually enters the box and becomes the backward time travelling passenger. I could be wrong about that part. There was something about reaching a point at which the backward flow of time inside the box and the forward flow of time outside the box would meet up at a point and nobody knew what would happen then.
This story might also be a subplot of a larger novel, but I seem to remember it being a short story.