Can Negative Mass at near Speed of Light go Back in Time?

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Call me James
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Sorry if the title was a little vague, character limits. The question at hand is this; If you were to accelerate an object to near speed of light, time around it would speed up, thus forward time travel. We all know this and I am no expert in this area but am incredibly curious. (Assuming we can harness negative mass) If we were to accelerate negative mass to near speed of light, would backwards time travel be possible? I doubt this myself but I am still curious. Alternatively, could negative mass has the ability to go faster than light? But I don't think the second one has any hope since it's more of a scale from -1, 0 1; 0 being the fastest. Despite it then being negative it would probably be identical in speed abilities to normal mass. At least that is my assumption.

Anyway, could negative mass have the ability to turn back the clock, making backwards time travel possible? (Incoming thought) Negative mass has been around since the birth of the universe means it is on the same timeline. So more doubt is in my mind, yet I would like to hear other opinions or thoughts.
 
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As far as we know, there is no such thing as negative mass and no theory that suggests it might exist or have particular properties if it does.