Is there a logical contradiction here?
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Original Question
A: Wouldn't it be great if modern technology could develop time travel? Travel to the future, revisit your past, etc. Exciting!
B: Indeed, but unfortunately logically impossible. The future, by definition, does not exist in the present. Neither does the past. Think about it. You get into your time machine, and travel to the past AFTER you have pulled the lever. See the problem?
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Answers
2I see no contradictions here.
Time is relative to the observers inertial reference frame. So someones future can exist in someone else present. But for both of them, they can only ever exist in their own present. This kind of time travel where you could go into the future and see yourself would have to create two of you so that the relativity of time travel can take place. So it wouldn't just be time travel, but also a cloning technology too.
Word games. We all travel to the future every day... in real time. When we arrive, the future becomes the present for us. For all practical purposes, we can (and do) travel to the future. Although we don't travel back in time, logically, the same word games apply here.
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"Time" travel is a misnomer. In order to move about in time, one must also move in space. A more accurate term would therefore be "space-time travel". Regardless of "when" you might arrive in the past, the painstaking calculations necessary to allow you to arrive at an absolutely precise and safe location are, I think, prohibitive. So when you get into your time machine and pull that lever, you are most likely going to arrive in the past floating around in the middle of space. And regardless of the method of activating your time machine, you are still going to arrive in the past "after" you have activated it. That's why it's called "the past".