If time travel will ever be invented, people from the future would know the actual spot rates of future periods from now, till then. With that knowledge, they can travel back in time and make undue profits merely because they know the rates of the future.
Because nobody has made consistent and continuous undue arbitrage gains, we can be certain that time travel will never be invented.
To put it simply: Now it is 2019. If someone from 2025 comes back to 2019 (who, from 2025 knows all the historical prices until 2025) can make unlimited arbitrage gains in 2019. But because nobody has made any such unlimited profit, it is clear that it is because no one has been able to travel through time.
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