From: The Physics and Philosophy of Time Travel: From Einstein's Equations to Paradoxes
evidenceexperimental

Experimental verification of time dilation confirms that forward time travel is already occurring: particles in accelerators and GPS satellite clocks experience measurable future shifts relative to Earth.

96% confidence

According to special relativity, a clock moving relative to an observer ticks slower—a phenomenon confirmed countless times. In 1977, Bailey et al. stored muons in a storage ring at CERN; their observed lifetime was dilated by a factor of ~29, matching relativistic predictions. Similarly, the Global Positioning System must correct for both special and general relativistic effects: satellite clocks gain about 38 microseconds per day due to weaker gravity and lose about 7 microseconds per day due to orbital speed, net +31 microseconds/day. Without these corrections, GPS positions would drift by kilometers each day. These real-world demonstrations show that traveling into the future at different rates is not only possible but routinely engineered.

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The Physics and Philosophy of Time Travel: From Einstein's Equations to Paradoxes
Evidence, perspectives, rabbit holes, and more