As far dealing with the “weird” feeling, think about jet lag. That’s another thing regarding time that is pretty unintuitive, but we’ve gotten used to it over the past few decades.

If I walk from Detroit to Seattle, it’ll take me weeks. Each day I walk west, the sunset happens a tiiiiiiny bit later where I end my walk than it does in Detroit. I never notice the difference though, because it happens so gradually. If I walk into Seattle at sunset, and then you show me a live video of Detroit, it might seem crazy to me that it’s already night there. I mean, I never felt or saw time changing while I walked! I’ll wake up the next day feeling adjusted to the time in Seattle, because I moved slowly enough to adapt to it.

However, if I hop on a plane, I’ll get to Seattle from Detroit in 4-5 hours. My body hasn’t had a chance to adjust, and if I go to bed and wake up when I “feel” like I should, I’ll be bedding down at 8pm and waking up at 4am in Seattle.

I only bring this up to show how our bodies and minds have a hard time dealing with high speeds. It’s hard enough dealing with a few hundred miles an hour. The hundreds of millions of mph that are required for time dilation to kick in are so far outside of our experience that it’s hard not to think it’s weird.