BTW, if you’re serious about wanting to understand this better, I very highly recommend a wonderful book called General Relativity from A to B. As the title suggests, it talks about relativistic effects more in the context of General Relativity than Special Relativity, but it is a remarkably clear presentation with plenty of “picture this” thought experiments and no advanced math, and I think it should be accessible to anyone with a grounding in high school math. It very clearly explains first the Aristotelean and Galilean worldviews, before explaining how they fail, and are superseded by General Relativity. I’ve read quite a few popular books on relativity and this is easily one of the best.
Bravo for books that make these things accessible.
I wanted to add that high school math is actually enough to work out special relativity and derive E = M c^2. It was an exercise we did in “Modern Physics” class about 45 years ago. I no longer remember – it might have required the use of limits, but I think limits are often part of high school math. You had to start with the information that the speed of light is the same regardless of how you and/or the light source are moving.
That said, it’s one thing to be able to follow the trail mathematically. Blazing the trail is something else.
I really should bookmark it, but the best introduction to relativity I’ve seen was on a website with a name something like “avi8ion.com”. Apparently it started out as a website about the physics of flight, but the guy who made it just kept on writing about other areas of physics.
Anyone remember the site I’m talking about?
Sounds tailor made for me. I just ordered it, thanks.
I am keeping my eye out for the answers…
There is, IMO, a simpler explanation than “it’s acceleration.”
Consider two people walking around a field at a constant speed. One person walks in a straight line towards a destination. The other zigs and zags.
On any given straight segment, the two people each think they’re going faster than the other one. After all, their path is “forward” (for whatever direction “forward” is), while the other person is heading off at some angle, and since they’re going at the same speed, that angle makes it look like the other one is falling behind.
And yet from a big picture view, it’s obvious that the zig-zag person must be taking a longer path than the straight-line person. Is it because zig-zag had to accelerate at certain points? Yes, sorta… but it’s a strange way of putting it. It’s really just the fact that it’s a longer path. And it doesn’t matter what angle you look at things at. That path is always longer.
The only difference between this and our actual reality is that due the strange geometry of the universe (Minkowskian), zig-zag paths are always shorter than straight-line paths in time. Hence, zig-zag ages more slowly.
Thanks for that. I’m getting closer! That truly helped.
Or to add another element, a zig zag path requires you to exchange some of that movement in space with movement in time, such that the overall distance metric in space and time remains constant. Standing still, and all your movement occurs in time. The zig zag path back to where you started requires the same total distance, as standing still, so you need to lose some of your time to make up the spacial movement. It is just Pythagoras after that. The hypotenuse is constant - always.
The longer the distance at speed spent on the zig zags the more time is required to balance things. In this respect it is apparent that it isn’t the acceleration that is key - that is just a requirement of switching between frames as you do the zig zag.
Yet another great thought. Spacetime is a tough concept for me to keep in mind.