Yes, you’re missing something. Seconds squared would come from seconds times seconds. As presented, the units are essentially seconds divided by seconds, a simple unitless ratio.
English and math don’t work together perfectly. You might be confusing the statement given with, say, the units typically given for the acceleration of gravity, 32 feet per second per second. There, the ‘per second per second’ does indeed mean ‘per second squared’, but that expression only works with both ‘per’ words in place – it really boils down to a quirk of language.
Okay… try this one more time. I’ve revised and bolded words from my previous post.
English and math don’t work together perfectly. You might be confusing the statement given with, say, the units typically given for the acceleration of gravity, 32 feet per second per second. There, the ‘second per second’ might seem to mean ‘second squared’, but that expression only works with both ‘per’ words in place – it really boils down to a quirk of language.
Seconds divided by seconds just gives you a unitless percentage. In mechanics, we define *strain *(compression or elongation) as inches per inch, or mm per mm. In either case, it just reduces to a percentage, such as “strain of .01” meaning an elongation of one inch per 100 inches of original length. I would think a time traveler could use a similar metric.
Of course it won’t do your joke any favors, if you have to refer to your time traveling ability as a time strain of 1.0.
I don’t think that there is a current unit like this, but it’s the sort of situation that historically gets named after a person, like the Mach number, the Reynolds number, the Planck constant, the Richter scale, the Chandrasekhar limit. So your best bet would probably be to take the time machine inventor’s name and Machify it: ‘we’re traveling forward at Venkatisan 12.5’. Or you could go with “Time Factor” from the old Star Trek pilot.
And of course, a speed of 1 second per second is c. In a sense, we’re all moving at the Speed of Light; we’re just doing so almost entirely in the time direction.
Your joke is actually a standard response by physicists when asked about how fast time is moving in a given frame of reference. It’s always 1 second per second. No matter where you go, there you are.
There is no such thing as “normal” when it comes to the passage of time (viz. Special Relativity). There is no one particularly privileged frame of reference. You might say, “We experienced 30 seconds of time but on the surface of the Earth they experienced 1 year.”