You go on a flight from New York to Los Angeles. The plane basically takes off and then flies in a straight direction to Los Angeles where it lands.
So if we wanted to build a mathematical model of your trip, we can basically plot it on a graph in two dimensions – on the Y axis is what you can think of as “percent of trip completed”, with “I’m still in New York” at 0 and “I’ve landed in Los Angeles” at 100, and 50 is “I’m halfway through the flight.” That’s one dimension. Since the flight takes about six hours, then we can plot the X axis as “how much time is elapsed.” At zero, you’re just taking off from New York so you’re at New York. At hour three you’re halfway through the flight so you’re halfway to LA. And then at hour six, you’re all the way at Los Angeles. And in fact we now have an implicit equation where we can insert time and return your position along the axis between New York and LA, or we can insert your position along the axis between New York and LA and find out what time you were there.
That’s what it means for time to be a dimension – in a model of a moving object where time is a dimension, we create an association between time and position in space. It’s nothing to do with Einstein, it’s just a function of how we study physics and model the movement of objects in math. I just did it with one spatial dimension and one time dimension, but there’s no reason I couldn’t extend the model and use two or even three dimensions in space and one dimension in time. That would be your “four dimension model.”
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