A race is about to take place. In fact, it is the legendary tortoise and hare competition, but with a “big” difference. The hare is incredibly huge. In fact, that’s an understatement. He is the size of small mountain, with front paws each the size of a huge building. It’s important to visualize this – two paws, each roughly the size of a ten story building. Sounds bizarre, agreed, but hold that thought.
The other competitor in this race is the tortoise and he is equally disproportionate to what your or I would call normal in size – but in the opposite “direction.” He is the size of a tiny mite. He’s so small, in fact, that he would be just barely visible if he were sitting on your thumb nail right now. Look down at your thumb nail and take a second to visualize that tiny little tortoise – just a barely visible speck.
The race is about to be run on a typical, straight, dirt track. It is the one hundred yard dash. As you visualize the track, try to imagine the size difference between these two competitors as both are stepping up to a chalk starting line. A literally mountainous hare and a microscopic speck of a tortoise.
A starter on the sidelines yells, “Ready…set…” and then he fires his pistol.
Now, let’s start with the hare. Looking down, that hundred yard track between the Start and Finish lines, is far below him and it’s a thin, short, tiny rectangle which he knows he can cover with the slightest forward movement of one huge paw. Positive of his win, when the gun goes off, he simply lifts and slightly moves a single foot in a very leisurely manner from the Start line across the Finish line. And, of course, it’s across the finish line almost instantly. Piece of cake for the hare, right?
Not so fast.
The microscopic tortoise has looked at that same hundred yard stretch and what he has seen appears to be an infinite distance in front of him. In fact, just the Start line itself is an incredibly wide band of white chalk powder in front of him. Visualize his view! And picture how the finish line is much too far out there to even be visible through the expanse of boulders (grains of sand) and huge white dunes (the starting line chalk powder) in front of him.
But, perched on one of those sand grain boulders, this microscopic little tortoise is about to prove he's slow poke. In a word, he’s “lightning!” So, as soon as the starting gun is fired, he takes off like a shot – literally like a shot!
And who wins the race? Who would you guess? Well, to everyone’s surprise, the race is a photo finish – an exact tie!
And this is where the relative connection comes in. You see, by the standard clock on the sidelines, the hare and the tortoise moved at exactly the same speed. They had to, right? Because they both started on the gunshot, and crossed the finish line at exactly the same instant.
But think about what that “same” speed was like in each of their perceptions – their surrounding “worlds.” To understand this you have to separate these worlds and look at them individually. And, of course, you have to visualize.
In the hare’s huge “world”, as we’ve noted, the motion was a slow, leisurely movement of one front paw. He just lifted it up and slowly eased it forward, but it was so big, it was across the finish line in an instant. In the microscopic “world” of the mite-sized tortoise, however, the motion was lightning fast, much faster than any speed he’d ever dreamed of in his normal world. To travel that far in such a short period of time, he had to literally blast down the track like a bullet! Just imagine the view of something that small going a hundred yards in less than a second!
So here’s the big question:
Are these differences only perceptions? Or, is the speed
of an object and the time elapsed in its movement somehow
relative to its size?
According to the timing clock standing on the sidelines, the elapsed time was exactly, let’s say, a half of one second, which, when applied to that hundred yard distance, comes out to, roughly hundred miles an hour. But would a timing clock in a huge hare world have recorded the race slower? In his world, would that slow leisurely movement have been the equivalent of, say, a hundredth of a mile per hour, since all he did was lift one huge paw?
And, of course, the same question can be asked in reverse for the tortoise. Would a tiny little timing clock in a microscopic world have recorded a different speed? Since that little tortoise moved so incredibly fast to tie the hare, would he have been clocked in his world at, say 1000 miles per hour?
In other words, is size somehow relative to an object’s speed? Would three different clocks – one on the sidelines, one on the head of the tortoise and one (a really tiny one) on the head of the hare record different times?
