Across and Back
Suppose you have a river 100 feet wide, flowing 3 feet per second. Suppose that two perfectly matched swimmers have a contest in which one will swim 100’ upstream and then 100’ downstream while the other swims across and back again. Both swimmers swim 5’ per second the whole way.
Obviously, the one who swims up and down is slowed by the stream going up and helped going down; the one who swims across is slowed a little the whole time, but the intuitive sense is that their trips should come out the same. Right?
Seems right, but let’s check the math.
Joe is going upstream 5’ per second, but actually, he only goes 2’ per second because of the river flowing down at 3’ per second. So it takes him 50 seconds to go 100’. Returning, he goes a speedy 8’ per second, swimming 5’ per second plus 3’ per second from the sweep of the river. Thus it takes him only 12.5 seconds. (12 x 8 = 96; so 12.5 x 8 = 100)
Joe’s whole trip is 62.5 seconds.
Ben swims across. Since the stream sweeps him 3’ downstream every second, he needs to aim upwards to get straight across. If he chooses the correct angle, he’ll get four feet across for every five feet he swims. This is the famous 3-4-5 right triangle where he’s swept 3’ downstream, and goes 4’ across while swimming 5’ on a well-chosen diagonal.
Every second, he’ll get four feet closer to the other side, and the same speed considerations govern his return. 100 / 4 = 25. He can go 100 feet in 25 seconds. Twice 25 is 50. He’ll be there and back in a cool 50 seconds. How did that happen?
Well, never mind how it happened. Just face it. The intuition that upstream and downstream is the same as across and back is wrong. Across and back is faster.
That is how Michelson explained things to his daughter as he (and Morley) prepared a famous experiment to test for the existence of the ether. He had devised an ether test based on the difference in speed between going upstream and down vs going across and back.
After all, if there is an ether, the earth is traveling through it. And if the earth is traveling through the ether, there should be an “ether wind” blowing across the earth. A very gentle wind, mind you, but a real one. Now, if the earth is also rotating on its axis, then there must be one moment a day when any given spot on the earth is moving exactly parallel to the motion of the ether wind, and one time a day when it’s moving exactly opposite that motion. This is still true even if we consider that the sun and the whole solar system are in motion, as is the galaxy so that the ether’s motion might be in some unexpected direction. No matter how many motions you have to take into account, the end result must be that at some time of day, the motion of, say, a man on top of Mount Everest, is parallel to the ether, and one time when it’s opposite. At those two times each day, couldn’t you send one light beam up and down the ether wind and one beam across?
Now, what Michelson did was too clever to explain quickly, but you can look up the Michelson-Morley experiment. The idea was that his apparatus would catch those two moments. Indeed, light goes so fast that if you put the beams on a turntable, you should be able to catch a flash of interference at any time of day. Here’s how:
A beam of light would travel across a turntable, be split into two beams in the middle (by a half-silvered mirror) and those two beams would travel across the rest of the table and return home. At some moment, one half-beam would be traveling parallel to the ether, like Joe, and one half-beam at right angles, like Ben. When they got home, and the slow one would make an interference pattern with the fast one.
An interference pattern?
Well, think of the waves in a pond when they come from two directions. Where they meet with one crest meeting one trough, the water is still. Where two crests meet, there is a high crest; where two troughs met, there is a deeper trough.
Light waves can also make an interference pattern, so that at their still point, certain colors go missing, or so that there are light and dark bands instead of a steady light. That was what Michelson was hoping to see.
You see, one beam would be like the stone in the wheel, just in top and bottom positions, first fighting the ether and then going with it. The other beam would be like a stone at the side of the wheel, going at an even speed and, like the swimmer who crosses the river both ways, making his trip faster. When the two beams returned, you would be able to detect the difference in their trips, because they would create an interference pattern.
Did it work?
So what happened?
Well, there was a tiny interference, but it was only 1/40th of what Michelson expected. Or, rethinking things, maybe one sixth of what he should have expected. Was this because the apparatus was badly designed? Or was it just experimental error – because the apparatus was not sensitive enough? Or was there no ether?
The experiment was conducted again and again. The apparatus was redesigned to be more sensitive. It always gave a result, always too small.
The consensus over time has been that there is no ether. Michelson himself never accepted that consensus.
How can you have a ripple without a pond?