I first became interested in Albert Einstein and relativity when I was a child. I remember my father telling me about Einstein’s claim that time goes by at different rates and that objects change size for people travelling at different speeds. “That’s ridiculous,” I remember thinking. “It doesn’t make any sense. How could that possibly be true?”
Well, it is true. And one of my pet hobbies throughout my life has been reading popular physics books in an attempt to answer my childhood questions. Coming to an understanding of it – OK, understanding is too grand a word. Let’s say I now accept it. – has not been an easy journey for me. It’s been about 35 years in the making.
Oddly, I’ve always intuitively understood relative speed. I got it from driving in cars. It was always clear to me, sitting in the back of my parents car as we zoomed down Perring Parkway, that our speed, relative to a car driving next to us, was zero; even though our speed relative to someone standing on the side of the road was 65 mph.
The next step in my journey was understanding relative motion. Imagine someone on a long train ride tossing a ball up and down as they cross the country. To the person riding in the train car, the ball behaves perfectly normally; it goes straight up and comes straight down, just as you would guess. However, to someone watching the ball from the ground as the train sped by, the ball would be moving forward as it moved up and down. The ball, therefore, would execute a sine wave motion through space. But no need to stop there. To someone watching the ball from orbit, the ball would not only execute a sine wave but the path of the wave would be bent into an arc, since the surface of the Earth on which the train is riding is curved. Move out another step and watch the ball from outside the Solar System. The motion of the Earth around the Sun comes into play making the ball execute a long, curving series loops (think of a SpiroGraph).
So which of those motions is correct? Einstein’s insight is that they’re all correct, simultaneously. Each is correct for that particular observer’s frame of reference. And no frame may be selected as being ‘more correct’ than any other observer’s frame. As long as we share an observer’s frame, we’ll all see and measure the same things. Therefore, the physics is constant. However, it changes from to frame. It’s unavoidable. All observer’s sharing notes within a frame will report seeing the same thing. Observers sharing notes between different frames will report seeing and measuring different things. Odd but clearly true.
Time and space dilation is more subtle and took longer for me to get a grip on. In honor of this being the 100th anniversary of Einstein’s paper on the Special Theory of Relativity, Astronomy magazine has done a special issue devoted to the subject. An illustration in one of the articles has finally made it clear to me how this works.
Imagine a sailboat passing a dock on which there stands a man. On the 32 foot high mast of the sailboat is another man who drops a rock onto the deck of the boat. From the viewpoint of the man on the mast, the rock drops straight down, taking one second to hit the deck. However, from the viewpoint of the man on the dock, the rock moved at an angle through space onto the deck below. It moved through a longer distance. And this is key, the faster the boat is moving, the longer a distance the man on the dock would see the rock traversing. This is not an illusion. It’s quite real.
And it gets scarier still. Velocity is distance travelled divided by the time it took to cover that distance; i.e., 60 miles per hour. The velocity (speed) of light is constant, 186,200 miles/second. It never changes. So let’s change the falling rock to a light beam from a flashlight. And let’s lengthen our pretend mast to 186,200 miles high and speed up our sailboat so it passes by more quickly. Our friend on the mast turns on his light and it hits the deck straight below him one second later. Our friend on the dock sees the light angle though space and take a much longer path to the deck. He sees the hypotenuse of a right triangle made by the deck, the mast and the front edge of the beam moving down to the deck. Think about this. The speed of light is the same for both observers. The distance the light beam has travelled is longer as measured by dock-man. So if we keep the speed of light constant and increase the distance it travelled how do we make the math work?
This is what the man on the mast measures (C equals the speed of light):
C = 186,200 miles/S = distance / time = 186,200 miles / 1 second
This is what the man on the dock measures:
C = 186,200 miles/S = distance / time = 190,000 miles / 1.02 second
Both time and space are different between observers moving at different speeds with respect to one another. They perceive lengths of distances to be different and time actually passes at different rates for them. Amazing.
Einstein called facing up to the result of that mind experiment “taking the step.” Once he knew the observers would measure different lengths for that light beam he knew that time had to be variable for them. That “step” was the beginning of a revolution in the way the universe is seen to function. Kip Thorne, physicist and author of Black Holes & Time Warps, Einstein’s Outrageous Legacy is still astonished by what he termed Einstein’s “breathtaking arrogance.” His complete confidence that his definition of time and space was correct and everything that had gone before was wrong. Close, yes. But wrong.
Lest you be tempted to think this is a lot of esoteric egghead nonsense that has no bearing on the real world, think again. When the constellation of GPS satellites was designed for US military in the 1980’s, relativity functions were built into the software. The functions were designed so they could be switched off from the ground just in case Einstein was wrong. They’ve never been switched off. Were they to be, users would experience locational errors on the surface of the Earth of about 7 miles. Relativity is completely real.
Congratulations Albert, on the 100th anniversary of your theory. As amazing as it seems, you were right.