Everything s Relative

Everything's Relative

Now that we understand the gravity of mistreating Newton, let's try a couple more popular idioms on for size. Two people disagree on something, and one says:

"Well, it all depends on your frame of reference."

Or, someone wants to make the point that "the old accepted laws of nature are no longer true." The usual expression of this is along the lines of:

"Einstein showed that Newton was wrong."

Well, as they say in the Hertz commercial, not exactly. Einstein did a hell of a job with relativity, but his theory has spawned some strange notions.

Frame of Reference

With respect to the first example, it's true that things can appear different depending on your perspective or point of view. But as Galileo first stated, things are not different depending on your frame of reference. When you are within a framework that's moving at constant velocity, you cannot know your velocity as perceived by a stationary observer, because everything else inside your framework behaves according to the laws of physics, and all appears to you just as it would if you were stationary. Einstein's work cleared up an apparent contradiction between Galileo's principle and Maxwell's electrodynamics. In a similar fashion, you also cannot distinguish between acceleration and space-time curvature.

Einstein Proved Newton Wrong?

As for the second claim, Newton's Laws are perfectly valid at velocities that we encounter in our daily lives. Change comes only when things are moving at or near the speed of light. Then you need to apply different rules. And that's where Einstein comes in. Newton works at low speed (that is, most of the time), and Einstein's Relativity Theory kicks in when you start to go very fast. If you use "just Newton" for too long, then you will get progressively more incorrect results as you approach the speed of light, and your answers will be completely wrong when you actually reach the speed of light. Just remember that, relative to our daily experience, the speed of light is a very, very big number.

The effects of relativity are completely negligible in our common experience. You can compute them if you'd like, using Einstein's Theory of Special Relativity, but you will find that your results don't change at all.

That is because the speed of light is so great. On the other hand, the speed of sound is something we relate to daily. You can observe that the speed of light and the speed of sound are very different by doing this experiment the next time you are playing golf. When you are about 250 yards or more down the fairway (you have just hit your second shot and are walking toward the green), look back and watch (and listen) for the next group's tee shots. You will see the club hit the ball, and then a split second later you will hear the impact. You can compute this discernible interval by using the speed of sound in dry air at sea level^[2] and by assuming that the speed of light is infinite; that is, it takes zero time for the light to travel from the golf club to your eyes. This will give you the right answer.^[3] If you do the calculation using the actual speed of light, then you will get basically the same answer.^[4] So although you can legitimately apply Einstein's Theory of Relativity here by using a finite speed for light, it won't buy you much.

^[2] Notice how precision just starts to creep into our language when we want to be careful about using physics. The speed of sound depends on a lot of things, including the temperature, which I did not specify.

^[3] I hope you were curious enough to do the calculation yourself. If not, here it is. At 68 degrees Fahrenheit, the speed of sound is 1127.3 ft/sec. Two hundred fifty yards is 750 feet, so the sound will reach you in 0.665 seconds, or roughly two-thirds of a second. This is a noticeable interval. And by the way, I used English units here, not metric, because golfers, by and large, are "calibrated" in yards, not meters.

^[4] Another common example of this calculation is determining how far away a lightning bolt is by timing how long it takes to hear the thunderclap after you see the lightning. Same idea.

There is a real-life situation in which you can experience the speed of light as finite. When making an international phone call, you are sometimes unlucky enough to go up to a geostationary satellite and back down to Earth, and that takes about a half-second. That's long enough to give you the impression that your interlocutor is pausing; you might misinterpret that pause as dissent, hesitation, apprehension, or the like, depending on the conversation.

And Another Thing…

When it comes to Einstein, we have just scratched the surface. All the phenomena we've just discussed are manifestations of his Special Theory of Relativity, which holds only for bodies moving at constant velocity. When bodies actually accelerate relativistically, then you have to use his General Theory, with consequent additional heavyweight mathematical baggage. Yet popularizers invoke the General Theory with equal impunity. In fact, there are only a small number of experimental tests that we know of to test the General Theory, all of them involving very, very small effects.^[5]

^[5] When I was doing physics around 30 years ago, there were only three tests. They were the precession of the perihelion of the orbit of Mercury, the gravitational bending of light as it passes by a massive object, and the gravitational red shift of light as it climbs out of the gravitational field of a mass. My sources tell me that, since then, several more have been added; one involves measurements on binary pulsars. Until recently, all these effects have been extremely small and hard to measure and have had very little connection to our everyday lives. However, today the clocks in GPS satellites have to be corrected for effects that are purely due to General Relativity, so technology has now brought even this realm into our daily lives.

None of this diminishes the magnitude of Einstein's accomplishments. However, applying his brilliant discoveries to situations in which they do not really apply in a sense cheapens them.