Thursday, July 09, 2009

On Time & Relativity - Part 1

The Theory of Relativity provides a sense of fascination for most thinkers, Me Thinks.

But similarly, it is often regarded as abstract, and difficult to understand. Part of that challenge is due to the fact that relativistic effects contradict everyone's, everyday experience.

When an object (of mass) moves at a velocity approaching the
speed of light, it's inherent properties are changed in surprising ways. There are three relativistic effects that occur on objects with mass. These are:

length contraction
time dilation
mass increase

Relativistic effects occur on any object (moving at any speed), but these effects are infinitesimally insignificant (largely, very small - giggle) unless the object is moving at a noticeable fraction of the speed of light (approximately 3.0 X 10^8 m/s).

AKA: Any mass, in motion.

It's our most familiar process - one that we all know "from experience".
Motion (as we "experience" it) is comprised of neither time dilation nor length contraction. A displacement at half the speed of light could correct this misjudgment (but it's not on offer just yet, I shall let you know).

Q. What is the minimum speed for relativistic effects?
A. There is no minimum speed for relativistic effects.

(Imagine that an Indy car is your
'time machine'. Your subjective elapsed time is shorter in a fast loop around the track, than it would have been if you had remained at the starting line. The catch is that at such speeds, the effect is very small - your relativistic clock would read [perhaps] slower by a couple of trillionths of a second. Eureka! Must one specify the degree of the desired relativistic effect? Yes.)

A possible alternative to an actual relativistic experience is simulation: i.e. cinematographic imagery (virtual reality). It allows us to conceptualize
relativistic flight, gravitational collapse, compact objects (collapsed stars, for example) and other extreme conditions. Extreme?

Well yes, extreme to-the-extreme (very small, but large? giggle)!

The general Theory of Relativity is also a theory of
gravitation. Its peculiar predictions (like the deflection of light) are not part of our everyday life (the gravity of the earth is simply too weak to impress mere mortals). Nope, there's nothing THAT extreme happening anywhere nearby, albiet our Sun does a nicer job of it. Let us look into Space. That's where the everyday experiences of even mortal men will reach those extremes. And in no time (pun).

I've yet to provide my readers (as promised) with "time words" - redefined or invented. Patience (is going to be one of them)...

At the beginning of the 20th century, the theory of relativity was considered to be one of the most difficult and abstract theories in science. This is expressed (e. g.) in Herr Einstein's famous question, "Why is it that nobody understands me and everybody likes me?" Or, in the anecdote on Sir Arthur Eddington, who (when someone remarked that he probably was "one of the three men in the world who really understood relativity theory") replied, "I do not know who might be the third."

I suspect that there are a few more than three today. Were it that everyone be so enabled, alas. Onwards. Why does time appear to run slower near a
gravitational field?

General Relativity. The geometric theory of gravitation developed by Albert Einstein, incorporating and extending the theory of special relativity to accelerated frames of reference and introducing the principle that gravitational and inertial forces are equivalent. The theory has consequences for the bending of light by massive objects (the nature of
Black Holes) and indeed, the fabric of space and time.

General Relativity. It predicts that time should pass more slowly when near a massive body. This is because there is a relation between the energy of light and its frequency: the greater the energy, the higher the frequency. As light travels upward in a gravitational field, it loses energy and so its frequency goes down. This means that the length of time between one wave crest and the next goes up. To an observer high up, it would appear that everything below was taking longer to happen. (This prediction was first tested in
1962 using a pair of very accurate clocks mounted at the top and bottom of a water tower. The clock at the bottom, i.e. nearer the Earth, was found to run slower, in exact agreement with General Relativity.)

Life for folks in New York (when compared to) life for folks at Denver - is INDEED a march to the beat of a different drummer! Let us not compare the "Big Apple" to the "Mile High" city, but rather to a somewhat smaller, Orange...

Do citrus trees grow in Colorado?

Did you know (relatively speaking), that the surface of the Earth (proportionately scaled) is far (FAR) smoother than the most convoluted wrinkles of an Orange peal?

And so it is...