Question

Dear Mitch, 

Answer

Dear Frequent, 

You are correct that I did promise to take a stab at presenting the basic theory of relativity in a way that I hope will make sense to people who don't have a lot of math experience.  

I did not forget, but in the collection of new questions we get each week, there's always one or two that seem like a good idea to answer and post on a website like this so that other people with similar questions could get an idea that they might not have considered on their own.  (As I point out from time to time, each week we do respond to almost every letter with what we hope are helpful answers, but most questions and responses are handled in private emails.) 

We try to keep the posted questions to one or two per week so we don't overwhelm readers.  Otherwise, we risk making the questions and answers resemble a book, and that would defeat our goal of being reader-friendly to people of almost all ages.  So, to select one or two questions a week, we put some aside, but that's usually temporary, and no interesting question is ever forgotten.  So now, here goes: 

The biggest challenge for people when it comes to understanding Albert Einstein's Theory of Relativity is this:  The main concept is almost always explained in terms of what is likely to happen if a person or thing were to travel at the extremely fast rate at which light travels.  Basically, it is believed that for that rapid traveler, time itself would slow down.  That means that the traveler would not age as fast as the people who remain still (it is important to understand that by 'still' we include all the people who continue doing whatever they happened to be doing at the time and moving the way that people normally move, each at his own rate, and we even include everyone who suddenly decides to fly around as fast anyone in the world has ever flown.  These people can be considered motionless because compared to the rate of 186,000 miles per second at which light travels, and which our experimental light-speed traveler goes as he starts to zip through space, even the world's fastest car, plane, or torpedo progresses at rates that are barely more than crawls.  And by lumping all the fast 'crawlers' in with the very still, we immediately simplify the discussion). 

Mathematics aside, the main concept that most people seem to want to understand, or at least get a logical sense of, is the relationship between super-fast travel and the slowing down of time..  

A lot of people find themselves stopped by the notion of traveling at rates that are just too fast to imagine ever happening, and so the whole idea ends up seeming so abstract and unbelievable that they might as well be thinking of going at an infinite speed. The famous number that comes up is 186,000 miles per second.  That is the rate of movement for just about every ray of light the world will encounter, and, of course, is not imaginable in the way that people usually imagine things.  It is abstract, of course, but the hard part is that it is abstract in a way that even the thought of a purple elephant is not. For the elephant, people are usually able to come up with an image by mixing and matching various pieces of real images from their life of experience. Part cartoon, perhaps, part recollection from a circus visited in one's childhood—whatever's necessary is culled to produce a satisfactory model in one's mind of a purple elephant. 

But for most people the obstacle to getting a real feeling for relativity is that there is no prior experience to call up that's similar enough to light-speed travel to even provide a foundation for a model that sticks.  The speed limit for automobiles on public roads is 55 miles per hour in most states, 65 miles per hour in some states, and 70 in a few states, and driving at these rates can give one the sense of moving through space rapidly.  In fact, more than half of all drivers admit to going 'a few miles over' the legal limit, and close to 40% of drivers admit to driving 'substantially faster' than the legal limit when " late for a meeting".  But even the drivers most committed to rapid travel on public roads reach their maximum speed not far above the highest number represented on the vehicle's speedometer. 

For distance travel, even those with a single experience as a passenger aboard a commercial airline discovers that 600 miles per hour is ordinary, and a thousand miles per hour is not unheard of.  Yet 1000 miles per hour is a mere 1/669,600,000th of the rate of movement that the theory of relativity requires for a traveler to benefit from the effects that would apply at the right speed.  Rounded to the nearest sensible place, the number becomes one-seven-hundred-millionth, (that's 1 over 700,000,000).  And to try to imagine zipping around at a speed so freakishly beyond anything anyone has ever experienced seems pointless.  Again, 1700 million times the speed of the 1000 miles per hour glide of the airplane. 

However, there is a problem with dismissing that situation as pointless, and that problem is this: that speed is in fact a very real speed, and it is traveled every moment of every day by almost every ray of light from every lamp in every home, and from every bulb in every lamp, and from every flashlight held by anyone taking his dog for a leisurely nighttime walk. 

Even more perplexing, perhaps, is the fact that this rate has not only been consistently confirmed in careful experiments carried out by researchers with perfect credentials, but that the same experiments have also confirmed the famous and very strange effects that traveling at such a rate purports to have:  time comes to a stop for the traveler, and he or she will not age during the journey.  In short, it seems, one could beat time by moving faster than light.  

Well, it should not surprise ANYONE that this idea sounds, seems, and feels absurd .  Nor should it come as much of a surprise that the idea continues to seem absurd no matter how much 'scientific' evidence there is to back it up.  It has been proven many times, and it still feels foreign to most people. 

So, rather than just repeat the explanations that most people do not find helpful, and rather than just repeating them in a louder voice or with a bigger font, let's try it another way:  

First, to quickly repeat the idea, which you do not have to understand or feel or even believe (yet), it can be reduced to this: 

Move fast enough (186,000 miles per second) and time slows down and then stops;  it may not slow down and stop everywhere for everyone (it won't), but it will slow down everywhere for you, that rapid traveler.  And here's where a tiny bit of math could actually help.  So, without even approaching the famous formula (e=mc²) that a lot of people find intimidating, we can use a much more ordinary setup that most people rely upon at least a couple of times a week, even if they don't realize they're using it.   

It's this one:  Distance = (rate of travel) x (the amount of time traveled).  

Example: a 10 mile stretch = (moving at RATE of 5 mph) x (a span of 2 hours) And by making only a minor switch in the arrangement of the three parts of that formula, we get its other form: rate of travel = (distance traveled) divided by (the amount of time traveled). Example: 5 mph = 10 miles divided up evenly between 2 hours

Well, if a person is traveling at a rate that is unimaginably fast, we might as well think of it as "almost infinite."   So, if you look at the big equation above, you see that infinite speed = some distance divided by some time.  Well, there are only three ways a fraction even as scary as d/t can be so huge (so close to infinity): 

1) the top part of the fraction is gigantic; 

2) the bottom part is infinitesimally small; (or) 

3) both 1 and 2. 

Now, multiplication has a property called "commutative".  This means that the order of the 2 items being multiplied by each other doesn't matter (i.e., 3 x 4 = 4 x 3), and that means you can just as easily say the 3 causes the 4 to turn into a 12 as you can say the 4 causes the 3 to turn into a 12.  They're equally correct, except that the word 'cause' is not a great choice because the numbers are a pair that works together that way,  (if a 3 can 'cause' a 4 to become a 12 through multiplication, then why doesn't a 3 cause a 5 to become a 12 too? Because it's the pair – not causing, but producing – a joint reaction.  

Okay so far? 

Good.  

Now, sometimes when something is hard to grasp, a way to have a better shot at it is by considering it in a different order from the way it is presented.  So if the fact is that infinite speed goes hand in hand with time slowing down, and the main operation to connect them is commutative, then the 'slowed-down time' can be thought of as allowing everything in existence to travel faster than usual.  It's like this:  If for some reason the world only had one clock, and the people used it to keep track of time and it got stuck for a little while, then anything that a person happened to do while the clock was frozen was done instantaneously or at a speed immeasurably short because it happened faster than the time changed.  Considering it this way, with the speed of something resulting from a lucky break in time's schedule from slipping into the sliver of slowed or stopped time, people find it makes perfect sense.  So, rather than overwork your brain trying to envision some vehicle of the future that might be able to move at speeds thousands of miles beyond anything any current technology would allow, why not take things slower, much slower, and just consider taking a pause, a brief rest, and give the same break to a relentlessly revolving planet, ours, and allow time to slow down for a second.  A single second...What?  How?  Well, keep in mind the fact that some things that initially seem odd turn out to make more and more sense as you think of them in different ways. 

When you compare the idea of a chance of coming up with a vehicle that would travel at speeds actually approaching infinity, well, forget it; I've never heard a car company or airline pretend that that's a realistic goal. 

But: When you pause to consider all of the sea's water, you have to conclude that its "salt content" is an average; when you analyze the chemical make-up of blood, even from the same 'blood-type', or the time-frames of gestation, or the temperature of the earth's core, or any other number describing a phenomena of nature, it has to be an average. 

Could it really be that the orbit of the earth is 100% identical moment to moment and millennium to millennium? No, there are pauses.  Just as there are times when even the human heart, on which a whole person's life depends, pauses and then tries to make up for the lapse by giving itself a push to catch the lost time, the elements of the solar system are entitled to vary their movements. 

Just as all things that are deemed possible cannot be described to be of equal likelihood (some things, in fact, are only known to be possible because someone somewhere managed to do it one time, but it doesn't mean that it is possible for anyone any time anywhere, the 'impossibles' are not all equally impossible.  In fact, some are just impossible to replicate, and others are simply impossible to explain. 

Consider a 'pause':  Now, if a pause in time lasted five seconds, surely it would be noted and recorded by astronomers, timekeepers, etc.  Even a pause of a second would be tough to slip by.  But a pause of one-ten-thousandth of a second would probably slip by without a single person blinking.  And here's the catch: an astute individual motivated to find a way to get that brief break in time when the universe catches its breath realizes that an un-timed fraction of a second is the same as no time recorded. 

Consider this: An arthritic man who usually struggles for over an hour to make it up the staircase of his childhood home ventures up and though in discomfort finds himself tickled by the realization that he made it up in less than a second.  Way less!   He climbed to the top before the clock had a chance to change from one moment to the next. 

As in life springing up from the universe's primordial soup of nonliving matter, when it happens, it'll probably be a one-time occurrence.  But, the single instance precludes the description of "impossible."  It happened, so it is true and possible. 

Well, math formulas are useful, and are often cited for their concise way of showing how certain relationships function, but it is a subjective thing, because other people find their experience with a mathematical formula to last an eternity, no matter how brief witnesses consider it.  Others read long books and articles and grasp their meaning, but report that the time it took felt endless.  As I've shown here, replacing formulas with words can take ten times the amount of space – but to those who take a moment to engage, the experience is a journey and they make it their point not to let it slip by too quickly. Fortunately, everyone enjoys something, and it comes down to a matter of preference.  Next time, back to numbers.  If we get the right question (and we almost always do), we'll calculate like crazy and teach a few new tricks along the way!