Relativity for Everyone: Part II, Time and Length are Relative

In part I, I talked about the constancy of the speed of light. If you haven’t read that yet, it’s required reading before continuing here. There are terms and symbols used here that were already explained in Part I.

Relativity for Everyone:  Part I:  The Speed of Light NEVER Changes!

By now, you should have allowed the post about the constancy of the speed of light to simmer for about a day and you’ve almost certainly rejected it and gotten mad at the very thought of it if you’ve also been discovering what appear to be massive logic problems with it. If so, GOOD! That means you’ve been thinking about it and you’re thinking appropriately.

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Now, we’re going to establish that there’s no such thing as an absolute coordinate system.  In other words, if you try to declare some point is space as x,y,z and it’s always that point and that point is always in the same place in space, you’ll find that has no meaning.  It makes no logical sense.  To give a coordinate, it has to be relative to some object.  Let me explain…


Suppose you’re on a long train and suppose that train is really a space ship and you’re out in distant space.  Let’s further assume that the train and everything in it are all that exists in the universe.  Now, answer this question:

Where are you?

The question doesn’t make any sense, does it?  All you can really say is where you are on the train.  You can’t really say where the train is!  In order for you to give a location of the train, there has to be something else “out there”.  Then, you could say the train is X miles from that other object.  That’s about all you could say and still make any sense about the train’s location.

Let’s get back to the train being the only object in the universe (along with the stuff and people on the train).  Now, answer this question:

How fast is the train going?

Again, this has no meaning.  You can’t answer it because it doesn’t make any sense.  You could only answer that question if there’s something else “out there” and you can see it going by while looking out the train’s windows.  Then, you could only say how fast you’re moving towards or away from the other object.  You couldn’t even say whether it was YOU or the OTHER object that was moving… Or BOTH, could you?  That’s because speed is relative.  It’s relative to some other object.  Just like standing on the back of a big flatbed truck traveling at 50 mph and holding a baseball.  How fast is the baseball going?  Someone standing on the street would say it’s going 50mph.  You might agree, but then you might say, “I’m holding it in my hand, therefore, it’s not moving.  It’s speed is zero.”  You’d both be right.  What if you throw the baseball forward at 50 mph.  How fast is the ball going?  Well, relative to you and the truck, it’s going 50mph.  If you throw it forward in the same direction the truck is traveling, someone stationary on the ground would say 100mph.  You’re both right because the speed of the ball is 100mph relative to the ground and 50mph relative to you and the truck.  Suppose you’re on the equator driving east.  How fast is the ball going to someone standing on the north pole?  Well, since the Earth rotates at roughly 1000mph at the equator, the ground at the equator is moving at 1000mph and your truck is moving at 1050mph and the ball is moving at 1100mph.  But, how fast is the ball going relative to the center of the sun?  The Earth orbits the sun at roughly 30km/s.  So the ball would be going at Earth’s orbit speed, plus it’s rotation speed (if it were midnight at the location on Earth of the ball and truck), plus the speed of the truck, plus the speed of the ball.  If it were noon, it’d be Earth’s orbit speed minus its rotation speed, minus truck speed, minus ball speed.  What about relative to the center of the Galaxy?  What about relative to the center of another Galaxy?  What about relative to the universe?  Ah ha!  There’s no answer to the last question, not even a relative one.  The universe has no center, no preferred frame, no preferred coordinate system.  The universe just “is”.

A Thought Experiment:

This is where it starts getting weird… in just a few moments.  Now, back to the train in space.  Imagine some unknown source of a flash right beside the front of the train… just a few inches to the right edge of the train, by the engine car.  Now, you’ve got two timing mechanisms on the train.  One at the front of the train and one in the back of the train.  They can time the precise moment they detect a flash of light.  Also assume you have two perfect clocks that are perfectly synchronized; one at the front of the train, hooked to the flash sensor there and the other at the back of the train, hooked to the sensor there.  Let’s say the train is 300,000 km long (one light second long).

You see the flash of light originate at the front of the train.  The front flash detector detects the flash at 12:00 noon, exactly.  The detector in the back of the train, being a full light second away, detects the flash at exactly 12:00:01 PM.  Exactly 1 second later.

You compare the time stamp recordings of both detectors and accurately determine that exactly 1 second elapsed between the front and the back detectors detecting the flash.  Now, since you know that light always travels at 300,000km/s, you can easily determine that the train is 1 light second long (300,000 km long).  As a matter of fact, you could say that distance is defined by light moving in a given amount of time, and vice versa; you could say that time is defined by how light traveled a certain distance.  When light travels 300,000 km, you know exactly 1 second has passed.  When 1 second has passed, you know that light has moved 3000,000 km.  This is always true, from every perspective.

So far, so good.  Let’s throw some freaky in there now.  Let’s add a second, identical space train.  Let’s say it’s passing you on the right at very high speed, moving in the direction of your train’s forward facing direction, parallel to your train.  Now, remember, speed is relative.  The people in the other train may believe it is they who are standing still and your train is passing them on their left, going towards their rear direction.  Both accounts are 100% identical and 100% correct.  Now, they also have 2 perfectly synchronized clocks that keep perfect time and two flash detectors… all just like your train.  If there’s a flash of light beside their front car, they’ll record the same things on their clocks as you did.  12:00 noon exactly on the front clock and 12:00:01 PM exactly on their caboose clock.

As your two trains are matched up (side by side) for just an instant, at that very instant, there’s a flash of light at what appears to be exactly the same location as the last one… just a few inches to the right of your train’s engine car.  It’s at exactly the same relative location to the other train’s engine car, except a few inches to its left (the flash is directly between the two passing trains’ engine cars).

Now, you already know how the timing results play out in your train, and you know how they play out in the other train.  But, there’s a problem!  Let’s say it’s 12:00 noon exactly again just as the flash happens and your clock in your train at the front records it as 12:00 noon exactly.  So does the front clock of the other car.  So far, so good.

As the flash of light travels towards the back of both of your trains, the other train is still moving forward.  Let’s say from your perspective, the other train is traveling at 50% light speed (or 50% c).  This means that the back of the other train and the flash of light will meet each other before the flash of light reaches your rear detector!  As a matter of fact, the back end of the other train will be roughly 1/4 of the way up from the rear of your train when that flash of light hits their rear detector!  See the problem yet?


Let’s say you have a 3rd flash detector location at exactly 1/4 of distance from the back of your train to the front… at exactly the spot where the flash meets the back of the caboose of the passing train.  YOUR clocks measure the flash at 12:00:00.75 PM (3/4 of a second past noon) when the light hits the back of the other train.  Several things to note:

  1. From your perspective, light has only traveled 3/4 of a light second (225,000 km).
  2. Only 3/4 of a second of time has passed!
  3. You perceive the origin of the flash as coming from the front of your train.
  4. The other train has measured a full second of time passing.
  5. The other train has measured that the light traveled a full light second (300,000 km).

You and the other train are disagreeing on both time and distance.  But, you’re both right!  Time and distance are truly relative… hence the term Relativity!

Now, let’s look at it from the perspective of passengers on the other train:

  • When your two trains are perfectly beside each other as YOUR train is racing backwards, there’s a flash of light, just outside and to the left of the front engine car.
  • The light travels a full 300,000 km to reach the back of their train.
  • One full second has passed and their perfect clocks will prove that.
  • While the light is traveling to the back of their car, YOUR train is moving backwards at 50% c and when the light reaches the back of their train, the back of their train is just now meeting up with your 3rd flash detector 1/4 of the way from the back of your train.
  • THEIR clocks have correctly determined that a full second of time has passed and that the light has traveled a full 300,000 km.
  • The light continues racing toward the back of your train as your train continues racing in the same direction as the light is traveling, but at 1/2 light speed.  Eventually the light catches up and meets the back of YOUR train.
  • The clocks on the other train correctly measure that light had to travel much more than 300,000 km to reach the back of YOUR train and that MUCH MORE than a second passed for the light to traverse the full length of YOUR train!

Whose measurements are correct?  They BOTH are!  Time and length are relative.  This disagreement in time is called, Time Dilation and it’s a real and measureable phenomenon!  In fact, it’s so real, that much of our technology works because of it.  Nuclear bombs wouldn’t work if this time dilation didn’t happen.  Nuclear energy wouldn’t work.  Our GPS satellites are traveling at roughly 4.6 miles per second.  That’s fast enough that the incredibly precise clocks on board, necessary to triangulate your position on Earth, would get out of sync with clocks on the ground because of the time dilation.  Because of this, the scientists that designed the GPS satellites had to change the speed of the clocks on board the satellites so they’d stay synchronized with the clocks on the ground!

Congratulations!  You now understand Einstein’s Theory of Special Relativity.  Check back later for Part III in my series to discuss Einstein’s Theory of General Relativity which deals with space and time distortions due to gravity.  This will be an equally strange section.  We’ll bring up black holes and why they exist and all the fun stuff you can do with them, like spaghettifying an astronaut falling into one, to name just a few.

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