Lesson 10: The Theory Of Special Relativity Part II

The Theory of

Special Relativity II

Time is not absolute.  You can no longer say one event happens before or after another.

The laws of physics are the same for everyone no matter where they are and as long as they are in uniform motion.  The speed of light is c in all reference frames. Everyone is going to measure time as c as long as they are moving in a straight line at a constant speed.  As we showed, this changes how we experience time in different frames of reference.  This is time dilation.  Again, you can no longer say one event happens before or after another.

As we discussed in the last lesson, the faster you move, the slower time elapses for you, but you need to be traveling at very fast speeds, like the speed of light (670,616,529 mph), to notice anything.

Time dilation has been proven to be a fact, and one of the first experiments to prove it involved Muons.

Muons are unstable subatomic particles of the same class as an electron but with a mass around 200 times greater. Muons make up much of the cosmic radiation reaching the earth’s surface.

These particles are radioactive and decay at a certain rate.  Therefore, since they have a definite rate of decay, they can be considered to be a clock.  It has been proven because muons move at high speeds close to the speed of light, they decay more slowly than they would at slower speeds. Everything fit perfectly with Einstein’s relativity calculations. The muons survived longer (aged slower) because they move at fast, crazy speeds close to the speed of light.

Experiments have also been done by using atomic clocks, which can measure very short time spans. They kept one clock on the ground and flew one around in a very fast jet airplane.  The clock in the plane slowed down when compared to the clock on the ground.  Less time passed on the clock in the plane.

Did you know because of relativity, time travel is possible?

To understand, you first need to know what a light year is.  A light year is the distance light travels in one year, which is about 6 trillion miles.  Remember, a light year is a unit of distance, not time.  If a star is 10 light years away from earth, it would take us 10 years to get to that star if we were traveling in a spaceship going the speed of light (670,616,529 mph).

Now let’s say on Earth we develop the technology to travel at half the speed of light, and we decide to travel to that star 10 light years away.  How long will the trip take?

We can figure this out with very simple elementary school math.

Time = Distance/Speed.

So, we take the distance of 10 light-years (remember, a light year is a unit of distance) and divide it by the speed of .5, the speed of light since we are moving at half (.5) the speed of light.  Our calculation gives us a time of 20 years, which makes absolutely perfect sense.

So, you get in the space ship and fly to a star 10 light years away at a speed half the speed of light. It will take double the time to get to the star, which is 20 years.  You make a round trip, and that will bring you back to earth in 40 years.

Here is where it gets wild.  The forty-year trip is from the view of the people on earth.  However, since you are moving very fast at half the speed of light, you are going to experience some time dilation. We won’t do the calculations, but from Einstein’s Special Relativity equations, we can determine the time to reach the star from your perspective will only be 17 years, so your round trip will be 34 years.  Everyone on earth will have aged 40 years while you will only have aged 34.

This is often called the twin paradox.  Take two twins.  Leave one on earth and send the second twin on the trip into space we just discussed. When the second twin returns to earth, he will find that he is now 6 years younger than his twin.  It is like he has traveled 6 years into the future.

But haven’t we been saying everything is relative? Couldn’t we say the earth was moving away from the ship at half the speed of light?  Yes, we can. So why can’t we say the twin on earth is younger?

This takes us back to motion.  Relativity only applies to things in uniform motion.  So, if you speed up, slow down, or change directions, you are no longer in uniform motion, and this is exactly what the twin in the spaceship did when returning home.

The twin on earth stayed in uniform motion the entire trip. The twin in the spaceship did not.  This is why the twins’ age at different rates.

But make it even wilder.  Let’s say the twin decides to go to a star 100 light years away, this time traveling at the speed of light. Traveling at the speed of light, the trip to the star and back will seem almost instantaneous. When the twin returns back to earth, 200 years will have passed on earth, but he will not have aged at all.  He will get to see what the earth is like 200 years from the time he left, but everyone on earth he knows will be dead.  

Think about this.  What if he goes to a star 1000 light years or 10,000 light years, or even 1,000,000 light years away?  There is no limit to how far he could go into the future.  However, he could never go back to the past.  Time travel is a one-way trip.

Okay, I know we’ve blown your mind this time, and we are going to keep doing that over and over again in this class.

Next lesson, we will continue discussing Special Relativity.  Do you think you can handle it?

Draw that picture.  Teach someone.