Quick, Dirty Relativity Review

Part of the What Time? series, an exploration in science fiction.

Relativity

Size is relative. Speed is relative. In my story, “Dunston Monster,” some of the characters refer to Sebastian as a giant while others just think he’s very big. Comparing to a tree, Sebastian is short. Scientist measure everything relative to something. A car travels 70 km in an hour (70 km/h or average 1200 m/s.)

Relative Measurement

Distance measured relative to a standard such as a meter (m.)
Velocity measured relative to distance per time standard: m/s.
Acceleration measured relative to m/s/s or m/s²

A train travels 40 km/h and Jason walks in the aisle towards the front of the train. Of course, we assume the train travels 40 km/h relative to the ground. If Jason walks at 4 km/h relative to the train, then Jason moves at 44 km/h relative to the ground. Simple, right?

Theory of Relativity

Actually, two theories, Special and General. We will deal with the Special Theory of Relativity by Einstein which generalizes Galileo’s relativity principal stating that the laws of physics are the same in all inertial frames of reference.

Brief History Lesson

Scientists wanted to know how fast light travels. The problem: relative to what? Earth zips around the sun, and the sun speeds through the universe. Someone suggested a solution: measure light from a star in the same direction as Earth travels then in the opposing direction. Much like Jason on the train, some arithmetic should leave us the answer of light traveling relative to some “ether.”

It didn’t work out. In every direction scientists measured the same velocity of light coming from distant stars. Scientists scratched their heads.

Einstein suggested a logical conclusion: time is relative to the observer. No matter how the observer travels, the observer will always measure the same speed of light.

Proof of Time Relativity

Using atomic clocks, scientists have compared measurements between an observer on the ground and an observer traveling around the globe on the airplane. The clocks disagreed. The larger the difference in motion, the more the clocks disagree.

Time is Relative

Space-Time Light Cone

In our exploration of time, we should keep this mind. Time is relative to the observer. Standing on Earth, we may safely assume our observations are the same. Even traveling in airplanes, the differences are so tiny that we’ll never notice. Traveling in spaceships is a different story.

Now we may interpret time as a 4th dimension to our spatial dimensions. Since imagining four dimensions is a challenge, we can draw a diagram using only one of the spatial dimensions on one access and time on the other. Apply it to the other two spatial dimensions. We end up with a light cone defining future, past, and elsewhere.

We can’t reach elsewhere using normal traveling means. Why? The Theory of Relativity gives us the equation, E = mc² where E is energy, m is mass, and c is the speed of light. The problem is accelerating mass to the speed of light requires infinite energy. Our future travelers will need to find another way to reach elsewhere, or be patient and reach

Light Cone for Mars and Earth

the same spatial location inside the future cone.

What happens now? Let’s say a robot on Mars breaks and sends a distress signal. Now for the robot is different than now for the observers on Earth. Seen in the diagram, the observers on Earth don’t find out about the problem until 20 minutes later relative to the robot. The present is relative.

Fun Time Facts

Light from the sun takes about 8 minutes to reach Earth.
Light from the next closest star takes 4 years.
Chatting with an astronaut in Saturn orbit requires over 2 hours to hear the reply.