﻿ relativity

# Relativity

Einstein's theory of relativity describes a universe where space and time are not constant, rather they are interconnected dimensions governed by the fact that the speed of light is constant, regardless of the observer.

For the spacial part of spacetime, we consider 3-dimensional space (3-D). For 1-D space, you only need one value to find the position of an object, like the ant in the diagram. For 2-D space, you need two values, an x and a y, to find the position of the ant. Fro 3-D space, you need 3 coordinates for a location.

For 4-D space, you also need to know when, so you need a fourth dimension, time.

But there is more to it than that. Space and time are connected in such a way that the speed of light is constant, no matter who is observing it and how fast they are moving.

Consider the diagrams of a skateboarder, Joe. When Joe is standing still, he can throw a ball at say, 5 m/s. He can ride his skateboard at 2 m/s. When he throws the ball while riding, to us it looks like the ball is moving at 7 m/s. To Joe, it looks like the ball is moving at 5 m/s and we are all moving backward at 2 m/s.

This kind of spatial relationship is called a Galilean transform.

Now consider if Joe was shining a flashlight instead of throwing a ball. Light travels at 300 million m/s (c). When Joe shines the flashlight while riding, he sees the light traveling at 300 million m/s and us moving backward at 2 m/s.

We also see the light moving at 300 million m/s, not 300 million + 2 m/s.

Even if Joe's skateboard was traveling at 200 million m/s, we would still see the light from his flashlight traveling at the speed of light, c.

If this seems perplexing to you, it is a good sign that you are thinking deeply.

When we talk about spacetime, we are considering 4-D, three spatial dimensions and one time dimension such that the speed of light is the same for all observers. Time and space are not absolute, the speed of light is. In other words, everyone does not agree on the rate of change of time or space, but everyone does agree on how fast light travels.

These two young women are sisters, but if they were identical twins, one could age faster than the other, according to special relativity.

One common illustration of special relativity is called the "twin paradox." Consider that you have an identical twin, and that you get into a spaceship traveling very fast, say at least half the speed of light. You travel quite a ways and then return home. You will find that you have aged less than your twin. The farther and faster you went, the bigger the difference in age.

The twin paradox is a thought experiment, because we don't have spaceships that can travel that fast and that far. But there are real experiments that have proven that special relativity is true.

For example, in the Hafele-Keating experiment very precise atomic clocks were placed on airliners and flown twice around the world at high speed, and then compared with clocks that stayed at rest on the ground. Afterward, the clocks were compared and the flying clocks showed that less time had passed, the difference that was predicted by the theory of special relativity.

It is perhaps important to note that there are two ways to use the word "theory." In one meaning, a theory is unproven conjecture. In the second usage, a theory is a body of interconnected knowledge. When we talk about the theory of relativity, we are talking about scientific fact that has been proven.

# General relativity

The reason special relativity is called "special" is because it is a special case of a broader theory. It is special because there is no gravity involved.

General relativity (GR) includes gravity in spacetime. Massive objects create curvature in spacetime. The curvature of spacetime determines how objects move.

Newton's laws describe orbital motion as a result of gravitational forces acting between massive objects. In general relativity, the concept of force is replaced with the concept of curved spacetime. A satellite moving around a massive planet is traveling the simplest possible path in curved spacetime.

This video is from the Denver Museum of Nature and Science demonstrates the concept of an object in motion in curved spacetime. This is a four-part video sequence, also illustrating concepts surrounding comets and black holes.

In Newtonian mechanics, light does not follow a curved path past a massive object. Light doesn't have mass, so it would not feel a force, and would travel in a straight line past a star or other gravitating object.

In General relativity, light takes a curved path past a star, because spacetime is curved. The image above from the Hubble Space Telescope shows a real effect of general relativity, called an Einstein ring. The bright object in the center is a large, massive, elliptical galaxy. The gravity of the elliptical galaxy creates curvature in spacetime that bends the light coming from a spiral galaxy far behind it. The light from the spiral galaxy is smeared into a ring.

This smearing effect is an example of gravity lensing. The curving of spacetime acts like a lens, bending the light rays.

So if relativity has been shown to be correct, does that mean we scrap Newtonian mechanics and use relativity to calculate everything?

No. The effects of special relativity are small unless the speed is high, a considerable fraction of the speed of light. The effects of general relativity are small unless there is a very dense massive object nearby.

If you are sending a probe to Jupiter, Newtonian mechanics works well enough. If you are modeling the gravity waves emitted from a merging pair of binary black holes, you absolutely need to use GR.

This computer simulation illustrates the curvature of spacetime resulting from the merger of a binary pair of black holes. The black holes in the simulation have different masses, so the black regions have different sizes. These black regions are inside the event horizons of the black holes.

An event horizon of a black hole is the radius where the escape speed equals the speed of light. That means no light can emanate from inside the event horizon, and it looks completely black.

Around the black holes, the curvature of spacetime distorts the light from behind them. The light from the stars behind the black holes is smeared out due to gravity lensing.

# Verification of general relativity

A major recent advance in astronomy involves the detection of gravitational waves at the Laser Interferometer Gravitational-Wave Observatory (LIGO). This small building houses a very powerful laser that emits pulses along the long tubes extending at right angles. The laser beams reflect from mirrors at the ends of the tubes, allowing for extremely precise measurement of distance in two directions. When a gravity wave passes through the observatory, the laser is used to measure the spacetime distortion of the wave.

Twin observatories detected the first gravity wave signature of a binary black hole merger on August 14, 2017. Numerous similar events have been recorded since then, verifying that gravity waves carry information across spacetime.

The detection of gravity waves is important in that it gives us another method for observing events in the universe. Previously, the only information we had about systems outside our own Solar system came from analyzing light.

The detection of gravity waves was not the first verification of the theory of general relativity. Bending of starlight due to a gravitational field was first observed in 1919 by Arthur Eddington and his colleagues during a total eclipse of the sun with simultaneous observations made by expeditions in West Africa and Brazil.

The Moon between the Earth and Sun darkened the Sun during the eclipse. This made it possible to see light from a star in the Hyades cluster which was actually behind the Sun. Bending of the starlight due to gravity lensing of the Sun caused the star to be visible.

If the effects of general relativity are so small, why should we care? How could they impact us in our everyday lives?

One place where we need to take relativity into account is in the Global Positioning System (GPS). GPS satellites orbit Earth at considerable speed, and because they have high altitude, the strength of the gravitational field is less than on Earth's surface.

The high speed means that time passes a bit more slowly than it does for an observer on Earth. The high altitude means time passes a bit more quickly than it does on Earth. The two effects counteract but do not cancel each other. Both effects of relativity have to be accounted for in the clocks aboard the satellites, otherwise they get out of sync with clocks on the Earth's surface.