## Relativity – Part I: Why is Relativity Exciting to Study?

2015 is the 100th anniversary of Einstein’s general theory of relativity.  In particular, on November 25, 1915, Einstein published the gravitational field equations of general relativity.  Ten years prior, in 1905, Einstein published his special theory of relativity.  To celebrate the 100th anniversary I’ll be writing a series of posts on special and general relativity.  These posts are based on a workshop I gave on special relativity for K-12 instructors this summer (you can find a link to the activities here.
The question running through you head right now is probably ‘what is the difference between special and general relativity?’  What’s so ‘special’ about special relativity?  Special relativity relates to a specific case (or special case in science-speak).  The special theory only deals with objects moving in straight lines at constant velocity with no external forces acting on the objects.  Although this may sound to be limited, the conclusions you can draw from this specific case are mind-boggling.  In particular special relativity requires us to rethink our notions of what space and time represent.  We’ll find that special relativity requires that we think of space and time as being a single thing called spacetime (but that is for a later post).  General relativity doesn’t place any limitations on how the objects or moving or what forces are present so it is more general than the special case.  General relativity tells us what the geometry  of spacetime looks like.  Mass actually bends spacetime, which results in the gravitational force

Spacetime curvature“. Licensed under CC BY-SA 3.0 via Commons.

## Conclusions of Relativity

These conclusions are loosely stated and may not be completely correct, but they at least convey the broad ideas.  In later posts I’ll discuss what is wrong with some of these statements.  Hopefully they will give you a flavor for what the theories of relativity say.

### Special Relativity

1) Moving clocks run slow (time goes more slowly for moving objects)
2) Moving objects are shorter along the direction of motion
3) No objects can move faster than the speed of light
4) Mass and energy are equivalent
5) Fast moving objects gain mass
6) Moving electric fields can look like magnetic fields and moving magnetic fields can look like electric fields

### General Relativity

1) Mass of objects bends spacetime, which is results in the gravitational force
2) Gravity causes time to move slower
3) Since masses bend spacetime, the path of light will bend near large masses
4) If an object is massive enough, light can be trapped near the massive object (black holes)

## Why is Relativity Interesting?

### GPS

The most common reason given for why relativity is relevant is the global positions system (GPS) used by our phones and cars to help us navigate.  Global positioning depends on our phone receiving a time-stamped signal from several orbiting satellites and, based on the differences in travel times, determining where we are relative to the satellites.  I’ll give you a simplistic idea of how GPS works to show why times are so important.  Imagine your phone gets two time signals from different satellites that differ by 1 microsecond (a thousandth thousandth of a second).  This tells your phone that you are 1 microsecond closer to one satellite than the other.  Since light travels at a constant speed of $3 \times 10^8$ meters per second so you’d be $(3\times 10^8\ m/s) (1 \text{ microsecond}) = 300\ m)$ This doesn’t tell you exactly where you are but, since the satellite positions relative to each other are known, it does give you are range of positions.  If your phone can get a time signal from two other satellites it can tell you where you are located (For the mathematically inclined, four satellites are needed to determine the four unknown quantities, x-position, y-position, z-position, and time.  If you have a highly-accurate atomic clock handy you would only need three satellites).  This is why accurate times are so crucial to GPS – if your clock is off by a microsecond your position will be off by $300\ m$ (approximately three football field lengths), which would cause trouble if you are trying to navigate in a dense city.  Since the satellites are orbiting and moving quickly, special relativity says that a phone on Earth will see the satellite clocks running slow relative to a clock on the Earth.  General relativity says that since the satellites are far from the surface of the Earth, the gravitational force is less so the satellite clocks run faster than clocks on the surface of the Earth. Both of these effects need to be calculated to give accurate position readings.  It turns out that the effects of general relativity are much larger than the effects of special relativity.  General relativity predicts satellites will get ahead of ground-based clocks by 45 microseconds each day but special relativity predicts a delay of 7 microseconds each day1.

### Electromagnets

You can explain how electromagnets and generators work using relativity.  I’ll explain more in a later post but relativity brings the electric and magnetic forces together in a similar way to how relativity brings space and time together.

### Color of Gold and Why Mercury is Liquid at Room Temperature

For heavier elements on the periodic table, the fact that particles masses increase as velocities increase starts to play a noticeable effect.  The electrons near the nucleus have average speeds that are a significant fraction of the speed of light (e.g. for mercury, the inner-most electron has an average radial speed of 58% the speed of light) so the mass of these electrons increase as a result.  The larger masses result in the orbits of the electrons being smaller, which affects how the atoms reflect light (e.g. the color of gold) or how the atoms interact with each other (e.g. why mercury remains liquid at room temperature)2.

### Blackholes

Face it, black holes are awesome!  Something that bends light and time is fun to think about.  There is still a lot we don’t know about black holes, such as what happens inside black holes (although Interstellar seems to indicate there is a giant library inside) and many they are an exciting area of theoretical research.

### Gateway to Mathematical Models of Physics

Here is what I consider the most exciting aspect of special relativity and this is what motivated me to write this series of posts.  With a knowledge of the Pythagorean theorem and a little algebra you can derive the results that show space and time become intertwined, that how we think of distance and time is not compatible with the way the theory predicts (and experiments support).  Given how mind-bending the results are, I think the mathematics involved are relatively easy to grasp.  Usually the mathematics associated with many theories ( quantum mechanics comes to mind) are fairly involved and go beyond what most folks pick up in high school or college math classes.  I’ll devote the next few posts to exploring how the conclusions of special relativity can be derived from two simple assumptions.  After that I’ll talk about general relativity.

#### Footnotes

1.100 Years of General Relativity at Nasa.gov
2. Why is Mercury a Liquid or Why Do Relativistic Effects Not Get into Chemistry Textbooks on Researchgate.net