The Theory of Relativity… for idiots!

Theory of relativity for idiots? Maybe written by an idiot…

Anyway, a week or so ago, scientists discovered a neutrino that surpassed the speed of light, thoroughly rattling the scientific world. But what does it mean? Why is this discovery so significant? What is so special about the speed of light and the theory of relativity anyway? Well allow me to explain. A bit of a warning… I love astrophysics so I might go a bit off topic or go off on random tangents but I’ll summarize it at the end!

Although the theory of relativity is most frequently attributed to scientist Albert Einstein, its history subtends deeper into time. The first known person to theorize about relativity was Galileo Galilei. Galileo removed the distinction between moving and stationary observers, arguing that people on Earth could not distinguish whether or not they were at rest if they were moving with the rotation of the Earth each day. He used a cannonball as an example, saying that a cannonball would land at the base of the mast whether the ship is moving steadily through the ocean or if the ship was at rest at a dock. Even if the falling ball is observed, people on the boat cannot tell if they are at rest or if they are moving with the ship. They cannot distinguish their state from the rest of the ship by observing motion that takes places within the reference frame of the ship. In simpler terms, it means that a person can’t tell if the ship is moving or if it is at rest based on actions that happen on the ship itself. That person needs to observe the ship relative to its surrounding environment in order to determine this movement conclusively. This discovery was important! It meant that what we consider ‘normal’ on Earth might not be constant for other things in the universe.

Let’s try and apply this to daily life. We “see” things at the speed of light. When we look around, what we are seeing is a bunch of pictures traveling at the speed of light. Now imagine that you are running away from a picture of a clock at the speed of light. If you were to look back while running away, you would still see the same “picture.” You could do whatever you wanted while running and time would be moving for you, but “time” has stopped, at least, in a particular frame of reference. Time for us on Earth is vastly different than time for someone on another planet hurdling away in some other direction. Thus the importance of a reference frame.

Now let’s talk a little bit about space and time. In order to travel through space, one must travel through time. We do this pretty much every day; for instance, it takes three hours to drive from Calgary to Edmonton. We traveled through space by also traveling through time. The fourth dimension, time, is how we travel through the third dimension, space. But then where does the speed of light come into play?

Think of space as a y axis on a graph, and time as an x axis.

Imagine a car traveling East at 100 km/h



Now imagine the car moves slightly to the North

Even though the car is still going 100 km/h, it is no longer going 100 km/h in the East direction; this is because some of the speed is being used to go north as well. This analogy can be used to understand space and time. Everything in the universe is traveling through space (Y axis) and time (X axis), only instead of moving at 100 km/h, everything moves at the speed of light. The faster you go through space, the slower your progress through time. When you are standing still, you are traveling through time at maximum speed. If you reach maximum speed through space, you will make no progress in the time direction.

This isn’t just a bunch of mumbo-jumbo either; this has been proven empirically many times in the past! For instance, in 1971, four cesium atomic clocks were synchronized and flown on planes that circled the earth twice. The clocks were then compared with the clock at the US naval observatory. The time on the moving clocks differed from the time on this reference clock. Time somehow “disappeared” between the clocks! In another experiment, scientists dug a 1 km deep hole and stuck a clock at the bottom. Time at the bottom of the hole differed from time at the top!

Below is a link to a gif I made that should help explain where the “time” went. Remember the analogy I made about someone running away from a clock at the speed of light? This is a similar idea. A spaceship “runs away” from Planet A at half the speed of light to Point B. It flashes a light every six minutes. Time on the spaceship does not change, but people on Planet A do not see flashes every six minutes because the Spaceship is moving away at half the speed of light. The people on Planet A see flashes every 12 minutes. People at point B see the flashes every three minutes and vice versa when the spaceship turns around.Confused? Try and think back to Science 10 when you learned about the Doppler Effect. As a siren approaches you, its pitch increases, and as it travels away, the pitch decreases. For someone inside the emergency vehicle though, the pitch remains constant. Now try and apply that in terms of light waves:

So now you’re probably thinking, awesome! Wait… why can’t we travel faster than, or at the speed of light? We would be able to travel back in time right? Well simply put, you divide by zero. Remember the car graph from earlier? We can’t find the slope of a vertical line, you divide by zero. In slightly more complicated terms:

Where:

– t is the time measured by an observer relative to the moving frame

– to is the “proper time” measured by an observer who is at rest relative to the moving frame

– v is the speed of the reference frame that is moving

If one were to travel at the speed of light, v and c would be equal to each other, and thus equate to one. When this is plugged into the formula, the denominator equates to zero, and one cannot divide by zero.

Similarly, if v is greater than c, when divided, the resultant number would be greater than one. When inserted into the formula this number is subtracted by one and turns negative. One cannot square root a negative number.

Summary

• Galileo came up with relativity
• Time and space are relative, it’s not the same for everyone
• In order to travel through space you have to travel through time
• You travel through the time and space graph and the speed of light
• The faster you travel through space, the slower you travel through time and vice versa
• You can’t travel faster than, or at the speed of light

And now back to the neutrino traveling faster than the speed of light. What does it all mean? Well quite honestly it’s insanely complex and people far more qualified than myself are worrying about it. This neutrino traveled back in time… sort of. Here is one astrophysicist’s P.O.V.

“Again, this is very interesting and the experimenters were likely very very careful. Its also interesting (that MINOS/NuMi) seemed to measure the same phenomenon in 2007. However, its a very bold claim that largely invalidates one of our best theories. It also is a difference of only 50 ns. E.g., mismeasure the distance, distances signals propagate by 50 feet and you have your 50ns. (Remember the neutrino beam is traveling 454 miles, so that’s just a difference of 0.002%). Sync the time in your computers incorrectly? Calibrate when the beam left incorrectly, etc. I’m sure they are trying to very carefully control all these things, but its easy to introduce a subtle systematic error somewhere. Also, you have to realize that neutrinos are particularly difficult to detect particles (e.g., a single neutrino will travel through a light-year of lead with a 50% chance of interacting with the lead at some point; and 50% chance of not).”

Here is the scientific paper if any of you guys are interested:

http://arxiv.org/abs/1109.4897

Let me know if you like this astrophysics-y type stuff. I’ll post more! String theory is next on the docket. If you still don’t understand, check out this video:

[youtube 30KfPtHec4s]