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# It's All Relative

Posted by

**Akano**, in Math/Physics Mar 22 2012 · 156 viewsmath physics Einstein relativity

**Being a physics grad student has seen me be in quite the scientific mood lately, hasn't it? Well, unfortunately, I still don't have a new comic made (I'm sorry, everyone! ><), but I do have another idea for a blog entry. Last week, Pi day (March 14) marked Einstein's 133**

According to the laws of physics laid down by Sir Isaac Newton, all non-accelerating observers witness the same laws of physics. This included an idea of spontaneity, the idea that someone traveling on the highway at 60 mph would witness an event occur at the exact same time as someone who was just sitting on the side of the highway at rest. The transformation from a reference frame in motion to one at rest for Newtonian physics is known as a Galilean transformation, where

However, during the 19

This brought about a dilemma: is Maxwell's new electromagnetic theory wrong? Or does Newtonian mechanics need some slight revision? This is where Einstein comes in. He noticed the work of another physicist, Lorentz, who had worked on some new transformations that not only caused space to shift based on reference frames moving relative to each other, but also shifted time. Einstein realized that if light had the same speed in all non-accelerating reference frames, then objects moving faster experienced time differently than those that moved slower. This would come to be known as the Special Theory of Relativity.

How does this make sense? Well, if you have some speed that must remain constant no matter how fast one is traveling, you need time to shift in addition to shifting space to convert between both reference frames, since speed is the change in distance over the amount of time that displacement took place. If you have two reference frames with some relative speed between them, the only way to shift your coordinates from one to another and preserve the speed of light is if both frames experience their positions and times differently. This means that, if something moves fast enough, a journey will take less time in one frame than the other. Special relativity says that moving clocks progress more slowly than clocks at rest, so someone traveling in a rocket at a speed comparable to the speed of light will find that the journey took less time than someone who had been anticipating his arrival at rest. This also means that if someone left Earth in a rocket traveling near the speed of light and came back ten years later would not have aged ten years, but would be younger than someone who was his/her age before his journey took place. Weird, huh?

If you think this is crazy or impossible, there have been experiments done (and are still going) to try to confirm/reject the ideas of special relativity, and they all seem to support it. There's another relativity at play as well known as general relativity, which states that gravitational fields affect spacetime (the combination of space and time into one geometry). General relativity says that the higher up you are in a gravitational field, the faster clocks run (time speeds up). A proof of this theory is GPS; the satellites that help find your position by GPS are all higher up in Earth's gravitational field than we are, and thus their clocks run faster than those on Earth's surface. If general relativity weren't considered in the calculations to figure out where you are on Earth, your GPS would be off by miles.

^{rd}birthday, and since my Classical Mechanics course is covering the Special Theory of Relativity, I thought I'd try to cover the basic ideas in blog form.According to the laws of physics laid down by Sir Isaac Newton, all non-accelerating observers witness the same laws of physics. This included an idea of spontaneity, the idea that someone traveling on the highway at 60 mph would witness an event occur at the exact same time as someone who was just sitting on the side of the highway at rest. The transformation from a reference frame in motion to one at rest for Newtonian physics is known as a Galilean transformation, where

*x*is shifted by*-vt*, or minus the velocity times time. Under such transformations, laws of physics (like Newton's second law,*F = ma*, remain invariant (don't change).However, during the 19

^{th}century, a man by the name James Clerk Maxwell formulated a handful of equations, known now as Maxwell's equations, that outline a theory known as electromagnetic theory. Of the many new insights this theory gleaned (among these the ability to generate electricity for power which every BZP member uses) one was that light is composed of oscillating electric and magnetic fields; light is an electromagnetic wave. By using his newly invented equations, Maxwell discovered what the speed of light was by formulating a wave equation. When his equations are used to describe electromagnetism, the speed of light is shown to be the same regardless of reference frame; in other words, someone traveling near the speed of light (as long as they weren't accelerating) would see light travel at the same speed as someone who was at rest. According to Newton's laws, this didn't make sense! If you're in your car on the highway and traveling at 60 mph while another car in the lane next to you is traveling at 65 mph, you don't see the other car moving at 65 mph; relative to you, the other car moves at 5 mph. The reason that light is different is because a different theory governs its physics.This brought about a dilemma: is Maxwell's new electromagnetic theory wrong? Or does Newtonian mechanics need some slight revision? This is where Einstein comes in. He noticed the work of another physicist, Lorentz, who had worked on some new transformations that not only caused space to shift based on reference frames moving relative to each other, but also shifted time. Einstein realized that if light had the same speed in all non-accelerating reference frames, then objects moving faster experienced time differently than those that moved slower. This would come to be known as the Special Theory of Relativity.

How does this make sense? Well, if you have some speed that must remain constant no matter how fast one is traveling, you need time to shift in addition to shifting space to convert between both reference frames, since speed is the change in distance over the amount of time that displacement took place. If you have two reference frames with some relative speed between them, the only way to shift your coordinates from one to another and preserve the speed of light is if both frames experience their positions and times differently. This means that, if something moves fast enough, a journey will take less time in one frame than the other. Special relativity says that moving clocks progress more slowly than clocks at rest, so someone traveling in a rocket at a speed comparable to the speed of light will find that the journey took less time than someone who had been anticipating his arrival at rest. This also means that if someone left Earth in a rocket traveling near the speed of light and came back ten years later would not have aged ten years, but would be younger than someone who was his/her age before his journey took place. Weird, huh?

If you think this is crazy or impossible, there have been experiments done (and are still going) to try to confirm/reject the ideas of special relativity, and they all seem to support it. There's another relativity at play as well known as general relativity, which states that gravitational fields affect spacetime (the combination of space and time into one geometry). General relativity says that the higher up you are in a gravitational field, the faster clocks run (time speeds up). A proof of this theory is GPS; the satellites that help find your position by GPS are all higher up in Earth's gravitational field than we are, and thus their clocks run faster than those on Earth's surface. If general relativity weren't considered in the calculations to figure out where you are on Earth, your GPS would be off by miles.

I always found the subject so fascinating, it's part of why Optics is my field of choice. (that and high-energy laz0rs, but I digress).

When I first learned about relativity, it was through the "light clock" explanation. Where you have a cylinder 3.0 X 10

^{8}meters tall, and a beam of light bounces back and forth, marking a second at each contact. Then as the clock moves the light traces a sawtooth path, and using Pythagorean theorem, you could tell the new distance, along with the new time for the clock.I always loved that explanation. It just seems so intuitive and counter-intuitive.