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Philosophy in Physics

by Eric Hall

May 11, 2013

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Donate The last week of the spring semester at the community college where I teach is next week. I had my last lecture session that covered new material on Thursday. The last topic discussed in my "Elements of Physics" class was that of special relativity. I am always excited to discuss this topic with students, because it can be difficult to understand, yet beautifully simple and elegant. It almost gains aphilosophicalquality in the implications coming out of measuring spacetime.

Special relativity is based on two concepts known as Einstein's postulates. There are various ways of restating these two points, but an example of a good summary would be:
  1. Relativity Principle: The laws of nature are the same in all inertial reference frames.

  2. The speed of light in a vacuum is the same in all inertial frames.

Although the Earth is not a perfect inertial reference frame because it is constantly being accelerated (for circular motion), it is a good approximation. The small variation in the measurement of normal physical interactions (such as Newton's Laws of Motion) isunnoticeable, and makes up a very small amount of the error. Unless specifically looking for these variations, normal lab conditions will produce much larger measurement errors, drowning out any small variation from an inertial reference frame.

The interesting consequences of special relativity come about when objects are moving at a high rate of speed relative to one another. Two things happen in ratio to one another. First, the dimension that is in the direction of the motion actually shrinks. Yes, it gets shorter. For example, if you were in a spaceship traveling at 0.8c (80% of the speed of light) towards Alpha Centauri it would appear to be about 2.6 light-years away as the spaceship went past the Earth. From the Earth, we measure that same distance to be about 4.3 light-years. To an observer on the Earth, it would appear the spaceship is actually smaller in length than it was when at rest on the Earth.

The second consequence is that of timedilation. When someone on the spaceship looks at the clocks on the Earth, it would appear the Earth clocks are running slower. However, to an observer on the Earth, the clocks on the spaceship appear to run slower. Yet, if someone were to take a trip on a rocket away from Earth, and then return, the person who took the rocket trip will have indeed aged less. It is a pretty amazing concept. The paradox is solved because the twin on the Earth stays in its reference frame, while the twin on the rocket changes reference frames by going through the acceleration anddeceleration of changing direction. The details can easily be found by searching for the Twin Paradox.

Relativity is interesting in how it sets the speed limit on the universe. Even if two rocket ships leave the Earth in opposite directions each going 0.6c, they do not actually move a total of 1.2c away from each other. Their relative speed to one another would be about 0.88c. Relativity also brings out the famous equation E=mc2, which explains how nuclear reactions give such large amounts of energy. Relativity is used to calculate the clock differences on satellites such as GPS, to make sure they stay synchronized with Earth and continue to provide accurate locations.

One other concept discussed within relativity is the idea ofsimultaneity. This is the idea that events that occur at the same time in one reference frame may not be at the same time in another frame. The concept can be explained by thinking of a flash of light happening at the center of a fast moving rocket. To a person in the rocket, the light hits the front and back of the rocket at the same time. But to an observer on the Earth watching the rocket pass by, the light would hit the back of the rocket first.

I am certainly glossing over many details in this post forbrevity, and the basic ideas of special (and general) relativity are well covered on the web as well as in any physics textbook. What I find interesting is how discussing this topic always makes me feel a bitphilosophical. On an absurd level, because we cannot occupy the same space - meaning each person's eyes, ears, etc., along with their brains, cannot be in the same exact point in space. This means because the Earth is accelerating, none of us see things at the same time. This means we all see events a little bit differently than anyone else.

I don't want people to think of this too literally. If two people are standing next to each other, this difference would not bemeasurable. But the reality is because space and time are intertwined as dimensions in which we live, we all have our own individual view of spacetime. I don't mean this to an absurd level, but rather I like to say it is physics which brings about our individual point of view - and Einstein proved this!

The science of relativity is really beautiful. It shows us that space and time are parts of the same universe in which we live. It can bring about a funphilosophicaldiscussion, but also has practical uses in moderntechnology.I enjoy the topic - discussing how time and length actually change based on relative velocity.It is also a great topic with which to end the semester, as it leaves students with acuriosityabout science which drives them to continue their study - which is the best celebration of science I can hope for!

by Eric Hall

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