At the heart of Special Relativity lies a simple idea: Physical laws are the same in any set of frames of reference that are in relative uniform motion.
If you take the constancy of the speed of light as a physical law, then lots of funky effects appear: Time Dilation, Length Contraction, Relative Simultaneity, etc. Light having a constant speed, independent of the frame of reference you measure it, is sometimes called the second postulate of the Special Theory of Relativity.
Frame of references are important and are not introduce for construction. When we talk about motion, we need a reference frame to describe the motion.
Take for example riding a train. When the train is arriving with passengers, from the station you see the train approaching. You are standing still, and you know this fact because you do not feel any other force (except our good old friend gravity). We can say that with respect of the station, the train is moving and changing its position.
Now from one of the passenger's point of view, he/she sees the station approaching. Our passenger is standing still in the train, in rest with respect to it (since the passenger is moving along with the train), and those not feel any force before the train starts to decelerate. This is one of those fancy trains...
Both points of view, whether the train or station were approaching are valid. Besides motion, relativity tells us that physics is the same in every frame of reference.
Speed is a measure of how positions changes along time. Galilean relativity assures us that according to our relative velocity, objects may be seen at rest (relative velocity is zero) or in motion (non-zero relative velocity). Since the speed of light is constant, then it has to be measure the same in every frame of reference relative to light. Hence, space and time have to arrange themselves in a certain way so that in any frame the speed of light is the same constant.
I consider this the thesis of Special Relativity: the study of space-time as a "dynamical" entity.
29 April 2006
Time, 2
Of all the many interpretations I've heard of time, the one I remember the most is the story about a famous graffiti that read "Time is God's answer to prevent all events happening simultaneously." This phrase made me think for some time. But I cannot take much from it. It is kind of obvious, but we must also take into consideration the relativity of simultaneity introduce by Special Relativity.
Other views of time I found were in Stephen Hawking's A Brief History of Time. As I recall, Hawking attempts to give time a vector like behavior (direction). He states three ways to measure the "directionality" of time: psychologically (biological), thermodynamically and cosmologically.
The psychological direction of time is the direction we see time pass by. People are born, grow up and get older; not the other way around.
The laws of thermodynamics say that states evolve to higher entropy states. This is viewed when ice cubes melt into water and not the other way around (you have to put water in a cold place to freeze it). Another example is the traditional breaking of an egg. If you let an egg fall to the floor it will break into pieces. You can wait in front of it and will never see the egg coming back together. This is the sense processes take place, and one can associate time to follow along this direction.
The third view of time's direction has to do cosmological observations. If you follow the trajectories of galaxies, you'll find that all of start their trek through space from a single point. The direction of cosmological evolution is then chosen as the chronological order of events in the universe. This analysis may imply the existence of the "origin" of time, a point where time began ticking.
All of this views just assign an orientation to time according to physical observations.
Other views of time I found were in Stephen Hawking's A Brief History of Time. As I recall, Hawking attempts to give time a vector like behavior (direction). He states three ways to measure the "directionality" of time: psychologically (biological), thermodynamically and cosmologically.
The psychological direction of time is the direction we see time pass by. People are born, grow up and get older; not the other way around.
The laws of thermodynamics say that states evolve to higher entropy states. This is viewed when ice cubes melt into water and not the other way around (you have to put water in a cold place to freeze it). Another example is the traditional breaking of an egg. If you let an egg fall to the floor it will break into pieces. You can wait in front of it and will never see the egg coming back together. This is the sense processes take place, and one can associate time to follow along this direction.
The third view of time's direction has to do cosmological observations. If you follow the trajectories of galaxies, you'll find that all of start their trek through space from a single point. The direction of cosmological evolution is then chosen as the chronological order of events in the universe. This analysis may imply the existence of the "origin" of time, a point where time began ticking.
All of this views just assign an orientation to time according to physical observations.
28 April 2006
Time, 1
I got a magazine from Scientific American titled A Matter of Time. It is about time and how it is view in physical theories, the role, the origin of it, the meaning, etc.
I have heard many interpretations of "what" time is? I'll try to discuss them some other time, because I am very tired tonight.
I have heard many interpretations of "what" time is? I'll try to discuss them some other time, because I am very tired tonight.
Back, again...
It has been quite a while since I have posted something. Not that I did not had anything to say, on the contrary...
17 April 2006
Back
Vacations are finally over. Thank God!
Now my last 15 days as an undergraduate students... Yippieee!!
Now my last 15 days as an undergraduate students... Yippieee!!
10 April 2006
BTW
I forgot to mention. I won a physics award in the Department of Physics. To the students by the students. My award was called "Premio Algebrita" which means little algebra. This is a reference to derivations and how algebra makes equation prettier. The award was given to "the person that solves everything".
It is funny cuz I felt very bad getting this award. The other people nominated included two professors and a 16 year old boy who is also graduating this year.
I guess I help a lot. I do it for the love of science. Thank you!
It is funny cuz I felt very bad getting this award. The other people nominated included two professors and a 16 year old boy who is also graduating this year.
I guess I help a lot. I do it for the love of science. Thank you!
Vacation
I guess I have some free time finally. I have been able to sleep and rest. Here in Puerto Rico it is customary to have Holy Week free. The Monday after Easter Sunday will be free too, so that gives a grand total of 10 days of happiness! When I return to school I will have approximately 15 days of class left. Wow, I still can not believe that in less than a month I'll graduate and have a Bachelor Degree in Theoretical Physics. Summer is going to be awesome.
Then Stony Brook...
Then Stony Brook...
02 April 2006
World-Sheet
I have found some free time lately. The best way to relax is to read some String Theory. I have the textbook A First Course in String Theory by Barton Zwiebach. This book is so easy to read. Someone with some background in Lagrangian Dynamics and Relativity can read it and take lots of things out. I am up to chapter 6 on Relativistic Strings.
Basically point particles trace out a curve in spacetime called a world-line. The action of the particle can be written in terms of a line element. Since strings are one dimensional objects, the classical action of a string can be written in terms of the proper area of the surface they trace in spacetime. This surface is called the world-sheet. The classical relativistic string action is called the Nambu-Goto String Action.
It is so cool to learn about this. The only thing that I find scary is a bit of lack of motivation. I guess real motivations will come when one meet QCD and its shortcomings.
Basically point particles trace out a curve in spacetime called a world-line. The action of the particle can be written in terms of a line element. Since strings are one dimensional objects, the classical action of a string can be written in terms of the proper area of the surface they trace in spacetime. This surface is called the world-sheet. The classical relativistic string action is called the Nambu-Goto String Action.
It is so cool to learn about this. The only thing that I find scary is a bit of lack of motivation. I guess real motivations will come when one meet QCD and its shortcomings.
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