I have not posted much lately. I should have been. Instead I've been reading other physics blogs. Some of this blogs are dudes arguing about theories. They also post news and comments on recent topics.
My personal favorite is the Lubos Motl and Peter Woit duo. They have a nice discussion. Peter Woit is a professor at Columbia University how is famous for his criticism to string theory. Lubos is the opposite of Petes, he is also a professor at Harvard.
Other blogs I have been reading included Cosmic Variance. You can get a pretty good idea of what is going on in theoretical physics right now (or for the past 2-3 years) by checking this blogs.
29 May 2006
26 May 2006
Free time...
Now that I am over with classes and moving things from my apartment back to my house, I am enjoying some real free time. Feels kind of weird, but good. I have decided to continue working on an old mission. When my Intro. to Relativity course was over, the professor asked me and other students to type the notes of the class in a nice LaTeX file. So I will be working on that until I fly to Stanford University for a refreshing summer internship at SLAC.
21 May 2006
29 April 2006
The flavor of Special Relativity
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.
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.
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.
Subscribe to:
Posts (Atom)