What is Special Relativity?
(This page still under construction)
Special Relativity (SR) or the Special Theory of Relativity (STR) explains the physics of space and time and the relationship between them.
A non-mathematical overview can be found at:
http://en.m.wikipedia.org/wiki/Introduction_to_special_relativity
A more detailed account can be found at:
http://en.m.wikipedia.org/wiki/Special_relativity
Galilean Relativity
Newton’s Laws of Motion will be the same whether you are sitting still on the platform of train station or sitting inside a train passing through the station at a uniform velocity.
Each person may consider themselves to be at rest and the rest ie the observer can consider themselves to be in a reference frame.
If I am moving towards you at 20 m/s and I throw a ball towards you at 10 m/s,
(a) how fast is the ball moving in my reference frame?
(b) how fast is the ball moving in your reference frame?
Inertial reference frames are reference frames where Newton’s Laws of Motion are valid. i.e. non-accelerating reference frames. There is no physics experiment you could do to prove that you were in a stationary lift or a lift moving up/down with constant velocity – Newton’s Laws would produce identical results.
No reference frames are better than any others they are just different. There is no such thing as stationary to the universe!
Einstein’s Principle of Relativity
Maxwell’s theory of electromagnetism was one of the greatest achievements of 19th century physics and with it came the prediction that light would travel at (approx.) 300 000 000 m/s.
This value is given the symbol c, and is now defined to be exactly 299 792 458 m/s.
At first it was assumed that this was with respect to the ether (assumed medium through which light would travel). But experiments were failing to find ether, it almost certainly didn’t exist.
So the propagation of light could be understood by considering electric fields changing and producing magnetic fields and vice-versa. But this would not happen if you were travelling at the speed of light. The fields would not be changing.
Einstein solved this paradox by realising it was not just the laws of mechanics that were the same, but all of the laws of physics were the same in all inertial reference frames.
Speed of Light
The consequence of this assumption is then the paradoxical one that the speed of light must be the same in all inertial reference frames.
I am moving towards you at half the speed of light. I shine a beam of light (torch) towards you,
(a) how fast will I measure the light beam leaving me?
(b) how fast will you measure the light beam moving towards you?
However you are moving, the speed of light will always appear to be c to you.
Spacetime Coordinates
To describe a position in space we could give coordinates (x,y,z). To describe an event we would also need to express the time t so we could give the space-time coordinates as (x,y,z,t).
To another observer in a different inertial reference frame, the coordinates describing the same event would be different – we could call these (x’,y’,z’,t’).
Note that in Galilean (Newton) relativity the new coordinates would be (x’,y’,z’,t) as time is the same for all observers and only the spatial coordinates would vary between the different observers in the different inertial frames.
Thus a consequence of SR is that time is not absolute. Time will be different for observers in the different inertial reference frames.
Spacetime diagrams (Minkowski diagrams) are useful way to visualise SR.
http://en.wikipedia.org/wiki/Minkowski_diagram
Try playing with this:
http://www.trell.org/div/minkowski.html
Relativity of Simultaneity
What does it mean to say that 2 events happened at the same time? In SR 2 events that appear simultaneous to one observer may not appear simultaneous to another observer.
Simultaneity – Albert Einstein and the Theory of Relativity
http://youtu.be/wteiuxyqtoM
Time Dilation
Another consequence of SR is that moving clocks tend to run slower than an identical clock at rest. This is called time dilation.
Time Dilation – Albert Einstein and the Theory of Relativity
http://youtu.be/KHjpBjgIMVk
https://www.fourmilab.ch/cship/timedial.html
Experimental Evidence
SR sounds so crazy. Does the experimental evidence really behave this way?
Decay of subatomic particles, such as muons entering the atmosphere agrees with SR. They ‘live’ much longer than those at rest do.
Also SR (as well as General Relativity) need to be taken into consideration in global positioning systems (GPS). clock ticks from GPS satellites must be known to nearest 25 ns or so, so as to be able to determine a distance to the nearest 10 m or so. SR effects alone (the satellite moving faster compared to the people on the Earth) account for a clock losing 7 microseconds a day.
GPS and Relativity
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
The Twin Paradox
A complete FAQ on this can be found at:
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParadox/twin_paradox.html
The paradox is NOT that one twin has aged greatly and the other has not aged as much. It is that they have not aged by the same amount as may be expected with SR. The solution to this paradox is to understand that one of the twins (the one in the rocket) does not spend all of their time in an inertial reference frame as they change direction (move to another reference frame) on arriving at the far away star.
http://www.adamtoons.de/physics/twins.swf
Length Contraction
The length of objects in a moving reference frame will be shorter than the length measured in the reference frame of the object. This is called a length contraction or Lorentz contraction.
https://www.fourmilab.ch/cship/lorentz.html
Velocities of Objects in Special Relativity
Relativistic Momentum
Relativistic Energy
The Equivalence of Mass & Energy
| Links – General |
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| Einstein and the special theory of Relativity http://www.youtube.com/watch?v=ajhFNcUTJI0&list=PL712E709B05086D32&feature=share |
| Proof of E=mc² http://youtu.be/hW7DW9NIO9M |
| E=mc² is not the complete picture http://youtu.be/NnMIhxWRGNw |
| Documentary: Einstein’s Big Idea http://youtu.be/YgpD4XZP0uM |
| Animated explanation of relativity (first 12 mins is Special Relativity) http://youtu.be/ev9zrt__lec |
| The following is a great course http://www.phys.vt.edu/~takeuchi/relativity/notes/ |
| https://www.youtube.com/watch?v=1rLWVZVWfdY&list=PLoaVOjvkzQtyjhV55wZcdicAz5KexgKvm&index=2&t=0s |
| The Twins Paradox Primer (Rotating TIME!) |
| Complete Solution To The Twins Paradox |
| Links – Minute Physics Series – Special Relativity Series |
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4 – Relativity of Simultaneity 5 – Length Contraction and Time Dilation 6 – Relativistic Addition of Velocity |