Muons, Pions and Eminem

The Muon Decay Experiment

What you need to know about Muons:

Muons are leptons - a type of subatomic particle. They are created created in the atmosphere, 10 km from the surface of the Earth. The cosmic rays from the sun hit the atmosphere and can create muons that travel up to 0.99c.

Muons have an average lifetime of 2.2 x 10^-6 seconds. This is measured in the frame of reference of the muon (so it is proper time)

So the maximum distance a muon can travel is 2.2 x 10^-6 x 3 x 10⁸ = 660m

Awwwww, isn't it cute?

The thing is, eventhough the muons are not supposed to reach anywhere near Earth, we are still able to detect them. (using the cute-o-meter...joke)

So, remember that anything moving at the speed of light (in this case it s 0.99c) will experience the effects of special relativity.

A muon moving at 0.99c has a Lorentz factor of 7.1.

In terms of time dilation:

From the muon's frame of reference: the muon measures proper time. 2.2 x 10^-6 seconds.

From the Earth observer's frame of reference: the muons move towards the stationary observers at 0.99c and is thus time dilated to 7.1 x 2.2 x 10^-6 seconds = 1.562 x 10^-7 seconds

Remember that time dilation is concered with longer time periods while length contraction is concerned with shorter distances.

 In terms of length contraction:

From the muon's frame of reference: everything around the muon will now appear shorter (but not the muon - imagine sitting on the muon like a train, everything on the train stays the same) due to length contraction by a factor of 7.1.



Mr. Lorentz likes to dilate time

Firstly, watch my video on deriving the time dilation equation 

(Thanks for the birthday coloured pens Rynda, Rita, Manini and Tanya! I'm putting them to good use =D)

Speaking of stationary and moving bulbs...this is what happens when you move a bulb into a microwave.

Anyway, what is important is the Lorentz function. Which is linked to the time dilation equation.

If you graph it, the Lorentz equation looks like this.

And some solutions from today's work.

Time Dilation

Makes me think of pupils.

Anyway, learn that a light clock is a device which uses a beam of light reflected between two mirrors to measure time. This is what you see below:



Now lets tackle Time Dilation.

So Jack is at rest.

Set Jill to move at 0.3 the speed of light c and click "play".

Notice that for Jack, the photon travels up and down in a straight line...nothing complicated.

Jill is moving away from Jack from Jack's perspective (we would say from Jack's frame of reference). Notice that Jill's photon travels a further distance as seen by the traingle shape path.

The description on the top right hand side is wrong...this is the correct interpretation

From Jack's frame of reference: Jack measures 10.0 seconds on the clock he is holding. When he looks at Jill's clock (so he takes out some binoculars to see Jill's clock which is very far away), he sees the clock read 10.4 seconds. This is time dilation.

From Jill's frame of reference: the ship, the floor, the walls and everything else around her are stationary while Jack appears to be moving away. From Jill's frame of reference, she will see 10 seconds on her clock and when peering through binoculars to Jack's clock, will see 10.4 seconds.

This is like the man and boat example. For the man on the boat, a ball dropped from the mast of the ship will follow a straight path downwards. For the external observer, the ball appears to follow a parabolic path as the boat is moving. Identical situation but different conclusions from different frames of reference. (This is Simultaniety...the same 

Time stretches and contracts because it is the speed of light which ios constant.

Inertial Frames of Reference and very Special Relativity

People always tell you to consider things from different perspectives because the same thing can look different to different observers.

Einstein proved this mathematically with Special Relativity! Isn't physics awesome?

Okay so first, learn that an inertial frame of reference is one in which Newton's Law of Motion apply. The two conditions neccesary for an intertial referece are constant speed or zero speed. An inertial frame of reference has no acceleration.

Dropping a ball to measure g in a static lab yields the same result as doing the experiment on a train moving at constant speed.

If speed is changing - this means there is accelration. Accelerated frames of reference are non inertial frames. In circular motion, velocity is changing and the body is accelerated towards the center, so a rotating frame is a good example for a non inertial frame of reference. Although the speed is the same, velocity is changing (due to its vector nature).

Lets build on that. The Two Postulates of Relativity state that:

1.) The Law of Physics are the same in all inertial frames of reference. If you are on a car at 30km/h, you can assert that you are travelling at 30km/h relative to the ground (so the ground is the inertial frame of reference). However you would be stationary relative to the car (this time the car is the inertial frame of reference).

2.) The speed of light is the same to all observers. The speed of light is measured relative to the observer and is a constant defined by Maxwell's equation.

Simultaneity can be explained using Special Relativity. If two events happen simultaneously, they are called simultaneous events.

Watch video:



The video is trying to say that two event CANNOT be simulateous in the two inertial frames of reference. The lady saw the flashes happen one before the other while the external observer saw both happen at the same time, the two observations are correct according to special relativity.

IB questions have the same style to simultaneous questions. You get marks for saying:

1.) No simultaneity can occur between the two inertial frames of reference. So if A sees something happening at the same time, then B will see them happening one before the other and vice versa.
2.) Speed of light is constant in all frames of reference
3.) The tricky part is determining which event happens first.

Stuff I have forgotten!

Capacitance relates specifically to CCD's. The CCD relies on the photoelectric effect to liberate electrons.

To get the equation for Escape Speed. Equate KE with Work done using Newton's Universal law of gravitation and solve.

Albedo is the ratio of reflected radiation to incident radiation. It is REFLECTED radiation, questions will try to catch you out with emitted radiation. A body can either absorb or reflect light. High albedo (90%) means a lot of the light is reflected (e.g Snow).

Emissivity is the ratio of the of the energy radiated by a particular body/material to the energy radiated by a black body at the same temperature. 

Why Relativity is relatively hard

The important thing to realize is that the point of view of the oberver is called the frame of reference.

In the animation above, the ball would be falling horizontally from the frame of reference of the man on the boat.

If the frame of reference is the lady, the ball would follow a parabolic path.

Its an identical situation - but the motions are different depending on the frame of reference.

Another example: If we had a mosquito flying in a car, from the driver's frame of reference, the mosquito flies at "mosquito speed"

From a person on the sidewalk, the mosquito travels at "car speed + mosquito speed". Again, same situation but different speeds depending on the frame of reference.

So...Study Guide says "When a frame of reference is adopted,the position of the observer in that frame becomes the zero of position. If the frame is a moving on, the zero of position moves with observer"

To understand this situation consider this scenario:

The last point is crucial -> V (A relative to B) = V(A) - V(B)

Do not confuse this with HL Math vectors where AB = b - a

Musical Quasars

When house music forms a binary star system with cosmic lyrics...the result is a song of intergalactic proportions.

Cosmic Girl (Tom Belton Remix) by Jamiroquai. One of the best songs I have in my music library.

Listen to the lyrics...the physics makes sense!




Anyway the lyrics talk about Quasars:

Quasars or Quasistellar objects appear to be point like sources of light and radio waves that are very far away. We know this due to very large red shifts - they are at the limits of our observable universe. Because we still see/detect these stars, they must be emitting a load of energy for their size (10^40 W!).

We still have yet to understand how this energy is made, but some theoretical models rely on super massive blackholes. They think the energy results from whole stars "falling" into these black holes.

Cool! Would love to see one!