H5 Eveidence to support Special Relativity

H 5.1 Discuss the Muon Decay as experimental evidence to support special relativity

Evidence	Conclusion
Muons can be detected on the surface of the earth, even if they have a short half life, if they have special relativity	Time dialation explains why the Muons can be detected on the earth surface.  It is also due to length contraction because of the inident of high speed of the muons travelling at 0.99c



H4 Some consequences of Special Relativity

H4.1 Describe how the concept of time dilation leads to the twin paradox.
Describe the twin paradox using your own name and a twin (your name backwards) to explain the paradox and why both of you cannot be the youngest if your lucky twin went exploring the Universe in a space rocket

If Yalee and Eelay are moving relative to each other,Yalee wit see Eelay's clock moving slower than her own clock and Eelay will see that Yalee's clock is moving slower than her own. This is because they are in a different frame of reference. 
If Eelay was to go on a journey into space, Yalee will expect Eelay to be younger since she sees Eelay's clock moving slower. However, according to Yalee, she would think that Eelay is aging much more slower than she is since she sees that Eelay's clock is moving much more slower than her own.
BUT they cannot both be younger. 
This is called TWIN PARADOX. 

Who will be the youngest?
Eelay will appear younger since she is the one that is accelerating. General relativity shows that during acceleration, clocks tick slower than when you are at rest. Therefore, Eelay will appear to be younger.

What was developed to satisfy the twin paradox?
The Hafele-Keating experiment was developed. 


H4.2 Discuss the Hafele-Keating experiment



H 4.3.Questions from Heinamenn: 

IB:

H.3. Relativity Kinematics

H3.1 Light Clock:



Describe the observations of observer A and B

Observer A and B have light clocks that time 1 nanosecond every time the light reflects through a cycle.  Observer B is inside a carriage glass box travelling at velocity v, relative to observer A. Since the carriage is moving, it would appear to Observer A that the the distance is greater with the same constant speed.  Thus, the light leaving the lower surface and returning would be greater than 1 nanosecond. Observer B would see the event happening in 1 nanosecond since he is inside the carriage.

Light clock: a beam of light reflected between two parallel mirrors may be used to measure time

H3.2 Define Proper time interval

Proper time interval: it is the time measured in a frame where the events take place at the same point in space.This turns out to be the shortest possible time that an observer could correctly record for an event.

H3.4 annotated graph showing the variation with relative velocity of the Lorenz factor

https://spreadsheets.google.com/ccc?key=0AmUEHSxTKgO2dHliQnBDT2h5LU93NVZCQWNKZ0JVSVE&hl=en#gid=0

At low velocities, the Lorenz factor is approximately equal to one - relativistic effect are negligible. It approaches infinity near the speed of light.

Questions:

H2.1- H2.3 Relativity

What conditions must be satisfied for an inertial frame of reference?
It must be at a constant speed

Give an example in which it appears as though there is an inertial frame of reference but in fact there is not
When it is in circular motion

What problem does special relativity not account for?

It does not account for Gravity

The concept of simultaneity.

Simultaneity is when two events happen together. 

Event that take place at the same time in space will be simultaneous to all observers where as events that take place at different point in space can be simultaneous to one observer but not another.

Introduction to Relativity

What is the limitation of Galilean transformation technique? What was 'invented' to overcome this?

• if the answer is equal to or greater than the speed of light then the Galilean transformation technique cannot be used, thus the theory of relativity was invented to overcome/ work out this problem

E.6.4-6.8

E.6.4 State Hubble’s law:

The relationship between the distance of the galaxy and how fast it appears to be moving away from us is known as HUBBLE's LAW. This supports the theory that universe is expanding.

E.6.5 Discuss the limitations of Hubble's law

(Heinamenn Physics textbook Chris Hamper)

• The data points on the graph are scattered around the best fit line which indicates that there are random errors in the experiment
• since there are gravitational attraction between the galaxies, the speed of the recession should be decreasing as the time

E. 6.6. Explain how the Hubble constant may be determined:

(Heinamenn Physics textbook Chris Hamper)

Hubble's constant can be determine by the gradient of the best fit line as shown in the graph above. The value of this is not certain but is in the region of 72 Kms^-1 Mpc^-1

E6.7. Explain how the Hubble constant be used to estimate the age of the universe

The age of the universe can be calculated by using the equation:

 which is the same as:

We need to calculate this in seconds, thus we need to convert the distance into km

we now need to convert this into years

This calculation assumes that the velocity is constant. However, we know that the gravitational attraction slows down the galaxies thus the recession velocity that we measure today is much smaller than it was. This makes the value that we'd calculated too large. According to these measurements, the universe can;t be bigger than 1.36 x 10^10 years!

E.6.8. Solve problems involving Hubble’s law

E6.1-6.3

E.6.1 Describe the distribution of galaxies in the universe

Galaxies tend to be found clustered together.
Galactic Cluster - a collection of galaxies that is drawn together by their mutual gravitational attraction. the clusters themselves are involved in larger groups called superclusters. For example, our own galaxy, the larger spiral galaxy Andromeda  and several smaller satellites, including the Large and Small Magellenic Clouds.

Galactic supercluster - they are typically seen as long and thin strands of clusters and galaxies, intra-cluster gases and, presumably, "dark matter" on a two dimensional surface.

http://www.dragonslain.com/Science_scene_Galaxies.html

E.6.2 Explain the red shift of light from distant galaxies

- A red shift implies that the star is receding, thus the light from the galaxy must also be receding since they are red shifted as well.
- It was found that light from all galaxies are red shifted and most importantly, the furthest ones are shifted more than the closer ones. Thus implying that the universe is EXPANDING!
- It is as if the a big explosion had occurred, causing the outer parts to fly off faster and is still travelling outwards with the greatest speed. - Heinemenn HL Physics Textbook Chris Hamper

Watch and embed these video: http://www.youtube.com/watch?v=BIW7EzHmndY&feature=related

Notes:

• our universe is continually expanding
• we know this because when we look at galaxies, they are all moving away from us
• the closer galaxies are moving at a slower rate then the ones that are further away
• the relationship between the distance of the galaxy and how fast it appears to be moving away from us is known as HUBBLE's LAW
• as the universe expands, it 'drags' the galaxies along with it
• the overall motion away from us is due to th expansion of the universe
• as our universe expands, the galaxies with it do not
• on small scale, gravity can hold things together. on large scale the expansion takes over causing everything to move apart
• astronomers now know that dark energy is causing our universe to expand at an accelerating rate
• however, we are NOT at the center of the universe. If we are to look at the galaxies of the universe from different galaxies, you would see the same thing
• The centre of the universe is nowhere or everywhere is the centre of the univers

http://www.youtube.com/watch?v=e6G2Z6iD-9M&feature=related

Why the galaxies furthest away are red shifted the most:

Because the universe is EXPANDING. It was found that light from all galaxies are red shifted and most importantly, the furthest ones are shifted more than the closer ones. 

Explain why it is the expansion of space itself rather than the motion of the galaxy that results in the relative velocities of the galaxies

Since the universe is expanding, it is causing the majority of the galaxies to move further away from us. it is the expansion of the universe that results in the galaxies relative velocities. We know that it is the expansion itself and not the motion of the galaxy because we can observe the galaxy that is visible to us that it is moving away from us. 

E.6.3 Questions: