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:

E5.1-5.8 Stella processes and Stella evolution

5.1 Describe the conditions that initiate fusion in a star.

1.     -   When a cloud collapses, a dense core is formed surrounded by a cloud of gas and dust

2.    -  The dense core then contracts rapidly which results in high temperature and pressure

3.    -   Due to the high temperature, a protostar then give out light. However this is not visible due to the cloud of gas which surrounds it

4.    -   After 10⁵ years of mass increase  the radiation of the protostar will blow away the dust cloud and the mass of the star will stabilize

5.    -  The star will now turn into a pre-main sequence star

6.    -  The core will continue to contract and heat up until the atoms are moving fast enough for fusion to take place. Since the hydrogen is abundant in the universe, it follows that this gas is mainly hydrogen, so the fusion that takes place is the fusion of hydrogen nuclei :

- once the fusion starts, the increase in temperature causes greater pressure, balancing the inward force of gravity. The star will now stop contracting and become a main sequence star like the sun

5.2 State the effect of a star's mass on the end product of a nuclear fusion

-        - A star fuses with hydrogen into helium and at some point hydrogen in the core will become rare

-        - The fusion reactions will then happen less often

-        -This means that the star is no longer in equilibrium and the gravitational force will cause the star to collapse once again

-        -The collapse increases the temperature of the core which means helium fusion is still possible

-       - The result is for the star to increase in size which means that other outer layers are cooler

-       - If it has sufficient mass, a red giant can continue to fuse higher and higher elements and the process off nucleo-synthesis can continue

-        -The fusion will come to an end with the nucleo-synthesis of iron. The iron nucleus has the greatest binding energy per nucleon of all nuclei which means that a star will no longer shine

Low mass star à Helium synthesis

High mass star à Iron (Fe – greatest binding energy per nuclear – not stable element) synthesis (in core)

5.3 Outline the changes that take place in nucleosynthesis when a star leaves the main sequence and becomes a red giant 

E 5.4. Apply the mass - luminosity relation

E 5.5 - 5.8

Question 15 from Heinamenn's Physics Textbook

Question 15 from Heinamenn's Physics Textbook


a) Explain the significant of the critical density of matter in the universe with respect to the possible fate of the universe
Since the critical density is the theoretical value of the density that creates a flat universe, if the the mass density were greater then the critical density then a closed universe would occur. However, if the critical density were greater than the mass density then an open universe would occur.


b) calculate the value of the critical density

P = 3 x ((2.7 x 10^-18) ^2) / (8 x π x 6.67 x 10^-11)

=1.3 x 10^-26

ii) Determine the equivalent number of nucleons per unit volume at this critical density

E4.11-E4.14

E4.11: Discuss the problems associated with determining the density of the universe 


Dark matter: A form of matter particles that does not reflect or emit electromagnetic radiation. The existence of matter is interfered from gravitational effects on visible matter  e.g. stars and galaxies.


Dark matter - which does not emit or reflect enough light to be "seen" - is thought to make up 25% of the Universe. The ordinary matter we can see is believed to make up no more than about 5% of our Universe - http://news.bbc.co.uk/2/hi/science/nature/5272226.stm


MACHOs : stands for Massive Astronomical Compact Halo Objects. There is some evidence that lots of ordinary matter does exist in these groupings. These can be thought of as low mass 'failed' stars or high mass planets. They could even be black holes which produces little or no light.


WIMPs:  stands for Weakly Interacting Massive Particles. these could be new particles which we do no know about. Many experiments around the world are in the search for WIMPs.


Why is the Density of the universe so difficult to determine?
- we can only see a maximum of 10% of matter that exists in the galaxy
- much of the mass of the galaxy and the universe is made out of dark matter - not sufficiently enough for us to detect
- dark matter is in the form of MACHOs or the undiscovered WIMPs


E4.12: State that current scientific evidence suggests that the universe is open


The current scientific consensus of most cosmologists is that the ultimate fate of the universe depends on its overall shape, how much dark energy (some unknown force that is opposing gravity which is pushing the universe apart) it contains, and how the dark energy density responds to the expansion of the universe. Recent observations have shown that, from 7.5 billion years after the Big Bang onwards, the expansion rate of the universe has actually been increasing, concurrent with the Open Universe theory. 


E4.13: Discuss an example of the international nature of recent astrophysics research.


- The Drake Equation
http://www.astronomynow.com/news/n1005/24seti7a/


E.4.14 Evaluate arguments related to investing significant sources into researching the nature of the universe.


For:
- Understanding the nature of the universe sheds light on fundamental philosophical question like for example:
why are we here? and is there life elsewhere in the universe? 
- fundamental research will give rise to technology and improve the quality of life
- life on Earth will be an impossibility and thus will be able to colonize new planets


Against:
- money could be spent elsewhere such as food, shelter, medical care to those who are suffering from hunger, homeless and disease
- worthwhile to spent the money on medical research as it will improve the quality of life as well as being able to save lives
- funding space research should not be a priority since it is expensive
- is the information gained worth the cost?


Source: Heinemenn HL Physics textbook by Chris Hamper

4.8-4.10 Cosmology

Graph showing the 3 possible fate of the universe:

Reference: Heinemann physics textbook

Definition of the 3 possible fates:

1. Open universe: open universe will continue to expand forever. Although gravity can slow down the rate of the expansion but it is not strong enough to stop the expansion completely

2. Closed Universe: this will continue to expand but will eventually collapse to its original self

3. Flat Universe: this is between the open and close universe. Gravity slows down the rate of expansion but will take an infinite time until it finally comes to rest

Define the Critical Density:

The critical density is the theoretical value of the density that creates a flat Universe.

Explanation of how the density of the universe relates to its fate in terms of the critical density

If the mass density were greater then the critical density then a closed universe would occur. 

If the critical density were greater than the mass density then an open universe would occur.