# Philosophy 2032F/G Study Guide - Final Guide: Hidden Variable Theory, Wave Packet, Event Horizon

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Published on 22 Apr 2013

Department

Philosophy

Course

Philosophy 2032F/G

Professor

1. Geodistics in special relativity

Timelike geodesic: The timelike curve connecting two events of greatest proper time.

2. Galileos principle of objects to free fall and how it is related to special relativity?

Galileo, who articulated the first "relativity principle" in the seventeenth century. In

generating his relativity principle, Galileo removed the distinction between

stationary and moving observers, arguing that people on earth cannot tell if they

are really at rest or if they are moving with the rotation of the earth each day. To

demonstrate this, Galileo used the example of a cannonball falling from the top of

a ship's mast. He noted that the cannonball will land at the base of the mast

whether the ship is moving steadily through the ocean, or whether it is at rest in a

dock. Even if they observe the falling ball, people on the ship cannot tell if they

are really at rest or if they are moving with the ship. They cannot distinguish their

state of rest from the ship's state by observing motion that takes place within the

"reference frame" of the ship. In other words, a person at rest on the deck of a ship

cannot determine whether the ship is at rest or moving at a steady speed through

the ocean by observing actions that happen on the ship itself. That person must

observe the ship relative to its surrounding environment in order to make such a

determination.

3. Revive statistical mechanics that went into the background work of quantum

mechanics.

Ideal gas Law, Diffusion, Browlie

4. Why Einstein used quanta?

Einstein used quanta because he concluded that light and gas obeyed the same laws at

high frequencies. Photoelectric effect- this effect showed that high frequency light

was needed to knock of cathodes. This showed that light behaved in a different

wave. When low frequency light hit the wall it wouldn’t have enough quanta

energy but when high frequency did it would.

5. You need to know qualitatively how time dialation works?

Since speed is equal to distance over time and light is a constant there needs to be

altercations to the equation when working with the speed of light. For example if

the distance increase the time needs to decreae to make up for this. And if the time

increases then to the length has to decrease to make up for this to. Can use

hyperplanes of simultaneity to judge telative time dilations. Twin paradox etc.

Special relativity: the laws of physics are the same in all inertial references, and

the speed of light is constant.

6. How Schawrazchild spacetime works and what can it be used for?

It is a universe where it looks like Minoskwi spacetime has you get closer ot

infinity. It has a central point in space where curvature around it is symmetrical.

Good spacetime around the sun ( assume no sun doesn’t rotate or electrical

charge)

Einstein had two problems with this spacetimes. First from the empirical date they

had at that time the universe was filled with equal distribution of stars. Second he

likes a fixed spacetimes depending on matter distribution based on General

relativity. Einstein didn’t like the arbitrariness of infinity when you reached closer

to infinity as you predicted a curvature without knowing the mass distribution.

7. Need to know the properties of the Einstein universe and what it can be used for?

He abolished spatial infinity. He did this by introduction a new constant in his

equations. It contains a uniform mass distribution so that matter is at rest and

geometry of space slices are unchanging with time. Overall is it s 5none geometry

with no infinity and space curving back onto itself. The space time is

Homogeneous with the same spatial curvature in all directions. It is spatially

isotropic, meaning it is the same in every direction of spatial direction. Einstein

added a constant to his equation in order to supply the missing curvature needed

for his universe:

Summed of Space curvate plus lamba= matter density

De sitter arugued that this lamba actually expanded the universe without matter

despite its intentions.

The lamba is a repulsive force that cancels out the gravitational force that

would be present in his spacetime so that his spacetime would not collapse.

Lamda was changed to show that spacetime=-lambda, it behaves like an odd

matter that expands the matter in the universe.

Time Travel Universe (Einstein Universe)- If you take the cylinder and have the

one dimension time on the surface you can go forward and meet youself in the

future. Grandfather Paradox. The grandfathers assasion would not occur. (global

constraints).

8. What do different type of geodesic deviation say about different kind of

curvature?

Spherical Geometry- Positive Curvature- 5NONE- Lines connect back to

themselves. Triangle- Sum More then 180 degrees. Perpindiculars

Converge(diverge slower then expected)

Euclidean Geometry- Flat- Infinite length- 180- perpendicular netiher converge or

diverge

Hyperbolic Geomtetry- Negative Curvature- 5MORE- Less then 180-

Perpindicualrs Diverge. (converge slower then expected)

9. What is superposition? And how do you interpret them?