Lecture 9: Relativity and Cosmology

there are two factors important to research of the end of the universe that we do not know much about

(1) How much matter there actually is in the universe, we can measure the amount of matter in the galaxy by counting up visible matter and extrapolating around the galaxy or we can determine the mass by how fast the galaxy spins without tearing apart (2) recently more sensitive measures fond in a small variation in the universe's rate of expansion, implying some other kind of energy gently varying the expansion of the universe, her,ed "dark energy"--some have suggested this could lead to a big rip where the expansion of the universe speeds up and rips itself apart

the death of the universe--what is the ultimate fate? with initial explosive force and gravitational force competing

(1) Not enough mass in the universe for the force of gravity to overcome the energy initially supplied by the big bang, the universe will continue to expand (2) there is plenty of mass in the universe and the force of gravity will overcome the expansion of the universe, the expansion of the universe will slow down and reverse with the end coming in a "big crunch" (100 billion years) (3) the force of gravity and energy supplied by the big bang are perfectly matched, the expansionists will slow down and approach 0, but the universe will never contract, and we don't know what will happen (evidence suggests the universe is closest to this possibility)

If the rate of expansion in the universe is constant (which it might not be) but would only vary slightly the age of the universe is

13.7x10^9 years

what if there is a scenario where the curved path IS the fastest path

Einstein proposed that light in this example does travel the shortest path through space, which can only occur in space itself is cured and not light (when working with accelerating reference frames we cannot use normal euclidean geometry where everything is parallel to eachother)

Measuring an event

an event is simply something that happens, all events can be assigned 4 values to represent it (x,y, and z coordinates) to tell us where the event happens and one time coordinate (t) to tell us when it happens **these are SPACETIME coordinates

nuclear fusion

a similar process to nuclear fission that happens in the other direction, mass can be lost when two small atoms are pushed together to form a bigger atom, simplest method is by combining two hydrogen isotopes to create a helium atom, while this process releases about 10x less than uranium fission, there are about 45 times more hydrogen atoms in a kg of material (plus no leftover byproduct) ***REALLY HARD TO DO, TAKES A TON OF ENERGY, more than what we get out of it

simultaneity is not a ______

absolute concept--it is relative and depends on the motion of the observer

time is not _____

absolute, the very essence of time itself is the first string test in the wake of the special theory of relativity

creation of the universe

all evidence points to the big band being the origin of the universe--in the beginning all of the universe was confined into one tiny point of infinite density, which "exploded" sending the universe expanding in all different directions. As the universe cooled, particles became attracted to each other and formed all of the objects currently in existence

2 postulates destroyed

all three units we began with in this class

on a curved surface, the shortest distance between 2 points will ____

also be a curve--presuming that the acceleration is causing space itself to curve

general definition of relativity of time

as you approach the speed of light, time slows down (such that the length of a second is NOT absolute). A time-dilation equation tells us that an object traveling at velocity v will experience a different time interval that one standing still **Note when velocity v is small the proper time and dilated time are nearly equal, so newtonian mechanics still applies

we could theoretically bend space and time, so that we could bend the end of the universe to us

because space is flexible--would be able to move faster across the universe than if we were light (example of wormholes)

relativity of time

because there are different examples of people measuring events differently in time based on their position, this implies that space and time are related (ex. we set up an experiment where a short burst of light travels straight up to a horizontal mirror, which reflects the light straight back down)--we have 2 events occurring at subsequent times: it takes a short time for the light to travel the distance D up to the mirror and then to travel the distance D back down. The speed at which the light burst moves if C, so the time (change in t1) it takes for the light to travel up and down is given by (change in t1= 2D/C). To continue this experiment, we can take out the little device and the observer and put them on an object moving with velocity v--even though we changed the reference frame, we've actually changed the frame for both the events and the observer--our observer will see the light move in the same manner as if they were standing still and the same equation holds true

if we have bigger stars the gravity crushing together is

bigger, we can then get a str created out of protons and neutrons....an even bigger star will experience a harder and harder pull of gravity as it becomes more dense--black holes are so dense, with so much mass that it creates an almost vertical dive, a huge star that has died (so so small and so dense, nothing can escape)

to measure the length of something...

both end points need to be noted simultaneously in the reference frame (know the beginning and endpoints)

the process for releasing nuclear energy relies on ____

changing the mass of particles (atoms) through e=mc^2. Methods for doing this were discovered by scientists at the turn of the 20th century working on radiation (the issue of)

example of a muom

comes our of collisions when particles hit our atmosphere (gamma rays). When created, only has a brief time to exist, cannot live long enough to be found on the surface of the earth, but, if we set a detector on the ground it will pickup a muom, and this happens because it is much longer for the muom than it is for us as a result of its high speed (an example of time dilation)

people in different reference frames may end up with _____

different coordinates for the same event--take relativity and throw in the speed of light is constant

rest energy (PE) of relativistic energy is most familiar in the form

e=mc^2, simply by existing, if a particle has mass it also has emergy--also the relationship between mass and energy is ENORMOUS, the speed of light squared has an order of magnitude of 10^16

more evidence that the big bang occured

energy from the big band is still floating around the universe. this energy is in the form of light radiation and is known as the cosmic background radiation that exists everywhere in space and is remarkably uniform in all directions and distances--again supporting the notion that it originated at some central point and moved uniformly forward

time dilation equation

equation: change in t=changein to/ sqr(1-(v/c)^2) which tells us how the time slows down for moving objects (an object traveling at velocity v experiences a different time interval than one standing still, change in To is the proper time and change in t is the dilated time) **as velocity increases will scale the changes in time, but 0 velocity will end up with no change **note when velocity (v) is small, the proper time and change in t (dilated time) are nearly equal, so newtonian mechanics still works at low speeds

difficulty in assigning spacetime coordinates to an event

ex. a blind person and a deaf person at a fireworks show, when an explosion occurs, the light will travel to our observers faster than the sound. Unless they take into account the different velocities, they will each assign different time coordinates to the same event. Since they are in the same reference frame (standing still) and the event only happened at one time, this velocity difference needs to be taken into consideration to establish a time-coordinate for the event

wormholes

examples of where spacetime is curved back onto itself to create an "Einstein Rosen Bridge" between two distant parts of space.

long posited formally proven in the 70s that light from distant stars/galaxies has been shown to bend around massive objects, such as our sun

experiments which took place during a solar eclipse showed that we could see stars which were located immediately behind the sun, we could only see their light because it was being "bent" by the mass of the sun itself...looking at the skies of the sun to see what was coming around it (stars being the sun see the light we see, exposing the object) even though the object should have blocked this light

relativistic energy

force and kinetic energy are released to the momentum of a system, and thus behave relativistically

Nuclear fission is how we _______

generate nuclear energy...however, nuclear fission often creates really bad radioactive nuclear material **we have a complete laboratory dedicated to recycling nuclear waste, but they to not have any to get rid of

classical physics and events

had events happening at a particular time and place and how it was viewed from different reference frames was covered by Newtonian mechanics (ex. a person standing still throws a ball forward--to that person, the ball appears to move away from him at the same velocity)--however, to be a person traveling in the same direction at the same velocity as the moving ball, this appears that the ball is standing still and the thrower is moving backward.... **this is because the person moving is in a different reference frame from the one standing still (relating our frames of reference to each other)

example of pulling an ice cube out of the freezer

ice itself is perfectly clear, but bubbles make it white (air impurities) when they (particles) are arranged perfectly, they are invisible to us. Impurities will disappear with creation of energy (light creates an electron and positron)

spacetime coordinates

illustrate where and when events happen. depend on the reference frame of the observer (people in different places or times (or moving at different velocities) will record the spacetime coordinates of the event differently and no single frame is more "correct" than any other--- (x, y, and z) (t) for when it happens

Einstein's 1905 postulates

in 1905 Einstein published a paper describing what has come to be termed the "special theory of relativity" coming up with two postulates

relativistic momentum

in classical mechanics, the total momentum of objects (defined as the product of mass and velocity) involved in a collision would be conserved by all observers, in any reference frame--but we have just demonstrated that the velocity of moving particles depends on the relative velocity(ies) of the observers reference frame--momentum is measured by an observer in the same reference frame as the moving particle (p=change in x/change in proper time **the faster you go the more the mass of the object increases, similar to time dilation, the momentum of an object increases as the particle moves faster relative to observers velocity

everything big from the big bang seems to have happened

in the first three mins, following the big bang, as the universe began to cool and energy began to dissipate, things started occurring, gravity took over and set our current universe in motion

relativistic momentum is ____

increased based on the mass of an object

simplify the time dilation equation by

introducing the lorentz factor (lorentz)= 1/sqr(1-(v/c)^2) where changeint=(lorentz)(changein t o)**in this equation v cannot = c or we end up dividing by zero

once we get to ____ we cannot use nuclear fusion

iron, all of the elements up until then are made by the sun in this process of fusion (beyond that we need supernovae)

Manhattan project

larges scientific collaboration in history, e=mc^2 was brought to the attention of the U.S. gov. around when the U.S. entered WWII, for fear that german scientists were already performing experiments *****found a way to change the mass of about 30kg plutonium atoms (a tiny amt.) On july 16th, 1945 the trinity test showed how much energy is released in the process

mass and energy are the same thing

law of conservation of energy still aplies--total energy of a system cannot change, though it can change forms. We can now add "mass" as one of the forms that energy can take

Postulate 1

the laws of physics are the same in any inertial reference frame (self explanatory, states whether you are moving with constant velocity or standing still, the laws of physics will be the same in either situation (not referring to measurements just that of v=ma and f=ma) **Note it doesn't say that the measured values of physical quantities are the same, only that relations BTWN them are

the first consequence of the principle of equivalence

light can be deflected (bent) by a gravitational field, imagine a person in a spaceship accelerating upward at a rate of 9.8m/s....as they accelerate through the beam of light, from their perspective it will appear that the light is curving down toward them similar to the way a projectile would on the surface of the earth--this creates a problem as the path of light illustrated is not taking the path through space (a straight line, the shortest/fastest path possible) which is one of the principles of light rays

Nuclear fission & Fusion

means of using mass to create energy

gravitational fields arise from the presence of some mass, so mass itself ____

must warp spacetime to form the curved state

most large atoms aren't very stable and have a tendency to decay into smaller atoms (ex. uranium into lead)

nuclear fission

all stars work through

nuclear fission--collide 2 hydrogen atoms until we get a helium atoms, means that our sun keeps its form because it is an ongoing nuclear explosion with 2 forces, gravity pulling everything to the center, but once it reaches the center, forces push it back

blackholes

objects of enormous mass which have collapsed into a (nearly) zero volume, they create a very deep bowl whose sides are practically vertical, not even light has enough energy to escape the bowl. As gravity pulls things together, the sun (for example will push further and further out creating a red giant...as it starts running out of fuel) will start fusing bigger and bigger atoms but cannot go beyond iron, so will then lose this explosive energy and gravity will take over, crushing everything into the center of where the sun used to be

relativity

one of the most basic concepts in all of physics: the measure of evens which occur in space and time, basically concerned with where and when events happen and how the events are separated in space and time. This includes how events appear from different reference frames (different situations of viewing an event)

gravitational lensing

proves einstein corrente: general theory of relativity is the best theory of gravity we have....light bends around huge gravitational objects

light does not see _______

relative motion

Manhattan project and chain reactions

scientists working on the manhattan project realized they could instigate a "chain-reaction" of this process, to trigger a very rapid decay of a huge number of atoms which would all release their mass energy at the same time. They begin with large unstable atoms and developed two processes to trigger a chain reaction which broke the atoms into smaller pieces (nuclear fission)

a moving object _____ in the direction of motion

shrinks, basically the same structure with regard to time, length contraction equation shows that the proper length of an object decreases the faster it moves relative to an observer.

scientists notices that when you add up all the mass of the particles before the decay and then added up the mass of all the particles after the decay the amounts weren't the same

some mass was being lost in the process, it turns out that the tiny amount of lost mass was merely being turned into energy, which was being turned into radiation (from nuclear energy released by decay)

Reference frame example

someone is traveling in a car at velocity (v) relative to the ground and then throws a ball forward with some velocity (v2) relative to the car. Newtonian mechanics (and common sense) tell us that the velocity of the ball relative to the ground (vo) is just the some of above velocities.

anti-matter

sort of the apposite of matter, like a hole leftover from when one marble is removed from a bucket of marbles (antimatter particle of an electron is a positron which has the exact same properties but is positively charged)

principle of equivalence

states that there is no difference between a uniformly accelerating reference frame and one which is in a uniform gravitational field--drop an object to see if you are in an accelerating frame of reference--standing still v. rocket shit (cant tell the diff. both 9.8m/s)

relativity of time experiment with another observer

suppose a second observer is standing still and watching the experiment roll by at velocity V, observer 2 will see the light take a different path than what observer 1 sees, to observer 2 the light burst will be moving to the right as well as up and down, resulting in a triangular path, to observer 2, the burst of light travels a greater distance (2l) than it does for 1 (2d). However, to both observers the light is traveling at the same speed C (change in t1=2d/c while change in t2=2l/c) FROM THESE TWO VALID EQUATIONS, time is not absolute

From newton's laws of gravitation, gravity is _____

the effect of two masses producing an attractive force between each other, if photons don't have mass, they shouldn't be affected by newton's gravity

2 american scientists trying to measure the speed of luminiferous ether

the experimental proof that the speed of light is a constant--a beam of light is shown at a beam splitter and half reflects and half goes straight through--but if mirrors are put on either side, the light will hit the beam splitter and combine them again to make 1 with identical wavelength and frequency (if we see constructive interference, the waves travelled the exact same distance) Problems arise if we rotate the setup--should have changed the speed (but they found that even light still moves at the speed of light, separate from the speed of the earth

using non-euclidean geometry we find _____

the presence of mass acts as a weight resting on a flat rubber sheet, a mass such as the earth stretches spacetime around it, forming a kind of bowl. Any object moving near the earth passes through this bowl, resulting in a curved path--this explains the attractive nature of gravity, particles (or photons) who carry enough energy, cane space this bowl, but all others will fall to the earth....from this rubber sheet, we see that the more massive an object is, it will curve the spacetime around it and fewer objects will be able to escape

Postulate 2

the speed of light in a vacuum has the same value (c) in all directions and all inertial reference frames (makes less intuitive sense than the first postulate, but proven true in many experiments including the Michaelson interferometer) **Ex. imagine someone traveling inn a car at velocity v1 relative to the ground who then "throws" light forward...tells us that the speed of the "thrown light" relative to the care and the speed of light relative to the ground is C. So, someone standing would see light travel at the same speed relative to the car

total energy of a particle

the sum of ke and pe

because of the cosmic background radiation

the universe is not exactly a vacuum, instead it has an average temp of ~2.7K, we can use sensitive measurements of the tiny fluctuations of this radiation made recent in order to trace it back to the beginning and develop a picture of the early universe--big variation in the center, cant really get a picture because the milk way blocks what is on the other side of our universe

the best piece of evidence for the big band?

the universe is still expanding and everything in the universe is moving away from everything else--the speed at which distant objects (such as galaxies)are moving away from us is directly proportional to their distance from us, implying that they all started form the same place

where did the big bang happen?

there was no space/time before the big bang

general theory of relativity definition

these curves in space or spacetime only appear in an accelerating reference frame, which is physically indistinguishable from a gravitational field.

whenever matter and antimatter come into contact

they annihilate eachother and give off a burst of gamma rays. While we can demonstrate that when matter is produced, antimatter is also produced, we cant seem to prove why there is more matter in the universe than antimatter

Einstein and complications with faster objects

things are more complicated with faster objects, specifically light, such that you cant just add up the some of the velocities--Because Maxwell determined that the speed of light is constant, it doesn't obey these principles

time is not a constant as

time runs more slowly the faster you move (in a specific reference frame)--can take two perfectly identical clocks and put one at sea level and one at the top of a high mountain, they will come back differently in a year (time moves more slowly on the mountain)--due to different frames of reference and because the speed of light is constant

at the speed of light ____

time stops, light doesn't see time. So, the faster we go, the bigger the effect is. If you aren't already traveling at the speed of light, you'll never get there, nor can you get faster than the speed of light

general theory of relativity

unlike the special theory of relativity, which only dealt with inertial reference frames, general relativity also covers (non-inertial) accelerating, reference frames. The basis of the theory is the "principle of equivalence"

mass has the ability to warp spacetime (that is what gravity is, the stretching of space and time around some object)

warping space and time through divets

If an electron or proton were the only particle created by energy, the law of conservation of energy would be violated

we cant create energy, we can only move it around, but whenever matter is created by energy, it doesn't create only one particle, they come in pairs (matter and antimatter)--to preserve charge neutrality

dark energy and matter

we know very little about both, but may make up as much as 68% of the total matter/energy in the universe--thats a total of 95% with the estimated 27% makeup of dark matter -- 95% of our universe that we do not understand, and we only count the matter we can see

How do we find proof of the general theory of relativity?

we turn to our constantly special case: light/photons. Photnos have no rest mass because if they're not traveling at the speed of light, they dont exist--also, they travel the shortest path at all times

intertial reference frames

what we discuss in the context of spacetime--non-accelerating frames

length of a meter depends on____

what you are doing

relativity of simultaneity

when reference frames move at different velocities, the issue of simultaneous events becomes a problem--ex. suppose a person standing still sees two events that happen simultaneously. If another person is moving with some velocity (v) past the first observer, they will generally not explain the events as simultaneous--depending on the velocities of travel for the light (which is finite) and the observer, the events will occur at different times. From the moving observer's point of view, he issei's standing still and the other person is moving backward **neither observation is correct, they are both equally valid descriptions which take place

how do we measure a moving box, where we cant know two end points simultaneously?

when we are moving, it becomes harder to measure length, we can use a stop watch to find its length (knowing velocity and the time it takes) **In this experiment our stationary observer 2 measures a stationary board to have length lo, while observer 1 moves by at velocity v (observer 2 notes that observer 1 moves the length of the board at Lo=vdeltat. Observer 1 notes the time it takes to pass the board is l=vdeltato *however because of time dilation, the relative times each observer notes for the same event cannot be equal. Thus their measured length cannot be equal

Can energy turn into matter?

yes, and this is how all the matter in the universe was created--also a process which can be recreated in high energy physics labs and occurs when huge amounts of energy are released from supernova and other cosmological phenomena--most common is when a very high energy gamma ray (high-energy photon/light) spontaneously creates a particle, such as an electron

cant reach the speed of light unless ____

you are at the sped of light for this reason--mass nears infinity and no infinite force (time stops, length would go to 0, mass is infinite)