PHYS- Exam 4
Quantum mechanics: The better we know where a particle is, the _____ we know about fast its going.
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Astronomers view light coming from distant galaxies moving away from Earth at speeds greater than 10% of the speed of light. How fast does this light meet the telescopes of astronomers? Explain.
Light always travels at the speed of light, 300,000,000 meters per second. Even though the galaxies are moving away from Earth at a very high velocity, the relative velocities do not add up because of special relativity, which says that the speed of light is always constant no matter what
What could you compare the uncertainty principle to?
A localized pulse. Because it doesn't really "wave", you cant really measure its frequency of crests.- thats the uncertainty principle in a nutshell. You can either know where a wave is or where it's going (position or frequency), but not at the same time.
Does anything in your everyday life depend on special relativity? A. Yes B. No
A. Yes
You find an object with such a high mass that the escape velocity is calculated to be 100 times the speed of light. Is this possible? A. Yes B. No
A. Yes
Are protons made up of anything smaller? A. Yes, definitely B. No, definitely not C. Maybe, we're not sure yet
A. Yes, definitely
What is the resolution to Olbers' paradox? A. There are only a small number of stars in the universe B. Light from very distant stars can't reach us C. Most stars die before their light reaches us D. The night sky isn't really dark
B. Light from very distant stars can't reach us D. The night sky isn't really dark
Can anything escape from black holes? A. Yes B. Probably C. No
B. Probably
If I instantaneously teleported to a planet 1 light year away and waved to you, when would you see my wave? A. 1 year before I waved B. Right when I waved C. 1 year after I waved D. 1 light year after I waved E. Never :(
C. 1 year after I waved
Your rocket ship has landed on a planet where gravitational acceleration is 15 m/s^2 and the escape velocity is 1500 m/s. What do you need to do to take off from the planet? A. Accelerate at 15 m/s^2 B. Decelerate at 15 m/s^2 C. Go faster than 1500 m/s D. Go faster than the speed of light
C. Go faster than 1500 m/s
Are electrons made up of anything smaller? A. Yes, definitely B. No, definitely not C. Maybe, we're not sure yet
C. Maybe, we're not sure yet
Is it possible that dark matter is just a bunch of black holes that we haven't found yet? A. Yes, definitely B. No, definitely not C. Maybe, we're not sure yet
C. Maybe, we're not sure yet
You approach this massive object to study it further. What do you see when you get there? A. A bright orange burning ball B. A dense ball of metal C. Nothing
C. Nothing
How is an electron's orbit around an atom like peanut butter? A. Many people are highly allergic to it B. Dogs love both of them C. The electron's possible location is smeared out due to quantum uncertainty D. Peanut butter can only be made with whole peanuts
C. The electron's possible location is smeared out due to quantum uncertainty
The Bullet Cluster
Collision of two galaxy clusters, of dark matter and the dynamics of million-degree gas; About 3.8 billion light years
If I spent 5 years traveling to a planet 1 light year away and waved to you, when would you see my wave? A. 1 year after I left Earth B. 4 years after I left Earth C. 5 years after I left Earth D. 6 years after I left Earth
D. 6 years after I left Earth
Relativity and quantum mechanics: A. Have no practical applications because they are not well tested B. Are mathematical curiosities but have no evidence supporting them C. Are very well tested and supported, but have no practical applications D. Are very well tested and supported, and a part of our everyday technologies
D. Are very well tested and supported, and a part of our everyday technologies
I walk at 1m/s. I step onto a moving walkway that moves at 1 m/s. How fast do I move? A. 0 m/s B. 1 m/s C. 2 m/s D. The speed of light E. More than one of the above are possible
E. More than one of the above are possible
What would happen if the Sun instantaneously disappeared? A. We would float off into free space B. We would freeze C. It would get extremely dark D. We would cease to exist E. Nothing. For 8 minutes and 20 seconds.
E. Nothing. For 8 minutes and 20 seconds.
Quantum physics is not only used in the laboratory but is essential for modern life. In lecture we talked about how lasers rely on quantum physics to create identical photons, and how understanding quantum effects can make a better clock. Find a different device (other than lasers and clocks) in our everyday lives that depends on quantum physics for their operation, and describe why it relies on quantum physics.
GPS. Your phone allows global positioning via satellites which broadcast time and work together to find your proximal distance to and between satellites.
What determines frequency of a wave?
How close wave crests are to each other
Astronomers announce that they have found a rocky planet orbiting around a star identical to our own, orbiting at the same distance as Earth does from our own Sun. However, the planet is only half the mass of the Earth, and has an escape velocity that is half of Earth's. From this information, what do we know about this planet's atmosphere, compared to Earth? From this information what do we know about its temperature, compared to Earth? Name at least one other thing we would need to know about this planet to determine whether it could be habitable.
If the planet is orbiting a star identical to our Sun, at an orbit the same distance as Earth is from our own Sun, then the temperature of the planet must be similar to Earth's. Since the planet is less massive than Earth, we know that it will have a harder time retaining its atmosphere since the lighter gases will escape, so it will have a thinner atmosphere with a different climate. Things that would help us study its climate and habitability:
In class I gave the example of a known measurement error, when I weigh myself wearing shoes. Give another example of a measurement with a known error, and how you can "account" for that error in the measurement.
If you measure yourself at a certain height with shoes on. You can account for this error by measuring the height of your shoe soles and subtracting that from your overall height to get the correct height. Other examples: I measure the pressure on my tires in my garage, but I know it is colder outside so I need to pump them up more. I measure the size of my foot to find shoes, but I know I will wear thick socks so I go up a half-size. I measure the temperature of my Thanksgiving turkey but take it out early because I know that it will keep rising after I take it out of the oven. My car gas gauge says empty but I keep driving because I know there's another gallon of gas past the empty mark.
If you were standing on the ground, watching your friend traveling in a rocket ship away from Earth at a speed close to the speed of light, what changes would you notice in his heart rate? Explain.
If you observed your friend traveling away at a very high speed, you would start to disagree about the passage of time (just like in the twin paradox). You would observe his heart rate slow down due to time dilation.
Even measurements without quantum effects can affect the object being measured. One example of how a measurement disturbs the measured object is the measurement of the temperature of a pan of water using a thermometer. How does this disturb the temperature? (Hint: In order to measure the temperature of an object, heat must flow until the thermometer and the object are at the same temperature.)
Measuring the temperature of a pan of water using a thermometer disturbs the temperature because of what we learned about heat transfer. If you insert a cold thermometer into a hot pan of water, some of the heat from the water will be transferred into the thermometer, slightly cooling off the water. You could try to match its temperature so this wouldn't happen, but then you'd need to know the temperature to start!
What situations do we expect that Newton's laws no longer explain motion? To state slightly differently, where do the laws of physics differ from what we encounter in our every day life? Give at least two examples. Also, explain why this does not mean that Newton's laws are "wrong."
Newton's laws are not accurate enough to explain motion when: -predictions of motion are needed in precise detail (quantum mech./general relativity) -in high gravitational fields (general relativity) -at very high speeds near the speed of light. (special relativity) Examples include: -the orbit of Mercury, -the precise location of some satellites, -motion around supermassive objects like black holes. Newton's laws also don't explain behavior like the deflection of starlight around the Sun, or gravitational waves. This does not mean that Newton's laws are "wrong," they are just not a complete explanation for gravity or motion under gravity. They are still useful and accurate enough for many situations.
What does it mean when we say that astronomical observations "look back in time?" Can we really see the past? Can we use this technique to see our own past?
Since the speed of light is finite, it takes time for light to get to us. We really are seeing the past when we look out far into space. If we found a giant mirror far out into space, we could look at it and see what the Earth looked like in the past. However, this mirror would need to be enormous. If we built it ourselves and sent it out into space, we could see into the past from the time when we installed the giant space mirror, but hopefully by then we'd have better methods of keeping records of the past.
Physicists often say that people will never be able to travel at the speed of light. Explain why they say that.
Special relativity says that the speed of light is special, it is a speed limit and nothing can go that fast (except light itself). We can travel very close to the speed of light, but it is a limit that we can never reach. It is not a problem with our technology, it is a fundamental aspect of nature.
If you were in a rocket ship traveling away from Earth at a speed close to the speed of light, what changes would you notice in your heart rate? Explain.
You would be very excited, but the actual passage of time would not change for you, because special relativity says that the laws of physics stay the same for any observer in a non-accelerating reference frame (going at a constant velocity), even if it is a very fast speed near the speed of light.
Schrodinger's Cat
has pervaded popular culture - "The cat is both dead and alive." • Schrodinger's cat is a thought experiment. • I place a cat in a box. • I have a single radioactive atom. • When that atom decays (a quantum process), it sends a signal to break a vial of poison. • The poison is released inside the box, killing the cat. • At any given time, without taking a measurement, how do I know whether the cat is alive or dead? • Examples of measurements: shaking the box, listening near the box, looking inside the box, testing the element to see whether or not it has decayed • Quantum physics says the cat is in a superposition of being alive and dead at the same time. • You will never see both states - by opening the box (making a measurement), you are forcing the cat into one state or the other.
Empty Space is not Empty
https://www.youtube.com/watch?v=J3xLuZNKhlY
Olbers' paradox
the apparent paradox that if stars are distributed evenly throughout an infinite universe of infinite age, the night sky should display a uniform glow, since every line of sight would terminate at a star. But with an expanding universe of finite age, visible light from very distant stars has not reached the Earth.
Wave interference
the interaction of waves with other waves. The same interference happens with light waves.
General Relativity
• A theory of gravity, that agrees with Newton's Laws for most situations • Newton's laws describe mass as creating a gravitational field (like the electric field), and we can predict how things move in that field • General relativity describes mass and energy as warping space and time, which also predicts how things will move
The Cosmic Microwave Background
• Accidentally discovered by Penzias and Wilson in 1964 • Completely uniform microwave signal across entire sky • Thought there was something wrong with their telescope, tried blaming it on pigeon poop filling up the dish
Einstein
• Albert Einstein is one of the world's most famous physicists, 1879-1955 • Although Einstein is best known for E=mc2 and the theory of special relativity, this is NOT what he won the Nobel prize for. • In 1921, he won the Nobel prize in physics for discovery of the photoelectric effect.
Scientific Theories
• All scientific theories • Are well supported (multiple different pieces of evidence) • Can never be proven • Can only be supported • Must explain observations • Must make predictions • Is string theory a scientific theory? Not really (not yet at least)
Black Holes
• Black holes are the result of mass collapsing inwards on itself • The escape velocity increases as mass increases and radius decreases • But relativity tells that velocity is ALWAYS less than or equal to the speed of light, 𝑐𝑐 = 3x10^8 m/s • If the mass gets big enough or the radius gets small enough [Schwarzschild radius], the escape velocity gets larger than 3x10^8 m/s . • Under these conditions, not even light can escape from a black hole - it doesn't have enough energy to do so! • Once something has become this dense, it collapses into a singularity - a single point with zero "diameter" • No known force can support it against the force of gravity
Three failures of 'classical physics'
• Classical physics - what we've covered so far • Newton's Laws, gravity, thermodynamics, waves, electricity and magnetism • Blackbody radiation - the ultraviolet catastrophe • Photoelectric effect - how solar panels work • The Hydrogen atom - an electron orbiting a proton
Dark Matter
• Dark matter is the "extra mass" we need to account for how quickly galaxies are rotating • Did they really take into account all the stars? Yes. • What about the stars hiding behind stars? Found em. • What about dust obscuring stars? Accounted for. • What about the black hole(s) at the center of the galaxy? Weighed precisely. • We've even found unusual objects with very little normal matter and lots of dark matter - "modifying" gravity doesn't seem to work • There isn't enough dark matter inside our solar system for us to see the effects, but measuring galaxies and the universe show it clearly
Mass and Cosmic Speed Limit
• Einstein said that 𝐸 = 𝑚𝑐^2 is called the "rest mass" of an object. Just by having mass, an object stores a lot of energy. • It is called "rest mass" because it's how much mass the object has when it is not moving. • The energy of nuclear bombs comes from "destroying" mass and releasing energy. • Special relativity says that nothing can travel faster than the speed of light. • This seems to contradict the fact that a force causes an acceleration, which increases speed. If I keep applying force, can't I accelerate something to the speed of light? • No, because as things speed up, they gain mass. The more mass they gain, the more difficult it is to continue speeding them up.
Einstein's Blunder
• Einstein, an incredibly established physicist, worked out some math and concluded the universe is expanding • This stood against logic - so he used a fudge factor to correct this • Hubble discovered - the universe is, indeed, expanding; galaxies are all moving away from each other
Key Ideas of Quantum Physics
• Energy must come in discrete quantities - it is quantized • Need enough energy to form an entire photon • We have already learned about how they realized that atoms formed all matter- atoms are like building blocks • Energy also comes in discrete packets - like photons • Very strange - what if your faucet only dispensed water 1 cup at a time?? • All particles have wave-like behavior, and all waves have particle-like behavior (because their energy is quantized) - wave-particle duality • Measuring a particle (like a photon, or an electron) affects its behavior - the uncertainty principle
Wave-particle Duality: Part II
• Even if we turn down the intensity of light until one photon (particle) at a time is passing through the slit(s), we still see an interference pattern. • If only one photon passes through at a time but there is still an interference pattern, it means that each photon (particle) must be interfering with itself. • Each photon must be passing through both slits. • So, we set up a device to measure which slit each photon passes through. • As soon as we do that, the interference pattern disappears. • By the act of measurement, we "forced" a photon to choose a path, whereas before it could take both paths.
What happens if you get close to a black hole?
• Event horizon • The "no turning back" point • Spaghettification (the noodle effect) 𝐹𝑔 = 𝐺(𝑀m/𝑟^2) • If Earth were shrunk to a black hole, g = 6·10^18 m/s^2 at your feet and g = 1·10^14 m/s^2 at your head
Antimatter
• Every quark and lepton has an antiparticle (its opposite). • The opposite of an electron is NOT a proton (a proton has a lot more mass) • The opposite of an electron is called a positron. It is the same mass as an electron but has a positive charge. • If an electron and positron encounter each other, they annihilate each other, producing energy. • Our universe contains MUCH more matter than antimatter. • This is an unanswered question - why is the universe this way?
Special Relativity: Part II
• Everything is relative - what I measure might look different than what you measure. • Some consequences of relativity: • Mass-Energy Equivalence • Mass and energy are the same thing. • Length Contraction • As you move close to the speed of light, things get shorter. • Time Dilation • As you move close to the speed of light, time slows down. • Cosmic Speed Limit • Nothing can travel faster than light in vacuum. • Relativistic Mass • As you accelerate close to the speed of light, things get more massive.
Supercolliders
• Fermilab, CERN, and the LHC (Large Hadron Collider) are particle accelerators. • They bring particles up to very high speeds (high energies) and smash them head-on • New particles are created in the process (mass = energy) and these particles are detected • We discover new particles this way! • They still cannot reach the energies found in the early universe, so some things need to be studied with observations of our universe
Gravitational wave astronomy
• Gravitational wave astronomy is a new way to observe the universe! • Observing these events will help us learn more about black holes and gravity • We also get to observe new things that are "hidden" in electromagnetic radiation
Relative Velocity
• I walk at 1m/s. I step onto a moving walkway that moves at 1m/s. How fast do I move? • Depends which moving walkway I step onto • 2m/s or 0m/s • This is called velocity addition • Velocity addition doesn't work in relativity • No matter how fast I'm going, light is still moving towards/away from me at 3·108m/s • I'm flying in my spaceship at the speed of light and turn on my headlights. The light moves away from me at the speed of light. • But an observer on Earth would "see" the spaceship and headlights traveling at the same speed. Thus, the light from the headlights would not move ahead of the spaceship.
Measurement Affects Outcome
• I want to measure the length of the table. I am handed a tape measure. • I place the tape measure against the table. In the process, I bump the table. • Even if I don't bump the table, the tape measure is still touching it, which can affect the table. • Ok, so I hold the tape measure above the table. • But now I'm eyeballing my measurement. Depending on the angle at which I'm looking at the tape measure, I may get a slightly different reading. My length measurement is less accurate. • In the process of measuring, I'm breathing. My breaths are hitting the table, warming it up slightly. The table gets longer as a result (NOT a quantum effect - heating up objects makes them expand). • Now my measurement is even less accurate.
Time Dilation
• If an observer on Earth measures the length of a fast- moving object to be different, they will also have a different perception of time. • This is an effect called time dilation - time moves more quickly for someone on earth than it does for someone on a spaceship. • Remember the 5 year journey to another planet? Here on the earth, we thought it took 6 years. • Thus, the clock on the spaceship moves more slowly. • It is theorized that if you were to move at the speed of light, the clock would slow down so much that time would stop. • In any case, the person on the spaceship wouldn't notice any change at all. They would see their clock as moving at a normal pace. • It's the person on the ground that would notice something strange.
The Hydrogen Atom: Part II
• If the electron is in a circular orbit, it should be constantly accelerating and emitting electromagnetic radiation, and losing energy • The electron should spiral into the proton • That doesn't happen - why? • Energy is quantized - it can't continuously lose small amounts of energy • If I don't have $2.50, I can't get on the bus
"Measurement" Affects Outcome - Quantum
• In order to see an object, light from that object must enter our eyes. • So when we observe something small, light (photons) are bouncing off of it. • Light carries energy, and that energy can transfer to small particles such as electrons, greatly affecting their speed. • In physics, "measurement" doesn't always mean a physical measurement like in our everyday lives. It may be as simple as light or air bouncing off of something.
Special Relativity
• In physics, special relativity is based on two rules: • The laws of physics are the same for all observers in uniform motion relative to one another. • As long as you are not accelerating, the laws of physics are the same. • The speed of light in a vacuum is the same for all observers, regardless of their relative motion or the motion of the light source. • No matter how fast you're going, light appears to be moving at 3·108m/s. • That's it! You're now experts on relativity, right? • Not quite...although these are the only rules, they have some strange consequences.
Reference Frames
• In special relativity, before we describe a position, time, or event, it is important that we define our reference frame. • Our reference frame describes our current position, velocity, and acceleration. • We make our observations and measurements from this reference frame. • People in different reference frames may make different measurements.
How is the cosmic microwave background so uniform?
• It is completely uniform across the sky, with variations of only 0.00001% • All these patches of the sky must have been in contact at some point in the past, since they are way too far apart now • We think that our observable universe started out so small that the tiny variations that eventually formed giant structure and galaxies began as tiny quantum fluctuations
Line emission and lasers
• Lasers work by starting a chain reaction of emission from atoms • All the atoms are identical, and all the photons emitted are identical • All the waves add up perfectly to form a very large amplitude • The opposite of active noise-cancelling headphones
Technology enabled by quantum mechanics
• Lasers: Lasik, laser printers, weapons, laser cutters, DVDs • Semiconductors and transistors: billions of these are in your phone's processor • LEDs (light-emitting diode) • Cameras: CCDs (charge-coupled devices) and CMOS (complementary metal-oxide- semiconductor) - these turn photons into electrons • Solar panels (photoelectric effect)
Physics and Technology
• Learning new laws of physics (and figuring out all the math and equations of how they work) has led to huge payoffs in technology, but it takes time and lots of other work to build these technologies • Understanding electricity, magnetism, and thermodynamics led to much of your grandparents and parents modern, electrified life (power plants, electricity, engines and cars, phones) • Understanding relativity and quantum mechanics has led to many of the very recent advancements in your modern life • Satellites for communication and GPS • Cell phones, laptops, smart everything • What will new physics discoveries lead to? It can be hard to even imagine!
Neutrinos
• Neutrinos are a bit different from the other particles you're familiar with • They are extremely light, and only interact through the weak force • This makes their interactions very rare • They are created in nuclear reactions • Like in the Sun, or nuclear power plants • It is difficult, but we can detect them
Why do we use Newtonian Mechanics?
• Newtonian mechanics (what we've learned in this class so far) is wrong. So why do we still teach it and spend so much time on it? • Because it's useful, it's simple, and it's mostly accurate. • Newtonian mechanics is a "special case" of relativity at low speeds. • It's nearly impossible for us to detect the difference between Newtonian mechanics and relativity at the sizes and speeds of our everyday world.
Particle Physics
• Particle physics asks the question, what are the fundamental building blocks of matter? • We're told that atoms are made of protons, neutrons and electrons. • But protons and neutrons are made up of smaller particles called quarks. • The "standard model" says there are 17 currently known particles that make up all matter. • Most particles are not as stable as protons, neutrons, and electrons (they don't stick around for as long).
Unification
• Physicists love equations. They love it even more when these equations look nice and are symmetric. • Physicists hate that there are no magnetic monopoles (north pole or south pole of a magnet without the corresponding other half) because it makes the equations messier. • Some physicists devote their entire lives towards searching for a magnetic monopole. • Likewise, a lot of physicists like to think there's only one type of force in the universe.
Photoelectric effect
• The opposite can also happen • If a photon with enough energy is absorbed, the electron will jump up to a higher orbit • It can also get kicked out completely, but only if the photon has enough energy • Millions of low-energy photons could hit it with zero effect! • It only takes 1 photon with the right amount of energy, too • Zero time needed for energy to 'build up', since it comes all at once • This is why ionizing radiation can only happen above a certain wavelength/energy
Learning about new science
• Physics and science are constantly being updated with new discoveries • What we learned in this class will stay relevant, but some things might be updated and modified • Newton's laws weren't discarded once Einstein discovered relativity • Knowing that quarks make up protons doesn't mean we need to know that to figure out the periodic table • We are still learning about new physics in exotic situations (like black holes), but once we know enough, we can create those exotic situations ourselves! • For example, Isaac Newton didn't need to know quantum mechanics, and would have had very few quantum systems to study • Now that we do understand it, we can create those exotic quantum systems and manipulate them! Transistors, processors, iphones, etc
Zero-Point Energy
• Quantum uncertainty says that even the vacuum of space has some energy, known as the zero-point energy or vacuum energy • Because of this energy, particle-antiparticle pairs can pop into and out of existence all the time. • It's a bit complicated, but this does not violate conservation laws • These particles can exert forces on objects, known as the Casimir effect
Cosmic Microwave Background
• Remember blackbody radiation? Some astronomers picked up a microwave signal associated with some very old blackbody • This Cosmic Microwave Background (CMB) has been linked with the Big Bang - specifically, we say it's the "missing link" between a hot soup and neutral atoms as we know them
Grand Unified Theory
• Some physicists would like to find a grand unified theory (GUT) which would unify all the forces together. • String theory is the leading theory to explain how gravity is related to the other forces. • Many theories include the idea that gravity is so weak because the force is "shared" between many different dimensions (more than the four we experience.) • Strings are able to move around these different dimensions.
Wave-particle Duality: Part I
• Sometimes, light acts like a wave, and other times it acts like a particle. • What light behaves like depends on what we're measuring. • The best example of wave-like behavior is an interference pattern from light passing through a pair of slits (constructive/destructive interference). • The best example of particle-like behavior is the photoelectric effect (light knocks electrons away from their atoms in a photovoltaic cell).
Theory of Relativity: Part II
• Special Theory of Relativity • Important when moving very fast • "Relativistic" speeds • Commercial airplanes go 0.00005% the speed of light • Relevant for satellites, rockets, very small particles • General Theory of Relativity • Agrees with Newton's laws for almost all situations • Becomes more accurate in describing motion under gravity for extreme situations, or when you need to be extremely accurate • Orbit of Mercury • Black holes • Clocks on satellites
Theory of Relativity
• Special Theory of Relativity • What would happen if you could 'catch up' to a beam of light? • Relates to the nature of time, space, energy, and momentum • General Theory of Relativity • A theory of gravity • Describes gravity as a bending of space and time
Blackbody Radiation
• Spectrum and intensity depend only on temperature • Cosmic microwave background across entire sky is very well described by blackbody radiation with T = 2.725 • The entire observable universe must have been a hot ball in thermal equilibrium at some point in the past (remember the zeroth law of thermodynamics)
String Theory
• String theories are a group of theories that say that all particles we know about are comprised of even smaller pieces called strings. • There are many versions of this theory • Why is this important? Why is it relevant? What could it mean?
The Twin Paradox
• The 'paradox' disappears once you realize that acceleration is involved. • Just like in Newton's laws, acceleration is special • "The unprecedented jaunt, which ended this past March, brought Scott Kelly's total time in orbit to 520 days — all of which he spent zooming around Earth at 17,500 mph (28,160 km/h)." • "So, where[as] I used to be just 6 minutes older, now I am 6 minutes and 5 milliseconds older," Mark Kelly said Tuesday (July 12) during a panel discussion at the ISS Research & Development 2016 conference in San Diego • https://www.youtube.com/watch?v=ERgwVm 9qWKA
Observations Consistent with the Big Bang Theory
• The Big Bang Theory started as a hypothesis, but overwhelming evidence has supported it, and disproven alternative theories • The "Four Pillars" of standard Big Bang Cosmology • The expansion of the universe (as measured by Hubble, the guy, and Hubble, the satellite) - galaxies are receding from us, and the further away, the faster they are receding • The cosmic microwave background - the relic radiation from the hot early universe which uniformly glows across the entire sky • The abundance of light elements - these atoms were formed immediately after the Big Bang • The formation of galaxies - the way that matter clumped to form galaxies
The Higgs Boson
• The Higgs boson was long predicted (in 1964!), but we also knew it would be difficult to detect • The LHC had a massive upgrade to reach the point where we expected to be able to see it • Still really exciting when it was finally confirmed in 2012
GPS Satellites and Relativity
• The clocks on GPS satellites run differently than on Earth because of their speed (special relativity) and their distance from Earth (general relativity) • If they did not correct for these effects, these errors would add up as the clocks got further out of sync, and your GPS position would be wrong by many miles
The Hydrogen Atom: Part III
• The electron must have enough energy to make a quantum leap from one energy level to another • If I get on the bus, I can only get off at the regular bus stops
The cosmic microwave background spectrum
• The observed CMB is an almost perfect blackbody spectrum T= 2.725 +/- 0.002 K Accuracy limited by reference blackbody source (They couldn't make a better blackbody to compare it to)
The Hydrogen Atom: Part I
• The simplest atom: one proton with one electron • Electron and proton have opposite charges, and they are bound by the electromagnetic force • Just like the Earth orbiting the Sun, the electron has angular momentum that keeps it spinning in orbit • EM force or gravity is the 'string' tying them together • We learned in section 1 that objects in a circular orbit are accelerating (changing velocity) • We learned in section 2 that accelerating electrons emit electromagnetic radiation • Radio antennas, or blackbody radiation
Uncertainty Principle: Part II
• The uncertainty principle also explains why negatively-charged electrons don't often enter the positively-charged nucleus. • Opposite charges attract, so we might think that the electrons would eventually fall into the nucleus. • But the nucleus is tiny. If an electron is inside the nucleus, its position is very well known. • As a result, there is a huge error/uncertainty in its velocity (momentum). It would have enough speed to fly out the other side of the nucleus.
And dark energy? There's even more of that
• The universe is expanding • So? We know things can keep moving at constant velocity without any forces or energy input • The rate at which the universe is expanding is accelerating and we don't know why! • How can we know so much about the past of the universe? • Because the speed of light is finite, the night sky is a history book - we can look back and study how things were, going back almost to the beginning
Hawking Radiation
• There are "ghosts" in the closet of physics, so to speak... • Namely how to "bridge" quantum mechanics and relativity • "I think I can safely say that nobody understands quantum mechanics." -Richard Feynman, one of the greatest theoretical quantum physicists • Relativity says that nothing can leave black holes • Quantum says a very very tiny amount of radiation leaves • Tiny black holes can "evaporate" • If you hear about supercolliders "creating black holes" - don't worry! • Hawking predicted this radiation, then bet against himself as an insurance policy, and eventually conceded the bet • Recently discovered - there may be loopholes in Hawking's understanding of black holes allowing for some information to escape!
Where are Black Holes?
• There are "stellar mass" black holes - formed when a large star dies. These can be almost anywhere in a galaxy • Black holes can orbit each other and eventually merge and combine into a bigger black hole • There is a supermassive black hole at the center of possibly almost every galaxy • If another (smaller) black hole forms in a galaxy, it will likely be eventually sucked into the black hole at the center.
What is time?
• Time is a dimension, just like space • Remember position vs time plots • Time is the fourth dimension (x,y,z,t) • Can we travel in time? • Can we travel backwards in time? • What determines the direction of time? • The nature of time is central to Einstein's theory of relativity
Blackbody Radiation- Why Microwave?
• Universe was ~ 3000 K at formation of CMB • 380,000 yrs after the Big Bang • Full of visible light (~1 micrometer wavelength) • Universe is expanding, which causes light to stretch out and change wavelength • Visible light becomes microwaves (~1 millimeter wavelength) First detailed measurements- COBE satellite launched in 1989
The Big Bang Theory
• Until the 1920's, it was assumed that the universe was in a steady state • It also wasn't yet realized that the fuzzy things in the sky were entire other galaxies full of stars • Hubble's measurements showed that the universe was expanding • But if everything is expanding, how did it get that way? Where is everything expanding away from? • The name "Big Bang" was meant to make fun of this theory of how everything started
Ok, so what is dark energy really?
• Using the "history book" we have in the night sky, we see evidence of an acceleration for which we have no explanation • We know even less about dark energy than we do about dark matter • It might have to do with "empty space" and the fact that particles are popping into and out of existence • Ok, then who says our current models are correct? • No one! But so far, they've explained everything Scientific theories and cosmology • Are there other theories that can explain dark matter and dark energy which go against Newton and Einstein's theories of gravity? • Yes. • Have they made predictions that we've been able to test and verify? • No. That's why we're still using the "old" theories - and will continue to do so until substantial evidence is provided otherwise
Ok, then what IS dark matter?
• We don't know, that's why it's called "dark" • All we know is that it interacts gravitationally with ordinary matter • It wasn't created with other normal atoms in the early universe • It does not appear to interact with the electromagnetic force (it doesn't emit or absorb light) • Maybe (hopefully?) it interacts through some other force, like the weak force • Some possibilities • New particles • New kinds of existing particles (like neutrinos) • Even weirder new things • Primordial black holes
Studying our universe
• We expect the laws of physics to be the same everywhere • So, we can apply what we know about the laws of physics to other planets, other galaxies, and other parts of our universe • Studying other planets in our solar system (like Mars) • Understanding exoplanets and their habitability (planets around other stars) • Studying exotic objects like black holes • Studying other time periods in our universe • Physicists study our observable universe - what we can measure
Relativity of Simultaneity
• We have a pretty good understanding that positions can be relative. • Something on my right can be on your left • Something close to me can be far from you • But it's harder for us to grasp that time can be relative. • If I think that two events happened at the same time (simultaneously), you might not agree, and we can both be correct. • The best analogy is lightning/thunder. If I am close by, I might think they happened at the same time. If you are far away, you might not. • But we understand that this is due to the difference in the speed of light vs. speed of sound. • However, when it comes to us disagreeing about two events that we can both see (which horse won the race?) it gets trickier. • The relativity of simultaneity has to do with the fact that the speed of light is not infinite.
How do we know about black holes?
• We have observed the things orbiting around them • From the orbits, you can derive the mass of the hidden thing they are all orbiting around • Sagittarius A* - the supermassive black hole at the center of our galaxy, has a mass about 5 million times the mass of our sun • Black holes can also destroy things and emit "shrapnel" radiation as they suck in gas, stars, etc • Dark in visible but can be very bright in other wavelengths like X-ray • Some supermassive black holes are brighter than their host galaxies • Another kind of radiation can be emitted from black holes • Accelerating mass can create gravitational waves • Must also be symmetric • Gravitational wave detectors have detected black hole mergers!
Forces
• We used to think there were five fundamental forces: gravity, strong, weak, electric, and magnetic. • But then we found out electric and magnetic forces are just different manifestations of the same thing (forces between charges). • Now, there are four fundamental forces: gravity, strong, weak, and electromagnetic. • We've made pretty good progress understanding how electromagnetism and the weak forces may be similar (electroweak). • There's been some attempts to show that in the early universe, electroweak and strong may be related. • But so far, gravity has escaped all attempts to be related to the others.
Escape Velocity and Black Holes
• We've talked about escape velocity for escaping a planet's gravity, whether its rockets or atmospheric gases • The more massive the planet, the more gravitational force it exerts, and the deeper a gravitational potential "well" is formed • There is no limit to how high the escape velocity can get for extremely massive objects • However, there is a universal speed limit - the speed of light • If the escape velocity is greater than the speed of light, nothing can escape
The Ultraviolet Catastrophe
• What we've learned so far explains why hot objects emit radiation, but it does not explain the shape of the spectrum • The ultraviolet catastrophe - why is absolutely no ultraviolet light emitted from warm objects? • Solution: light can only be emitted in discrete quantities • Can't emit ½ a UV photon
Mass-Energy Equivalence
• When molecules undergo chemical reactions, they gain/lose extremely small amounts of mass. • When we use chemical reactions for energy (batteries), we are using small amounts of mass in a different form (energy). • The energy from large explosions comes from the destruction of a small amount of mass. • The nuclear bombs dropped on Japan released around 8 · 10^13 J of energy. This corresponds to 0.9 grams of mass (a grape). • The sun is losing 4 · 10^9 kg of mass every second.
Length Contraction
• When we look out into space, all of our information is "old". • The farther away the object, the older our information. • We know very little about space as it is right now. We know about space as it used to be. • We'll come back to talk about space more next week. • But for now... • As a spaceship moves away from us, "information" from the front side is older than "information" from the back side, since it is farther away. • Thus, we will see the front side as closer than it actually is. • The faster the spaceship is moving, the more noticeable this effect. • This is something called length contraction - fast moving objects look shorter. • However, length contraction is ONLY noticeable to an observer in another reference frame (standing on the earth). • If you are on the spaceship and measure the length of your ship, it will be the correct length.
Uncertainty Principle: Part I
• You can't know exactly where something is AND how fast it is going at the same time. • The more precisely you know where something is, the less you know about how fast it is going. • This is tied closely to the concept of measurement in physics. By measuring something, I affect it.
What happens if you enter a black hole?
• You'd be squished. • That's the only thing that's not up for debate. • We've never gotten close to a black hole and even if we did, there would be no way to get information back out about what happened. • There's lots of theories about wormholes and traveling to other dimensions/places/time travel, but none of this has any evidence