Lbst 304 final exam
the speed of light
300,000 km/s 186,000 miles per second The speed of electromagnetic radiation in a perfect vacuum
Aether
A space-filling substance or field, thought to be necessary as a transmission medium for the propagation of electromagnetic or gravitational forces. Upper air, clear sky
The Twin Paradox
An object in motion experiences time dilation, meaning that time moves more slowly when one is moving, than when one is standing still. Therefore, a person moving ages more slowly than a person at rest. So yes, when astronaut Scott Kelly spent nearly a year aboard the International Space Station in 2015-16, his twin astronaut brother Mark Kelly aged a little faster than Scott. When the 15-year-old gets back to Earth, according to NASA, he would be only 20 years old. His classmates, however, would be 65 years old.
gravitational lensing
Einstein's Cross, a quasar in the Pegasus constellation, is an excellent example of gravitational lensing. The quasar is about 8 billion light-years from Earth, and sits behind a galaxy that is 400 million light-years away. Four images of the quasar appear around the galaxy because the intense gravity of the galaxy bends the light coming from the quasar. Gravitational lensing can allow scientists to see some pretty cool things, but until recently, what they spotted around the lens has remained fairly static.
gravitational lensing
Einstein's General Relativity mass bends light in a special way when a star with planets passes in front of another star light is bent by galaxies more than it should because of dark matter the distortion of the appearance of an object by a source of gravity between it and the observer Light around a massive object, such as a black hole, is bent, causing it to act as a lens for the things that lie behind it. Astronomers routinely use this method to study stars and galaxies behind massive objects.
Discoveries in electricity and magnetism
Electric current produces a magnetic field. This magnetic field can be visualized as a pattern of circular field lines surrounding a wire. One way to explore the direction of a magnetic field is with a compass, as shown by a long straight current-carrying wire in.
Maxwell's theory of relativity continued
Even more than this rotational symmetry, the equations stay the same if I boost my speed. And in particular, the speed of those waves described above stays the same. That is, the speed of light is the same for me, you and everyone, even if we are moving at different speeds relative to each other. This violates Newtonian mechanics, and it required Einstein and his relativity (for which the universality of the speed of light in a vacuum is a founding principle) to sort it out.
The twin paradox
Has been observed and confirmed to be true
Theory of Electromagnetic Fields: Maxwell
His theory of the electromagnetic field is one of the main pillars of modern theoretical physics and, of course, played a key role in the formulation and the development of Einstein's special theory of relativity. Electromagnetic Waves come in many varieties, including radio waves, from the 'long-wave' band through VHF, UHF and beyond; microwaves; infrared, visible and ultraviolet light; X-rays, gamma rays etc.
Einstein's theoretical framework: Theory of Special Relativity
In 1905, Albert Einstein determined that the laws of physics are the same for all non-accelerating observers, and that the speed of light in a vacuum was independent of the motion of all observers. This introduced a new framework for all of physics and proposed new concepts of space and time. Because light always travels at the same speed, time dilates and length contracts to compensate.
Young's crucial experiment
In May of 1801, while pondering some of Newton's experiments, Young came up with the basic idea for the now-famous double-slit experiment to demonstrate the interference of light waves. The demonstration would provide solid evidence that light was a wave, not a particle. In the first version of the experiment, Young actually didn't use two slits, but rather a single thin card. He covered a window with a piece of paper with a tiny hole in it. A thin beam of light passed through the hole. He held the card in the light beam, splitting the beam in two. Light passing on one side of the card interfered with light from the other side of the card to create fringes, which Young observed on the opposite wall. Young also used his data to calculate the wavelengths of different colors of light, coming very close to modern values.
Einstein's special relativity
It applies to situations where objects are moving very quickly, at speeds near the speed of light. Generally, you should account for relativistic effects when speeds are higher than 1 / 10th of the speed of light. Relativity produces very surprising results. We have no experience dealing with objects traveling at such high speeds, so perhaps it shouldn't be too surprising that we get surprising results. These are a few of the things that happen at relativistic speeds: Moving clocks run slow. Lengths contract when traveling at high speeds. Two events that occur simultaneously for one observer are not simultaneous for another observer in a different frame of reference if the events take place in different locations.
Define length contraction
Length contraction is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer. Length contraction arises due to the fact that the speed of light in a vacuum is constant in any frame of reference. By taking this into account, as well as some geometrical considerations, we will show how perceived time and length are affected.
Theory of electromagnetic waves
Maxwell further concluded that light propagated in electric and magnetic waves, which he believed would vibrate perpendicular to one another. Following this discovery, Maxwell revised his papers and gathered the findings, eventually publishing them together in his 1873 'Treatise on Electricity and Magnetism'. Maxwell's electromagnetic theory of light propagation eventually paved the way for a number of major technological innovations. The first and possibly most significant of these occurred in 1888, when Heinrich Hertz used Maxwell's theory to create instruments capable of sending and receiving radio pulses. This discovery, contributed to the creation of the television and the microwave and without Maxwell's tireless efforts, many of the modern conveniences upon which society has come to depend would not exist.
The Standard model: Maxwell's theoretical ideas
Maxwell's equations don't contain quantum mechanics. They are classical equations. But if you take the quantum mechnical description of an electron, and you enforce the same charge conservation law/voltage symmetry that was contained in the classical Maxwell's equations, something marvellous happens. The symmetry is denoted "U(1)", and if you enforce it locally - that it, you say that you have to be allowed make different U(1) type changes to electrons at different points in space, you actually generate the quantum mechanical version of Maxwell's equations out of nowhere. You produce the equations that describe the photon, and the whole of quantum electrodynamics. Together, and with the Higgs boson thrown in to cope with the masses, they constitute the "Standard Model", the best theory we have of fundamental particle physics so far.
Discoveries in electricity and magnetism pt.2
Oersted's experiment that when an electric current is passed through a conducting wire, a magnetic field is produced around it. The presence of magnetic field at a point around a current carrying wire can be detected with the help of a compass needle.
Einstein's famous equation
One of the most famous equations in mathematics comes from special relativity. The equation — E = mc2 — means "energy equals mass times the speed of light squared." It shows that energy (E) and mass (m) are interchangeable; they are different forms of the same thing. If mass is somehow totally converted into energy, it also shows how much energy would reside inside that mass: quite a lot. (This equation is one of the demonstrations for why an atomic bomb is so powerful, once its mass is converted to an explosion.) This equation also shows that mass increases with speed, which effectively puts a speed limit on how fast things can move in the universe. Simply put, the speed of light (c) is the fastest velocity at which an object can travel in a vacuum. As an object moves, its mass also increases. Near the speed of light, the mass is so high that it reaches infinity, and would require infinite energy to move it, thus capping how fast an object can move. The only reason light moves at the speed it does is because photons, the quantum particles that make up light, have a mass of zero.
Muon
Particle discovered in a cloud chamber A lepton that is negatively charged and has a greater rest mass than the electron
2. Velocity of light is constant/ The speed of light: postulate of special relativity
Says that the speed of light in vacuum is the same for any inertial reference frame (c = 3.00 x 108 m/s). This is true no matter how fast a light source is moving relative to an observer. How x-rays travel. 186,000 miles per second 300,000 km/s
Maxwell
Scottish scientist who laid a foundation for Einstein Founder of modern physics
time dilation
Slowing down of time for an object moving at relativistic speeds. the slowing of moving clocks or clocks in strong gravitational fields the apparent slowdown in time for a rapidly moving object Example: twin paradox
Red shift
The electromagnetic radiation of an object is stretched out slightly inside a gravitational field. Think of the sound waves that emanate from a siren on an emergency vehicle; as the vehicle moves toward an observer, sound waves are compressed, but as it moves away, they are stretched out, or redshifted. Known as the Doppler Effect, the same phenomena occurs with waves of light at all frequencies.
Maxwell's theories on FIELDS and WAVES
The equations show that electric and magnetic fields can exist even in the absence of electric charges. A changing electric field causes a changing magnetic field, which will cause more changes in the electric field, and so on. Mathematically this is expressed in the fact that the equations can be rearranged and combined to get a new kind of equation, that describes a travelling wave. So not only do the fields become real physical objects - something that Faraday was the first to propose - but they can carry travelling waves. Those waves are electromagnetic radiation. That is, visible light, radio, wifi, X-rays and the rest, depending on the wavelength.
Maxwell's Relativity
The equations work in three dimensions, and relate fields pointing in different directions to each other. So the electric field in north-south direction depends upon what the magnetic field in the east-west direction is doing, for example. Maxwell wrote it all out component-by-component, direction-by-direction, in twenty seperate equations. These days we use vectors (objects with a length and an orientation, like an arrow) to condense the equations down to four. This makes a symmetry of the equations apparent. Like a sphere, they are the same from any angle. If I rotate the directions so that north becomes east, or southwest, or whatever, so long as I rotate all the axes together, nothing changes and the same equations still work.
The relativity of simultaneity
The first consequence of special relativity is known as the relativity of simultaneity. This shows that events that appear simultaneous in one reference frame, may not do so in another. If, for example, we place a light source between two observers that emits a beam of light in each direction, then the observers will think that the beams were emitted simultaneously if they reach each observer at the same time. If the observers are moving, however, then the beams will not reach both observers at the same time, and so they may conclude that they were not emitted simultaneously. Galileo's relativity shows that both views are correct. This means that what we perceive as the present only corresponds to what is occurring simultaneously to us, in our reference frame.
1. The Principle of relativity: postulate of special relativity
The laws of physics apply in every inertial reference frame. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and still in other frames, the New York crash may occur first. If the two events are causally connected ("event A causes event B"), then the relativity of simultaneity preserves the causal order (i.e. "event A causes event B" in all frames of reference).
time dilation: implication of special relativity
The second consequence of special relativity is time dilation. This states that for someone in an inertial reference frame, moving clocks appear to run slower. This means that the time between ticks is longer. This can be illustrated by imagining that we bounce a beam of light from two mirrors and observe it from both perspectives, one where the mirrors are stationary with respect to the observer and one where the mirrors are moving
The twin paradox: NO ABSOLUTE SIMULTANEITY
The twin paradox can be resolved within the standard framework of special relativity (because the twins are not equivalent; the space twin experienced additional, asymmetrical acceleration when switching direction to return home), and therefore is not a paradox in the sense of a logical contradiction. The Earth and the ship are not in a symmetrical relationship: regardless of whether we view the situation from the perspective of the Earth or the ship, the ship experiences additional acceleration forces. The ship has a turnaround in which it accelerates and changes direction whereas the earth does not. Since there is no symmetry, it is not paradoxical if one twin is younger than the other. Nevertheless twin paradox is useful as a demonstration that special relativity is self-consistent. In the spacetime diagram, drawn for the reference frame of the Earth-based twin, that twin's world line coincides with the vertical axis (his position is constant in space, moving only in time). On the first leg of the trip, the second twin moves to the right (black sloped line); and on the second leg, back to the left. Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg. Just before turnaround, the traveling twin calculates the age of the Earth-based twin by measuring the interval along the vertical axis from the origin to the upper blue line. Just after turnaround, if he recalculates, he'll measure the interval from the origin to the lower red line. In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the world line of the Earth-based twin. The traveling twin reckons that there has been a jump discontinuity in the age of the Earth-based twin.
Effects of Time Dilation: The Twin Paradox
The twin paradox is a thought experiment: one twin makes a journey into space and returns home to find that twin remained aged more. The twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This occurs because special relativity shows that the faster one travels, the slower time moves for them. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. In other words, from the perspective of the rocketship, the earth is traveling away from the ship and from the perspective of the earth, the rocket is traveling away.
time dilation
This is an actual difference of elapsed time between two events as measured by observers moving relative to each other. Time dilation effects are extremely small for speeds below 1/10 the speed of light and can be safely ignored at daily life. Time dilation effects become important when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light). The slowing of the passage of time experienced by objects in motion relative to an observer; measurable only at relativistic speeds.
2 postulates of special relativity
This is based on two very simple ideas; everything else follows from these. These are: The relativity postulate : the laws of physics apply in every inertial reference frame. The speed of light postulate : The speed of light in vacuum is the same for any inertial reference frame (c = 3.00 x 108 m/s). This is true no matter how fast a light source is moving relative to an observer.
Conservation of charge
This is built into Maxwell's equations is the conservation of electric charge. The equations can be rearranged to show that the only way to change the amount of electric charge in a given volume is to have an electric current take it away. You can't just "vanish" the charge. Or create it. That's what a conservation law means. Now there is a theorem due to the mathematician Emmy Noether which is well-known to physicists, and which states a deep relationship between conservation laws and symmetries. The conservation of charge should be associated with a symmetry, but what symmetry is it? The symmetry is a little obscured in the usual form of Maxwell's equations, which uses electric and magnetic fields. But if, instead of the electric field, we use the voltage, and if we do a similar thing with the magnetic field, we get a new, equivalent set of equations which now do have a more obvious symmetry, in that only voltage differences matter. The absolute voltage has no meaning. This is why birds can sit on high-voltage electric cables without turning into tasty fried snacks. The wires are at a high voltage, but as long as the birds are at the same voltage, no electric current flows and no harm is done. Changing the voltages everywhere in the world at once makes no difference to anything. In fact for all you know, I just did it then, while you were reading that sentence. Invariance under changes of voltage is a symmetry of the equations, which has important consequences, especially once quantum mechanics comes along. equations which now do have a more obvious symmetry, in that only voltage differences matter. The absolute voltage has no meaning. This is why birds can sit on high-voltage electric cables without turning into tasty fried snacks. The wires are at a high voltage, but as long as the birds are at the same voltage, no electric current flows and no harm is done. Changing the voltages everywhere in the world at once makes no difference to anything. In fact for all you know, I just did it then, while you were reading that sentence. Invariance under changes of voltage is a symmetry of the equations, which has important consequences, especially once quantum mechanics comes along.
The Lorentz factor to special relativity
Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be "running slow". Note that for speeds below 1/10 the speed of light, Lorentz factor is approximately 1. Thus, time dilation effects and extremely small and can be safely ignored in a daily life. They become important only when an object approaches speeds on the order of 30,000 km/s (1/10 the speed of light).
Resolution of paradox leads to an insight in:
___ is relative to the observers reference of frame
The Nature of Light
a form of electromagnetic energy with properties of particles and waves
frame of reference
a system for specifying the precise location of objects in space and time a system of objects that are not moving with respect to one another Everything is relative; it depends on your frame of reference. Different observers see different things if they are in different reference frames (i.e., they are moving relative to each other). Special relativity deals with observers moving at constant velocity; this is a lot easier than general relativity, in which observers can accelerate with respect to each other. Note that frames of reference where the velocity is constant are known is inertial frames.
gravitational waves
a wavelike bending of space generated by the acceleration of massive bodies. Ripples that travel outward from gravitational sources at the speed of light. fluctuations or waves in four-dimensional spacetime Violent events, such as the collision of two black holes, are thought to be able to create ripples in space-time
length contraction
dx'=dx/gamma decrease in length of an object as measured by another frame of reference Shrinkage of space, and therefore of matter, in a frame of reference moving at relativistic speeds. Objects that are moving undergo a length contraction along the dimension of motion; this effect is only significant at relativistic speeds. Length contraction is negligible at everyday speeds and can be ignored for all regular purposes. Length contraction becomes noticeable at a substantial fraction of the speed of light with the contraction only in the direction parallel to the direction in which the observed body is travelling. An observer at rest viewing an object travelling very close to the speed of light would observe the length of the object in the direction of motion as very near zero.
special relativity
helped point to idea of singularity the laws of physics are equally valid in all frames of reference moving at a uniform velocity In 1905, Albert Einstein determined that the laws of physics are the same for all non-accelerating observers, and that the speed of light in a vacuum was independent of the motion of all observers. This theory introduced a new framework for all of physics and proposed new concepts of space and time. Einstein then spent 10 years trying to include acceleration in the theory and published his theory of general relativity in 1915. In it, he determined that massive objects cause a distortion in space-time, which is felt as gravity.
Gravitational lensing occurs when
massive objects bend light beams that are passing nearby.
inertial reference frame
reference point where velocity is constant one in which Newton's law of inertia is valid
gravitational redshift
the shifting to longer wavelengths of radiation from an object deep within a gravitational well The lengthening of the wavelength of a photon due to its escape from a gravitational field. a redshift caused by the fact that time runs slowly in gravitational fields
Lorentz Transformation Factor
β=sqrt 1-v^2/c^2 The formula for determining time dilation is: where Δt is the time interval between two co-local events (i.e. happening at the same place) for an observer in some inertial frame (e.g. ticks on his clock), this is known as the proper time, Δt' is the time interval between those same events, as measured by another observer, inertially moving with velocity v with respect to the former observer, v is the relative velocity between the observer and the moving clock, c is the speed of light, and
