NAME: Adam Seering
Directions: Answer ALL of the questions. You may use notes. This is an untimed, INDIVIDUAL, take-home quiz. Please type your answers.
1. State the twin paradox, using special relativity to argue each side. Why is this not really a paradox? Describe two experiments that corroborated Einstein's theory of special relativity. Use the observation of light on a moving train to explain the origins of time dilation.
The twin paradox is as follows: There are two people on Earth who are twins, of the same age. One stays on Earth; the other goes into a rocket ship that travels away from Earth at near the speed of light. At some point, the spaceship turns around and returns to Earth. Based on the basic theory of relativity, the twins should experience time at different rates, because they are moving relative to each other. But which would experience less time in between the rocket's takeoff and its landing? After all, they are both moving at the same velocity relative to each other; there should, by all accounts, be no difference. But there actually is a difference: The spaceship accelerates. Acceleration is not relative; if an object is accelerating, it can easily be determined that it is the object that is accelerating, not the observer. The twins do experience time differently, and the only difference between their two circumstances is that one has accelerated, and the other has not. Therefore, acceleration, not velocity, must be the cause of time dilation.
Time dilation can be seen as a necessary idea through another thought experiment, involving a laser on a train. Say you had a train, pulling a really long car at near the speed of light. Say that there was a laser at one end of the train, pointing towards the other end. To an observer on the train, a beam of light emitted from the laser would seem to take a certain length of time, t seconds, to hit the far wall of the train. But while light travels at a constant speed in all reference frames, the train does not; an observer would see the train moving at near the speed of the beam of light, so it would take much longer for the beam of light to reach the back wall. This means that the two t's would be different. But this can't be true; an event occurs only once, not many different times. The only possible explanation for this situation is that the two observers experience time differently. This difference in the experiencing of time is called 'time dilation'.
One experiment that was conducted to verify special relativity was a direct verification of time dilation. Two synchronized, extremely high-precision clocks were created; one was left on the ground, and one was put into a jet airplane and flown around at high speed for a significant period of time. After the jet landed, the clocks were checked, and they were found to have desynchronized by exactly the amount predicted by relativity. Another experiment verified that light moved at the same speed in all reference frames. A beam of light was split into two separate beams, going in two different directions. After an equal distance, the beams of light were re-joined, and the intensity of the light was measured. If the light traveled at a constant speed according to a universal reference frame, or an 'aether', the fact that the Earth would be moving through that reference frame would cause the two beams of light to appear to move at different speeds to an observer on Earth. Thus, when they were re-joined, they would no longer be synchronized, and their waves would interfere with each other and the intensity of the beam of light would decrease. But there was no decrease in intensity, so the two beams of light must have been moving at a constant speed without reference to a universal reference frame.
High energy particle physicists spend much of their time smashing subatomic particles together with enormous energy. How are they able to energize these particles? How do they smash them together? And most importantly, why are they doing this? How do these collisions give us insight into the origins of the universe?
Subatomic particles are accelerated to near the speed of light using devices called, not suprisingly, particle accelerators. These accelerators, as was discovered in Puzzle #2, use magnets to propel a magnetically-charged particle stream forward. The particles are smashed together by taking a single stream of accelerated particles, splitting it into two different streams, and aiming the two separate streams at each other. The streams then hit each other, and the products of the collision are detected and measured, so that we can learn from the collision.
We are smashing particles together because doing so can help us simulate the conditions of the early universe, and in the Big Bang. During those periods of time, the universe was essentially a massive grouping of extremely high-energy subatomic particles; studying the properties of high-energy subatomic particles can teach us a lot about how these particles behaved during the Big Bang.
3. In The Elegant Universe Greene helps to explain some of the strange phenomena of quantum mechanics using clever analogies. Describe your favorite of his analogies and explain how he uses it to better grasp aspects of this bizarre theory.
I find many of his analogies to be quite interesting and effective, so to pick one, I'll talk about his on-going analogy using George and Gracie. In particular, I'll refer to their experience in the H-bar with ice cubes. It helped me understand this theory more effectively by giving an example of what quantum mechanics would be like if its effects could be percieved on a macro scale. Among other things, it demonstrated how strange and counterintuitive quantum mechanics really is; no one would ever expect that an ice cube could simply appear outside of its glass.
4. What is invisible astronomy? Why is it such an important field of astronomical research? Why do radio dishes have to be so big to achieve comparable resolution to a much smaller visible telescope? Describe the advantages of setting up arrays of telescopes, working in tandem. How can you use a single, unmovable, large antenna (like the enormous one at Arecibo) to look at more than just one region of the sky?
Invisible astronomy is astronomy based on non-visible ranges of the electromagnetic spectrum. It is very important to astronomy because visible light makes up a tiny portion of the electromagnetic spectrum; light from other portions of the spectrum contain information that cannot be gathered from the visible spectrum. Also, there are advantages to examining other regions of the spectrum, especially the radio region. Radio signals penetrate even a cloudy, sunlit atmosphere, so there is little that forces a radio telescope to cease operation. Also, many objects that are not energetic enough to give off optical light give off radio signals, so it is possible to detect far less energetic objects with radio astronomy.
Resolution of a detector is proportional to the wavelength of the incoming radiation; a shorter wavelength leads to a higher resolution. Radio waves have a much longer wavelength than visible light, so they have an inherently lower resolution. Resolution can be increased by increasing the area covered by the detecting mechanism, so to get a comparable resolution with radio detectors, the detectors must be much bigger than optical detectors. But area of the detector is much less important to resolution than is diameter. As a result, many small detectors can be connected to effectively simulate one very large detector, whose diameter is the distance between the farthest-separated radio dishes. This instantly multiplies resolution by a factor of a hundred at least, if not far more, without nearly a hundredfold increase in cost or equipment. Clearly, linking radio dishes like this is well worth the effort.
A single, immovable, large antenna can view different regions of the sky in two different ways. The easiest way is simply to wait for the Earth to rotate so that the antenna directly faces the different region. One, much more useful way is to move the detector mechanism. With a spherical mirror, light from different regions of the sky can be detected by moving the detector over different regions of the mirror; the mirror is spherical, so it will have the same properties regardless of what angle it is viewed at. Using a spherical mirror leads to spherical distortion, the focusing of light along a line instead of to a point, but this can be compensated for by using a linear, as opposed to a one-point, detector.
5. Some physicists believe that as we live we choose one path, but all the other possible paths are being played out in parallel universes. Do you believe this? What experimental evidence has been found to show that this IS actually true for electrons? Can there be any other way to explain this strange result?
I take a practical point of view on this idea; I say that it may well be true, but it really doesn't directly affect me because, by definition, I can't interact with these other, parallel universes. Should this situation change, I will have to change my point of view, but until then, I'm staying pragmatic on this issue.
Electrons have experimentally been shown to exist as a probability until they are 'observed', although observation is ill-defined, if not in science in general than at least in my experience. If observing them causes them to appear in a location, who is to say that there are not other universes, where they appear in a different place? We really can't prove definitively either way at this point; there may be other universes, with us simply selecting one and following it, or it just may be that the actions of electrons are random.
6. Explain why there is great conflict between quantum mechanics and relativity (be sure to use such terms as quantum fluctuations and quantum claustrophobia.)
One point of conflict between quantum mechanics and relativity is that relativity is not dependent on the scale of objects. According to it, size does not matter; space is smooth, and objects react identically, regardless of their size. But quantum mechanics states that objects become more unpredictable as their size, and the scale of observation, becomes smaller. This is quantum claustrophobia, the effect that objects, especially extremely tiny objects near or on the Planck scale, behave more erratically as their precise location is more precisely identified. Also, quantum mechanics describes space as incredibly twisted and warped on an extremely small scale, but relativity assumes it to be smooth on any scale.
Quantum fluctuations are where a particle and an antiparticle appear, and then annhilate each other and disappear. They appear due to a random fluctuation in the energy level in their area of the universe, a fluctuation that can be predicted, if not pinpointed, by quantum mechanics. But according to relativity, nothing 'random' exists; relativity is seemingly the last major scientific theory that rests on the idea that the universe is entirely predictable. Because of these two apparent paradoxes, as well as many others, quantum mechanics and relativity are inherently mutually exclusive.