CK-12 21st Century Physics: A Compilation of Contemporary and Emerging Technologies Read online

  Yes, that’s correct. By the end of the century, Henry Cavendish utilized a sophisticated piece of equipment to measure the gravitational attraction between massive lead balls. Comparing this amount of force of attraction to the sphere’s weight (their attraction to the sphere Earth) he was able to determine the density of the Earth. This allowed others to then determine the mass of the Earth and ultimately (as far as understanding gravity at least) the value of , the universal gravitation constant.

  Today that value is known to be with an uncertainty of about . Or put another way, about %.

  Wow. They know the value of really well!

  No, not very well at all in some respects. To put that in perspective, we know the mass of the electron with 2000 times more certainty, Planck’s constant with 2000 times more certainty, and the electron’s charge with 4000 times more certainty than we know the Universal Gravitation Constant! http://physics.nist.gov/cuu/Constants/index.html. Another interesting thing about the universal gravitation constant is that we don’t have any strong evidence to believe it is necessarily universal or constant. In conjunction with Newton’s law of gravitation it does work very well for examining the motions of the planets around the Sun and for getting spaceships to the Moon, Mars, and even the outer fringes of our solar system with great precision. But, there are still some pretty basic questions that can be asked for which we don’t know the answers. Such as, has always been this value from the big bang until now? Is the same value near the super massive black hole in the center of our galaxy as it is here in a physics lab? What does the value of really tell us about the fabric of our universe?

  Um, I’ll hold onto those for later. We have a universal law of gravitation, and we know the value of at least pretty well. Any luck on how gravity applies a force without touching?

  Figure 2.7

  Albert Einstein at the age of at the time of his most amazing year of work that he published the next year in 1905.

  Yes, and this question brings us into the century and to the famous physicist Albert Einstein (1879 - 1955). In 1905 Albert Einstein had a rather remarkable year. Notice in the 1904 picture of Einstein that he is not the iconic old man with unruly hair. This is Albert Einstein at the age of , at his sharpest. In 1905 he published three amazing papers. These papers explained the photoelectric effect, explained Brownian motion, and introduced his special theory of relativity. All three are amazing and you may wish to do some studying on any or all of these topics. However, it is the third paper on the special theory of relativity that will forge a connection to gravity for us. In this paper he postulates that the speed of light is a constant in all inertial reference frames and that it is the ultimate speed limit in the universe. The paper postulates that the law of physics are the same (or are "invariant") for all observers moving with a constant velocity. Einstein’s paper did away with a need for "luminous ether," changed concepts of time and space and the concept of simultaneity, but still did not deal with gravity.

  In 1915 Einstein published his paper on general theory of relativity, in which he postulated that the laws of physics are the same for observers moving with constant acceleration (that's why it is more "general" than the "special" relativity). In this paper, Einstein introduces the concept that mass bends the fabric of space and time and that this warping of space and time IS gravity.

  Bending space and time…science fiction? And, if I did believe it, how does it account for gravity exerting a force without touching?

  Not fiction, way stranger than science fiction, because it really happens. This amazingly complex idea is easy and fun to model. Time for some more homework.

  Warping the Fabric of Space

  Materials: large metal coffee can, bubble solution, pipette or eye dropper, and mineral oil

  The empty coffee can has one end that is open and one that is closed. Punch or drill a hole through the side of the can near the closed end. A couple of holes the size of a pencil would be good. Dip the open end of the can into the bubble solution. A film of bubble solution should cover the opening. Use the pipette to place a drop of oil in the center of the film of bubble solution. Place another drop on the film off center. Watch what happens. Why do the drops attract each other? Experiment with placing the drops in different ways. Can you create a drop that orbits another drop?

  An alternative to this experiment can be done with a trash bag slit to make a single layer of plastic anchored between tables with various balls placed on its surface or if you have a trampoline it can serve nicely as a model universe.

  OK—I’m through playing with oil drops on a soap film. Remind me how that experiment models general relativity and the warping of space and time.

  The film represented space (or at least two dimensions of it). The oil drop was modeling a massive star. The drop’s mass bent the space (bubble film) around it. When another drop was placed nearby, it felt "attracted" to the first one because it just slid downhill to it. The first drop didn’t reach out and grab the second drop, instead it created a bend in space that affected the motion of the second drop. With a little practice you can easily create two small drops orbiting a larger drop similar to planets orbiting the Sun.

  And what about time?

  It doesn’t really model that part. But it should help you see how mass can bend the space around it. It turns out time is just another dimension. There are three dimensions of space and one of time in our normal everyday world. When you are in class you are separated from the people to either side, in front and behind you, and in the classroom above you (assuming there’s a floor above you) by three dimensions of space. You are separated from the person who uses your desk next by a period by time. In his work on general relativity, Einstein’s mathematics led him to believe mass distorted space and time.

  I’m a science student. I want some evidence. Does this really happen?

  Figure 2.8

  Einsteins letter shows how to look for mass bending light during a solar eclipse.

  Remarkable claims demand remarkable evidence. Einstein knew that others would be skeptical—it is the nature of science! He even offered a few ways for others to test his ideas. One test he suggested was to look at Mercury’s orbit. It is so close to the Sun that the way the Sun warps space around it should affect Mercury’s orbit. General relativity correctly accounted for some motions of Mercury that were known and could not be explained by Newtonian gravitation. He also suggested utilizing a total eclipse of the Sun to see if the positions of stars located behind the Sun would appear to be shifted because their light had to pass so close to our massive Sun.

  In 1919 the first attempts were made at making these measurements. These results were inconclusive but subsequent measurements during an eclipse in 1922 matched wonderfully with Einstein’s predictions. This science was newsworthy in 1919.

  Figure 2.9

  The 1919 Illustrated explains the science of the dayverification of aspects of Einsteins general theory of relativity by British astronomer Arthur Eddington.

  Figure 2.10

  The 1919 Solar eclipse. The small white circles were drawn around stars visible during this 1919 solar eclipse.

  Cool. Did general relativity predict any other interesting astronomical occurrences?

  Boy, it certainly did. It was so amazing that Einstein didn’t believe it himself! His mathematics indicated that something was totally wrong according to what was held to be true at that time. It was so remarkable that Einstein introduced a “constant” to get rid of it and to make the mathematics fit the “known” reality.

  What was it? What did it indicate?

  General relativity showed that the universe should either be expanding or contracting—that it could not simply “be.” It could not exist in a static manner.

  But I thought that the universe is expanding—at least I think I’ve heard that.

  Right. But in the first half of the century that is NOT what scientists held to be true. Many religions have a moment of creation as part of thei
r theology. The scientific community of the early 1900s did not share that paradigm. The widely held scientific view of the universe was very different from what it is today in many ways. One substantial way it was different was that most scientists believed that the universe was and always had been very much the way it was seen to be at that time.

  And how was it “seen to be” at that time?

  All the stars that you can see with the naked eye in the clearest, darkest night sky are part of our Milky Way galaxy. In fact, the terms Milky Way and galaxy represented the same celestial bodies in the late 1800s. In fact, even if you have a really nice backyard telescope, all of the stars you can see belong to the Milky Way galaxy. In the mid-1800s that was the extent of our knowledge. Astronomers of the time would have referred to “the galaxy” and the faint glow of it in our sky as “the Milky Way.” What we now call our galaxy was considered to be the entire universe. There were a few interesting non-star things in the sky known as nebulae (cloudy spots). You can see a lovely nebula in the constellation Orion in the three stars that make his sword. You can also see a much smaller (smaller in appearance from Earth that is) nebula in the constellation Andromeda known then as the Andromeda nebula.

  I thought that was called the Andromeda galaxy.

  Figure 2.11

  On a very dark night the Andromeda galaxy (in green box) is barely visible to the naked eye in the constellation Andromeda. It is the only object visible with the naked eye in the northern hemisphere that is not within the Milky Way galaxy.

  It is now. In the late 1800s some very large telescopes were created. When astronomers looked at some nebulae like the Andromeda nebula and the Whirlpool nebula, they were able to observe individual stars. Because such large telescopes were needed to resolve these into individual stars, it meant that these stars were VERY far away. Examining other nebula like the Orion nebula showed they were truly wisps of glowing and reflecting gas. We also made observations of our own galaxy that led us to understand that we actually exist in a flattened out collection of stars. At this point, we then realized that the universe was MUCH larger than our own cluster of stars and actually contained many far-flung collections of stars. The term galaxy was eventually re-tooled to describe the isolated large clusters of stars and the word universe came to mean all of the known space including these island galaxies.

  The term Milky Way came to be the name of our galaxy. So three terms—Milky Way, galaxy, and universe, which were originally synonymous, came to mean three different things as our understanding of the structures in space evolved from the late 1800s into the 1920s. A galaxy is a collection of billions of stars held together by mutual gravitation, the Milky Way is our galaxy, and the universe is ALL of it with some billion individual galaxies each containing billions of stars.

  Figure 2.12

  Photographed through a large telescope using a long exposure the spiral structure of the Andromeda galaxy becomes apparent.

  So the universe is a lot bigger than we thought, and it contains lots of galaxies. But what does this have to do with gravity?

  In the early to mid–1900s, astronomers turned their attention to these very distant galaxies to try to determine how big the universe was. There is some very interesting history of astronomy that I’m going to have to leave out. These amazing details are provided at http://cosmictimes.gsfc.nasa.gov/1929/guide/andromeda_farther.html. The full story involves some fascinating discoveries and early contributions of women in astronomy. The end result is often attributed to Edwin Hubble. One major physics concept that played a key role in Hubble’s discovery, as well as later work regarding our universe and galaxies, is the Doppler effect.

  I think I’ve heard of that, but can you review for me?

  Sure. The standard example is what you observe when a train is coming toward you blowing its horn. As the train approaches, the frequency of the sound you hear is transformed to a higher pitch by the train’s motion. As the train passes you, the sound of the horn will drop to a lower pitch as it travels away from you. If you don’t have a speeding train nearby, just tune your TV to a NASCAR race. When the coverage cuts to the camera stationed right down along the track you will hear a change. The sound that the engines make shifts frequency as the engines pass the camera. The sound shifts from a high-pitched whine to a deep roar. As the cars race toward you (the camera) the pitch is shifted to a higher frequency. When the car then moves away from you it is shifted to a lower frequency. A microphone riding alongside the car would hear a frequency in between the two. This is a noticeable effect because the speed of the observer is a significant fraction of the the speed of the sound. As the car rushes toward you, the vibrations causing the roar of the engine are occurring closer and closer to you and thus taking less time to travel to you. Therefore, they arrive at your ears with less time between them, which makes the pitch higher. Of course, the similar argument applies to the car moving away from you. A more detailed explanation can be found at the Physics Classroom, http://www.glenbrook.k12.il.us/GBSSCI/PHYS/Class/waves/u10l3d.html. This is known as the "Doppler effect," and applies to all waves, including electromagnetic waves such as light. We do not observe the Doppler effect with light in every day life because the speeds of the observer and source are a very small fraction of the speed of light.

  And a much more detailed explanation with history and mathematics can be found at http://www.phy6.org/stargaze/Sun4Adop2.htm.

  What Hubble concluded from his work and the work of others was that the light arriving from distant galaxies had been Doppler shifted. It had been shifted toward the red end of the spectrum, which meant the galaxies were moving away from us (or vice versa) at speeds that are significant compared to the speed of the wave—which in this case is the speed of light! Note, though, that this does not mean that the Earth is at the center of the universe. Imagine the universe as a bread pudding with the raisins representing the galaxies, and pick any raisin to represent our galaxy. As the pudding expands, the distance between the raisin you picked and any other raisin increases just as distant galaxies move away from us. This shows that the observed expansion of the universe does not imply that the milky way is at its center.

  What he determined was the more distant the galaxy was, the faster it was moving away from us. Every direction he pointed the giant Mount Wilson telescope, every distant galaxy was moving away from us. The conclusion: The universe is expanding!

  Figure 2.13

  Edwin Hubbles research showed the Milky Way was one of billions of galaxies and that the universe is expanding.

  That’s what Einstein’s general theory of relativity predicted!

  Good, I see that you’ve been paying attention. But, at that time it was such a radical departure from what was “known” to be true, that even Einstein couldn’t believe what his own work was telling him. In hindsight, it makes perfect sense. Here on Earth you can throw a ball up in the air. Because it’s under the influence of gravity it can either be moving upward and slowing down or it can be moving downward and speeding up. The one thing it can’t do is just sit in the air without accelerating. The same thing is true of the universe. Since all the galaxies are pulling on each other with gravity it makes sense that it could either be collapsing in on itself and speeding up as it does so, or expanding outward but slowing its rate of expansion due to gravity trying to pull it all together. Once Hubble’s data and conclusions were presented, Einstein proclaimed the addition of the stabilizing constant his biggest mistake.

  This is the big bang, right?

  Correct again. If the universe is expanding today, it had to be a bit smaller yesterday. Play the film backwards in your mind, and eventually the universe had a beginning and took up no space at all. Run it forward in time and you have the Big Bang—the creation of the universe. You’ll understand, of course, that such a major shift in the understanding of the universe doesn’t happen easily or overnight. There were many very bright scientists who tried very hard to argue that the universe wasn’t tr
uly expanding. One prominent astronomer, Fred Hoyle, was still arguing against the possibility in the 1950s when he used the term “big bang” to ridicule the concept that the universe had a beginning and was presently expanding. The name stuck, but unfortunately it is somewhat misleading.

  How so?

  A “big bang” sounds like a loud explosion. Of course, in space there is no sound. Also, an explosion, like a stick of dynamite in a rock quarry, throws energy and matter out into space. The big bang did not throw energy and matter out into space. It is the creation OF space and time and eventually matter condensed out of the energy (but that is “matter” for another chapter!).

  So if the universe is expanding, what’s it expanding into?

  Nothing. It is creating more space and time. It’s no more or less confusing than to ask where does the time for tomorrow come from. It doesn’t exist today, but by the end of tomorrow there will have been one more day in the life of the universe. The dimension of time expanded.

  Is there other evidence for the big bang besides Hubble’s receding galaxies?

  Lots of evidence. Because the idea of the big bang assumes the universe started very small it also started off with immense heat and energy. Because it has not been expanding for an infinite amount of time, there should be some remnants of that energy left over in empty space. In the mid-1960s Arno Penzias and Robert Wilson were working for Bell Laboratories with microwave communication. While doing this work they accidentally discovered that no matter where they aimed their microwave receiver they received a constant background static. It was determined that this signal came from the leftover energy from the big bang and is called background cosmic radiation. This cosmic microwave background radiation (CMBR) tells us the temperature of space is about Kelvin. This level of background radiation had been predicted earlier by George Gamow. It is always a great test of theory to PREDICT something and then later find out that it really exists! Another case of this occurred in the findings of the Cosmic Background Explorer (COBE) satellite. It was launched in 1989 to look for variations in the background radiation. Earlier examinations from Earth showed the CMBR to be very constant in every direction. This fit the theory, but it couldn’t be perfectly constant or there wouldn’t be clumps of matter (galaxies and stars) like we have now. COBE mapped the entire sky looking for minute variations in the CMBR and found exactly what theories predicted should be there—variations of about one part in .