Suppose you are driving on a highway right next to another car and you are both traveling at the same speed. What do you see if you look over at the other car? Does it look like it is moving? To you, the other car may seem like it is at rest and that you are at rest as well (and that the ground is moving behind you). This observation is because there is no difference in your speeds. So what would you see if you could travel next to a beam of light and look over at it just as you did with the other car?
And, better yet, consider this. We know that in order for us to see, light bounces off an object and into our eyes, and our brains interpret the light signal. What if you are traveling at the same speed as light and you hold up a mirror. Would you see your reflection? When you are sitting still the light bounces off your face, then bounces off the mirror to your eyes. If you are traveling at the speed of light, would the light ever be able to go ahead of you, bounce off the mirror, and then travel back to your eyes, or would you see a blank reflection because you are traveling with the light?
These are questions that Einstein spent many years thinking about before he developed any answers, and he built his theories on those of many other physicists that came before him. By the end of the century the speed of light had been tested to a pretty accurate meters per second (that’s about miles per hour!). What Einstein postulated is that light always travels at this speed, which we call , no matter how fast you are going. Our experience tells us that if we are going miles per hour and another car passes us at miles per hour, that other car seems to be going only miles per hour, which is called the relative velocity. This approximation works for us, but when you begin thinking at extremes, just adding or subtracting velocities does not work, however strange it may sound. In our experience we know that if we are in a truck going miles per hour and throw a ball in the direction we are traveling, the ball will have the velocity of the truck ( miles per hour) plus the velocity we give it, say miles per hour. In the absence of air resistance, an observer on the side of the road would see the ball go miles per hour. Along the same thread, suppose you are on a ship going % of the speed of light and you launch a missile at half the speed of light. According to Newton (and our intuition), the missile would have a velocity of , which cannot happen if light is the maximum speed. In reality, according to special relativity, it is incorrect to simply add the velocities. The most important thing to remember is that light travels at a constant speed, and it is the fastest anything can travel. The way to combine velocities is a bit more complicated than that, but results different than Newton would have predicted only become apparent at very fast speeds. This is why here on Earth at a tiny speed of miles per hour we don’t have to worry about relativity. Light-speed is the limit for speed. Therefore, if light were coming toward you, and you started to run, it would still approach you at a speed of , no matter how fast you run.
If you are in a car going almost the speed of light and you turn on your headlights, the light from your headlights would still appear to travel away from you at the speed of light. If you are watching somebody drive by at nearly the speed of light and they turn on their headlights, you would see the light still travel at the speed of light. The velocity of the car does not add to make the light go faster, as you might suspect. This seems ridiculous, it’s true, but there is experimentation to support this. Let’s look at some of the ramifications.
If we set the speed of light as a constant in all reference frames, whether you are moving or not, and we know that speed is displacement over time, then what must be varying from one observer to another is displacement and time. The variable (which is ) cannot change for light, so the displacement and time must change.
The concept is often explained by considering a flashlight on a moving vehicle. Suppose you are on a vehicle that is traveling at a constant speed. On this vehicle you have a flashlight mounted to the floor and pointed toward the ceiling and you watch as a beam of light travels from the flashlight toward the ceiling where you have placed a mirror. You use a stopwatch (a very fast one) to time how long it takes for the beam of light to travel from the flashlight to the mirror and back again. Because you know that light travels at a constant speed of , you can calculate the distance over which the light traveled . Now you jump off the vehicle (it’s still moving at a constant speed) and repeat the experiment, but this time you measure from the side of the road. Notice that when you were on the vehicle, the light only had to travel up to the ceiling and then back to the flashlight. When you are on the side of the road, the light has to travel a bit further. Consider the diagrams above to help clarify.
Figure 6.2
Diagrams of Distance Travelled by Light.
Notice in the diagrams that the light as viewed by the observer on the side of the road has to travel farther to reach the mirror and then return back to the flashlight. If the speed of light does not change, how do we reconcile these two observations? Is one of the observers wrong? The explanation given by Einstein and special relativity is that time slows down for observers who are traveling faster. The faster you go as the observer, the more time slows down for you. This is called time dilation. So the passenger on the vehicle taking the time for the light will measure a longer time than a person on the side of the road measuring the same light traveling at the same instance (or same event). The person on the side of the road measures a longer time on their stopwatch (the stopwatch ticks faster, so more time passes). The person on the vehicle measures a shorter time (the stopwatch ticks slower, so less time passes). That is, the stopwatches tick at different speeds. With this remedy we have reconciled the problem with the speed equation: .
For the passenger on the vehicle:
For the observer on the side of the road:
And so the proportions remain intact and the speed of light can remain a constant.
Not only is it true that time depends on the observer, but if we apply the laws of physics with this constant speed limit for light, then an object’s size and mass depend on the relative speeds of observers as well. What Einstein was able to show is that the faster your speed, the slower your time ticks (time dilation), and the faster you go in a straight line, the shorter you become in that direction (Lorentz contraction). It seems the deeper we probe and question, the stranger the explanations become!
But we have also seen this with real experimental evidence. One case in which this phenomena has been observed is with the muon in particle accelerators. A muon is just a particle, like an electron except much heavier. When just sitting, a muon will decay (kind of like radioactive decay) into other particles in about two millionths of a second (very, "very fast"). If accelerated at nearly the speed of light, the muon has been measured to last about ten times longer. Imagine if you lasted ten times longer than you normally would. For example, if you would normally live for 80 years, you’d live for 800 years if you were accelerated at such a rate! A factor of ten is quite significant. However, with the slowing down of your clock comes the slowing down of all your functions, and therefore you would not get “more done.” You would digest slower, think slower, etc. Everything would slow down. Essentially, from the slow person’s perspective, he or she would be living the same amount of life, just slower. It’s just relative. As it turns out, going super-fast to slow down your clock is not the fountain of youth (Greene ).
We have also seen evidence of special relativity on an airplane. Scientists placed an atomic clock (a clock that works by detecting the back-and-forth movement of electrons by detecting the emitted frequencies) on a plane while measuring the amount of time the plane was in the air according to an observer on the ground. When comparing the time shown on the “stopwatch” from land to the atomic clock on the plane, there was a definitive difference. The atomic clock measured less time, which means its “ticking” must have slowed down, evidence of special relativity (time dilation).
Another important application of special relativity is the global positioning system, or GPS. GPS uses satellites that are o
rbiting the Earth and traveling very fast, to locate positions, say, of cell phones. Because of their fast speeds, the clocks inside the satellites tick slower. Furthermore, there are the effects of general relativity. General relativity predicts that time ticks faster the further the clock is from a massive object, like Earth. Therefore, according to general relativity, the clocks on the satellites will tick faster. Combining the effects of special relativity (time dilation) and general relativity (distortions in the fabric of space-time due to massive objects), the satellites have a slightly fast clock (slowed by the speed and quickened by the distance from our planet). Because GPS is used in measuring position, and time is a very important ingredient in calculating position, scientists have to take relativity into account to achieve any decent accuracy. Without using calculations considering time dilation the GPS would not work accurately (Pogge “GPS”).
This all may seem hard to swallow and if you are really engaging your brain, it should. If you continue with your physics studies in college and take a modern physics course, you will get a more rigorous treatment of these concepts, and get to use actual mathematics to aid your brain in processing these new, strange theories.
Section 2: What Parts of Modern Physics are Still Being Researched?
“A successful unification of quantum theory and relativity would necessarily be a theory of the universe as a whole. It would tell us, as Aristotle and Newton did before, what things are made of, and what kind of laws those things obey. Such a theory will bring about a radical shift—a revolution—in our understanding of what nature is. It must also have wide repercussions, and will likely bring about, or contribute to, a shift in our understanding of ourselves and our relationship to the rest of the universe.” (Smolin )
Question 13: What can be considered the big problem facing physicists today?
We use general relativity for the physics of the very massive (planets, stars) and we use quantum mechanics for the physics of the very small (electrons, protons), so in most situations, they do not overlap. However, there are at least two situations that would be small and massive. The first is in black hole theory (black holes are very dense), and the second is in analyzing theory for the whole universe at the moment of the big bang.
In trying to combine the theories of general relativity and quantum mechanics, physicists currently get nonsense answers like infinity for calculated probabilities. The two theories at present cannot co-exist. This is the big problem for physicists today: The reconciliation of quantum mechanics and general relativity into a unified theory. It does not sit well with physicists when they have to stick two theories together that do not fit properly, like a piece-wise defined function.
Section 3: What are the Implications of Some of Modern Physics (Including String Theory, Nanoscience, Dark Matter, Black Holes, Parallel Universes, and The Graviton)?
Question 14: What are some of the implications of quantum mechanics and relativity? In the news there is mention of string theory, black holes, parallel universes, and other bizarre things.
One of the theories that is being explored as a possible unification theory (a theory that is more general and works to bring together quantum theory and general relativity) is string theory. The idea is that instead of the universe being composed of small point-particles, it is composed of infinitely-thin, rubber-band-like strings that vibrate. Recall how earlier we said that protons are made of three quarks, but the electron is an elementary particle, and it has no building blocks. In saying this about the electron we say that it exists only at a point, and does not have any radius (it’s not the sphere that you may be picturing). If an electron took up any space at all, there would be some sort of building-block material that is smaller than the electron. However, string theory says that these tiny, vibrating strings are the basic building blocks of all matter (including electrons), and what’s more, the theory seems to smooth out the problems that exist between general relativity and quantum mechanics. String theorists are attempting to rectify inconsistencies that have been observed by finding a more general theory that encompasses all of the laws of physics.
The length of a string in string theory would be about a Planck length (Planck was a scientist who made great leaps in quantum mechanics), which is about one hundred billion billion times smaller than the nucleus of an atom (that’s way too many zeros after the decimal to type here). They are so tiny that scientists cannot even begin to find experimental evidence of them. Presently string theory lies in the realm of mathematical theory.
How would we detect them? Well, it would help to know how scientists currently detect the particles inside an atom. It may seem archaic, but essentially physicists shoot tiny particles at other particles and then measure what happens. It’s kind of like closing your eyes and trying to find the shape and size of an object by throwing marbles at it and watching what the marbles do after they bounce off the object. What happens if you use big marbles as opposed to small marbles? You might gather by intuition that the smaller the marble, the better and more refined your understanding of the mystery object is. Have you ever played with that toy that’s made of hundreds of pins in a frame? If you push your hand into the pins and then take your hand away, you can see a “picture” or relief of your hand, like a mold. If the toy only had a few pins, the picture of your hand would not be very clear, but because there are so many pins that map out the landscape of your hand, you can see a very clear mold of your hand. The same is true for the “atom smashers” (the fond name we give the machines that speed up particles and shoot them at other particles). The smaller the particles are that we shoot, the better picture we get of the thing at which we are shooting.
The problems with general relativity and quantum mechanics occur at lengths a bit shorter than a Planck length, which is about the size of a string, or so it is theorized. This is extremely tiny. If physicists can shoot strings at particles, perhaps they can see inside the atom to its very tiniest of structures. However, we have a problem, assuming strings do exist. When you give a string a lot of energy (higher frequency), after a certain point, it starts to grow in size (again, theoretically), which does not help the cause of trying to peer into the very tiny world of the subatomic (Greene ). This “growing” effect is not expected until you try to pump the string with enough energy to probe scales that are smaller than that of a Planck length, so anything larger than a Planck length should still be accessible. Scientists are at a bit of an impasse here, but string theory has a ways to go if it’s going to be supported by experimental evidence. We are not even close to experimenting at this energy level.
There is some hope for string theorists at the new Large Hadron Collider at CERN in Europe. The energy that this atom smasher can give the accelerated particles (the “bullets” being shot) is much less than it needs to be to see strings (it’s not even in the ballpark). However, physicists might be able to see the effects of string theory. For example, you may not be able to see around a corner, but you may be able to detect that somebody is standing behind the corner by seeing his or her shadow. You are not directly seeing them, but you see the effects of their existence. One of the results of string theory is that gravity is not just a field, as you may have learned earlier in the year in your physics class, and physicists may be able to detect this by using the collider at CERN.
Let’s take a moment to discuss general relativity. Einstein helped us view gravity in a new way that is described in general relativity. We discussed special relativity earlier when we were exploring time dilation and Lorentz length contraction (and the constant speed of light), and we mentioned general relativity, but did not go into a conceptual description. General relativity addresses time and space as a fabric, and Einstein helps us visualize by telling us to picture the space-time fabric as a giant rubber sheet (although in reality space-time is not flat like a piece of paper). On this rubber sheet you should picture all the celestial bodies (Sun, planets, stars, etc.) resting. The larger the object, the more it presses dow
n on the rubber sheet. (Please suspend the fact that there is no gravitational force to pull the planets and stars down on the rubber sheet. This isn’t quite a perfect metaphor.) This view of space-time helps us to better picture how gravity is communicated from object to object and helps us answer the question of how the Moon knows or feels the presence of the Earth, and thereby causes it to have its present motion. The problem with Newtonian physics is that there is no mention of how planets “feel” gravity. In Newtonian physics, gravity just “is.” Newton was aware of this problem as you can see in the quote below.
“Tis unconceivable [sic] that inanimate brute matter should (without mediation of something else which is not material) operate on and affect other matter without mutual contact…. That gravity should be innate, inherent and essential to matter so that one body may act upon another at a distance through a vacuum, without the mediation of anything else by and through which their action or force may be conveyed from one to another is to me so great an absurdity that I believe no man who has in philosophical matters any competent faculty of thinking can ever fall into it….” (Newton, “Letter”)
Picture yourself and an elephant standing on a trampoline. Even with your eyes closed you could sense the presence of the elephant (although you may not know that it’s an elephant) by the way it causes you to slide and lean in a little toward it on the trampoline. And, the larger the elephant, the greater it would affect your position next to it. Einstein managed to help us resolve Newton’s problem by helping us see that the celestial bodies affect one another through the distortion of the fabric of space-time in which they exist.
CK-12 21st Century Physics: A Compilation of Contemporary and Emerging Technologies Page 15