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| Moving Light Clock |
Everyone has seen this question at some point in their lives: If a car was traveling at the
speed of light with its headlights on, would any light come out? Almost everything your grade 11 (and under) physics teacher has taught you about kinematics will be completely useless to you, so to find the answer, you'd best read on.
Way back when, scientists believed that light traveled through a medium called "ether", much in the same way sound traveled through air. They were promptly proven wrong. Light does not behave like sound. A snail witnessing the first light of dawn would measure the speed of light the same as a starship captain heading at medium impulse towards the exact same sun. No matter how quickly you are heading to or away from the source of light, you will always measure the speed of light the same. In other words, the captain would not measure a faster speed of light just because he is traveling towards it at medium impulse. However, it is important to note that an outside observer would definitely see the light moving quicker relative to the ship.
Some people refused to acknowledge this, but some people, like Einstein, accepted it and built giant theories of physics from it. This theory was called "relativity". It becomes less incomprehensible when you think of it as a bunch of (albeit) weird conclusions derived from just a few, basic premises. These premises are...
There is no such thing as absolute space. There is no universal coordinate map. Everything that is to be measured can only be measured relative to something else. For example, if I asked you how far you walked to school on Monday, you could either say 5 km relative to the Earth, or you could go to the trouble of taking into account the Earth's rotation by measuring it relative to some arbitrary point in space.
There is no such thing as absolute time. There is no universal clock. Believe it or not, the people who ride past you on a bus (traveling at constant motion) are actually aging slower than you are (of course, it's only by miniscule fractions of a second). Conversely, the people on the bus believe that YOU are aging slower than THEM. And the beautiful part is that all of you are right.
This is because, when in constant motion relative to a stationary object, it is impossible to determine which object is the moving one.
The only exception to this rule is light. No matter how you run from it, a death ray will always kill you just as quickly as if you had stayed still. Only your friends watching you at a safe distance would measure the light moving slower relative to the running you.
Time is the fourth dimension.
A consequence of these premises has already been mentioned. Here is some sort of explanation to the bus thing: Let's say you have a photon bouncing between two horizontal mirrors. This is called a light clock (A). Then, let's say you add another one (B), and this one is stationary while A is moving at a constant 10 m/s. You would think that, like in a game of pong, the photon would bounce off the bottom one and then fly up into the air, missing the top mirror. But it wouldn't. This is because these clocks have no way of determining which clock is moving because in constant motion, you really can't tell. Therefore the photon is forced to travel at an angle, and this makes it have a longer trip. Since the speed of light is constant (the photon must move at the same speed, but now at an angle), the photon takes longer to reach the other mirror. Time slows down.
Another consequence is that in constant motion, observers will measure your width to be shorter. This works the same way as the previous example, only since it takes longer to tick (time decreases), you can infer that distance also decreases. This is because with constant motion time is directly proportional to distance.
Einstein also postulated that we are all moving at the speed of light. Remember how time is the fourth dimension? Well, when we're stationary, we are moving through time at the speed of light. When we move in any of the three spatial dimensions, we "borrow" from that speed and move slower through time. This neatly explains the oddity of time slowing down in constant motion.
So to answer the question so far is that, yes, the headlights would shine. The sad bit is that since it is going at the speed of light, it will have an infinitely small length, according to an outside observer.
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| Moving Light Clock |
Once, there was a man named Simon who had spent most of his life in a large box. For years he had been eating, drinking, and reading sports magazines in that box (and doing other things that constitute the life of an average North American male), never wondering what lay outside. One fateful day, he opened the door and asphyxiated in open space but not before seeing that his box had been propelled in a single direction this whole time at precisely 9.8 m/s2, the acceleration due to gravity.
If poor Simon had not died, he would have reached the same conclusions that Einstein did: that the effects of acceleration were the same as gravity. This meant that the mysterious force of gravity could be explained by using the more familiar acceleration. This realization goes under the names "Einstein's Happiest Thought" and/or "The Equivalency Principle".
This realization also brought about his famous idea of curved space. Let's resurrect Simon for a moment and put him in a giant spinning top with a measuring stick. From our point of view, as he is trying to measure the circumference of his new prison, his ruler shrinks in length, as demonstrated by special relativity; therefore, he measures a smaller circumference. This troubles him because now the circumference is not twice the value of pi times the radius, it's smaller.
Einstein realized that this could only happen if the plane on which the circle was drawn was not flat - it had to be curved. Acceleration, and conversely gravity, causes the curvature of the universe. All matter does not move in a straight line anymore. They follow the path of least action by gliding along the curves. These paths are called geodesics.
Einstein did not just pull this idea out of a hat. He had read up on Newtonian theories of gravity, and he was unsatisfied with some of the details. Newton said that gravity was instantaneous. Any shift in mass anywhere in the universe would immediately effect all matter everywhere else. This violated the principle of nothing going faster than the speed of light, so Einstein scratched that part out and rewrote it. Any shift in mass will cause "gravity ripples" that move at, and no faster than, the speed of light.
Where...
Don't ask how he derived this, but Einstein also discovered that mass and energy were not independent concepts. This means that matter is, in essence, frozen energy. This relation becomes very important later on when describing the way mass is conjured up from one-dimensional stringy objects. Note: Since c2 is such a large number [(299,792,458 m/s)2], a little mass means a lot of energy. This also means something very odd happens to the car.
This equation shows why nothing can go faster than light. The formula for kinetic energy is Ek=[m x v2]/2. As you can see, mass (m) and velocity (v) are directly related to energy. Say the car has a mass of n. The faster it goes (the higher the value of v), the more energy it has. Since E=mc2, this energy translates into more mass. For the car to go at the speed of light, it would have infinite mass. A crushing defeat for Star Trek fans everywhere.
Another thing physics teachers neglect to mention is that our chemistry teachers have been lying - or at least shamelessly misleading - us. The atom is not anything like a Bohr diagram. There are no neat circles connecting the stationary electrons. In the quantum world, nothing is where or what it was a moment ago, nothing is defined as anything more than a probability, and things constantly jump through walls and walk on water. In fact, the atom may not even be nature's fundamental building block. What's more, this has all been scientifically proven.
Scientists studying thermodynamics in the 19th century came to the odd conclusion that an oven at any temperature contained an infinite amount of energy. This was mostly because they had based their conclusion on the assumption that energy was continuous. In a stroke of genius, Max Planck solved their problems by proposing that energy came in discrete chunks called quanta (singular: quantum).
Not to be outdone, Einstein concluded that light, too, came in discrete chunks. These chunks of light are called photons. He observed that light can infuse enough energy onto a metallic surface to actually displace some of its electrons. Here is how he came up with his conclusion: If light came in chunks, each of them carrying a certain amount of energy depending on its frequency, then the amount of electrons displaced would be effected by the brightness of light (not to be confused with frequency), but the rate of displacement would only increase if the frequency was shorter. Imagine it this way: Pretend there are 100 cars lined up behind 100 red lights. Each car is programmed to go at 60 km/h (it's frequency) when the red light turns green. When you increase the brightness, it's like turning a red light green. No matter how many you turn green, the cars still go at 60 km/h.
This was not the end of the matter, however. Another experiment showed that light beams, when passed through two splits, interfere with each other like waves. Even when single photons were passed through, they somehow had pre-arranged cancellation areas with other photons. Wave or particle, the people asked. The debate raged on for a while, but now it has waned slightly. Scientists have concluded that light does not behave like a wave or a particle. Light behaves like light.
This may seem like a discouraging barrier on the frontiers of discovery, but it is not the last. Louis de Broglie, a man unfortunate enough to be in France during WWI, found that matter has a similar duality. Energy had been related to both frequency and mass. Once more, scientists found themselves in a situation they had been in before. But this time, it was accompanied by some new insight into the subatomic world.
Max Born suggested that an electron wave is like a graph of all its possible locations, with the highest magnitudes representing the highest probabilities. Now that it had been reduced to a probability, there was no going back. An electron is described as having no absolute location. All of its movements are described in a wavefunction (a function of a wave, but that was self-evident). The change of wavefunctions over time is described in Schrodinger's equation (no, we are not delving into his cat!); it is a differential equation.
A function (such as x+y=2) can be solved by knowing the value of certain variables. The thing about a wavefunction is that once it's solved, it "collapses". This brings to mind condominiums on the San Andreas Fault, but it's actually very mathematical and quite painless. This happens because we cannot know everything about an electron at any given time. Which bring us to the next big thing in quantum mechanics...
Heisenberg did a very neat thing with Planck's constant, 6.626 x 10-34 J/s (just to forewarn you, Planck is a person who appeared to have pulled many miniscule but precise numbers out of thin air that describe everything from string length to particle mass and more. It may not have been thin air in reality, but like Einstein's energy-mass relation, it is useless to derive it here). He mathematically described the futility of trying to know everything about an electron at a given time like so:
For a given particle,
Uncertainty of position x Uncertainty of velocity x mass = Planck's constant
As you can see, since Planck's constant is, well, constant, the more certain you are of a particle's velocity, the less certain you are about its position. In order to measure the position of an electron, you cannot put a ruler up to it. You could, however, hit it with a light wave. The higher the frequency, the more certain you are of its measured position, but now the energy has been transferred to the electron; you've changed its momentum. You could then use a smaller frequency, but now you are not so sure of the position.
This brings about many of the things designated "weird" about quantum mechanics. There is also a variation on the uncertainty principle involving energy and time. This means that particles can borrow gigantic amounts of energy as long as it can pay it back very quickly. This is similar to a guy who borrows a million and pays it back a second later, borrows a millions, pays it back, etc. He does not leave with any more money than he started out with.
Since physicists work in very specialized fields, quantum mechanics and relativity rarely converse. When they do, however, they tend to disagree. At the sub-Planck level, anything under 10-33 cm, something starts to happen to the continuous space described by Einstein. When no mass is present in an area of space, the space should be flat, according to the dictates of general relativity. However, according to the dictates of quantum mechanics, no space is ever flat. It is constantly undulating and fluctuating. This is because of Heisenberg's Uncertainty Principle which says that space can borrow huge amounts of energy in short periods of time. So according to this, two of the biggest theories in physics today contradict each other. What is to be done?
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