HomeworkToday was the last day of January term, and the course I finished just a few hours ago was about relativity and spacetime and Einstein and physics and stuff. I took this class for two reasons: first, because I am interested in physics to some extent, even though I’m really much more of a literature- and-writing person than a math-and-science person, and second, because it would be cool to actually know what I’m saying when I start talking about the spacetime continuum and making up crazy science fiction theories. I’m not sure that this class has caused revolutionary developments in my science fiction ideas, but I definitely have gotten stuff out of it, and it’s cool that I can now say that I understand the concepts of Einstein’s relativity. Because of the coolness of these topics, I now present a summarized list of stuff I have learned.

1. Aristotle’s observations of gravity led him to believe that each of the four elements (earth, air, water, and fire) had a different natural tendency and that the tendency of any object was determined by its proportion of the elements. Earth is heaviest and its tendency is to fall. Water also has a tendency to fall, but it’s lighter than earth, so anything that contains a lot of the earth element will sink beneath the surface of the water. Air is light, so its tendency is to rise above earth and water. Fire is the lightest, and so it will rise even above air. Of course, according to Aristotle, every substance familiar to us is a combination of the four elements. For example, dirt is not pure earth; it just contains a much larger quantity of the element earth than any of the other elements. It is also worth noting that Aristotle believed in the existence of a fifth element called the aether, an idea which is similar to, but not the same as, the idea of the aether mentioned in the following paragraph.  Also, I personally feel that it is worth noting that Aristotle was wrong, because this is something that I like to note as frequently as possible.

2. For centuries, scientists have believed in the existence of a substance called the aether that fills all of space and acts as the medium through which light waves can travel. In the nineteenth century, there were many experiments that attempted to detect and describe this aether, the most famous of which was done by Michelson and Morley in 1887. All of these experiments failed to detect any such thing as aether, but it was Einstein who eventually proposed the idea that the aether did not, in fact, exist. This dissatisfied many physicists, but it made Einstein’s theories work out very nicely, and they turned out to be true.

3. The speed of light is 299,792,458 meters per second. This is the equivalent of 670,616,629 miles per hour. When I’m driving to or from dance class, I am driving at an average of only 0.00000000894 of the speed of light. (When I’m driving to or from church, I drive a bit faster than that because people drive crazy fast on that interstate and everyone would seriously run right over me if I tried to drive at a normal speed.) Earth’s average speed is about 0.0001 the speed of light, by the way, which is about 67,061.66 miles per hour.

4. This doesn’t exactly count as something new I learned, but in this class, we used a slightly different definition for inertia than what I’ve usually heard. We basically defined inertia as a force that resists change in velocity. (I wrote a bit more about that here.) In discussing special relativity, the terminology “inertial reference frame” shows up a lot. That basically means that you’re either motionless or moving at a constant velocity.

5. The Principle of Relativity (which, by the way, predates Einstein) says that, if one is in an inertial reference frame, the laws of physics work the same way regardless of whether or not the reference frame is moving. For example, if you’re flying in an airplane and you drop a bookmark or something, that bookmark will fall to the floor of the airplane, just as it would if the airplane was sitting motionless on the runway. However, if you’re in a vehicle that is accelerating, decelerating, changing direction, or bouncing because of a bumpy road or air turbulence, it’s not an inertial reference frame, which is why things slide around in a moving car. This is inherent in the definition of inertia, but the implication of the Principle of Relativity is that, if you are in a completely inertial reference frame, you can’t even tell whether or not you’re moving. Even if you are looking out a window and see the view changing, you can’t scientifically prove that it is you and not the scenery itself that is in motion. Technically, relativity says that it’s equally true and valid to interpret it either way; the significant point is not who is moving and who is stationary, but just that the reference frames are not stationary relative to each other.

6. Einstein’s big breakthrough (or, to be more precise, his first postulate in the Special Theory of Relativity) was that the principle of relativity applies not only to forces such as gravity, but also to things such as the way light behaves. It had recently been suggested by various physicists that the principle of relativity didn’t apply to light and to Maxwell’s equations regarding light, so Einstein was basically just disagreeing with that hypothesis. His second postulate, which was really just a necessary result of the first postulate, was that the speed of light is the same in any inertial reference frame. The weird thing, which leads to all of the weirdness inherent in relativity, is that this requires giving up on the assumption that time is a constant. Time has to go at a different speed depending upon how fast the clock is moving relative to the speed of light. (The faster the clock is going, the less time passes, so basically, time goes faster at higher speeds.) But this doesn’t have much of an effect on everyday life because the speed of light is so extraordinarily fast that people never travel at a significant fraction of the speed of light.

7. We defined an “event” as a single point in space and time. In most of our homework assignments, we labeled events that described the emission or reception of a light beam or the collision between two particles or spaceships, but technically, even a point where nothing of interest happened is an event. Unfortunately for my lovely time gravity theory, it turns out that all events are equal, and there’s apparently no such thing as time mass.

I posted this on tumblr a couple weeks ago.

I posted this on tumblr a couple weeks ago.

8. Simultaneity is relative. This is the title of this blog post because the professor emphasized this very strongly and used any relevant occasion to remind us of it. Because of the relativity of time, two events can happen at the exact same time in one inertial reference frame and at different times in another inertial reference frame. It’s weird, but it’s true, and we did a lot of homework problems with spacetime graphs to prove it. The coolest one involved a Klingon ship firing laser blasts at a Federation starship in neutral territory shortly before passing into Klingon territory. From the reference frame of the Federation starship, it was hit while the Klingon ship was still in the neutral zone, which meant that the Klingons committed a crime. But from the Klingons’ reference frame, they passed into Klingon territory before the laser blast actually hit the Federation starship, and thus, they didn’t do anything wrong. Except that they were definitely in the neutral zone when they fired the laser blast, and the Federation starship was definitely in the neutral zone both when the blast was fired and when the blast hit, but for the sake of that problem, we assumed that the law was so poorly written that the only thing that mattered was where the Klingons were when their laser blast hit the Federation starship.

This is what a spacetime graph looks like.

This is what a spacetime graph looks like.

9. On a spacetime graph, if two events are farther apart in space than time, then they are spacelike separated, which means that the order of the events is relative. Depending upon how fast an observer is moving, either one of them could have happened first, or they could have happened simultaneously. It is impossible for one to have been the cause of the other, because they are too far away in space for the effects of one to reach the other in time to have caused it. If two events are farther apart in time than space, they are timelike separated, which means that the first one happened before the second one from the perspective of any inertial reference frame. Therefore, it is possible (but not necessarily true) that the first event caused the second event. However, depending upon the speed of the observer, the events may or may not have happened in the same place. If two events are separated by an equal amount of time and space, they are lightlike separated, and this will be true from the perspective of any inertial observer, regardless of his or her speed.  Incidentally, there is one way of measuring the distance between two events that does not vary between observers. This measurement is written as delta S, and the equation is delta S squared equals delta T squared minus delta X squared where T is time and X is space. Even though delta T and delta X will be different for different observers, delta T squared minus delta X squared will yield the same result for every observer. (You can read more here about the stuff that passed through my brain on the day that we discussed these things.)

10. In addition to affecting the passage of time, high speeds also affect length. For example, in a video we watched, a couple scientists measured time dilation by tracking particles descending rapidly through the atmosphere past a mountain. It would take too long for me to explain exactly how that worked, and that isn’t the point of this paragraph anyway, so I’ll just say that they did in fact demonstrate that less time passed for those particles than for the mountain that was stationary relative to the Earth. But, according to special relativity, the particles may as well have been stationary and the mountain may as well have been traveling upwards. The result is the same, and the result is that the time interval between the particles’ presence at the top of the mountain and their presence at the bottom of the mountain was a shorter time interval for the particles than for the mountain. So, from the particles’ point of view, the mountain is actually shorter than it is from its own perspective. To put this in general terms, the length of a very quickly moving object is contracted. Yes, in this particular case, it was the particles that were moving quickly and the length-contracted mountain wasn’t, but that’s only from the perspective of the scientists observing this incident. (And anyone or anything else that is stationary relative to the planet’s surface) Relativity says that it’s just as true and valid to say that the particles are stationary and the mountain is moving. The question of which object’s length is contracted is a matter of perspective.

11. The Doppler Effect applies to light as well as sound. As explained in high school physics books, the Doppler Effect is when sound waves are perceived as being grouped closer together (and therefore, higher pitched) when the thing emitting the sound is travelling towards the observer, and they are perceived as being spread farther apart (and therefore, lower pitched) when the thing emitting the sound is travelling away from the observer. According to most textbooks, one should learn about this phenomenon by getting someone to drive their car past you while honking their horn continuously, but my parents didn’t do this for me and I somehow still managed to understand the concept of the Doppler Effect. Anyway, it turns out that a moving light source will produce the same effect, except that the perceived pitch of light can’t change, for the simple reason that light doesn’t have a pitch. But the frequency still changes, just as it does for the sound. In the visible range of light, this is perceived as a change in color. The other thing worth noting (in order to avoid disagreeing with the principle of relativity) is that the Doppler Effect works the same way if it’s the receiver rather than the emitter that’s moving. It also works if the receiver and emitter are both moving, but in that case, you have to do actual math to figure out what exactly happens. (But it’s actually pretty simple math.)

Some more stuff from my tumblr page

Some more stuff from my tumblr page

12. Even though we actually spent several days of class time talking about “E equals M C squared” and radiation and subatomic stuff, I’m not going to say too much about that because, to be honest, I find that kind of thing a lot harder to understand than special relativity and its effects on space and time. But I will say this much: I know how nuclear bombs work. Some types of atoms are more stable than others, depending upon the number of electrons, neutrons, and protons. One factor is simply the size of the atom. The most stable kinds of atoms are iron atoms and atoms of similar masses. Smaller atoms are more likely than medium atoms to join together (nuclear fusion) and heavier atoms are more likely to split apart (nuclear fission). Fusion and fission both give off energy, which can be proven by adding up the energy and mass in the ingredients and the products of the event and taking into account that “E equals M C squared”. Uranium 235 (an atom that has 92 protons, 92 electrons, and 143 neutrons) is very radioactive. If you smash a neutron into a Uranium 235 atom, it’ll probably decay into Barium 144, Krypton 89, and three more neutrons which can go on to smash into more Uranium 235 atoms. If you have a critical mass of Uranium 235 and bombard it with a bunch of neutrons, you get a chain reaction that leads to a massive explosion and kills Hiroshima. (Unless, of course, you drop it on someplace other than Hiroshima, but I wouldn’t recommend that. In fact, I wouldn’t recommend dropping it on Hiroshima, either. Nuclear bombs are nasty things.) Incidentally, Uranium 238, which is more common than Uranium 235, is much less reactive, and unless I’ve misunderstood some things, it’s because of those extra neutrons. In really big atoms, larger amounts of neutrons make the atom more stable because the protons are trying to repel each other, and the neutrons are necessary to hold the atom together. Okay, that’s it; that’s the extent of my knowledge of nuclear stuff.

Ooh, here's something else I learned in this class which isn't quite worthy of a place on this list.

Ooh, here’s something else I learned in this class which isn’t quite worthy of a place on this list.

13. Even after finishing this class, I don’t quite get the concept of General Relativity, but we didn’t go into it in great detail because apparently the mathematics is well beyond the scope of this course. (I think that the real reason I decided to be a math minor is because I’m sick of hearing professors end sentences with the phrase “But we’re not going to go into that because the mathematics is beyond the scope of this course.”) But I do have a better grasp of it than I did before. The explanation of general relativity that I have heard many times before is that space is like a cushion. If you put a bowling ball in the middle of it, it will bend under the weight of the bowling ball, and if you put a marble near the bowling ball, it’ll roll down the cushion towards the bowling ball. This, I have been told, explains gravity according to Einstein’s Theory of General Relativity. When I questioned this, adults would explain to me that this was just the way it was and would give me looks that said, “It’s relativity, Small Child. Don’t expect it to make sense. Don’t be presumptuous and assume that you can understand the thoughts of The Great Albert Einstein.” Okay, it’s just one person in particular who seemed to be telling me this, and I am willing to accept the possibility that I was grossly misinterpreting this person’s lack of inclination to answer my question. My question wasn’t exactly a question anyway; it was more of a complaint. I felt that using this explanation was like using a word in its own definition. The reason that a bowling ball will bend a cushion is that it is heavy and is being pulled towards the Earth below the cushion, and the reason that the marble will roll down this bend is that it is likewise being pulled towards the Earth. And gravity is the thing doing the pulling. I guess I was being a bit too literal and failing to understand that the cushion explanation was merely an analogy. But my professor gave the class a similar analogy that I like better. This analogy involves an ant walking around the inside of a bowl that is empty except for a sugar cube at the bottom. Now, the ant doesn’t realize that it’s inside a bowl; it thinks that it’s walking in a straight line on a flat surface, and that there’s a sugar cube off to one side. As the ant keeps walking, it realizes that no matter how far it goes, the sugar cube stays in the same place relative to it. The ant is kind of clever for an ant, and quickly determines from this that it is in fact circling around the sugar cube. However, it still has no idea that it’s inside a curved bowl, so it can only conclude that there is some force, like gravity, attracting it to the sugar cube and causing it to orbit. In fact, there is no force; the ant is simply following a curved path because it’s walking on a curved surface. This analogy still isn’t perfect because General Relativity does say that mass (the sugar cube) causes space (the bowl) to curve, and the analogy doesn’t explain how that could happen. But it’s still a better illustration than the cushion one because it makes the point that Einstein was making with General Relativity. According to Einstein, gravity isn’t a real force. He came up with the Equivalence Principle, which says that the effect of perceived gravity is the same as the effect of being in a non-inertial reference frame that is accelerating upwards. (The acceleration is why it isn’t inertial) I’m not sure if Einstein literally meant that what we perceive as gravity is caused by acceleration of the Earth; I had thought we were considering the Earth to be an inertial reference frame. And I also don’t quite understand how curved spacetime relates to the Equivalence Principle. Like I said, General Relativity still doesn’t quite make sense to me, but at least now I’ve got analogies that make sense, and that’s progress.

black hole14. In class today, we were talking about black holes, and the professor was explaining why it is that nothing can escape from a black hole once it’s within a certain distance from the black hole, known as the event horizon. (Note to self: remember to use the phrase “The Event Horizon” as a title for something awesome someday.) The common explanation is that the gravitational pull is acting so quickly that you’d have to travel faster than the speed of light to get farther away from the black hole. Unfortunately, travelling faster than the speed of light is impossible. (Yes, I have grumpily accepted this fact, despite having spent years trying very hard to deny it.) There’s another way of explaining this that is both weirder and cooler. If you will remember, one can find delta S, a non-relative measure of spacetime separation between two events, with the equation delta S squared equals delta T squared minus delta X squared. The result of this equation is the fact that, no matter how we move in space, we are unavoidably drawn forward in time at the speed of one second per second. (According to our own perspective, that is. If we are moving at relativistic speeds, of course, our speed through time will be different from the perspective of an observer who is not moving likewise. But even then, we’ll still be moving forward in time from any perspective.) Now, here comes the awesome bit. For some reason that I don’t actually understand, apparently inside the event horizon of a black hole, this equation changes to delta S squared equals delta X squared minus delta T squared. In other words, time and space change places. The implication is that, in this situation, you are drawn into the black hole in the same way that, in a more typical scenario, you are drawn towards the future. The other implication (which is the really, really awesome bit) is that I was right when I wrote a certain passage in a certain science fiction story a long time ago. I didn’t even have any idea what I was talking about; I was just writing random science-fiction-sounding stuff about gravity and time, and I threw the phrase “time gravity” and “black time hole” in there for the sake of awesomeness. But, from what I learned today, it would appear that there was some validity to that stuff. Clearly, I am a genius. Or something like that.

15. I don’t understand quantum physics at all. In fact, I’m not even quite clear on what the word “quantum” means. This is clearly something that I need to learn. You know, now that I understand relativity.

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