I had never really thought about space and time before in as much depth as the book presented. It really amazed me how complex the whole spacetime four-dimensional fabric worked and made me realize how crucial Minknowski’s discovery was. The fact that gravity is produced by a curvature of spacetime’s fabric, making it a warpage of spacetime seems very strange. At first it made me wonder how can this could be so. I feel like a warpage of spacetime is something to be regarded as scary and mysterious like the black holes and wormholes mentioned, but gravity isn’t all that mysterious nowadays, maybe a little scary if you’re far above ground, but that’s it. In today’s society, our viewpoints have changed dramatically since BC times, but does his implications of humans not realizing spacetime in this reading still apply? Do we really not notice our spaces and times are relative and unified? I feel as if this would only be true if we did not have the ability to imagine ourselves in other places, including other organism’s lives, like the phrase of “putting yourself in someone else’s shoes”. But most of us have this ability, don’t we? Is this ability learned or innate? (This also reminds me of the tv series “24” which follows several characters in 24 hours of real life time, all at the same time.)
Gravitational time dilation really intrigued me, but I still don’t understand how it’s possible. The clock example made me really curious, but as I was reading I couldn’t understand what it was saying. Could someone possibly explain it to me how you understand the example to prove gravitational time dilation?
I had always wondered every time I boarded a plane, how the heck they stayed parallel to the earth’s surface. I noticed that most trips I took, the plane was substantially higher at the end of its journey than at the beginning (on board computers on overseas flights), but thinking back now that distance was far smaller than if the plane had gone linearly straight unrelative to the earth after first taking off. Up until class Tuesday, I had never realized parallel lines could be drawn on spherical objects or even intersect, but seeing it now makes everything make a lot more sense. Has anyone had a similar experience before? I was also wondering if anyone here has gone skydiving before? I was wondering if one would feel the vertical stretch and lateral squeeze of tidal gravity during those long seconds free falling, even just a tiny bit.
I was also wondering what do you guys thought about the “enormous energetic wealth contained in mass itself.” I found this to be intriguing, but it’s hard to wrap my mind around it. Then, my biggest ‘a-ha!’ moment was when I read this: “two balls thrown into the air on precisely parallel trajectories, if able to pass unimpeded through the Earth, will collide at the Earth’s center” (p110). So, I wonder to you, as a though experiment, do you think that if we dropped only one ball, that it would stop at center of the Earth unretrievable, or do you think it may have enough energy to come back out on the other side?
Joelle, I was also interested in the idea of gravitational time dilation. Over the last few classes we have been discussing how many of the things we consider to be absolute truths are not absolutely true at all. These readings really got me to reflect more on this idea. Personally, I have always enjoyed studying math and science because they make sense. The things we study in math and science classes can be tested and proven repeatedly. I have always considered these fields to be objective. However, Einstein’s theory of relativity points out that many of these truths may be somewhat subjective after all. In fact, there can be multiple truths depending on your vantage point. Many experiments and theories are tested with respect to time. The second has been long established as a standard unit of measurement in the scientific community. I have always considered it to be something that is absolute and unchanging. However, our measure of time is relative to our position. Time actually flows more slowly near the floor than the ceiling. If I understand the implications of the reading correctly, an experiment performed near the floor will thus result in slightly different results than one performed on the tenth floor of a building. More dramatically, one year on the horizon of a black hole would be equivalent to millions of years on Earth. This just goes to show that the majority of the things we have proven to be true, are only true with respect to our position on Earth. While repeated experimentation may seem to prove our hypotheses correct, they cannot be confirmed as universal truths. We must take into consideration each object in relation to another, and what we see as true depends entirely on our perspective. This is further illustrated in the example of the canon that is fired as you jump off a cliff. What you interpret as the trajectory of the canon is dependent on your perspective and your surroundings. Is everything that we know about the natural world only true with respect to something else, or are there any absolute truths that apply universally? Einstein was considered a genius for discovering E=mc2 as a means of relating energy and mass. His genius however did not lie in his basic mathematical observation, but instead his ability to look beyond centuries of misunderstanding and notice that there was in fact a relationship between energy and mass. The final article attests to the fact that we have yet to discover a unified theory. Could it be that we are also suffering from a misunderstanding, and some of the theories we consider to be accurate today may in fact be hindering our ability to discover a basic unified theory?
ReplyDeleteErin, I really enjoyed reading your response, but your last line got me thinking: if everything is relative, is it even possible to discover a basic unified theory? Won't any theory we create be dependant, in some way, on where and when our frames of referance are at the creation of the theory? In a way, I really like this idea of multiple Truths. It kind of means that physicists should follow some sort of "scientific agnosticism". I mean, simply think about how other people's opinions on things differ so far from your own, yet it is "true" to them much as your opinions are "true" to you. How can you tell, with absolute certainty, which truth is actually "True"? This line of thinking brings me back to philosophy 101 freshman year and discusions of Descartes. I don't want to make this discussion too philosophical; but really, wasn't what Einstein doing honestly just a philosohpical exercise that led to scientific thought? I mean, the readings say that he basically reached his conclusions by just throwing out Newton's ideas without any evidence, only because Einstein had an idea of how the universe should work in his mind, and so he made a model of it. If this way of doing things can honestly lead to such great things as atom bombs and nuclear power, why don't more scientists simply throw out what the "rules" are and try to create models of the universe that they like best? A follow-your-gut kind of approach. Reading scientific journals would be a lot more interesting, I'm sure.
DeleteAfter reading the papers on the theory of gravity coming to being and reading your post Joelle, I really like the thought of your last statement about dropping a ball into hole that stretched from one side of the earth to the other. As a kid this was always one of those questions that I would like to theories about, what would happen if you dug a hole through the earth and dropped something through it. On the theoretical premise of it being possible to dig such a hole without being crushed building it or the hole imploding under the tremendous pressure, I would imagine that the ball would be stuck in a perpetual motion of oscillation, neglecting air resistance of course. If such a hole was constructible I believe frictional forces, (i.e. the ball hitting the sidewalls and it reaching its terminal velocity), would slow its oscillation diminishing the frequency exponentially. The period of such a frequency on the other hand would take quite some time to reach the center of the earth, seeing as the earth has a radius of 6,378.1km. With the force of gravity acting as it should as such depths, being 9.81m/s-2 it would take 19 minutes for the ball to reach the center of the earth where it, in theory would be met by a gravitational force in the opposite direction pulling it back towards the center of the earth, once again overshooting and repelling once more. This cycle would continue until the ball retains a slow enough speed that it would eventually come to rest. This is where my ideology of such a theoretical system breaks down, at least mentally for me, as to how gravity might act at the center of mass on the scale of a planetary system. I did not find any evidence eluding towards such theories in the readings but I find it quite fascinating to think about. Of course as we all know this entire premise is in fact illogical because in a physical sense such an element able to withstand such pressers and/or the tempters the inner core is capable of achieving is unbenounced to man. But if such an object/element did exist I propose to you guys what would happen to it if it were to reach the exact center of the earth? Would it be stretched because of the opposing gravitation or simply crushed? How do you think the laws of physics would interpret themselves at a location such as this, would they break down? Or can we even fathom such an idea?
ReplyDeleteI was also intrigued by this idea of "warping" space and time. I've heard some of the ideas presented in Thorne's article before, and for me they're interesting because, for one, they point to a sort of mechanism by which gravity operates. In learning Newton's equation which describes the magnitude of the force of gravity (given the mass of two objects and the distance between them), I think many forget to ask the question, how does the force, gravity, actually operate? How can two objects, which have no apparent, direct physical contact exert a force on one another through no apparent medium? Einstein, I think, not only invented a more universal theory, but also provided the mechanism by which the forces, earlier described and quantified by Newton, work.
ReplyDeleteI also found it interesting to learn that Einstein was not proficient in mathematics. This was new to me. In popular culture, Einstein is most often pictured in front of a chalk board on which all sorts of formal mathematical lingo, symbols, equations, etc. are written. The article implies that, rather, Einstein’s genius stemmed from his remarkable intuition and insight into the universe. The mathematics proved to be the necessary tool set Einstein needed to move beyond his initial work, but Einstein’s mathematical abilities were certainly not what separated him from his contemporaries. Sometimes “genius” is in simple realizations, recognition of relationships, or the ability to generalize or “universalize” previous ideas which had been thought to be only narrowly applicable.
To be quiet honest I had to read the articles by Thorne multiple times to make sense of the base of the theories.
ReplyDeleteWhat fascinated me and stuck with me the most however was the proof of Einstein’s prediction, the gravitational time dilation in the clock experiment. The two clocks were different in time flow between the ceiling and the floor and the two areas experienced time at a different pace. Time closer to the floor flows more slowly. Perhaps, the best way to put it is "If one is at rest relative to a gravitating body, then the near one is to the body, the more slowly time must flow" (pg. 150) Next to a black hole time passes much more slowly than on earth. If you spent a year near a black whole, millions of time would have passed on earth. Time travel was referenced to take advantage of the differences of time elapsing. How does one begin to define time relative to all the time elapsing in different areas? In Greene’s article the following was perplexing and I am interested to know everyone’s’ thoughts on the following quote: “Einstein’s first relativity paper, the one in June 1905, shattered the idea that time elapses identically for everyone. Instead, Einstein showed that if from your perspective someone is moving, you will see time elapsing slower for him than it does for you.” (p 3.) Can anyone give any more applicable examples?
I feel like I just read something out of “The Twilight Zone.”
Joelle,
ReplyDeleteIn response to your question about whether or not you can feel the tidal forces from the difference in the gravitational pull. The answer is no. Why? well, just using newton's gravitational laws (which are extremely valid for gravitational physics in that length scale) the difference in gravitational potential for a person that is roughly 2 meters tall (a very tall person), 70kg, and that is roughly 3000 meters above the surface of the earth (~9000 feet above the surface of the earth!). the difference in the gravitational force between their feet and head would be ~0.0003763 Newtons. To give you an idea of how small this is, if i dropped a marble (roughly 1 gram) from 1 meter above your head, it would hit your head with 118 times the force. So, the difference in force has the magnitude of a grain of sand (~0.01 gram mass) hitting your head from a fall of about one meter. I'm guessing you wouldn't notice. Plus, as soon as you take into account air resistance that difference would be completely negligible compared to the force of friction you'd feel from the air.