Thursday, April 30, 2009
Tuesday, March 24, 2009
The Equivalence Principle
Ah, equivalence. A property that our lives revolve around. Yet, some people don't appreciate the relativity of equivalence, possibly because they don't understand how it works.
First, think of an elevator in space. Even though this is not physically possible, pretend that the elevator is free of all gravitational forces. There are two people in this elevator. Without any gravity, these two unlucky people are floating freely. Now, let's bring the elevator up to the free fall rate, or the speed required to emulate the effect of Earth's gravity (9.8 meters per square second, I believe). Next, pretend that the observers still believe they're on Earth (not remotely possible, hopefully). Will they know the difference between gravity and acceleration? Most likely not, as in this case acceleration has simulated gravity.
For the next example, let's take that elevator and the two brave astronauts and place them in the Willis Tower (Sears Tower, whatever). Now, we'll drop the elevator into a free fall. Not counting air resistance, the elevator should fall at a constant rate of approximately 9.8 meters per square second, as mentioned before. What will happen to the people inside the elevator? In this case, acceleration has cancelled gravity out as it is going toward gravity's pull.
Finally, picture the same elevator one last time, but instead of two travelers there is a beam of light stretching across the elevator in a perfectly horizontal line. Now, we'll raise the elevator one last time. The beam of light will appear to arc downward to an observer due to the motion of the elevator, even though its path actually remains undisturbed.
This theory usually is updated to use a rocket ship, but you know me. I'm old fashioned.
Credit: Leonard Susskind's Black Hole Wars. An excellent, highly recommended book!
First, think of an elevator in space. Even though this is not physically possible, pretend that the elevator is free of all gravitational forces. There are two people in this elevator. Without any gravity, these two unlucky people are floating freely. Now, let's bring the elevator up to the free fall rate, or the speed required to emulate the effect of Earth's gravity (9.8 meters per square second, I believe). Next, pretend that the observers still believe they're on Earth (not remotely possible, hopefully). Will they know the difference between gravity and acceleration? Most likely not, as in this case acceleration has simulated gravity.
For the next example, let's take that elevator and the two brave astronauts and place them in the Willis Tower (Sears Tower, whatever). Now, we'll drop the elevator into a free fall. Not counting air resistance, the elevator should fall at a constant rate of approximately 9.8 meters per square second, as mentioned before. What will happen to the people inside the elevator? In this case, acceleration has cancelled gravity out as it is going toward gravity's pull.
Finally, picture the same elevator one last time, but instead of two travelers there is a beam of light stretching across the elevator in a perfectly horizontal line. Now, we'll raise the elevator one last time. The beam of light will appear to arc downward to an observer due to the motion of the elevator, even though its path actually remains undisturbed.
This theory usually is updated to use a rocket ship, but you know me. I'm old fashioned.
Credit: Leonard Susskind's Black Hole Wars. An excellent, highly recommended book!
Tuesday, March 10, 2009
An Analysis of Stupid
I think that there's some sort of mental disease affecting the sophomores in my classes. When you tend to breeze through classes like I do, then you get placed in the integrated ones quite often. Unfortunately, instead of being a third wheel to them with all my geeky, glavin glory, it seems to be the other way around. And don't worry, I'll include something scientific to make it count.
Now, just last week, I was doing my homework in my intervention. Now, I'm the picture of a geek: long, messy brown tresses, dark blue eyes hidden behind thick brown wireframe glasses, extremely tall and quite flabby with a tendency to stutter. So obviously the sophomores in my classes have picked me out as their foil. I have below the transcript of a conversation with them. Be astounded at their pernicious natures!
Me: *humming and working on trigonometry*
"T": Hey, Rebecca.
Me: Salutations.
"T": *stares and rolls his eyes* Listen, my friend "J" is havin' some trouble with his homework. Can you help him?
J: Yeah!
Me: I have my own homework. I need to keep my grade up at 107%, you know.
T: Yeah, but J is, like, failing. He needs help.
Me (Believing him but wondering where the study tables are): I'll see what I can accomplish. What do you have here?
J: Dunno.
Me (genuinely dumbfounded): Inequalities? We learned those in the seventh grade! They're as simple as pi!
T: Hey! He's older than you! Respect your elders!
Me (taking papers with reserve): Yes, but you'll never become an engineer if you don't learn your inequalities!
J: What does drivin' a train have to do with math?
Me (OMG jawdrop): Here. Let me help you with the first few dozen...
Now, what could possibly make those boys that vapid? Beyond me. But somehow, analyzing their brains, I suspect that their hippocampus (memory center) has been affected from too many blows during football practice. Also, their rampaging hormones may be affecting their trains of thought (I'll admit even my mind strays occasionally!).
Then again, we only differ from chimps by about 1.6%. Maybe these boys are "throwbacks", and share a bit more DNA than normal with our prehensile cousins.
Now, just last week, I was doing my homework in my intervention. Now, I'm the picture of a geek: long, messy brown tresses, dark blue eyes hidden behind thick brown wireframe glasses, extremely tall and quite flabby with a tendency to stutter. So obviously the sophomores in my classes have picked me out as their foil. I have below the transcript of a conversation with them. Be astounded at their pernicious natures!
Me: *humming and working on trigonometry*
"T": Hey, Rebecca.
Me: Salutations.
"T": *stares and rolls his eyes* Listen, my friend "J" is havin' some trouble with his homework. Can you help him?
J: Yeah!
Me: I have my own homework. I need to keep my grade up at 107%, you know.
T: Yeah, but J is, like, failing. He needs help.
Me (Believing him but wondering where the study tables are): I'll see what I can accomplish. What do you have here?
J: Dunno.
Me (genuinely dumbfounded): Inequalities? We learned those in the seventh grade! They're as simple as pi!
T: Hey! He's older than you! Respect your elders!
Me (taking papers with reserve): Yes, but you'll never become an engineer if you don't learn your inequalities!
J: What does drivin' a train have to do with math?
Me (OMG jawdrop): Here. Let me help you with the first few dozen...
Now, what could possibly make those boys that vapid? Beyond me. But somehow, analyzing their brains, I suspect that their hippocampus (memory center) has been affected from too many blows during football practice. Also, their rampaging hormones may be affecting their trains of thought (I'll admit even my mind strays occasionally!).
Then again, we only differ from chimps by about 1.6%. Maybe these boys are "throwbacks", and share a bit more DNA than normal with our prehensile cousins.
Thursday, February 26, 2009
Where'd the Hole Go? - Hawking Radiation
NOTE-This post is being revised for incorrect information.
We (us Simpson fans, anyway) all probably know who Stephen Hawking is - author, physicist, genius with an IQ estimated at nearly 200. While wheelchair bound and nearly immobile, Hawking is by far one of the most prolific and prodigious minds to ever touch on cosmology. He came up with some pretty impressive stuff.
One of my favorite theories is Hawking radiation. Since I plan to make a career on studying black holes, I couldn't resist learning exactly what "kills" these monsterous universal garbage disposals. Accordingly, in the quantum world, black holes do radiate a type of energy: "Hawking radiation".
Hawking theorized that, over time, a black hole expends energy. Every time it swallows an object, it gains a bit of energy, but usually its net intake is negative. According to Dr. Andrew Hamilton, "the evaporation time is prodigiously long - about 10 to the power of 61 times the age of the Universe for a 30 solar mass black hole". Wow. A solar mass, by the way, is the size of our sun. So, theoretically it would take 13.7 billion times 10 novemdecillion years for a black hole 30 times the size of our sun to evaporate.
However, smaller black holes can indeed evaporate within our universe's age. Some micro black holes are predicted to last just a fraction of a second.
For a page written by a college-educated expert (with all the proper facts!), try here. I recommend you check out the rest of the site while you're at it. It's one of my very favorites.
http://casa.colorado.edu/~ajsh/hawk.html#hawking
We (us Simpson fans, anyway) all probably know who Stephen Hawking is - author, physicist, genius with an IQ estimated at nearly 200. While wheelchair bound and nearly immobile, Hawking is by far one of the most prolific and prodigious minds to ever touch on cosmology. He came up with some pretty impressive stuff.
One of my favorite theories is Hawking radiation. Since I plan to make a career on studying black holes, I couldn't resist learning exactly what "kills" these monsterous universal garbage disposals. Accordingly, in the quantum world, black holes do radiate a type of energy: "Hawking radiation".
Hawking theorized that, over time, a black hole expends energy. Every time it swallows an object, it gains a bit of energy, but usually its net intake is negative. According to Dr. Andrew Hamilton, "the evaporation time is prodigiously long - about 10 to the power of 61 times the age of the Universe for a 30 solar mass black hole". Wow. A solar mass, by the way, is the size of our sun. So, theoretically it would take 13.7 billion times 10 novemdecillion years for a black hole 30 times the size of our sun to evaporate.
However, smaller black holes can indeed evaporate within our universe's age. Some micro black holes are predicted to last just a fraction of a second.
For a page written by a college-educated expert (with all the proper facts!), try here. I recommend you check out the rest of the site while you're at it. It's one of my very favorites.
http://casa.colorado.edu/~ajsh/hawk.html#hawking
Monday, February 23, 2009
I Tawt I Taw A Puddy Tat - Or Did I?
"One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks."
These are the words of Erwin Schrödinger, Austrian scientist/theoretical physicist, who, in a sheer flash of brilliance, came up with one of my (and my feline-loving friend Jessa's) favorite theories! For those of you who just skimmed, Schrödinger claimed that if he built the device described, then the cat would have an equal chance of living or dying. That's the "magic" of quantum mechanics, you see.
Although no Hugh Everett, Schrödinger's theory may have set the whole ball rolling. Why not, I suppose, have the cat's chances at living or dying expressed simultaneously? Can it be done? In our universe, if the cat has died, could it be alive in another? What is the true reality here?
For those of you who know Neils Bohr's Copenhagen observation: dis-proved! According to Bohr, the cat would remain both dead and alive until the box is opened and it is observed. That was the way of the Copenhagen observation: particles could be in several places at once until they were observed; during observation, they'd be as still and unipresent as lambs. Sure.
The multiversal element wasn't brought in until 1957, when personal hero Hugh Everett suggested it (he said that once the cat was observed, the two elements split the box-and the observer-from each other in a decoherent universal state, with no interaction). The multiversal theory has been expounded on since then, but Schrödinger's cat will, to me, be one of the commanding factors in multiversal physics.
This information is largely from a ThinkTV report that I memorized from a few months ago. Praise PBS!
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks."
These are the words of Erwin Schrödinger, Austrian scientist/theoretical physicist, who, in a sheer flash of brilliance, came up with one of my (and my feline-loving friend Jessa's) favorite theories! For those of you who just skimmed, Schrödinger claimed that if he built the device described, then the cat would have an equal chance of living or dying. That's the "magic" of quantum mechanics, you see.
Although no Hugh Everett, Schrödinger's theory may have set the whole ball rolling. Why not, I suppose, have the cat's chances at living or dying expressed simultaneously? Can it be done? In our universe, if the cat has died, could it be alive in another? What is the true reality here?
For those of you who know Neils Bohr's Copenhagen observation: dis-proved! According to Bohr, the cat would remain both dead and alive until the box is opened and it is observed. That was the way of the Copenhagen observation: particles could be in several places at once until they were observed; during observation, they'd be as still and unipresent as lambs. Sure.
The multiversal element wasn't brought in until 1957, when personal hero Hugh Everett suggested it (he said that once the cat was observed, the two elements split the box-and the observer-from each other in a decoherent universal state, with no interaction). The multiversal theory has been expounded on since then, but Schrödinger's cat will, to me, be one of the commanding factors in multiversal physics.
This information is largely from a ThinkTV report that I memorized from a few months ago. Praise PBS!
Random Factoids #1
Funny Faulty Cause-and-Effect Reasoning #1
If you've ever seen VeggieTales (I'll admit that I loitered behind the couch a few times while Gloria was watching), you may know that quirky little ditty that Larry the cucumber sometimes sings during the "Silly Songs" segment. You know,
"If it doesn't have a tail, it's not a monkey, it's an ape."
So, then most computer mice, for example, would be monkeys? Computer monkeys? Well, not mine. Mine is a wireless beauty. That makes it an ape, right?
Strangely enough, my sister doesn't have a tail. I guess I was wrong in insulting her status on the evolutionary scale. She probably is an ape, just like the rest of my family.
Fun Fact #1
Neanderthals had larger brains than homo sapiens.
That's probably why they never thought of television, Bath 'n Body Works, and door-to-door encyclopedia salesmen.
Debunking the Myths #1
Most body heat escapes through your head.
45-50% of body heat escapes from your head? Not so. Your head is nothing special. Only 10% of body heat leaves your head during a frigid jaunt. Indeed, when this military study was performed, the guinea pigs happened to not be wearing any headgear, and were in an Arctic environment. Therefore, their heads were colder because the heat wasn't trapped by a hat and was allowed to escape. You see, it's sort of a "diffusion of heat", or conduction.
Diffusion is the movement of something from a high concentration to a low concentration. Energy also equalizes over time. That's why an ice cube melts-it is slowly heating up to room temperature as it takes energy from the air around it. After a while, the cube will achieve equilibrium-that is, it will be the same temperature as the air around it, and have about the same energy. Heat also escapes the same way. With a blanket, heat is trapped and conserved, and your body heats up the interior of the blanket, keeping you warm. But when your head is sans covering in the winter, the heat will be drawn into the air to equalize the temperature. That's why you will end up with with a cold scalp by trying this experiment out for yourself.
Don't believe me, Mom? Check out this link:
http://www.dailymail.co.uk/health/article-1097078/Losing-heat-head-Discover-barefaced-truth-hats-myths.html
I'm recalling the scientific parts from memory from my textbook...I'm pretty sure I have all the definitions just about right. Feel free to add any corrections.
If you've ever seen VeggieTales (I'll admit that I loitered behind the couch a few times while Gloria was watching), you may know that quirky little ditty that Larry the cucumber sometimes sings during the "Silly Songs" segment. You know,
"If it doesn't have a tail, it's not a monkey, it's an ape."
So, then most computer mice, for example, would be monkeys? Computer monkeys? Well, not mine. Mine is a wireless beauty. That makes it an ape, right?
Strangely enough, my sister doesn't have a tail. I guess I was wrong in insulting her status on the evolutionary scale. She probably is an ape, just like the rest of my family.
Fun Fact #1
Neanderthals had larger brains than homo sapiens.
That's probably why they never thought of television, Bath 'n Body Works, and door-to-door encyclopedia salesmen.
Debunking the Myths #1
Most body heat escapes through your head.
45-50% of body heat escapes from your head? Not so. Your head is nothing special. Only 10% of body heat leaves your head during a frigid jaunt. Indeed, when this military study was performed, the guinea pigs happened to not be wearing any headgear, and were in an Arctic environment. Therefore, their heads were colder because the heat wasn't trapped by a hat and was allowed to escape. You see, it's sort of a "diffusion of heat", or conduction.
Diffusion is the movement of something from a high concentration to a low concentration. Energy also equalizes over time. That's why an ice cube melts-it is slowly heating up to room temperature as it takes energy from the air around it. After a while, the cube will achieve equilibrium-that is, it will be the same temperature as the air around it, and have about the same energy. Heat also escapes the same way. With a blanket, heat is trapped and conserved, and your body heats up the interior of the blanket, keeping you warm. But when your head is sans covering in the winter, the heat will be drawn into the air to equalize the temperature. That's why you will end up with with a cold scalp by trying this experiment out for yourself.
Don't believe me, Mom? Check out this link:
http://www.dailymail.co.uk/health/article-1097078/Losing-heat-head-Discover-barefaced-truth-hats-myths.html
I'm recalling the scientific parts from memory from my textbook...I'm pretty sure I have all the definitions just about right. Feel free to add any corrections.
The Sesquipedalian Scientist is Here!
Felicitations, and welcome to literati-cognoscenti.blogspot.com, a.k.a Esoterica. If you have randomly stumbled upon this blog by accident, I hope you will plan to book it, to help salvage my sense of importance. If you do not like, or downright hate, esoterica, then perhaps this is not the place for you. However, if you are of the intelligentsia or simply like to explore new fields, this may be worth reading.
My name is Rebecca, I'm German-American, and I'm nearly 15 (I haven't calculated my exact age down to the hundreths place since December. I need to save my calculators' batteries, you know). Now, don't let my age deter you, adults. I plan to keep this blog concise, clear, and purely metaphysical (or something of the sort). I have a LiveJournal to keep my girly side in check. I plan to use this small space on the internet for my ramblings on the way life works. After all, as a future astrophysicist, I need to keep my mind sharp!
This blog will probably only be updated on occasion, whenever I see fit (or whenever I need to let off steam). After all, I am an honors high school student, and school must always come before my personal enjoyment. Some of the topics I hope to cover in the future are the sciences, mathematics, Murphy's law, cosmology (my specialty), and of course, the ever-popular metaphysics ("the way we was", as you fellow Garfield fans may know).
If you happen to go to school with me, I beg of you to forget you ever viewed this blog and abstain from pulverising me at school tomorrow (although being of the female persuasion doeth lower the risk by about 60%, except in gym class). Although what are the chances of any of you locating this page? At least 8,383, 123,047 to 1, I hope. I hope.
Hey Jessa/Holly.
My name is Rebecca, I'm German-American, and I'm nearly 15 (I haven't calculated my exact age down to the hundreths place since December. I need to save my calculators' batteries, you know). Now, don't let my age deter you, adults. I plan to keep this blog concise, clear, and purely metaphysical (or something of the sort). I have a LiveJournal to keep my girly side in check. I plan to use this small space on the internet for my ramblings on the way life works. After all, as a future astrophysicist, I need to keep my mind sharp!
This blog will probably only be updated on occasion, whenever I see fit (or whenever I need to let off steam). After all, I am an honors high school student, and school must always come before my personal enjoyment. Some of the topics I hope to cover in the future are the sciences, mathematics, Murphy's law, cosmology (my specialty), and of course, the ever-popular metaphysics ("the way we was", as you fellow Garfield fans may know).
If you happen to go to school with me, I beg of you to forget you ever viewed this blog and abstain from pulverising me at school tomorrow (although being of the female persuasion doeth lower the risk by about 60%, except in gym class). Although what are the chances of any of you locating this page? At least 8,383, 123,047 to 1, I hope. I hope.
Hey Jessa/Holly.
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