J.J. Grandville , 'A Comet's Journey' , Illustration from 'Un Autre Monde', 1844. Who made the little green spacemen, well, green? Long before the midcentury Space Race set the standard for collective extraterrestrial clichés, people were having out-of-this-world experiences that chilled them dow
A particle is trapped inside a black hole. What is the probability it will escape via quantum tunneling? To figure this out, we begin by defining the variables involved: The diagram below shows two regions: I and O. Region I is inside the event horizon, within the Schwarzshild radius (rs). Region O is outside the event horizon. The question we ask is what is the probability the particle (red dot) will reach region O? And, we could also ask what is the probability the particle will fail to reach O and remain trapped in region I? These probabilities, when added together should equal 1. Region I covers a distance (r) from zero to rs. Region O is from rs to infinity. These will be the boundaries we will be using in the integrals below. To find a probability in quantum mechanics we are told to square the wave-function amplitude. To see how this works, let's consider finding the probability without squaring the wave function. (See equations 1 and 2 below.) We can model the wave function using right triangles. This is appropriate, since sine and cosine represent waves. At the second triangle above we substitute some dummy wave functions for demonstration purposes. The trigonometric proof below shows why it is important to square a wave function to get a probability: At equations 3 and 4 we didn't square the wave functions--they rarely add up to one, so they can't be probabilities. However once they are squared, they add up to one and could be probabilities (see equations 5 through 9). You may have noticed the wave functions have negative exponents. This feature prevents an exponential blow up to infinity. Now, to get the right values for the probabilities we also need to include a normalization factor (A). At equations 10 to 15 below, we calculate the value of A and see why we need it. When we take the sum of all probabilities, from zero to infinity, we want the grand total to be one. Equation 16 below is our new-and-improved wave function. Equation 17 is the one we use to calculate the probability densities of regions I and O. Equations 18 through 22 yield our desired result: equation 23, the probability density of region O; i.e., the probability that the particle will successfully escape the black hole. Equation 24 should be the probability density for the particle's failure to escape. Let's check this: Equation 28 confirms and matches 24. Below we use Schrodinger's equation to find the value of the wave number k: Equation 34 shows that k is a function of V--the black hole's potential. The bigger V is, the bigger k is, the smaller the wave function and the probability that the particle will escape. For more on the topic of quantum tunneling and QM, I highly recommend Robert Eagle's (aka: DrPhysicsA) video series:
by steemblogger
artist- Charlie Allen
Weird connections through space-time might make reality real, giving us a promising new route to a theory of everything
Many researchers believe that physics will not be complete until it can explain not just the behaviour of space and time, but where these entities come from.
There are four distinct types of galaxies in the universe, elliptical, spiral, barred spiral, and irregular. Although these are the four main types, there are various types of galaxies and the way in which they are classified is by their shape. A galaxy is a cluster of stars, gas, and dust that are kept together...
Designed by London-based photographer Cameron Baxter A Comprehensive Guide To Navigating Parallel Dimensions is a lovely bought of retro-themed fakery...
A poster series, showing the very humbling quality that space provides for us all. This poster is available on my online store.
INSTANT DOWNLOAD - DIGITAL PRODUCT - NO PHYSICAL ITEM SHIPPED Simply download, print and hang! - - - - - Printable Wall Art - Mass-Energy Equivalence, Albert Einstein (Dark Version) This lovely print of one of the most famous equations will look lovely as part of any office, classroom or science lab. Also makes THE BEST gift for teacher, professor, major or graduate and the people in your life who love sciences. No need to wait, simply download your art files and print! - - - - - — I N C L U D E D - F I L E S — YOUR ORDER WILL INCLUDE 1 ZIPPED FILE WITH 5 PDF FILES IN COMMON SIZES. Included are 5 high-resolution PDF files (300 dpi), ready for print. A 4x5 ratio file for printing 4"x5", 8"x10", 16"x20", 40x50cm. A 3x4 ratio file for printing 6"x8", 9"x12", 12"x16", 18"x24". A 2x3 ratio file for printing 4"x6", 6"x9", 8"x12", 10"x15", 12"x18", 16"x24", 20"x30", 24"x36" An international paper size file for printing 5"x7", A5, A4, A3, A2, A1, 50x70cm. An 11"x14" file - - - - - If you require a custom size, we can provide this for no extra charge. Simply purchase as normal then get in touch with the size you need and we’ll get back to you! — P L E A S E - N O T E — No physical product will be shipped and the frame is not included. Colors may vary slightly due to different color monitors/calibration. This purchase is licensed for PERSONAL USE ONLY. © Artwork is copyright of Urban Art Prints Store. — D I S C O V E R - M O R E - A R T - P R I N T S — https://www.etsy.com/shop/urbanartsprintsstore Thank you for visiting!
Through the wormhole.
Art,fashion,design,technology etc from the atomic space age
Physics Homework Help UK: Get Help with Physics Homework by experts to score top grades. We offer online Physics Homework Help to students at best price.
Subtle Energy Sciences offers vibrational energy solutions in digital format. Transform your electronic devices into powerful personal energy tools today!
Mathematically, it is a monster, but we can understand it in plain English.
