Videos uploaded by user “Jonathan Doolin”
Suppose that IQ scores have a bell-shaped distribution with a mean of 100 and a standard deviation of 15. What percentage of people should have an IQ score between 85 and 115?
Views: 56418 Jonathan Doolin
Relativity 2:  Superluminal Motion
See more at http://www.spoonfedrelativity.com Consideration of the appearance of an object moving away from you and moving toward you taking into consideration the delay caused by the finite speed of light. You can experiment with some of these ideas here: http://www.wiu.edu/users/jdd109/stuff/relativity/LT.html For further discussion, see http://groups.google.com/group/sci.physics.relativity/browse_thread/thread/793dedd752de36e3?hl=en#
Views: 1475 Jonathan Doolin
My Intro to Schwarzschild Metric
Created 2013-01-08 Uploaded 2014-11-25
Views: 3638 Jonathan Doolin
Sloan Digital Sky Survey, Hubble Deep Field, Cosmic Background, and SCM vs. Milne
In Playlist: https://www.youtube.com/watch?v=BQ_AGe0_5GU&list=PLC-qVSnsyc7_24tKNLFKrSTB5ZkwjkFuH&index=10 0:30 The Sloan Digital Sky Survey - two dimensional image. 1:00 How big is 8000 square degrees? This gets a bit boring, but the whole sky is about 41,000 square degrees, so it's about 20% of the sky. 3:10 More information on Sloan Survey 2005-2008 stars within our own galaxy. 4:30 Penetrating the dust that obscures the inner galaxy... I got this one wrong. They are looking toward the inner galaxy, not looking out past the center of our galaxy. 5:00 Trying to extend the range. 5:30 https://www.youtube.com/watch?v=Bo9EQ6mIhRY Sloan Digital Sky Survey from Mars Underground. This video comes from 2005, so they probably have somewhat more data now than they did then, but I don't know when that was released. 7:30 Superimposed on the SDSS is the Cosmic Microwave Background Radiation. 8:00 The scale of the image seems to assume that the universe is about 13.8 billion light year radius. This shows the Sloan Digital Survey on that scale. 9:00 Trying to explain what "20% of the sky means. 9:45 The Hubble Deep Field survey was only 2.5 arcminutes by 2.5 arcminutes 10:00 Describing the resolution of the human eye, and how big that Hubble Deep Field Survey is. 10:50 https://www.youtube.com/watch?v=fgg2tpUVbXQ This is the region where the FIRST use of the technology was used. This was an image of a big galaxy. 11:30 The SECOND use of the technology was Southeast of Orion. This time, it was 13:00 Zooming in on several regions of the 2.5x2.5 arcminute section. 13:29 Cluing into the fact that the Big Dipper location was an image of a galaxy, while the Orion location was an image of an "empty" patch of sky 14:10 The size of the universe is 47 billion light years in radius? Where does he get that? 15:00 Nobody gives the same answer for the size of the universe. 15:58 The stretchy space-vs-big bang concept. 16:27 Milne's Relativity Gravitation and World Structure is available online https://archive.org/details/RelativityGravitationAndWorldStructure 17:00 What do things look like from the perspective of the Blue Dot? 17:10 Visual representation of the spacetime transformation called the "Lorentz Transformation" 18:00 The Lorentz Transformation takes trajectories from the red dot's perspective, and shows them in the blue dot's perspective. 18:42 Milne argued that the universe was isotropic, but NOT homogeneous. 20:00 Let's start to describe the Standard Cosmological Model. (By the way, Veritasium does a great job explaining this at https://www.youtube.com/watch?v=XBr4GkRnY04 ) 21:00 I used to think this idea was silly, but now I just think it is incorrect, but I am not sure whether they have the data to find a measurable distinction. 22:00 Both models predict low frequency radiation from the edge of the observable universe. 22:20 My expectations. We will expect that the dipole anisotropy of the cosmic bacground radiation will be lined up with an asymmetry in the distribution of galaxies beyond 7 billion light years. 23:30 I predict a significant peak in the distribution of supernova explosions and other collision-type activity in the region 7 billion light years away, lined up with the dipole anisotropy in the cosmic background radiation. 24:30 I've been making this argument for years, but still haven't found anybody that understands me or cares. Oh well... Unfortunately whining about it only invites trolls. 25:00 When Galileo compared the models of Copernicus and Ptolemy, he didn't say "No one may discuss Ptolemy's model anymore because it is wrong." He took the two models, set them side by side, made comparisons in their predictions, and using his telescope, determined which of the two models was correct. It's not so much that I care whether Milne's hypothesis is correct, or Friedman/Robertson/Walker's model is correct. It's just that I'd like to see the scientific method applied to this situation. Take the two ideas, and acknowledge that they really are different, and compare them to the empirical data!
Views: 1134 Jonathan Doolin
emc2-part01 Maclaurin Series Expansion of Gamma
Part 1 of trying to follow the 1-minute physics derivation of E = m c^2. At this point, I'm stuck, because I can't figure out where the first premise of the calculation comes from. If this factor (1+v^2/(2 c^2)) really comes from the relativistic Doppler Shift equation then this is a great proof. If a correction in this equation could lead to E^2=(mc^2)^2 +(pc)^2 then this is an even better proof! This first video shows that the given equation is a second-order Maclaurin Series expansion for 1/sqrt(1-(v/c))^2 This is sometimes known as gamma, or the Time-Dilation factor. But unfortunately, this is not the Doppler-shift equation. The Blueshift Doppler equation factor would be sqrt[(1+beta)(1-beta)] The Redshift Doppler equation factor is sqrt[(1-beta)(1+beta)] The Transverse Doppler equation factor is sqrt(1-beta^2)... which is the reciprocal of what I am expanding in this video. If you want to watch more of me being confused: http://www.youtube.com/watch?v=Sw3UKHHsHjk&list=PLC-qVSnsyc7_y_DplTKw-AT6blkecTmK9
Views: 1812 Jonathan Doolin
Why Is The Universe Accelerating
This is a much simpler description for the shape of the universe than what's called the "Standard Model." Instead of assuming that the galaxies only "seem" to be moving away from us, it really just assumes that everything actually IS moving away from us. This model uses the Special theory of Relativity, Lorentz Transformations, and the idea of a "secondary bang" to explain some of the large-scale features of the universe. This video uses a software simulation "Animated Spacetime Diagram" from http://jdoolin.spoonfedrelativity.com/LT.htm
Views: 640 Jonathan Doolin
2015 01 31 Electric Fields & Potential 01 Draft
0:00 Relationship between electric potential and electric field 0:10 Can Mathematica generate a vector field map 0:20 The Potential of a point-charge 0:20 Typo in video. Should b 8.99*^9. 2:00 Plot3D[V[x,y],{x,-5,5},{y,-5,5}] 2:40 Set r[x_,y_]:=sqrt{x^2+y^2} 3:00 I don't think that mathematica accepts subscripts in the names of variables. 3:30 I simply set the amount of charge as 1/k_e, so that the potential would be V=1/r. That way we can focus on the shape, rather than all the physical constants 3:50 Can I get mathematica to show me the electric field? Gradient, and VectorPlot 4:20 The Gradient: Nabla. a vector made of partial derivatives in each direction. 5:30 The electric potential in Cartesian Coordinates. 6:00 The derivative of the electric potential in the x direction. 7:30 Similarly, the other components of the gradient can be found. 8:30 Vector expression of the electric field, and how the familiar form is the same as what we just derived. 9:20 The unit vector in the r-direction. 9:50 A vector plot of the vector field E={x,y}; Growing radial field 10:10 A vector plot of the vector field E={x/r,y/r}; constant radial field. 11:00 Attempts to show E={x/r^2,y/r^} and E={x/r^3,y/r^3} failed 12:00 Why did it fail? Because these have infinitely large electric field at {0,0} the other vectors look like zero in comparison 12:40 Replacing VectorPlot with StreamPlot 13:00 Playing with PlotRegion 13:08 Streamplot does not duplicate the functionality of Electric Field Lines... New lines are added as you get away from the center. 13:30 StreamDensityPlot - instead of attempting to represeent the strength of the field by the density of the lines, Mathematica just adds a shading to the graph where darker shading represents a low value, and light shading represents a high value. 13:50 The same issue that I had before is occuring. Because the density of the field lines goes to infinity at {0,0}, all of the surrounding region is treated by the shading algorithm as approximately zero. 14:06 Syntax is shown for telling the shading algorithm to use the logarithm of the strength of the field instead of the direct strength of the field. 14:20 Suggestion for next video. Lets see what the VectorPlot looks like if we put in two positive charges, or a positive and a negative.
Views: 3022 Jonathan Doolin
Animated Spacetime Diagram
See the applet at http://www.spoonfedrelativity.com/demos/LT.htm
Views: 4159 Jonathan Doolin
2014 10 10 CO2 Spectrum Saturation
https://www.youtube.com/watch?v=bEMSDhLpdKw&list=PLC-qVSnsyc784DHAblViT2q1XX9kulZ-x&index=36 As a teacher of physics and astronomy, I don't have the luxury of pointing at consensus, or correlation. These things might be effective in politics and debate, but if I want to be consistent with the principles of the scientific method, I can only really justify a "belief" in Carbon Dioxide induced global warming if I see evidence of causality. I don't feel that the scientific method is served by showing correlation studies, because one of the first things a good statistics teacher tells you is that correlation is not causality. I also don't think that the scientific method is served by consensus arguments, because history is strewn with cases where 100% of the scientific community has been wrong or confused. In the debate on global warming, the only argument I would feel comfortable presenting to my students is one that establishes CAUSALITY. The other types of arguments are distracting and time-consuming, and leave me unconvinced, regardless of how much care goes into them. The CO2 causality argument can involve (1) Knowing precisely how much heat Carbon Dioxide can trap, and by how much that increased based on the concentration of CO2 in the atmosphere. (2) Comparison of heat absorbed by CO2 to other heat inputs. (3) Knowing how heat transfers between stratosphere, troposphere, hydrosphere. There are probably a lot of other questions to ask, but these are the leading questions which I would like to be able to present to my students, and not feel like I'm fear-mongering or standing on a bully-pulpit. This video is asking "Is the Carbon Dioxide Spectrum Saturated?" It doesn't get into the numerical values of just how much extra heat is caught by an increased concentration, but I learn some of the considerations necessary in setting up the problem.
Views: 631 Jonathan Doolin
Electrostatics Experiments
Demonstrations of various phenomena in electrostatics.
Views: 4651 Jonathan Doolin
Temperature and the Thermosphere
2014 03 20 In this video, I am trying to develop my understanding of temperature, with particular emphasis on the nature of the ionosphere/thermosphere. This relates to overall questions of global warming that I've had for some time. Update 2015-11-09: In the comments below, you'll see further references to Emissivity (How fast a body can be expected to lose heat by electromagnetic emissions) Conductivity (How good a body is at losing heat by conduction into other materials) Heat Capacity (How much heat a body stores per unit of temperature)
Views: 1997 Jonathan Doolin
2015 01 30 Ch17 Charge Density and the meaning of electrical current
0:00 The basic concept of density. 0:30 ordinarily density is a function of position, for instance: $\lambda(x), \sigma(x,y), \rho(x,y,z)$ 1:15 On Wikipedia, volume density is rho, linear density is lambda, But they use rho_A for area density. 1:50 sigma is used for linear charge density in our textbook on page 574. 2:25 Distinguish between Mass Density and Charge Density, as well as linear, planar, or volumetric, depending on the context of the problem. 3:30 The textbook uses symbol n for volumetric charge CARRIER density. 3:50 Density is NOT an inherently countable quantity. While the mass or charge may be countable, the meaning of density changes greatly with the scale of the unit in the denominator. 4:00 Water has a density of 1000 kg/cubic meter. But only 1 gram per cm^3. 4:30 Take out a little thimble-full of water and it still has a density of 1000 kg/cubic meter even though there's no where near a kilogram, or a cubic meter. 5:00 But what does it mean to say there is a density AT a given geometric point in space? In the particle conceptualization of density, it really doesn't make sense, but in the fluid conceptualization of density, the material can be subdivided down to arbitrarily small region, so that density has a value even at a point. 5:50 Water on the scale of picometers is not perfectly homogeneous. 6:10 Sloan Digital Sky Survey. The bright parts of the universe is not perfectly homogeneous at our scale, or galactic scales, but may be homogeneous at scales of billions of light-years. 7:50 The Continuity Equation $A1 v1 = A2 v2 = \frac{\Delta V}{\Delta t}$; Equation 17.2: I = n q v_d A. 9:00 n is the volumetric charge-carrier, density, q is the charge of each carrier, v_d is the drift velocity, and A is the cross-sectional area. 9:45 The wandering electrons are called valence shell electrons. 10:15 The volumetric charge density is $\rho = n q$. 10:45 If you multply Coulombs per cubic meter times the cross-sectional area, you have the linear charge density. 11:20 Multiply the Linear charge density by the drift velocity and you get the current. 11:50 Even though it might take hours for an individual electron to complete the circuit, because of the sheer number of electrons, you can get quite a bit of current out. 12:03 (Sound issues: microphone not engaged.) The electrons bounce around like a herd of chickens, with a slow but steady bias to move opposite the electric field. 13:00 If the temperature drops below some critical level in a superconducting material, you just need to give the electron an initial nudge, and the current continues around the circuit without interference from thermal collisions.
Views: 1332 Jonathan Doolin
Twin Paradox Explanation
From http://bit.ly/1Isek8D
Views: 964 Jonathan Doolin
Hydrogen Implosion? or math mistake?
I found an interesting looking problem to do in my physics textbook, and worked on it until I was interrupted. (parts e and f aren't done) I found an interesting result which indicated a reduction in pressure! This made me look up "hydrogen implosion" on youtube to see if this sort of thing really happened! Yes, it does! I found footage of a oxy-hydrogen emplosion on youtube and incorporated that into my video. Unfortunately, only then did I discover I made a mistake in the math. Forgot to use kiloJoules instead of Joules. And this is going to be an EXplosion rather than an IMplosion. I'd still like to know what kind of set-up to use to generate an IMplosion. It looks like the guy in this video is using liquid water and hydrogen gas rather than gaseous hydrogen and gaseous oxygen.
Views: 555 Jonathan Doolin
2015 02 02 ElectricField & Potential Mathematica Demonstrations
Faraday's Lines of Electrical Force mapped with Mathematica.
Views: 669 Jonathan Doolin
Rayleigh Diffraction Limited Resolution and Heisenberg Uncertainty
Name Dropping means: Something you can google.
Views: 209 Jonathan Doolin
A little differential equations problem about RC circuits.
Views: 1248 Jonathan Doolin
Relativity 1:  The Principle of Relativity
The Principle of Relativity. You are not moving. Other things are. You can experiment with some of these ideas here: http://www.spoonfedrelativity.com/
Views: 574 Jonathan Doolin
Lv Uus Uuo (periodic table song)
Adapted from the Periodic Table; Melody by Jonathan Doolin Accompaniment: Casio PSR-550 Style 105; P-Boogie GGFG-GGFG-GGFG-CGDG-CGDG (Transpose -5) Image at http://en.wikipedia.org/wiki/Periodic_table#mediaviewer/File:Periodic_table_(polyatomic).svg Inspired by Big Bird's Abc-Def-Ghi https://www.youtube.com/watch?v=pr5er4ueWBQ Other adaptations? https://www.youtube.com/watch?v=W2Wwf1UVdFo Having trouble memorizing the words? https://www.youtube.com/watch?v=ZO7ejM8hmh8&feature=youtu.be
Views: 653 Jonathan Doolin
Big Bang (Milne Model)
See more at http://www.spoonfedrelativity.com This describes the Big Bang You can experiment with some of these ideas here: http://www.wiu.edu/users/jdd109/stuff/relativity/LT.html
Views: 644 Jonathan Doolin
Schwarzschild Metric Derivation
Uploaded 2015-01-31 Playlist: https://www.youtube.com/watch?v=lvIOjkQ8N3o&index=18&list=PLC-qVSnsyc796Mjr5o0blz7u5-hk11UWZ 0:00 I don't believe I have sufficient reason to expect the Schwarzschild metric to be "true" in the region of the event horizon of a black hole. Schwarzschild metric is an approximation built on approximation built on approximation. 1:40 My own post from Jun 30,2011 on Physics Forums were motivated by a more precise definition from "Reflections on Relativity" in a chapter called " 2:30 Short screen shot, showing the summary of Kevin Brown's "Reflections on Relativity". 1. Enclosed accelerating platform. 2. Light of given period from bottom to top, 3. Compare period at bottom to top. 4. Use Maclaurin Series expansion to give second-order approximation of 3. 5. Use infinite products of lagarithms to figure ratio of wave-perieod near and far from planet. 6. Maclaurin Series expansion of 5. 7. ...and another approximation. 3:05 Animation of accelerating elevator 4:00 A review of frequency, wave-number, period, and wavelength. The small dots in my elevator animation could be thought of as individual photons, OR as the peaks or troughs of a wave of EM radiation. 5:45 The dots hitting the top of the elevator at the top are hitting with greater and greater frequency, in the galilean case. In the Lorentz Case, a number of other phenomena are occurring so that the frequency at the top remains constant. 7:40 Equations on Mathpages say we have parabolas directly above one another. Calculation of speed of light from (x2-x1)/(t2-t1) using a single photon or wave-peak. 9:45 We could fix equations so they follow hyperbolas instead of parabolas. *OR* we could consider... how do I say? Imagine diagrams where speed of light is nearly vertical. 12:15 We will ignore everything except one... (actually two) photons right around the time the elevator comes to a stop. The curves are nearly identical in that region. 13:20 If elevator accelerates significantly while photon is under way, the parabolic expression will be very bad. (This seems a fundamental problem with derivation at highest gravitational fields.) 15:00 At any given moment we are stationary with respect to ourselves, so we are in a constant temporary state of rest. Is this part of a new and better description of The Principle of equivalence? Since we are in a constant temporary state of rest, without looking out a window, to tell if we are stationary in a gravitational field, or in an accelerating rocket. 17:00 Back to the math. We need to make both t1 and t2 a function of some other variable. We can't have just the emission time of a single photon. We need a set of t1s and a set of t2s to get a comparison of the rates. But once we realize that, the math is fine. 19:10 Taking the derivative of both sides of the equation. (treating the set of t1s and t2s as continuous "parts" of the wave leaving the bottom of the elevator and arriving at the top.) 21:30 I have got the answer for dt2/dt1 at this point. But what does it mean? It means, if I give you any pair of consecutive t1 events at the bottom of the elevator and any pair of consecutive t2 events at the top of the elevator, this is giving you the period at the top of the elevator (dt2) compared to the period at the bottom, (dt1) This comes out as a function of a, c, t1, and t2. But we already have a function giving t2 as a function of a, c, L and t1 22:30 We will use the approximation that t1 is 0, which puts us in the perspective of someone ON the elevator, and this allows us to calculate t1. This actually gives two solutions, because of the parabolas, but we ignore the second solution where the elevator's speed has passed the speed of light. Kevin Brown picked the one answer without mentioning that the other answers are there. 28:00 Spouting frustrations about the people who say "Math cannot be expressed in language" and I can't imagine people who just read these mathematical expressions and just see all this in their head. Things I spend weeks or months figuring out. Three and a half hours this morning, and I already knew where I was going. Of course it can be expressed in language, and the inability to express it in language just represents a lack of understanding of the material. 28:50 Where am I in the derivation. About one page of Kevin Brown's "Math Pages" And I've just finished step 3 of my derivation shown at 2:30. The next step is to use a first order Maclaurin series expansion
Views: 824 Jonathan Doolin
Adding Polar Vectors on TI-83
20 minute Video shows how to use list-multiplication and sums to add together vectors given in polar coordinates. TI-89 users can access list and sum functions from the MATH menu, I think.
Views: 2957 Jonathan Doolin
PaulGradenwitz 2018 06 03 Part15 LambdaCDM
Paul mentioned the Lambda CDM model, and I wanted to do my best to get an accurate representation, so I'm reading a big caption from Davis & Lineweaver 0:00 Paul Gradenwitz Response from June 2, 2018 0:20 Is Paul arguing for or against the Lambda CDM model. 0:40 Is "Expanding Confusion" a good source for describing Lambda CDM? It should be. 1:14 The caption and the diagram. Lets read the caption and point to the diagram. 1:40 Starting to read the caption. 2:05 Dotted lines are the worldlines of comoving objects. 2:20 What does comoving mean? Circular? 2:55 Definition of comoving means following the Hubble flow? The path of most gallaxies. 3:40 I don't think proper distance is observed or Euclidean distance. It's some other concept I don't know. 4:10 Our worldline is vertical in all diagrams. The redshift of the comoving worldlines appear as labels of all but two of the dotted lines. (I guessed 5:15 The normalized scale factor is drawn as an alternate vertical axis. 5:50 Conformal time tau is at 46 billion years. proper time at 13.7 billion years. 6:05 How does the 46 billion years come into play in the modified Milne model? We have an outer big bang at 46 billion years and several inner bangs at 13.7 billion years ago. 7:30 Ridiculously dense... Inconceivable. Even at 13.7 billion years ago, the density was denser than a neutron star. But no gravitational collapse because symmetry. No central direction to pull. 8:30 The past light-cone appears straight in comoving distance vs. conformal time. 10:20 In Milne's model there is not going to be a distinction between time and conformal time. And we don't bother with comoving distance or proper distance, but just use Euclidean distance. 11:05 Everything beyond hubble sphere is expanding faster than the speed of light. 11:50 In the Milne model, there are two hubble spheres, one that started 13.7Gy ago, (r=v*13.7gy) and an earlier one that started 45 Gyr ago. (r=v*45Gy). There is more noise in this Hubble sphere, because we're seeing a lot of other explosions. 13:30 Comparing the velocity of light to the recession velocity of the Hubble sphere. 14:15 Before 5 billion years, the photons coming TOWARD us were moving away from us, because the space at that time was expanding faster than the photon was moving. (I would call this stretching space, but they get very offended if you call it that.) 16:00 Region of superluminal recession, (past hubble sphere, but within event horizon) vs region of subluminal recession, (closer than Hubble sphere). 17:30 Our past light-cone in comoving coordinates appears to approach t=0 asymptotically, but actually it ends at 46 billion years ago. 18:40 The 0 proper distance radius is actually equal to 46 billion light-years comoving distance. 19:30 I show the particle horizon here, but I don't figure out quite what it represents.
Views: 29 Jonathan Doolin
Convince Me CO2 is GHG 3
This is part of a playlist: http://www.youtube.com/watch?v=2CIYL_6DLVY&list=PLC-qVSnsyc784DHAblViT2q1XX9kulZ-x I never really finish the original question in this video, regarding Venus vs. Earth. 02:00 What is the height of the atmosphere? About 10 km, at half atmospheric pressure. 04:00 Elastic Potential energy of a gas in a gravitational field 04:40 vs Thermal Energy; the ideal gas Law 05:10 Total Kinetic Energy is linear plus rotational plus vibrational modes of energy. 05:40 Moment of Inertia of a particle 06:05 Are the two modes of 06:45 Video of a book rotating around two rotational degrees of freedom 07:00 Video of a contained fluid quickly changing rotational state to line up along largest moment of inertia. 08:30 Does Carbon Dioxide have some kind of rotational property that makes it more ... I don't know what? 09:25 I Would like this settled: Is CO2's status as a greenhouse gas based on its infrared absorption spectrum, or is it based on its specific heat and degrees of freedom? Or are we in a part of the electromagnetic spectrum where the absorption spectrum is specifically tied to the CO2's specific heat? 11:20 Will nothing convince me that CO2 is a greenhouse gas? Actually, yeah, there IS something that would convince me. Unfortunately, I don't exactly know what that thing is. But I know it has something to do with establishing causality, not showing statistical correlation. This video cuts off at the end because it was time for bed. :) Please go to the playlist and watch more of my musings. And let me know anything that you think might help!
Views: 190 Jonathan Doolin
2018 05 20 Metric for Spherical Coordinates
0:00 The Euclidian metric: ds^2=dx^2 + dy^2 + dz^2. I express it as an inner product of a 1x3 and 3x1 matrix. 1:00 The spherical-to-cartesian coordinate conversions, and calculating the Jacobian. 1:30 My new notation for Jacobian, shows little arrows to indicate the direction which a matrix should be written. I show how the arrow notation builds a matrix in an explicit form. (This is an improvement on Einstein Notation) 3:00 calculating a few of the partial derivatives in my head. 3:30 Better... Use Mathematica to find the Jacobian. 4:30 I've got things plugged in, by pasting 9 times, and then going across and down, making replacements with x,y,z, r, theta, phi. 6:00 Jacobian is protectes,so I name it "Jake" 6:30 I explain how the value of (dx, dy, dz) is equal to (dr, dtheta, dphi) times the Jacobian. 8:11 Going through what dx is as you multiply (dr dtheta dphi) by the first column of the Jacobian. 9:27 When finding the transpose of a product of two matrices, you have to swap the order of the factors, when you transpose them. 10:30 Take our Jake.Transpose[Jake]. It looks enormous... But there are hints of some things that should simplify. 11:18 Simplify boom, we have a very simple looking diagonal matrix. The huge mess from the jacobian 11:50 Writing out the equality, how the metric goes between the (dr dtheta dphi) written horizontally and vertically. 12:40 After the matrices are multiplied out, we obtain the first equation in the Wheeler article linked by George Dishman on Researchgate on May 19, 2018. 14:30 Wheeler sets dr = 0 and eliminates two of the columns of the three-dimensional metric. 15:40 What was the mapping for? What if we had x,y,z and wanted to convert to r,theta,phi. Instead of giving x,y,z as functions of r,theta,phi. We want r,theta,phi as functions of x,y,z. I determine that theta and phi can be expressed as arccosines of functions of x,y,z. 18:20 We've got the Jacobian, and multiplied by its transpose, to get the metric... What would we do for the inverse metric? 19:20 Test this: The inverse metric is done up by putting the r theta phi on top, and the x,y,z on bottom. I want to check if these are inverse metrics in the next video.
Views: 140 Jonathan Doolin
Is positive zero equal to negative zero?
Forum thread at http://www.spacetimeandtheuniverse.com/math/5451-positive-zero-equal-negative-zero.html 1:10 Could they be considered to be different parts of the same real number? 1:30 Summation Notation; lower part and upper part. 2:05 Any algorithm that can produce an infinite string of zeros... Infinite zeros exists as a concept, but infinite 9's does not???? 3:20 Choice of representations: Start with 0 or start with 1 3:45 The arithmetical argument 4:20 1/9 does not have a terminating decimal expression. 4:50 In base 3, 1/9 has both terminating and nonterminating expression. (Dual representation.) 5:50 Representing the right side and the left side of a real number. 6:10 limit as x approaches from the left, and from the right. 6:40 Common convention: Just disallow the question... If there is an infinite discontinuity in the graph, you just don't get to ask what the function is equal to AT the point of discontinuity. 7:30 Every number x has a left hand side x+(-0) and a right hand side: x+(+0); It's the same real number, but there are two sides to every number. 9:00 Graph of 1/x 9:30 Definition of +0 and -0, using summation notation given any base n &gt 1 10:50 Roy Tomes: Agrees, since 1/0+ not equal 1/0-, the two numbers must be different. 11:10 Conventional mathematics "Don't think of it that way. We'll remove 0 from the domain of 1/x" 12:25 You can approach a door from the left or right. 12:40 David Eaton: IEEE standards 13:00 Coelacanth, A field; Once you add infinity to a set, it is not a field. 13:10 The unit step function's ambiguous value at t=0. 14:00 (Extended Real Number Line) Property treats +0 and -0 as the same, while +infinity and -infinity are different. (No other reason, I don't think, than because they wanted to define it that way.) 14:50 A lousy argument on wikipedia... Since there ARE functions whose value is ambiguous at x=0, (output a range of values) we decide we will treat ALL functions as though the output is ambiguous. 15:20 Typo in wikipedia. The sinc function does not have an ambiguous value at 0. 15:50 sin(1/x) is much more interesting, and really becomes undefined at x=0. 16:25 u(x) and 1/x provide unambiguous values around 0 17:10 Atomic-S question of plotting complex-valued functions arounc zero, and graph of real part and imaginary part of 1/(a+bi)
Views: 2061 Jonathan Doolin
EFE-04:  Equation 3; Transformation of a vector field.
Video 4: Equation 3: Recorded 2014-12-19 Playlist: https://www.youtube.com/watch?v=DKrwCzNZFLo&index=3&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl 1:20 Whereas Einstein notation at least seems to be commutative, matrix multiplication is definitely not. 1:50 Putting in little arrows to indicate the shape of the matrices. 2:50 Instead of having dummy variables, what if we actually used the relevant non-dummy variables? Here I replace x with (x,y) and y with (r,theta) 3:20 Now using the arrows with the variable-lists. 3:50 I am attempting to represent the Jacobian as an outer-product differential. But I put the matrix-multiplication for inner product. 5:20 There's nothing about the partial derivative that says it has to come before the operand. In order to have (r,\theta) down, and (x,y) across, and do it with an outer-product, it really has to be $(r,\theta)\downarrow (\partial_x, \partial_y)\rightarrow$ 6:50 Now doing the horizontal form, there's slightly less confusion because the partial derivatives appear in their natural order from an outer product. 9:00 Hmmm, I say here that I'm not a perfectionist, but really, just because I'm unable to be perfect doesn't mean I don't try to be. I think I'm being defensive. 9:20 Just showing how the transpose of a product is equal to the commutation of the product of the transposes. 10:15 Equation 3 is a more general form of Equation 2. 11:00 Equation 2 was the gradient of a scalar field. Equation 3 is presumably ANY vector field. 11:30 Some bold statements about What are Equations 1, 2, and 3. 12:05 Equation 1 is actually USING equation 2, since equation 2 is the definition of gradient , and equation 1 uses the gradient dot-producted with the differential path element to describe a differential change in a scalar field. 12:15 To be continued...
Views: 312 Jonathan Doolin
Special Relativity Demonstration Applet Part 1
See more at http://www.spoonfedrelativity.com
Views: 2758 Jonathan Doolin
RelativityNotes 01 Angle  and Rapidity (Hyperbolic Trigonometry)
Views: 779 Jonathan Doolin
EFE-02: The gradient of a gravitational field
Recorded: 2014-12-17 Playlist: https://www.youtube.com/watch?v=0gYOD-0yujM&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl&index=2 0:20 Me watching Einstein Field Equations for Beginners has grown into a novel. 0:50 Summarize by asking "What is equation 1, What is equation 2" 1:00 Equation 1 multiplies the gradient of a scalar field, and a differential path element. 1:50 Equation 2 shows how to convert the gradient of a scalar field from one set of coordinates (the x-coordinates) to another set of coordinates (the y-coordinates) 2:20 I hate and distrust Einstein Notation, because of commutativity and associativity. 3:10 If I can see multiple representations of the notation, I can gain some understanding, and possibly trust in the methods. 3:30 What about an example? How about converting from polar to cartesian coordinates, or vice versa? 4:00 Writing Equation 2 with the the y-coordinates being polar and the x-coordinates being Cartesian. 5:45 Plugging in the conversion from polar to Cartesian into the matrices. 6:15 Pulling the two equations out of the matrix multiplication. 7:40 (In brainstorming for coming up with an example, the first thing to come to mind, was more complicated than necessary, and didn't meet the criterea. See 10:30) Imagine a situation where we need to find the tidal forces in Io's polar coordinate system where the tidal forces are known in a more-or-less Cartesian coordinate system 9:30 Centripetal acceleration is $\omega^2(R-x)$ and gravitational acceleration is $\frac{G M}{(R-x)^2}$ 10:00 I said force here, but I meant a field. 10:30 Oops. Hmmm, I was looking for an example where the vector field would be easy to figure out in the polar coordinate system, but difficult in the cartesian coordinate system. I've gone and done the exact opposite; finding a field where it was fairly easy to express as a function of cartesian coordinate, $x$, but will be more complicated in polar coordinates $r,\theta$. 10:50 The equation for gravitational potential is well known in polar coordinates (r,\theta) since it is a function of r alone, but it is not so well known in (x,y) coordinates. (Meets the criteria because it is easier to express in r coordinates, AND it's a scalar (I won't get around to telling you what the gravitational potential is until 15:15.) 12:45 Using the LaTeX "newcommand" to deal with automating the process of writing various matrices. 15:15 I finally say what that gravitational potential is, and working through the use of equation 2. 16:30 I don't know if my three-and-a-half-minute explanation is any help here, but if you can pause it when I'm not talking or magnifying anything, you can see the gradient of the gravitational field in cartesian coordinates.
Views: 676 Jonathan Doolin
2015 05 06 Terrell Rotation Video Simulations
https://www.physicsforums.com/threads/terrell-revisited-the-invisibility-of-the-lorentz-contraction.520875/page-6#post-5098812 http://www.spacetimetravel.org/bewegung/bewegung3.html http://www.spacetimetravel.org/tompkins/tompkins.html http://commons.wikimedia.org/wiki/File:St_Bartholomae_panoramic_view.jpg
Views: 1207 Jonathan Doolin
How did Adams and Leverriere predict the location of Neptune?
This video comes from before I started typing up what I was going to say before I said it... But it does show the approximate positions of Uranus and Neptune between the dates of discovery of Uranus, and that of Neptune. Also shows Orbit Path of Pluto, Eris, and Sedna relative to Mars, Jupiter, Uranus, Neptune.
Views: 46 Jonathan Doolin
Equatorial, Ecliptic, and Galactic Coordinates
0:20 Diagram of the Ecliptic from Pearson's "Astronomy, A Beginner's Guide" 1:10 Meaning to find the location of the Summer Solstice, I accidentally look up 23.5 degrees above the Vernal Equinox (in Pegasus) 1:40 Correction to find (6h, 23.5°) Alt-248 2:25 Locating Taurus and the Summer Solstice between Gemini and Taurus above Orion's hand. 4:29 Errata. I say summer solstice point is (6h, 90°) but it should be (6h, 23.5°) 5:30 Identifying th (6h, 0°) point, and the equatorial plane 6:20 Equator and ecliptic appear parallel near orion, taurus, gemini, but intersect at Vernal Equinox just south of pisces 7:50 Errata: Drawing the lines toward the wrong Pisces 8:30 Alignment of stars in Cetus with Vernal Equinox. 9:10 Curvature of the ecliptic and equator on a spherical star-map. 11:10 Virgo (12h, 0°) Autumn Equinox 11:30 Sagittarius Winter Solstice 11:45 Galactic Center lies near "Teapot," Sagittarius, Winter solstice 13:10 Feature comparison of Teapot and Sagittarius 14:20 Location of M8, "The Lagoon Nebula" is almost exactly the same as the Winter Solstice (18h, -23.5°) 15:15 (18h, 0°) point on Equatorial plane, in Ophiuchus. 16:00 Global Star Map is drawn curiously inside out and backwards so that constellations look right from the outside instead of looking right from the inside. 19:30 Orthogonal vs Unit Spherical Coordinate System 20:20 Identifying directions toward Vernal Equinox, Summer Solstice, Autumn Equinox, Winter Soltice, Ecliptic North Pole in Equatorial Spherical Coordinates. 21:35 Converting Unit Spherical coordinates to Unit Orthogonal coordinates 22:45 Right-handed vs Left-Handed system. 24:20 Unit Spherical Equatorial Coordinates of Ecliptic North Pole 25:40 Calculating the orthogonal coordinates given the angles. 27:00 Equatorial Coordinates: (100-Pisces, 010-Orion, 001-Polaris) 27:30 Spherical to Orthogonal 28:40 Orthogonal to Spherical Transformation, ArcTangent 30:00 Converting Ecliptic to Equatorial Coordinates: Coordinates of Vernal Equinox, Summer Solstice, and Ecliptic North 33:30 Creating the EclipticToEquatorial Transformation Matrix 33:45 EquatorialToEcliptic (Inverse Transformation) 35:10 Convertin Galactic to Equatorial Coordinates; Galactic North Pole, Galactic Center 36:20 Finding the (010) 'galactic east' vector; Right-handed Coordinates; Cross-Product 37:45 GalacticToEquatorial and EquatorialToGalactic Transformation Matrix. 38:20 Verifying our Matrix using (3h, 30°) 38:50 The matrices are actually correct, however, when I plugged it into Mathematica I named them incorrectly. 39:20 Plugging Wikipedia data into the online tool to verify galactic center and galactic north pole. 41:40 I discovered my mistake here, and confirmed that my test should have worked if I had named them correctly.
Views: 4373 Jonathan Doolin
EFE-06: Bewildered about Contravariant and Covariant.
Playlist: https://www.youtube.com/watch?v=OtgTfKO20vU&index=8&list=PLC-qVSnsyc7-6MXt0ZakH4s4EDOINGiOl Recorded 2014-12-20 (Postscript) I am suspecting that the difference is the contravariant form should be used when converting differential path elements, and the covariant form should be used if converting differential changes in vector fields. I have not confirmed this yet, but perhaps another video will be forthcoming. 0:00 Equation 4: Contravariant. 1:00 Recording of a recording... I listen to DrPhysicsA's description of the difference between the contravariant and covariant forms of the equation. 2:00 Equation 5: Covariant 2:10 The differences: Contravariant have their indices upstaris. Covarient have ther indices downstairs. Contravariant have dy/dx terms. Covariant have dx/dy terms. Covariant are of interest to us. Contravariant, I guess, are boring to us. 2:40 The reason I made a video of a video was that I'm trying to get across exactly how completely confused I am. 3:20 We've made no restrictions on what x and y coordinates are. 3:41. I worked out an example in a previous video. But you can express the Jacobian matrix in terms of (x,y) or (r,theta) regardless of whether the final expression is intended to have (r,theta) on the bottom or (x,y) on the bottom. 5:45 If I am using this covariant form, and my input formula is in Cartesian form, wouldn't I go ahead and use the form of the jacobians that also use Cartesian form, and get an output in Cartesian form? 6:40 When I do a derivative with respect to (r,theta) it is natural for the result to be in terms of (r,theta) and when I do a derivative with respect to (x,y) it is natural for the result to be in terms of (x,y). 8:40 In short, I have no idea how to distinguish what is meant, and I'm speculating wildly throughtout this video. 12:25 While I could sit here and guess all day, I can find no meaningful difference between contravariant and covariant transformations.
Views: 777 Jonathan Doolin
As Good as You
Views: 45 Jonathan Doolin
Einstein Notation as Matrices - Matrix Arrow Notation
Please visit http://www.spoonfedrelativity.com/pages/index.php? to find my latest adventures in understanding Einstein Field Equations.
Views: 207 Jonathan Doolin
Temporal Facing 3: Galilean vs Lorentz Transformations
Temporal Facing 3: Galilean vs. Lorentz Transformations Here I consider a space-time plot where the horizontal scale is in BIllions of meters (Gigameters). On this scale, there is a big difference between the Galilean Transformations and the Lorentz Transformations. After expressing my "epilepsy concern" I begin the animation of the Galilean Transformation, showing, a continuous infinite transformation of coordinates to greater and greater velocities to the right, catching up with faster and faster coordinate systems. I then show an animation with a much, much greater distance scale, showing a lorentz Transforation, which reveals the presence of the hyperbolic arcs. Finally I show a couple of animations, showing how the Lorentz Transformation can be continuously stretched horizontally until it becomes the Galilean Transformation.
Views: 155 Jonathan Doolin
Contraction and Time Dilation
In Special Relativity, why do Lorentz Transformation Equations cause the length of time, to increase and the length of objects to decrease? Because we believe (rightly or wrongly) that where an object's here-ness intersects our now-ness is more meaningful than where it's now-ness intersects our here-ness.. Length contraction answers "Where does that object's 'here' occur in our 'now'. Time dilation answers the question 'when does that object's 'now' occur in our 'now.'" Why the asymmetry? An object's hereness extends through our 'now', but an object's nowness doesn't typically extend through our 'here' https://www.quora.com/In-theory-of-relativity-for-deriving-the-length-contraction-expression-we-use-Lorentz-transformation-equation-while-for-deriving-the-time-dilation-expression-we-use-inverse-Lorentz-transformation-equation-Why?__snids__=1428610096&__nsrc__=1&__filter__=all
Views: 214 Jonathan Doolin

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