tachyon

A tachyon /ˈtæki.ɒn/ or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from theGreek: ταχύ pronounced tachy /ˈtɑːxi/, meaning rapid. It was coined in 1967 by Gerald Feinberg.[1] The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than […]

A tachyon /?tæki.?n/ or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from theGreek: ???? pronounced tachy /?t??xi/, meaning rapid. It was coined in 1967 by Gerald Feinberg.[1] The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than light), which both exist. The possibility of particles moving faster than light was first proposed by O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan in 1962, although the term they used for it was “meta-particle”.[2]

Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics.[3][4] If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according tospecial relativity) would lead to violations of causality.[4] Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.

In the 1967 paper that coined the term,[1] Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,[5] and instead represent an instability known as tachyon condensation.[3] Nevertheless, negative squared mass fields are commonly referred to as “tachyons”,[6] and in fact have come to play an important role in modern physics.

Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found. In September 2011, it was reported that a tau neutrino had travelled faster than the speed of light in a major release by CERN; however, later updates from CERN on the OPERA project indicate that the faster-than-light readings were resultant from “a faulty element of the experiment’s fibre optic timing system”.[7]

tachyon

A tachyon /ˈtæki.ɒn/ or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from theGreek: ταχύ pronounced tachy /ˈtɑːxi/, meaning rapid. It was coined in 1967 by Gerald Feinberg.[1] The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than […]

A tachyon /?tæki.?n/ or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from theGreek: ???? pronounced tachy /?t??xi/, meaning rapid. It was coined in 1967 by Gerald Feinberg.[1] The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than light), which both exist. The possibility of particles moving faster than light was first proposed by O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan in 1962, although the term they used for it was “meta-particle”.[2]

Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics.[3][4] If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according tospecial relativity) would lead to violations of causality.[4] Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.

In the 1967 paper that coined the term,[1] Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,[5] and instead represent an instability known as tachyon condensation.[3] Nevertheless, negative squared mass fields are commonly referred to as “tachyons”,[6] and in fact have come to play an important role in modern physics.

Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found. In September 2011, it was reported that a tau neutrino had travelled faster than the speed of light in a major release by CERN; however, later updates from CERN on the OPERA project indicate that the faster-than-light readings were resultant from “a faulty element of the experiment’s fibre optic timing system”.[7]

bowling balls

Got to see this demonstration of physics by bowling balls this weekend. It’s beautiful and cool. Watch all the way to the end to see the balls move back in phase with each other, as they are at the start. In between, it moves from beautifully ordered to apparent chaos and back, again and again. […]

Got to see this demonstration of physics by bowling balls this weekend. It’s beautiful and cool. Watch all the way to the end to see the balls move back in phase with each other, as they are at the start. In between, it moves from beautifully ordered to apparent chaos and back, again and again.
Because this video has been very popular, here are answers to some common questions:
** What am I seeing? How does this work? **
The length of time it takes a ball to swing back and forth one time to return to its starting position is dependent on the length of the pendulum, not the mass of the ball. A longer pendulum will take longer to complete one cycle than a shorter pendulum. The lengths of the pendula in this demonstration are all different and were calculated so that in about 2:40, the balls all return to the same position at the same time – in that 2:40, the longest pendulum (in front) will oscillate (or go back and forth) 50 times, the next will oscillate 51 times, and on to the last of the 16 pendula which will oscillate 65 times. Try counting how many times the ball in front swings back and forth in the time it takes the balls to line up again, and then count how many times the ball in back swings back and forth in the same time (though it’s much harder to keep your eye on the ball in back!).
** Why are they not perfect at the end? **
This large frame is built from wood and is outdoors, which means it expands, contracts, and flexes. Because the position of the frame changes, the cycle lengths are not perfectly aligned. Over time, the minor differences become more pronounced.
** Where is this? **
This was built on private property in the mountains of North Carolina (United States), near Burnsville. It is not open to the public.
** Can I get a copy of this video to use in my classroom? **
Yes. But I don’t have a link for you yet. Come back in a day or so to get the link here.
** How can I make my own? Where can I learn more? **
Here are some links to information about the physics behind this demonstration. There are some small scale versions of this demonstration that can be purchased commercially as well, but if you want a 20’ version like this, you’ll have to make your own! I didn’t make this and I don’t have plans for it, but work through the physics at these links and design your own – you’ll learn a lot about physics, math, and construction!

http://www.arborsci.com/cool/pendulum-wave-seems-like-magic-but-its-physics
http://io9.com/5825639/a-simple-physics-demonstration-that-shows-why-science-still-sometimes-seems-like-magic
http://sciencedemonstrations.fas.harvard.edu/icb/icb.do?keyword=k16940&pageid=icb.page80863&pageContentId=icb.pagecontent341734&state=maximize&view=view.do&viewParam_name=indepth.html#a_icb_pagecontent341734
http://scitation.aip.org/content/aapt/journal/ajp/69/7/10.1119/1.1349543?ver=pdfcov

Published on Mar 8, 2012

A pendulum wave with 16 bowling ball pendulums of different lengths, Doc’s Pasture, Celo NC. Another good view with people lying undeneath: http://youtu.be/RNxqEudZ-hE The math behind this and some more details are at: http://celophoto.blogspot.com/2012/03…

seven red lines

Published on May 5, 2014 How to draw seven red lines, all perpendicular, some with green ink, some with transparent ink, and one in the form of a kitten. This is a caricature but experienced engineers do not behave like this. Users NEVER know with precision what they want and it is the job of […]

Published on May 5, 2014
How to draw seven red lines, all perpendicular, some with green ink, some with transparent ink, and one in the form of a kitten.

This is a caricature but experienced engineers do not behave like this. Users NEVER know with precision what they want and it is the job of the engineer put these wants into appropriate specs. When they say red the engineer must extract the Pantone scale range they want. Transparent does not mean invisible and the engineer must define the degree of transparency. Lines here clearly not straight lines and perpendicular means something different from the mathematical definition.


axioms and dogmas

Axioms are self evident truths that require no proof, which is similar to a dogmatic belief in the sense that dogma is a set of beliefs or doctrines that are established as undoubtedly in truth. Axiom is a statement taken to hold within a particular theory. One can combine the axioms to prove things within […]

Axioms are self evident truths that require no proof, which is similar to a dogmatic belief in the sense that dogma is a set of beliefs or doctrines that are established as undoubtedly in truth.

Axiom is a statement taken to hold within a particular theory. One can combine the axioms to prove things within that theory. One may add or remove axioms to the theory to get another theory.

An axiom is something that is self-evidently true; it is so obvious that there is no controversy about it. In mathematics, you just have to accept some very basic notions in order to avoid circular reasoning. These can’t be proven, but they can always (and often very easily) be observed.

Example from Euclid’s Elements:

Common notions:

Things that are equal to the same thing are also equal to one another (Transitive property of equality).
If equals are added to equals, then the wholes are equal.
If equals are subtracted from equals, then the remainders are equal.
Things that coincide with one another equal one another (Reflexive Property).
The whole is greater than the part.

Dogmas are axioms of cultural, religious, political belief systems.

A dogma refers to (usually a religious) teaching that is considered undoubtedly and absolutely true. It is something you accept without any direct observation; dogmas are accepted by faith only.

Some people would say that there is no difference between axioms and dogmas, because ‘self-evident truths’ are in some sense based on faith; that is that you accept on faith that anything that seems obvious and self-evident is true. An interesting read on this subject is Wittgenstein’s On Certainty. Take the axiom of choice, for example: there is huge division in mathematics as to whether it’s true or not, and many proofs are written based on a by-faith acceptance (or rejection) of said axiom.

The difference is that it is perfectly ok to handle different sets of axioms in, say, mathematics and prove a theorem in Euclidean geometry one day and a theorem in Lobachevskian the next – just remembering when the fifth postulate does or doesn’t hold, but it’s not considered acceptable to hold several sets of dogmas at once.

Common Core Math

Published on Apr 14, 2013 Presented by Joy Pullmann Managing Editor of School Reform News and an Education Research Fellow at The Heartland Institute Uploaded on Nov 7, 2011 Talk title: Why math instruction is unnecessary John is a teacher … Continue reading


Published on Apr 14, 2013
Presented by Joy Pullmann
Managing Editor of School Reform News and an Education Research Fellow at The Heartland Institute

Uploaded on Nov 7, 2011
Talk title: Why math instruction is unnecessary

John is a teacher of math and a homeschooling parent who offers a radical-sounding proposal: that we cease to require math instruction in middle and high school. He came to this point of view over a number of years, as he attempted (and failed) to convince students that the math they were learning was beautiful, useful, or an imperative component of their future prosperity. When he stopped trying to connect math with students and simple tried to connect with the students themselves, he made a profound discovery – kids are suffering from “math anxiety.” If the goal of teaching math is to teach us deductive and inductive reasoning, might games and puzzles be equally effective in developing kids’ reasoning skills – and allow them to fulfill their life missions? “We want to reawaken analytical and critical thinking schools that have been anesthetized by the standard curriculum,” says John.

John Bennett is a math teacher in the San Francisco Bay Area and a home-schooling father of four. An outspoken advocate of education reform, he has presented lectures and workshops throughout California. He uses logic puzzles and strategy games in the classroom (and at home) to supplement the traditional mathematics curriculum. John has written three volumes of Pentagrid Puzzles, a new puzzle form he created to challenge deductive logic and visual-spatial reasoning.

Uploaded on Jan 15, 2007
M.J. McDermott is speaking about the current state of math education, as a private citizen .

The main argument for the new way of teaching Mathematics is that this isn’t the 1950’s and nobody does numerical calculations by hand anymore. Scientists, engineers, economists, etc. all use computer programs to do their calculations. If you spend too much time teaching kids how to calculate, you aren’t teaching them mathematics, yAt the core (not pun intended) of this discussion is a basic misunderstand about what it means to understand. Experts at whatever can never explain how they do what they do. Expert knowledge is in the form of pattern recognition procedures regulated by the basal ganglia and not in the form of explicit coding of rational rules. Yet a rich area of research, what is the best way to teach children math in the era of smartphones?

The Tea Party has found another front to attack the Obama administration: elementary arithmetic. The 32-12 problem is making the rounds. I do not know the source and I do not know anything about the core math curricula. There is no context to understand where this example comes from or even if it is really in some workbook. What is the rule? What is the purpose of the exercise? What level? It is not possible to discuss the merit of the method without the context. In any case the video is misleading as “old fashioned” method shown is shorthand for a complicated procedure with the complexity of “borrowing.”

For example 32-17:

17 = 10 + 7

12-7 = 5

32-12 =20

20- 10 = 10

10+5=15

Whereas the new method seems to be

17+3 = 20;

20+10 = 30;

30+2 = 32;

(3+10+2 = 15)

Arkansas is well down in the bottom half of states in educational achievement. The woman doing the presentation doesn’t even realize what she is presenting. What she’s showing is what they teach so kids understand the PRINCIPLES underlying multiplication and division. The kids will eventually do it the “normal” way. A geometric visual explanation of the meaning of addition and multiplication is misconstrued as a procedure to do the calculations.

I am not qualified to discuss how to teach children but I am a parent myself. The fact that a parent gets emotional or pokes fun at the way their children are taught does not make her opinion valid.


Spectral theorem

Spectral theorem From Wikipedia, the free encyclopedia In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a matrix can bediagonalized (that is, represented as a diagonal matrix in some basis). This concept of diagonalization is relatively straightforward for operators on finite-dimensional spaces, but […]

Spectral theorem

From Wikipedia, the free encyclopedia
In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices. In broad terms the spectral theorem provides conditions under which an operator or a matrix can bediagonalized (that is, represented as a diagonal matrix in some basis). This concept of diagonalization is relatively straightforward for operators on finite-dimensional spaces, but requires some modification for operators on infinite-dimensional spaces. In general, the spectral theorem identifies a class of linear operators that can be modelled by multiplication operators, which are as simple as one can hope to find. In more abstract language, the spectral theorem is a statement about commutative C*-algebras. See also spectral theory for a historical perspective.
Examples of operators to which the spectral theorem applies are self-adjoint operators or more generally normal operators on Hilbert spaces.
The spectral theorem also provides a canonical decomposition, called the spectral decompositioneigenvalue decomposition, or eigendecomposition, of the underlying vector space on which the operator acts.
In this article we consider mainly the simplest kind of spectral theorem, that for a self-adjoint operator on a Hilbert space. However, as noted above, the spectral theorem also holds for normal operators on a Hilbert space.