strings of ideas

Entropy, information and gravity

2011-12-21T03:27:00.000-05:00

Recall that the overall entropy of the universe is always increasing. You could have an "isolated system", like the earth for instance, in which the entropy could decrease, but when you enlarge that system, earth + sun, the total entropy is increasing. So looking at the earth by itself is really not a good idea in defining what is considered to be an isolated system -- a common mistake people

Why FTL violates causality

2011-09-28T10:48:00.002-04:00

Suppose we have two observers, one in relative motion with respect to the other. We can represent this in fig 1 with one of the observer at rest -- frame of reference in black -- while the second one in motion -- frame of reference in blue. The line cutting in the middle represents the speed of light, c = 1. In particular, from the point of view of a stationary observer, an observer moving at

Why massive particles can't travel faster than the speed of light

2011-09-23T09:42:00.001-04:00

In the news, there is a team at CERN stating that they have measured the speed of neutrinos to be greater than the speed of light. What's wrong with that? One of the fundamental concept in physics is Lorentz invariance. What this means is that if I apply the Lorentz transformation laws to an equation that I think is valid in one frame of reference, this equation would not changed in another

Gauge Theory and Higgs Mechanism

2011-09-23T05:12:00.005-04:00

HERE'S A GENERAL RUNDOWN OF THE THEORY: (1) in QM: x → operator But to satisfy Relativity, in which time is on an equal footing with space, in QFT: x → parameter, and Φ(x) → operator. Now Φ(x), a function of x, is called the “field”. (2) L = T – V. The Lagrangian plays an important role. From Noether’s theorem, we know that if the Lagragian is invariant under a symmetry, this symmetry points

Twin Paradox

2011-09-05T19:05:00.001-04:00

The Twin Paradox Two twins, one stays at home, while the other travels to the stars at speeds close to the speed of light. Upon her return, the traveling twin will look much younger than her twin, why? The twin who leaves and returns has the trajectory depicted in red-blue in fig 1. While for the twin staying on earth, the trajectory is in green. The diagram is deceiving as it gives the

Zeta function is ok

2011-03-31T11:39:00.000-04:00

This is a sequel to, Why String Theory is wrong.Some refresher:The zeta function is given by ζ(s) = Σ 1/ns, where s is any complex number. The earliest calculation of this function was made by Euler with s = 2ζ(2) = Σ1/n2 = 1/12 + 1/22 + 1/32+ ... = π2/6.Note: for s = -1ζ(-1) = 1 + 2 + 3 +... = -1/12This is what prodded me to investigate this sum, as mentioned in Why String Theory is wrongIn my

Two-slit experiment

2011-02-02T19:15:00.029-05:00

A second look at the two-slit experiment:In Quantum Mechanics, two states can evolve, and we write this process as, |A> → |A'> |B> → |B'> By the principle of linear superposition and unitarity, the superposition of these two states will also evolve as,

Why String Theory is wrong

2011-01-03T11:27:00.023-05:00

In String Theory, one of the most crucial calculations involves summing all the numbers from 1 to infinity, which obviously should be infinite. But not in ST, where the Rieman Zeta Function is used, and gives a value of -1/12??? Yes, if you add all the numbers from 1 to a million, you get a big number; if you add all the numbers from 1 to a trillion, you get an even bigger sum. But should you add

Quantum Entanglement Demystified

2010-08-17T15:42:00.012-04:00

A...................................←●O●→....................................BYou have two particles that are released at O, sent in opposite directions with opposite spins, moving toward A and B, where observers are stationed. These particles are by definition entangled.This is the claim: when A makes a measurement of the particle spin, say, it is an up spin. Then he can conclude that B will

2009-06-06T12:24:00.005-04:00

Quantum EntanglementThere are three degrees of spookiness in quantum entanglement:A ← ●● → B1) Observer A, called Alice, will measure the spin of incoming particle. If it has spin, say, up then she knows that observer B, called Bob, will measure its counter-part particle’s spin to be down.This is like Alice tossing a coin, heads or tails, and say it comes down heads. Her counterpart Bob who is

ADS/CFT correspondence

2009-04-08T12:47:00.003-04:00

String Theory and extra dimensions

2005-11-27T09:25:00.000-05:00

Theory of Relativity and Spacetime Coordinates

2005-11-23T09:54:00.000-05:00

The Scheme of Things

2005-11-14T04:44:00.000-05:00

Standard Model and the Higgs Field

2005-11-10T02:05:00.000-05:00

The Standard Model unifies the nuclear, electromagnetic, and weak forces and enumerates the fundamental building blocks of the universe:6 leptons: electron, electron neutrino, muon, muon neutrino, tau, tau neutrino6 quarks: d (down), u (up), s (strange), c (charm), b (bottom), t (top)Each of these has half-integral spin (called fermions) and each has an anti-particle equivalent.4 Bosons(integral

Hamiltonian and Lagrangian Formalism

2005-11-07T06:03:00.000-05:00

Isaac Newton discovered the relationship between force and acceleration,which he expressed asAfterwards Leonhard Euler developed the calculus of variations that was to become the most important tool in the tool kit of the theoretical physicist. The calculus of variations was useful for finding curves that were the maximal or minimal length given some set of conditions. Joseph-Louis Lagrange took

The Cyclic Theory

2005-11-02T07:15:00.000-05:00

A new paradigmIn 2003 Steinhardt from Princeton and Turok from Cambridge published their landmark paper on what will be the next paradigm: the cyclic theory.Here are its salient features:- space and time exist forever- the big bang is not the beginning of time; rather, it is a bridge to a pre-existing contracting era- the Universe undergoes an endless sequence of cycles in which it contracts in a

Entropy, black holes, string theory

2005-10-31T06:07:00.000-05:00

One of the most dramatic recent results in string theory is the derivation of the Bekenstein-Hawking entropy formula for black holes obtained by counting the microscopic string states which form a black hole. Bekenstein noted that black holes obey an "area law", dM = K dA, where 'A' is the area of the event horizon and 'K' is a constant of proportionality. Since the total mass 'M' of a black hole

Groups, rings, modules, vector spaces, Hilbert spaces

2005-10-27T14:11:00.000-04:00

Consider a set of elements X= {a,b,c,...}and an operator *.Group Theory requires four axioms. They are:i) closure law: for any a and b in X, then a*b is also in X,ii) associative law: a*(b*c) = (a*b)*c,iii) Identity law: there is an element e such that a*e = e*a = a,iv) Inverse law: for any a there is an element a-1 such that a * a-1= a-1*a = e. (For ordinary multiplication, the element a cannot

Hilbert Space And Quantum Mechanics

2005-10-26T08:30:00.000-04:00

Consider the class of infinite real sequences (a1, a2...), such that the sum of all (an)squared< infinite.Example:i) p=(1,1,...) does not converge, that is, 1+1+1+1+...does not converge to a point.ii) q=(1,1/2,1/4,1/8,) converges.Consider two points for which its infinite real sequence converges.p=(an) and q =(bn)Now if one defines the function d, also called a metric, asd(p,q)=square root of

Quantum Entanglement

2005-10-14T19:06:00.000-04:00

There are three degrees of spookiness in quantum entanglement:A … <… oo …> …BA particle decays sending two fermions in opposite directions (conservation of momentum) towards A and B.1) Observer A, called Alice, will measure the spin of incoming particle. If it has spin, say, up then she knows that observer B, called Bob, will measure its counter-part particle’s spin to be down.This is like Alice

The theory that matters

2005-10-09T09:42:00.000-04:00

Three outstanding features of String theory:i) The number of dimensions is inherent into the theory. If you work in classical physics or quantum mechanics, the problem you are dealing with pretty much determines in how many dimensions you will write your equation. Say you are dealing with a particle moving along a straight line. A one-dimensional equation would be sufficed. If you are dealing

The ghosts of physics

2004-09-29T14:52:00.001-04:00

Newton – Coulomb – Faraday – Maxwell – Einstein – Q.M.Ever since the heydays of relativity and quantum mechanics, we’ve been told to leave our common sense behind and get with it, and ever since then physics has been getting weirder and weirder. Although we shouldn’t be surprised, for when we evolved as a distinct branch of the primates, the appeal to our imagination was a necessary evil for the