## Thursday, January 31, 2008

### Electroweak theory in Quantum Field Theory Demystified

Today I am posting another sample chapter from the soon to be released Quantum Field Theory Demystified. This is chapter 10, which is a follow-on chapter to chapter 9, which was posted on January 25th. Chapter 9 discusses spontaneous symmetry breaking and the Higgs mechanism for generating mass in a kind of abstract sense. In chapter 10, we apply those methods to the specific case of electroweak theory and show how the procedure gives mass to the W/Z bosons (the massive gauge bosons).

## Wednesday, January 30, 2008

Working on a book on string theory I want to stay focused on the concepts and not just the math, so I've been reading Lisa Randall's fascinating book warped passages. Last night I was reading the section about the Higgs mechanism which physicists believe gives particles mass. That got me curious about the construction of the Large Hadron Collider (LHC) in Europe, since they expect to detect the Higgs at the LHC among other things.

Well apparently they recently put the last detector element in place, the compact muon solenoid detector. This detector is designed to study high energy (TeV scale) proton collisions, that may not only allow scientists to detect the Higgs boson, but might give experimental hints about supersymmetry and even extra dimensions of space. Supersymmetry and extra dimensions fall in the realm of what physicists call "physics beyond the standard model", which may or may not include string theory.

The startup of the LHC, which should be this summer, will be an exciting time in particle physics. It has been some time since there has been a major breakthrough result in experimental particle physics but this device will certainly change that. The most exciting possibilities will be if it detects particles and interactions that nobody has thought of yet. You can read about the construction of the detector here:

http://www.sciencedaily.com/releases/2008/01/080122154445.htm

Lisa Randall's book is a good popular read:

http://www.amazon.com/Warped-Passages-Unraveling-Mysteries-Dimensions/dp/0060531096/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1201706246&sr=8-1

## Monday, January 28, 2008

### Complex Variables Demystified

Below please find a sample chapter from the upcoming book Complex variables demystified. The topic of complex variables is rich and interesting enough just considering mathematics, but it also has widespread application in the physical sciences and engineering. One application is to string theory so readers of string theory demystified might want to brush up on their complex variables as well.

## Saturday, January 26, 2008

### Tests of General Relativity

Two things that have really fascinated me over the past few years are the Pioneer anomaly and dark energy/matter. Apparently the pioneer spacecraft are not traveling exactly on the trajectories expected. This might not mean anything or it could be an indication that our understanding of gravity has to be modified. You can read about the Pioneer anomaly on Wikipedia:

http://en.wikipedia.org/wiki/Pioneer_anomaly

A listing of papers on the archive that discuss the pioneer anomaly can be found here:

http://xxx.lanl.gov/find/grp_physics/1/ti:+AND+pioneer+anomaly/0/1/0/all/0/1

Of course so-called dark energy has revived the need for Einstein's cosmological constant term. Or does it? Alternative theories have been proposed which modify gravity on large scales. If you're more technically inclined you might want to check out a recent paper titled Distinguishing Modified Gravity from Dark Energy. The abstract reads:

The acceleration of the universe can be explained either through dark energy or through the modification of gravity on large scales. In this paper we investigate modified gravity models and compare their observable predictions with dark energy models. Modifications of general relativity are expected to be scale-independent on super-horizon scales and scale-dependent on sub-horizon scales. For scale-independent modifications, utilizing the conservation of the curvature scalar and a parameterized post-Newtonian formulation of cosmological perturbations, we derive results for large scale structure growth, weak gravitational lensing, and cosmic microwave background anisotropy. For scale-dependent modifications, inspired by recent $f(R)$ theories we introduce a parameterization for the gravitational coupling $G$ and the post-Newtonian parameter $\gamma$. These parameterizations provide a convenient formalism for testing general relativity. However, we find that if dark energy is generalized to include both entropy and shear stress perturbations, and the dynamics of dark energy is unknown a priori, then modified gravity cannot in general be distinguished from dark energy using cosmological linear perturbations.

It is available as a PDF at this link:

http://xxx.lanl.gov/PS_cache/arxiv/pdf/0801/0801.2431v1.pdf

Here is a paper recently posted on the archive which reviews tests of general relativity in the solar system:

http://xxx.lanl.gov/abs/0801.3407

Tests of gravity performed in the solar system show a good agreement with general relativity. The latter is however challenged by observations at larger, galactic and cosmic, scales which are presently cured by introducing dark matter'' or dark energy''. A few measurements in the solar system, particularly the so-called Pioneer anomaly'', might also be pointing at a modification of gravity law at ranges of the order of the size of the solar system. The present lecture notes discuss the current status of tests of general relativity in the solar system. They describe metric extensions of general relativity which have the capability to preserve compatibility with existing gravity tests while opening free space for new phenomena. They present arguments for new mission designs and new space technologies as well as for having a new look on data of existing or future experiments.

## Friday, January 25, 2008

### Quantum Field Theory Sample Chapter

This is a sample chapter from the upcoming Quantum Field Theory Demystified. The chapter introduces the concept of symmetry breaking and explains the Higgs mechanism which is responsible for the acquisition of mass by particles.

## Thursday, January 24, 2008

### String Theory Demystified and other upcoming titles

Readers who want to continue their studies in physics will be interested to hear about several upcoming books. Recently we just finished with the typesetting of "Quantum Field Theory Demystified". This book is a sequel to Quantum Mechanics Demystified that introduces Feynman diagrams, the Dirac equation, quantum field theory for scalar fields, electroweak theory, the Higgs mechanism and a bit of supersymmetry.

I am also hard at work wrapping up String Theory Demystified. This is a tough subject and writing a book about it is a lot of work. But I think I am putting together a presentation that readers who've finished Quantum Mechanics Demystified and Relativity Demystified will really find useful. You should also read Quantum Field Theory Demystified before tackling string theory and-you might also want to know that Complex Variables is an important area of mathematics that is used in string theory. Complex Variables Demystified will also be coming out this spring to help you in your studies.

All of these books will be available soon. In all of the books I recommend other books readers can go to after the Demystified book to really get into the subject.

String Theory Demystified can be pre-ordered on Amazon at:

http://www.amazon.com/String-Theory-Demystified-David-McMahon/dp/0071498702/ref=sr_1_4?ie=UTF8&s=books&qid=1201199530&sr=1-4

Quantum Field Theory is at:

http://www.amazon.com/Quantum-Field-Theory-Demystified-McMahon/dp/0071543821/ref=sr_1_5?ie=UTF8&s=books&qid=1201199530&sr=1-5

And Complex Variables is here:

http://www.amazon.com/Complex-Variables-Demystified-David-McMahon/dp/007154920X/ref=sr_1_11?ie=UTF8&s=books&qid=1201199530&sr=1-11

Still planning on doing an Advanced Quantum Mechanics book soon.

## Wednesday, January 23, 2008

### Quantum Gravity Textbook

Funny I stumbled on this today, after putting up the post on the quantum gravity experiment. Amazon.com recommended a book on quantum effects in curved space-time (reportedly for beginners according to the only reviewer). Check it out at the link below. If anyone has read it I'd like to get your impressions.

http://www.amazon.com/Introduction-Quantum-Effects-Viatcheslav-Mukhanov/dp/0521868343/ref=s9_js_pop_title?ie=UTF8&pf%5Frd%5Ft=101&pf%5Frd%5Fm=ATVPDKIKX0DER&pf%5Frd%5Fp=278240701&pf%5Frd%5Fs=center-1&pf%5Frd%5Fr=163H33BNHRK5BNHKXEV2&pf%5Frd%5Fi=507846

### Quantum Gravity Detection?

The search for experimental tests of quantum gravity is on. A few years ago Valery Nesvizhevsky and colleagues found the first hints of quantum gravity involving quantized bound states of neutrons. The potential well used to trap the neutrons was created using the earth's gravitational field, and the researchers reported that as neutrons fell into the well toward the center of the earth, they did not move continuously but rather jumped from one height to another in discrete intervals.

http://www.aip.org/pnu/2002/573.html

The original paper can be found here:

http://www.nature.com/nature/journal/v415/n6869/abs/415297a.html

While string theory and loop quantum gravity get all the attention, there are other approaches being studied. One of these (which I confess I don't know much about) is called non-commutative geometry. I found this interesting paper which builds upon the neutron work, claiming to study non-commutative geometry using this type of experiment:

http://www.citebase.org/abstract?id=oai%3AarXiv.org%3Ahep-th%2F0505064

## Tuesday, January 22, 2008

### Casimir Force

The Casimir effect is a phenomenon found in quantum field theory that sounds like pure science fiction. But recently, scientists have been finding practical applications for this bizarre concept. First let's describe the Casimir effect and then I'll point you to an article about it.

Basically, the Casimir effect is a quantum mechanical force that arises from the vacuum energy or "zero point" field. The so-called zero point energy results from a left over infinite sum you get when writing down the energy of a quantum field. So in everyday terms you can think of the vacuum energy as an energy field that fills all of empty space, everywhere.

Casimir did some calculations and discovered that if you had two conducting metal plates in a vacuum, the vacuum energy would cause them to move closer together. The bottom line here is put two metal plates in a vacuum, and they are going to be attracted to one another, even though from a classical perspective you would expect nothing to happen since the vacuum is supposedly empty space. The Casimir effect proves that this is not the case, and is one more illustration of how quantum theory leads to interesting and bizarre effects. The gory details on the Casimir effect can be found in this Wikipedia article, I have to warn you its pretty mathematical and hard to wade through.

http://en.wikipedia.org/wiki/Casimir_effect#The_Casimir_effect

So let's get to the interesting part. Recently, scientists have figured out how to exploit the Casimir effect in nanotechnology. Apparently "nanomachines" have a tendency to stop running (like all machines do) but they figured out how to use the Casimir force to counteract this problem. This is described here:

http://www.sciencedaily.com/releases/2008/01/080112163117.htm

## Monday, January 21, 2008

### Communication with Quantum Entanglement?

One of the most interesting phenomena in quantum mechanics, first proposed by Schrodinger along with Einstein, Podolsky, and Rosen way back in the 1930's is entanglement. This is a quantum phenomenon where two systems (two particles that have interacted say) become linked across space and time. When this happens the properties of the particles become correlated, so if you know the spin of one of the particles, you know the spin of it's entangled partner, or should I say you know what the result of a measurement on the spin of its partner would be-even if it was located on the other side of the universe.

Entanglement is often described with two parties denoted as Alice and Bob each taking one member of the entangled pair. Generally its a given that although this phenomenon is interesting, it would not be possible to communicate using it-because measurement results would appear to be random unless Alice and Bob compare their results. A paper released a few years ago indicates that under certain special circumstances, it may in fact be possible to transmit some information from Alice to Bob in a quantum way. I have provided a link to this interesting (but dense) paper below.

The paper makes use of two topics I cover in detail in Quantum Mechanics Demystified-spin and the density matrix ( I also cover these topics in detail in my book Quantum Computing Explained published by Wiley). In any case, if you understand quantum theory at the level of quantum mechanics demystified you will be able to grasp this paper.

http://xxx.lanl.gov/abs/quant-ph/0407236

### Learning Theoretical Phyiscs

Learning theoretical physics is hard, but the fact is it doesn't have to be impossible. If you build a solid foundation I believe just about anyone who is willing to put the work in can gain a general understanding of physics. Its my goal to help make that happen for thousands of people with my Demystified series books.

The first book in the series that came out teaches what most universities would consider first semester quantum mechanics, either at the undergraduate or graduate level. The difference with my book is that I've tried to write it with the student in mind. So instead of long, detailed, wordy explanations that leave your head spinning I cut to the chase and just say what needs to be said. More importantly each chapter is packed with solved examples that don't leave out any details. You can find it on Amazon at:

http://www.amazon.com/Quantum-Mechanics-Demystified-David-McMahon/dp/0071455469/ref=pd_bbs_sr_1?ie=UTF8&s=books&qid=1200934345&sr=8-1

To master quantum mechanics you also have to learn linear algebra. Linear algebra demystified is available at:

http://www.amazon.com/Linear-Algebra-Demystified-David-McMahon/dp/0071465790/ref=pd_sim_b_title_2

All of the books follow the same format.