Tuesday, February 28, 2006

An Ion Temperature of 2 to 3 Billion Kelvin,

hotter than the interior of any known star, has been achieved in New Mexico.  This temperature record was set recently in a test shot at the Z Pinch device at Sandia National Lab where an immense amount of electrical charge is stored in a device called a Marx generator.  Many capacitors in parallel are charged up and then suddenly switched into a series configuration, generating a voltage of 8 million volts (a process captured in a famous photograph). This colossal electrical discharge constitutes a current of 20 million amps passing through a cylindrical array of wires, which implodes.  The imploding material reaches the record high
temperature and also emits a large amount of x-ray energy. Why the implosion process should be so hot and why it generates x rays so efficiently (10-15% of all electrical energy is turned into soft x rays) has been a mystery. Now Malcolm Haines (Imperial College) and his colleagues think they have an explanation. In the hot fireball formed after the jolt of electricity passes through, they believe,
the powerful magnetic field sets in motion a myriad of tiny vortices (through instabilities in the plasma), which in turn are damped out by the viscosity of the plasma (ionized atoms). In the space of only a few nanoseconds, a great deal of magnetic energy is converted into the thermal energy of the plasma. Last but not least, the hot ions transfer much energy to the relatively cool electrons, energy
which is radiated away in the form of x rays. (Haines et al., Physical Review Letters, 24 February 2006)

The American Institute of Physics Bulletin of Physics News
Number 767 February 28, 2006 by Phillip F. Schewe, Ben Stein, and
Davide Castelvecchi

Formation of Large Fluid Vortices: Corporate Merger or Hostile-Takeover

Large, energetic vortex structures commonly form in irregular or turbulent two-dimensional flows. Familiar examples are Jupiter's Red Spot or hurricanes and typhoons on Earth. What is
the mechanism that transfers energy from small-scale vortices to these often long-lived, large-scale circulation patterns? Many suggestions have been made, such as a merger of small vortices into larger ones. According to this scenario, the process is similar to
the consolidation or merger of many small corporations into a mega-corporation. In a new paper, researchers verify by experiment and simulation a quite different mechanism based on elongation and thinning of small-scale vortices, stretched like taffy by large-scale strain. This process weakens the velocity of the small vortices and transfers their kinetic energy into the large-scales. The thinning mechanism allows the large vortices to drain the energy of the smaller ones, squeezing them dry. Thus, the process is more like a hostile takeover of many small corporations by a larger one that strips their assets and liquidates them. According to the
authors, the work provides quantitative models of how a population of small-scale vortices sustains on the large-scale circulations. These results will help to model and predict formation of
large-scale vortices in atmospheres and oceans (Chen et al., Physical Review Letters, 3 March 2006; contact Gregory Eyink, Johns Hopkins, image,)

The American Institute of Physics Bulletin of Physics News
Number 767 February 28, 2006 by Phillip F. Schewe, Ben Stein, and
Davide Castelvecchi

Atom Wires

The smallest wire width in mass produced electronic devices is about 50 nm, or about 500 atoms across.  The ultimate limit of thinness would be wires only one atom wide.  Such wires can be made now, although not for any working electronic device, and it is useful to know their properties for future reference.  Paul
Snijders and Sven Rogge from the Kavli Institute of Nanoscience at the Delft University of Technology and Hanno Weitering from the University of Tennessee build the world's smallest gold necklaces by evaporating a puff of gold atoms onto a silicon substrate which has first been cleared of impurities by baking it at 1200 K. The crystalline surface was cut to form staircase corrugations. Left to
themselves, the atoms then self-assemble into wires (aligned along the corrugations) of up to 150 atoms each (see figure). Then the researchers lower the probe of a scanning tunneling microscope (STM) over the tiny causeway of gold atoms to study the nano-electricity moving in the chain; it both
images the atoms and measures the energy states of the atoms' outermost electrons. What they see is the onset of charge density waves---normally variations in the density of electrons along the wire moving in pulselike fashion. But in this case (owing to the curtailed length of the wire) a standing wave pattern is what results---as the temperature is lowered. The wave is a quantum
thing; hence certain wavelengths are allowed. In other words, the charge density wave is frozen in place, allowing the STM probe to measure the wave (the electron density) at many points along the wire. Surprisingly, two or more density waves could co-exist along the wire. The charge density disturbance can also be considered as a particlelike thing, including excitations which at times possess a fractional charge. (Snijders et al., Physical Review Letters, 24
February 2006)

The American Institute of Physics Bulletin of Physics News
Number 767 February 28, 2006 by Phillip F. Schewe, Ben Stein, and
Davide Castelvecchi

Sunday, February 26, 2006

Choosing a Science Fair Project Topic

Making Sure Your Science Fair Project Topic is Right

Choosing a topic is one one of the most crucial parts of this process. It is important that you choose a topic that is “right.” By this, I don't mean that you need to be on the absolute edge of physics research – there is no need for your project to be about string theory or Bose-Einstein Condensation (although, if you relish a challenge...!). Instead, make sure the topic is right for you.

Choosing a topic can seem hard, and it often is. Don't get too worked up about it, most people get stuck on this step for a little while. If you don't come up with a topic right away, that's o.k. You will get there.


- Choose a topic that interests you or that you're curious about. Don't feel that you need to impress anyone with the “difficulty” of the topic – impress them with your actual work, instead.

- Ask yourself the following questions:

    What interests me?

    What do I like to do?

    Is there something I've always wanted to know the answer to?

    How can turn one of these answers into a science fair topic?

- There is bound to be a way to do this – for any answers you could possibly have come up with. Stuck? Ask your teacher or mentor for advice on how how to approach your interests from a scientific point of view. Try searching the internet for “the science of...” Chances are, there will be many pages full of things you can try.

- Choose a topic that you can investigate in the time you have (it is plain impossible to study things that take years to happen in an eight week period!) – simpler is usually better.

- While you're trying to pick a topic, don't put the rest of your life on hold! Live your life as always, but pay close attention to the world around you as you go about your day – ask yourself questions about things you might have previously taken for granted, like:

    Are the ads on TV telling the truth?

    What science went into the design of your favorite toy?

    Where does your garbage go? How much do you create each week?

    How does your favorite sports star's signature shoot/pitch/move work?

- If you want (or need) to produce a physics related project, remember that there are many fields within physics. Go to the library and read newspapers, magazines, websites and science journals.

- Go to museums, especially a science museum if you have one locally.

- Ask people – teachers, family, friends.

- Write down all your ideas in your notebook!

- Narrow down your list of ideas until you have the one you like best. It's ok if you don't know everything about this topic yet – there is plenty of time to do more research.

Saturday, February 25, 2006

Tire Wear

Estimation and Order of Magnitude

As the rubber wears off the tread of your tires, it mostly becomes airborne pollution called "particulate matter." Estimate what mass of rubber is worn off all the tires in the United States each year. (Assume the depth of the tread on new tires is 1 cm and the density of rubber is 1200 kg/m3)

There are approximately 300 million people in the US. They are (on average) divided into families of four, with two cars for each family, with the typical car having four tires.

This means that there are 600 million (6 x 108) tires in use.

How much tread rubber does each tire have? Lets assume that a typical tire has a tread that is a rectangle 1 cm thick and 10 cm across, wrapped around a wheel with a diameter of 1m (that is, about three meters long).

There volume of this tread is: 1 cm * 10 cm * 300 cm = 3000 cm3 = 3 x 10-3 m3 per tire.

Thus, the 600 million tires, between when they’re new and when they’re bald, produce:

600 million * 3 x 10-3 m3 = 1.8 x 106 m3 of rubber.

Which has a mass of 1.8 x 106 m3 * 1200 kg/m3 = ~2 x 109 kg.

Now, this rubber is not all used up in one year – a typical tire lasts a lot longer than that – perhaps four years:

Mass of rubber per year: 2 x 109 kg/4 years = 5 x 108 kg/year.

Calculate the Thermal Capacity of a Fluid

a) What is the Thermal Capacity of a liquid, given the following details:

    Volume = 200ml

    Specific Gravity = 0.8

    Specific Heat = 1.5 cal/g/degC

b) Also, assuming there are no external heat losses, calculate the energy required to raise the sample's temperature to 37 degC.

a) The Thermal Capacity of a sample is the amount of heat energy required to raise the specific sample by one degree celcius. This can calculate from the given data as follows:

    Weight of Sample = Specific Gravity * Weight of Same Volume of Water

    Weight of Sample = 0.8 * 200 g

    Weight of Sample = 160g

Water has a density of one gram per milliliter.


Thermal Capacity = Weight of Sample * Specific Heat

Thermal Capacity = 1.5 cal/g/degC * 160g

Thermal Capacity = 240 cal/degC

It is reassuring to see that the final result has the correct units to be a thermal capacity - an amount of energy per unit of temperature!

b) The thermal capacity we just calculated is the energy required to raise this samples temperature by one degree celcius. Now, we want to go from 22 to 37 degC, so we need to multiply the thermal capacity by 15 degC to get the number of calories required.

Energy = Thermal Capacity * Temperature Change

Energy = 240 cal/degC * 15 degC

Energy = 3600 cal

/ul] Again, we are reassured by the fact that the units work out correctly.

In fact, it should be noted that this entire problem can be done with very little physics knowledge - pure application of dimensional analysis to the quantities given and wanted (and their units) can quickly solve this problem!


definition: A symmetry that can be applied to elementary particles so as to include both bosons and fermions. In the simplest supersymmetry theories, every boson has a corresponding fermion partner and every fermion has a corresponding boson partner. The boson partners of existing fermions have names formed by adding 's' to the beginning of the name of the fermion, e.g. selectron, squark, and slepton. The fermion partners of existing bosons have names formed by replacing '-on' at the end of the boson's name by '-ino' or by adding '-ino', e.g. gluino, photino, wino and zino. The infinities that cause problems in relativistic quantum field theories are less severe in supersymmetry theories because infinities of bosons and fermions cancel one another out. If supersymmetry is relevant to observed elementary particles, then it must be a broken symmetry, although there is no convincing evidence at present to show at what energy it would be broken. There ism in fact, no experimental evidence for the theory, although it is thought that it may form part of a unified theory of interactions. This would not necessarily by a unified-field theory; the idea of strings with supersymmetry may be the best approach to unifying the four fundamental interactions.

Friday, February 24, 2006

superstring theory

Definition: A unified theory of the fundamental interactions involving supersymmetry, in which the basic objects are one-dimensional superstrings. Superstrings are thought to have a length scale of about 10-35m and, since very short distances are associated with very high energies, they should have energy scales of about 1019 GeV, which is far beyond the energy of any accelerator that can be envisaged. Strings are only consistent as quantum theories in 10 (or more)-dimensional space-time. It is thought that four macroscopic dimensions arise according to Kaluza-Klein theory, with the remaining dimensions being 'curled up' to become very small. One of the most attractive features of the theory of superstrings is that it leads to spin 2 particles, which are identified as gravitons. Thus, a superstring theory automatically contains a quantum theory of the gravitational interaction. It is thought that superstrings are free of the infinities that cannot be removed by renormalisation, which plague attempts to construct a quantum field theory incorporating gravity. There is some evidence that superstring theory is free of infinities but not a complete proof yet. Although there is no direct evidence for superstrings, some features of superstrings are compatible with the experimental facts of elementary particles, such as the possibility of particles that do not respect parity, as found in weak interactions. Also Known As: string theory

The Physics of Superheroes by James Kakalios

Guide Rating -4/5

Teaching physics to undergraduates, James Kakalios encountered a problem almost every physics teacher has run afoul of: “When will this ever relate to my life?” students ask, referring to the typical pulley, rolling ball or inclined plane example. These examples have been the staples of physics education dating back to the oldest texts I have found – but, admittedly they are a little dry, especially if you are not a physics major.

"This Looks Like a Job for Comic-Book-Reading-Physicist!"

Fortunately for students at the University of Minnesota, mild mannered professor Kakalios has a secret identity – Comic book reading physicist! Well, it’s not that secret anymore, nor is it that unusual: I am not the only physics student at Harvard who waits for the new comics to arrive every Wednesday at my local comic store. However, there is a truly amazing aspect of James’ other identity – he realized that while students will complain about the relevance of the old saws to their lives, they will happily listen and calculate for hours the gravitational force on Krypton, based on Superman’s ability to leap tall buildings in a single bound! Kakalios has turned his “Everything I Know About Science I Learned From Reading Comic Books” freshman seminar into a book “The Physics of Superheroes” (published, appropriately, by Gotham Books) that covers much of the typical “College Physics” course with only a minimum of mathematics and examples pulled entirely from Superhero comic books. Kakalios surveys a wide range of physics at a level that is appropriate for any interested reader – a feat that stretches the talents of many popular physics books.

No equations more difficult than simple arithmetic!

Kakalios’ examples come from a number of comics, from both Marvel and DC, including Superman, the Flash and Spiderman. Standing out among Kakalios’ favorites is The Atom and Henry Pym/Ant Man/Giant/Yellow Jacket (his codename changes often) – two wonderful choices: characters who are both heroes and physicists. Kakalios also spices up the education with a short history of the comics industry and details of the histories of the characters he draws upon. In his introduction, Kakalios explains basic algebra as a simple extension of arithmetic, and promises not to go beyond that level of difficulty. In the only 19 equations he prints, he almost keeps to his promise – including the Schrödinger equation introduces some calculus, but he never uses the calculus, so there need by no fear of the partial differentials involved the central equation of quantum mechanics

"It's a physics text-book that will be interesting! No, but it is a good book!"

While he never claims to have written a physics text – much as I would love to be able to teach a course based upon a text full of comic book references - in his quest to keep the level of book accessible and to avoid any principles he cannot explain with comic book references, Kakalios neglects a number of central principles of the college physics course and skimps on the details a real text would have. However, he does cover a number of interesting topics that are neglected in courses like this. Standing out amongst these is the modern physics section, with chapters on Atomic Physics (explained in reference to Dr Doom and the Fantastic Four’s journeys to microscopic worlds within atoms), Quantum Mechanics (What The Atom should see when he shrinks to the size of an electron and the “Many Worlds” idea meets the “Crisis on Infinite Earths”), Tunneling (Kitty Pryde passing through walls) and solid state physics (Iron Man’s transistor powered super armor).

Attack of the imperial forces (and imperial lengths and imperial units of energy)!

A shortcoming of Kakalios’s work is his insistence on using imperial units in his calculations – despite constant references to kilograms and meters as he sets up basic mechanics, he switches to feet and pounds when he starts talking about actual weights and lengths. This is probably a change made purely to please the average American reader. I cannot imagine that his university level course could use non-metric units, and I found their intrusion into the books is very distracting. This book has many good qualities – the explanations are generally clear and the examples are imaginative. I look forward to the chance I can base a tutorial session on calculating the strength of Spiderman’s webbing or the number of cheeseburgers the Flash needs to consume to fuel his high speed running. For a trained physicist and comics fan, the book is a quick read, but very entertaining.


Definition: A one-dimensional object used in theories of elementary particles and in cosmology (cosmic string). String theory replaces the idea of a point like elementary particle (used in quantum field theory) by a line or loop (closed string). States of a particle may be produced by standing waves along this string. The combination of string theory with supersymmetry leads to superstring theory. String theory is a candidate for a theory of quantum gravity.

Also Known As: superstring


Definition: A streamline is a fictitious curve in a fluid flow such that the velocity vector of the fluid is tangential to the streamline. In a two dimensional flow, the streamline can be determined in terms of the streamfunction as lines of constant Ψ.


Definition: The stream function ψ for a two dimensional flow is defined such that the flow velocity can be expressed as:
    u = -∂ψ/∂y

    v = ∂ψ/∂x

where the velocity in Cartesian coordinates is given by (u,v).

Alternate Spellings: stream function

streak line

Definition: is a line formed at some instant by a series of fluid particles that have all passed through a common point during their history. Experimentally, this is arranged by having a dye or smoke released into the flow from a point into the flow over time. The streaklines and streamlines of a flow are only identical for a steady state flow.

STP - Standard Temperature and Pressure

Definition: Standard temperature and pressure. The standard conditions used as a basis for calculations involving quantities that vary with temperature and pressure. These conditions are used when comparing the properties of gases. They are 273.15 K (or 0°C) and 101325 Pa (or 760 mmHg).

Scanning Tunneling Microscope - STM

Definition: A type of microscope in which a fine conducting probe is held close to the surface of a sample. Electrons tunnel between the sample and the probe, producing an electrical signal. The probe is slowly moved across the surface and raised and lowered so as to keep the signal constant. A profile of the surface is produced, and a computer-generated contour map of the surface is produced. The technique is capable of resolving individual atoms, but works better with conducting materials.

Special Relativity

from Stewart Walker

Verse 1

In 1905 some of Newton's jive got up Einstein's nose

He said you can't explain from a classical frame what the world already knows

That the ether idea ain’t hip, it simply doesn't fit

With reality so it's plain to see, we need special relativity


Special relativity dilates my time and blows my mind

Special relativity oh it's easy to see m c squared equals e

Special relativity will increase your mass if you go too fast

Special relativity

Repeat intro

Verse 2

Try as you might the speed of light is as fast you can go

And I'll tell you again there is no preferred frame, ‘cos Einstein tells me so

And if you don't believe it's true, just accept it all like I do

‘Cos in reality it's plain to see, no-one understands relativity

Repeat chorus


And if you need experimental proof

Look at the muons coming down through the roof

Their decay slows down as they approach the ground

Just like Einstein said it would, ain't that good? Yeah good

Repeat chorus Copyright © 1983 Stewart Walker. All rights reserved

Stefan's Law

Definition: The total energy radiated per unit surface area of a black body in unit time is proportional to the fourth power of its thermodynamic temperature. The constant of proportionality, the Stefan-Boltzmann constant has the value 5.6697*10-8 J s-1 m-2 K-4. The law was discovered by the Austrian physicist Joseph Stefan (1853-93) and theoretically derived by Ludwig Boltzmann.

steam point

Definition: The temperature at which the maximum vapour pressure of water is equal to the standard atmospheric pressure (101325 Pa). On the Celcius scale it has the value 100°C.

statistical mechanics

Definition: The branch of physics in which statistical methods are applied to the microscopic constituents of a system in order to predict its macroscopic properties. The earliest application of this method was Boltzmann's attempt to explain the thermodynamic properties of gases on the basis of the statistical properties of large assemblies of molecules. In classical statistical mechanics, each particle is regarded as occupying a point in phase space, i.e. to have an exact position and momentum at any particular instant. The probability that this point will occupy any small volume of phase space is taken to be proportional to the volume. The Maxwell-Boltzmann law gives the most probable distribution of the particles in phase space. With the advent of quantum theory, the exactness of these premises was disturbed (by the Heisenberg uncertainty principle). In the quantum statistics that evolved as a result, the phase space is divided into cells, each having a volume hf, where h is the Planck constant and f is the number of degrees of freedom of the particles. This new concept led to Bose-Einstein statistics, and for particles obeying the Pauli exclusion principle, to Fermi-Dirac statistics.


Definition: Symbol s. The part of the total angular momentum of a particle, atom, nucleus, etc. that is distinct from its orbital angular momentum. A molecule, atom or nucleus in a specified energy level, or a particular elementary particle, has a particular spin, just as it has a particular charge or mass. According to quantum theory, this is quantised and is restricted to multiples of h/2π, where h is Planck's constant. Spin is characterised by a quantum number s. For example, for an electron, s=+/-½, implying a spin of +h/4π when it is spinning in one direction and -h/4 when it is spinning in the other. Because of their spin, particles also have their own intrinsic magnetic moments and in a magnetic field the spin of the particles lines up at an angle to the direction of the field, precessing around this direction.

Also Known As: spin angular momentum

Special Relativity

by Joey Stew

In 1905 some of Newton's jive got up Einstein's nose

He said you can't explain from a classical frame what the world already knows

That the ether idea ain’t hip, it simply doesn't fit

With reality so it's plain to see, we need special relativity

In the 1980s, Stewart Walker was a physics student at the University of Melbourne in Australia. Like every other physics student, Stewart had to get his head around the strange concepts of special relativity:

Special relativity dilates my time and blows my mind

Special relativity oh it's easy to see m c squared equals e

Special relativity will increase your mass if you go too fast

Special relativity

Time dilation – the effect that makes moving clocks slow down, the equivalence of mass and energy and the relativistic increase in the mass of moving bodies were just a few of the strange ideas contained in Einstein’s theory that Stewart (and I, and all our colleagues) had to try to understand.

But, rather than just memorizing the formulae and hoping to be able to reproduce the theorems on the exam like many of us, Stewart incorporated his interest in music into his studies and wrote a song called "Special Relativity" that combines some basic concepts of Special Relativity with a healthy dose of comedy and a catchy rhythm and guitar tune.

Try as you might the speed of light is as fast you can go

And I'll tell you again there is no preferred frame, ‘cos Einstein tells me so

And if you don't believe it's true, just accept it all like I do

‘Cos in reality it's plain to see, no-one understands relativity

Stewart went on to other things, forming a folk rock duo with Joey Hassall called Joey Stew. They play regular gigs around Melbourne and recently recorded an EP entitled "Girls, Cars, Beer… and Special Relativity" which includes the Special Relativity song, in time to coincide with 2005, the International Einstein Year. The EP (and individual songs) is available for downloading from joeystew.com, which also has mp3 samples of their songs.

Special Relativity is a great song that deserves to be more widely heard. Stewart’s lyrics cover many of the important points of special relativity with both comedy and physical understanding, making it a useful addition to a classroom presentation on special relativity, or a party full of physicists.

Hear a Sample of Special Relativity (128kbs mp3)

space time

Definition: A geometry that includes the three dimensions and a fourth dimension of time. In Newtonian physics, space and time are considered as separate entities and whether or not events are simultaneous is a matter that is regarded as obvious to any competent observer. In Einstein's concept of the physical universe, based on a system of geometry devised by H. Minkowski, space and time are regarded as entwined, so that two observers in relative motion could disagree regarding the simultaneity of distant events. In Minkowski's geometry, an event is identified by a world point in a four-dimensional continuum.

1927 Solvay Conference Film - Footage of the Giants of Quantum Theory

Video Rating - rating

One of the most famous photos in the history of physics captures the illustrious participants at the fifth Solvay Conference in Brussels, October 1927. 29 physicists, the main quantum theorists of the day, came together, 17 of the 29 attendees were or became Nobel Prize winners. This is a home movie shot by Irving Langmuir, (1932 Nobel Prize winner). Twenty-one of the 29 attendees are on the film. The film includes shots of Erwin Schrödinger, Albert Einstein, Marie Curie, Dirac and Niels Bohr.

Available Formats:

  • Real
  • Flash


Definition: A state of matter in which there is a three-dimensional regularity of structure, resulting from the proximity of component atoms, ions, or molecules and the strength of the forces between them. Solids can be crystalline or amorphous. If a crystalline solid is heated, the kinetic energy of the components increases. At a specific temperature, called the melting point, the forces between the components becomes unable to contain them within the crystal structure. At this temperature, the lattice breaks down and the solid becomes a liquid.

S-Matrix Theory

Definition: A theory introduced by Werner Heisenberg in 1943 and developed extensively in the 1950s and 1960s to describe strong interactions in terms of their scattering properties. S-matrix theory uses general properties, such as causality in quantum mechanics and the special theory of relativity. The discovery of quantum chromodynamics as the fundamental theory of strong interactions limited the use of S-matrix theory to a convenient way of deriving general results for scattering in quantum field theories. String theory, as a theory for hadrons, originated in attempts to provide a more fundamental basis for S-matrix theory.

Abandoning attempts to sum all the terms in the strong force expansion, they chose to limit themselves to talking about quantities that could be experimentally measured - probabilities of transitions from an incoming set of quantum states to an outgoing one. The work of field theorists like Chew and Gell-Mann showed that the S-Matrix was a relatively straightforward function of the relevant variables and amenable to various mathematical techniques. This made it possible for S-Matrix research to be conducted without reference to the quantum field theories that it had developed from. Chew proposed the bootstrap philosophy: if the S-Matrix was really an infinite set of coupled equations that determined everything about the hadrons, then it had to have a unique solution, even if it couldn't be calculated exactly.

asic Tools for Physics: Simultaneous Equations

If Ax + By = C and Dx + Ey = F, then what are x and y?

Often in physics (and algebra generally), we find that an equation contains multiple unknowns "x and y (and maybe z and others)" – these problems cannot be solved based on what we’ve talked about so far.

For example:

One day, I bought 3 gallons of milk and two cartons of eggs and it all cost me 7 dollars. The next day I bought 2 gallons of milk and 5 cartons of eggs and this time I spent 12 dollars – how much are milk and eggs individually?

So, we could attempt this with trial and error – and if you’re lucky, you’ll quickly find that milk is one dollar per gallon and eggs are 2 dollars per carton. But, in general problems the trial and error approach can take an impossibly long time! In order for us to learn from this example, let’s try to solve it in a way that is general and can be applied to more difficult problems.

So, in a way you will by now be familiar with, let’s rewrite this problem in algebra fashion:

    3 * $priceofmilk + 2 * $priceofeggs = $7 (1)

    2 * $priceofmilk + 5 * $priceofeggs = $12 (2)

As you can see, this problem gives us two equations to deal with – which is good, because you always need as many equations as you have unknowns.

Now, we spent a long time working out ways to solve equations with only one unknown – do we have to throw them away for simultaneous equations? No – we just need to find a way to turn these equations into equations with only one unknown so that we can make progress with this problem

For now, lets look at equation (1) and pretend that $priceofeggs is just a constant – something we might have called B in earlier problems. Then, we can "solve" this equation for $priceofmilk:

    3 * $priceofmilk + 2 * $priceofeggs = $7 (1)

    3 * $priceofmilk = $7 - 2 * $priceofeggs

    $priceofmilk = $(7/3) - (2/3) * $priceofeggs (3)

Now we have an "answer" for $priceofmilk - but it still depends on $priceofeggs, so we haven’t really found the answer to our question. But, we can use this relationship to find the price of eggs! If we perform this algebra essentially in reverse, by putting this "answer" for $priceofmilk (called equation 3) into the other equation (Equation 2), we see that we now really have an equation with only one unknown - $priceofeggs!

    2 * $priceofmilk + 5 * $priceofeggs = $12 (2)

    2 * ($(7/3) - (2/3) * $priceofeggs) + 5 * $priceofeggs = $12

    $(14/3) – 4/3 * $priceofeggs + 5 * priceofeggs = $12

On rearranging this equation, we see that:
    (5-4/3) * $priceofeggs = $12 - $14/3

    11/3 * $priceofeggs = $22/3

    $priceofeggs = $2

Now that we have a value for the price of eggs, we can take this value back to equation 3 and find the price of milk:

    $priceofmilk = $(7/3) - (2/3) * $priceofeggs (3)

    $priceofmilk = $(7/3) - (2/3) * $2

    $priceofmilk = $1

Thus we have solved for the prices of milk and eggs

This process works for any general problem:

    Ax + By = C

    Dx + Ey = F

If we take the first equation and rearrange it to give y as a function of x, we get:
    y = (1/B) * (C – Ax)
Now, we can take this "value" for y and put it into our second equation:
    Dx + (E/B)*(C-Ax) = F

    (D-EA/B)x = F-EC/B

    x = (F-EC/B)/(D-EA/B)

Now, we can take this expression for x and put it back into our expression for y, we get:
    y = (1/B)* (C-A*(F-EC/B)/(D-EA/B))
So, we can generalize how to solve these equations:

1) Take one equation and rearrange it to give one variable in terms of the other.

2) Substitute this expression into the other equation – this gives you an equation with a single unknown.

3) Solve this equation in the fashion we learned earlier.

4) Take the solution for this variable and substitute it into the rearrangement we found in step one – this will then give you the value for the other variable.

Significant Figures

Representing Prescision in Physics

Whenever we measure some value (like a length), we can only find it to a finite accuracy (perhaps a millimeter on a typical ruler). We need to acknowledge the limited accuracy of our numbers, by considering how many digits are "significant". These "Significant Figures" allow us to represent the prescision of our measurements and results calculated from the in an umambigous fashion.

If we tried to measure the distance from home to school with a meter long stick, it would not be possible to say, reliably, that the distance was 343.643m. You could say 344m or maybe even 343.5m but trying to imply that you can accurately judge tenths of millimeters on an unmarked meter long stick is dishonest.

In this case we would say that there are four significant figures (in 343.5m) These are the parts of the value that are reasonably reliable. Not necessarily 100% rock solid as there is rounding off and the possibility of other errors, but reasonably reliable. The final two digits of 343.643m are completely unreliable and should be ignored.

Typically, you can assume that (given no other information) any number given is accurate to within plus or minus one in the smallest place written out. Eg: 406 means a number somewhere between 405 and 407, 1.11 means 1.10 to 1.12 etc.

Rules for Significant Figures:

    1) Counting from the left and ignoring all the leading zeros, keep only the digits up to the first doubtful one. As written. 22.568 has five significant figures and 7002 has four, but 0.0072 has only two, the zeros in this case are merely place holders and don’t really describe any part of the number.

    It is not always clear, in traditional notation, how many significant figures some numbers have. For example, 80km might have two (if the distance was known to be between 79 and 81) or only one (if the distance was known to be between 70 and 90km) with the zero acting as a placeholder. In these cases, the use of scientific notation allows us to remove the ambiguity: the distinction between 8x101km and 8.0x101km is clear. Conversely, if we knew the distance was somewhere between 79.9km and 80.1km, we would be well justified in using three significant figures, writing the distance as 80.0km.

    2) When multiplying or dividing, you should only keep as many significant figures as in the least precise of the numbers used in the calculation. (Only go to significant figures as a final step – rounding off in intermediate steps can introduce errors in your calculations.) For example, say we want the product of 11.3 and 6.8

      11.3 x 6.8 = 76.84.

    But, if we look at the extremes possible
      11.2 x 6.7 = 75.04

      11.4 x 6.9 = 78.66

    So, the range of possible answers spanned by the possible values of the input, belies the four significant figures given in our answer above. However, if we round off to two significant figures, our answer becomes 77, which is within one or two units of our possible answers.

    Notice that if we had rounded the 11.3 off to two significant figures before we started, we would have ended up with 11 x 6.8 = 75, an incorrect answer!

    3) When adding or subtracting, the least significant digit of the answer occupies the same position as the least significant digit in the least precise number used in the calculation.

    For example: 2.3 + 3.145 = 3.4, not 3.445.

Significant Figures and Scientific Notation

Why use scientific notation for small numbers like 8800?

How many significant figures do each of the following numbers have?

a) 2143

Four significant figures

b) 82.60

Four significant figures. The final zero in this number is not just a place holder, it is a part of the number.

c) 7.63

Three significant figures.

d) 0.03

One significant figure. The zeros in this number are merely placeholders. The number is better represented as 3x10-2.

e) 0.0085

Two significant figures.

f) 3336

Four significant figures.

g) 8800

This number is unclear. It might have two or four significant figures, depending on whether the zeros are a “real” part of the number or simply placeholders. If the number is only approximately 8800 (with the exact tens and units figures unknown), the number is properly written as 88x102 and has two significant figures. If, however, the number is known to be 8800 with uncertainty only in the tenths and smaller parts, then the number is correctly written and has four significant figures.

It is unfortunate that “normal” notation gives no way to distinguish between the two and four significant figure version of this number – a good reason to stick to scientific notation, which removes the ambiguity in these cases, even though 8800 is not so large that scientific notation is required to write it without a large string of zeros.

shearing force

Definition: A force that acts parallel to a plane rather than perpendicularly, as with tensile or compressive force. A shear stress requires a combination of four forces acting over (most simply) four sides of a plane and produces two equal and opposite couples. It is measured as the ratio of one shearing force to the area over which it acts. The shear strain is the angular deformation in circular measure. The shear modulus is the ratio of the shear stress to the shear strain. Also Known As: shear

Gamma radiation dose from radioactive cobalt

Radiation Energy Transfer and Dose

5727Co emits 122 keV gamma-rays. If a 70kg person swallowed a 4 micro Curie sample of this, what would the dose rate (rads/day) averaged over the whole body. Assume that 50% of the gamma ray energy is absorbed by the body.

4 micro Ci is equivalent to 4.0x106*3.7x1010 = 148000 disintegrations per second.

This is equivalent to 148000*122keV*1.6x10-19 J/s = 1.4x10-9 J/s released into the body, which absorbs half of this:

7x10-10 J/s

0.000062 J/day

9x10^-7 J/kg/day

9x10^-5 rad/day

How many fissions per second occur in a 200MW Uranium reactor?

Nuclear Energy Release.

How many fissions per second occur in a 200MW Uranium reactor? Assume 200MeV are released per fission.

200MW is equivalent to 200x106 Joules/second

200x106 J/s is equivalent to

200x106 J/s / (200x106 eV/fission * 1.6x10-19 J/eV)

= 6.25x1018 fissions/second

Understanding and Using the Scientific Method

Finding the Answers
The scientific method is a process that scientists developed to form and answer questions. The scientific method arose mostly in the 17th and 18th centuries. This was a period of great scientific revolution in England and Europe, the era of Copernicus, Kepler, Galileo, Hooke, Leibniz, Halley, Newton and Young.

We (scientists and science students) spend a lot of time making observations about the world around us, conceiving and running experiments, making guesses and finding creative solutions to problems and mysteries. The scientific method is an important procedure we follow to work through these questions and guesses and arrive at the truth (or, at least, as close to the truth as we can get).

There are six basic steps to the scientific method:

1)Ask a question.

2)Research the topic – it is important to understand as much as you can about what people already know about your question, so you will know which direction to head in.

3)Form an hypothesis – a personal opinion about what the answer to your question will be, based upon all the research you have done and your physical intuition about how the world works.

4)Test the hypothesis with an experiment.

5)Draw conclusions about the validity of your hypothesis based upon the results of your experiment.

6)If you are performing ongoing research, then you can use your conclusions to formulate further questions, starting the cycle over again.

For the past three hundred years, physicists have used the scientific method to make innumerable discoveries: the Copernican model of the solar system; Newton's laws of motion; Thermodynamics; Electromagnetism; Quantum Mechanics; and Relativity and Statistical Mechanics. We are continuing to apply this powerful tool to the unresolved questions – from String Theory to Weather Prediction.

How To Create a Great (Physics) Science Fair Project (and Learn Something at the Same Time)

To do well in a science fair, you need to do two things – You need to not only demonstrate knowledge of science, but also knowledge of the process of science. While this can be a daunting task if you've never produced a successful science fair project before, you should rest easily – it is really not that difficult, especially if you follow a system that will help you cover all your bases and makes sure that you learn everything you need to learn.

Time Required: Over Night to Eight Weeks (or More)

Here's How:

1. Understand the Scientific Method The scientific method is a process that scientists developed to form and answer questions. In order to truly do science for your project, you need to understand how we do science – and to do that, you need to understand the scientific method.

2. Buy a notebook: Easy, but very, very important. From this moment on, this notebook is your "Project Log" where you will keep track of everything to do with your project (and only you project).

3. Write Down all the Questions You Have. This is not as easy as it sounds. Ask every question you need to know the answer to. Don't be embarrassed, if you need an answer, you're probably not the only one who doesn't know.

4. Create a Schedule That Will Get Everything Done in Time, That You Can Stick To. Get a calendar and mark off the date of the fair (or when your project is due). Spread out the tasks you need to complete over the time you have. Don't wait to the last month, week or day(!) to try to do everything. Science Fair Project Schedule Checklist

5. Choose a Topic. This seems hard, and it is important, but don't get too worked up about it: most people get stuck for a little while on this step.

6. Fine-tune Your Topic. You need to turn your topic into a question that can be answered. If you can't get to a question right now, do some more research (that is step seven, but its ok to mix these two steps up a bit).

7. Research Your Topic. As discussed in the scientific method, we need to find out as much as we can about our topic. This will ensure that you will have a deep understanding of your topic, as well as helping you to develop a question that will work for your project. This will make the rest of your project easier.

8. Develop Your Hypothesis - an educated (you did educate yourself with allthat research, right?) guess about the answer to your question.

9. Design Your Experiment to test your hypothesis.

10. Conduct Your Experiment. Gather all the equiptment you need and follow the steps of the experiment you designed.

11. Analyse the Data and Draw Conclusions. Once you have your data, make any calculations you need for the analysis, produce graphs and charts as required to visualize the data. Then, determine whether your data supports your hypothesis.

12. Write Up Your Project Report. This is a written record of your project. Use the detailed notes you took during each step (you did take them, didn't you?) to help you here.

13. Put Together Your Display. Check with the rules of your science fair (or the directions from your teacher) to make sure your display is correct.

14. Collect your ribbon - or at least enjoy the fair


  1. There are many common misconceptions about what is needed for a great science fair project. It is not about how much money you can spend and it is not about whether you are a geek or not. It is about whether you can put together a project that shows you understand science and the process of doing science. What you Do and Do Not Need for a Great Science Fair Project

What You Do and Do Not Need for a Great Science Fair Project

Do I need to be a rich geek to win the fair?: There are many common misconceptions about what is needed for a great science fair project. It is not about how much money you can spend and it is not about whether you are a geek or not. It is about whether you can put together a project that shows you understand science and the process of doing science.

Things you do not need for a great science fair project:
    A lab coat

    A lab

    An MRI or a Scanning Tunneling Microscope

    A cage full of mice

    40 textbooks

    Racks of beakers and test tubes, bubbling over rows of Bunsen burners

    A hunchbacked assistant with a limp and an Eastern European Accent

    An underground (or castle-based) lair

    Wild hair, a crazy laugh or lightning

The only thing you absolutely have to have is: Curiosity. Most people figure things out by doing. Whiles there is a lot to be learned from reading texts, doing homework and paying attention in class, to really understand the world around you, you need to investigate it yourself – and you need to want to.

Scientific Notation and Significant Figures

Write the following in scientific notation: 1105, 21.9, 0.0068, 0.006800, 17.635, 0.319, 33. Be aware of the significant figures.

a) 1105


b) 21.9


c) 0.0068


d) 0.006800


e) 17.635


f) 0.319


g) 33


Schrödinger's Cat

Definition: A thought experiment introduced by Erwin Schrödinger in 1935 to illustrate the paradox in quantum mechanics regarding the probability of finding, say, a subatomic particle at a specific point in space. According to Niels Bohr, the position of such a particle remains indeterminate until it has been observed. Schrödinger postulated a sealed vessel containing a live cat and a device triggered by a quantum event such as the radioactive decay of the nucleus. If the quantum event occurs, cyanide is released and the cat dies; if the event does not occur the cat lives. Schrödinger argued that Bohr's interpretation of events in quantum mechanics means that the cat could only be said to be alive or dead when the vessel has been opened and the situation inside it has been observed. This paradox has been extensively discussed since its introduction with many proposals made to resolve it. These paradoxes (Schrödinger's Cat and Wigner's Friend) are intended to indicate the absurdity of the overstated roles of measurement and observation in Bohr's interpretation of quantum mechanics.

Tuesday, February 21, 2006

Schrödinger Equation

Definition: An equation used in quantum mechanics for the wave function of a particle. It was devised by Erwin Schrödinger, who was mainly responsible for wave mechanics.

Also Known As: Schrodinger's Wave Equation, Schrodinger's Equation

Alternate Spellings: Schroedinger Equation, Schrödinger Equation

The Right Hand Rule

Determining the Direction of a Cross Product

The direction of the cross product between two vectors is perpendicular to the plane the two vectors lie in. However, there are two ways this vector could point – essentially “up” or “down.” Conventionally, the choice between these two directions is determined by the “right hand rule.”

There are several contortions of your right hand that will tell you the direction of the cross product. My favorite is not the most well known, but I feel it is the easiest to remember. If you are calculating AxB, then you start with your hand open and flat, with your index finger parallel to A. Then, orient your wrist so that you can curl your fingers from the direction of A to that of B in the natural direction. Now, your thumb is pointing in the direction of the cross product.

The direction of the cross product differs depending on the order of the terms: AxB is not the same as BxA (in fact, these two cross products are negative multiples of each other).

As you can see, the unit vectors are all linked by cross products:

    i x j = k

    j x k = i

    k x i = j

This relationship can be more concisely written as:
    ea x eb=ec ε abc
where ea is as defined earlier and ε abc is equal to one when the numbers a b c are an “even permutation” of 1 2 3; negative one when the numbers a b c are an “odd permutation” of 1 2 3 and zero when a b c are not a permutation of 1 2 3 at all. This is often known as the “permutation tensor.” These relationships between the unit vectors are the definition of a Right Handed System. If you use the same relationships, but with the directions determined by your left hand in place of your right, you will have a :Left Handed System.

Reynolds' number

Definition: Symbol Re. A dimensionless number used in fluid dynamics to determine the type of flow through a pipe, to design prototypes from small-scale models, etc. It is defined as the ratio of the inertial and viscous forces.

    Re = ρDu

where D is a characteristic length (for example, a pipe diameter) , u is the characteristic velocity and μ is the viscosity. The Reynolds' number can be used to discriminate between laminar and turbulent flow, with Re <>3000.

Common Misspellings: Reynold's number

reversible process

Definition: Any process in which the variables that define the state of the system can be made to change in such a way that they pass through the same values in the reverse order when the process is reversed. It is also a condition of a reversible process that any exchanges of energy, work or matter with the surroundings should be reversed in direction and order when the process is reversed. Any process that does not comply with these conditions when it is reversed is said to be an irreversible process. All natural processes are irreversible, although some processes can be made to approach closely to a reversible process.

Resolving the Incompatibilities Between Special Relativity and Newtonian Gravity

Inspiring the search for General Relativity
There are two manifest incompatibilities between Einstein’s special theory of relativity and Newton’s theory of Gravity.
1) In special relativity, nothing, not even information, can travel faster than c, the speed of light. If this was allowed, then it would be possible to violate causality, leading to effects preceding their causes. However, in Newtonian Gravity, the gravitational field propagates instantly. If we somehow wiggled the sun up and down, this effect would instantly appear in the gravitational field felt on Pluto. We could essentially send Morse Code messages to Pluto (or anywhere else in the universe) instantly by wiggling the sun up and down (actually, it wouldn’t need to be the sun – with sufficiently sensitive gravity detectors, a much smaller objects gravity would do just as well).
2) In Newtonian gravity, Fg=Gm1m2/|x1-x2|2, which retains its form under a Galilean Transformation. However, in special relativity, the Galilean transform is not a true symmetry of space-time. Instead, we have the Lorentz Transform.
Space-time coordinates are now represented as a four dimensional vector:
x`=Mmunuxnu where Mmunu is the four by four Lorentz matrix that describes “boosts” (transforms into frames moving relative to the original frame, which mix the space and time coordinates) and rotations. Maxwell’s equations of Electromagnetism are invariant under the Lorentz Transform, but not under the Galilean Transform. This fact was part of the evidence that lead Einstein to Special Relativity.
But Newton’s law of gravity is simply incompatible with the Lorentz Transform.
Like every major breakthrough, general relativity came from the intellectual tension caused by the clash of incompatible theories, in this case Special Relativity and Newtonian Gravity. These events closely follow Kuhn’s theories of a paradigm shift.

Motion is Relative

Frames of Reference

How fast is your chair moving? Compared to you, when you’re sitting in it, it had better be stationary, or you’ll end up on the floor pretty quickly! But, even if your chair is sitting still relative to the room and to the ground outside, the Earth is rotating at a great speed (almost 1700km/hr at the equator) and the Earth is orbiting the sun at about 28 km/second (that’s over one hundred thousand km/hr)!

And the sun is moving around the center of the galaxy!

And the galaxies are all moving too!

Velocity is only sensibly defined when it is relative to something – generically, this thing is referred to as a “reference frame”.

For example, in the frame of the room, your chair is stationary, but in the frame of the sun, it is moving at about 28km/second.

Relative Uncertainty

Length and Volume

What is the relative uncertainty in the following:

a) 3.26+.25m

b) The volume of a sphere with a radius r=2.86 +/- 0.08 m

a) relative uncertainty: 0.25/3.26 = 0.077 = 7.7%

b) V=4/3 pi r3

DeltaV/V=4/3 3 (Delta r) pi *r2/(4/3 pi r3)
= 3 Delta r/r

= 8.4%

Divers with Flashlights

Refraction and Snell's Law

A diver shines a flashlight upwards from beneath the water at a 42.5 degree angle to the vertical. At what angle does the beam of light leave the water?

Snell’s law:


    sin(?r)=nwater sin(?i)

    ?r=1.3 sin(?i)


Rankine Cycle

Definition: A cycle of operations in a heat engine. The Rankine cycle more closely approximates to the cycle of a real steam engine than does the Carnot cycle. It therefore predicts a lower ideal thermal efficiency than the Carnot cycle. In the Rankine cycle, heat is added at constant pressure p1, at which water is converted in a boiler to superheated steam; the steam expands at constant entropy to a pressure p2 in a condenser; the water so formed is compressed at constant entropy to pressure p1 by a feed pump. The cycle was devised by the Scottish engineer W. J. M. Rankine (1820-70).

radio frequency

Definition: The range of frequencies, between about 3 kHz and 300 GHz, over which the electromagnetic spectrum is used in radio transmission. It is subdivided into eight equal bands, known as very low frequency (VLF), low frequency (LF), medium frequency (MF), high frequency (HF), very high frequency (VHF), and extremely high frequency (EHF).


Definition: The study of the radio-frequency radiation emitted by celestial bodies. This branch of astronomy began in 1932 when a US engineer, Karl Jansky (1905-40), first detected radio waves from outside the earth's atmosphere.


Definition: The spontaneous disintegration of certain atomic nuclei accompanied by the emission of alpha-particle (helium nuclei), beta-particles (electrons or positrons), or gamma radiation (short-wavelength electromagnetic waves).

radioactive series

Definition: A series of radioactive nuclides in which each member of the series is formed by the decay of the nuclide before it. The series ends with a stable nuclide. Three radioactive series occur naturally, those headed by thorium-232 (thorium series), uranium-235 (actinium series), and uranium-238 (uranium series). All three series end with an isotope of lead. The neptunium series starts with the artificial isotope plutonium-241, which decays to neptunium-237, and ends with bismuth-209. Also Known As: radio decay series

radioactive equilibrium

Definition: The equilibrium reached by a radioactive series in which the rate of decay of each nuclide is equal to its rate of production. It follows that all rates of decay of the different nuclides within the sample are equal when radioactive equilibrium is achieved. For example, in the uranium series, uranium-238 decays to throium-234. Initially, the rate of production of thorium will exceed the rate at which it is decaying and the thorium content of the sample will rise. As the amount of thorium increases, its activity increases; eventually a situation is reached in which the rate of production of thorium is equal to its rate of decay. The proportion of thorium in the sample will then remain constant. Thorium decays to produce protactinium-234; some time after the stabilisation of the thorium content, the protactinium content will also stabilise. When the whole radioactive series attains stabilisation, the sample is said to be in radioactive equilibrium.

radioactive dating

Definition: The age of an archaeological or geological specimen as determined by a process that depends on a radioactive decay. Techniques include carbon dating, fission-track dating, potassium-argon dating, rubidium-strontium dating and uranium-lead dating.

Pear-shaped particles probe big-bang mystery

"A University of Sussex-led team of scientists is ahead in the race to solve one of the biggest mysteries of our physical world: why the Universe contains the matter that we’re made of.In a paper submitted to Physical Review Letters, the team has just announced the results of a ten-year project to make one of the most sensitive measurements ever of sub-atomic particles. Theories attempting to explain the creation of matter in the aftermath of the Big Bang now have to be tuned up - or thrown out."

Read more at www.innovations-report....

Physics News Update: AIP 75th Anniversary, Electron Microscope Imaging, High Pressure Molecules

PHYSICS NEWS UPDATE                                                      
The American Institute of Physics Bulletin of Physics News
Number 766 February 21, 2006 by Phillip F. Schewe, Ben Stein, and
Davide Castelvecchi

anniversary this year. AIP was established in New York City in 1931
to help facilitate publishing and other services for five scientific
organizations: the American Physical Society (APS), the Optical
Society of America (OSA), the Acoustical Society of America (ASA),
the Society of Rheology (SOR), and the American Association of
Physics Teachers (AAPT). Later five more Member Societies were
added: the American Crystallographic Association (ACA), the American
Astronomical Society (AAS), the American Association of Physicists
in Medicine (AAPM), AVS: Science & Technology of Materials,
Interfaces, and Processing, and the American Geophysical Union
(AGU). Today, AIP is one of the largest physics journal publishers
in the world, and the non-overlapping membership of its 10 member
societies numbers more than 100,000 (general AIP website:
http://www.aip.org/index.html ). Physics News Update, the weekly
summary of physics research you are reading at this moment, is
prepared the AIP Media and Government Relations (MGR) division,
operating out of AIP's headquarters in College Park, MD, just
outside Washington, DC (associated websites are www.aip.org/pnu and
www.aip.org/news/links.html ). To mark AIP's 75th anniversary, we
plan to run a series of occasional comparisons between noteworthy
physics topics from 1931 and 2006. Herewith the first of these:

Germany have taken a crucial step towards achieving sharper images
of biological samples and other "weak-contrast" objects. Typically
microscope images of samples made of low-weight elements like
hydrogen, carbon, nitrogen, and oxygen, are characterized by poor
contrast. In the new approach, contrast will be improved for a
transmission electron microscope (TEM) by imposing a large relative
phase shift to the electron waves scattered from samples. The use
of a beam of electrons as an illumination source for microscopy was
pioneered in the early 1930s by Ernst Ruska, who won a Nobel Prize
for the effort half a century later. Since then, electron
microscopes have been a workhorse for imaging small things, often
with a spatial resolution superior to that available with light
microscopes. Nevertheless, even electron microscopes have
resolution problems. In a TEM device most of the electrons pass
through the thin electron-transparent sample without scattering.
Scattering of electron waves, when it does happen, occurs not
because of absorption---the amplitude of the electron beam is
largely undiminished---but through the shifting of the electron
phase. Scattered and unscattered waves are focused and recombine
downstream of the sample in a recording medium, typically a charged
coupled device (CCD).
Unfortunately, in weak phase objects the phase shifting is slight,
resulting in poor contrast. What scientists at the University of
Karlsruhe and the Max-Planck Institute for Biophysics in Frankfurt
have done to remedy this situation is to interpose a special
free-suspended micro-scaled electrostatic lens beyond the sample;
this electrostatic lens has the effect of shifting the phase of the
unscattered waves by a further 90 degrees but leaving the scattered
waves unshifted (see figure at http://www.aip.org/png/2006/249.htm
). This dramatically improves the contrast in the resultant
images. This electrostatic lens is called a Boersch phase plate in
honor of Hans Boersch, who proposed the technique in 1947. It has
not been achieved until now because of its demanding size
specifications. (Schultheiss et al., Review of Scientific
Instruments, March 2006; website,
http://www.lem.uni-karlsruhe.de/ )

MOLECULES GET MORE CLASSICAL at high pressures. That is, a new
study of molecules being squeezed in a diamond anvil cell shows that
as the pressure goes up, the force between atoms in a diatomic
molecule behaves more and more like the classic Hooke's law,
according to which the force between two objects connected by an
elastic spring is proportional to the contraction or extension of
the spring. Two scientists at the Carnegie Institution of
Washington, and Lawrence Livermore National Laboratory, Alexander
Goncharov and Jonathan Crowhurst, have loaded several species of
molecule, such as H2, D2, and N2, into their cell and then observed
what happened at high temperature and high pressure. By varying
these two parameters the molecular sample can often be transformed
from a fluid into a crystal or back again, or the molecules
themselves might even be broken apart. The researchers first heated the samples using a
near-infrared laser and then probed the various excited vibrational
quantum states using the technique of Raman spectroscopy. By
carefully noting the frequency and linewidths of these stretching
modes, they could deduce the energetics of the binding between the
atoms even as the molecule was being subject to the extreme
conditions. The findings, such as the realization that the binding
becomes more like a classical harmonic oscillator at high pressure,
should aid in such pursuits as the quest to observe metallic
hydrogen. (Physical Review Letters, 10 February 2006)

Monday, February 20, 2006

African-American achievers in modern science | csmonitor.com

"Meet scientists who work with invisible lights, nanomachines, and robots that sing songs.By Keely ParrackFebruary is Black History Month. In celebration of the contributions that African-Americans have made to science, we talked to three black scientists who are making history today with their groundbreaking work.

Hakeem Oluseyi, astrophysicistHakeem Oluseyi, astrophysicist and professor of physics at the University of Alabama in Huntsville, is currently researching the soft X-ray area of the sun's atmosphere. "This is one of the most difficult areas to work with because of the nature of this light and its interaction with matter," he explains. Soft X-ray light is extreme ultraviolet (EUV) light, part of the electromagnetic light spectrum that cannot be seen by the naked eye due to its short wavelength. Because it's at the extreme end of the light spectrum, it's very difficult to detect even with scientific instruments. Dr. Oluseyi has developed a special detector that he plans to send in a rocket to the sun. It will be able to send back new information about this region of the sun's atmosphere"

Read more at www.csmonitor.com/2006/...


Definition: fundamental constituent of hadrons. There are 6 varieties (or flavors), two in each of the mass generations:

Name (symbol) Charge

up (u) 2/3e

down (d) -1/3e

charm (c) 2/3e

strange (s) -1/3e

top (t) 2/3e

bottom (b) -1/3e

In order of increasing mass and e is the charge on an electron

Top and bottom quarks are also sometimes known as truth and beauty.

The name quark was coined by Murray Gell-Man, from a line in James Joyce's Finnegan's Wake: "Three quarks for Muster Mark". Although Joyce appears to have meant it to be pronounced as it is spelt, physicists (for reasons unknown) pronounce it to rhyme with fork.

Quarks carry color charge and interact through the color force of quantum chromodynamics.

Pronunciation: quork

quantum gravity

Definition: An aspect of quantum theory that attempts to incorporate the gravitational field as described by the general theory of relativity; no such theory has been accepted yet, however. Unlike the quantum field theories for the other three fundamental interactions, the procedure of renormalisation does not work for quantum gravity, although there is some evidence that superstring theory can provide a quantum gravity free of infinities. An approximation to quantum gravity is given by quantum field theory in curved space-time, in which the gravitational interactions are treated classically, while all other interactions are treated by quantum mechanics. An important aspect of quantum field theory in curved space-time is its description of the Hawking process. It is necessary to consider quantum gravity in the very early universe, just after the big bang, and the singularities associated with black holes can also be interpreted as requiring a quantum theory of gravity.

quantum field theory

Definition: A quantum mechanical theory applied to systems that have an infinite number of degrees of freedom. In quantum field theories, particles are represented by fields that have quantised normal modes of oscillation. For instance, quantum electrodynamics is a quantum field theory in which the photon is emitted or absorbed by particles; the photon is the quantum of the electromagnetic field. Relativistic quantum field theories are used to describe fundamental interactions between elementary particles. They predict the existence of antiparticles and also show the connection between spin and statistics that leads to the Pauli exclusion principle. In spite of their success, it is not clear whether a quantum field theory can give a completely unified description of all interactions (including the gravitational interaction).

quantum entanglement

Definition: A phenomenon in quantum mechanics in which set of (more than one)particles do not individually have a definite state but exist as an intermediate form of multiple “superposed” states. Each of these states describes each particle in a definite individual state. One of these states is realized when a 'measurement' is made on any one of the particles, placing all the other particles in the corresponding definite states, with out any measurements being directly carried out upon them! This effect (described by Einstein as "spooky action at a distance") was the subject of the "Einstein-Podolsky-Rosen Paradox" that was part of the reason that Albert Einstein did not particlarly like quantum mechanics - despite his role in creating it!


Definition: The minimum amount by which certain properties, such as energy or angular momentum, of a system can change. Such properties do not vary continuously but in integral multiples of the relevant quantum. This concept forms the basis of the quantum theory. In waves and fields, the quantum can be regarded as an excitation, giving a particle-like interpretation to the wave or field. Thus, the quantum of the electromagnetic field is the photon and the graviton is the quantum of the gravitational field.

Basic Tools for Physics: Quadratic Equations

If Ax2 + Bx + C = 0, then solve for x

One of the most common sorts of algebraic equations found in physics is the quadratic equation - one where the equation involves an "x squared" as well as (possibly) an x and some other constants.

The simplest quadratics to solve are ones like: x2 = A - there are said "to have no linear term" meaning that there is no term that is just "x." In these cases, the answer can be obviously found by applying our rule of "doing whatever we need to do to get the unknown by itself" In this case, simply taking the square root of both sides.

    x = sqrt(A).
There are, however, a couple of important points that need to be considered. Firstly, the sqaure root of A is not the only correct solution to this equation! Observe:
    (-1 * sqrt(A) )2 = (-1)2 * (sqrt(A))2 = 1 * A = A

Thus, the negative of the solution we originally found is also a solution! So, we need to write, for completeness, that x = +/- Sqrt(A). However, the situation in physics (as opposed to mathematics) is made simpler by the fact that we are usually trying to solve for some physical value that has to make sense. If, for example, we are trying to find the time a ball lands after being dropped at time t=0, a negative answer will make absolutely no sense - so we know that we only need the positive answer. If instead, we were looking at a ball that was thrown upwards and we observed that at t=0, it was momentarily at rest (at the top of it's flight) and we wnated to infer the time it was thrown upwards (a question that is solved with exactly the same equation as the previous one) we know that the time we want must be negative, so we take that solution.

Secondly, there is a further complication if A is not a positive number - for as we all know, the square root of a negative number is not a real number - it is an imaginary one! It is important to think about whether an imaginary solution makes any sense at all - in a problem like those above, getting imaginary times makes no sense - either we have made a mistake, or there are simply no times where what ever we were looking for happened - in this case we say that there are "no solutions" (as opposed to saying that there are "imaginary solutions" when such solutions make sense).

The more general quadratic equations – the ones involving an "x" term as well as an "x^2" term are slightly more complicated to solve. There are two main ways of solving these equations – factorizing or using the "quadratic formula."


All quadratic equations can be factorized into the product of two linear terms. For example:

    x2 + 3x +2 = (x+1)(x+2)
I’ll leave it as an exercise for you to check that this is correct.

Then, if we have the equation

    x2 + 3x +2 = 0
Then we can equivalently say that
    (x+1)(x+2) = 0
In this case, we can clearly see that if
    x = -1

then the equation becomes:

    (-1+1)(-1+2)=0 * 1 = 0
so x=-1 is a solution.

Similarly, it is clear that x=-2 is also a solution.

In general, if we have an equation of the form,

    Ax2 + Bx + C = 0

Then we can rewrite this as

    x2 + B/A x +C/A = 0

and then factorizing

    (x+D)(x+E) = 0

and x = -D and -E


    D+E = B/A
    D*E = C/A
Again, I will leave this as an exercise for you to check.

In all cases, it is possible to factorize the equation in this way. However, in many cases, the required D and E are difficult to find from simply looking at the equation (that is how I found the 1 and 2 in the numerical example above.

There are two cases where the factorization is especially easy – they are known as “difference of two squares” and “perfect square.”

The Difference of Two Squares

In this case, we have a quadratic equation that looks like
    x^2 - c = 0
In this case, as discussed above, x= +/- Sqrt(c)

We can also find this by factorizing the equation – we need to find two numbers that add to give zero and multiply to give c

It is clear that the only answer is:

    (x – sqrt(c))(x + sqrt(c))
which gives the answer we found earlier. Any quadratic that has no "x" term can be factorized this way.

The perfect square.

Consider the quadratic equation that is factorized to give


Multiplying this out, we get:

    x^2 + 2d + d^2 =0
So, anytime we have a function like this, where the constant term’s square root is exactly half the coefficient of the linear term, the quadratic equation is a perfect square and has a "double solution"

In many cases, the fact that this is a double solution (rather than a single solution) is usually unimportant – if you are trying to find a solution, then your situation is even easier – there is only one choice!

The Quadratic Formula.

Although every quadratic can be factorized (as long as you are ok with imaginary and complex solutions), it is generally hard to find the factorization by simple inspection of the equation. Fortunately, we have an expression that gives the solutions to any quadratic equation.

    If ax2 + bx + c = 0
    x= (-b +/- Sqrt(b^2-4ac))/2a

This expression gives the answer to any quadratic equation. It is important to consider the possible types of solutions.

There are three distinct possibilities, each based on the value of the discriminant: b2 – 4ac. This value can be positive, negative or zero, giving distinct types of solutions to the quadratic equation (assuming a, b and c are all real numbers).

1) Positive Discriminant: In this case, the square root gives a real value. Then the plus or minus in front of it gives you two distinct solutions to quadratic equations.

2) Zero Discriminant: In this case, we have only one solution. The equation is a perfect square.

3) Negative Discriminant: When we take the square root of a negative, we get imaginary solutions. This leads to a pair of solutions that have the same real part and imaginary parts of opposite sign – complex conjugate solutions.

quantum chromodynamics (QCD)

Definition: a gauge theory that describes the strong interaction between particles possessing color charge - quarks and gluons. In QCD, quarks and antiquarks interact by exchanging massless bosons called gluons.


Definition: An elementary particle that is stable, bears a positive charge equal in magnitude to that of the electron and has a mass of 1.672614*10-27 kg, which is 1836.12 times that of the electron. The proton occurs in all atomic nuclei. The number of protons in a nucleous determines which element it is (the atomic number). A proton is a Baryon.


Definition: The force acting normally on unit area of a surface or the ratio of force to area. It is measured in pascals in SI units.

Keeping a Project Notebook

A Useful Tool for Science Fair Projects and Physics Research

This book will be your "Project Log," where you will keep track of everything to do with your project (and only stuff for your project). The notebook serves two very important purposes:
    a) It allows anyone else who reads the notebook to see exactly what you did to recreate your project (if they had to). This is important as skill for any future career in science you might consider.

    b) The notebook also helps you prove that project is, in fact, your own work (should your teacher need convincing that you did not just copy an older relative or friend's project from a previous year).

In order to do this, your notebook should:
    1.Contain all your notes, thoughts and ideas.

    2.List the books and articles you read during your research – keeping track of the Titles, Authors, and possibly pages (check with your teacher about their preferred reference style)

    3.Develop your hypothesis (see “The Scientific Method”)

    4.Design your experiments

    5.Record your data and observations

    6.Analyze the data to find results and draw conclusions

    7.Draft your report

Everytime you write anything down about your project, make sure it is in your log, and note the date, time and anything else that seems important.

Hints for keeping a useful notebook

1. Keep the left margin clear, except for a few descriptive words. Write more detailed text to the right of the keywords. Some keywords you should use are:
    Research Summary – summarizing something relevant you've read.

    Questions to ask – Keep track of any questions you want to ask your teacher (or anyone else who can help you).

    Possible Topic – If your research sparks an idea about a topic you could focus upon, write it down so you don't forget.

    The Question – The same applies for your "question" once you've got a topic – write down your ideas, and annotate them in the margin so you can find them again.

    Experiment design - Sketch out your experimental design – in images and/or words, depending on the type of experiment you are going to do.

    Problem – describe a problem you have encountered – this may be a step on your experiment that isn't clear immediately.

    Proposed Solution – describe an idea for solving the problem.

    Success – describe how the proposed solution worked.

    Failed Attempt – describe how the proposed solution failed, and what you learned from the failure.

    Measurement – describe a measurement (e.g. of a spring constant) and how it was made.

    Predictive Calculation – describe a calculation that predicts something.

    Observations – keep track of what you see as you conduct your experiment.

    Data Analysis - crunching the numbers you observe to find out the answer to your question

The idea of these annotations is to keep the various things you write down for yourself easily accessible. For example, when you get up to choosing a question for your project, it will be easiest if you can flick through your notebook and find all the ideas you've had during your reading and topic fine tuning.

2. Leave time at the end of each period you work on your project for a summary.

    Briefly summarize the accomplishments of the session.

    list your goals for the next time you work on your project.

    clean up anything that needs to be cleaned up and put anything that you're keeping together somewhere safe – nothing is worse than having your project cleaned up by a well meaning parent.

3. If there is a digital camera available to you, you can photograph your apparatus at each stage of your work. Paste these photos in your lab notebook, with a caption describing what the image is of – this will help you keep track of what you're up to.


Definition: A collective excitation of quantised oscillations of the electrons in a metal (and the electromagnetic field near the surface ofthe metal in the case of surface plasmons).

Planck's radiation law

Definition: A law stated by Max Planck giving the distribution of energy radiated by a black body. It introduced into physics the novel concept of energy as a quantity that is radiated by a body in small discrete packets rather than as a continuous emission. These small packets became known as quanta and the law formed the basis of quantum theory.

Sunday, February 19, 2006


Definition: One millionth of a millionth of a second - 10-9 seconds.

The Physics of Santa

Can the Jolly Fat Man really exist?

This essay appears in many places on the internet, with no obvious author. I have modified it slightly to SI units and fixed a few terms that bugged the physics pedant within me.

1) There are 2 billion children in the world (persons under 18), but since Santa doesn't (appear) to handle Muslim, Hindu, Jewish, or Buddhist children, or even many christian groups, that reduces the workload by 85% of the total - leaving 378 million according to the Population Reference Bureau. Furthermore, since the introduction of the Gregorian Calendar, the orthodox religions and the catholic religions disagree on when December 25th happens, meaning Santa has two Christmas eves to distribute gifts over. Lets assume that the split is roughly even, meaning Santa has 189 million children to deal with each night.

2)At an average (census) rate of 3.5 children per household, that's 45.9 million homes. One presumes there is at least one good child per house.

3) Santa has 31 hours of Christmas to work with, thanks to the different times zones and the rotation of the earth, assuming he travels east to west (which seems logical). This works out to 411.3 visits per second. This is to say that for each Christian household with good children, Santa has 1/500 th of a second to park, hop out of the sleigh, jump down the chimney, fill the stocking, distribute the remaining presents under the tree, eat whatever snacks have been left, get back up the chimney, get back into the sleigh and move on to the next house. Assuming that each of these 45.9 million stops are evenly distributed around the earth (which, of course, we know to be false, but for the purposes of our calculations we will accept), we are now talking about 3km per household, a total trip of 120 million kilometers, not counting stops to do what most of us do at least once every 31 hours, plus feeding, etc. That means that Santa's sleigh is moving at 1040 miles per second, 3,000 times the speed of sound. For purposes of comparison, the fastest man-made objects - depp space probes like Voyager one travel at around 20 kilometers per second - a conventional reindeer can run, at top speed, 24 kilometers per hour.

4) The payload on the sleigh adds another interesting element. Assuming each child get nothing more than a medium-sized Lego set (1 kg), the sleigh is carrying 189 million kilograms, not counting Santa, who is invariably described as overweight. On land, conventional reindeer can pull no more than 150 kg. Even granting the "flying reindeer" can pull TEN TIMES that normal amount, we cannot do the job with eight, or even nine. We need 107,100 reindeer. As the typical January weight of a reindeer is about 60kg, this increases the payload - not even counting the weight of the sleigh to 195 million kilograms (not accounting for the fact that Santa's reindeer are probably better fed during winter than their wild counterparts. Again, for comparison, this is twice the weight of the Queen Elizabeth II.

5) Any object traveling at 1040 miles per second creates enormous air resistance. This will heat the reindeer up in the same fashion as spacecraft re-entering the earth's atmosphere. The lead pair will absorb 14.3 QUINTILLION joules of energy per second, each. In short, they will burst into flames almost instantaneously, exposing the reindeer behind them, and creating a deafening sonic boom in their wake. The entire reindeer team will be vaporized in 4.26 thousandths of a second. Santa meanwhile, will be subject to an average acceleration 8700 times greater than gravity as the sleigh speeds up and slows down between stops. A 120kg pound Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by an average force of 10 million newtons.

In conclusion, if Santa ever DID deliver presents of Christmas Eve, he's now dead. (This will be something you can tell your kids someday!)

Physics 101: Introduction to Physics

What is This Page?: Physics is, sadly, not well understood. Few people know what physics is, or what physicists actually do. I have put together this page to answer some of the most common questions about physics.

What is Physics?: Physics is the science of matter, energy and the interactions between the two. Read More About What Physics Is

Why do we Study Physics?: Physics is one of the cornerstones of science, so we study physics because we study science.Read More About Why We Study Physics

What Fields are Part of Physics?: What sort of specific things do physicists study? Physics incorporates many subfields, such as quantum mechanics, thermodynamics and (my current specialty) meteorology/atmospheric physics. Read About the Various Fields of Physics

How do we go About "Doing" Physics?: Physics is all about exploring the way the universe works, by asking and answering questions. The process we use has been formalized into the "Scientific Method".

What do Physicists actually do?: Physicists do lots of different things, research, teaching, reading.

Why Should I Have to Study Physics When I am Going to be a Doctor, Lawyer, etc?: Short answer: Physics is cool, but I'm biased.

Longer answer: Physics, as a discipline - especially at an undergraduate level, teaches many things that are important in all walks of life. Read About Why You Should Study Physics

Where Can I Find Help With My Science Fair Project?: I have put together a collection of Science Fair resources, including a guide to creating a really great project, as well as a number of project ideas to get you rolling. Science Fair Projects

Where Can I Find Out More About Physics?: There is a great deal of information about physics located on the internet, including on this site. A good place to start is with more Physics 101

Where Can I Get Answers to More Physics Questions?: There are several ways to find more answers: The Physics FAQ, Search Physics or you can contact me.

Saturday, February 18, 2006


Definition: A particle with zero rest mass consisting of a quantum of electromagnetic radiation. The photon may also be regarded as a unit of energy equal to hf, where h is the Planck constant and f is the frequency of the radiation in hertz. Photons travel at the speed of light. They are required to explain the photoelectric effect and other phenomena that require light to have particle character.

US and Canadian skiers get smart armour

Flexible body armor is currently in use by US and Canadian skiers. This armor is normally flexible, but reacts automatically to impact, hardening into a protective layer around the skier. The armor is made from a "material [that] exhibits a material property called "strain rate sensitivity". Under normal conditions the molecules within the material are weakly bound and can move past each with ease, making the material flexible. But the shock of sudden deformation causes the chemical bonds to strengthen and the moving molecules to lock, turning the material into a more solid, protective shield."

This effect is quite like the cornflour putty you can create in this experiment .

Read more at www.newscientist.com - US and Canadian skiers get smart armour.


Definition: Physics is the science of matter, energy and the interactions between the two. Within this framework, physics encompasses essentially all of nature: the laws and properties of matter and the forces acting upon it, especially the causes (gravitation, heat, light, magnetism, electricity, quantum effects etc) that modify the general properties of bodies.

Physics is the study of motion – from objects as small as neutrinos to ones as massive as galaxies or even the entire universe – and forces – the interactions between bodies.

Physics is traditionally divided into a large number of subfields, including thermodynamics, quantum physics, electromagnetism, acoustics, optics, atomic physics, nuclear physics, cryogenics, relativity, solid-state physics, condensed matter physics, particle physics and plasma physics.

Also Known As: natural science, natural philosophy
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