Thursday, July 5, 2012

Two days ago, the CERN team announced that they had found a new particle whose properties are consistent with the long sought-after Higgs Boson’s. Whether or not it is the elusive boson however, is still to be determined by further research. To read more about the event, follow this link to the new BBC article.

If you have no clue what this is about, the above video is a quick and nice introduction to the Higgs Boson submitted by one of our followers, the lovely oh-yeah-and-what. Thanks for the awesome submission!
SIWS loves feedback from followers and we’ll do our best to respond. If you have any questions, ideas, or concerns, feel free to drop us a message, email us at sayitwithscience@gmail.com or like and post on our Facebook page. You can even make a submission post and we might publish it and credit you, like we did with this one!
Take care and happy science-ing! 

Friday, October 14, 2011
Going superfluid!
A liquid goes superfluid when it suddenly loses all internal friction and gains near infinite thermal conductivity. The combination of zero viscosity but nonzero surface tension allows a superfluid to creep up walls and back down the outside to drip from the bottom of open containers, or to completely cover the inner surface of sealed containers. Lack of viscosity also allows a superfluid to leak through a surface that is porous to any degree, because the molecules can slip through even microscopic holes. Superfluids furthermore exhibit a thermo-mechanical effect where they flow from colder to warmer temperatures, exactly the opposite of heat flow as stated by the laws of thermodynamics! That implies the remarkable property of superfluids of carrying zero entropy. Because of this, a perpetual fountain can be set up by shining light on a superfluid bath just below a vertical open capillary tube, causing the fluid to shoot up through and beyond the tube until its  contact with the air causes it to cease being a superfluid and fall back  down into the bath, whereby it will cool back into the superfluid state  and repeat the process.
So how does superfluidity work, exactly?
Makings of a superfluid
Physicists first got the inkling of something stranger than the norm when, around 1940, they cooled liquid helium (specifically, the 4He isotope) down to 2.17 K and it started exhibiting the above-mentioned properties. Since the chemical makeup of the helium didn’t change (it was still helium), the transformation to a superfluid state is a physical change, a phase transition, just like ice melting into liquid water. Perhaps for cold matter researchers, this transition to a new phase of matter makes up for the fact that helium doesn’t solidify even at 0 K except under large pressure - whereas ALL other substances solidify above 10 K.
[Phase diagram of 4He, source]
Helium is truly the only substance that never solidifies under its own vapor pressure.
Instead, when the temperature reaches the transition or lambda point, quantum physics takes hold and a fraction of the liquid particles drop into the same ground-energy quantum state. They move in lock-step, behaving identically and never getting in each others’ way. Thus we come to see that superfluidity is a kind of Bose-Einstein condensation, the general phenomenon of a substance’s particles simultaneously occupying the lowest-energy quantum state.
Read more:”This Month in Physics History: Discovery of Superfluidity, January 1938”. APS News: January 2006
Based on a project by Barbara Bai, Frankie Chan, and Michele Silverstein at Cornell University.

Going superfluid!

A liquid goes superfluid when it suddenly loses all internal friction and gains near infinite thermal conductivity. The combination of zero viscosity but nonzero surface tension allows a superfluid to creep up walls and back down the outside to drip from the bottom of open containers, or to completely cover the inner surface of sealed containers. Lack of viscosity also allows a superfluid to leak through a surface that is porous to any degree, because the molecules can slip through even microscopic holes. Superfluids furthermore exhibit a thermo-mechanical effect where they flow from colder to warmer temperatures, exactly the opposite of heat flow as stated by the laws of thermodynamics! That implies the remarkable property of superfluids of carrying zero entropy. Because of this, a perpetual fountain can be set up by shining light on a superfluid bath just below a vertical open capillary tube, causing the fluid to shoot up through and beyond the tube until its contact with the air causes it to cease being a superfluid and fall back down into the bath, whereby it will cool back into the superfluid state and repeat the process.

So how does superfluidity work, exactly?

Makings of a superfluid

Physicists first got the inkling of something stranger than the norm when, around 1940, they cooled liquid helium (specifically, the 4He isotope) down to 2.17 K and it started exhibiting the above-mentioned properties. Since the chemical makeup of the helium didn’t change (it was still helium), the transformation to a superfluid state is a physical change, a phase transition, just like ice melting into liquid water. Perhaps for cold matter researchers, this transition to a new phase of matter makes up for the fact that helium doesn’t solidify even at 0 K except under large pressure - whereas ALL other substances solidify above 10 K.

[Phase diagram of 4He, source]

Helium is truly the only substance that never solidifies under its own vapor pressure.

Instead, when the temperature reaches the transition or lambda point, quantum physics takes hold and a fraction of the liquid particles drop into the same ground-energy quantum state. They move in lock-step, behaving identically and never getting in each others’ way. Thus we come to see that superfluidity is a kind of Bose-Einstein condensation, the general phenomenon of a substance’s particles simultaneously occupying the lowest-energy quantum state.

Read more:
This Month in Physics History: Discovery of Superfluidity, January 1938”. APS News: January 2006

Based on a project by Barbara Bai, Frankie Chan, and Michele Silverstein at Cornell University.

Thursday, August 25, 2011
The Stern-Gerlach Experiment
In 1922 at the University of Frankfurt in Frankfurt, Germany, Otto Stern and Walther Gerlach sent a beam of silver atoms through an inhomogeneous magnetic field in their experimental device. They were taking a look at the new concept of quantized spin angular momentum. If indeed the spin associated with particles could only take on two or some other countable number of states, then the atoms transmitted through the other end of their machine should come out as two (or more) concentrated beams. Meanwhile if the quantum theory was wrong, classical physics predicted that the profile of a single smeared-out beam would result on the detector screen, due to the magnetic field deflecting each randomly spin-oriented atom a different amount on a continuous, rather than discrete, scale.
As you can see above, the results of the Stern-Gerlach experiment confirmed the quantization of spin for elementary particles.
Spin and quantum states
A spin-1/2 particle actually corresponds to a qubit
|ψ> = c1|ψ↑> + c2|ψ↓>
a wavefunction representing a particle whose quantum state can be seen as the superposition (or linear combination) of two pure states, one for each kind of possible spin along a chosen axis (such as x, y or z). The silver atoms of Stern and Gerlach’s experiment fit in this description because they are made of spin-1/2 particles (electrons and quarks, which make up protons and neutrons).
Significantly, the constant coefficients c1 and c2 are complex and can’t be directly measured. But the squared moduli ||c1||2 and ||c2||2 of these coefficients represent the probability that a particle in state |ψ> will be observed as spin up or down at the detector.
||c1||2 + ||c2||2 = 1 : it is certain that the particle will be detected in one of the two spin states.
That means when we pass a large sample of particles in identical quantum states through a Stern-Gerlach (S-G) machine and detector, we are actually measuring the probabilities that the particle will adopt the spin up or spin down states along the particular axis of the S-G machine. This follows the relative-frequency interpretation of probability, where as the number of identical trials grows large the relative frequency of an event approaches the true probability that the event will occur in any one trial.
By moving the screen so that either the up or down beam is allowed to pass while the the other is stopped at the screen, we are “polarizing” the beam to a certain spin orientation along the S-G machine axis. We can then place one or more S-G machines with stops in front of that beam and reproduce all the experiments analogous to linear polarization of light.

The Stern-Gerlach Experiment

In 1922 at the University of Frankfurt in Frankfurt, Germany, Otto Stern and Walther Gerlach sent a beam of silver atoms through an inhomogeneous magnetic field in their experimental device. They were taking a look at the new concept of quantized spin angular momentum. If indeed the spin associated with particles could only take on two or some other countable number of states, then the atoms transmitted through the other end of their machine should come out as two (or more) concentrated beams. Meanwhile if the quantum theory was wrong, classical physics predicted that the profile of a single smeared-out beam would result on the detector screen, due to the magnetic field deflecting each randomly spin-oriented atom a different amount on a continuous, rather than discrete, scale.

As you can see above, the results of the Stern-Gerlach experiment confirmed the quantization of spin for elementary particles.

Spin and quantum states

A spin-1/2 particle actually corresponds to a qubit

|ψ> = c1> + c2>

a wavefunction representing a particle whose quantum state can be seen as the superposition (or linear combination) of two pure states, one for each kind of possible spin along a chosen axis (such as x, y or z). The silver atoms of Stern and Gerlach’s experiment fit in this description because they are made of spin-1/2 particles (electrons and quarks, which make up protons and neutrons).

Significantly, the constant coefficients c1 and c2 are complex and can’t be directly measured. But the squared moduli ||c1||2 and ||c2||2 of these coefficients represent the probability that a particle in state |ψ> will be observed as spin up or down at the detector.

||c1||2 + ||c2||2 = 1 : it is certain that the particle will be detected in one of the two spin states.

That means when we pass a large sample of particles in identical quantum states through a Stern-Gerlach (S-G) machine and detector, we are actually measuring the probabilities that the particle will adopt the spin up or spin down states along the particular axis of the S-G machine. This follows the relative-frequency interpretation of probability, where as the number of identical trials grows large the relative frequency of an event approaches the true probability that the event will occur in any one trial.

By moving the screen so that either the up or down beam is allowed to pass while the the other is stopped at the screen, we are “polarizing” the beam to a certain spin orientation along the S-G machine axis. We can then place one or more S-G machines with stops in front of that beam and reproduce all the experiments analogous to linear polarization of light.

Saturday, August 13, 2011
Quark-Gluon Plasma
First of all… What are quarks and gluons?
Quarks are tiny subatomic particles that make up the nucleons (protons & neutrons) of everyday matter as well as other hadrons. Gluons are massless force-carrying particles which are necessary to bind quarks together (by the strong force\interaction) so that they can form hadrons.
QGP (Quark-Gluon Plasma)
A tiny fraction of a second after the Big Bang, the universe is speculated to have consisted of inconceivably hot and dense quark-gluon plasma. QGP exists at such high temperatures (about 4 trillion Kelvin — 250,000 times warmer than the sun’s interior), that the quarks and gluons are almost free from colour confinement (in other words, they do not group themselves to form hadrons). QGP does not behave as an ideal state of free quarks and gluons, instead it acts like an almost perfect dense fluid.
It then took only a few micro-seconds until those particles were able to cool down to lower energies and separate to form nucleons. 
RHIC & ALICE
To study the properties of the early universe, physicists have created accelerators that essentially recreate quark-gluon plasma. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (in Upton, NY) collides heavy ions (mainly gold) at relativistic speeds. This accelerator has a circumference of about 2.4 miles in which two beams of gold ions travel (one travels clockwise, and the other anticlockwise) and collide. The resulting energy from the collision allows for the recreation of this mysterious primordial form of matter.
ALICE (A Large Ion Collider Experiment) at CERN (in Geneva, Switzerland) is the only other current heavy ion collider experiment which studies QGP. However, instead of gold, ALICE uses lead ions.

Quark-Gluon Plasma

First of all… What are quarks and gluons?

Quarks are tiny subatomic particles that make up the nucleons (protons & neutrons) of everyday matter as well as other hadrons. Gluons are massless force-carrying particles which are necessary to bind quarks together (by the strong force\interaction) so that they can form hadrons.

QGP (Quark-Gluon Plasma)

A tiny fraction of a second after the Big Bang, the universe is speculated to have consisted of inconceivably hot and dense quark-gluon plasma. QGP exists at such high temperatures (about 4 trillion Kelvin — 250,000 times warmer than the sun’s interior), that the quarks and gluons are almost free from colour confinement (in other words, they do not group themselves to form hadrons). QGP does not behave as an ideal state of free quarks and gluons, instead it acts like an almost perfect dense fluid.

It then took only a few micro-seconds until those particles were able to cool down to lower energies and separate to form nucleons. 

RHIC & ALICE

To study the properties of the early universe, physicists have created accelerators that essentially recreate quark-gluon plasma. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (in Upton, NY) collides heavy ions (mainly gold) at relativistic speeds. This accelerator has a circumference of about 2.4 miles in which two beams of gold ions travel (one travels clockwise, and the other anticlockwise) and collide. The resulting energy from the collision allows for the recreation of this mysterious primordial form of matter.

ALICE (A Large Ion Collider Experiment) at CERN (in Geneva, Switzerland) is the only other current heavy ion collider experiment which studies QGP. However, instead of gold, ALICE uses lead ions.

Tuesday, July 12, 2011
Many people have heard of Maxwell’s famous four equations:
∇·E = 0 ∇·B = 0 ∇ x E = -∂B/∂t ∇ x B = μ0J + μ0ε0(∂E/∂t)
But did you know that they can actually all be captured in one simple expression? When we extend classical electrodynamics into Minkowski 4-space (the geometry of special relativity), the time derivatives that appear in the derivation of Maxwell’s equations can be mixed into the same mathematics that takes care of the spatial expressions. By generalizing the Laplacian (∇2) to 4-space, we obtain the d’Alembertian (□2, sometimes written without the exponent). This operator allows us to rewrite Maxwell’s equations in tensor notation as one simple formula, sometimes called the Riemann–Sommerfeld equation:
□2Aμ = -μ0Jμ
Where Aμ is the four-potential (φ, cA) (with φ and A the familiar scalar and vector potentials) and Jμ the four-current (ρc, J) (with ρ and J the familiar charge and current densities), thereby using the power of differential geometry and tensor notation to capture all of classical electrodynamics in one swift stroke.
Background
Maxwell’s Equations describe how electric and magnetic fields relate to each other and how they relate to the presence of charged particles and currents. The way we’ve presented them above is in differential form, which describes how electric fields (E) and magnetic fields (B) change in space and time; they can also be presented in integral form, which describes how the total measure of these fields scales with quantities like current density (J).
Although these equations were originally formulated in terms of fields, physicists would later find that the equations could be much cleaner when expressed in terms of potentials. A similar revolution happened in classical mechanics; although Newton’s forces were a good start, Lagrangian dynamics showed us that understanding the potential energy of the system made solving for equations of motion much simpler than trying to add up dozens of force vectors. In electrodynamics, we have two kinds of potentials: the scalar potential φ (or, sometimes, V), which most people know by the term “voltage”; and the vector potential, A, which is related to magnetic fields and may be less familiar.
Tensors notation (for our purposes) is little more than a convenient way to represent vectors and matrices. When you read the Riemann-Sommerfeld equation, then, you’re really reading 4 equations at once. What are those equations? Repeat the equation four times but each time replace μ with a different value; so, one equation might be □2A1 = -μ0J1. The 1’s in this equation aren’t exponents, but rather tensor indices; just like you might see vector components written as vx, vy, and vz representing different components of v, A0, A1, A2, and A3 represent the four components of the (vector) tensor A.
What are the funny upside-down triangles? The symbol is called a nabla, and is often read as “del”. In some ways, it’s an abuse of notation, but it gives us a convenient way to write the gradient, divergence, curl, and Laplacian operators. The exercise for how this notation works is left to the reader, but note the definitions: ∇U = grad(U), the gradient; ∇·U = div(U), the divergence; ∇ x U = curl(U), the curl; and ∇2U = ∇·(∇U) = div(grad(U)), the Laplacian. Each of these functions has a very important place in vector analysis. Since we represent electric and magnetic fields mathematically as vector fields, these operations give us information about the geometry of those fields. The gradient function tells us the direction that a field changes most at each point; the divergence tells us how much the field is dispersing (a field where everything pointed away from one center point would have a high divergence); the curl tells us how much a field is swirling, so to speak; and the Laplacian tells us how much a field changes in strength as it disperses.
And finally, we have our partial derivatives (∂B/∂t, for example) that give us rates of change (like how a magnetic field B changes with respect to the time t), and our constants, ε0 and μ0. These constants have the interesting relation that, for the speed of light c, ε0μ0=1/c2.
Picture credit: Geek3, from Wikipedia. Licensed under CC-3.0 Attribution Share-Alike.

Many people have heard of Maxwell’s famous four equations:

∇·E = 0
∇·B = 0
∇ x E = -∂B/∂t
∇ x B = μ0J + μ0ε0(∂E/∂t)

But did you know that they can actually all be captured in one simple expression? When we extend classical electrodynamics into Minkowski 4-space (the geometry of special relativity), the time derivatives that appear in the derivation of Maxwell’s equations can be mixed into the same mathematics that takes care of the spatial expressions. By generalizing the Laplacian (∇2) to 4-space, we obtain the d’Alembertian (□2, sometimes written without the exponent). This operator allows us to rewrite Maxwell’s equations in tensor notation as one simple formula, sometimes called the Riemann–Sommerfeld equation:

2Aμ = -μ0Jμ

Where Aμ is the four-potential (φ, cA) (with φ and A the familiar scalar and vector potentials) and Jμ the four-current (ρc, J) (with ρ and J the familiar charge and current densities), thereby using the power of differential geometry and tensor notation to capture all of classical electrodynamics in one swift stroke.


Background

Maxwell’s Equations describe how electric and magnetic fields relate to each other and how they relate to the presence of charged particles and currents. The way we’ve presented them above is in differential form, which describes how electric fields (E) and magnetic fields (B) change in space and time; they can also be presented in integral form, which describes how the total measure of these fields scales with quantities like current density (J).

Although these equations were originally formulated in terms of fields, physicists would later find that the equations could be much cleaner when expressed in terms of potentials. A similar revolution happened in classical mechanics; although Newton’s forces were a good start, Lagrangian dynamics showed us that understanding the potential energy of the system made solving for equations of motion much simpler than trying to add up dozens of force vectors. In electrodynamics, we have two kinds of potentials: the scalar potential φ (or, sometimes, V), which most people know by the term “voltage”; and the vector potential, A, which is related to magnetic fields and may be less familiar.

Tensors notation (for our purposes) is little more than a convenient way to represent vectors and matrices. When you read the Riemann-Sommerfeld equation, then, you’re really reading 4 equations at once. What are those equations? Repeat the equation four times but each time replace μ with a different value; so, one equation might be □2A1 = -μ0J1. The 1’s in this equation aren’t exponents, but rather tensor indices; just like you might see vector components written as vx, vy, and vz representing different components of v, A0, A1, A2, and A3 represent the four components of the (vector) tensor A.

What are the funny upside-down triangles? The symbol is called a nabla, and is often read as “del”. In some ways, it’s an abuse of notation, but it gives us a convenient way to write the gradient, divergence, curl, and Laplacian operators. The exercise for how this notation works is left to the reader, but note the definitions: ∇U = grad(U), the gradient; ∇·U = div(U), the divergence; ∇ x U = curl(U), the curl; and ∇2U = ∇·(∇U) = div(grad(U)), the Laplacian. Each of these functions has a very important place in vector analysis. Since we represent electric and magnetic fields mathematically as vector fields, these operations give us information about the geometry of those fields. The gradient function tells us the direction that a field changes most at each point; the divergence tells us how much the field is dispersing (a field where everything pointed away from one center point would have a high divergence); the curl tells us how much a field is swirling, so to speak; and the Laplacian tells us how much a field changes in strength as it disperses.

And finally, we have our partial derivatives (∂B/∂t, for example) that give us rates of change (like how a magnetic field B changes with respect to the time t), and our constants, ε0 and μ0. These constants have the interesting relation that, for the speed of light c, ε0μ0=1/c2.

Picture credit: Geek3, from Wikipedia. Licensed under CC-3.0 Attribution Share-Alike.