16 April 2009

A Mathematical Disguise

As promised by sir Josh deca-Hertz, ASD is posting its first physics/math rant/challenge to you all in the web-o-sphere. So sharpen those pencils, light your stogies, and pet your fish in preparation 'cause here we go!

For the first posting in this series we are going to go ahead and dive right in to some heady yet interesting terrain; the principle of gauge invariance. Our current understanding of the way the universe is put together is based on an idea known as the gauge principle. Put simply, the way the universe behaves should not depend on the way we look at it. A basic version of this principle has been known for some time in the form of space-time invariance. By space-time invariance we mean to say that the laws of physics should not change simply by moving around in space or time: if you are listening to your local rockin' band playing live and then decide to move to a different location in the room or perhaps wait for the inevitable mind-bending refrain one minute later, the way the sound waves propogate (for example) should not correspondingly change. You might be hearing different frequencies due to the acoustics in the room or in that the refrain has a different set of chord progressions, but the fundamental physics behind the sound waves does not change. This may seem obvious, but the best ideas in science are those obvious ideas that have profound consequences. In our example, as a consequence of the physics not changing in time we can actually prove the law of conservation of energy. That's right, this simple idea is the origin of the world's energy crisis... talk about profound.

Space-time invariance has been well known since Galileo (and likely significantly earlier), but another kind of symmetry has popped up more recently which is gauge invariance. To understand this we must review some quantum field theory (it's okay, just keep petting your fish) which says that all kinds of matter can be described by a field that exists everywhere in space, and the properties of that field will dictate how different kinds of matter will interact with each other. This idea is itself nothing new. Photons (the particles that make up light) are described by electromagnetic fields for example, which has been known for over a century. But, our new theory predicts that everything; electrons, protons, neutrinos, etc. have an associated field and that oscillations of that field produce the particles in question. Pretty neat, eh?

Let us focus on electrons, those damn things that shock you when moonwalking too much on your grandma's shag carpet. The field associated with electrons is known as a Dirac field. Now, it turns out that if we take a Dirac field and multiply it by a complex number, the physical quantities that we can measure from the field do not change. Therefore we also expect that the equations that dictate the behavior of the Dirac field should also not change. This process of multiplying a Dirac field by a complex number is known as a guage transformation, and the expectation that the behavior of the field should remain unchanged is known as gauge invariance (or the gauge principle). Now here is the punchline: it turns out that as a by-product of imposing the gauge invariance restriction on the equation that dictates the behavior of the field (known as the Lagrangian), we have to by hand put terms into this equation, and those terms predict the interaction between electrons and photons! Yes indeed. Before we had to just assume that an electron and a photon interacted in a particular way (our cell phones work, so we're pretty sure they interact), but now we actually have a physical principle that predicts this interaction. This theory is known as quantum electro-dynamics, or QED. One can take this principle furthur to tie together QED with other particles, leading in the end to a unified view of the universe that connects together all the known forces... except for gravity, but that's a different story.

So, here is the challenge: the Lagrangian which describes the Dirac field is given by

Here the psi symbol is the Dirac field (which is a column vector), the gamma symbol is a constant matrix, and m is the mass of the electron. The bar over the psi refers to the vector that has been transposed, complex-conjugated, and multiplied by another constant matrix, and the derivative (the delta symbol) is with respect to position. If we make the transformation on our Dirac field

where theta is a general function of position x, then we will also transform the Lagrangian into a new function, and this new function had better have the same form as the old one. Show that by taking the derivative of the Dirac field transformation we get two terms: one that is proportional to the derivative of the field, and another that is proportional to the field itself.

This second term is what must be cancelled in the Lagrangian equation, thus leading to the inclusion by hand of a cancelling term which coincidentally predicts electromagnetic interaction. Holy cow!

Email your responses to aseasonaldisguise@gmail.com , and remember that the first correct response wins some ASD goodies! Have fun and rock on.

Sup

Terrifying Tidbits of Torch-Fired Terra Cotta

Several things of note:

1. Last Sunday, A Seasonal Disguise had the great pleasure of playing a show with Clem Snide, Heligoats, and Sleepy Seeds. For those of you unaware of these fine bands, get thee out of thy nunnery and down to your local record store. Or find them on the internet. Thanks to those brave folks who tempted the wrath of the Easter bunny and came out for the show. And especial thanks to Clem Snide and Heligoats for stopping in Boise on what would have been their day off.

2. ASD is soon going to be gearing up to shoot our first music video, (queue gasps of awe). You know music videos, right? Those things with light, and motion, and sound, that you never see on MTV anymore. You know MTV, right? The alleged purveyor of music and youth culture which will “rot on the windmills of eternity”.
Here’s what information I can give you now, dear readers. The video will be for the song, “Won’t You Hibernate With Me?”. It will involve bears. Also, tentative love. And sweat. And we may be calling upon you, our loyal readership, to assist us in this endeavor, so keep your eyes tuned to this channel.

3. Lastly, our comrade in musical arms, Sup, keyboardist extraordinaire and distinguished Special Lecturer in Physics at a local institution of higher learnin, will be posting a question mathematical, to this very blog. The first person who sends the correct answer to the aforementioned question will be rewarded with something ASD related. Perhaps a shirt, cd, or other item of shwag. Ideally this will become a regular contest of cunning, so tell all of your friends who enjoy the occasional equation to keep their pencils sharp.

We are now well into April, and though I don’t generally like to quibble with the dead, I think Old Possum may have been a bit off in his assessment. I like lilacs, after all.

Josh

09 April 2009

Sunday, Sunday, Sunday


We had yet another drum session last night. It yielded quite a nice track upon which the song "Golden Butterfly" will sit. Progress was also made on the drum track to Krug's Fires. Huzzah! Back to the studio on Friday to continue work on Golden Butterfly.

In other news....we have a show on Sunday and hope you all can make it!

Signing off, Z.

06 April 2009

Stop Frenching That Porcupine! : A non-standard and wildly inaccurate portrait of A Seasonal Disguise

WARNING: For entertainment purposes only. Not for edification, or to be used as an emollient.

Bejar Be Praised!

With a sound ranging from acoustic folk, to outright mind melting rock, A Seasonal Disguise has something for all comers. Having emerged successfully from the warm, nurturing abattoir of the Boise, Idaho music scene, and having finally conquered their collective addiction to Flintstones chewable vitamins, the members of ASD are prepared to bring sweet, sweet accordion and glockenspiel to your doorstep. Few other bands can boast such an extensive knowledge of popular 80's cartoons, theoretical physics, and Joycean intertextuality, while still assiduously avoiding any kind of popular or critical acclaim. Juxtaposing a real and burning desire for violent world conquest, with a predilection for petting kittens and frolicking in dandelion fuzz, ASD hopes to show that it is possible to achieve your dreams, so long as they are mundane and require little effort.

Roaming the wild Idaho steppes like the great musical nomads of days past, Genghis Khan, Rumi, Tolstoy, Prince, ASD leaves no stone unturned in their search for nourishing grubs and succulent camas roots. This strict dietary regimen is primarily responsible for the bands outsized mental prowess and significantly reduced visual acuity. One would be wise to approach the group cautiously, as their poor eyesight makes them easily confused and prone to attack, often hugging a victim until they no longer believe in love or the standard procreative processes. Witnesses have variously described this behavior as “charming”, “unsettling”, and “a complete derangement of the normal Western socio-political paradigm”. While sometimes dangerous as a group, when approached individually, band members are docile and nearly defenseless. Their unfocused eyes rarely leave their shoes. Be gentle with them when they are in this vulnerable state, as any sudden movement will trigger the flight response, thus spoiling any chance of a meaningful conversation about the finer points of molting in Etruscan humming birds.

ASD's FBI file reveals that several members are full fledged acolytes in the Cult of Destroyer, Bejar Be Praised, and this has led some to erroneously compare the band to a shorn and repentant wombat. Though their metaphors are obscure, and skeptics abound, the real joy of this group is not found in their penchant for separating muons from their attendant bremsstrahlung radiation, or in their quaint and futile attempts to speak English, but in their music. Audiophiles, and even some humans, have suggested that listening to the smooth, curvaceous, occasionally atonal, songs of A Seasonal Disguise pleasantly invokes the feeling of a rowdy and illicit shag with a coked out steel worker in a truck stop restroom, while Krishna, in all his azure glory, hovers above, gently plucking a zither and belting out Burt Bacharach standards. Other, less verbose observers sum it up thusly, “Fucking Awesome!”. So, by all means, go, listen, give them your money, and your phone number, or just say hello. But watch out for the claws!

It's gonna be the best Easter ever this year!


Busy week ahead! Two or three recording sessions working on the new album, postering for a show on Easter Sunday...a show on Easter Sunday...that's a lot of work for a band with a collective total of 7 tax reportable jobs (two of which are held by a full time university student to boot) and active, totally rock 'n roll lifestyles. Totes.

All ridiculousness aside, we have a show this Sunday! Easter Sunday! April 12! We are playing some fine fine bands like: Clem Snide, Heligoats, and Sleepy Seeds. Huzzah I says. Huzzah!

Signing off, Z.

01 April 2009

I was born an April fool

"I was born an April fool" is something Mr. Otis from the low frequency sect of our fine band said this morning. Well as Mr. Krug has said - can I use that it in a song?

Big couple of weeks coming up in ASD land (we should totally start an amusement park called that). On Friday and Saturday we will descend upon the recording studio yet again to work on drums for a couple of songs. Sunday April 12th we will play what is sure to be a fabulous show at VAC with Clem Snide, Heligoats, and Sleepy Seeds. Ok - so that doesn't sound like a lot but it's big for us.

Happy April 1st. We forgot about it and are too slow on the draw to prank ya'll out. Instead we shall leave you with a video from our CD release party.



Signing off, Z.