Vikings, Relativity and Couch potatoes

Abstract: It's not my fault I'm lazy,
Physics made me this way

dedicated to my sister-in-law and  her fresh hubby's mawwiege

Mazal Tov!!!

Recently I attended my sister-in-law's wedding...

After a full month of being forgotten, taken as granted and ultimately being treated as some ungainly babysitter to my own girl, it has arrived...

The event dreaded and anticipated, probably by the bride and groom, but also by yours truly -

THE WEDDING

Awesome and gruesome, with a multitude of family-related potential calamities, just waiting to happen, hanging on the off chance of someone sitting in the wrong seat or uttering the wrong sentence, incurring a death sentence, with the obvious exception of the crazy and otherwise fully-certifiable-bunkers pseudo-relative  (She can say whatever the hell she wants, nobody's home thus no-one really listens or cares what she says).

The food was good, the company better, and the music divine. well, not really... the first two statements are correct whereas the third - not so much....

The DJ was poor, probably not in the fiscal sense after the presumed hefty sum he was paid, but poor taste in music, poor know-how of his trade, poor execution, and ultimately, the only reason his music was anywhere near palatable, was this was their wedding and we were so damn happy for them, that everything else vanished, not  unlike the 10th order Taylor term for a quadratic potential function. 

At some point the music was pounding so hard, I literally saw hordes of vikings working at a huge smithy, pounding away with all their might to mold some unfathomably hard metal into some equally mysterious shape.

Now, if you follow my posts you know full well what happens to me when faced with potential demise - physics comes into play!

I immediately went on to contemplate vikings and physics, and stumbled upon Dichroism, which is basically when light polarized in different directions go through a certain special material, only one polarization survives (the otherwise polarized rays are reduced to a point of vanishing altogether).

Now since sunlight is non-polarized, this normally doesn't mean squat, but when there's heavy cloud cover, the light rays disperse over the clouds so you get a general bright haze, but no obvious direction for the sun.

Enter dichroism: by using dichroic glass the light that passes through the stone is brightest in the direction of the sun, because right in front of the sun (through the clouds) the light is differently polarized.

The trick is you have to find the right direction to hold the dichroic stone in, else you'll basically get nothing.

Anyway, this dichroism trick is how vikings were able to sail across wide stretches of open sea, since they didn't have land in sight for coastal navigation, and either they didn't know their celestial-nav basics, or the skies were constantly cloud-covered.

BOOM!!

One of the loud pounding beats threw me back into consciousnesses, in time to  realize how horribly out of shape I was...
You see, I was actually dancing (well, more like contorting) on the dance floor, sweating and panting, and  the all too familiar "why am I so lazy?" question kept burning in my mind...

Which again set a chain of events in my mind culminating with physics:

It's not my fault!!! Even physics is lazy!!!

And I will prove this immediately:

First off, remember old Newt's law: 

"Every body persists in its state of being at rest or of moving uniformly straightforward, except insofar as it is compelled to change its state by force impressed"

Translated: every body is basically a fat blob. you really have to exert force to change its current state.

I will now delve into a bit of Lagrangian physics to prove a point:

<Warning: Physics ahead>
This is a simplification of deriving Lagrangian Mechanics but here goes:
Consider Newton's 2nd Law:
\[F=ma\]
And if you're a physicist you know this is a simplification of:
\[\frac{dP}{dt}=F\]
So, now, applying D'Alambert pricnciple we can constrict ourselves to "external" forces, and taking F to always mean a conservative force (i.e. arising from some scalar potential function) we can write:
\[F=-\nabla \left(U\right)\] where U is just the potential function otherwise known by the name "Potential Energy". If we constrict ourselves to one dimension we can see:
\[F=-\frac{\partial U}{\partial x}\] 

Looking at the left hand side of the above equation where we treat \(P=mv\) let's explore the relations between the kinetic energy term - \(\frac{mv^2}{2}\) and the above term.
It's fairly easy to see that:
 \[ mv=\frac{\partial}{\partial v}\left(\frac{mv^2}{2}\right) \]

Let's call the kinetic energy term T and the potential energy term U, so we now get:
\[\frac{d}{dt}\left(\frac{\partial T}{\partial v}\right)=\frac{\partial (-U)}{\partial x}\]

Understanding kinetic energy to be non-dependant on location, and potential energy to be solely location dependant we can add expressions to both sides that vanish in derivation thus defining:
\[\mathcal{L}=T-U\]
to get the Euler-Lagrange equations
\[\frac{d}{dt}\left(\frac{\partial\mathcal{L}}{\partial \dot{q}}\right)=\frac{\partial\mathcal{L}}{\partial q}\] 
Where here I've also switched to some generalized coordinates \(q,\dot{q}\).

Now, defining the action \(\mathcal{A}\) as the time integral of the Lagrangian \(\mathcal{L}\), or in other words:
\[\mathcal{A}=\int\mathcal{L}dt\]

We have now successfully exchanged Newton's rules formulation by the "Principal of least action", since it follows that demanding minimal Action, actually yields Euler-Lagrange equations which are the equations of motion.

A word of caution though: 
First off this derivation is a sketch, the true process is a lot more rigorous, but I assure you, it works.

Secondly, Lagrangian Mech is a heavy canon, all you need to do is describe the problem in some sensible coordinates, find the kinetic energy and potential energy, perform some derivations...

and BAM!!! 

you get equations of motion, as well as conserved quantities and symmetries of the system like magic!!

But, since we use a couple of assumptions in deriving the Lagrangian, this actually covers LESS general physical situations. In reality there's ALWAYS friction, which is by no means a conserving force, thus adaptation to Lagrangian Mech are needed and they are not always as simple.

<Warning: Physics ahead/>

The obvious conclusion of all this mess, is that Newton laws of motion are equivalent (under some basic assumptions) to a first principle that states the following:

"Every physical system aspires to minimize the action taken"

for instance, water will flow in the path of least resistance, and light will travel the path of least (optical) distance, and I, ladies and gentlemen will aspire to do practically NOTHING if I can possibly get away with it.

This means I will absolutely abhor every single time I really have to get up, for instance to go to the fridge and get some grub, I'd much rather my lovely wife make lunch for me and serve it while I leisurely sit back and enjoy the latest mind-numbing episode ofsome stupid comedy show.

By the way, this is EXACTLY why light bends in the presence of gravitation. Not to watch stupid comedy shows, the other thing - being lazy.

See, gravitation can be thought of as a property of space(-time), rather than some force or field that occupies said space. by comrade Einstein's equivalency principle you can not tell whether you are being pulled by gravity, or being accelerated in the opposite direction.

And by that virtue, even light itself (having no mass is irrelevant here) bends to accommodate for this equivalency.

One might even say (and be wrong) that light is the submissive partner in the energy-gravitation relationship... But as I said, this is not correct, since light is a form of energy, and gravitation is a product of energy concentrates. So really, it's a marriage of energy and gravity, or in oriental philosophy terms, marriage of heaven and earth, or ying and yang, or horse and carriage (err... that's from a different philosophy methinks).

To conclude, marriage is such a blessing in one hell of a disguise, since left to our own devices we will do absolutely nothing until some external force propels us to action. When in a relatively successful marriage, the same is true, only the external force is called a wife, and hopefully, most of the times she kicks you in the gonads, it's for your own good.

This also enables two people to become a system of coupled equations, thus redefining the least action to actually produce some interesting dynamics, at least until a third little equation comes into play to dominate the hell out of their lives... if you're a parent, you know what I mean, right?

My own sweet third coupled equation 

Alternatively, if your marriage sucks, well, this explains why people stay in dysfunctional relationships for too long - it simply is to much ACTION to get out of one, better (by physical standards, not mine), to become mentally dislodged and otherwise apathetic to a fault.

But we know it's the former rather than latter. we really do.

Anyway we love you guys very much.

Mazal Tov!!