Thursday, 29 July 2010

Quantum handbags

As a physicist, I hate it when women in physics intentionally make something overly female-friendly just to get across the point. It's like screaming “look at me, I'm a woman, and I know I'm not very good at physics but they are so desperate to have women in this field they promoted me anyway!” For younger women interested in physics its what I’m told is called: Inspiration? Fail. Besides, it's a destructive thing to do to your own reputation. The point is you're a physicist, it doesn't matter if you're a woman or a man.

On that note, one of my male colleagues recently went to a seminar by an eminent female physicist in a different field from his own. It was all fine... until she introduced a diagram which he'd never heard of before: the "Handbag Diagram".

Now imagine my friend's shock: on the one hand he thought this female physicist appeared to know her stuff, but on the other she was trying to feminise physics by introducing diagrams which looked like handbags! How dare she?

Turns out - it's not her fault.

It has to be said, most of the other diagrams used in physics have boring names, except perhaps for the "Penguin diagram" - introduced by John Ellis after a bet with (then) student Melissa Franklin. (The bet was that if he lost a game of darts he had to put the word 'penguin' into his next publication. She left early and the person who took her place won. John Ellis felt obliged to keep the wager.)

So where does the handbag diagram come from, and what is it? Fortunately, this female physicist didn't invent the handbag diagram, so it's not her fault that it gave off the impression that she overtly feminised the main topic of her talk. The term describes a particular Feynman Diagram for particle interactions.

Here is an example of a Feynman Diagram:

On the surface, it looks like you can read these diagrams literally - two particles come in from the left hand side, something happens (a photon is exchanged) and two go out on the right hand side with an extra squiggly thing (a gluon radiated by a quark, in this case). Physicists use these diagrams all the time as a useful tool to imagine what is happening in particle interactions. But don’t be fooled...

In fact, they are in momentum space. Try to get your head around that and you will definitely need a beer and since you probably don't have one to hand, I'm not going to try to explain it here. Suffice to say that each line and each vertex represent terms in the 10-page calculation that poor graduate students have to do when we’re learning Quantum Field Theory in order to calculate the probability of this particular interaction. It’s not fun. Trust me.

But back to the topic: the handbag diagram. Here, ladies and gentlemen, is the famous diagram itself (as per Spin in Particle Physics by Elliot Leader pp. 312).

This particular one describes a process called deep inelastic scattering. It is just another Feynman diagram, which has a particular shape. Unfortunately I was unable to get to the bottom of who named this the handbag diagram, so if anyone out there knows, please fill me in!

More importantly though, I think you’ll agree that it takes a fair stretch of the imagination to look like handbag. For one - how would you put it on your shoulder? You couldn’t - so it would have to be a clutch bag... And on a practical note, what is with the lines pointing out at the bottom? They would seriously get in the way of any real use of this thing as a handbag.

I don’t think Louis Vuitton or Mulberry are going to be jumping on this trend any time soon...

Friday, 16 July 2010

A physicists view of teetering high heels

Recently, I stumbled across this website: and was reminded of an idea that I had a while ago: relating the ideas of physics and fashion. OK, it sounds lame, but if Dr. Debbie Berebichez (PhD in physics, don’t you know?) can make a go calling herself “the science babe” then maybe there is hope for making it less lame than other people might.

I then found this article. My first reaction: "are you serious!? They actually press released this!" Now, alright, on the surface it looks like calculating the highest heel a woman can wear is a kind of funny thing to do, and clearly just done for fun. But then you read on and you realise that factors such as “the probability that wearing the shoes will help you 'pull' (in a range from 0 to 1, where 1 is pwhooar and 0 is stick to carpet slippers). If the shoes are a turn-off, there's no point wearing them.”

Well, lets be a bit more academically rigorous about this. Whether the shoes are in fashion or will help you ‘pull’ only changes the likelihood that you will wear them, it’s not physically impossible to!

So instead let’s model the female foot as a right-angled triangle, where the point is the toes and the ankle is the largest part. Now let’s assume that most women (not being ballet dancers) can rotate their foot so that the top of it is 5 degrees from vertical.

Now, theoretically you can fit some kind of shoe under that foot – and no, I don’t care for now if it’s in fashion or if I want to pull when I’m wearing it, as it doesn’t affect the height! So, lets calculate (given your shoe size) how tall the shoe could be.
The result of the theoretically tallest heel a woman can wear depending on her foot size is shown in the graph below. I’ve included my calculation for transparency, feel free to have a go at me about it. Just remember – at least I didn’t include the ‘pull’ factor. Tissh.

At a massive UK size 8, I can wear a heel of almost ten inches! OK, so I wouldn’t want to actually try wearing heels that high, but I’d like to believe it were theoretically possible for me to.

Well, according to Wikipedia

Adult shoe size =  3 * length in inches – 25

So rearranging this, length = (Shoe size +25 )/3

That is the base length of the triangle. Assuming that the distance from top of foot to base of heel is ~ 4 inches we can use pythagoras’ theorem to calculate:

Angle of foot triangle = arctan(4/length)
                                   = arctan(12/(shoe size+25))

We want to add to that the 5 degrees from vertical that we decided on before, so the angle that the base of the foot makes with vertical is:
total angle = 5 degrees + arctan(12/(shoe size+25))

Finally, to calculate the heel height in inches we take:
heel height=cos(total angle)*length

So for me (size 8 UK, biggest possible heel size!)

Heel height = cos(5 deg + arctan(12/33))*(33/3)
            = cos(5+19.98)*11
            = 0.9065*11
            = 9.97 inches!