A very good lecturer

I came across a very good lecture online – given in MIT concerning work, energy, etc. The end of the video shows a very good illustration of conservation of energy!
The video is available as a Real player file to download from http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/Video-Segment-Index-for-L-11.htm.
“Physics works and I’m still alive, see you Wednesday.”

The Manchester Museum & Science Week

I really like the University’s museum here in Manchester. It is on Oxford Rd. about 2mins. walk from the Physics and Astronomy buildings. It is very nice to eat your lunch while wandering around looking at the various exhibits! From ancient Egypt to dinosaur bones to ancient money it’s all very interesting!
One nice thing I noticed today: it’s Science Week here in Manchester and in the museum there are a few people telling and showing people about magnets. I thought it was quite nice to see a small child (who couldn’t have been more than explain to one of the demonstrators what he discovered. He reckoned the North poles don’t like the South poles and they try very hard to avoid each other. He asked the demonstrator why this was … that boy might be a scientist one day me thinks …

Evan

xkcd

xkcd is a web-comic with new entries on mondays, wednesdays and fridays. It concerns “romance, sarcasm, math and language”* in the words of the site’s author. It is certainly weird and contains a lot of stuff you might not get if you have not had experience with computers or basically if you are not a scientist/interested in science more than the average person. There are a number of long running and recurring themes (eg. the author seems to have an irrational fear of velociraptors!). Every so often it does produce some absolute gems though so I recommend for a look.

* math = american way of saying maths

Can You Find Higgs?

Here’s a cool game which my friend Mars has found – the Find Higgs game!

He’s embiggened the role with a cromulent performance …

Flip Tanedo points out that string theorists have a sense of humour … or at least some of them do!

click here.

Neutrino Mass

I had an interesting chat with a neighbour of mine yesterday regarding the mass of neutrinos. Now the issue of whether neutrinos have mass or not was once contentious but it is now (I think!) generally accepted that they do have mass. The evidence for them having mass is given from the fact that neutrino oscillation has been observed. What is this?
Well, there are three types of charged lepton – electrons, muons and tauons with the last two being unstable and decaying to electrons in a short time when they are created. Each of these has a neutrino pair – so there are three types of neutrino (and each of these particles has an anti-particle also). Now in the sun nuclear reactions occur which spit out neutrinos. Clever astrophysicists can work out how many neutrinos one should expect if you try and detect them (and this is no mean feat!). It turns out that the number detected is less than what is predicted. Hmmm.
The solution lies in some basic quantum mechanics. The neutrino wave-function is a superposition of 3 types of neutrino mass eigenstates. Each of these mass eigenstates is a superposition of the 3 “flavour eigenstates” mentioned above (and we could go in a circle here!). Over time as the neutrino travels from the sun to us, the larger mass eigenstates travel slower than the lighter ones so in a way we get interference between the 3 flavour states. In general then the neutrino is a superposition of the 3 eigenstates. So if the neutrino started as being an electron neutrino (probability of measuring electron neutrino =1) after travelling some distance it would then turn out to be a superposition of the 3 flavours (probability of measuring electron neutrino = 1/3 say). –>. This solves the solar neutrino problem where experiments detected a deficit in the number of neutrinos expected from the sun. These exps were only sensitive to one flavour, so could only detect 1/3 of the neutrinos hitting the Earth.
As this oscillation of flavours is observed we know that neutrinos have mass (massless particles do not change types like this – there is only 1 type of photon for instance!). Now the interesting question is what is there mass? One thing is for sure it is VERY SMALL!! We can constrain this using cosmological obs and theory. The mass of a neutrino is less than 1eV (and that is bloody small!!).
The fact that neutrinos have mass is significant – for instance the standard model of particle physics treats them as massless (uh oh). Also the question of why neutrinos have the masses that they do have is a big one? There is no reason for their masses to be on the scale that they are … or so i thought. This was the topic of my neighbourly chat. Apparently in extra-dimensional QFT models of particle physics the mass scale of the neutrino arises naturally. Ok cool – what is it about? Well apparently the flavour eigenstates are not only superpositions of mass eigenstates but of massless eigenstates. In fact one of the massive eigenstates is apparently of a huge mass (the left handed one is high mass, right handed low mass, or vice-versa, i can’t recall!). The overall mass of the neutrino is not “huge” as the high mass eigenstate’s contribution is diluted by that of the massless eigenstates.
Apparently this state of affairs falls out of a higher dimensional theory and could explain the obs mass scale of neutrinos. This is kinda cool and i will definitely be trying to find out more about this during my random internet wanderings …

Tachyons – Do They Exist?

I just realised i never actually filled in this post! I had been meaning too but i guess it just went deeper and deeper down my to do list.

I should say that well – tachyons don’t exist*. But anyway …

One thing that i wanted to note about tachyons is that if they did exist there would be a way of investigating for their existence – via ‘Cerenkov Radiation.’

What is this? Well we know that the local speed of light can be surpassed. This occurs when a charged particle passes through a medium with refractive index n, say. Now the refractive index of a medium is just the ratio of the speed of light in vacuum to the speed of light in that medium. So if c=300,000 km/s in a vacuum and n=1.5 (for glass say) then light travels at v=200,000 km/s in this medium. But this speed of v as relativity tells us that only the speed c cannot be surpassed. When this occurs the particle will emit Cerenkov radiation.

Now suppose tachyons existed and that they carried charge** then they would contunously be losing energy by Cerenkov radiation as they always travel above c. But as tachyons speed up as they lose energy*** the tachyon goes to infinite velocity. At infinite velocity it annihilates with another tachyon which is OK as infinite velocity means zero energy but finite momentum***

Weird stuff indeed!

* In QFT tachyons are quanta (particles) of fields with negative squared mass. When they arise in quantum field theories (or string theories) they signify that the theory is unstable, i.e. we are at an unstable point in the vacuum so we would roll down to a stable minimum and then the particles will no longer be tachyons.
* if tachyons exist then they could certainly carry charge – sure why not!
** see previous post about odd things like this

Tachyons – What Are They?

Some people are curious about tachyons. So what the hell are they? I will endeavour to explain.
Tachyons are particles with spacelike four-momentum and imaginary mass. What does this mean? Well it is probably best to explain this using a space time diagram.
Here the ordinary spatial dimensions are in the x-y plane and the z axis represents time since an event. The event is at the origin. The -z axis is thus the past and the +z axis the future.
A particle travelling at the speed of light is represented as a line with slope c [the slope is drawn as slope=1. This is because some people, especially particle physicist like setting everything =1. Other people actually define the z axis as ct instead of t as i said]. This “world-line” defines the “light cone” shown in the diagram. Any world-line represents a path of a particle moving at a constant speed. As we’ve said the slope of the line gives the speed in units of the speed of light c. So particles travelling at v>c will have world-lines outside the light cone. The lines inside, along and outside the light cone are called “time-like”, “light-like” and “space-like” in the jargon of relativity.
Tachyons are the space-like particles. Now one important aspect of special relativity is that everything is relative – you see particles move differently based on your reference frame. If you know what a world-line looks like in one reference frame you can see what it looks like in a reference frame by applying a Lorentz transform. These are just equations that relate position and velocity between two reference frames (discovered by Joseph Larmor and Hendrik Lorentz with Lorentz getting the credit as he had a knack of doing as Ludvig Lorenz would have attested to).
An important result is that Lorentz transforms transform time-like to time-like and space-like to space-like, i.e. if you are in the cone you will be seen differently by different observers but you will always be seen to be moving along a line inside the cone. Likewise if you are outside the cone you will be seen differently by different people but you will always be outside the cone. Now this is very important! As z>0 is the future, z=0 is now and z<0 is the past then this means that if you are moving along a space-like world-line you can simply move to a refrence frame in which your world-line points backwards in time!! You can then send messages back to yourself and others through time!
There are many examples of why this is bad (not in the sense of bad for book-makers, lottery operators, etc. but bad in a logical sense! google the grandfather paradox to see what i mean) and this is why tachyons are held by most as not existing. They are generally viewed as hypothetical objects.
The second thing i mentioned is that they have imaginery rest mass. The energy of a particle is :

But if v>c then the denominator is imaginery (it contains the square root of a negative number). So as energy is not imaginery it means that the mass must be to cancel the imaginery denominator.
It is worth noting that this problem can easily be circumvented by defining the mass* to be:

So the energy equation of relativity becomes:

which basically says that while ordinary particles cannot accelerate to the speed of light (it would require infinite energy) tachyons cannot slow down to the speed of light!
If i think of other basic properties of tachyons i will add them here.

* note that this is perfectly fine to do mathematically speaking

A Watched Kettle Will Certainly Boil…

The saying: “a watched kettle never boils” might upset a physicist or two. It violates all that is good about quantum mechanics. Indeed I would argue that i could round up some people who would take the view that an unwatched kettle doesn’t boil. Surely it is the acting of observation which makes the kettle boil … have you not heard of Schrodinger’s kettle?!
Well anyway why the rant about kettles? Well it struck me as i was making tea for myself that all physicists in the world will have at some time or another watched and timed a kettle boiling. I thought that was a weird thing that people should know!
Why you ask? Well if you know how much water you have and what temperature it is at you can work out how much energy is needed to boil the water. If you time this you get the power rating of the kettle. You can then check this against the value on your kettle to see if you managed to do the calculation correctly. Very nerdy but somebody is probably doing it right now in some high school/college physics 101 class somewhere and that has to make you smile!

Equations … excellent!

Ah so i have figured out how to use equations in my posts! Good old wordpress allows you to use LaTeX (pronounced “lay-tech”). Hmmm i think i will practice …
These are some of the most important equations in physics…

Classical Mechanics
Hamilton’s Equations …



Lagrange’s Equations …

Special Relativity
The Minkowski metric …

Time Dilation …

Fitzgerald-Lorentz Contraction …

Energy-Mass-Momentum Relation …

Electromagnetism
Maxwell’s Equations (in vacuum) …

General Relativity
Einstein’s Field Equations …

The Einstein Tensor …

Quantum Mechanics
The Schrodinger Equation …

Quantum Field Theory
The Dirac Equation …

Astrophysics
The Blackbody Spectrum …

The Stefan-Boltzmann Equation …