Superconductors - Resistance is futile

This post is part of a pub physicists quest to find a new theory for superconductivity. In the previous post I listed some of the well known properties of superconductivity. They are re-listed here;

• Zero resistance
• Meissner effect
• Discontinuity in the Specific heat capacity
• Type I and Type II behaviour, ideally with some values for the magnetic field strengths
• The isotope effect
• The Josephson effect

The most famous of these is probably the Meissner effect, though this is only because of the levitating magnet experiment. For me though the one that really appeals is the zero resistance.

Just think about that, no resistance whatsoever. As mentioned previously, although we can't know for sure that the resistance really is zero, we are fairly confident that it is. All experimentation points to this conclusion.

Now anyone who has done some science at school would have come across Ohms law which can be stated as follows

V = IR or I = V/R

The current (I) passing between two points is directly proportional to the potential difference (V) across the two points. This gives us the resistance (R). All wires have resistance. It is estimated that 6 % of the electricity produced in the USA is lost just transmitting it to the end user.

Imagine if we could transmit electricity with no loss! None, not even a little bit, absolutely no loss. It can be done with superconductors. That's one thing that zero resistance gives us, zero loss. That would be something, because if nothing else it means we could generate electricity anywhere on the planet and move it to the end user anywhere else on the planet without loss.

Anyway, back to it.

Bose with Einstein

One of the great theories of superconductivity, the BCS theory (named after the authors) explains that the electrons in a material pair up, creating Cooper pairs. These are what are known as Bosons. I think this is one of the first great clues, the BCS guys thought this also. Here is why...

The universe can be considered to be made up from two elementary particles, these are your boson and your fermion. Bosons are named after Satyendra Nath Bose. Fermions are named after Enrico Fermi.

The most famous boson is undoubtedly the Higgs boson, which has now taken its place in the Standard Model along with the other four force carrying gauge bosons, the photon, gluon, the W and Z particles.

Here is the thing that makes bosons important to superconductivity. There are other particles besides those just mentioned that are also bosons. Check this out.

Single electrons are NOT bosons 

they are fermions, and behave according to Fermi Dirac statistics (more on this later). They adhere to the Pauli exclusion principle (doesn't that sound cool).

Two electrons can pair up to become a boson

In superconductivity these are known as Cooper pairs. For me this is massive.

In the Standard model fermions are sometimes described as the constituents of matter, while bosons are the force carriers. I can help thinking this is important. If we use this analogy then is it correct to say that a single electron, a constituent of matter, joins up with another electron to create an electron pair that is a boson, a force carrier! We have switched from one type of elementary particle to another.

I'll come back to this in a later post, but I just want to make a note here that an electron pair (bosons - force carrier) can interact with regular electrons (fermions).

OK. So lets take a little look at bosons. They behave according to Bose Einstein statistics, which is a description of how indistinguishable particles may occupy available energy states. Just think of it as how we may stick a load of white tennis balls on shelves.

Back in the day London (we will come to the London penetration depth in a later post) thought that B-E stats may help explain superconductivity. The B - E condensate.

Two bosons with identical properties can be in the same place at the same time (two fermions most certainly cannot). There is NO limit to the number of bosons that can occupy the same quantum state. You can swap two bosons of the same type and the over all system does not alter, we say that the wave function of the system is unchanged. This is like saying you can put an unlimited amount of tennis balls on the one shelf. Can't help thinking I have that wrong.

Another thing I think I may have wrong is this... A photon is a combination of an E field and a B field described by Maxwell's equations. The E and B fields are a 90 degrees to each other and are perpendicular to the direction of motion.

An electron also as an E field and a B field. This time though the E field is perpendicular to the electron and the B field circulates with a standard N/S. Does it really? Going to have to think about this because I think the behaviour of the magnetic field is different in the electron because of gravity/mass, not charge. More on this later.

Previous post
Next post.

I write this listening to Pink, http://www.youtube.com/watch?v=q-XLvUpvjZo. Thanks for that.

Superconductors - what do we know

First evidence of a superconductor

The most famous thing about a superconducting material is its apparent lack or resistance. I say apparent because we will never know for sure that the resistance is absolutely zero. We only know that the most sensitive experiments so far tried have failed to detect any resistance.

Onnes, the discoverer of superconductivity, performed the best test for detecting resistance. He tried to detect any decay in an electric current flowing in a closed superconducting ring. If any resistance to electric current exists then the superconducting current would gradually be converted into Joule heat. No such decay was observed. Variations on this experiment designed to give even greater accuracy failed to detect any resistance whatsoever.

So the first thing we will say is that

superconductors offer no resistance to electric currents

This is true of all superconductors and is one of the tests used to define a superconductor.

Discontinuity in the heat capacity shown in blue

The second thing we will say is that this is not entirely true. If we use an alternating current rather than a direct current then we cannot say that the resistance is zero (more on this later).

If we continue to increase the current in a superconducting wire then we will reach a point where the superconductor stops being a superconductor, this point is known as the critical current. The critical current is temperature dependent and will be examined in further detail later.

Measurements of the specific heat capacity of a superconductor show a discontinuity at the critical temperature of the superconductor.

Any theory that explains superconductivity will have to explain how current can circulate in a superconducting ring forever. 

There was no theories around at the time that superconductivity was discovered that where adequate to explaining this fantastic behaviour. The development of quantum theory has offered a possible solution. Superconductivity is described as a "macroscopic quantum phenomenon".

The Meissner Effect

The second amazing property of a superconductor is the Meissner effect. In 1933 it was discovered that superconductors expel magnetic fields. What this means is that if a metal is placed inside a magnetic field, the magnetic field will penetrate the metal. When the material is cooled and becomes superconducting the magnetic field is completely expelled from the interior of the superconductor except for a very thin layer at the surface of the material. This is known as an ideal diamagnetic state and is another definitive test of superconductivity.

If the magnetic field is increased, much in the same way we discussed increasing the electric current, then another feature of superconductivity is discovered. Some superconductors will eventually stop being superconductors when the magnetic field reaches a critical value, B_C. These are Type I superconductors. Other superconductors allow the magnetic field to start to penetrate the material at a value B_C1, but continue to be superconducting until a second value B_C2 is reached. These are known as Type II Superconductors.

superconductors are perfectly diamagnetic

The magnetic field that penetrates Type II superconductors is quantized. This means that it has very specific values, rather than just random magnetic values.

Not all elements are superconductors. Copper for example. Yet Yttrium Barium Copper Oxide is an example of a High Temperature Superconductor. Below is a list of all the elements that become superconducting. Note that some require high pressure.

Superconductors have different critical temperatures. The critical temperature of an element or material is the temperature that the element or material becomes superconducting. In 1987 the first high temperature superconductors were discovered. These ceramic materials had critical temperatures in excess of 100 K. No superconductivity theory can explain temperatures this high.

different isotopes of an element have different T_cs 

The final property of superconductors will be mentioned here is the Josephson effect, which earned its discoverer Brian Josephson the Nobel Prize. This will be covered in detail later, but is such an important property of  superconductivity that it gets a mention here.

The Josephson effect predicted how two superconductors should behave if they are separated by a thin insulating material. The idea depends on quantum mechanics and was found to be true.

So to round this all up. Any theory of superconductivity has to explain the following;

• Zero resistance
• Meissner effect
• Discontinuity in the Specific heat capacity
• Type I and Type II behaviour, ideally with some values for the magnetic field strengths
• The isotope effect
• The Josephson effect
• The maximum critical temperatrue

That's enough for starters I reckon.

Link to previous post
Link to next post

This post was written while listening to Jimi Henrix. http://www.youtube.com/watch?v=G3VOLJPcldM. Thanks Jimi.

Things you agree to down the pub

Onnes - the bloke who
started it all

I was having a bit of a ponder the other day with my mate Max. After a glass of the red wine or a pint or two of the black stuff, also lovingly known simply as the Pint, I often wax lyrical about that favourite subject of mine, physics.

Depending on the mood this could be any of the great topics, though recently it was superconductivity. Now I have previously done a couple of introductory posts on this subject and was planning another in a similar vein, but this all changed after some serious reflection last weekend.

See the problem with superconductivity is that there is no accepted theory to explain it. Even though it was discovered 102 years ago (and counting). The best theory came about in the 1950s, the BCS theory, almost 60 years ago and was considered a major success. It was a brilliant theory.

It had one small draw back. The theory predicted that the highest temperature a material could achieve while remaining a superconductor would be about 30 Kelvin (-243 C). In 1987 someone discovered Yttrium Barium Copper Oxide, a ceramic material that was superconducting at 93 Kelvin. I could imagine the conversation going something like this.

"BCS theory, brilliant you know, explains superconductivity."

"Yes...Bit of a problem there though"

"Really, what?"

"New superconductor, YBCO, 93 Kelvin"

"You sure?"

"Yep, Meissner effect, zero resistance, the lot"

"Well that blows BCS out the water"

"Yep, certainly does"

"Well, you win some you lose some, not like they got the Nobel Prize or anything"

"Ah..."

"They got the Nobel Prize? ... But it's wrong!"

"Yes, but we didn't know that at the time"

"Bugger!"

So, the best idea we had turned out to be wrong, but to be fair, it is a great idea... just wrong. Shame that, or is it? because it brings me back to the post and the pondering that went on last Saturday.

It occurred to me that if the most brilliant minds in physics can get it wrong, and have yet to get it right, how would some bloke down the pub fair, if he decided to have a serious go?

So here is the challenge that will occupy a fair number of up and coming posts.

Can a pub physicist really come up with a new theory for superconductivity? If I was a betting man, I would have to agree that this is a bit of a tall order. If those brilliant minds can't crack it then how is some inebriate going to unravel one of the most profound mysteries of the universe over a pint of the black stuff?

Well, I am not to sure, but as someone once said you have to be in it to win it. So to quote another phrase I shall toss my hat into the ring and announce here and now that I am going to find a theory for high temperature superconductivity. I shall report on my progress in this blog.

So were to start... while the majority of ideas on superconductivity are wrong, this may be a reasonable place to start. After all don't want to make the same mistakes as others. Taking a look at what we do know about superconductors may also be something of interest. My theory is going to have to explain every single one of the phenomena so far observed, so I best know what they are.

OK, existing theories and existing experimental results. That's probably enough for now and will no doubt fill a post or two and that is were I shall start.  See you soon.

Next time, so what do we know about superconductors?

One last note. Not only must the theory be right, but it also as to be so simple as to be able to explain it to a 7 year old, if that can't be done then chances are the theory is wrong.

Superconductivity part 2

High Temperature Superconductor

A while back I did an introductory post on superconductivity. In this second post I am going to dig a little deeper into this wonderful subject to describe the Meissner effect and its consequences.

Briefly, a superconducting material will exclude any magnetic field during its transition to the superconducting state. If the material is already superconducting when a magnetic field is applied it will set up an electric current near the surface. The magnetic field associated with this surface current will cancel the applied magnetic field. This is the Meissner effect and was discovered in 1933 by Walther Meissner and Robert Ochsenfeld. Meissner was the boss, so he got the credit!

Above it's critical temperature, T_c, the temperature at which it becomes a superconductor, a superconductor is just a regular material, for metals it behaves Ohms law for electric flow etc.
At  T_c, we have something called a phase change (water turning into ice is a phase change), at this point its resistance drops to zero. In addition it becomes a perfectly diamagnetic.

Diamagnetic materials are those that create a magnetic field in opposition to an externally applied magnetic field. For many materials this diamagnetic effect is very weak, and the magnetic field goes straight through the material. In superconductors the magnetic field is completely expelled from the interior of the superconductor. The magnetic field penetrates a very thin layer of the superconductor known as the London penetration depth. This is named after the two brothers who discovered it.

Furthermore, it was realised that the superconducting current does not travel through the body of the superconductor but in a thin layer of the material, which is the London penetration depth.

So imagine, we have a magnetic field penetrating our material. The temperature drops and we reach T_c. At this point things start to change. After the change and when things have settled we have an electric field expelling the magnetic field, the Meissner effect.

Above T_c we have magnetic field through the material, no current flowing. Below T_c we have no magnetic field in the material because we have a current flowing that cancels the field. So during the phase change we witness the creation of an electric current to cancel the magnetic field. 

Although we have now known about this effect for coming up to 80 years there is no dynamical explanation of the Meissner effect with the conventional understanding of superconductivity. We know what happens, the expulsion of the magnetic field. We cannot explain the stage when the super-current (this is the current that flows without resistance) goes from zero in the normal phase to the steady current required to exclude the field in the superconducting phase.

Many of the great minds in physics have had a go at this one including Einstein and Feynman and they have all failed to find a solution.

It may come as a surprise that we cannot explain what is probably the best known property of superconductivity. So let's have a little think and see if we can actually figure out just why it is so difficult.

Well it is difficult because we don't actually have a working theory for superconductivity, we have some good guesses and a real good theory called BCS (Bardeen, Cooper, Schrieffer - the authors), but none of them really hit the mark.

We do know an awful lot, but it just doesn't give us the clue we need to get a real break through. We may be just waiting for that single piece of information that opens the door and gives us a solution. Though the same argument could be applied to many areas of Physics.

I decided to cut this post short, I'll explain why later :-)

Neutrons - Part 2

A neutron as 1 up and 2 down quarks

A while back I did a post on neutrons. I have always had a bit of a soft spot for the neutron because while it may seem a little dull, having no charge and all. It is actually an amazing particle.

A neutron is one of the three basic particles we learn about at school. The others being the proton and the electron. We are taught that all atoms are made up of these 3 particles. Great, no problem there.

The neutron, if it finds itself outside of an atom, (say it has been kicked out during the radioactive decay of something like Uranium 235) actually gives up the ghost and changes into a proton, electron and an anti neutrino, represented by this ...

n0 → p+ + e− + ν
e

What I find amazing though is the following. If we assume that the Big Bang was correct then we are fairly confident that a besides a load of electro magnetic energy we got some very basic particles, protons, neutrons etc.

Your basic hydrogen atom as a single proton at its centre. The water you drink is made up of molecules consisting of 2 hydrogen atoms and one oxygen atom, good old H₂0. These protons were probably produced 13 billion years ago at the start of everything. Mind blowing. There is more though. At the beginning some single protons joined with single neutrons to produce a hydrogen atom that we call deuterium and give it the letter D. Hydrogen is the only element that has more than one symbol.

D can form water molecules, D₂0. In fact 1 in about 6500 water molecules is made of D₂0. A glass of water contains billions and billions and billions of molecules of the stuff. It is thought that most deuterium was also created soon after the big bang! This stuff has been around for ages which brings me back to neutrons.

What happens if we manage to pop another neutron next to the proton and first neutron? well we end up with Tritium, this does decay with an average half life of about 12 years. So

protons are stable
neutrons are not stable
deuterium is stable
tritium is not stable

when a neutron decays it does so as shown above. Although some think that this is not actually true, what really happens is this

n0 → p+ + W−
W−→  e− + ν

The W particle, is a really, really short lived particle which decays rapidly into the electron and the anti neutrino. By short I mean about 10^-25 of a second. This is way to small for the brain to even contemplate. It got me thinking though, inside Deuterium, does the neutron decide to behave itself? Does it think, I've got a proton buddy don't think I'll bother with any more of this radioactive suicide? Or does it pull a little bit of body snatching I wonder.

Imagine if the neutron does actually decay as I've described above, but after the first step

         n0 → p+ + W−

The W particle thinks "No chance mate" and instead of decaying into the electron actually pounces on the other unsuspecting proton like so

         p+ + W−→ n0 

So we still end up with a single proton and a neutron, only now they have swapped places. Then, a little time later, they do the same dance back. How cool would that be these two little particles doing this dance over and over for billions of years.

Now, imagine the centre of a very large star that is just in the process of undergoing a catastrophic collapse. Most of its fuel has gone and gravity is starting to crush the atoms, closer and closer and closer together. Space-time is getting all bent out of shape and then atoms themselves start to collapse. Electrons actually get pushed into the nucleus, react with protons and produce neutrons. This goes on and in no time at all we have a star that is now only about 20 km across and consists entirely of neutrons.

Lots of people struggle with the last part, after all, electrons have the opposite charge to a proton, since opposites attracted they should jump on each other. But here is one of those really strange things that are "explained" using quantum mechanics. so why don't they just jump on each other, I'll save that one for another post. Suffice to say that to get an electron into the nucleus of an atom you have to put on some tremendous pressure, like the type you get inside a collapsing star.

So now we have something really amazing, a neutron star. Which is pretty much just a super enormous nucleus consisting of loads of neutrons. A nucleus with a radius of about 10 km. The gravitational pull of this star at its surface is about 100 Billion times stronger that on earth, a number far to big for the brain to understand. The gravitational field is so strong that it bends light so much that if you are looking directly at the star you can see some light from the far side! That would be like looking at the moon and being able to see some of the far side, even though it is still on the far side!

Neutron stars spin many times a second, again I find this incredible, these massive objects some spinning hundreds of times a second. The angular momentum is just huge.

I'll end this post pretty much were I started, the decay of a neutron into a proton and an electron. In about 1 in 250,000 of these decays the electron does not have the energy to completely escape the proton and the result is a hydrogen atom.

What I wonder is this... if neutrons can decay into hydrogen atoms, then was there any need for protons to be produced in the big bang? couldn't it just have been a shed load of neutrons, that decayed very very rapidly a short time after.

With a half life of just shy of 15 minutes, even if every particle produced by the big bang was a neutron then within 15 minutes half of them would be protons. Within an hour we would have less that 7% of the free neutrons still in existence. By the end of the second hour this would be less than half of 1%. The big bang theory doesn't think this is what happens, in that theory there are protons as soon as particles begin to form and most of the neutrons join up with the protons to form Deuterium and Helium nuclei, not sure I am convinced.

So there we have... the humble neutron.

Expanding Universe

Not all space-time is the same

Recent experiments seem to show that the universe is actually expanding faster than we initially thought. In fact the universe is actually accelerating in its expansion.

This causes a bit of a problem though. In a previous post I mentioned Newton's second law. This law basically says that to accelerate something you have to be giving it a shove. So the question then arises as to what is actually giving the universe a shove? If it is accelerating then some force must be in play.

I have no problem with an accelerating expanding universe. I quite like the idea because it gives us something to think about. It's not supposed to be that way, so we must have something wrong. It is just a question of what?

We measure the speed that galaxies are receding using a technique called red-shift  This can be explained as the Doppler effect on light. All atoms emit light radiation at very particular frequencies when an electron drops from an excited state to a lower state. This amazing property that I shall cover elsewhere allows us to determine some of the elements in stars.

If a star is moving away from us then it was discovered that the frequency of the emitted light tended to be shifted slightly towards the red end of the spectrum. Taking this a step further it was realised that the amount of this shift was dependent on the speed that a star or galaxy was receding from us. The faster the stars or galaxies are receding the greater the red shift.

This is not all though, oh no my friend, see there is more, we know the universe is expanding, Hubble proved this back in the day, and it was soon realised that there may be an additional red shift due to the fact that gravity can cause red-shift in light. An explanation for this can be found in General Relativity and experiments show that it real. Basically the higher the gravitation field the greater the red shift in the light escaping.

I could be wrong about this but it seems to me that we assume that space-time is the same in flat space. Flat space are those regions were there are few stars, the space between galaxies. There is an awful lot of this by the way. Seriously, there is a lot of the universe that just appears to have practically nothing in it. You want to find something close to the perfect vacuum... deep space. We are looking at 1 atom in a cubic meter of space, compare this with the best vacuum ever achieved on Earth. The best we vacuum we have achieved on Earth has about 100 million atoms per meter cubed. That is a fantastic vacuum by the way.

There is virtually nothing in deep space, I am serious, talk about the void, this is it mate and the amount of it is beyond the imagination of everyone. You might think you have a great imagination, but it is nowhere near capable of imagining the vastness of deep space.

Another thing is that we are working on the basis that our interpretation of the current observations of red-shift are correct, in other words the current theories are right.

OK so lets tackle these in reverse order.

The theories are correct. Well here is the thing, almost all of them are bound to be wrong. There are so many things we simply can't explain already, small galaxies that appear to have super massive black holes, 4 billion solar masses no less, galaxies that don't appear to behave Newton's laws of gravity even though they should! This madness actually gives rise to the idea of dark matter and dark energy. So are the correct... no, so if they are incorrect then chances are they may have a fault or two when it comes to red-shift.

Yes this is a bit of a cop out, but I genuinely think that the way we are measuring red-shift may be an issue, which brings me to point one.

I was on a ship once that crossed the Drakes Passage, it is an area of sea south of Argentina (named after Frances Drake, an English privateer, a pirate,  who knew a thing or two about sailing). This sea is where the Pacific meets the Atlantic oceans.

Now to the ignorant, namely me, sea is just sea, it's water, salty water. This is not the case though.  There is a very clear point where the Pacific meets the Atlantic and the salt concentration in the water is different between the two seas. Not only that, but where the world meets Antarctica there is a detectable sharp drop in the temperature of the water. This was a bit of a revelation to me because I'd wrongly assumed that sea water was pretty much the same. Not so and this got me pondering.

It occurred to me that something similar could happen in space. Image regions that have a greater concentration of energy than another region, much in the same way that galaxies contain a far greater concentration of mass than deep space, where there is practically none. Now I would have thought that given enough time, the balance of salt between the pacific and Atlantic oceans would balance out, but no. Something (the Amazon basin probably) is reducing the concentration of salt so it never matches up to the pacific ocean.

Again, imagine if something like this is occurring in space. So one region is continually being topped up, or depleted compared with another.

Now if something like this did take place then the regions of space-time may actually be different and their properties with regard to the way light propagates may be different. My thinking then is that the results we see may be erroneous because we are assuming the space time is linear and constant in the regions of deep space, when actually it may not be. Imagine if there are similar sharp changes between space-time depending on where you are in the universe?

So to try and some this one up, what I may be saying (bit of sitting on the fence here) is that the idea of the universes expanding faster than it should could actually be wrong. The observations are clear, but our interpretation of them may be skewed because space time is not flat in the way we think even in deep space. You can have two flat regions with a clear gradient between them. This gradient, or the different nature of the regions of space-time causes some of the light shift itself, thus distorting the results.

I am just having a play with the Doppler equations for red-shift, if I find anything interesting I'll post it later.

Newton's second law

This short post is a little break in my current series on light. It came about because I got to thinking about Newton's law of gravity, which got me thinking of Newton's laws of motion. Which got me thinking about Newton's second law of motion.

Newton's second law of motion results in one of my favourite equations of all time. It is fabulously simply and yet gives one of the most profound insights into the nature of the universe.

You may be thinking at this point that I am getting a little carried away, but I don't think I am and here is why.

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.


This was how Newton first stated his second law. According to a Wiki entry the modern equivalent of this is

The change of momentum of a body is proportional to the impulse impressed on the body, and happens along the straight line on which that impulse is impressed.

This just doesn't do it justice though. Now, if you have read any of my other posts you may have noticed that I sometimes have a bit of a moan about mathematics and its place in science, but on this occasion I freely admit that only mathematics allows us to do write this law in a manner that portrays its true wonder. Here it is (see the image above if you haven't already guessed) ...

F = m a

F - force applied
m - mass of the object
a - acceleration.

That is it. That is all there is to it. A single line with only 3 terms.

It tells is that the resulting acceleration is directly proportional to the applier force.

This means that if we push an object it will accelerate away from us. If we push it twice as hard it will accelerate at twice the rate. Push it 10 times harder and it will accelerate 10 times faster.

It also tell us that if the object as twice the mass then we need to apply twice the force to get the same acceleration.

Let's just have a think about that for one minute. We live in a universe where if we push something it will start to accelerate, once we stop pushing it will immediately stop accelerating, although it will continue moving at the same velocity, unless acted upon by another force, friction for example.

This is how the universe works!

What is odd for me is that these days we have something called the conservation of momentum and we can derive Newton's second law from this, so it sort of makes Newton's second law redundant. It is no longer "required" in fundamental theories within physics.

Personally I think this is a mistake. See what we appear to be saying is that Newton was undoubtedly brilliant for point out his second law. But it is not really necessary after all.

It is true that we can derive the above result from conservation of momentum, but I think this actually robs us of something because we are not seeing force any longer.

We are seeing momentum and energy and this does give us some greater insight.

In a way though I think that while we are able to see the trees in far greater detail, we are maybe losing site of the knowledge that it is a forest and what this can tell us about the over all system.

F = m a

how utterly simple, how amazingly brilliant.