Thursday 6 December 2012

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.

Saturday 1 December 2012

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.

Wednesday 28 November 2012

On the nature of light - part 2

Einstein's General Relativity
In a previous post titled "On the nature of light - part 1" I began a discussion on what a photon my look like if I were also travelling at the speed of light. Later in the post I began wondering about gravity, which is what this post is about.

Einstein realised that gravity could have some profound effects on light. Probably the best known is the bending of light near a star.

The the idea for an experiment to confirm this is one of my favourites. The most obvious large object, capable of bending light according to Einstein's theory of general relativity, is our sun. The problem of course is that it is also remarkably bright and any stars near it are lost to its glare. The solution depends on one of those truly remarkable quirks of nature, the lunar eclipse. During a full eclipse it is actually possible to see stars near the edge of the sun.

So we measure angles between stars really close to edge of the sun and some further out. We then repeat the same measurement some time later after the sun as moved round and the stars are no longer in the direct line of site. The idea being that if light is being bent then the two angles, before and after, will be different.

Bending of light (Exaggerated) 

The result was that the angles actually change and by an amount predicted by Einstein. Which is simply amazing. The explanation for this phenomena is that space-time is actually warped by gravitation fields and so the path of a light ray will also be warped. What a mind blowing idea that is!  It is particularly odd if you find yourself in a box in space.

This wasn't the only effect gravity has on light. Another absolute beauty is gravitational red shift. Imagine standing in a long lift shaft and shining a torch upwards.

According to Einstein the difference in the gravitational pull on the light is different at the bottom of the shaft than at the top. This change in gravity causes time dilation.

What this means is that two clocks, one at the bottom of the lift shaft and one at the top run at slightly different rates, even if they are identical clocks. What this means for the light shining up the lift shaft is that the frequency of the light is shifted slightly to the red end of the spectrum.

Shining the light from the top of the shaft to the bottom of the shaft has the opposite effect and in this case the light is shifted to the blue end of the spectrum, known as blue shift.

Great, so let's give it a go. There is a slight problem though, the amount of shift is very very small and is difficult to measure. The solution was an experiment by Robert Pound and Glen Rebka using an idea known as the Mossbauer effect (I'll cover this in a post of its own at a later date).

What Mossbauer had realised was that atomic nuclei can emit gamma rays that can be absorbed by a second atom of the same type. What Pound and Rebka realised was that if this gamma ray went down a lift shaft then its frequency would change just enough that it would no longer be absorbed.

They took it one step further and realised that if they moved the source of the gamma rays at a particular speed they could cancel out the shift due to gravity with a Doppler shift (I'll cover this one later as well!) and the gamma ray would once again be absorbed by the atom at the bottom of the lift shaft!

They performed these experiments using a radioactive type of iron, Fe-57, and sure enough it came out as predicted by Einstein. This was a fantastic result, and shows just how brilliant Einstein was.

Many theories try to explain phenomena that we have already witnessed by experiment. Einstein's theory not only explained what we had already seen, but went further to make predictions about things we had not seem, yet were found to be true.

In a way this is what makes things both interesting and difficult in physics. General relativity has been tested by experiment and found to be true. So has quantum mechanics. Quantum Electro Dynamics (QED) has been tested to a higher degree of accuracy than any other theory. The problem is that it has not been possible to reconcile these two different theories. One works on the macro, the other, the micro.

So, we were discussing the nature of light and somehow we have staggered into gravity! Really, this is the point of this post. Irrespective of the physical phenomena, bending of light, red or blue shift gravity, gravity has an observable effect on light. Which means that it must be having the same effect on individual photons of light.

Now it can be argued that gravity is distorting space time and it is this distortion of space time that we are observing when we look at how light is effected by gravity.

I am not completely convinced by this and the reason is that I don't think it is possible to separate out space-time and light. I think that the two are intrinsically linked. It will be this link that I will be covering in the next post on the nature of light. It is this link that I think shows that light must have a gravitational component.

Then again, I could be completely wrong!

Sunday 25 November 2012

On the nature of light - part 1

Gravity waves, I think not.
Years ago I read a book that said that Einstein had once pondered what a wave of light would look like if you were travelling along side it. Now we know that light is an electromagnetic wave that and can be described by Maxwell's equations. 


Einstein, so the story went, started looking for solutions to Maxwell's equations that would describe a stationary light wave, and found that there is none. This lead him to do some serious pondering that brought him to the Special Theory of Relativity. A serious result! For me though this was a bit of a sad ending.

For many years I have imagined light travelling through space in a kind of spiral motion and I wanted to know what would happen as I got faster and faster until I was chasing the photon at the speed of light. I know that I have mass and so I am forbidden from travelling at the speed of light, but say I was a photon and so I was a photon chasing a photon, I have always wondered what would it look like. In addition to looking at the photon ahead of me, what would I see if I actually stopped and had a look at the universe

Now I know there is no point in going back to Maxwell's equations because Einstein, a far finer mind than my own, had already been there and discovered there was nothing doing. So that was out, then I got thinking about Louis be Broglie. I have always had a soft spot for de Broglie if only because a physics teacher of mine was really jealous of this guy for some reason I never understood. 

Louis came up with the idea of wave-particle duality, giving us this equation





where
is the wavelength,
is the Planck's constant,
is the momentum,
is the rest mass
is the velocity
is the speed of light in a vacuum. 

If we consider a photon, the value of   is  and so the equation brakes down since   becomes zero. If your maths is a little weak, this is because the last part of the equation, the  /  part becomes 1, and 1 - 1 = 0, and anything multiplied by zero is zero. So   becomes zero. 

We know that electrons can behave like waves and photons can behave like particles.

So back to my photon, I think that if I am travelling at the speed of light directly behind my friend the photon I see the photon as a type of standing wave. If the wave is travelling in the x direction then the standing wave exists in the y/z plane.

Conventional thinking is that the magnetic field induces an electric field and the electric field in turn induces the magnetic field and it is by this mutual induction that the photon travels through space (see equations 2 & 4 below for the mathematical representation of this sentence!). This seems to be the way, but I can't help thinking there is more to it than this and I'll explain why I think this.

Gravity.

We know, from experiment no less, that light can be bent when it passes by a star. This was what pushed Einstein to public fame because he had predicted this. The light bends because space time is bent and light just travel along the most direct route. This is gravity at work.

Fine, but here is the thing I think that light as an additional component to the electric and magnetic fields. I think there is another component, gravity.

I have several reasons for thinking this, though the first is that gravity waves, if they exist, travel at the speed of light. Just like light. I just find it too coincidental that gravity waves and light waves both travel at the speed of light. Now you can argue that the theory of  general relativity is derived using the speed of light as a constant and that the speed of gravity waves comes out of this. I would turn this around and say that the reason gravity waves travel at the speed of light is that they are actually a component of light.

Gravity waves have never been detected, I find this amazing given the amount of effort that has gone into actually finding these fellas. Maybe we are looking in the wrong location and in the wrong way. I think that there are gravity waves but they are different to what we actually think. More on this in the next post.

So Maxwell's equations, now I know I said that I was not going to go anywhere near these. After all, finer minds than mine have already gone down this road and found it a dead end, but I can't help thinking I just need to take a quick look.

Let's consider the Maxwell equations for an electro magnetic wave in free space. It goes something like this,









don't worry about the meaning of these at the moment, we will cover them in the next post. My point in actually listing them is so that I can point out that there is something else. See I think there is an extra term that needs to be added to these equations to represent gravity.

But! I hear you cry, photons, don't have mass, so it doesn't make sense to even consider gravity here. I think this is were we have are going wrong, and in the next post on the nature of light, I'll show you why.

To finish this post though I want to point out a few "similarities" between gravity (G) and electromagnetism (EM).

EM - Coulomb's law. F = qE
G - Newton's law F = ma

G and EM both act in a vacuum
Both obey the inverse square law (more on this next time, suffice to say they both have an inverse square law).

True there are a number of differences.

Gravity is always attractive, particles with similar charge repel each other.
Electromagnetic forces are considerably larger than gravity IF we compare the electro static repulsion of two electrons with the gravitational attraction, based on existing theories.

I think we need to explain the differences and also explain the similarities, and this I will try to do in my next post.

Coming soon to a cinema near you!

Monday 19 November 2012

Radioactivity

Marie Curie - winner of two Nobel prizes
Recently I did a bit of a general post on atoms and atomic nuclei, which got me thinking about radioactivity and nuclear magnetic resonance (NMR). The first of these, radioactivity, I am going to post about here, the other, NMR, I'll do in a post shortly.

While Rutherford was undoubtedly one of the great contributors to the study of radioactivity, I think that the most famous must be Marie Curie, Nobel Prize winner in both Physics and Chemistry, the only person to win two prizes in the sciences.

Curie discovered polonium and radium. These elements provided Rutherford with the materials he need to do his great works. She came up with the name Radioactivity. She was also instrumental in the development of the use of X-rays in medicine. The Red Cross actually made her head of its radiological service.


Today there are numerous schools and institutes bear her name. Her research and long term exposure to radioactive substances would eventually cause her cancer that would ultimately kill her. Cancer research and cancer charities now carry her name.

Albert Einstein once remarked that she was probably the only person not corrupted by fame. What a superstar!

Marie Curie I think you are great.

I also think Radioactivity is great because it features the nucleus of the atom, that magnificently tiny speck at the centre.

Apart from Hydrogen, which is a bit of a special case in many ways, all nuclei consist of combinations of protons and neutrons. It is the protons in the nucleus which determine what element we are dealing with. For example, any atom with 6 protons in the nucleus is Carbon. If it had 7 protons it would not be Carbon, it would be Nitrogen.

Carbon typically has 6 protons and 6 neutrons, but it can have 8 neutrons, this is C14. Nitrogen usually has 7 protons and 7 neutrons, so it is N14. N14 is very similar in mass to C14, but it is the difference of just 1 proton that changes everything and gives us two very distinct elements. There are NO two elements with the same amount of protons. Though there are some with the same amount of neutrons.

Isotopes are variants within a single element, by this we mean that an element can have atoms with a different number of neutrons, eg Carbon 12, Carbon 13 and Carbon 14 are said to be isotopes of Carbon.

Some isotopes are found to be unstable and are known to be radioactive. They can undergo a reaction resulting in particles being ejected from the nucleus. The most common types of radiation, are alpha, beta and gamma radiation. There are certainly more than this, including proton emission and neutron emission.

The names alpha, beta and gamma are from the Greek alphabet and were used by Rutherford and Villard to describe the different types of radiation they had witnessed in experiments. At the time they had no idea what they actually were. It took Rutherford 7 years to prove that alpha particles were actually the same as a Helium nucleus. The beta particle was known to be far more penetrating than the alpha particle, but again it took a considerable time to prove it was in fact and electron.

The realization that a beta particle was an electron was a major discovery because it showed that electrons can originate from a nucleus, even though a we know that the nucleus only contains neutrons and protons. This in turn lead to the idea that a neutron can decay into a proton and an electron that is then ejected as a beta particle.


It was Villard who discovered gamma rays while studying radium in 1900 and it was Rutherford who gave it its name in 1903, these are not particle but are high energy light waves, so energetic that they can go through a fair amount of lead shielding!

The discovery of radioactivity and its associated properties lead to a rather astonishing idea and it was that it should be possible to use this behaviour to calculate just how old the earth is! The idea was dreamed up by Rutherford, who you may have gathered was a bright chap, in 1905, the same year Einstein was publishing is ideas on Special Relativity.

Rutherford realized that radioactivity was due to some atoms changing into lighter elements and emitting alpha, beta or gamma radiation. They also discovered that particular "isotopes" of a specific element decay at a distinctive rate, now called its half life.

Imagine you had a billion atoms of Uranium 235, the half life is the time it takes for 0.5 billion of them to decay into something else. It turns out that Uranium and thorium have very long half lives and so stay for long long periods, which is why they are so difficult to manage when we take them out of nuclear reactors.

Rutherford figured that it may be possible to work out the age of the earth from the relative proportions of radioactive materials in rock samples. This is slightly trickier than you might think because some of the particles that are produced by the radioactive process are themselves radioactive and decay! So you end up with a sort of family decay tree, with parents, children, grand children and so on.

In the following 50 years this method was investigated and refined, there are about 40 different techniques that have been used working with a fairly large variety of radioactive materials.

The results put the earth at about 4.5 billion years old. Which is only about 1/3 the age of the known universe, but similar in age to the sun, it was thought to have formed within 100 million years of so after the sun.

100 million years! You pop it in a sentence as if it is nothing, but think about that for one minute. 100 million years after the sun fired up with think the earth formed. The earth has been here for about 4.5 Billion years! the is a period of time that is just so far beyond our imagination.

Atoms on earth have been undergoing radioactive decay for about 4.5 billion years. That is loads of atoms undergoing loads of decay and it is still going on. We still have radioactive elements in the earth. For all that time, this process has been going on and on and on.

It really does stagger my brain. I think I need to go for a lie down!

Monday 12 November 2012

twisting the light away

Twisted light
Most people these days know that light is made up of photons, while we are still a little vague on what a photon actually is, we know that light is made up of them. It is the most basic unit of light, we think.

Light, has no mass, but does have energy and more importantly to this post, it has momentum. In fact, you can use this property of momentum to help derive Einstein's most famous equation E=mc2. A photon actually has two components of momentum. The first is one that many are familiar with, spin angular momentum, or polarisation to you and me. It is the polarisation of light that allows us to make some really clever things like 3D TVs using 3D glasses.

It also has something called orbital angular momentum, the earth going round the sun as orbital angular momentum, which some people think is a good analogy. Can't say as I do, because I can't see what the photon is orbiting!

Anyway, this property of orbital angular momentum (OAM) as got everyone in a bit of a spin because if it is in fact true, then there may be a really clever way of using this property to transmit loads of information. Which would come in very handy, mainly because we are currently running out of bandwidth.

The problem is that lots of people have lots of smart phones that can download lots and lots of information. As demand for higher definition images and faster download speeds increases the available bandwidth shrinks and shrinks and will at some point run out. May be not...

OAM potentially offers the ability to reinvigorate bandwidth, if the theories are correct there is the opportunity to tap into a massive reservoir of bandwidth which will keep us happy for at least a couple of years. Not everyone believes this is true though. Some physicists do, particularly those currently doing research in the field, others don't.

An experiment, a very public one, sent data across a Venice lagoon at a tremendous bit rate. There is little doubt about the transfer rate, up in the gigabit range. What I find really interesting is that some of the detractors think that the interpretation of the experiment is wrong. They don't think we are seeing OAM, they think we may be seeing something called Mimo, multiple input multiple output transmission. Mimo has been around since the 70s and some of the latest WiFi technologies, the 802.11n, type that you get in your latest routers exploit this technology.

So who is right, and how can anyone actually get this wrong? after all wouldn't it be obvious? Well, this is were it all gets a little human, shall we say. The Physicists involved are saying the engineers don't understand the physics. The engineers are pointing out that when it comes to telecommunications the physicists don't understand and that this is nothing more than telecommunications.

In fact the engineers go a step further and say that all the physicists did was replicate Mimo and if they try to extend their work they will realise that it does not work as expected, because it is not OAM.

We shall see.

While I feel a certain allegiance to the Physicists can't help thinking the engineers may be right on this one. Maybe that is because I haven't read that paper on Poynting's vector, I'm going to read it now and will get back to you later.

Tuesday 25 September 2012

Elements

The Periodic Table
Just about everyone is familiar with the image of the periodic table.

Even the name is familiar, you say "periodic table" to some one and chances are, providing they have had some education, they are likely to picture something that looks a little like the image to the left.

I have always loved the periodic table, when I was a kid and I first saw one in a class room I was instantly struck by just how beautiful it was. In those days there were 103 elements, the last being Lawrencium named after Ernest Lawrence the Nobel prize winning physicist who had quiet a lot to do with radioactivity. These days there are more than 112, the last being Copernicium.

Livermorium at 116 has been added as of May 2012, so far 35 atoms of Livermorium have been produced in the 12 years since it was first discovered!

The periodic table as it is now was first dreamt up by Dmitri Ivanovich Mendeleev and presented by him in 1871, it looks a little different to the modern day, but that is partly because there were only 56 known elements at the time.


What fascinated me about the periodic table was that it listed each and every element that makes up the known universe. All in one little table. Each element having one more proton than its predecessor. The elements are stacked into rows consisting of 2 elements, H and He, then 8, that's Li through to Ne, then 8, then 18, then another 18, then 32 and finally the remaining 25 to make a total of 112. If we get as far as element 118 then chances are we will have to start a new row.

Carbon, which gives us diamonds the hardest known material, sits right next to nitrogen which is a gas! Yet the differ by only a single proton. Potassium, the highly reactive metal that burns with a purple flame has only one more proton than Argon, a gas. Some of the elements become superconducting when cooled, others do not. Some are great at carrying electricity, others are semi conducting or have insulator properties.

The chemistry of the elements seems to be governed by the number of electrons each atom has around it, this is governed by the number of protons, the number of electrons being equal to the number of protons in electrically neutral atoms. While this makes sense in a way, it is still quiet staggering when you consider the differences between the different elements.

Some elements have radioactive isotopes which means that can undergo some form of particle emission from the nucleus and turn into another element. Some of the large atoms, Uranium for example can decay into two elements!

What I also find completely mind blowing is that apart from Hydrogen and Helium, which we currently believe have been here since the beginning of the universe, and excluding those that have been made in the lab, the rest were actually made inside stars.

Every atom that makes up our bodies is listed in the periodic table. We are mainly made from Hydrogen that has been here since the beginning of time. There may be atoms in your body that are 13 Billion years old and were there to witness the birth of the universe (that is if the Big Bang theory is correct!).

How cool is that, to think that we contains atoms of Hydrogen from the very beginning of the universe. Know wonder there are some days I feel old, it's because my constituent parts are really, really, really old.










Tuesday 11 September 2012

Beta emissions and quarks, really?


Up becomes down and out comes a positron
All atomic nuclei are made up of different numbers of protons and neutrons, the different combinations of protons and neutrons give us the elements and their isotopes.

Radioactivity is the emission of particles from the nuclei of atoms.


Of all the different types of radiation, I think my favourite is probably beta emission and it is this I am going to talk about in this post.


Beta emission is where an electron, or a positron, is ejected from the nucleus of an atom. Now for those of you paying attention, I am sure you have just raised an eye brow and thought, "hold on a minute, you said that the nucleus is made up of protons and neutrons, no mention of electrons there!" and this is absolutely true. There are NO electrons in the nucleus of an atom. None whatsoever and yet, they can still be ejected from the nucleus!

I think this is absolutely fantastic.

Many believe that we can view a neutron as a proton and an electron bound together. By that logic, positron emission, the emission of a positively charge electron, implies that a proton is a positron and a neutron bound together. This is not right.

The current thinking is that protons and neutrons are actually made up of quarks. This is part of the Standard Model, which appears to have had a rather spectacular result recently with the discovery of the Higg's boson.

Quarks can change and as a result of this change electrons or positrons can be produced that come whizzing out of the atomic nucleus.

Take Fluorine 18, this has 9 protons and 9 neutrons. The stable form of fluorine is fluorine 19, 9 protons and 10 neutrons. The extra 1 neutron in fluorine 19 makes it a happy bunny. But fluorine 18, completely unhappy and it shows this by kicking out a positron, like so

18F -> 18O + e+

one of the protons has changed to a neutron, so only 8 protons remain, and the 9 neutrons become 10, making it an Oxygen atom. Oxygen 18 is also a happy bunny and does not decay any further.

So, this is the thing that I am going to be pondering for the next week or two, Fluorine 19 - happy, Fluorine 18 - unhappy, Oxygen 18 happy. One neutron difference between F19 and F18 is enough to make the second, F18 unstable. It seems that the neutron has a calming effect. Will ponder this in a later post.

Now, to finish, fluorine had 9 protons and 9 electrons to balance it out. Oxygen, the final product, only has 8 protons so only needs 8 electrons to balance it out and make it electrically neutral. So what happened to that extra electron?

Well, maybe, the positron, which is the anti particle of the electron, interacts with the extra electron to form something that we could call positronium. The two particles could then annihilate each other and decay into gamma rays.

Now that would be really cool.

Sunday 9 September 2012

Size of an atom

Helium nucleus surrounded its electron cloud
The size of the atomic nucleus is an absolute wonder to me. Atoms are incredibly small and yet they are massive compared with the size of the nucleus. When I was a kid I once read that if an atom of Helium was the size of the Albert Hall in London, then the nucleus would be about the size of an orange.

The size does vary according to the atom in question, Uranium atom nuclei are about 8 times larger than a hydrogen nuclei, which only contains a single proton. The largest come in at about 15 fm (Femto metres).

15 fm is tiny, it is about 10,000 times smaller than an atom, and this is why people often say that atoms are mostly made up of nothing. I think this is wrong. Atoms cannot be any smaller than they are, you cannot make them any smaller. You increase the pressure and eventually atoms will collapse into neutrons, this is what we believe happens in neutron stars. They do not collapse into smaller atoms.

So I think that they are actually as full as they possibly can be. They are full to capacity, which got me pondering to what they are actually full off.

Take the hydrogen atom, a single proton and a single electron. The proton is tiny and the electron is also very tiny. They carry equal but opposite charges. The proton is about 1830 times the mass of the electron. The interact to create the hydrogen atom. They both spin. This leads us to imaging the proton like a large planet with a small satellite, the electron in orbit around it, which is wrong*, but looks nice.

The size of the hydrogen atom is about 0.03 nanometers, which is huge compared with either the electron or the proton, yet this is the smallest it can possibly be.

The best explanation we currently have for the behaviour of an atom comes from quantum mechanics (QM). I have been told that the Heisenberg Uncertainty Principle (HUP) explains why the electron, which is negatively charged, does not drop straight into the positively charged proton to form a neutron, after all opposites should attract.  I've never really understood or been convinced by the argument, seems a little odd to me. That said

Atoms do change size as we move through the period table, Hydrogen is the smallest and the largest has a radius almost 10 times the size of Hydrogen, which is comparable to the change in size of the atomic nucleus for the two extremes. Is this coincidental or is there something in this?

The reason we think the atoms change size is due to the electrons having to pack in around the atomic nucleus. Hydrogen has a single electron so it is small, Uranium has a whopping 92 electrons surrounding each atomic nucleus, so it is larger!

All atoms are small compared to the wavelength of visible light, which is about 1000 times bigger, which really baffles me, because visible light should not be able to see something as small as an atom, and yet interactions occur between visible light and atoms. Just take a look in the mirror! This is just visible light striking atoms and being reflected back.

The interaction of light and atoms is currently explained by Quantum electrodynamics or QED for short. A brilliant theory that has been tested over and over and has come through time and again. Something I will cover in another post.

So what is the point of this post?

Atomic nuclei are typically 10,000 time smaller than atoms, which are in turn 1,000 times smaller that visible light. So from visible light to atomic nuclei that is a change is scale of 10 million. Let's see if we can get that in perspective. Imagine a ball with a diameter of about 1 metre then the wavelength of light would be comparable to the width of the planet earth. Which is once again, too big for us to image.

I suppose the point is, than even on tiny scales, those of visible light, atoms and nuclei, the distance from the largest to the smallest is absolutely massive and is so big to be beyond our imagination.

What I still can't figure out is why atoms are the size they are and why nuclei are the size they are, why approximately 10,000 times, why not 50, or 5,000,000? will have to ponder, when I come up with something I'll let you know.






Tuesday 14 August 2012

Pendulums

A wonder of the modern world
I was on the train from Slough to London pondering spin when I spotted a picture of a pendulum in a magazine.

I began to think that there are some similarities between spin and the behaviour of a pendulum and figured that it was definitely worth 20 minutes of my thinking time. Unfortunately the train to London was faster than my thought process and I arrived before I'd thought of anything interesting.

A couple of weeks later I am in a museum when I see an old antique grand father clock with a pendulum, so I gave it a little more thought, fortunately I had time to stop and think and this lead to this post.

The pendulum, discovered by Galileo apparently, is one of the most amazing inventions/discoveries ever. It completely changed the way we measured time.

You bung a weight on the end of a piece of string and you let it swing backwards and forwards. Provided that the swing angle is not too big then this thing will go on swinging in regular intervals for ages. Backwards and forwards, happy as Larry. This action is said to be isochronous, do like that word. It is this regular nature of the pendulum that allows its use in measuring time.

The equation of a pendulum is also rather straight forward, and is derived from Newton's second law of motion, F=ma, I got this from Wikipedia

L - length of the string
T - time period
g - local acceleration due to gravity
θ0 - angle of the swing, small

What is amazing is that the actual period of the swing, the time it takes to swing from one side to the other and then back again, is directly proportional to the square root of the length of the string. Sorry, went into techno babble for a minute, what I meant to say was, the longer the string, the longer it takes to do one swing. The shorter the string, the shorter the time it takes to do a swing.

The time period of the pendulum is NOT dependant on the mass of the weight on the end of the string, 1 kg, 2 kg, provided it does not stretch the string, it does not matter what mass we use, the time period will stay the same. The only two factors we have to think about are the length of the string and gravity.

This is great, seriously, I genuinely can't help thinking there is something massively profound going on here, only we are not quite sure what that is yet.

Equation (1) above is very similar to another equation

C = 2π r  

which is just the equation for the circumference of a circle.

C - circumference of a circle,
r - radius of the circle

so if we take

r =  L/g                                (2)

C = 2π  L/g   

T =  2π  L/g  

The circumference of the circle is the same as the time period, T. Which is cool in a way, as L gets smaller the circle will shrink and T will get smaller. L gets larger then the circle gets bigger and T increases.

This got me thinking about circles, area of circles, area of spheres and volume of a sphere, the equations for these are
area of circle, A =  π r2 

area of sphere, Asphere =  4π r2 

volume of sphere, V =  4/3 π r3 

using r in equation (2) above, we have


area of circle, A =  π L/g               (4)

area of sphere, Asphere  =  4π L/g      (5)

volume of sphere, V =  4/3 π   L/g 3   (6)


If T from equation (1) is the time period, what are A, Asphere  and V in equations (4), (5) and (6) physically? Do they actually represent anything at all? I am not sure at the moment. Will get the pencil and paper out and have a play. If I find anything interesting I'll put it in the next post.





Wednesday 13 June 2012

Things you think about in Slough

Gravitons on a small scale
Finding myself in Slough (England) with very little to do I got thinking about spin again. I say again, because I did a little post on spin a while back

I can't help thinking that the great mysteries of the universe will be unvailed once we have a proper handle on spin. Anyway, here I am in Slough, won't bother explaining why I am here, other than to say tomorrow I get a train back to London. Oh happy days.

So spin.

It occured to me that the effect we call gravity is not actually dependent on mass, but rather on spin.

Mass certainly exists (at least I think it does for now) and this is one of the properties of matter that make it distinct from electromagnetic radiation. But here is the thing. Protons, electrons, photons etc all spin and so all have gravity.

Even though a photon has no mass it does have "gravity". Of course this means that the term gravity has a different meaning here from traditional gravity which is linked to mass.

So, here are some things I will be thinking about on my train back to London tomorrow.

If photons do have gravity is it related to the photon frequency? If so then won't xrays be deflected more that light rays when they pass near the sun?

Do neutrinos actually have no mass,  travel at the speed of light, but have enough spin to have gravity?

If we accelerate protons to almost the speed of light is the increase in mass actually an increase in spin?

Are neutrinos actually gravitons? don't know where that one came from! will give it some pondering though.

Looking forward to the journey.


Tuesday 17 April 2012

E = m c squared?!

Small equation - big meaning
When I first started this blog I was planning on a post about Einsteins most famous equation. Then I got a bit side tracked. But I am back on track now, so lets see how we go.

E = m c2 

Probably the most famous equation in the world, certainly of the 20th century. This tiny equation that says such a lot. The equation showing mass-energy equivalence. While many people can quote, I suspect that a smaller number can tell you what each of the components of the equation are. So let's start there.

The equation has 3 components, E, m and c. We will tackle them in reverse order.

c - is the speed of light in a vacuum. By this we mean approximately 186,282 miles per second, or exactly 299,792,458 meters per second. We say "in a vacuum" to indicate that we are talking about the maximum speed of light. Light travels more slowly in materials such as water.

The closest we get to a vacuum is the space between galaxies, so strictly speaking we are saying the speed of light as it crosses these vast regions of inter galactic space. The speed of light in a vacuum is constant. This is the value of c that we are referring to in Einstein's E=mc2 .

m - mass. Philosophically it can get a bit tricky here. Most of us get out mass from standing on scales. We weigh our selves. What we are doing here is getting our weight. Weight is our mass multiplied by the acceleration due to gravity. So what we are describing is a quantity of inertia! That said we know things have mass. Take a proton or the electron. From various experiments we have worked out that that have a well defined mass. So we'll go with that for now, I'll cover mass in detail in another post.

E - energy. Once again this is a bit of an oddity. We believe that energy can neither be created (produced) nor destroyed by itself. It can only be transformed from one state to another. Energy is an amount of something. If we have the same amount of something, then we have the same amount of energy.

So now we know what the 3 terms are that make up our wonder equation. The next thing to consider is how Einstein managed to show they were related. When you look at it, it is an amazingly simply equation, you would have thought that someone would have stumbled upon it way back when. The answer is that deriving the equation and understanding what it means takes a giant leap of the imagination. This is how Einstein made the leap...

Note: If your maths is a bit weak, take this slow and you'll get it, although it may take a couple of reads. Hang in there, its worth it.

Light, any electromagnetic radiation for that matter, has momentum. This can be measure and is found to be

Pphoton = h / λ    --- (1)


Pphoton - momentum
h - Planck's constant
λ - wave length of light

the shorter the wavelength the higher momentum. So gamma rays have the highest momentum. A photon also has energy and this is given by

E = Pphoton c    ---(2) or Pphoton = E / c

E - energy
Pphoton - momentum of the photon
c - speed of light

Now image a train carriage that has a length of L (see diagram near the bottom). The carriage has a mass of M. The carriage is symmetrical in shape and mass. At the right hand end is a radioactive source. This source gives out a single photon. Hey, this is a thought experiment, so it can happen. The photon travels from the right end of the carriage to the opposite left end. It takes a finite time for the photon to reach the other end of the carriage. Now as soon as the photon takes off, the carriage recoils and takes off in the opposite direction.

The photon goes to the left, the carriage goes to the right.

When the photon reaches the other end of the carriage it is absorbed completely by the carriage wall and  the carriage stops. During the time of flight of the photon the the carriage has shifted, Δx.

Next bit is important - because the carriage has not been acted on by any external forces the center of mass of the carriage cannot have changed. But the carriage has actually moved to the side a distance, Δx. The only explanation is that the mass of the carriage has been redistributed slightly. The only thing that moved was a photon from one side to the other. The implication then is that the photon ray must have mass, m.

When the photon takes off with its momentum Pphoton, the law of conservation of momentum tells us that the carriage goes in the opposite direction with momentum Pcar ,and the two are the same, so

Pcar = Pphoton

now from standard mechanics we have

Pcar = M vcar

Pcar - momentum of the carriage
M - mass of the carriage
vcar - velocity of the carriage

Pcar = M vcar  = Pphoton = E / c   --- from equation 2 above, so

M vcar  = E / c    --- (3)  or  vcar  = E / (c M)


The next thing is to work out how long it takes the photon to travel from one end of the carriage. It travels at the speed of light, c, and has to travel the length of the carriage minus Δx the distance the carriage has traveled to meet the photon. Δx is small compared with L so we ignore it. So we have

t = L / c     --- (4)  , this is just the time it takes light to travel a distance L.

The velocity of the carriage is given by the distance travelled divided by the time it takes, so during the time of flight of the photon this is

vcar = Δx / t    ---(5) (for example, you go 60 miles in 2 hrs, v = 60/2 = 30 mph)

the t in (4) and (5) is the same so we can do some re-arranging to give

vcar = Δx c / L    ---(6), but take a look at (3) above, we have an equation for vcar so again re-arranging

E / (c M) = Δx c / L ---(7)

Now the center of the box is initially at a x=0, this is also the center of mass is xm. After the photon has done its thing xm is still the same, because the carriage has not been acted on by any external forces the center of mass of the carriage cannot have changed. The carriage has moved though by a distance Δx. This has happened because we have redistributed the mass of the carriage, a photon moved from one side to the other, taking a mass, m, with it.

This bit about center of mass is important, you have to get this part to crack it. You have to understand how we get from equation 8 to 9 below.

Look at the diagram below carefully. The top rectangle is the carriage before the photon is fired, the bottom of carriage after the photon is fired. The carriage has a mass of M and we imagine that it is distributed evenly at either end of the carriage. 
The carriage before and after the photon moves from right to left

It turns out that the center of mass is given by

Massleft x Distanceleft = Massright x Distanceright  . --- (8)

In the top carriage above (8) is just

M/2 x L/2 = M/2 x L/2   , which is the same on both sides and so is obviously true.

Now we have said that the center of mass is the same after the event, but after the photon has moved from right to left and the carriage has moved from left to right and we have

(M/2 + m) ( L/2 - Δx ) = (M/2 - m) ( L/2 + Δx )

expanding this gives a bit of a mess, take your time with this

(M/2)(L/2) + mL/2 - (M/2)Δx - mΔx = (M/2)(L/2) - mL/2 + (M/2)Δx - mΔx

The first term on each side is the same, so is the last, so we can simply remove them. Leaving

mL/2 -(M/2)Δx = - mL/2 + (M/2)Δx

doing a bit of swapping we get

m L = M Δx    --- (9) which becomes  m / M = Δx / L  --- (9a)

taking (7) we can replace Δx / L on the right with m / M, so we now have

E / (c M) = c m / M    and we are now on the home straight

E = c m ( c M ) / M = c m c  , we have just cancelled the Ms

and so with one last bit of re-arranging we get...


E = m c2 


Albert Einstein, that really is beautiful. Thank You.


Sunday 15 April 2012

Atoms

Atoms don't really look like this
Atoms. Just about everyone who has any form of education knows that the universe is made of atoms. Many also know that there are three sub-atomic particles that actually make up an atom. These are the proton, the neutron and the electron. A few will also know that the current best bet is that protons and neutrons are in turn made out of something called quarks.

Quarks I am not to sure about, despite the fact that they have been "seen". Some think that the quarks may in turn be made out of strings, this is were I draw the line. String theory for me is currently nonsense. The mathematicians have taken over the asylum.

Back to the atom. Before 1905 we didn't know for sure that atoms actually existed. So why didn't we know? We knew about gravity, electricity, light, radioactivity and loads of other things such as chemistry! Why was it that some people thought that the idea of atoms was little more than a mathematical abstraction, rather than something real? Well, for one thing they are remarkable difficult to see. They are really small. So small in fact that I don't believe it is possible for the human brain to comprehend just how small they are. You can talk about how many atoms make up a millimeter, but this number, about 6-10 million, is so large that you can't appreciate it.

So how did we finally crack this one. Well bring on Einstein, he had read about a paper written 80 years earlier by a bloke named Brown, a biologist (I think).

Now Brown had watched pollen particles in water and had noticed how they had bounced around in a random way. He hadn't been able to explain it and his idea and it could not be explained using classical thermodynamics.

Einstein was able to take this observation to determine the size of atoms. This was a brilliant paper (and that of the photoelectric effect) and won him a Nobel Prize. He did not win it for Special Relativity or General Relativity as many appear to think.

The paper also proved that classical thermodynamics was not valid on atomic scales. In fact Einstein opens the paper stating this.

What I think is great is that he actually comes up with an experiment (which he does not do himself, he leaves that to others) that will be able to calculate certain values that can then be used to determine the size of atoms.

The paper also derived an equation which showed that it would be possible to calculate the site of molecules and atoms.  The equation he derived was this

N = Avogadro's number = 6.0221415 x 1023
R = Gas constant = 8.3144  (Aside: The Boltzmann Constant is just R divided by N)
T = temperature in Kelvin, so room temperature ~ 293 K
k = viscosity of the liquid  ~ 0.001 for water
λx = average distance moved in a given time during Brownian motion.

P = the size of the particle or molecule.


In 1908 Perrin began to study Brownian motion using the newly developed ultra-microscope. He carefully observed the Brownian motion of particles and provided experimental confirmation of  λx and P in  Einstein's equation. His experiments enabled him to estimate the size of water molecules and atoms as well as their quantity.

1908 was the first year that the size of atoms and molecules were reliably calculated from actual visual experiments. Perrin's work moved atoms from being hypothetical objects to observable entities. He was awarded the Nobel Prize in 1926 for his work.

It seems strange to me that just over 100 years ago atoms were still considered by many to be hypothetical and not really based on real objects. These days children are taught about atoms in primary school. 100 years from now will children accept "facts" from physics that we still consider just theoretical today?

Of course they will, I just wish that I was there to see what those facts will be.


Thursday 12 April 2012

Magic numbers

A constant we made earlier
There are a fair amount of numbers used in Physics that really are magic. They are known as physical constants, but the reality is that they might as well be called magic numbers. Now many physicists would not be to happy about using the word magic in the same sentence as physics, but its true.

We have absolutely no idea why these constants have the values they have!

What's more is that there are a fair number of these... Planck's constant, Boltzmann constant, elementary charge (charge on an electron/proton), speed of light, mass of an electron, proton or neutron, the Bohr Magneton, the electron magnetic moment, the atomic mass unit and the fine structure constant (personal favorite of mine) and on it goes.

They define the universe in which we live. We know their values from experiments. Now and again we realize that one is a composite of some of the others, but ultimately we still don't know why they have these values. Here are a few of them...

Atomic mass unit amu 1.66054·10-27 kg
Bohr radius a0 5.29177·10-11 m
Electron radius re 2.81792·10-15 m
Planck constant h 6.6260755·10-34 J·s
Boltzmann constant kB 1.380658·10-23 J/K
Elementary charge e 1.60217733·10-19 C
Avogadro number NA 6.0221367·1023 particles/mol
Speed of light c 2.99792458·108 m/s
Permeability of vacuum μ0 4 π·10-7 T2·m3/J
Permittivity of vacuum ε0 8.854187817·10-12 C2/J·m
Fine structure constant α 1 / 137.0359895
Electron rest mass me 9.1093897·10-31kg
Proton-electron ratios mp / me = 1836.152701


It turns out that

c2 = 1 /(μ0ε0)

c is the speed of light
μ0 is Permeability of vacuum
ε0 is Permittivity of vacuum

so we can see an example were some of the parameters are related. Most are not. Most appear to be independent. I say independent because we currently don't have a theory linking them all.

More intriguing for me is why they have the values they do. The speed of light, the mass of an electron, the charge on a proton, the fine structure constant all have values that seem somehow arbitrary. Consider Einstein's famous equation

E = m c2

if the value of c (the speed of light) changed then the amount of energy associated with a give mass would be different to what it is now. Imagine if we are looking at this equation the wrong way. Re-arranging we get

 E / m = c2 = k

I have just divided each side by m. Imagine the energy of the rest mass of a particle is quantized. By this I mean that an electron has an E of say 10. Now if c had a different value say twice what its value currently is then would this force m to be a quarter of its current value in order to keep E the same? eg

E = 10, c = 1 so m = 10

E / m = c2 = 10 / 10 = 12

but if c doubled  we would have

10 / m = 22 = 4 , so m = 2.5.

So rather than E being governed by m and c, m and c are actually governed by E. So c actually has the value it has because m has the value it has, and vice versa. Similarly there is another equation relating energy and wave frequency

E = h f

where h is Planck's constant, f is the frequency of the radiation and E is the resulting energy. Again, imagine if we have this the wrong way round and h and f are dependent on one another. If this were the case it would be necessary to show why E behaved in the way it did and why it was quantized in such a fashion. This would not be a trivial task!!!

What is the point of this post? Well in a way, there isn't one, other than to show that I think that any theory that explains "everything" needs to explain each of these numbers. If we can do that, then we really are cooking. 


Monday 9 April 2012

Prefixs

From big to small
This is a short post on size and prefixes. Most things in physics are really large or really small. Number of atoms in a sugar cube, massive number. The charge on an electron, tiny number. Most of these numbers are so big, or small, as to have no real meaning, it is impossible for our brains to comprehend them.

Take the speed of light, 186,000 miles per second. Now the number 186,000 is well within our imagination, after all, that is about the average house price. One second in time is easily within our grasp, just look at the second hand on any clock. 186,000 miles per second though is too large for our brain to imagine.  1.3 seconds is the approximate time it takes light to travel from the moon to earth. But we have no real comprehension of the distance from here to the moon.

Many of us know what a meter looks like, or a centimeter or a millimeter, but then go to the next level, the micrometer, also called a micron. A micron is to small for the eye to see and to small for the brain to imagine.You can see things micron size using a microscope, but the image is then enlarged so it doesn't really count.

This problem of scale is true in many things and our range of experience is actually quiet small. The band of electromagnetic radiation that we can detect with our eye, that we call the visible spectrum, or visible light is very small. The frequency range is so high that once again it is beyond comprehension.

In a way things have started to change with the introduction of computers into every day life. Many people have GHz processors and GB of RAM. In hard drives these days we started out with mega byte disks that became gigabyte disks that became terabyte disks. Large storage facilities already deal in petabytes.

Many of use have heard of micro computers and nano technology. People are starting to recognize these terms as they are now part of every day experience. We may not understand properly what the terms mean, but we are starting at least to recognize the names.

So what is the difference between micro and nano? or the difference between a kilobyte, megabyte, gigabyte or terabyte?

Each step from kilo to mega to giga is a 1000 fold increase. Each step from milli to micro to nano is a 1000 fold decrease.


A mega is a thousand times bigger than a kilo, in the same way that a million is a thousand times bigger than a thousand. Similarly a gram is a thousand times smaller than a a kilogram. A milligram is a thousand times smaller than a gram, a microgram a thousand times smaller than a milligram.

Many people have heard of nano, micro, milli, kilo, mega, giga, Tera. That is a fair range, we have gone from 10-9 to 1012. That is 21 orders of magnitude (9+12 = 21). There are others, below we list those ranging from 10-24 to 1024. Some of them have some great names and using the naming conventions can be... interesting. Here are a few.

An electron has a charge of about 1.6x10-19 Coulomb, this is 160 zepto Coulombs or 160 Trilliardths of a Coulomb.

The mass of the earth is about 6 x 1024kg, or 6 yotta kilograms or 6 Septillion kilograms. 

1 light year, the distance you would go in 1 year if you were travelling at the speed of light, is approximately 1016meters which is 10 peta meters or 10Pm, or 10 Billiard meters.

Here is a list going from the very big to the very small. I think you will surprised by how many you have heard of.


Prefix Symbol 1000m 10n Decimal Short scale Long scale Since[n 1]
yotta Y 10008 1024 1000000000000000000000000 Septillion Quadrillion 1991
zetta Z 10007 1021 1000000000000000000000 Sextillion Trilliard 1991
exa E 10006 1018 1000000000000000000 Quintillion Trillion 1975
peta P 10005 1015 1000000000000000 Quadrillion Billiard 1975
tera T 10004 1012 1000000000000 Trillion Billion 1960
giga G 10003 109 1000000000 Billion Milliard 1960
mega M 10002 106 1000000 Million 1960
kilo k 10001 103 1000 Thousand 1795
hecto h 10002/3 102 100 Hundred 1795
deca da 10001/3 101 10 Ten 1795

10000 100 1 One
deci d 1000−1/3 10−1 0.1 Tenth 1795
centi c 1000−2/3 10−2 0.01 Hundredth 1795
milli m 1000−1 10−3 0.001 Thousandth 1795
micro μ 1000−2 10−6 0.000001 Millionth 1960
nano n 1000−3 10−9 0.000000001 Billionth Milliardth 1960
pico p 1000−4 10−12 0.000000000001 Trillionth Billionth 1960
femto f 1000−5 10−15 0.000000000000001 Quadrillionth Billiardth 1964
atto a 1000−6 10−18 0.000000000000000001 Quintillionth Trillionth 1964
zepto z 1000−7 10−21 0.000000000000000000001 Sextillionth Trilliardth 1991
yocto y 1000−8 10−24 0.000000000000000000000001 Septillionth Quadrillionth 1991
The metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the General Conference on Weights and Measures.

There are some numbers in physics that are outside of the ranges given above. The mass of an electron is approximately10-30kg, which is,  hmmm, a micro yocto or is it a yocto micro?  ... think I need to take another at my scale.


When a tera byte hard drive isn't.... 

The definition of a kilobyte needs clarity, see a kilobyte is 1024 bytes but in physics a kilo is 1000. So in computer speak kilo means 1024, in physics it is 1000. This has allowed hard drive creators to pull a little trick, and steal 9% of your Tera byte hard drive. Here is how they do it.

In computer speak a hard drive size is measured in kilobytes, megabytes and so on. A kilobyte is 1024 bytes

1024 = 210 =2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

but in physics a kilo is 1000.Hard drive manufacturers use physics notation rather than computer notation, so,

A 1 terabyte hard drive = 1000 gigabytes = 1,000,000 mega bytes = 1,000,000,000 kilo bytes, which is a large number,

1 Tera byte = 1,000,000,000,000 or 1012 bytes

but if we used the computer definition then

1 Tera byte = 1024 gigabytes = 1,048,576 mega bytes = 1,073,741,824 kilo bytes

1 Tera byte = 1,099,511,627,776, an even larger number!

So by using physics notation rather than computer notation, hard drive manufacturers have managed to skim 9% of the size of a drive. Our 1TB drive is actually missing 99,511,627,776 bytes, which is about 92GB! So a 1TB hard drive is really a 0.909TB hard drive or 932GB.

92GB + 932GB = 1024GB,

which is the proper definition of a terabyte, in computing. This is why your new shiny 2 TB hard drive shows up as 1.818TB as soon as you load it into your computer!






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