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!






Friday 6 April 2012

It's all in the spin

Electron spinning in hydrogen
Try this one out for size... the next time you have a clear night and can see the stars. Go out into your garden and stand there, your arms resting by your sides. Look up at the stars. Now start spinning. The stars spin around you AND your arms start to move away from your body. If you spin fast enough your arms will be straight out.

It could be that the spinning of the stars and the motion of your arms is just coincidence or may be there is some underlying physics connecting the two.

This may seem a bit if a silly idea, the stars and galxies having an effect on my arms when I start to spin. It just doesn't seem to make sense. It makes more sense that it is likely to be some interaction with the earth than the stars, after all that would be more immediate.

The idea mentioned here is known in the trade as Mach's principle, also, Mach's conjecture. It was given this name by Albert Einstein. Mach was convinced that there is indeed a physical law which binds the motion of distant stars to a local inertial frame, us standing in the garden.

Einstein used some of the ideas of Mach's to help him in his development of his theories of relativity.

With spin you can actually over come gravity in your back yard. Take a bucket and half fill it with water. Now swing it from side to side, start small and gradually make the swings bigger.When you feel brave enough let the swing go right over the top. You can now rotate the bucket through full circles without the water falling out.

The water is stuck in the bucket even when the bucket is directly over head and there is nothing to stop the water falling out. Now stop. Turn the bucket upside down and the water comes pouring out because of gravity. So we have to conclude that the spinning motion over comes gravity.

This method of over coming gravity is explained using the idea of inertia or ficticious forces and they are covered in a post on non-intertial frames of reference. They are called ficticious because they disappear as soon as the bucket stops spinning.

Spinning is not only limited to large scale, or macroscopic, phenomena. When we make observations on a tiny scale the idea of spin once again comes into play. When quantum mechanics started there were a number of issues that needed to be addressed to reconcile theory with experiment and one of these was the idea of electrons, protons and other sub atomic particle having spin.

A Gyroscope
But hold on a second, we know that when we get down to quantum mechanics things get odd, in a way this is true of spin at a quatum level. Electrons can have spin, but they do not spin faster or slower. They can be made to behave a little like a gyroscope by placing them in a magnetic field. In the same way that a gyroscope can precess and electron will have similar behaviour in a magnetic field and it is this that is exploited in Nuclear magnetic resonance (NMR).

At a quantum level spin is vital to existing theories.

Now lets think this through for a minute, from the massive to the miniature everything spins. Galaxies spin, the stars in galaxies spin, our sun spins, the earth spins, the electrons spin, protons spin, quarks (if they exist) are thought to spin. Light sort of spins as it goes charging through space.

Spinning tops stand upright when they spin, gyroscopes spin. Although we don't think we spin we are actually standing on a planet that spins on it's axis as it orbits a sun that spins and so on.

It appears that angular momentum associated with spin is conserved just like linear momentum.So spinning is important.

Coming back to the idea of standing in my garden spinning round with my arms in the air. Is there really something profound about all this spinning? By spinning am I genuinely interacting with every star and galaxy in the universe? I actually really like that idea.

Simply by spinning round I am touching and being touched by the entire universe and if God is the universe then you are touching God himself? I like that idea as well.





Tuesday 3 April 2012

Vacuums- not a lot in them

A vacuum we all know and love

A vacuum is "a volume of space empty of matter", in other words a something that has absolutely nothing in it, no atoms or particles. The word itself comes from the latin from "empty".

It seems that this is impossible to achieve. There is no container that we can get with a special gate keeper that only lets particles out but not back in. If there was and we managed to get every particle out then there might still be some thermal radiation in there, after all the entire universe is full of the stuff, just take a look at Cosmic Background Radiation (CBR).

CBR as I like to call it, being an old friend and all, is thought to be radiation that was created in the very earliest stages of the universe after the Big Bang. It is one of the main "proofs" to the theory of the Big Bang.

When the Big Bang happened things were very very hot, so hot in fact that it is impossible to try and image just how hot. A hot day, even a very hot one in a desert somewhere, take the hottest day ever recorded, Aziziya, Libya, a blistering 57.8 °C(136 °F) on 13 Sept 1922, is low in comparison.

In addition to the high temparatures there were also some hydrogen particles, helium, my money is on some electrons etc. (Actually, I think the very first things produced where neutrons. Every thing stems from neutrons in my book. )

So even if we could get rid of all the atoms and other sub atomic particles from our container there would still be a fair amount of radiation in there. What is more. I am convinced that if you have a really really high quality vacuum, the likes of which you find in deep space, then before you know it... bingo, a neutron pops into existence. This then decays into a proton and a neutron and your on your way to the components for a star.

But I digress. Let's take a look at just how good the vacuums that we create here on Earth are compared with those out in space. So finding a place to start. Let's use atmospheric pressure. There are a number of different units for pressure, just as there are for speed. For example, in speed  we have meters per second, feet per second, miles per hour, kilometers per hour and so on. In terms of vacuum we have similar varieties.

Pascals, named after Blaise Pascal,  a real genius, he died at the age of 39 having lead a quite remarkable life. Probably best known for Pascal's triangle and Pascal's wager. Pascal's triangle is a rather useful tool for calculating binomial coefficients (you have probably used this at school without realizing it). Pascal's wager is betting on whether God exists or not. He also contributed to numerous other fields including the study of pressure. I am tempted to do a post just on this guy alone. He really was something. Anyway, as a result of his contributions, one unit of pressure is the Pascal.

So if we have a pressure of 1 atmosphere, which is the pressure you feel every day and are normally unaware you are feeling it, the equivalent measurement in Pascals is approximately 101,000 Pa. Another interesting measurement is the number of particles (molecules or atoms) per cubic meter. A cubit meter is the volume of a cube with edges of 1 meter. These are the two that we will use today. The Pascal and the number of particles per cubic meter. So, here we go, a little list;

1 atmosphere (atm)101000 Pa2.5x 1025a massive number of particle, bigger than brain can imagine
vacuum cleaner only reduces the pressuse to about 0.8 atm80,000 Pa2x 1025
Freeze drying 100 Paabout 1022 particles
Light bulb , this is about 1/10000 atmospheric pressure.10 Pa1021 particles
Thermos (the values vary by a factor of about 100 depending on the quality. We are considering the best here)0.01 Paabout 1018 particles
Vacuum tube (these values vary by a factor over over a thousand from 10 micro Pa down to 10 nano Pascals) lets go with the highest vacuum10 nano Pa (that is 1 billionth of a Pa
about 1012 particles
(1000 particles in a cubic millimeter)



The lowest pressure achieved on earth is around about 13 pPa, a thousand times higher than for the best vacuum tube, though this can be reduced by a thousand fold with cryogenic system, actually achieving vacuums with only about 100 particles in 1 cm3, or about 100 million in 1 meter3.

Next, let us see how the best on Earth stacks up against the best in space.

On the moon the vacuum is about 10 times better than the best vacuum tube.

In the space between planets in the solar system the vacuum is about 10 times better than the very best achieved on Earth, about 10 million  particles in 1 meter3.

In the space between stars in our galaxy the vacuum as about 1 particle / cm3, (1 million  particles in 1 meter3) so about 100 times better than anything we have achieved on Earth.

In the space between galaxies there is typically only 1 particle in 1 m3, this is about 100 million times better than anything currently achievable on earth.

Think about that for one minute.

1 single atom in 1 m3 of space.

These numbers are averages of course and so there will be regions of inter galactic space that have more than 1 atom per cubic meter and some that have less than 1 atom per cubic meter. In other words there can be some regions of approximately 1 m3 that sometimes have NO atoms in them. Though they still have the electromagnetic radiation discussed earlier.This is about the closest it gets to a perfect vacuum.

So, this brings us to "horror vacui", nature abhors a vacuum. I don't think nature cares one way or the other about a vacuum, Aristotle was just tripping a bit there I reckon. What is does do though is to take advantage of the conditions of the vacuum of inter galactic space to do something rather clever. I think that the universe uses the vacuum of space-time to create particles.

I am just not sure how yet!

Sunday 1 April 2012

Pulsars

Pulsars, like Quasars are one of those things that don't get much attention these days, but 40 years ago they really were the talk of the town.

A pulsar is a star that has collapsed to create a rapidly spinning neutron star. The name pulsar comes from pulsating star because the neutron star gives out very regular pulses of electro-magnetic radiation very similar to a light house.

They were discovered by a PhD student Jocelyn Bell Burnell on the November 28, 1967. I can only try and imagine just how exciting that must have been. A pulsating signal that was amazingly regular, pulsing every 1.33 seconds and came from the same location in the sky. At the time there was no known astrophysical sources that could generate something like this, I can't help thinking that there must have been many who thought that it just might be some extraterrestrial signal.

Jocelyn Bell Burnell said this

 "we did not really believe that we had picked up signals from another civilization, but obviously the idea had crossed our minds and we had no proof that it was an entirely natural radio emission. It is an interesting problem—if one thinks one may have detected life elsewhere in the universe, how does one announce the results responsibly?"

The gave the signal the name LGM-1 (little green men). It was only when a second source from an entirely different part of the sky was discovered that the idea of LGMs was entirely dismissed.

The idea that pulsars may be neutron stars came about a year later. Fritz Zwicky, he of dark matter, had first proposed the idea of a neutron star back in the 1930s about a year after the discovery of neutrons by Chadwick. These seemed the best fit. This was strengthened by the discovery of a very rapid pulsar, 33 millisecond (a very rapid clicking) shortly afterwards.

The discovery also gave strength to the ideas coming out of general relativity relating to black holes. Black holes are believed to be stars that have under gone a catastrophic collapse resulting in something called a singularity. The gravitational pull of these objects is so great that not even light can escape, hence the name, black hole. If neutron stars can exist, why not black holes?

In 1982 a pulsar with a rotation period of just 1.6 milliseconds, about the same frequency as an E5 on a piano. Some of these millisecond pulsars are considered to be excellent clocks with an accuracy and stability comparable to the best atomic clocks. They are currently being used to to help try and determine if gravitational waves exist. These where predicted by Einstein back in 1916 but have yet to be seen.

A pulsar forms when the center of a massive star is compressed during a supernova. The neutron star keeps the majority of its angular momentum and since it is only a tiny fraction of the size of the original star it has a very high rotation speed. This is in much the same way that a rotating skater with their arms out stretched suddenly starts to spin faster when they draw their arms closer to their body. The exactly same rules apply to the skater and the neutron star, how amazing is that?

The beam of radiation that we detect as the pulse is emitted along the magnetic axis of the pulsar which may not be the same as the rotational axis and it is this misalignment that givesthe pulse effect (think of a light house). The reason for the beam is thought to be due to the rotational energy of the pulsar. A changing magnetic field causes an electric field to be created (as explained by Maxwells equations, we'll cover these else where).

The strong electric field accelerates protons and electrons on the stars surface which in turn creates an electromagnetic beam.

It is thought that as the electromagnetic power is emitted that stars start to slow down and when they reach a certain point the pulsar mechanism stops, this is called the "death line". It is thought that neutron stars are pulsars for only 10-100 million years. I say only, but 10-100 million years is a staggering amount of time. Once again it was one of those things we say without really thinking about it. 100 millions years, that is such a long long time. It is also thought to be the length of time it takes our sun to do one orbit of our galaxy.

100 million years, compared to the length of the universe,  means though is that most of the neutron stars in the universe don't pulsate any more. Which I think is rather sad.


I suppose the best thing about pulsars are that they gave us the neutron star. While black holes are still theoretical, neutron stars seem to definitely exist and is the only object we know off that has such high densities and have allowed us to test general relativity under truly enormous gravitational fields.

It staggers my brain that something larger than the sun can collapse into something so small that can spin so fast giving out so much power. I wonder what they would look like up close?

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