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This week I’m going to talk about what I am learning in my studies of Astro Physics and Cosmology.  It may get a bit technical but I am hoping some of the more experienced astronomers that read this blog will find these occasional sessions interesting and thought provoking.

Firstly I would like to explain that there are two fundamental principles/observations around which all modern day cosmology is based.  The first is Uniformity – The Universe is the same everywhere.  The second is The Hubble Law – Everything is moving away from us, with a speed that is proportional to distance.

Uniformity;

Is the universe really homogeneous, the same everywhere?  Looking locally on the scale of planetary systems, it is most certainly not uniform, the difference in density between the middle of the earth and outer space is extreme to say the least.

Even on scales of thousands of light-years, it is also very non-uniform; you have dense Galaxies in some regions and empty space in others.  Galaxies themselves are gathered into groups and clusters, which themselves gathered into super clusters, separated by voids.  So even here we are still not uniform!

But on larger scales still, things do appear to smooth out.  Super clusters do not themselves seem to cluster into anything bigger.  Surveys for things like quasars that probe distances of billions of light-years do find a very uniform distribution.

So, what we should say is that, on really big scales, the Universe does appear to be homogeneous.

The Hubble Law:

If you take a spectrum of anything out in space, you will usually see spectral lines, caused by electrons jumping up and down energy levels and either emitting or absorbing light.  Each element has characteristic wave lengths at which it produces lines: for example the very famous H-alpha line of hydrogen occurs at 656.3nm wavelength.  In the photos of this article you can see a plot of a star spectrum showing some of the strongest and most common spectral lines.

If you look at distant galaxies, however, all these spectral lines appear to have shifted to longer wavelengths.  This effect is called redshift and the redshift of a given object is given as:

z=Δλλ0

where z is the redshift and Δλ is the shift in wavelength (i.e. observed wavelength minus the wavelength λ0 you would get for this spectral line in a laboratory on Earth.

This shift is caused by the doppler effect: all these distant galaxies are moving away from us at a speed v, which can be found from the equation v=cz where c is the speed of light.

Edwin Hubble showed that the recession velocity is proportional to distance: i.e. that v→=H0r→, where H0 is Hubble’s constant and has a value of around 70km s−1Mpc−1  (i.e. a galaxy that is one mega-parsec from us is moving away at a speed of around 70 km/s).

Could this mean that we are in a special place in the Universe and that nothing else wants to be near us and is in actual fact moving away from us?  NO – using vectors it is possible to show that you would see exactly the same thing wherever you were in the Universe.

From these two principles then we can see that we do indeed live in a uniform and seemingly endless universe and that wherever you are in the universe, everything seems to be moving away from you with a speed proportional to its distance.

“Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.”
― Albert Einstein

Two Masses:

Einstein came up with this theory by pondering the puzzle of why mass crops up in two quite different contexts in physics.  The first context is gravity: Mass is something like a gravitational “charge” that indicates how strongly an object attracts another object or is attracted by it.  This gravitational mass is the mass that you find in the equation

F=GMmr2

The second context is inertia – how much something else resists being pushed around.  This “inertial mass” is the mass you find in the equation

F=ma

The puzzel is why these two should be the same.  Why should something that resists being pushed around also attract other objects?  There is nothing like this for the other forces of nature.  Take electromagnetism, for example.  How much something attracts or is attrated by this force is determind by the charge.  But charge has nothing to do with inertia.  There are objects with the same charge but very different inertia (like a positron and a proton).

One manifestation of this is that all objects fall at the same rate – the mass cancels when gravity accelerates something.  But an electrical field will not attract everything equally.

Einstein was wondering – why are these two masses the same?  To answer this, he had to think very deeply about the nature of space time.

The Metric:

How can you define space, without using self-referential terms?  The only real way is using mathmatics.  Space is defined by three numbers, possesed by every particle.  These can be their x, y and z coordinates, or something different in a different coordinate frame, but there have to be three of them because we live in a three dimensional universe.  In addition to the coordinates, we need some way to measure how much one particle affects another.  Thi is called distance (written as s).  In Cartesian (x, y & z) coordinates, the distance between two objects is given by Pythagorus Theorem:

δs2=δx2+δy2+δz2

where δs is a small distance element coming from small changes δx, δy and δz in the three coordinates.  We could also use cylindrical polar coordinates r, θ and z, as shown in an accompanying picture with this article.  In this case, the distance element is given by

δs2=δr2+r2δθ2+δz2

This equation relating distance to the three coordinates is called the metric. Einstein’s brilliant idea was to modify it.  This will make objects move in strange ways.  If, for example, you leave out the r2 in the cylindrical polar version of the metric, objects will move in circles rather than straight lines. The way you work out motion in a strange metric is to imagine a wave-front and see how far each edge of it moves. Where these waves add up in phase is where something will go.

General Relativity:

This is Einstein’s theory of general relativity.  There is no such thing as gravity.  Instead, matter changes the metric of space around it.  This change in the metric causes spacecraft to go in circles (orbits) and it causes objects to fall. When you drop something, it doesn’t fall because a force is applied to it.  It falls because accelerating downwards is its natural motion in the curved space-time of the Earth.

If something doesn’t fall (for example if it is resting on a table), it is being accelerated away from its natural motion by the compression of the tabletop beneath it. This force from the table is the only real force present.  There is no such thing as a gravitational force.  Massive things are heavier because the table needs to apply a bigger force to accelerate them away from their natural motion.

Thus gravity turns out to be a fictitious force like centrifugal force. We feel a centrifugal force when a car goes around a corner, but in reality our body is just trying to follow its natural motion (a straight line) and the car has to push us sideways.  Similarly we feel gravity pulling us downwards, but all that’s really happening is the ground pushing us upwards against our natural motion.

This natural motion is called the Geodesic.

Well if you’ve made it this far then well done.  There is some complicated math in the article today.  For those of you who have made it.  I am now going to show you how you actually go about measuring a redshift.

So imagine that you have found a galaxy somewhere and have obtained a spectrum of it.  So as usual, the spectrum shows peaks and wavelengths and flux per wavelength and gently it drops off.  But it has a whole bunch of absorption lines which you can hopefully use to measure the redshift.

Firstly you would need a reference sheet to tell you what lines are likely to happen of a spectrum of something like our own sun.  You would notice that the patterns look very similar.  Lets say that two lines are both near 400 nanometers.  There is one just above 650.  Another just above 500.  All in all both patterns look very similar.  Straight away that is telling you that this galaxy seems to be made up of roughly sun like stars and that they all have the normal absorption lines.  Telling you that you have got calcium CH.

Its also telling you that the redshift is not very big.  Because its the wavelengths your measuring.  So just below the 400 matches our suns wavelengths.

On a large scale it would be very hard to measure the redshift so you would have to zoom in.  Lets zoom in on calcium.  Lets say that the middle of the line is around 394.1nm roughly.   We would also know that the laboratory wavelength is 393.3nm.  So the shift, delta lamda, is 394.1 minus 393.3, equals 0.8 nanometers.  The redshift, written as z, is defined as delta lambda over the lab wavelength.  So that’s 0.8 over 393.3 which is 0.002.  That’s our redshift.

Using the doppler effect equation, you can work out what speed this corresponds to.  Now velocity is equal to the redshift times the speed of light.  So that’s 0.002 times 300,000 kilometers per second, which is 600 kilometers per second. So that’s how fast the thing is moving.

Is it going away or towards us?  You can see from a graph that the wavelength has moved from the laboratry length to a longer wavelength, towards the red spectrum.  So it’s a redshift, so it’s receeding from us, moving away.

Wow, a lot of information there today guys and every once in a while I will do a blog like this one.  If you have actually got all the way to the end of this blog then I commend you.  I will be back next week with some more stories from the stars and hopefully something a little more light hearted for my amateur astronomer followers.

Until the next time, this is Stargazing Tenerife team signing out.

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