Last week we learned about vectors and I showed you the scale diagram method for solving a vector problem, such as determining the displacement of an object after a journey. The video is a short re-cap of the scale diagram technique.
We started our study of Einstein’s special theory of relativity this week. Special relativity is tricky get your head round, so I’ve put together a collection of videos that help to explain the ideas we’re going to consider. Let’s start with a video about the speed of light.
The next video follows Einstein’s thought process as he worked through his special theory of relativity.
When I walked around the room throwing the tennis ball, I showed that what I saw as purely vertical motion looked to you like the curved path of a projectile. For me (the moving observer) and you (the stationary observer), the ball appeared to travel different distances. Extending this situation to a ray of light, as in the video, we need to consider two aspects of special relativity, time dilation and length contraction. The speed of light can only be constant for all observers if something happens to time and length (distance) when considering fast moving objects.
We’ll look at time dilation first.
Here is another take on special relativity and the twins paradox
…and the Glesga Physics version
This video has helpful examples to explain length contraction.
Sometimes it’s easier to imagine we’re a stationary observer watching a fast moving object go whizzing past. For other situations, it’s better to put yourself into the same frame of reference as the moving object, so that everything else appears to be moving quickly, while you sit still. The muon example in this video shows how an alternative perspective can work to our advantage in special relativity.
Another way to think about this alternative frame of reference is that it’s hard to measure distances when you yourself are moving really quickly. Think about it, you’d get tangled up in your measuring tape like an Andrex puppy.
It would be far easier to imagine you’re the one sitting still and all the objects are moving relative to your position, as if your train is stationary and it’s everything outside that’s moving. That keeps everything nice and tidy – including your measuring tape. Got to love Einstein’s postulates of special relativity.
This week, we’ve looked at calculating radiation doses. The absorbed dose D, measured in Grays (Gy), takes into account the energy E absorbed and the mass m of the absorbing tissue.
The higher the energy, the greater the absorbed dose. If you are wondering why the absorbing mass is important, consider the different masses of tissue involved in a dental x-ray and a chest x-ray….
We also learned about equivalent dose in Sieverts (Sv). The equivalent dose H gives an indication of the potential for biological harm by considering the absorbed dose D and a weighting factor .
Different types of radiation have different weighting factors, e.g.
|type of radiation||weighting factor|
The more damaging forms of radiation have a larger weighting factor.
Absorbed dose and equivalent dose are usually expressed in smaller units; μGy, mGy, μSv, mSv.
In the UK, the population receives an average equivalent dose of 2.2mSv per year due to background radiation produced by cosmic rays, radon gas and materials dug up from the Earth’s crust, such as rocks and soil. In addition to this exposure to background radiation, the Government has set a further equivalent dose of 1mSv per year for members of the public. This limit can be increased to 20mSv for people who work in the nuclear industry, certain medical occupations (such as radiographers) and airline pilots – all of whom will exceed the public limit in the course of their job.
This occupational increase for some individuals can be justified on the grounds that workers are not as vulnerable to the effects of radiation exposure since they are neither children (high rate of cell division so more chance of dna damage being copied) or elderly (reduced ability to repair damage). In many cases, these workers will also be screened on a regular basis by occupational health staff at their place of work.
Here is a poster from the excellent xkcd site that explores examples of the different levels of equivalent dose.
Click on the picture for a larger version.
Notice that the scale changes as you move through the poster from blue to green to red.
The dosimetry topic is comprehensively covered at BBC Bitesize.
It’s complicated and cosmologists are not certain. One of the issues is only being able to see about 4% of the mass in the universe – the stars, planets, gas and dust. About 25% of the mass of the universe is Dark Matter. It’s “dark” because it doesn’t emit light that enables us to see it. Vera Rubin and Fritz Zwicky were the two astronomers who produced observations that led to the dark matter theory.
Vera Rubin measured star velocities in the Andromeda galaxy and plotted these against the star’s distance from the centre of the galaxy. Knowledge of rotational speeds within our Solar System would predict a graph similar to curve A. What she obtained was a relatively flat graph (B).
image from Quantum Diaries
The rotational speed of the stars in curve B are far too fast for the Andromeda galaxy to stay together. The only explanation for the galaxy staying together was the presence of an awful lot of additional mass that couldn’t be detected. This new mass was named dark matter.
Rubin talks about her discovery in this video.
Zwicky had been looking at clusters of galaxies, rather than individual stars within galaxies. He found something similar; the galaxies were swirling round at too great a speed and should fly apart. There had to be an awful lot of invisible mass in that part of space to produce a gravitational force strong enough to hold the cluster together.
There’s a further complication. The expansion of space appears to be caused by an unknown force called Dark Energy, that fights against the pull of gravity which should be reducing the rate of expansion.
Saul Perlmutter was awarded the Nobel Prize for Physics in 2011 for his work on Dark Energy. This video explains where we are in our understanding of where the universe will end up. It contains some similar footage from the end of the Vera Rubin video, so any déjà vu is real.
You might remember that we looked at some paradoxes when we studied special relativity earlier this term. Here is another situation where a paradox can arise. The German astronomer Heinrich Olbers (1758–1840) asked why the night sky was dark. At the time, astronomers believed that the Universe was both infinite and steady state (unchanging), so it seemed like a good question.
- Wouldn’t there be a star in any direction you chose to look?
- Shouldn’t the light from that star prevent the night sky from looking dark?
Well, the problem is that the Universe is not infinite because it is still expanding. The Universe also isn’t steady state because it is… expanding. It turns out that a question posed by a follower of the infinite, steady state model of the Universe is actually a decent piece of evidence in support of the Big Bang model of the Universe.
Watch these two videos and see how they chip away at the paradox and show how the answers to the question turn out to support the expanding Universe model.
As we worked through the diagram explaining the stages of the Big Bang model, we looked at a section of the diagram where the Universe was hot enough for nuclear fusion. At this point, hydrogen nuclei were fusing together with other hydrogen nuclei to create helium nuclei. As the Universe expanded, it cooled and further fusion was not possible. As a result, we have a Universe with the same proportion of hydrogen to helium wherever we look: we find 75% hydrogen and 25 % helium. This can only be the case if all of the helium was produced at the same place and the same time, i.e. in a very small, very hot Universe.
Georges Lemaître’s theory of an expanding Universe, which has become known as the Big Bang, was supported by Hubble’s observations. The expanding Universe idea was challenged by influential scientists who believed the Universe was both infinite (and therefore not expanding) and steady state (unchanging). Supporters of the Big Bang idea needed to find other evidence that could confirm their model was correct.
The cosmic microwave background radiation (CMBR) is radiation left over from the big bang. When the universe was very young, only 380,000 years old, just as space became transparent to light, electromagnetic energy would have propagated through space for the very first time. At this stage in its development, the temperature of the Universe would have been about 3000K. Nowadays, the temperature of space has fallen to approximately 2.7 K (that’s 2.7 K above absolute zero!) and, using Wien’s Law, we can confirm that the peak wavelength of the electromagnetic radiation is so long that the background radiation lies in the microwave portion of the em spectrum.
The CMBR was first detected in 1964 by Richard Woodrow Wilson and Arno Allan Penzias, who worked at Bell Laboratories in the USA.
In the 1920s, Edwin Hubble had access to the Hooker telescope on Mount Wilson, Los Angeles. This was the largest telescope in the world at that time. His first breakthrough was the discovery of a cepheid variable star in the Andromeda nebula. This enabled him to calculate the distance to Andromeda and he quickly realised this was not a nebula but a galaxy outside the Milky Way.
This video follows his work.
Hubble then turned his attention to other galaxies, looking for cepheid variable stars that would allow him to determine their distances from the Milky Way. He used redshift to calculate their recession velocity and plotted a graph against their distance from us.
He found that the recession velocity (v) was directly proportional to distance (d). We can express this relationship as
which is known as Hubble’s law, where is the Hubble constant. Astronomers agree that the current value of the Hubble constant is
Since this is a SQA course, we need to convert the constant into SI units – giving
In this second video, Professor Jim Al-Khalili looks at Hubble’s work on measuring redshift for different galaxies and his discovery of an expanding universe.
Although he was American, Edwin Hubble transformed himself into a tea drinking, pipe smoking, tweed wearing Englishman during his time as a Rhodes Scholar at Oxford. He probably wouldn’t approve of this last video.
It is said that when Hubble died, he left his collection of tweed jackets to Mr Jamieson-Caley.
Unfortunately, astronomers were not eligible for the Nobel Prize for Physics while Hubble was alive. The rules have now been changed.
For the past two weeks, we’ve been looking at equations that describe time and distance changing according to speed. It’s been quite heavy on theory and maths with no supporting evidence to suggest Einstein’s ideas were correct. I want to address that lack of evidence by pointing you to some practical work that had been carried out before Einstein’s theory was developed and by introducing measurements that scientists are still making today.
The speed of light is the same for all observers
Einstein’s Special Theory of Relativity was published in 1905 but I want to go back to an experiment carried out 1887, the Michelson-Morley experiment. Throughout the 19th century, scientists believed that waves needed some form of matter through which to travel. From your National 5 knowledge, you know that electromagnetic radiation, such as light or radio waves, can travel through the vacuum of space where there is an absence of matter but this was not known way back then. Instead, scientists believed that the Earth was moving through a mysterious substance called the ether (also known as the aether).
At the time, it was believed that Earth moved through the ether, so a stationary observer on Earth should be able to measure the relative speed of the ether as we moved through it. Michelson and Morley devised an experiment where light beams were directed in different directions and brought back together to produce something called interference (we shall study interference in the Particles & Waves unit). The idea was that there would be a change in the speed of light when it had to move against the direction of the ether and, through relative motion, they could determine the speed of the ether.
It was a total flop! They found that the speed of light was the same in all directions. It was only later, when Einstein was looking for ways to prove that the speed of light was the same for all observers, that the importance of the Michelson-Morley experiment became apparent.
This video summarises the evidence nicely.
You can’t prove that time and distance change according to speed
Actually we can. The upper atmosphere is constantly bombarded with very high energy particles from space, mostly protons. These particles are called cosmic rays. When cosmic rays collide with atoms at the edge of our atmosphere, many different subatomic particles are produced. We will meet these particles at the start of the Particles & Waves unit. The particle we’re interested in just now is one called the muon (μ). Muons are similar to electrons, but about 200 times heavier.
image by Los Alamos National Lab
The trouble is that muons can’t exist for very long, they have a very short half-life (think back to National 5 radioactivity). In fact, the half-life of a muon is so short that we should never be able to detect the muons produced in the upper atmosphere with a particle detector at ground level, yet we can detect them. Lots of them!
video from the exploratorium
There are two ways in which Special Relativity explains why we can detect muons. The explanation depends whether you are in Earth’s frame of reference, in which case the time dilation explanation is appropriate, or the muon frame of reference, where the length contraction explanation is appropriate. This video from minute physics explains the situation quite well.
For the more curious among you, there is a comparison of the two different frames of reference on the hyperphysics site, with a simulator where you can vary muon parameters and distances to see how the outcome changes.
By now you should have watched the video about satellites. This screenshot showing a satellite passing over the Highlands was taken from about 17 minutes into the programme – did you notice at the time?
It was quite eye-opening to see just how much modern society relies on satellite technology. I’ve got some more examples of the uses for satellites below.
A satellite moves horizontally at constant speed but also accelerates vertically towards the planet’s surface due to gravity. Thankfully, the curvature of the Earth means the satellite doesn’t crash but keeps on orbiting the planet.
Satellites can be used for environmental purposes, such as