evidence that special relativity is real

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.

 

applications of satellites

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

monitoring volcanoes

weather forecasting
Screen Shot 2015-10-07 at 23.22.35

 

 

 

 

 

 

 

 

climate change

Read moreapplications of satellites

re-entering the atmosphere

In space there is no air resistance to oppose motion, so the Space Shuttle orbiter could travel at very high speeds, up to 17,000 mph!  At these speeds, the orbiter experienced enormous air resistance as it descended into the Earth’s atmosphere at the end of its mission.

Air resistance is just like any other form of friction – it converts kinetic energy into heat energy.  The effect of this heat energy is demonstrated in this video clip taken by a Canadian police car camera.  It shows a meteor burning up in the atmosphere above Edmonton.

Thankfully most meteors do burn up in the atmosphere, although the dinosaurs were not so lucky.

The high temperatures created during re-entry ionised the gas around the orbiter and this is often seen as a bright light in NASA cockpit videos, such as the one shown below.

To protect the vehicle and its crew from these high temperatures, the underside of the orbiter was covered by a layer of heat resistant tiles called the thermal protection system.  This NASA clip explains how the tiles are constructed and arranged on the underside of the orbiter.

When Columbia was launched in 2003, something fell against the insulation on the left wing and knocked off some of the tiles.  This hole in the thermal protection system caused Columbia to explode over the US as it re-entered the atmosphere.  There is a wikipedia article about the Columbia disaster.

Video footage of NASA’s Houston control room from the morning of the disaster was included in the BBC Horizon documentary Final Descent – Last Flight of Space Shuttle Columbia.

WARNING: This last film is an excerpt from the Horizon programme and includes genuine cockpit video that was found in the wreckage, with some clips of the crew’s final minutes before they were killed.

There is a good description of the Space Shuttle at How Stuff Works.

Before the space shuttle, each spacecraft was designed to be used only once and it was only the capsule containing the crew that returned to Earth. This was a small conical vehicle that had a thick heat shield on its base to withstand the heat of re-entry.

drawing of Apollo capsule re-entering the atmosphereartist’s impression of Apollo capsule re-entering the atmosphere

An ablative heat shield was used for these capsules. The material covering the base was designed to heat up until it sublimed (changed from solid to gas). The latent heat of sublimation is much greater than that required for fusion or vaporisation, so much more heat energy could be absorbed by the shield material as it changed state. Obviously there is a catch…the longer the shield protects the astronauts, the thinner it becomes! Here is an image of a Gemini IV capsule on display at the Smithsonian National Air and Space Museum showing what was left of the heat shield after successful return to Earth.

Gemini IV crew capsule photo: Richard Kruse

 

x-rays

X-rays are a form of electromagnetic radiation.  They have a much higher frequency than visible light or ultraviolet.  The diagram below, taken from Wikipedia, shows where x-rays sit in the electromagnetic spectrum.

image by Materialscientist

Wilhelm Röntgen discovered x-rays and the image below is the first x-ray image ever taken.  It shows Mrs. Röntgen’s hand and wedding ring.  The x-ray source used by Röntgen was quite weak, so his wife had to hold her hand still for about 15 minutes to expose the film.  Can you imagine waiting that long nowadays?

This was the first time anyone had seen inside a human body without cutting it open.  Poor Mrs. Röntgen was so alarmed by the sight of the image made by her husband that she cried out “I have seen my death!” Or, since she was in Germany, it might have been

Ich habe meinen Tod gesehen!

that she actually said.

Röntgen continued to work on x-rays until he was able to produce better images. The x-ray below was taken about a year after the first x-ray and you can see the improvements in quality.

Notice that these early x-rays are the opposite of what we would expect to see today. They show dark bones on a lighter background while we are used to seeing white bones on a dark background, such as the x-ray shown below.  The difference is due to the processing the film has received after being exposed to x-rays.

In hospitals, x-rays expose a film which is then developed and viewed with bright light.  X-rays are able to travel through soft body tissue and the film behind receives a large exposure.  

The x-rays darken the film.

More dense structures such as bone, metal fillings in teeth, artificial hip/knee joints, etc. block the path of x-rays and prevent them from reaching the film.  Unexposed regions of the film remain light in colour.

Röntgen’s x-ray films would have involved additional processing steps.  The exposed films were developed and used to create a positive.  In creating a positive, light areas become dark and dark areas become light.  So the light and dark areas in Röntgen’s x-rays are the opposite of what we see today.  Our modern method makes it easier to detect issues in the bones as they are the lighter areas.

Röntgen was awarded the first ever Nobel Prize for Physics in 1901 for his pioneering work in this field of physics.

X-rays are a very high energy form of electromagnetic radiation. This means they have the potential to harm living cells. Medical staff only take x-rays of a patient when it is necessary to give a correct diagnosis but that wasn’t always the case.

I have attached a recording of a short BBC radio programme about the first x-ray and what people in the Victorian era thought of these new images.  Click on the player at the end of this post.

dosimetry: absorbed dose and equivalent dose

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.

D = \displaystyle {E \over m}

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 W_R.

 H=DW_R

Different types of radiation have different weighting factors, e.g.

type of radiationweighting factor
gamma1
x-ray1
beta1
alpha20

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 Government has set an effective 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.

source: XKCD

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.

geiger-müller tube

We’ve examined the operation of a Geiger-Müller counter as part of the radiation topic.

image by Theresa Knott

The Geiger-Müller (GM) counter is used to detect ionising radiation such as alpha and beta particles or gamma rays.  The radiation enters through a very thin window at one end of the tube.  This window is usually made of mica.

Mica flakes.  Photo by Rpervinking

Mica is a mineral that forms in layers called sheets.  These sheets can be split apart into very thin layers, so thin that even an alpha particle can pass through it (remember that alpha particles can be stopped by something as thin as your skin or a sheet of paper).  The mica window prevents the argon inside the tube from escaping and also stops air from getting into the tube.

When radiation enters the tube and collides with an argon atom, an electron may be knocked off the atom – we call this process ionisation.  When ionisation occurs, a positively-charged argon ion and a negatively-charged electron are produced.  The argon ion is attracted to the outside wall of the tube, which is connected to the negative terminal of the power supply, while the electron is attracted to the central electrode, which is kept at a high positive voltage – typically 500V.

A small pulse of current is produced each time an electron reaches the central electrode.  These pulses can be counted by an electronic circuit and a displayed on a 7-segment display.  Sometimes a small speaker is added to the system to produce a click for each pulse.  On its own, the GM tube cannot tell the difference between alpha, beta and gamma radiation.  We need to place different materials (e.g. paper, aluminium, lead) in front of the mica window to discover which type of radiation is responsible for the reading.

Here is a short video demonstrating the use of a Geiger-Müller tube.

 

x-rays

X-rays are a form of electromagnetic radiation.  They have a much higher frequency than visible light or ultraviolet.  The diagram below, taken from Wikipedia, shows where x-rays sit in the electromagnetic spectrum.

image by Materialscientist

Wilhelm Röntgen discovered x-rays and the image below is the first x-ray image ever taken.  It shows Mrs. Röntgen’s hand and wedding ring.  The x-ray source used by Röntgen was quite weak, so his wife had to hold her hand still for about 15 minutes to expose the film.  Can you imagine waiting that long nowadays?

This was the first time anyone had seen inside a human body without cutting it open.  Poor Mrs. Röntgen was so alarmed by the sight of the image made by her husband that she cried out “I have seen my death!” Or, since she was in Germany, it might have been

Ich habe meinen Tod gesehen!

that she actually said.

Röntgen continued to work on x-rays until he was able to produce better images. The x-ray below was taken about a year after the first x-ray and you can see the improvements in quality.

Notice that these early x-rays are the opposite of what we would expect to see today. They show dark bones on a lighter background while we are used to seeing white bones on a dark background, such as the x-ray shown below.  The difference is due to the processing the film has received after being exposed to x-rays.

In hospitals, x-rays expose a film which is then developed and viewed with bright light.  X-rays are able to travel through soft body tissue and the film behind receives a large exposure.  The x-rays darken the film. More dense structures such as bone, metal fillings in teeth, artificial hip/knee joints, etc. block the path of x-rays and prevent them from reaching the film.  Unexposed regions of the film remain light in colour.

Röntgen’s x-ray films would have involved additional processing steps.  The exposed films were developed and used to create a positive.  In creating a positive, light areas become dark and dark areas become light.  So the light and dark areas in Röntgen’s x-rays are the opposite of what we see today.  Our modern method makes it easier to detect issues in the bones as they are the lighter areas.

Röntgen was awarded the first ever Nobel Prize for Physics in 1901 for his pioneering work in this field of physics.

 

I have attached a recording of a short BBC radio programme about the first x-ray and what people in the Victorian era thought of these new images.  Click on the player at the end of this post or listen to it in iTunes.

total internal reflection

Earlier this week, we used semi-circular perspex blocks to investigate total internal reflection.

I’ve put together a short video showing total internal reflection in a semicircular block and a perspex model of an optical fibre.

total internal reflection from mr mackenzie on Vimeo.

There are some nice ray diagrams explaining total internal reflection on BBC Bitesize.

Cyberphysics has some examples of how optical fibers are used and the youtube video below shows how they can be used by doctors to see inside a patient’s body.

using linest to obtain a gradient and uncertainty

The period T of a simple pendulum can be calculated using

T=2 \pi \displaystyle \sqrt{l \over g}

where l is the pendulum length and g is the gravitational field strength.

Using a single value of length and period, we can determine the acceleration due to gravity.  However, it would be better experimental practise to vary the length of the pendulum and plot a graph of T^2 against length, determining g from the gradient of the line of best fit.

You’re going to spend the next few periods analysing your simple pendulum data.  The attached pdf will walk you through the steps.  It would be better if you used your own results but I’ve put some sample data on the first page if you’ve forgotten to bring yours.

If you are using your chromebook, there may be subtle differences from the Excel instructions I have provided.  Let me know if anything doesn’t work and I’ll try to help.

Note that if you are using your own data, there will be no random uncertainty as measurements were not repeated.