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# Special relativity framework

Updated Friday, 14th December 2012

Here we look at the framework of special relativity and examples of measured time dilation and length contraction

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Watch this animated video on special relativity

Our everyday ideas about the way objects move are mostly embodied in Isaac Newton’s laws of motion. However, these turn out not to be true when the speeds involved approach the speed of light, about 300,000 kilometres per second.

In that circumstance, the formulae derived by Newton turn out to be only approximations to the real situation. For a more accurate description of nature we must turn to the theory of special relativity derived by Albert Einstein and published in 1905.

Crucial to this is the idea of a frame of reference. This is a system for assigning coordinates to an object’s position and times to events that occur. An inertial frame is a frame of reference is one that is not itself accelerating. Bearing that in mind, Einstein’s theory is based on two principles:

I: The laws of physics can be written in the same form in all inertial frames of reference

II: The speed of light in a vacuum has the same constant value in all inertial frames

These two simple ideas lead to many intriguing and counter-intuitive results. Among these is the fact that the duration of a time interval is a relative quantity: the rate at which a clock ticks depends on the frame of reference in which it is measured. This is often paraphrased as ‘moving clocks run slow’ and referred to as time dilation.

Another result is that length is also a relative quantity. The length of a rod depends on the frame of reference in which it is measured. This is often paraphrased as ‘moving rods contract in the direction of motion’ and referred to as length contraction.

Of course, these effects are simply not noticeable at everyday speeds and they only become apparent when the speeds concerned approach the speed of light.

An example of time dilation and length contraction in action concerns the subatomic particles known as muons.  These are a somewhat heavier counterpart of the electron which decay into electrons with a typical lifetime of around two microseconds.

A ready source of muons is from cosmic rays (high energy nuclei originating from the depths of space) that strike atoms in the Earth’s upper atmosphere. If the number of muons liberated in the upper atmosphere is measured at the top of a mountain, then knowing the lifetime of a muon and the fact that they are travelling close to the speed of light, it’s possible to calculate the proportion of muons that should survive to be measured at sea level.

However, far more neutrons survive to reach sea level than would be predicted based on non-relativistic assumptions. This can be understood by the realisation that, for the rapidly moving muons, time runs more slowly, so allowing more of them to survive the trip.

Alternatively this may be understood by realising that length is also contracted for the muons. So the distance they travel from the top of the mountain to sea level is shorter than that which a stationary observer would measure, so once again allowing more to survive the journey.

These predictions of special relativity are measured and confirmed to a high level of accuracy on a routine basis in laboratories around the world. It’s not just that time ‘seems’ to pass at a different rate, or objects ‘seem’ to become shorter – these are real physical effects.

Question:  Why is knowledge of special relativity vital for ensuring that the Global Positioning System (GPS) built into many Smartphones and SatNavs operates accurately? Share your answer using our Comments facility.