Einstein’s Postulates – Learn

Frames of Reference

A frame of reference describes where an observation is being made from. This small statement, whilst simple, has strong consequences for how we observe the world – two people observing the same event from different frames of reference will describe that event quite differently. Galileo first explored this concept and its effects on velocity. Einstein later applied these ideas to light and electricity to think about the consequences for time, kinetic energy, length and mass. It implies that these measurements are all relative to the observer.

One of Galileo’s famous experiments had him demonstrate his idea by dropping a cannon ball from the top of the mast on a ship that was sailing at a constant velocity. To the observer at the top of the mast, the cannon ball falls directly downward. Contrast this to a stationary observer on land who describes the motion of the cannon ball as parabolic. Who is more correct? Both are correct as one frame of reference is no more correct or true than another frame of reference.

Newton developed Galileo’s ideas to say that his observations would only hold true in frames of reference that were either stationary or moving at a constant velocity. He called these inertial frames of reference. Inertial frames of reference include a person standing still or a car travelling at a constant speed. Non-inertial frames of reference include a train accelerating or a car travelling around a corner.

Einstein conducted many thought experiments with the idea of relativity in inertial frames of reference. He developed incredible ideas about the relativity of space, time and mass which were later proven to be true by experiment.

Relativity

Relativity is the idea that measurements made in different frames of reference can lead to observers recording different results. It was demonstrated that no frame of reference was more correct or truer than another frame of reference with the simple test, that in an inertial frame of reference one could not determine if they were moving or not. Consider a rock hanging from a string – in a stationary car or a car moving with constant velocity, that rock will hang directly downward perpendicular to the ground – you observe the same result. However, if that car is speeding up or slowing down you will observe the rock at a different angle – thus proving motion.

Einstein concluded that all inertial frames of reference must be equally valid and that the laws of physics must apply in any inertial frame of reference.

Resolving the Ether

Einstein was fascinated with the idea of relativity and the impact of Maxwell’s equations. Maxwell had predicted that the speed of light would be constant. Most scientists simply assumed that this constant speed of light would be relative to some medium which permeated through all space which light travelled through. It was thought any measured speed of light would need to be adjusted to account for the observers own speed through this medium.

As light travelled from the Sun to Earth this medium was considered to be particularly special or ‘ethereal’. It was conveniently termed the ‘aether’. It was described as a massless, rigid medium which could ‘carry’ electric and magnetic waves. The idea that the speed of light was dependent on some other inertial frame of reference troubled Einstein as this completely went against the theory of relativity – particularly that no frame of reference was more correct than another.

Whilst many failed experiments tried to detect the aether, none was more famous than the Michelson-Morley experiment. They tried to detect the speed of the Earth through the aether by measuring the changes in speed of light beams that started on the same path and were split perpendicularly before rejoining. If the Earth was travelling through the aether, the light rays would have arrived at different times out of phase. An analysis of the resulting interference pattern would allow the speed to be determined. Despite trying this experiment at different times of the year and at different orientations, no aether was ever detected. The experiment was considered a null result – it didn’t prove the existence of the aether but it also did not prove that it did not exist.

Einstein resolved the issue by suggesting that there was just no need for the existence of an aether. However, doing away with the aether could not resolve the issue of the speed of light being a constant and the principle of relativity – What was this constant speed of light in reference too?

Einstein’s Postulates

Despite their contradictions, Einstein was enthralled with the simplistic, yet elegant theories proposed by Galileo and Maxwell. This left the question – how can two observers, in different frames of reference, observe the same light beam to be travelling at the same speed? Einstein believed that the answer was in the very nature of how we perceive space and time. To this end, Einstein proposed his two postulates (statements assumed to be true):

• The laws of physics are the same in all inertial frames of reference
• The speed of light has the same value for all observers regardless of their motion or the motion of the source

When Newton expanded on the work of Galileo, he made two assumptions about space and time – they were both absolute – any observation of space and time would be the same for any observer. Einstein realised that the assumptions that Newton made were not valid, especially on the scale of the Universe and relativistic speeds (speeds approaching the speed of light). Einstein concluded that the only way his postulates can be true is if space and time are not fixed and unchangeable. From this, Special relativity was born – space and time are relative!

The Evidence for Einstein’s Postulates

Cosmological Studies

When stars explode it causes a Supernova. The particles from a Supernova can travel out at speeds which are 3% the speed of light. If the speed of light depended on the speed of the source then there should be some observable difference between the fragments which are moving away from us and those which are moving toward us. Astronomers have observed no such difference. This further confirms that the speed of light is absolute, irrespective of your frame of reference.

Physicists and astronomers have also never managed to observe or record any matter travelling faster than the speed of light.

Muons

Muons are particles which have a mass that is about 200 times larger than that of an electron. They are produced naturally when cosmic rays from the Sun interact with the upper atmosphere. The muons that are produced in the upper atmosphere then travel toward the Earth at a speed close to the speed of light.

In the laboratory (same frame of reference), muons are observed to have an average lifetime of 2.2 × 10−6 s (2.2μs). In early work with muons, they were observed and detected on a mountain top at an altitude of 1900m above sea level and travelling at a speed of 0.995c. This relativistic speed makes them ideal for observing relativistic effects.

Considering the lifetime of a muon and their relativistic speed, Newtonian physics predicted that on average a muon would travel only 658m. Muons are created at an altitude of approximately 15km above sea level and after several average lifetimes it was expected that no muons would make it to the surface of the Earth. Muons have been detected at the surface of the Earth and this means that they have existed for a much longer timeframe than was expected – 22.8 times their expected lifetime.

This observation can only be explained if the lifetime of the muon was increased well beyond its expected lifetime. Relativity and time dilation explains and predicts that this result is to be expected. Relativity closely predicted the number of muons making it to the surface of the Earth. An observer on Earth would see the muons time run much slower. This means that the muons will exist long enough to be observed on the surface of the Earth in the same frame of reference as the observer.

Atomic Clocks

Atomic clocks are extremely precise and achieve precisions of around 1 second/100,000,000 years. Atomic clocks use the frequency of radiation emitted during electronic transmissions in atoms to measure time. Their precision makes them useful for observing relativistic effects when speeds are not particularly high.

In 1971 an experiment was conducted by placing an atomic clock on the Earth. From the same location, passenger jet planes flew east and west also carrying atomic clocks. The jets flew around the Earth twice and returned to have the clocks compared with the atomic clock that was stationary. When compared the clocks that had flown around the Earth were found to have different times to the stationary clock – the differences were predicted by relativity.

Particle Accelerators

More recent experiments have tested time dilation predictions to high precision. In 2014 a team of physicists conducted experiments using particle accelerators. They measured the rates of transitions between energy states of atoms moving at one-third the speed of light in the particle accelerator. They were then able to compare these rates with the rates of transitions of the same atoms at rest in the laboratory. The difference in rates matched Einstein’s predictions to the highest levels of precision achieved to date.