Universal Speed Limit and Relativistic Mass Physics 12

Length Contraction A concept related to time dilation is that of length contraction In a way that is similar to time changes depending on the frame of reference, length is also affected This can be used to explain the behaviour of the mu meson (or muon)

Muon Muons are particles that are created high in the atmosphere due to UV radiation These particles are created about 9000m above the surface of the Earth and travel at about 0.998c

Muon Time Dilation According to time dilation, the muon’s half-life (measured in the frame of reference of the Earth) should be 30μs in the muon’s frame According to time dilation, the muon’s half-life (measured in the frame of reference of the Earth) should be 30μs in the muon’s frame As a result, the muon can travel a.998c for 30μs covering a distance of 9000m As a result, the muon can travel a.998c for 30μs covering a distance of 9000m

Muon Length Contraction According to length contraction, the distance that the muon needs to move through (measured in the frame of reference of the Earth) should be 600m in the muon’s frame According to length contraction, the distance that the muon needs to move through (measured in the frame of reference of the Earth) should be 600m in the muon’s frame As a result, the Earth rushes towards the muon at.998c for 2μs covering a distance of 600m As a result, the Earth rushes towards the muon at.998c for 2μs covering a distance of 600m

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Gamma For calculations using special relativity, gamma is often used in order to save time when writing equations:

Universal Speed Limit When we consider gamma, we know that we must be dealing with real numbers so the value under the root must be positive Therefore speed (v) cannot be greater than or equal to the speed of light (c) or the denominator becomes imaginary or zero This speed limit only applies to objects with mass (therefore the massless photon can travel at the speed of light)

Cerenkov’s Glow While it is impossible for anything to travel faster than light in a vacuum, it is possible for an object to travel faster than light in a medium This is what leads to Cerenkov’s Radiation which is seen in the cooling pools of a nuclear power plant The particles in the water are travelling faster than the speed of light in the water and the glow is thus produced

Mass and Energy While the gamma term leads to the mathematical understanding that the speed of light is the limit for massive objects, it does not explain why The reason is found in Newton’s Second Law and Einstein’s Special Theory of Relativity Einstein found that in addition to time dilation and length contraction, mass is also affected by relativistic effects

Relativistic Mass As a result, the mass increases as an object’s speed increases Therefore, according to Newton, an object travelling at.999c would require an infinite force to accelerate it to c as:

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