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Consider an apparatus similar to that used in Michelson-Morley experiment kept in a frame (S') moving with a constant speed (v) to the right of an inertial frame (S).

The apparatus consists of a light source, a partially silvered glass (B) in front of the source and two mirrors facing B (at a length L from B) and perpendicular to each other.

Light leaves the source and is reflected as well as transmitted at B. Let $T_1$ and $T_2$ be the total times to reach the mirrors from B and return back.

According to Special Relativity, the speed of light (c) is constant in both the frames. Thus, for S' $T_1=T_2=2L/c$ and for S $T_1=\frac{2L/c}{1-u^2/v^2}$$T_1=\frac{2L/c}{1-v^2/c^2}$ and $T_2=\frac{2L/c}{\sqrt{1-u^2/v^2}}$$T_2=\frac{2L/c}{\sqrt{1-v^2/c^2}}$.

From this it is evident that the two beams of light reach back B simultaneously in S' but not in S. But how can the two frames observe two different events - light reaching simultaneously at the same point and light not reaching simultaneously?

Consider an apparatus similar to that used in Michelson-Morley experiment kept in a frame (S') moving with a constant speed (v) to the right of an inertial frame (S).

The apparatus consists of a light source, a partially silvered glass (B) in front of the source and two mirrors facing B (at a length L from B) and perpendicular to each other.

Light leaves the source and is reflected as well as transmitted at B. Let $T_1$ and $T_2$ be the total times to reach the mirrors from B and return back.

According to Special Relativity, the speed of light (c) is constant in both the frames. Thus, for S' $T_1=T_2=2L/c$ and for S $T_1=\frac{2L/c}{1-u^2/v^2}$ and $T_2=\frac{2L/c}{\sqrt{1-u^2/v^2}}$.

From this it is evident that the two beams of light reach back B simultaneously in S' but not in S. But how can the two frames observe two different events - light reaching simultaneously at the same point and light not reaching simultaneously?

Consider an apparatus similar to that used in Michelson-Morley experiment kept in a frame (S') moving with a constant speed (v) to the right of an inertial frame (S).

The apparatus consists of a light source, a partially silvered glass (B) in front of the source and two mirrors facing B (at a length L from B) and perpendicular to each other.

Light leaves the source and is reflected as well as transmitted at B. Let $T_1$ and $T_2$ be the total times to reach the mirrors from B and return back.

According to Special Relativity, the speed of light (c) is constant in both the frames. Thus, for S' $T_1=T_2=2L/c$ and for S $T_1=\frac{2L/c}{1-v^2/c^2}$ and $T_2=\frac{2L/c}{\sqrt{1-v^2/c^2}}$.

From this it is evident that the two beams of light reach back B simultaneously in S' but not in S. But how can the two frames observe two different events - light reaching simultaneously at the same point and light not reaching simultaneously?

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Big Brother
Big Brother
  • 259
  • 3
  • 15

How can two different inertial frames observe two different events?

Consider an apparatus similar to that used in Michelson-Morley experiment kept in a frame (S') moving with a constant speed (v) to the right of an inertial frame (S).

The apparatus consists of a light source, a partially silvered glass (B) in front of the source and two mirrors facing B (at a length L from B) and perpendicular to each other.

Light leaves the source and is reflected as well as transmitted at B. Let $T_1$ and $T_2$ be the total times to reach the mirrors from B and return back.

According to Special Relativity, the speed of light (c) is constant in both the frames. Thus, for S' $T_1=T_2=2L/c$ and for S $T_1=\frac{2L/c}{1-u^2/v^2}$ and $T_2=\frac{2L/c}{\sqrt{1-u^2/v^2}}$.

From this it is evident that the two beams of light reach back B simultaneously in S' but not in S. But how can the two frames observe two different events - light reaching simultaneously at the same point and light not reaching simultaneously?