So I understand the basic premise on which Special Theory of Relativity hinges:
1. Speed of Light is the same no matter from what frame of reference it is measured. So a guy inside a moving train measures it at 300,000 Km/s as much as a guy standing still at the railway station
2. There is no experimental setup that can prove one object to be stationary and the other one to be moving. In other words, there is no preferred constant speed. It can always be argued that object A is stationary and another object B is moving at 5 Km/Hr as much as it can be argued that object B is stationary while A is moving at 5 Km/Hr in opposite direction.
These two postulates throw up a set of equations we collectively refer to as Special Theory of Relativity. One of these equations explains time dilation:
T' = T * SQRT(1 - v^2/c^2)
where, T is time at rest, v is the speed at which the object is moving and c is the speed of light. T' is the speed of light while the object is moving at speed v.
Here's the problem that I have not yet been able to comprehend:
Assuming two brothers A and B were at railway station. At exactly 3PM, B boards a train that travels at 99% the speed of light only to return back after 2 seconds according to B's watch while A is still at the railway station. The way I have been told how theory of relativity will manifest itself is:
Once B is back to the station and the two brothers check the time on their respective watches, B sees that it has been 2 seconds past 3 PM while for A, the time is about 10 seconds past 3 PM (T' in above equation is B's time and T is A's). Apparently for B, time slowed down. Turning this problem around, can it not be argued that B and the train were stationary and that it was A who traveled at 98% the speed of light in the opposite direction? In that case one would infer that the time slowed down for A and not B. If the example is correct then it appears that Special Theory of Relativity is contradicting itself and that indeed there is a preferred frame of reference and A is to be treated at speed 0 only and B is to be treated as the one that is moving.
I am sure I am missing something. Can someone please help me as to what is going wrong here?
1. Speed of Light is the same no matter from what frame of reference it is measured. So a guy inside a moving train measures it at 300,000 Km/s as much as a guy standing still at the railway station
2. There is no experimental setup that can prove one object to be stationary and the other one to be moving. In other words, there is no preferred constant speed. It can always be argued that object A is stationary and another object B is moving at 5 Km/Hr as much as it can be argued that object B is stationary while A is moving at 5 Km/Hr in opposite direction.
These two postulates throw up a set of equations we collectively refer to as Special Theory of Relativity. One of these equations explains time dilation:
T' = T * SQRT(1 - v^2/c^2)
where, T is time at rest, v is the speed at which the object is moving and c is the speed of light. T' is the speed of light while the object is moving at speed v.
Here's the problem that I have not yet been able to comprehend:
Assuming two brothers A and B were at railway station. At exactly 3PM, B boards a train that travels at 99% the speed of light only to return back after 2 seconds according to B's watch while A is still at the railway station. The way I have been told how theory of relativity will manifest itself is:
Once B is back to the station and the two brothers check the time on their respective watches, B sees that it has been 2 seconds past 3 PM while for A, the time is about 10 seconds past 3 PM (T' in above equation is B's time and T is A's). Apparently for B, time slowed down. Turning this problem around, can it not be argued that B and the train were stationary and that it was A who traveled at 98% the speed of light in the opposite direction? In that case one would infer that the time slowed down for A and not B. If the example is correct then it appears that Special Theory of Relativity is contradicting itself and that indeed there is a preferred frame of reference and A is to be treated at speed 0 only and B is to be treated as the one that is moving.
I am sure I am missing something. Can someone please help me as to what is going wrong here?
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