Length Contraction: Why Must dx be Measured in the Prime Frame?

In summary, the Lorentz transformation can be used to derive the length contraction formula for motion in the same direction on the x-axis of two frames. When converting from dx to dx', t must be 0 in order for the formula to work. The reason dx has to be the length measured in the prime frame is because if we pick an object in the prime frame, it will appear longer to the prime observer. Even if we pick an object from the unprimed frame, it will still appear longer to the primed observer. This is because dx represents the length of an object measured in the prime frame with a relative velocity, and it cannot be a stationary object.
  • #1
Pezz
8
0
The Lorentz transformation for motion in the same direction along the x-axis of two frames can be used to derive the length contraction formula. Say we are converting from dx to dx'. The t would obviously have to be 0. That would leave us with dx'=gamma(dx). My question is why dx here has to be the length measured in the prime frame? If we do pick an object in the prime frame we get a longer length that the prime observer measures. However what happens if we pick dx to be an object length in the unprimed frame? Then again it turns out that the primed observer would get a longer measurement but I know this isn't correct. I'm just trying to find the reason as to why dx has to be the length of an object measured in the PRIME frame with a relative velocity and why it cannot be a stationary object.
 
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  • #2
I mean why can I not measure the object instantaneously in my own frame and enter it as dx.
 

1. What is length contraction?

Length contraction is a phenomenon described by the theory of relativity, where an object's length appears to shorten when it is moving at high speeds relative to an observer.

2. How does length contraction work?

According to the theory of relativity, as an object moves at high speeds, its length in the direction of motion appears to decrease from the perspective of an observer. This effect is caused by the distortion of space and time at high speeds.

3. What factors affect length contraction?

The main factor that affects length contraction is the relative speed between the object and the observer. The closer the object's speed is to the speed of light, the more significant the length contraction effect will be.

4. Can length contraction be observed in everyday life?

No, length contraction is only noticeable at extremely high speeds, close to the speed of light. In everyday life, objects are not moving at speeds that would cause a noticeable contraction in their length.

5. What are the implications of length contraction?

Length contraction has significant implications in the field of physics, particularly in the study of particle physics and space travel. It also plays a crucial role in understanding the concept of time dilation and the relativity of simultaneity.

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