Relativistic length, 2 viewpoints

In summary, the problem statement discusses two identical cyclists with constant velocities Va and Vb, wondering if one perceives the other as shorter or longer based on the relative speed equation V = Va+Vb/(1+(Va*Vb/c^2)) and relative length equation l = lo * square root from 1-(V/c)^2. The conclusion is that the relative speed and lo are equal for both cyclists, meaning there is no difference in how they see each other. However, this conclusion is only correct if the cyclists are the same length to begin with, and it's important to consider the loss of simultaneity in this scenario.
  • #1
pacu
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Problem statement:

Two identical cyclists ride past each other with constant velocities Va and Vb, which are close to the speed of light. Can it be that cyclist A perceives cyclist B as shorter or longer that cyclist B perceives cyclist A ? Or simply La is NOT equal to Lb ? (La-length of cyclist A as seen by cyclist B, Lb -length of cyclist B as seen by cyclist A).

Relevant formulas:

Relative speed V = Va+Vb/(1+(Va*Vb/c^2))
Relative length l = lo * square root from 1-(V/c)^2

Conclusion:

The V from the second equation is equal for both cyclists, since addition and multiplication are alternate. lo is also equal. So there is no difference in the way cyclists A and B see each other.

Is this conclusion right?
 
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  • #2
its correct if the cyclists are the same length to begin with.

dont forget that there is also a loss of simultaneity. once you factor that in it stops seeming so impossible.
 
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  • #3


Yes, this conclusion is correct. According to the equations provided, the relative speed and relative length are the same for both cyclists. This means that cyclist A and cyclist B will perceive each other as having the same length, regardless of their velocities. This is a result of the principles of relativity, which state that the laws of physics are the same for all observers, regardless of their relative velocities. Therefore, it is not possible for one cyclist to see the other as shorter or longer.
 

1. What is relativistic length?

Relativistic length refers to the concept in Einstein's theory of special relativity that states that an object's length can appear to change depending on the observer's frame of reference and the speed at which the object is moving relative to the observer.

2. Can two observers have different measurements of an object's length?

Yes, according to the theory of special relativity, two observers moving at different speeds will have different measurements of an object's length due to the effects of time dilation and length contraction.

3. How does the speed of light play a role in relativistic length?

The speed of light is considered to be the universal speed limit in the theory of special relativity. As an object approaches the speed of light, its length appears to contract in the direction of motion according to the observer.

4. Can an object's length be measured accurately in both viewpoints?

No, due to the effects of time dilation and length contraction, it is not possible for an object's length to be measured accurately in both viewpoints simultaneously. The measurements will always be different depending on the observer's frame of reference.

5. Is relativistic length a significant concept in modern physics?

Yes, relativistic length is a fundamental concept in Einstein's theory of special relativity and has been experimentally verified through various experiments, including the famous Michelson-Morley experiment. It has also played a crucial role in our understanding of the universe and has been applied in fields such as particle physics and cosmology.

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