Calculate Speed of Relativistic Rocket by Observation

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Discussion Overview

The discussion revolves around the calculation of the speed of a relativistic rocket as observed from different reference frames. Participants explore how observers in different locations (point A and the rocket) can measure speed based on their respective clocks and the distance between points B and C, considering the effects of relativity such as time dilation and length contraction.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that an observer at point A can calculate the speed of the rocket using the formula v = L / TimeA, where TimeA is the time measured by the observer.
  • Another participant argues that the passenger in the rocket cannot calculate the speed of the rocket using v = L / TimeB, as in their rest frame, their speed is zero, and they would measure a different distance due to relativistic effects.
  • It is noted that while the passenger can calculate the velocity of points B and C, the distance they measure will differ from L due to their frame of reference.
  • Length contraction is mentioned as a key phenomenon affecting measurements of distance based on the observer's speed.
  • Participants discuss the interplay between length contraction, time dilation, and the relativity of simultaneity, suggesting further study of Lorentz transforms and Minkowski diagrams for deeper understanding.

Areas of Agreement / Disagreement

Participants generally agree that measurements of speed and distance depend on the observer's frame of reference. However, there is disagreement on how to interpret the calculations made by the passenger in the rocket versus the observer at point A, indicating that the discussion remains unresolved.

Contextual Notes

Participants highlight that the calculations are influenced by relativistic effects, and there is an emphasis on the importance of using consistent measurements within the same frame of reference. The discussion does not resolve the nuances of how different observers perceive speed and distance.

Azaravicius
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Hi, here are image of situation. We have observer in point A. He have clock and know distance L between points B and C. He is observing rocket travel from point B to point C at speed near light speed. Can he calculate the speed of rocket using v = L / TimeA?

In rocket at point B here are passenger with clock. He knows distance L between points B and C. After arrival in point C he calculates time it took to travel from point B to point C for him. Can he calculate the speed of rocket using v = L / TimeB?

From relativity we know that time in rocket will be slower nor for point A. And if rocket speed are 100 km/h?
 
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Azaravicius said:
Hi, here are image of situation. We have observer in point A. He have clock and know distance L between points B and C. He is observing rocket travel from point B to point C at speed near light speed. Can he calculate the speed of rocket using v = L / TimeA?
Yes.

Azaravicius said:
In rocket at point B here are passenger with clock. He knows distance L between points B and C. After arrival in point C he calculates time it took to travel from point B to point C for him. Can he calculate the speed of rocket using v = L / TimeB?
No. In his rest frame he knows his speed - zero. He can calculate the velocity of the dots you labelled B and C (perhaps they are space stations or marker bouys or something) using measurements in his frame. He will come up with the same answer as A, although with the opposite sign because the dots are moving left to right while he is moving right to left.

Azaravicius said:
From relativity we know that time in rocket will be slower nor for point A. And if rocket speed are 100 km/h?
Relativistic calculations work at all speeds. It's just that at 100km/h the difference from the Newtonian form is so small that it's not worth the more complex maths.
 
Azaravicius said:
Hi, here are image of situation. We have observer in point A. He have clock and know distance L between points B and C. He is observing rocket travel from point B to point C at speed near light speed. Can he calculate the speed of rocket using v = L / TimeA?
Yes, that's how he can determine that "rocket travel from point B to point C at speed near light speed". It's very important to note here that both L and TimeA are measured in the same frame of reference, that of A.
Azaravicius said:
In rocket at point B here are passenger with clock. He knows distance L between points B and C. After arrival in point C he calculates time it took to travel from point B to point C for him. Can he calculate the speed of rocket using v = L / TimeB?
Here you are making a common mistake, you are mixing up measurements from different frames. In the reference frame of the passenger the distance between B and C is not L. It would be ok to calculate the speed of B-C (not of the rocket, which is at rest in this frame) that way by using a correct distance in that frame. It would come up to the same v as calculated by A, just in the opposite direction.
 
So, distance isn't absolute but it depends at the speed of observer who makes measurements?
 
Yes. Usually the phenomenon is called "length contraction". There's a fairly subtle interplay between that, time dilation, and the relativity of simultaneity. Your best bet is to study the Lorentz transforms, and I strongly recommend looking up Minkowski diagrams too.
 
Thanks.
 

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