Length Contraction & Time Dilation: Relative Velocity Impact?

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Discussion Overview

The discussion revolves around the concepts of length contraction and time dilation in the context of special relativity, particularly focusing on how relative velocity impacts these phenomena. Participants explore the implications of these effects from different frames of reference, considering both theoretical and conceptual aspects.

Discussion Character

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

Main Points Raised

  • One participant questions whether the distance covered by an object moving close to the speed of light also contracts, suggesting that from the traveling object's perspective, its surroundings would appear contracted.
  • Another participant agrees with the initial claims but advises more precise formulation regarding the observer's perspective.
  • A different viewpoint states that the two frames of reference agree on the velocity of each other, referencing the relativistic velocity addition formula.
  • One participant seeks clarification on whether the distance to a destination contracts for an observer at rest, implying that only the rocket itself contracts.
  • It is confirmed that the rocket perceives itself as normal while the distance to its destination appears contracted, whereas observers on Earth see the rocket as length contracted.
  • A participant presents a hypothetical scenario involving a light clock moving vertically at near light speed, questioning the time it takes for light to travel within the clock due to contraction effects.
  • Another participant suggests that the duration of a complete cycle of the clock should be calculated to verify consistency across frames, encouraging the sharing of calculations if discrepancies arise.

Areas of Agreement / Disagreement

Participants generally agree on the principles of length contraction and time dilation but express differing views on the implications of these effects in various frames of reference. The discussion remains unresolved regarding the specifics of how these concepts apply in the presented scenarios.

Contextual Notes

Some assumptions regarding the observer's perspective and the application of relativistic formulas may be implicit in the discussion. The calculations related to the light clock scenario are not fully explored, leaving potential gaps in understanding.

sqljunkey
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So an object moving close to the speed of light will be length contracted. Does that mean the distance it covers also contracts in length? From the traveling object's point of view it's surrounding's would contract as he sees them moving along.

In these scenarios wouldn't velocity be a relative component too? will the two frames of reference disagree about the velocity? given that time and space has been different.
 
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Generally: yes, yes and yes. You want to formulate a bit more precisely (in particular who is the observer drawing such a conclusion), but you will learn that quickly enough when you do exercises.

Check out the MIT game -- it's fun
 
Apart from the sign, the two frames agree on the velocity of the other. In general, velocities are related by the relativistic velocity addition formula.
 
Okay. To be sure I understand this right, the distance the rocket traveling at near speed doesn't contract for an observer at rest right, only the rocket contracts
 
Yes. The rocket sees itself as normal and the distance to its destination contracted. Observers on Earth see themselves as normal and the rocket length contracted
 
I doodled a sketch here. Let's say there is a light clock 299792458 meters tall (or one light second) and instead of moving horizontally it moves vertically, with speed .999999c . Along this y-axis that it's moving it contracts to 24,486.42 meters. Wouldn't it be close to 1 second when the light traveled from the bottom of the light clock to the top of the light clock, since now the ceiling of the clock contracted. Instead of taking 570 something seconds if it was traveling horizontally ?
 
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You need to work out the duration of a complete cycle of the clock - from bottom to top and back down. Then you should get the same answer in both cases.

Edit: if you don't, post your maths and we'll see where you went wrong. I recommend working in units of seconds and light seconds. Then the speed of light is 1.
 

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