Object Moving Faster Than Light?

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Discussion Overview

The discussion centers around the concept of an astronaut traveling to a galaxy 200 million light-years away while accelerating at 1 g, exploring the implications of relativistic effects such as time dilation and length contraction. Participants examine how these effects might lead to the perception of the galaxy moving faster than light from the astronaut's perspective.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes a scenario where an astronaut accelerates towards a distant galaxy, experiencing only 26 years of time passage while observing the galaxy initially 200 million light-years away, suggesting it appears to move at 8 times the speed of light.
  • Another participant requests clarification on the initial question, indicating that the claim of exceeding the speed of light can be interpreted in multiple ways.
  • A participant relates the scenario to the "twin's paradox," asserting that while the astronaut and light from the galaxy do not exceed the speed of light, relativistic effects could make the galaxy appear to move faster than light due to length contraction.
  • One participant challenges the application of the twin paradox, arguing that the scenario does not involve a round trip and suggests that length contraction would allow the astronaut to reach the galaxy in 26 years.
  • This participant also notes that the rocket's non-inertial frame complicates the situation, mentioning that the speed of light may not be constant in such frames and that the galaxy's apparent speed could vary based on simultaneity conventions.

Areas of Agreement / Disagreement

Participants express differing interpretations of relativistic effects, particularly regarding length contraction and the implications for perceived speeds. There is no consensus on the interpretation of the astronaut's experience or the applicability of the twin paradox.

Contextual Notes

Participants highlight the complexities of non-inertial frames and the implications of simultaneity conventions, indicating that the discussion involves unresolved assumptions and interpretations of relativistic physics.

swampwiz
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I had read in the Time-Life Science Library book "Man And Space" about the possibility of a very, very ambitious mission in which an astronaut would go to a galaxy 200 million light-years away, with the spacecraft simply being accelerated at 1 g during the whole time (in the direction of the galaxy for half of a leg, then in the other direction for the other half), and thus going for the most part at nearly the speed of light as observed from the Milky Way, with the net effect that the astronaut would experience about 26 years of time pass by for each leg. This astronaut would start his trip by observing that galaxy as being 200 million light-years away, but then reach the galaxy in only 26 years, thus he would conclude that the galaxy appears to be moving at about 8 times the speed of light. What gives?
 
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Hi Wiz,

Could you formulate your actual question a bit clearer ? 'What gives' can be replied in umpteen ways, e.g. with: it is not possible to exceed the speed of light
 
This is basically part of the "twin's paradox". Yes, the astronaut & light from the galaxy would not be exceeding the speed of light, but nonetheless the net effect of traveling near the speed of light and the increase in the length contraction would make the galaxy appear to be traveling at greater than the speed of light.
 
This isn't the twin paradox because it's not a round trip.

I think you have length contraction wrong. To an observer in the rocket the distance between the galaxies is length contracted, sufficiently so that 26 years is enough time for the destination galaxy to reach the rocket.

We're being a bit sloppy here because the rocket frame is not inertial, but the gist of it is as above. Edit: do note that the speed of light is not constant in non-inertial frames, so the rocket observer may see the galaxy travel very quickly (whether it ever exceeds c depends on the simultaneity convention used, I suspect). It will never overtake light, however.
 
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