Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How does relativity affect the appearance of large objects?

  1. Jun 19, 2015 #1
    I had more information linked but i received a warning saying i can't like to external resources so I'm not sure how to illustrate this with words only.

    Take a Dyson's sphere (empty) as a hypothetical example. Make it 10 light seconds across. (i.e. 5 light second radius). The sphere has surface features which change with time - like solar flares do. Machinery is dedicated to repairing asteroid strikes.

    Ok, think about a 'mountain' - a surface feature jutting out of the sphere large enough to be seen from orbit.

    Beta and Gamma have watches synchronised. Ignore gravitational effects on time (we cannot guess what the sphere weighs).

    The both travel to different sections on it's 'equator' from the centre and up inside the mountains. These are placed the furthest apart you can be and still be in the field of vision of an observer in space - i think that is about 5 light seconds, but I might be misunderstanding the issue and it might be about 7. ( Right angle triangle, a, b 5 light seconds in length (from the radius), so hypotenuse is square root of a^2 +b^2 = root 50 = 7)

    Call the mountain Beta goes out MBeta and Gamma's mountain MGamma.

    An equally damaging explosion - that will take equal time to repair- has occurred at each mountain, recorded to have occurred at the same time from the PoV of the centre - perhaps enemies are responsible for such precision.

    Beta and Gamma initiate repairs then leave their mountains and travel perpendicularly to observe it taking place.

    My understanding is that Beta will see Gamma as being 5 seconds (or 7?) behind schedule, and Gamma will see Beta as the same time behind schedule. Whereas if Newton had been right and light had been instantaneous, then the time lag between furthest and nearest parts would be the same. Beta and Gamma would then both see each other's progress as equally on time.

    They travel back to the exact centre when their work is complete. Comparing watches, they find each was synchronised, they arrived at the centre at the same time, and yet recordings from the surface clearly show the other as being behind time.

    Is this correct? If so I'd like to consider what would happen if a signal pulse, switching on and off, sent from the centre were to inform the surface to light up in colour briefly. How would that look like? I think that under Newton, the whole globe would wink on and off simultaneously - but Einstein means it would appear to someone at a reasonable distance to have concentric rings of light on it's surface? If so, would they appear to move in towards the centre - or out?
  2. jcsd
  3. Jun 19, 2015 #2


    User Avatar
    Science Advisor

    You are mostly talking about the travel time of light here, which is not necessarily a relativistic effect. That the speed of light is finite was known for around fifty years before we put all the pieces of relativity together.

    Yes, if the sphere was made to flash by the method you describe then it would appear to light up at the point nearest the observer and then spread outward. The observer could, of course, correct for the varying lag and deduce that the flash had been simultaneous (although he'd have to assume Einstein's simultaneity convention).

    Where relativity comes in is that if the observer is moving, the flash will not be simultaneous even after correcting for the travel time of light. You may wish to look up "relativity of simultaneity".

    By the way, we can easily measure the mass of the sphere - just drop something and time its fall.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook