# How Does Relativity Affect the Appearance of Large Objects?

• Brett Caton
In summary, the conversation discusses the hypothetical scenario of a Dyson's sphere with changing surface features and machinery dedicated to repairing asteroid strikes. Beta and Gamma, who have synchronized watches, travel to different sections of the sphere's equator and observe each other's progress in repairing equally damaging explosions. The discussion also touches on the concept of relativity of simultaneity and how it would affect the observation of a signal pulse traveling across the sphere's surface.
Brett Caton
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?

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.

## 1. How does relativity affect the appearance of large objects?

Relativity affects the appearance of large objects by distorting the way we perceive their shape, size, and color. This is due to the concept of spacetime, where gravity can bend and warp the fabric of space, causing light to follow curved paths. As a result, the observed appearance of large objects can appear significantly different from their actual appearance.

## 2. Does relativity have a greater impact on larger objects?

Yes, relativity has a greater impact on larger objects because their mass and gravitational pull are stronger. This means that the bending of spacetime around them is more pronounced, resulting in a greater distortion of their appearance. However, the effects of relativity can still be observed on smaller objects, but they may be less noticeable.

## 3. Can relativity change the color of large objects?

Yes, relativity can change the color of large objects. The distortion of spacetime can cause light to follow curved paths, which can result in a phenomenon called gravitational lensing. This can cause the perceived color of an object to appear shifted towards the blue or red end of the spectrum, depending on the direction of the light's path.

## 4. How does relativity affect the apparent size of large objects?

Relativity can affect the apparent size of large objects in two ways. Firstly, the distortion of spacetime can cause the object to appear stretched or compressed, making it seem larger or smaller. Secondly, gravitational lensing can magnify or shrink the perceived size of an object, depending on the direction of the light's path.

## 5. Can we use relativity to measure the mass of large objects?

Yes, relativity can be used to measure the mass of large objects. By studying the effects of relativity on the appearance of objects and their surroundings, scientists can make calculations and estimations about the mass of these objects. This has been successfully used to measure the mass of stars, galaxies, and even entire clusters of galaxies.

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