# Time dilation in de Sitter Special Relativity

• Parvulus
In summary, this equation determines how the time of a point in a de Sitter spacetime is stretched by a factor (1+v/c) relative to a clock at rest within the spacetime.
Parvulus
Since in the papers by Guo & Huang and Aldrovandi & Pereira I couldn't find a practical formula for time dilation in de Sitter Special Relativity, I wonder if anyone here has it (or can derive it from the high-level formulas in those papers).

Specifically,

let be a de Sitter spacetime with horizon R.
Let O be the center of that spacetime.
Let a point P be moving with velocity v with respect to O.

When point P is at distance r with respect to O, a local event starts in P, lasting a proper time interval Delta_ts.

In Special Relativity, Delta_t, the interval of the event as observed from the frame of reference centered in O, would be:

Delta_t = Delta_ts / sqrt[1 - (v/c)^2]

What is the corresponding formula in de Sitter Special Relativity? (most probably involving r/R)

Thank you very much in advance.

Parvulus said:
Let a point P be moving with velocity v with respect to O.
When point P is at distance r with respect to O, a local event starts in P, lasting a proper time interval Delta_ts./QUOTE]
The starting point seen will be t=t_0+r/c and the ending point will be t'=t_o+delta_ts+(r+delta_ts*v)/c.
difference = delta_ts(1+v/c).
I Know about the Sitter and how he rejected emission theorie, for images would get blurred if light would get superluminous with aproaching lamps and subluminous with receding lamps, so: lightvelocity is independent of velocity of the source, c. But I do know that the time of the local event which starts a P of endurance delta_ts is strectched by a factor (1+v/c), assumed that v is the radial velocity.
greetings jm

Hi Parvulus,
my guess is to divide the line element by $dt^2$ to get

$$\frac{d\tau}{dt}=\sqrt{g_{00}-g_{11}\beta^2}$$

the ratio of this for different r gives relative clock rates.

## 1. What is time dilation in de Sitter Special Relativity?

Time dilation in de Sitter Special Relativity is a phenomenon in which time appears to pass at a different rate for observers in different reference frames, specifically in relation to the curvature of spacetime in a de Sitter universe. It is a consequence of Einstein's theory of general relativity and is often used to explain the observed differences in time measurements between objects moving at different speeds or in different gravitational fields.

## 2. How does time dilation in de Sitter Special Relativity differ from time dilation in other theories of relativity?

Time dilation in de Sitter Special Relativity differs from time dilation in other theories of relativity, such as special relativity, in that it takes into account the effects of a non-zero cosmological constant on the curvature of spacetime. This results in a different mathematical formulation for time dilation and can lead to different predictions for observed time differences between objects in different reference frames.

## 3. Can time dilation in de Sitter Special Relativity be observed in everyday life?

No, time dilation in de Sitter Special Relativity is typically only observed in extreme conditions, such as near black holes or in very fast-moving objects. The effects of time dilation are only noticeable when there is a significant difference in the speeds or gravitational fields of the objects being observed.

## 4. What are the implications of time dilation in de Sitter Special Relativity for space travel?

The implications of time dilation in de Sitter Special Relativity for space travel are significant. As an object approaches the speed of light or enters a strong gravitational field, time appears to slow down for that object. This means that astronauts traveling at high speeds or near massive objects will experience time passing at a different rate than those on Earth. This can have practical implications for the coordination of missions and the aging of astronauts.

## 5. Can time dilation in de Sitter Special Relativity be explained without using complex mathematical equations?

While the mathematical equations used to describe time dilation in de Sitter Special Relativity can be complex, the concept itself can be explained without them. Essentially, time dilation occurs when objects are moving at different speeds or in different gravitational fields, causing time to pass at a different rate for each object. This can be visualized using thought experiments and analogies, such as the "twin paradox" or the slowing down of a clock on a fast-moving spaceship.

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