Consider a situation where immediately after birth, twins are separated. One continues to live on earth, while the other is whisked away in a space ship at 90% of the speed of light. After 65 years they are reunited. Will they look the same?
I know that the twin that was whisked away will look older
Your answer is not correct. The twin who is "whisked away" at high speed and then returns (presumably at the same speed) will have aged less, by a factor of sqrt[1-(0.9)^2] = 0.436
He will have aged 28.3 Earth years.
In order to determine whether the twins will look the same or not, we need to consider the concept of time dilation, which is an effect of special relativity. According to this theory, time can pass differently for different observers depending on their relative motion.
In this scenario, the twin who stayed on Earth will experience time passing at a normal rate from their perspective. However, the twin on the spaceship traveling at 90% of the speed of light will experience time dilation. This means that time will pass more slowly for them compared to the twin on Earth.
To calculate the time dilation effect, we can use the time dilation formula:
t' = t * sqrt(1 - (v^2 / c^2))
Where:
t' is the time experienced by the moving twin (in their reference frame)
t is the time experienced by the stationary twin (65 years in this case)
v is the velocity of the spaceship (90% of the speed of light)
c is the speed of light
Now, let's do the calculations:
v = 0.9c (c = speed of light = 299,792,458 meters per second)
t' = 65 years * sqrt(1 - (0.9^2))
After calculating, we find that t' is approximately 27.6 years.
So, when the twins are reunited, the twin who stayed on Earth would have aged 65 years, while the twin who traveled on the spaceship would have aged only around 27.6 years. Therefore, the twin who was whisked away will indeed look older than the twin who stayed on Earth.
It's important to note that the degree to which the traveling twin ages less depends on their speed relative to the speed of light. If the spaceship traveled even closer to the speed of light, the time dilation effect would be more significant, causing the aging difference to be even greater.