eli5: If space is expanding faster than light in all direction. Why hasn’t the space between our atoms expanded to infinite?
In: 530
The expasion rate of the universe is today estimated dto be around 73km/s /MegaParsec
The speed of light is around 300 000 km/s so two points needs to be 4100 MegaParsec apart of the distance in between to example at the speed of light.
1 parsec= 3.26 light years. 1 megaparsec = 3.26 million light years.
So 4100 MegaParsec = 13.3 billion lightyears
The atoms you talk about are not billions of lightyears apart, that is the distance required for space in between to expand at the speed of light. Atoms in molecules are less than a nanometer apart.
Let do come caulatioin and round to multiple of 10 for simplisity
13.3 billion lightyears = 12.6* 10^23 meter~10^24 meter, 1 nanometer = 10^-9 meter. This means the distance need to be 10^24/10^-9 = 10^33 times longer for the expansion to be the speed of light. That is another way to write 1 million billion billion billion times longer.
The speed of light is 3 * 10^8 m/s so the distance between to atoms expan by 3 * 10^8 /10^33 = 3* 10^-25 m/s
One year is 3600* 24* 365 =31536000s ~ 3*10^7 second
The mean a expansion at 3* 10^-25 m/s in a year is 3* 10^-25 *3*10^7 ~10^-19 m
The diameter r of a atom is around 10^-10 meters so the expansion is around 10^-9 of an atom.
So the space between to atoms expands by around 1 billionth of the diameter of a atome each year. That is counted by the forest that holds atoms together in molecules.
To get distance numbers that are a bit simple to understand, the expansion of space between Earth and the sun in a year is around 11 m. The distance to the sound is around 150 million kilometers = 150 billion meters It will not change the orbit because gravity counteracts it.
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