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Universe - Infinite or finite?

One of the presently unanswered questions about the universe is whether it is infinite or finite in extent.

Two possibilities exist: either the Universe is finite and has a size, or it’s infinite and goes on forever. Both possibilities have mind-bending implications.

For intuition, it can be understood that a finite universe has a finite volume that, for example, could be in theory filled up with a finite amount of material, while an infinite universe is unbounded and no numerical volume could possibly fill it. Mathematically, the question of whether the universe is infinite or finite is referred to as boundedness. An infinite universe (unbounded metric space) means that there are points arbitrarily far apart: for any distance d, there are points that are of a distance at least d apart. A finite universe is a bounded metric space, where there is some distance d such that all points are within distance d of each other. The smallest such d is called the diameter of the universe, in which case the universe has a well-defined "volume" or "scale."

Note - Below writeup may not be winning writing. You can write much better essays than below sample. These are just guidelines for your preparation. You can read more information and include in your essay.

Sample Write-up on The Infinite Universe

(Source: https://mathshistory.st-andrews.ac.uk/Astronomy/universe/)

As early as 1344 Bradwardine attacked the Aristotelian idea that the universe was finite in size, arguing that the universe was infinite in extent as God himself was. This was a view shared by many such as Oresme in the 14th century. Nicholas of Cusa in the 15th century also argued that the universe was infinite and full of stars, and that, as the universe was infinite, the Earth could not be at its centre ‚a debate continued long after his death.

However, it was not until the 20th century that the question of the universe's size became of huge importance. Einstein's revolutionary general theory of relativity in 1916 had a finite universe (Einstein had to include a cosmological constant to achieve this as he believed the universe was static) and depended on non-Euclidean space. Astronomers such as de Sitter were uncomfortable with this idea. In 1917 de Sitter suggested an infinite universe to make Relativity and Euclidean space compatible. Then considered to be a flaw in his theory, de Sitter's universe required that matter move apart from each other. While his theory was incorrect, this was not the reason why. Following on from his determination of the distance to the Andromeda galaxy, and the realisation that Andromeda was composed of stars similar to those in the Milky Way, Hubble was able to determine that galaxies are moving away from us. Indeed, that they receded with a speed proportional to their distance from us. After visiting Hubble's observatory, Einstein then set his cosmological constant to zero. His theory of relativity helped us make great advances such as finally explaining the movements of Mercury and Eddington's observation of light bending round the sun.

Friedmann and Lemaître independently explored solutions to Einstein's field equations and came to the conclusion that the universe was expanding in the 1920s, before Hubble observationally established that this was the case in 1929. If the galaxies are moving away from each other, it made sense that they started from an original point, a conclusion Lemaître came to in 1931. (It was not until 1950 that Hoyle derisively coined the term 'The Big Bang'). In 1948 Gamow and Alpher calculated that in order for chemical elements to be synthesised in the ratios we see them today, it was necessary for the universe to have a hot, dense phase in its early stages. Also in 1948, Alpher and Hermann probed deeper into the early universe and came to the conclusion that there would be leftover thermal radiation from this stage. Today this is known as cosmic microwave background radiation. It was first measured by Penzias and Wilson in 1965 and forms part of the static you hear on the radio.

A plethora of astronomers, scientists and mathematicians have made progress on astronomy, from planetary orbits to stellar structure to the existence of black holes. Recently, over one hundred years after they were predicted by Poincaré in 1905, gravitational waves were detected in 2016 to the excitement of the scientific community. It is incredible that even in the light of so much discovery, we can still gaze up at the stars in as much wonder as our ancestors once did.

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