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Post by vincent on Jan 24, 2021 6:49:51 GMT 10
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Post by dennisw on Jan 24, 2021 8:25:54 GMT 10
Scientists are used to dealing with very large and very small numbers. Take the age of the universe, for example. Dated at 13.8 billion years old, it has existed for a hundred thousand times longer than Homo sapiens. At the opposite end of the number spectrum, the rapid speed of atomic and subatomic processes are measured in tiny slivers of time. It takes light a mere trillion-trillionth of a second to cross an atomic nucleus.
The ratio of these two time scales, macro and micro, is itself a very big number – about 1040. In the 1920s, British astronomer Sir Arthur Eddington became fixated on a curious coincidence regarding this huge number.
An atom of hydrogen – the simplest atom of all – consists of one electron, negatively charged, bound by electric forces to a positively charged proton. But there is a tiny gravitational attraction between these two particles as well. The ratio of these two forces is also about 1040.
Physicist Paul Dirac came up with a possible explanation. He pointed out that the age of the universe is not a fixed number, but grows over time. At one second after the Big Bang, for example, the time scale ratio was not 1040 but 1024. Dirac thought it was too much of a coincidence that humans just happened to live when the two ratios were about the same.
He was convinced there was an unseen link between the two. As the universe changes over time, Dirac proposed, the ratio of gravitational and electric forces must change along with it. Each year, he suggested, gravity weakens by about one part in 10 billion.
When Dirac published his theory in 1937, it became the subject of much discussion. If the force of gravity really did decline with time, it would have a profound effect on the structure of stars and galaxies. It would also mean that the orbits of the planets grow slowly larger; Earth, for example, would gradually move away from the Sun. But at the time, there was no accurate way to test this prediction.
Recent tests have not been able to discover any supporting evidence and so the theory is largely shelved but measurements are still being taken to prove or disprove the hypothesis.
I came to a very similar conclusion as Dirac from a different perspective, I was trying to establish the nature of time and why I have precognitive glimpses of things often long before they happen. The main reason we are unable to detect changes is, I believe, due to what Einstein called "Mach's Principle" which states we really can't know anything because there are actually no inertial frames of reference - everything changes, and right down to the quantum level. Gravity affects the rate at which time passes so that as the universe expends its gravitational field weakens because gravity is inversely proportional to the square of the distance. The weakening gravitational field means that time accelerates, each second is minutely smaller than the one that preceded it and all time occurs in a single instant, it means that all our measurements change as well as the things we measure so we cannot detect the changes.
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Post by Ian Thomas on Jan 25, 2021 5:42:09 GMT 10
@denny
Do you know of a good introductory text about Tensors?
Either a book or PDF course notes. Hopefully authored by someone who can write good, clear English alongside the maths ...
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Post by dennisw on Jan 25, 2021 9:04:47 GMT 10
@denny Do you know of a good introductory text about Tensors? Either a book or PDF course notes. Hopefully authored by someone who can write good, clear English alongside the maths ... There are books called "Calculus for Dummies" and "Pre-calculus for Dummies" that have very good basic concepts to get some started I think they also have recommendations for more advanced books. I have looked at them one of the grandkids was learning some concepts and had them, the best is often find a professor or expert sometimes a ten or fifteen minute chat can turn on a light and make it easy. My Ah-Ha moment came from reading notes of a lecture given by Einstein in 1931 it suddenly made sense. It usually just takes one little key to get the whole concept. It depends on your end goal but you could try something like this; machinelearningmastery.com/introduction-to-tensors-for-machine-learning/ |
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