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When one says that Newton believed in the concept of "absolute space" and "absolute time" does it simply mean that the length interval between two points in space and time interval between two events is independent of the state of motion of the observer? If there is something more to it or if I am incorrect please disabuse my misconception.

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    $\begingroup$ Yes, this is what he believed. It is easy to prove using Galilean transformations. $\endgroup$ – TheAverageHijano Feb 26 at 16:30
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Newton does not reference intervals in his work. Quoting from the Scholium (appendix) to Philosophiae Naturalis:

...And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

  1. Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external, and by another name is called duration; relative, apparent, and common time is some sensible and external ... measure of duration by the means of motion, which is commonly used instead of true time, such as an hour, a day, a month, a year.
  2. Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces, which our senses determine by its position to bodies and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude, but they do not remain always numerically the same...

I've edited out some bits to avoid burdening the quote, but the key points are that absolute time refers to time measured by some imaginary ideal "absolute" clock, whereas absolute space refers to some position measured by some imaginary ideal "absolute" coordinate system, which are postulated as ipso facto existing on their own, without relation to anything external.

It is Galilei who discussed what we now called invariants of the state of motion, in the "Second Day" of his Dialogue Concerting the Two Chief World Systems, between Savatius and Sagredius.

Source: The translation of Newton's is by Andrew Motte (1729) as revised by Florian Cajori (Berkeley: University of California Press, 1934).]

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