# I Why absolute space cannot be represented as fibers on the axis the absolute time?

#### Thytanium

Summary
The relative space of Galileo and Newton can be considered as fibers of the axis of absolute time but the absolute space time of Aristotle cannot.
Aristotle's absolute space and time can be represented as ordered pairs (s, t) but not as fibers π(s) = t of time as is the case of Galileo and Newton's space time. That is to say that the space of Galileo and Newton is the projection π(s) = t on the time axis. The time space of Galileo and Newton cannot be represented as ordered pairs. How is that understood?

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#### fresh_42

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2018 Award
Can you give us any references of what you mean? And what are fibers of axis?

#### martinbn

Penrose makes distinction between Aristotelian and Galilean space-times (and Newtonian), for example in "Structure of Space-time". May be in "The Road to Reality" as well, but if you didn't understand it, you probably need some more background in mathematics. I don't see how discussing it here could help you.

In any case it would help if you cite your sources and ask more specific questions than "How is that understood?".

#### Thytanium

Thanks for answering friends of the forum: fresh_42 and martinbn. My question arises from Bernard Schutz's book entitled: "Geometrical Metothods of Matematical Physics," Chapter 2, Section 2.11, which deals with fiber spaces. There is a figure 2.13 that shows space as fibers of time. I have also read an article entitled "Fibrated spaces and connections in relativity" that appears on the Web and whose author is the physicist Williams Pitter of the Zulia University and in Spanish language that refers to the cartesian product of the absolute space and time of Aristotle and mentions also the space time of Galileo and Newton and other examples. But in reality what I do not understand is that absolute time space cannot be represented as fibers, and relative time spaces have geometric structure of fibers, that is what I do not understand. Thank you friends for your help and for answering my questions. Grateful to you.

#### fresh_42

Mentor
2018 Award
It would help a lot if we had a description of the spacetime models of Aristoteles and Newton. AFAIK they are all classical Euclidean spaces, i.e. trivial fiber bundles, and then we have absolute spacetime and time as a fiber of a spatial point.

In general relativity there is no distinction between time and space anymore, except that they are different coordinates. We do not have a global coordinate system anymore, but that was not what you asked.

Here is a description of what we are talking about mathematically:
Since you have posted this under differential geometry, the question is: What is $(E,B,p)$ in your various models?

#### Thytanium

Thanks friend fresh_42. Grateful to you.

#### Thytanium

Hello friends of the Forum. I have continued researching on this issue of the space time of Aristotle, Galileo and Newton and I have achieved some results to know what you think about that. For Aristotle, space was absolute because he considered that the earth was motionless and the center of the universe and space outside the earth or cosmic was motionless and subject to the earth, so the mainland was the only valid reference system, and excludes the mobile reference systems and therefore the space referred to the mainland was absolute. With Galileo and Newton things changed because the transformations of them for inertial systems leave the acceleration invariant in all those systems moving at constant speed and in a straight line so there are infinite mobile inertial reference systems in addition to the mainland and therefore the relative space of Galileo and Newton can be considered fibres of the time axis as it appears in the figure of attach file in which an object at rest would be represented as a paralell time line and a mobile would be represented as a diagonal line. This fibre structure could not be done with the absolute time space of Aristotle because it admits infinite inertial referential systems and for Aristotle there is only one and it is the mainland. Aristotle's absolute time-space events can then only be represented as the Cartesian product of two different sets that are space and time. Excuse me because it isn't Theme of differential geometry. Excuse me. Thanks for all.

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