This is an outline of an article on “The Symmetry of Space and Time”. I’ll update it as needed and add links to the parts as they are written.

0.0 Abstract

1.0 Introduction

1.1 Examples of multi-dimensional time, ancient and modern

1.2 Reference to related work

1.3 Overview of the paper

2.0 Simple motion in 1+1 dimensions (space and time)

2.1 Distance and duration

2.2 Symmetry of space and time

3.0 Motion in 3+1 (space-time) is symmetric with motion in 1+3 dimensions (time-space)

3.1 Classical Kinematics

3.1.1 Angles and turns in 3D

3.1.2 Speed and pace, velocity and celerity

3.1.3 Equations of motion

3.2 Classical Dynamics

3.2.1 Mass and vass, momentum and celentum

3.2.2 Equations of motion

3.2.3 Newtonian gravitation in time-space

4.0 Motion in 3+3 dimensions (spacetime)

4.1 Mechanics in spacetime (3+3), reduction of 3D into 1D

4.2 Lorentz transformations in 3+3, invariant interval for 3+3

5.0 Conclusion

6.0 References

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Claims:

- Physics (mechanics) begins with the study of local simple motion in 1+1 dimensions
- Physics (mechanics) may be done in either space-time (3+1) or time-space (1+3)
- Physics (mechanics) is within a spacetime (3+3) framework
- Time may be seen as having 3-dimensions just as well as space
- Time is duration with direction. That is, time is a vector variable similar to a space vector (a distance with a direction). Duration is measured by a standard rate of change
- The magnitude of time is that which is measured by a stopwatch, similar to length
- Replacing time with its negation produces a duration in the opposite direction. It does not reverse time or switch past and future
- Rates require a scalar in the denominator, which can be either space (distance) or time (duration)
- The spatial and temporal perspectives are complementary opposites. Time and space are symmetric with one another, and so may be conceptually interchanged
- Both time and space have continuous symmetries of homogeneity and isotropy
- Minkowski spacetime may be expanded to six dimensions, three for time and three for space. That is, the invariant distance is: (
*ds*)² = (*c dt*)² + (_{x}*c dt*)² + (_{y}*c dt*)² – (_{z}*dr*)² – (_{x}*dr*)² – (_{y}*dr*)²_{z} - Overall claim: space and time are symmetric