4D Music – ExperiMental Music

Double or Triple

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Double-or-Triple-0.mp3

Double-or-Triple-0.mp4
Double-or-Triple-I.mp3
Double-or-Triple-I.mp4
Double-or-Triple-intro.mp3

[Intro]

Are you talking two bars
… or three
(Double or triple)
Is it yours or ours
… tell me
(Feel the ripple)

[Verse 1]

(After all) Free-fall…
motion
(in a gravitational field)
Is indistinguishable
(from acceleration in empty space)
Watch the human race

[Chorus]

Are you talking two bars
… or three
(Double or triple)
Is it yours or ours
… tell me
(Feel the ripple)

[Bridge]

As we flow
(Through spacetime)
Get to know
(All that I’m)

[Verse 2]

(Lyrical rhymes)
Two spacetimes
(are conformally equivalent)
Still relevant…
(Angles are preserved)
… but distances may change
(Do you find it… a bit strange)
Angels disturbed

[Chorus]

Are you talking two bars
… or three
(Double or triple)
Is it yours or ours
… tell me
(Feel the ripple)

[Bridge]

As we flow
(Through spacetime)
Get to know
(What’s not mine)

[Outro]

As we flow
(Through spacetime)
Get to know
(How far to climb)

A SCIENCE NOTE

≡ (Triple bar) → Used in logic and mathematics to denote strict equivalence, such as identity relations and logical equivalence.

= (Double bar) → Used in mathematics to denote equality, meaning two expressions have the same value.

In spacetime, equivalence and equality can have different meanings depending on the context:

Equivalence in Spacetime
  • Equivalence Principle (General Relativity) → The key idea that gravitational and inertial mass are equivalent, meaning that free-fall motion in a gravitational field is indistinguishable from acceleration in empty space.
  • Metric Equivalence → Two spacetime metrics are considered equivalent if they can be transformed into each other through coordinate transformations (diffeomorphisms).
  • Conformal Equivalence → Two spacetimes are conformally equivalent if their metrics differ by a scaling factor (a conformal transformation), meaning angles are preserved but distances may change.
    • Equality in Spacetime
    • Equality of Events → Two events in spacetime are equal if they have the same coordinates in a given reference frame.
    • Equality of Metrics → Two spacetimes are equal if their metric tensors are identical at all points (not just conformally related).
    • Einstein Field Equations → Express equality between the Einstein tensor (which describes spacetime curvature) and the stress-energy tensor (which describes matter and energy).
      • From the album “Equals“
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