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).