1

Laurent NottaleLaurent NottaleCNRSCNRS

LUTH, Paris-Meudon Observatory LUTH, Paris-Meudon Observatory

http://www.luth.obspm.fr/~luthier/nottale/

BUDDHISM AND SCIENCE COLLOQUIUMUNIVERSITY OF OXFORD. 4-5 March 2010

2

Western science:Relativity

Physical quantities like position, orientation, motion (speed,acceleration), scale (resolution), … cannot be defined in anabsolute way, but only relatively to the coordinate system.

Buddhist philosophy: Emptiness (shunyata)

All phenomena are empty of intrinsic existence;their mode of being is always relative, interdependent, never absolute

––> same principle ?

3

Prajnaparamita sutra:Form is empty, emptiness is form

Theories of relativity:

Bruno ~~1590: relativity of positionGalileo ≈ 1600: relativity of inertial motion and orientationEinstein Poincaré 1905: relativity of inertial motion (generalizationto high speeds), relativity of space and timeEinstein 1916: general relativity of motion (accelerated), ofgravitation, of geometry (curved), of space-timeModern attempt (1980-2010): relativity of scales, of geometry(fractal) —> of quantum ‘objects’ + gauge fields

4

« for all things that take part equally in it, it does notact, it is as if it were not; [...] the motion is asnothing. »« Let us therefore set as a principle that, whatever bethe motion that one attributes to the Earth, it isnecessary that, for us who [...] partake of it, itremains perfectly imperceptible and as not being. »

Galileo, 1630 (Dialogo): relativity of (inertial) motion

Nagarjuna (~0-200) (Philosophy of the Middle Way)

« The agent of motion does not move »« Motion, its beginning and its cessation are analogous to motion »« The agent of motion, motion, and the place of motion do not exist(according to their proper nature) »

5

Form is emptyForm is emptyBuddhism: « form » (first of five aggregates = physicalaggregate): not only geometry, but all physical properties (areempty of proper existence).

Science:-position (translation in space and time) and therefore energy(derived from time uniformity) and momentum (derived from spaceuniformity); then color (energy of electromagnetic wave = light)-orientation (rotation in space) and therefore angular momentum(derived from space isotropy)-motion : inertial (rectilinear)—> kinetic energy; accelerated —>gravitation / geometry

But: what about elementary particle quantum properties (mass, spin,charges…) ? —> new suggestion: originate from relativity of scales

6

Example: GalileoExample: Galileo’’s boats boat

Impossibility of detecting by a local experiment the existence ofan inertial motion (rectilinear uniform at constant speed)

Motion is only relative, between the boat and the Earth. Absolute motion, in itself,has no meaning. Motion or rest are not properties intrinsic to Earth or boat. They arenot ascribable to a single object, but characterize couples of objects. There is noindividual motion in itself, but only « inter-motion ».Other well-known example: two trains in a station, which one moves, which one isat rest ?

7

Example: NewtonExample: Newton’’s and Einsteins and Einstein’’s viewss viewsabout gravitation and geometryabout gravitation and geometry

NEWTON : apple fallsthen moon falls !

EINSTEIN : moon doesn’tfall then apple doesn’t fall !

In both case, use of relativity principle: change of reference system, nonabsoluteness of statement (falling, not falling) in dependance of the choice ofreference system (for the same motion)

8

Einstein 1907: an observer in free fall does not feel anylonger his own weight (—> equivalence principle)In the reference system involved with the movement(locally):

•no force, no field, no acceleration, no gravitation —>relativity-emptiness of gravitational field

•no form: the parabolic trajectory seen from Earthbecomes a point at rest or a straight line —> relativity-emptiness of geometry

9

Curved space-time: trajectory =Curved space-time: trajectory =geodesicgeodesic

Other example: banked bicycle race ring. Form (circle motion) seen by spectatorsdoes not exist for cyclists (straight motion: they do not turn their handlebar).

10

Emptiness is formEmptiness is formMore mysterious statement ?

But : *implemented by Einstein’s general relativity methods*generalized to scale relativity

i.e.,-in relativity theories, the principle of relativity is not only auniversal truth, but it also yields a method for finding the laws ofnature-it is the « emptiness » aspect of the principle which provides thisuniversal tool

11

The relativity-emptiness method forconstructing laws of nature:

- Things, objects, properties, etc… have no properexistence. They appear in some manner in a referencesystem, in another manner in another reference frame. Intheir proper frame, they disappear:(Inside motion, no motion; inside color, no color, insideform, no form, etc…)In buddhist view: empty appearances.

-Therefore, they find their existence in the very change ofreference system itself.

- Then, instead of attempting to establish laws in observerframe: (1) write them in proper system (2) change system

12

- Since, in the proper reference system, the searched law isknown (disappearance of the property : A = 0, for example, ofacceleration in geodesic free falling reference system), all thework of constructing laws is brought back to the description ofvarious changes of reference systems.

- Consequence: evolution of theories of relativity since Galileo= account of more and more complicated changes ofcoordinate systems (and of geometries of space-time):

• inertial Cartesian, flat space (Galilean relativity of motion)• inertial, speed close to speed of light, flat space-time (specialrelativity of motion)• curvilinear coordinate systems, curved space-time(generalized relativity of motion, gravitational field)• fractal coordinate systems, fractal space-time (relativity ofscales, quantum laws, gauge fields)

13

RELATIVITY

COVARIANCE EQUIVALENCE

weak / strong

Action Geodesical

CONSERVATIONNoether

THEORIES OF RELATIVITY: FIRST PRINCIPLESTHEORIES OF RELATIVITY: FIRST PRINCIPLES

14

Example 1: derivation of Lorentz transform fromExample 1: derivation of Lorentz transform frommere principle of special relativitymere principle of special relativity

(LN 1992, Int. J. Mod. Phys. A7, 4899)

- Principle of relativity (Einstein’s statement, philosophical): thelaws of nature are valid whatever the state (here, of motion) of thereference system —>- Principle of covariance (physical translation of the principle): theequations of physics keep their form in changes of reference system- Axioms (mathematical translation of the principle: cf Galileo’s « the book of nature is written in mathematical language ») * special relativity —> linear transformation *form invariance of transformation (continuous) —>internal composition law (one of the axioms of group theory) * arbitrary character of axes orientation (discreterelative transformation) —> reflexion invariance

From only these three axioms, one derives Lorentz transformation !

15

Example 2 : equation of motion inExample 2 : equation of motion inEinsteinEinstein’’s general relativitys general relativity

- definition of a covariant derivative which accounts for theeffects of curved reference system /geometry (rotation of vectorsinduced by translation):

- geodesic principle (minimize proper time)- strong covariance (same form of equations of motion as Galileo’sinertial free motion in vacuum, i.e. acceleration = 0)- equivalence principle (locally, between gravitational field andacceleration field)

All three —> same vacuum equation:

16

Example 3 : geodesic equations in scale relativityExample 3 : geodesic equations in scale relativity——> quantum mechanical equations> quantum mechanical equations

- definition of a covariant derivative which accounts fornondifferentiable / fractal space

- geodesic / strong covariance principle —> equation of motion:

-change of variable —> Schrödinger equation (Dirac in fractal S-T)

Including external field ->Newton fundamental equation of dynamics