Sur la pluralité des temps

 

[With apologies to Fontenelle, Entretiens sur la pluralité des mondes (1686). ]

A historian writes, that our modern sense of Time is no older than the industrialism of the United States;  though Time, to be sure, itself is rather older.

How does this fit in with the Bergsonian dichotomy of temps vesus durée (Essai sur les données immédiates de la conscience, 1889) ?

 

~

Note:

Newton himself, not concerned with psychology,  conflates the two:

Absolute, true, mathematical time, of itself and from its nature, without relation to anything exernal, flows equally; and its other name is duration.

-- Principia Mathematica

 

In histories of science, that passage may be cited in distinction to Einstein’s relativistic doctrines.  But one historian notes a caveat well prior to relativity:

 

Somehow Newton failed to see the circularity of this definition.  It has become clear since his day  that his concept of uniform (“equal”) flow of time  was redundant, since it is impossible to give any meaning to such an assertion of uniformity  unless the concept of time is already established.

-- Lloyd Taylor, Physics: the Pioneer Science (1941)

In the context of Relativity, self-standing Time  is abolished altogether:

 

“Raum für sich  und Zeit für sich  sollen völlig zu Schatten herabsinken, und nur noch eine Art Union der beiden soll Selbständigkeit bewahren.” (Minkowski, 1909)

(“Independent Space and Time  must sink into the shadowland”.)

 

~

Temps (the usual word for ‘time” in French) is a feature of physics;  durée (lit. ‘duration’), a feature of lived experience, of the mind.

The former experienced its own bifurcation into (absolute) Newtonian time, and (relative to the observer) Einsteinian or Relativistic time.  Though cognitively uncomfortable to the many, at the time of its introduction, after a bit of familiarity  it all fits comfortably into basic math and physics, the former being simply a limiting case of the latter.   (Similarly, the intelletual scandal of the discovery of Non-Euclidean Geometry  was eventually digested, with the Euclidean being a sort of limiting case of the Spherical and the Hyperbolic.)

So now (per our historian) we must wrestle with a new entity:  Taylorized time -- time cut into lengths by the stop-watch brandished by a steely-eyed time-and-motion man, seeking to squeeze the last ounce (excuse me -- millilitre) out of the workforce.

Since that has nothing to do with physics, it is no contribution to our understanding of temps, but is rather a new take on durée, varying historically and culturally.

~

Footnote:  I have always been a bit puzzled by Proust’s title A la recherche du temps perdu.   How shall we characterize his use of temps here?  One subtlety:  its implications and connotations evolve in the course of the novel.   A literal translation, In Search of Lost Time, sounds trivial, terrible.  Translator Scott-Moncrieff neatly skirted the problem with his resort to the Shakespearian Remembrance of Things Past.

~

For further pensées concerning Time, from both literature and from physics, try these:

=>  https://worldofdrjustice.blogspot.com/search/label/time

 

A simple recipe

Re Einstein’s relativity theory of 1905:

The new theory is based  in its entirety  on two postulates:

 1.  The laws of physics take the same form in all inertial frames.

 2. In any given inertial frame, the velocity of light is the same  whether the light be emitted by a body at rest  or by a body in uniform motion.

-- Abraham Pais, Subtle is the Lord (1982), p. 141

A simple recipe -- but which requires some care in the baking !

[For our own essay at minimalist postulationism, try:  

Theologia mathematica. ]

Zen Physics

A wristwatch worn

by a particle of light

would  not  tick     a-tall.

(-- after Brian Greene; slightly modified, to please the Muse)

Dr. Greene delivers himself of this epigram, in the course of explaining that we

 each of us, all of us,

 even Achilles and the tortoise,

move equally at the speed of light.

To be sure, in a Pickwickian sense (dividing our motion between space and time).

~

Clocks on Earth    tick

a tiny bit

s l o w l y

relative to those in interstellar space.

[ -- Richard Gott, The Cosmic Web (2016), p. 16 ]

The Big Bang itself   is at the bottom

where all the worldlines  converge.

There is no time

before    that …

-- ibid, p. 81

Emmy Noether zum Geburtstag

Alles Gute zum Geburtstag, Emmy !

Today's Google-doodle commemorates Emmy Noether.   Noether really is a significant creative figure in the history of mathematics.

Unlike Ada Lovelace, she wasn't anyone's famulus, but forged her own way independently.   And, despite the ferocious abstraction of her research, she was a nourishing and accessible person to her circle of mathematicians.  As one leading algebraist wrote in his memoirs:

Emmy Noether jouait le rôle de mère poule protectrice.

-- André Weil, Souvenirs d’apprentissage (1991)

~

As an undergraduate math major at Harvard, I had barely heard of Noether;  and this, for three good reasons, none of which had to do with Noether herself.

(1)  Undergrads generally need to learn the subject (i.e., what’s on the test) and not worry about its history.

(2) The exact sciences generally hew to “Whig history”:  whatever the present state of the field, is all you really need to know.  The pioneers were blunderers.

(3) For math specifically, the Platonic outlook  singularly minimizes the role of the individual researcher.   All mathematical truths are already stored-up in Platonic heaven;  whoso proves this theorem or that, has simply managed to claw loose a pre-existing nugget from the hoard.

The closest I came to having heard of her, was that I’d heard of (but not studied) “Noetherian rings” (an adjective I still do not know how to pronounce).  These figured prominently in the introductory algebra text by Van der Waerden, one of her pupils.

Now:   Noetherian rings (along with the eponymous modules) are all very well in their way;  but they must take their place in a menagerie of such constructions. 

Thus:  If you stick with it  long enough,  you will learn such gems as this:

In a short exact sequence of R-modules, A and C noetherian imply B noetherian, and conversely.

--  Saunders MacLane & Garrett Birkhoff, Algebra (1967; 3^rd edn. 1999), p. 380

Hmm!  Mmyess!  Good to know!  Must make a note of that!

But that is not why she’s famous.

~ ~ ~

Emmy Noether

Separated at birth ??

Emma Goldman

 ~ ~ ~

The discovery (or invention) of Noetherian rings, was internal to algebra.  What inscribed her name on the scrolls of History in letters of gold, was the linking of algebra to something seemingly outside itself:  specifically, the linking of each algebraic symmetry with a conservation law -- which puts her work at the center of modern physics.   In this it bears comparison with the previous Erlangen Program led by Felix Klein, which characterized the plethora of newly recognized geometries (prior to Gauss & Lobachevsky, there was but one) by their symmetry-groups.

Technically stated:

Noether’s principle:  To any continuous one-parameter group of symmetries of the Lagrangian,  there corresponds a conservation law for the associated Euler-Lagrange PDE.

--  Timothy Gowers, ed., The Princeton Companion to Mathematics (2008), p. 479

or (seen from the standpoint of QFT):

Noether’s theorem:  If a Lagrangian has a continuous symmetry, then there exists a current associated with that symmetry  that is conserved when the equations of motion are satisfied.

-- Matthew Schwartz, Quantum Field Theory and the Standard Model (2014), p. 34

Noether’s results antedate post-quantum particle physics, but their reach remains.  As, “If there is a gauge invariance, expect to find a conserved charge,” (Roger Penrose).  Penrose however goes on to note, that the principle is not unlimited:  it does not apply to derive the conservation of the energy-momentum in General Relativity (The Road to Reality (2004), p. 489-90).