2903 Time (and Space)

" M. C. Escher: Relativity"

Time is an Illusion: lunch-time doubly so Hitchhiker's Guide

What is Time?

• What does a clock measure?
• What does "prediction" mean?
• When did time measurement start?
• Do we experience time in the same way?
• Psychological Time
• Physiological Time
• What exactly is causality?
• Is time travel possible?
• If so, why can't we do it?
• If not, what forbids it?
• How do we know that two clocks measure the same time?
• How are time and space linked?
• Is time "smooth"?

The Sapir Whorf hypothesis.

• The strong form: you cannot discuss a concept unless you have the language to describe it.
• The weak form: your views of the universe are modified and restricted by language.
• A famous (wrong) example: Eskimos have 56 words for snow
• (they actually have one!).
• However skiers have at least 10:
• (powder, crud, hard-pack, ice, crusty, slush, spring, corn, sugar, fresh, wet....).
• Most of these distinctions are meaningless to non-skiers, but they allow a concepts to be transferred in compact form.

Time in English

• Measurement of time: hour, minute, second, year, epoch, age, period, watch (two meanings) , clock,.....
• Passage of time: brief, momentary, lengthy, overlong, tedious ....
• Temporal ordering, or relative time: before, after, future, past, history, late, early, first, second, causal, prediction .....
• Absolute time (usually in phrase) : 9/11, last Tuesday, Death of Ceasar ....
• Change: rapid, slow, languorous, flow, dragging,speed, acceleration,......
• Many more that involve time and some other concept: paleolithic, oscillatory, periodic, ancestor, descendant, son, breakfast (all-day breakfast!), teatime.....
• Note (very important for later) we already have the idea that things change with time ; e.g.
  \color{red}{ speed = \frac{{{\rm{distance}}}}{{time}} = \frac{d}{t}}

Tenses

from Verbix

• Note that this is grossly simplified: these are Indicative active tenses
• We also have Subjunctive active (amem ⇔ May I love)
• Indicative passive (amor ⇔ I am loved)
• Subjunctive passive (amer ⇔ May I be loved)
• Imperative (ama ⇔ Love! (or else))
• These are "moods", but we are really only interested in the temporal aspects

Stolen and adapted from Wikipedia

• "I speak" & "I am speaking" ⇒ "je parle"
• "I speak" & "I am speaking" ⇒ "Ich spreche"
• but "I speak" ⇒ "Sto parlando" & "I am speaking" ⇒ "Parlo"
• This does not imply that those langauges are incomplete
• Also note that other languages have other tenses (again from Wikipedia)
  • Near future tense: in the near future, soon
  • Hodiernal future tense: sometime today
  • Post-hodiernal future tense: sometime after today
  • Remote future tense: in the more distant future
  • Predictive future tense: a future tense which expresses a prediction rather than an intention, i.e., "I predict he will lose the election, although I want him to win". As such, it is really more of a mood than a tense. (Its tenseness rather than modality lies in the fact that you can predict the future, but not the past.)
  • Nonfuture tense: refers to either the present or the past, but does not clearly specify which. Contrasts with future.
  • Nonpast tense: refers to either the present or the future, but does not clearly specify which. Contrasts with past.
  • Not-yet tense: has not happened in present or past (nonfuture), but often with the implication that it is expected to happen in the future. (As such, is both a tense and a modality). In English, it is expressed with "not yet", hence its name.

• Note many subtleties: e.g prediction

  We will overcome (Negro Spiritual)

  vs volition

  We shall overcome (Peter Seeger's adaptation)

• Linguists refer to "aspects" of a verb rather than tenses
• Other solutions: (thank you Cho & Marcus Watson)
• Chinese; verbs do not have tenses in the European sense, but have modifier words. Tense usually obvious by context
• Japanese; no tenses, but concepts conveyed by adverbs

  "I speak futurely"

  "I speak pastly"

• Simplest model of time:
  
• Note 3 s "now" is confirmed by psychology
• However we tie down past and future with events.
  
• Note "events:" are used in physicist's sense: occur at definite time (t) and place (x,y,z).
• The horse-riders "Three-day event" isn't an event!
• Was the collapse of the World Trade Centre in 9/11 one event or two? (costs you $3500,000,000 if you have the answer wrong

• Absolute time (rather than relative)
  
• Multiple Frames of reference. Note we agree on common events, past and future
  
• Past is immutable, future is fluid: note this is assumed not just in philosophy and physics, but poetry as well

• The Moving Finger writes; and, having writ,
  Moves on: nor all thy Piety nor Wit
  Shall lure it back to cancel half a Line,
  Nor all thy Tears wash out a Word of it.
  Rubaiyat of Omar Khayyam tr. by Edward FitzGerald

• Time past and time present
  Are always present in time future.
  T. S. Eliot Burnt Norton

• And the seasons they go round and round And the painted ponies go up and down We are captive on the carousel of time We can't return we can only look behind from where we came And go round and round and round in the circle game Joni Mitchell The Circle Game

  (Ian and Sylvia)

The simplest form of English is pidgin: e.g. in Northern Nigeria, just 3 tenses:

• Present: I eat bread ≅ I eat bread
• Future: I go eat ≅ I will eat the bread
• Past: I done eat ≅ I ate the bread
• Note this leads to oddities such as "I go come' and "I done come"!
• Oral cultures tend to have relative time but not absolute time.
• Whorf claimed that the Hopi have no word for "time" or "past, present or future", (apparently true)
• and hence had no concept of time (certainly false, since they have a calendar and understand crop planting etc.

The Pirahã:

1. No words for colour
2. No words for number
3. No creation myths
4. No words for ancestors

• Even taught the Portugese words for numbers, "not one of them had learned to count to 10 or even to add 1 and 1" New Scientist, March 18th 2006

• Some concepts they use do not exist in English: e.g xibipiio ≅ "appear" and "disappear".
• and apparently no concept of time in the Western sense.
• see Daniel Everett, "Don't Sleep, There are Snakes"

Final thoughts

• More advanced the language, more sophisticated the description of time.
• Can we argue that language developed to explain our relationship with time?
• Are there time-related concepts that we cannot describe in English?
• Yes: will show examples later on
• In physics, we need to describe concepts which don't map well on to the English language, and don't necessarily have translations. e.g. "mass" and "weight" are almost synonymous in English and many languages have the same word. They also carry cultural baggage. Further, we have concepts which have no correct mapping e.g. "electron".
• Maths represents a (more-or-less) culture-free way of describing concepts. Also it allows predictions in a quantitive way.

• No human investigation can be called real science if it cannot be demonstrated mathematically Leonardo da Vinci

Work, eat, play, mate

• Sleep, play, mate

Cell Cycle: :

• Even bacteria need to keep time: e.g CyanoBacteria

• Eldon Emberley, SFU, finds 3 proteins give an oscillatory system

Measurment of Time

Position of Sunrise and Sunset varies throughout the year

• Midsummer day: when the sun rises/sets in most northerly position. Measured at Stonehenge: important do define seasons and hence time to plant crops Probably 2000 BC ± 1000.

  ---

  Alignments let you measure summer soltstice Midsummer sunrise Winter moonrise low point Midwinter Sunrise Southern moonrise (minimum) Southern moonrise (maximum) Midwinter sunset Northern moonset (minimum) Northern moonset (maximum) Winter moonrise high point

  http://www.fas.harvard.edu/~scidemos/ AstronomyAstrophysics/Stonehenge/Stonehenge.html

Babylon

• Star Catalogs 1600 BC.
• Eclipse Observed 1500 BC.
• Continuous Records 900 BC.
• Records on stone tablets.
• Day: interval between time that sun is due S.
• Month: Roughly lunar cycle (29.4 days) but too short

Astronomical records

It reads: On the 1st of Nisannu the Hired Man becomes visible. On the 20th of Nisannu the Crook becomes visible. On the 1st of Ayyaru the Stars become visible. On the 20th of Ayyaru the Jaw of the Bull becomes visible. On the 10th of Simanu the True Shepherd of Anu and the Great Twins become visible. On the 5th of Du'uzu the Little Twins and the Crab become visible. On the 15th of Du'uzu the Arrow, the Snake, and the Lion become visble; 4 minas is a daytime watch, 2 minas is a nighttime watch. On the 5th of Abu the Bow and the King become visible. On the 1st of Ululu [. . . .] On the 10th of Ululu the star of Eridu and the Raven become visible. On the 15th of Ululu Shu-pa, Enlil, becomes visible. On the 25th of Ululu the Furrow becomes visible.

http://www.mesopotamia.co.uk/ astronomer/explore/exp_set.html

Sundials

Good to few minutes but ....

• It moves against the fixed stars because
• the earth orbits the sun
• the earths axis is tilted

it also moves in the sky at a given time of day: (i.e. the time of noon varies) because the earth moves at varying speeds in its orbit, so we actually need a better clock than the sun to measure this

Water in a containter drains out throuigh small hole: problme is that the flow is non-uniform. Hence keep container full with valve: clepsydra (= "water thief"

www.mlahanas.de/ Greeks/Clocks.htm

Eclipses

Tablet with a list of eclipses between 518 BC and 465 BC, mentioning the death of king Xerxes. British Museum, London

• Why do these matter?

• CALPURNIA: When beggars die, there are no comets seen;
  The heavens themselves blaze forth the death of princes.
  

  Julius Caesar

• Chinese astronomers Hi and Ho executed for failing to predict eclipse in 2136BC or 2159BC.
• See Eclipse Quotations at http://www.mreclipse.com/Special/quotes1.html.

• Eclipses repeat after 18 years and 11.3 days.
• The .3 days shifts the eclipse about 110º degrees west.
• Also some saros sequences start at the south and drift North, others at the North and drift South.
• This means that the cycle is very complex: can only see it after many years.
• Why is it so complicated? Need to combine
• 1. Earths rotation
  2. Moons orbit (not quite circular)
  3. Earth's orbit (ditto)
  4. and the plane of the moons orbit precesses

Fascination with eclipses remains: e.g. An eclipse seen from Mir. e.g. FEC story

• Observed total Eclipse 15 April 136 BC.
• and they would even have seen it from the moon !

• But they shouldn't have!

• Earth's rotation has slowed down, by 1/100 sec/century, because of tidal effects! i.e. earth isn't a very good time-keeper

Babylonian Astronomy?

• What was wrong with Babylonian Astronomy?
• They had no model (but they were very good at arithmetic!)
• e.g. the month: Kidinnu arrived at 29.530594 days, which is only 0.432 seconds more than the modern estimate of 29.530589 days.

Hipparchus: 160-127 BC.

Precession of the Equinoxes

March 21st & Sept 21st are special days: Sun is on the equator (now), but where on the equator? In 2000 BC

• Aries 2000 BC
• Pisces 100 BC (which is why the Christians chose the fish as their symbol)

• And now This is the dawning of the age of Aquarius

• Except it isn't!

How does precession happen

The most baffling example of ang momentum conservation is a spinning top/gyroscope

• Watch the demo.
• Precession occurs when a top is has an external torque acting on it. Paradoxicallly, the precession speed is greater the slower the top is spinning
• This same precession happens on a totally different scale. Since the Earth is not perfectly spherical, the Moon exerts a torque on the equatorial bulge, => Precession,

• Period = 26000 yrs: Now N pole points towards Pole star, 13000 yrs will point at Vega

• Also this gives saros cycle: plane of Moon's orbit precesses once every 18 years

Antikythera Mechanism

An extraodiinary discovery from 1901: probably from late second century BC

National Archaeological Museum in Athens: wikipedia

X-rays show very complex structure

T. Freeth et al, Nature 444, 587-591 (30 November 2006), wikipedia

The front dial has two concentric scales. The inner scale shows the Greek zodiac with 360 divisions. The Parapegma is a star almanac showing rising and settings at dawn or evening of particular stars or constellations Consistent with Egyptian calendar of 365 days, with twelve 30-day months and 5 extra The effect of the extra quarter day in a year could be corrected by turning the scale one day every four years The spiral upper back dial displays the luni-solar Metonic sequence of 235 lunar months with a subsidiary dial showing the Callippic cycl spiral lower back dial displays the 223-lunar-month Saros eclipse cycle with a subsidiary dial showing the Exeligmos cycle.

Pendulum Clock

• Period:
  \color{red}{ P = 2\pi \sqrt {\frac{L}{g}} }
• What should period be for the Foucault pendulum? (L ~ 20 m.)
• What would period of a 1 m simple pendulum be?
• Accuracy ~ 1 minute/day

Chronometer

need to determine time to better than 1 s/day Harrison (1721) constructed chronometer accurate to better than 1/5 s/day

Pulsars

Very regular radio pulses, period of 4 s ⇒ 2 ms Note that height of pulse is very irregular

• Best known is Crab. Known to be remnant from supernova in 1054 (seen by Chinese) Pulsar at centre has period of ∼ .03 s

  < Walter Nowotny (U. Wien, Nordic Optical Telescope

• But............ This leads to more problems: circumference of earth differs at various places,....rotation speed of earth varies...
• Need reproducible unit, so any lab can measure it
• Define time via the oscillations of a caesium atom 1 s = 9,192,631,770 f
• Distance used to be via wavelength of red line from Kr⁸⁶ light ( 1 m = 1,650,763.73 l)
• but now speed of light (c) is much better measured, so 1 m = distance travelled by light in 1/299,792,458 s

Atomic clock

Best is now at NRC: Caesium fountain clock better to 1 part in 1012 i.e. would lose or gain ~ hour over lifetime of universe: so accurate that the only comparison is one Cs clock to another!

Time in Literature

• Unity of Space
• Unity of Time
• Unity of Action

• e.g. The prisoner in the "Count of Monte Cristo" cannot escape his three-dimensional cell: trivial to do so in a four-dimensional world it becomes quite like a child playing hop-scotch can step out of a square in two-dimensions.
• What stories really satisfy the three unities?
• "High Noon"
• "Rope" (Hitchcock's retelling of the Leopold-Loeb case).

• Simple variants:
• compression of time.
• Philip Sydney grumbled about this 400 years ago:

  Now of time they are much more liberal; for ordinary it is, that two young princes fall in love; after many traverses she is got with child; delivered of a fair boy; he is lost, groweth a man, falleth in love, and is ready to get another child; and all this in two hours' space; which, how absurd it is in sense, even sense may imagine;"Philip Sidney

• flashback: the insertion of a little bit of past time into present time. In practice, a character relating what has happened to him in the past is almost the same author dropping the story back into the past. Either way the past is fixed
• two or more threads of a story sequentially, this 3-dimensional space and a linear time represent the physics framework of the vast majority of stories.
• e.g. "Oliver Twist" starts with a long description making it clear that the space is England and the time Victorian, but the 3 dimensions of the space fail to be mentioned.

Time Travel

So how about time travel?

TIME TRAVEL INTO THE PAST

There is no debate, even among science fiction writers, that this is completely impossible. It not only involves violations of the laws of physics, particularly the Second Law of Thermodynamics, but literally and actually involves gross logical contradictions. The idea is that mad Dr. Soandso gets into his time machine (not clearly described) and somehow goes back to ancient Rome, where he gives a translated handbook of physics and chemistry to a Roman scholar, and thus utterly changes the course of human history .... the atomic bomb, for instance, is then invented by Claudius Festus Arpinna in 350 AD.
Despite the fact that even the writers agree time trips into the past are an impossibility, they love to play with them, because of the plot complications that can be generated by the logical contradictions that arise. My favorite books of this type are Dinosaur Beach by Keith Laumer and The End of Eternity by Isaac Asimov. The time-travel short story to end all time-travel short stories is All You Zombies! By Robert A. Heinlein. Wells' 19th Century The Time Machine is the genre's daddy.

• WHY ????????
• So we can measure time to fantastic accuracy: what does it mean?