Tempus

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Horologium armillare

Fluxus harenae in horario vitreo adhiberi potest ad metiendum tempus intercessum.

Tempus (-oris, n.) nuncupatur et eventuum durationum mensura^[1] et continuum abstractum in quo ipsi eventus accidunt, quod tribus partibus praeterito, praesente, futuro successione rationali ordinatis constat.^[2]^[3]

Physici quidem strictiore sensu tempus definiunt sicut quantitatem unius dimensionis^[4] adhibita ad eventus in seriem definitam ordinandos, ut durationes eventuum eorumque intervalla enumerentur, et ut enumerentur scianturque motus rerum aliarumque mutationum.^[5] Temporis mensurae unitas in Systemate Internationali (seu S.I.) definita secundum est littera s abbreviatum.

Tempus antiquitus intellegitur dimensio esse in qua eventa ordinantur, ut quodam modo futura a praeteritis discernantur. Quia autem physicae scientia exactam temporis definitionem requirit, temporis definitio novis theoriis excogitatis mutata est. Cum vulgus horologium parvum satis habet ad temporis mensuram, physici atomicis horologiis saepe utuntur, non solum quia atomica horologia optima sunt, sed etiam quia tempus atomicis transitionibus definitur.

Tempus saepe indicatur per s (secunda), min (minuta), h (horas), d (dies), a (annos).

Index

1 Historia
2 Tempus secundum relativitatis theoriam
- 2.1 Relativitas Specialis
- 2.2 Relativitas Generalis
3 Vide etiam
4 Notae
5 Fontes

[recensere] Historia

Constat philosophos Graecos de temporis natura valde cogitasse. Paradoxum Zenonis est praeclarissimum exemplum quod tempus semper expectationem hominum movit.

Newtoni temporibus, scientia nondum tempus accurate definiebat, sicut in scholio primo libri a Newtono scripti Philosophiae Naturalis Principia Mathematica^[1] (pg. 5 editionis primae, 1687) legitur:

...Nam tempus, spatium, locum et motum ut omnibus notissima non definio.

Nihilominus sententiis sequentis Newtonus has observationes facit:

Dicam tamen quod vulgus quantitates hasce non aliter quam ex relatione ad sensibilia concipit. Et inde oriuntur praejudicia quaedam, quibus tollendis convenit easdem in absolutas & relativas, veras & apparentes, Mathematicas et vulgares distingui

Tunc, praeclarissima sententia tempus absolutum statuens, quae anno 1905 ab Einstein abrogata est, sequitur:

I. Tempus absolutum verum & Mathematicum, in se & natura sua absq; relatione ad externum quodvis, aequabiliter fluit, alioq; nomine dicitur Duratio; relativum apparens & vulgare est sensibilis & externa quaevis Durationis per motum mensura, (seu accurata seu inaequabilis) qua vulgus vice veri temporis utitur; ut Hora, Dies, Mensis, Annus.

Hanc temporis definitionem esse veram omnibus usque ad annum 1905 videbatur. Einstein autem, de celeritate luminis cogitante, tempus (etiam spatium) non esse absolutum sed relativum recte intellexit. Sic, post nimis computationes, theoriam relativitatis specialis solum instituit, quae spatii temporisque comprehensionem secundum scientiam physicam valde mutavit. Theoria relativitatis generalis eius, anno 1915 excogitata, connectionem inter tempus spatiumque et de relativa eorum natura plura patefecit. Ut a multis experimentiis iampridem comprobatur, theoriae relativitatis praecepta circa temporis spatiique naturam veritates sunt, nullum experimentum unquam ad relativitatis theoriam non obtemperavit et exempla sunt multa quod tempus est relativus.

[recensere] Tempus secundum relativitatis theoriam

[recensere] Relativitas Specialis

Secundum Relativitatis Specialis theoriam, temporis definitio ex simultaneitatis concepto originem habet. Non unum tempus absolutum est, quemadmodum Newtonus cogitavit, quia constantia celeritatis luminis obtemperata, tempus ex inertialibus referentialibus pendet, sicut ab Einstein anno 1905 demonstratus est. Duo autem homines dissimiles velocitates habentes unus cum alio non consentiunt circa temporis durationem. Manifestum est hanc affirmationem esse contrariam ei qua a Newtono scripta est, sicut in Principia (p. 7) legitur:

Accelerari & retardari possunt motus omnes, sed fluxus Temporis absoluti mutari nequit. Eadem est duratio seu perseverantia existentiae rerum, sive motus sint celeres, sive tardi, sive nulli.

Mathematicas aequationes usum faciendo, temporis durationem ex duobus hominibus mensuratam non eandem esse expedite comprobare possumus, si velocitates quibus illi se movent dissimiles sint. Facilior intelligendae causa, sit $Δ t 0$ temporis duratio sive intervallum quam Carolus, qui nullam velocitatem habet, horologio suo metitur (hoc tempus est saepe a physicis vocatum tempus proprium). Si autem Iosephus velocitatem $v$ habet (secundum Caroli referentialem) sequitur ut intervallum $Δ t 1$ ab Iosepho mensuratum est,

$\Delta t_1 = \Delta t_0\sqrt{1-\frac{v^2}{c^2}}$

unde c celeritatem luminis denotat. Ex quo sequitur ut tempus ab Iosepho mensuratus minor quam Caroli tempus est. Hoc est praeclarissimus temporis dilatatio effectus, qui usque ad hodie vulgi comprehensionem excitat.

[recensere] Relativitas Generalis

Einstein anno 1915, quando relativitatis generalis theoriam excogitavit, temporis comprehensionem rursus mutavit. Non solum spectatoris relativa velocitas temporis fluxum mutat sed etiam acceleratio. Rustice relativitas generalis afirmat quod accelerans spectator minus senescit quam maior est eius acceleratio. Deinde, post accelerationem cum campo gravitationalis identificare (Equivalentiae Principium), temporis fluxum prope massiva corpora esse lentior recte conclusit.

Sit, exempli gratia, spectator super planetam sphericum radium r atque massam M habentem. Hic spectator temporis intervallum $Δ t 0$ metitur. Si $Δ t 1$ temporis durationem mensuratam a maxime distante homine (i.e. $r\to\infty$ ) denotat tunc mathematice sequitur quod inter eas relatio est

$\Delta t_0 = \Delta t_1\sqrt{1-\frac{2GM}{rc^2}}$

unde $G$ est Newtoni constans.

[recensere] Vide etiam

[recensere] Notae

↑ "MacMillan Dictionary" (2010). – "the quantity that you measure using a clock (Latine "quantitas quam horologio metiris""
↑ Seneca, ep. 124.7. Nota Senecam futurum appellavisse "venturum".
↑ "The American Heritage® Dictionary of the English Language" (2010). – "1a. A nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future. 1b. An interval separating two points on this continuum; a duration: a long time since the last war; passed the time reading. 1c. A number, as of years, days, or minutes, representing such an interval: ran the course in a time just under four minutes. 1d. A similar number representing a specific point on this continuum, reckoned in hours and minutes: checked her watch and recorded the time, 6:17 A.M. 1e. A system by which such intervals are measured or such numbers are reckoned: solar time.... 11. The rate of speed of a measured activity: marching in double time."
↑ "Internet Encyclopedia of Philosophy" (2010). – "Time is what clocks measure. We use time to place events in sequence one after the other, and we use time to compare how long events last.... Among philosophers of physics, the most popular short answer to the question "What is physical time?" is that it is not a substance or object but rather a special system of relations among instantaneous events. This working definition is offered by Adolf Grünbaum who applies the contemporary mathematical theory of continuity to physical processes, and he says time is a linear continuum of instants and is a distinguished one-dimensional sub-space of four-dimensional spacetime."
- "Collins English Dictionary" HarperCollins (2003). – "2. (Physics) a quantity measuring duration, usually with reference to a periodic process such as the rotation of the earth or the vibration of electromagnetic radiation emitted from certain atoms.... In classical mechanics, time is absolute in the sense that the time of an event is independent of the observer. According to the theory of relativity it depends on the observer's frame of reference. Time is considered as a fourth coordinate required, along with three spatial coordinates, to specify an event. See space-time continuum."
- "Eric Weisstein's World of Science" (2007). – "A quantity used to specify the order in which events occurred and measure the amount by which one even preceded or followed another. In special relativity, ct (where c is the speed of light and t is time), plays the role of a fourth dimension."
- "Glossary for Extragalactic Astronomy" CalTech (2005). – "A dimension distinguishing past, present, and future. In relativity, time is portrayed as a geometrical dimension, analogous to the dimensions of space."
↑ "Merriam Webster Online Dictionary" (2010). – "1a: the measured or measurable period during which an action, process, or condition exists or continues : duration; 1b: a nonspatial continuum that is measured in terms of events which succeed one another from past through present to future; 2: the point or period when something occurs : occasion"
- Encarta Online Dictionary. (2010) Textus interretialis. – "1. system of distinguishing events: a dimension that enables two identical events occurring at the same point in space to be distinguished, measured by the interval between the events."
- "Webster's New World College Dictionary" (2010). – "1.indefinite, unlimited duration in which things are considered as happening in the past, present, or future; every moment there has ever been or ever will be... a system of measuring duration 2.the period between two events or during which something exists, happens, or acts; measured or measurable interval"
- "Dictionary.com Unabridged, based on Random House Dictionary" (2010). – "1. the system of those sequential relations that any event has to any other, as past, present, or future; indefinite and continuous duration regarded as that in which events succeed one another.... 3. ( sometimes initial capital letter ) a system or method of measuring or reckoning the passage of time: mean time; apparent time; Greenwich Time. 4. a limited period or interval, as between two successive events: a long time.... 14. a particular or definite point in time, as indicated by a clock: What time is it? ... 18. an indefinite, frequently prolonged period or duration in the future: Time will tell if what we have done here today was right."
- "The American Heritage® Stedman's Medical Dictionary @dictionary.com" (2002). – "A duration or relation of events expressed in terms of past, present, and future, and measured in units such as minutes, hours, days, months, or years."
- "Collins Language.com" HarperCollins (2010). – "1. the past, present, and future regarded as a continuous whole,... 2. (Physics) a quantity measuring duration, measured with reference to the rotation of the earth or from the vibrations of certain atoms"
- "Britannica Concise Encyclopedia" (2010). – "Measured or measurable period. More broadly, it is a continuum that lacks spatial dimensions."

[recensere] Fontes

^ Isaacus Newtonus, Philosophiae Naturalis Principia Mathematica, editio prima, 1687
Philosophiae naturalis principia mathematica (omne opus in forma .pdf)
Tempus apud "Open Directory"
Regium Observatorium et historia astronomiae: John Harrison et quaestio longitudinis

[recensere] Perceptio temporis

Studia de perceptione temporis apud Universitatem Mancuniensem

[recensere] Physica

[recensere] Philosophia

Philosophia orinetalis

Philosophia Occidentalis

Crouch, Will (2006-2008). "Is there a defensible argument for the non-existence of time?" On Philosophy. (Nexus die 2008-01-24 confirmatus)
Dowden, Bradley (California State University, Sacramento) (2007). James Fieser, Ph.D., Bradley Dowden, Ph.D.: Time. Textus interretialis.
Le Poidevin, Robin (Winter 2004). Edward N. Zalta: The Experience and Perception of Time. Textus interretialis.
Mcdonough, Jeff (Harvard University) (Winter 2007). Edward N. Zalta: Leibniz's Philosophy of Physics. Stanford University Textus interretialis.
Ross, Kelley L., Ph.D. (Los Angeles Valley College). "The Clarke-Leibniz Debate (1715-1716)" The Proceedings of the Friesian School, Fourth Series (1996, 1999, 2001). (Nexus die 2008-01-17 confirmatus)
Ross, Kelley L., Ph.D. (Los Angeles Valley College). "Three Points in Kant's Theory of Space and Time" The Proceedings of the Friesian School, Fourth Series (1996, 1999, 2001). (Nexus die 2008-01-17 confirmatus)
Savitt, Steven, Ph.D. (University of British Columbia) (Fall 2007). Edward N. Zalta: Being and Becoming in Modern Physics. Textus interretialis.
Wilson, Catherine (City University of New York) (Summer 2004). Edward N. Zalta: Kant and Leibniz. Stanford University Textus interretialis.

[recensere] Conservatio temporis

[recensere] Miscellanea

Tempus Exploratum a Tempore Planck ad vitam universi
Societas Internationalis pro Studio Temporis

[0] "MacMillan Dictionary" (2010). – "the quantity that you measure using a clock (Latine "quantitas quam horologio metiris""

[1] Seneca, ep. 124.7. Nota Senecam futurum appellavisse "venturum".

[2] "The American Heritage® Dictionary of the English Language" (2010). – "1a. A nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future. 1b. An interval separating two points on this continuum; a duration: a long time since the last war; passed the time reading. 1c. A number, as of years, days, or minutes, representing such an interval: ran the course in a time just under four minutes. 1d. A similar number representing a specific point on this continuum, reckoned in hours and minutes: checked her watch and recorded the time, 6:17 A.M. 1e. A system by which such intervals are measured or such numbers are reckoned: solar time.... 11. The rate of speed of a measured activity: marching in double time."

[quantity-3] "Internet Encyclopedia of Philosophy" (2010). – "Time is what clocks measure. We use time to place events in sequence one after the other, and we use time to compare how long events last.... Among philosophers of physics, the most popular short answer to the question "What is physical time?" is that it is not a substance or object but rather a special system of relations among instantaneous events. This working definition is offered by Adolf Grünbaum who applies the contemporary mathematical theory of continuity to physical processes, and he says time is a linear continuum of instants and is a distinguished one-dimensional sub-space of four-dimensional spacetime."

"Collins English Dictionary" HarperCollins (2003). – "2. (Physics) a quantity measuring duration, usually with reference to a periodic process such as the rotation of the earth or the vibration of electromagnetic radiation emitted from certain atoms.... In classical mechanics, time is absolute in the sense that the time of an event is independent of the observer. According to the theory of relativity it depends on the observer's frame of reference. Time is considered as a fourth coordinate required, along with three spatial coordinates, to specify an event. See space-time continuum."

"Eric Weisstein's World of Science" (2007). – "A quantity used to specify the order in which events occurred and measure the amount by which one even preceded or followed another. In special relativity, ct (where c is the speed of light and t is time), plays the role of a fourth dimension."

"Glossary for Extragalactic Astronomy" CalTech (2005). – "A dimension distinguishing past, present, and future. In relativity, time is portrayed as a geometrical dimension, analogous to the dimensions of space."

[5] "Collins English Dictionary" HarperCollins (2003). – "2. (Physics) a quantity measuring duration, usually with reference to a periodic process such as the rotation of the earth or the vibration of electromagnetic radiation emitted from certain atoms.... In classical mechanics, time is absolute in the sense that the time of an event is independent of the observer. According to the theory of relativity it depends on the observer's frame of reference. Time is considered as a fourth coordinate required, along with three spatial coordinates, to specify an event. See space-time continuum."

[6] "Eric Weisstein's World of Science" (2007). – "A quantity used to specify the order in which events occurred and measure the amount by which one even preceded or followed another. In special relativity, ct (where c is the speed of light and t is time), plays the role of a fourth dimension."

[7] "Glossary for Extragalactic Astronomy" CalTech (2005). – "A dimension distinguishing past, present, and future. In relativity, time is portrayed as a geometrical dimension, analogous to the dimensions of space."

[DicDefs-4] "Merriam Webster Online Dictionary" (2010). – "1a: the measured or measurable period during which an action, process, or condition exists or continues : duration; 1b: a nonspatial continuum that is measured in terms of events which succeed one another from past through present to future; 2: the point or period when something occurs : occasion"

Encarta Online Dictionary. (2010) Textus interretialis. – "1. system of distinguishing events: a dimension that enables two identical events occurring at the same point in space to be distinguished, measured by the interval between the events."

"Webster's New World College Dictionary" (2010). – "1.indefinite, unlimited duration in which things are considered as happening in the past, present, or future; every moment there has ever been or ever will be... a system of measuring duration 2.the period between two events or during which something exists, happens, or acts; measured or measurable interval"

"Dictionary.com Unabridged, based on Random House Dictionary" (2010). – "1. the system of those sequential relations that any event has to any other, as past, present, or future; indefinite and continuous duration regarded as that in which events succeed one another.... 3. ( sometimes initial capital letter ) a system or method of measuring or reckoning the passage of time: mean time; apparent time; Greenwich Time. 4. a limited period or interval, as between two successive events: a long time.... 14. a particular or definite point in time, as indicated by a clock: What time is it? ... 18. an indefinite, frequently prolonged period or duration in the future: Time will tell if what we have done here today was right."

"The American Heritage® Stedman's Medical Dictionary @dictionary.com" (2002). – "A duration or relation of events expressed in terms of past, present, and future, and measured in units such as minutes, hours, days, months, or years."

"Collins Language.com" HarperCollins (2010). – "1. the past, present, and future regarded as a continuous whole,... 2. (Physics) a quantity measuring duration, measured with reference to the rotation of the earth or from the vibrations of certain atoms"

"Britannica Concise Encyclopedia" (2010). – "Measured or measurable period. More broadly, it is a continuum that lacks spatial dimensions."

[9] Encarta Online Dictionary. (2010) Textus interretialis. – "1. system of distinguishing events: a dimension that enables two identical events occurring at the same point in space to be distinguished, measured by the interval between the events."

[10] "Webster's New World College Dictionary" (2010). – "1.indefinite, unlimited duration in which things are considered as happening in the past, present, or future; every moment there has ever been or ever will be... a system of measuring duration 2.the period between two events or during which something exists, happens, or acts; measured or measurable interval"

[11] "Dictionary.com Unabridged, based on Random House Dictionary" (2010). – "1. the system of those sequential relations that any event has to any other, as past, present, or future; indefinite and continuous duration regarded as that in which events succeed one another.... 3. ( sometimes initial capital letter ) a system or method of measuring or reckoning the passage of time: mean time; apparent time; Greenwich Time. 4. a limited period or interval, as between two successive events: a long time.... 14. a particular or definite point in time, as indicated by a clock: What time is it? ... 18. an indefinite, frequently prolonged period or duration in the future: Time will tell if what we have done here today was right."

[12] "The American Heritage® Stedman's Medical Dictionary @dictionary.com" (2002). – "A duration or relation of events expressed in terms of past, present, and future, and measured in units such as minutes, hours, days, months, or years."

[13] "Collins Language.com" HarperCollins (2010). – "1. the past, present, and future regarded as a continuous whole,... 2. (Physics) a quantity measuring duration, measured with reference to the rotation of the earth or from the vibrations of certain atoms"

[14] "Britannica Concise Encyclopedia" (2010). – "Measured or measurable period. More broadly, it is a continuum that lacks spatial dimensions."

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Tempus

Index

[recensere] Historia

[recensere] Tempus secundum relativitatis theoriam

[recensere] Relativitas Specialis

[recensere] Relativitas Generalis

[recensere] Vide etiam

[recensere] Notae

[recensere] Fontes

[recensere] Perceptio temporis

[recensere] Physica

[recensere] Philosophia

[recensere] Conservatio temporis

[recensere] Miscellanea

Instrumenta personalia

Spatia nominalia

Variantes

Visae

Actiones

Quaerere

Navigatio

communitas

Arca ferramentorum

Linguis aliis