Tom Parson's List: Time & Space

• A paradox in logical and scientific usage refers to results which are inherently contradictory, that is, logically impossible, and both men argued that out of the time differential illustrated by the story of the twins no self-contradiction could be constructed. In other words, neither Einstein nor Langevin saw the story of the twins as constituting a challenge to the self-consistency of relativistic physics.

• Specific example

   

  Consider a space ship traveling from Earth to the nearest star system outside of our solar system: a distance d = 4.45 light years away, at a speed v = 0.866c (i.e., 86.6 percent of the speed of light). The Earth-based mission control reasons about the journey this way (for convenience in this thought experiment the ship is assumed to immediately attain its full speed upon departure): the round trip will take t = 2d / v = 10.28 years in Earth time (i.e. everybody on earth will be 10.28 years older when the ship returns). The amount of time as measured on the ship's clocks and the aging of the travelers during their trip will be reduced by the factor , the reciprocal of the Lorentz factor. In this case and the travelers will have aged only 0.500×10.28 = 5.14 years when they return.

• The ship's crew members also calculate the particulars of their trip from their perspective. They know that the distant star system and the Earth are moving relative to the ship at speed v during the trip. In their rest frame the distance between the Earth and the star system is εd = 0.5d = 2.23 light years (length contraction), for both the outward and return journeys. Each half of the journey takes 2.23 / v = 2.57 years, and the round trip takes 2×2.57 = 5.14 years. Their calculations show that they will arrive home having aged 5.14 years. The travelers' final calculation is in complete agreement with the calculations of those on Earth, though they experience the trip quite differently.

   

  If a pair of twins are born on the day the ship leaves, and one goes on the journey while the other stays on Earth, they will meet again when the traveler is 5.14 years old and the stay-at-home twin is 10.28 years old. The calculation illustrates the usage of the phenomenon of length contraction and the experimentally verified phenomenon of time dilation to describe and calculate consequences and predictions of Einstein's special theory of relativity.
• In special relativity there is no concept of absolute present. A present is defined as a set of events that are simultaneous from the point of view of a given observer.
• so switching between frames requires an adjustment in the definition of the present. If one imagines a present as a (three-dimensional) simultaneity plane in Minkowski space, then switching frames results in changing the inclination of the plane.
• Blue lines show the planes of simultaneity for the traveling twin during the first leg of the journey; red lines, during the second leg. Just before turnover, the traveling twin calculates the age of the resting twin by measuring the interval along the vertical axis from the origin to the upper blue line. Just after turnover, if he recalculates, he'll measure the interval from the origin to the lower red line. In a sense, during the U-turn the plane of simultaneity jumps from blue to red and very quickly sweeps over a large segment of the world line of the resting twin. The traveling twin reckons that there has been a jump discontinuity in the age of the resting twin.
• These signals carry the images of each twin and his age-clock to the other twin. The vertical black line is the Earth's path through space time and the other two sides of the triangle show the ship's path through space time (as in the Minkowski diagram above). As far as the sender is concerned, he transmits these at equal intervals (say, once an hour) according to his own clock; but according to the clock of the twin receiving these signals, they are not being received at equal intervals.

• The asymmetry in the Doppler shifted images

   

  The asymmetry between the earth and the space ship is manifested in this diagram by the fact that more blue-shifted (fast aging) images are received by the Ship. Put another way, the space ship sees the image change from a red-shift (slower aging of the image) to a blue-shift (faster aging of the image) at the mid-point of its trip (at the turnaround, 2.57 years after departure); the Earth sees the image of the ship change from red-shift to blue shift after 9.59 years (almost at the end of the period that the ship is absent). In the next section, one will see another asymmetry in the images: the Earth twin sees the ship twin age by the same amount in the red and blue shifted images; the ship twin sees the Earth twin age by different amounts in the red and blue shifted images.

6 more annotations...

• Whatever your age, your body is many years younger. In fact, even if you're middle aged, most of you may be just 10 years old or less.
• a few of the body's cell types endure from birth to death without renewal, and this special minority includes some or all of the cells of the cerebral cortex.

• Greek legend

   

  According to Greek legend as reported by Plutarch,

   

   

   

  The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.

   

   

  —Plutarch, Theseus^[1]

• Locke's socks

   

  John Locke (a 17th-century English writer) proposed a scenario regarding a favorite sock that develops a hole. He pondered whether the sock would still be the same after a patch was applied to the hole. If yes, then, would it still be the same sock after a second patch was applied? Indeed, would it still be the same sock many years later, even after all of the material of the original sock has been replaced with patches?^{[citation needed]}
• The average age of cells in an adult body may be less than 10 years.

1 more annotation...

• Some philosophers believe that you take up time by having different temporal parts at different times. Your spatial parts are things like your head, your feet and your nose; your temporal parts are things like you-yesterday, you-today and you-tomorrow.
• What happens to a ship if you replace all of its planks one by one? What if you keep the old planks, then build a new ship out of them?
• So, yes, some of your (former) parts lie in the past, and some of your (future) parts lie in the future, but that doesn't mean that you're somehow less than a whole person, right here and now.
• Endurantists think about what parts you have at different times, past, present or future. But perdurantists prefer to think atemporally about what parts you have, full stop (what parts you have, period). And they claim that you have you-yesterday, you-today and you-tomorrow amongst your parts. Endurantists don't accept this atemporal way of talking about parthood, and so they find it difficult even to say what they don't like about temporal parts.
• Other non-standard views take the basic perdurantist idea that persistence is much like spatial extension, then they develop the idea in different ways. For example, perhaps persisting things stretch out four-dimensionally through time, but without being subdivided into temporal parts. Or perhaps, as stage theorists claim, the world is full of four-dimensional objects with temporal parts, but when we talk about ordinary objects like boats and people, we talk about brief temporal parts or ‘stages’ of four-dimensional objects.
• How is this supposed to work? Imagine that someone refers to you by name. According to perdurantists, the name refers to a ninety-year-long (let's hope) four-dimensional object. According to stage theorists, the name refers to a brief part of that ninety-year-long object, a different one at different times. This sounds peculiar: after all, your name refers to you and you have a future (and quite a past), while stages exist only momentarily. Stage theorists say that when we speculate about what you're going to do next week, our speculations are made true or false by the behaviour of your counterparts next week. These future counterparts of yours are the very objects which, according to perdurantists, are your future temporal parts.
• Typically, objects which have any temporal parts are thought to have instantaneous temporal parts (‘time-slices’), which do not themselves persist through time. (Most perdurantists think that things have non-instantaneous temporal parts too, like you-during-1999.)
• an object has only as many temporal parts as it has genuinely differentiated periods in its existence; this is a mixed view, because changing objects will have temporal parts, while unchanging objects and temporal parts will persist without having temporal parts of their own.
• One idea is that we can't know for sure whether things have temporal parts:
• If this is true, it doesn't undermine the debate unless consensus and certainty are our only goals. A second idea is that metaphysical enquiry is pointless, since irrelevant to daily life.
• ‘worm theory’,
• this has recently become known as the ‘problem of temporary intrinsics’
• But it would be nice to understand why this fact is crucial: what is it about the passage of time which makes it possible for one and the same object to have apparently incompatible properties?
• One objection is that perdurance-style temporal variation is not really change at all:  the whole four-dimensional banana is neither unripe nor overripe, so can't change between these states, and the temporal parts are either permanently unripe or permanently overripe, so they don't change either.
• In response, perdurantists distinguish two ways of talking about persisting things - an atemporal way, which takes in all times at once, and a temporal way of talking, relative to various times.
• According to perdurantists, talk about the same banana at different times is straightforwardly made true by one and the same four-dimensional object existing at different times. But some fancy footwork is needed to explain what it is for that object to be overripe right now: it's for it to have an overripe temporal part right now. In contrast, according to stage theorists, talk about the banana being overripe right now is straightforwardly made true by the banana being overripe, since the banana just is a momentary stage which exists right now.
• One radical answer is presentism, the view that only present objects, events and states exist: past and future do not exist.
• There's no mystery in an object which bears apparently incompatible relations to different things: you are bigger than the Mona Lisa, and smaller than the Louvre, but metaphysicians don't puzzle over how you can be both bigger-than and smaller-than.
• Those who oppose this relational view of changeable properties claim that it's just too relational: the banana seems to lose all its intrinsic nature.
• We may also worry that, as with the temporal parts account, it's not clear whether anything really changes on this picture: the banana always stands in the same relations to the various times.
• What's on the plinth? Well, the statue is. Is the original lump of clay also on the plinth? It seems so: you didn't destroy or even damage the lump of clay just by changing its shape. So are there are two statue-shaped things on the plinth, a statue and a lump of clay?
• This argument is sometimes expressed using Leibniz's Law, the principle which says that if objects differ in their properties, they cannot be one and the same thing.
• Leibniz's Law should be distinguished from the more controversial Principle of the Identity of Indiscernibles, which says that if objects share all their properties, they must be one and the same thing.
• These differences suggest that, after the accident, Tibbles and Tib are two different things occupying the same place at the same time.
• This explains both our intuition that there's only one object there (there's just the one arty-looking temporal part) and our intuition that the statue and the lump are different objects with different properties
• This view is sometimes called the ‘standard account’ of coincidence.
• One popular endurantist option is simply to accept that two different objects can wholly occupy exactly the same location at the same time.
• The relationship between wholly-coinciding objects is often called ‘constitution’, and so the slogan of the standard account is ‘constitution is not identity’.
• According to some versions of the standard account, constitution is always a one-way relationship: the lump constitutes the statue, but not vice versa.
• it entails that when a 1kg statue is constituted by a distinct 1kg lump, the result ought to weigh 2kg; and, most seriously, it fails to explain how two distinct objects, made of the same parts and matter, arranged in the same way and at the same place and time, can be distinct objects with different properties.
• and others simply accept the multitude.  After all, it's not so bad having all those objects when you realise they don't all need separate locations.
• your various internal organs and limbs weigh several kilos each, but we wouldn't expect these to show up on the scales in addition to your total body mass, since you are made of the same stuff as your organs and limbs.
• Likewise, supposedly, although the lump and the statue are distinct 1kg objects, we shouldn't expect these to show up separately on the scales, since they are made of the same stuff.
• Why expect all the properties of a composite object to be determined by the identity, properties and interrelations of its present parts?
• Perhaps identity can be temporary: the statue and the lump are identical once the statue exists, although the lump was not always identical to the statue; Tib and Tibbles begin as non-identical, and become identical. This proposal requires us to change our views of identity, and of the connection between identity and sharing of properties.
• Or perhaps objects can be destroyed more easily than we had realised: the lump of clay ceases to exist when the statue is created (it is replaced by a new, statue-shaped lump of clay, made from the same clay particles)
• the cat's tail-complement ceases to exist when it is separated from the tail.
• After all, a tail-complement seemed like a dubious object from the beginning, and if there is no such thing as Tib, we don't have to explain what relationship holds between Tib and Tibbles (we may grandly deny that cats have ‘arbitrary undetached parts’).
• Similarly, perhaps it is a mistake to think that there literally are such things as statues and lumps of clay, as opposed to mere quantities of stuff or pluralities of particles.
• Suppose that, instead of first forming or digging up the lump of clay then later moulding it into a statue, you make the two halves of the statue separately, then create both statue and large lump in one fell swoop, by sticking the halves together. Later, you petulantly smash the thing into pieces, destroying statue and lump simultaneously. Here, it seems that the lump of clay and the statue coincide at every moment at which either exists, yet they seem to be distinct objects because they differ in how they could have been: for example, the statue could have been made of a different lump of clay, but the lump could not. Talk of temporal parts doesn't help here: lump and statue share all their temporal parts, and differ only in their modal features (in how they could have been different).
• Perdurantists are better advised to claim that the statue and the lump of clay are one and the same object, then come up with some explanation of why they appear to have different properties.
• We may say that the object in question could, qua statue, have been made out of a different lump of clay, but could not, qua lump, have been made out of a different lump of clay. There are various ways of explaining what the ‘qua’ clauses are doing in this peculiar claim, and perhaps the most popular explanation involves counterpart theory, a controversial theory about our talk of possibilities.
• think of a lake or haystack which gradually comes into existence, or a building or a rock formation which slowly crumbles away. Let's call this phenomenon ‘fuzzy temporal boundaries’.
• Indeterminacy can also arise when objects intermingle in a way which seems to leave it clear that they survive the process, but unclear which object is which. Suppose you remove about half the parts from the bicycle your uncle gave you, about half the parts from the bicycle your aunt gave you, and switch them over. Afterwards, you have two bicycles, each half-made of parts that used to be in the bicycle your uncle gave you, and half-made of parts that used to be in the bicycle your aunt gave you. Which post-repair bicycle is the one your uncle gave you, and which the one your aunt gave you? There seems to be no clear fact of the matter. Let's call this phenomenon ‘radical disruption’.
• Typical temporal parts theorists argue that such indeterminacy results from a mismatch between human language and temporarily-coincident objects
• According to most temporal parts theorists, there are very many ‘nested’ four-dimensional objects involved in this process, some of which end before others do. We are unclear about when the building ceases to exist because our use of language just doesn't determine which of these many four-dimensional objects is ‘the building’.

• Perdurantists recognise (at least) the following four-dimensional objects:

    
   
  1. something that begins with A and B, then continues with A and C;
    
  2. something that begins with A and B, then continues with B and D;
    
  3. something that begins with C and D, then continues with A and C;
    
  4. something that begins with C and D, then continues with B and D.
• Objections to the typical temporal parts account of indeterminacy in persistence turn on the sheer number of temporarily coincident objects required to make the story work; or on independent objections to the language-based account of vagueness (see the separate entry on  vagueness);  or on particular objections to telling such a story about indeterminacy involving people (see  section 9).
• One option is to mimic the perdurantist temporary-coincidence account, but without the temporal parts. That's to say, endurantists could claim that there are very many wholly-present coincident building-like objects where the building stands, each of which ends at a slightly different moment from all the others.
• Likewise, endurantists could recognise objects (1)-(4), just as perdurantists do, but claim that each is wholly present whenever it exists. This strategy is unpopular, because temporarily-coincident enduring objects can seem worse than temporarily-coincident perduring objects
• Even those who don't mind a bit of worldly vagueness may have reason to reject worldly vagueness in persistence, because this amounts to worldly vagueness in identity: it's vague whether the original bicycle your uncle gave you is identical with the bicycle you now ride to work. Worldly vagueness in identity is thought to be especially problematic, because all identity is self-identity, and it's hard to see how there could be any vagueness in self-identity.
• This claim could be developed in one of two ways. In the case of the crumbling building, for example, endurantists could claim that there is a single building-shaped object with an unknown final moment. Or they could claim that there are very many temporarily-coincident building-like objects, each with a different final moment, that we refer to just one of these when we say ‘the building’ but we do not know which.
• Finally, endurantists could adopt a restricted ontology, as some do in response to temporary coincidence. If there aren't really any such things as bicycles, buildings or lakes, just particles moving around and interacting, then there are no issues to resolve about the careers and identities of bicycles, buildings or lakes. As before, the main difficulty here is in reconciling our everyday beliefs with a sufficiently restricted ontology: after all, people and even fundamental particles seem sometimes to be indeterminate. (Again, it is open to perdurantists to adopt a restricted ontology, but typically they do not.)
• Typical perdurantists posit temporary coincidence between objects, and a failure on our part to talk determinately about any one of these.
• A temporary-coincidence view could instead be paired with an epistemic account of vagueness, and our failure to know which object we're talking about.
• Alternatively, vagueness may be either attributed to objects themselves, and their failure to have determinate careers, or else to our failure to know what careers they have.
• A radical option is to deny that any genuine object is involved (thus restricting ontology)
• The most relevant debate for our purposes turns on whether distant times are like distant places.
• What about eighteenth-century people, objects and times? Does David Hume exist, despite being far away in time? Or is it more reasonable to say that Hume used to exist, but now does not exist? 
• Eternalists believe that past and future things exist, just like present things.
• Presentists, in contrast, believe that distant times are not like distant places: things in distant places exist, but things at distant times do not. According to the intermediate ‘growing universe’ theory, past and present things exist, but future things do not.
• It's natural to suppose that presentists should be endurantists, claiming that things are wholly present whenever they exist. If you don't believe in either the past or the future, there's nowhere and nowhen for any ‘missing’ parts to be.
• What connection is there between the eternalism-presentism debate, and the debate about temporal parts?
• Presentists think that only the present exists, but they're happy for us to talk about the causes of the First World War, about next week's seminar, or about David Hume.
• Can presentists claim that, although past and future temporal parts of the banana do not exist, the banana did have temporal parts in the past, and will have other temporal parts in the future? This takes us back to the question of how to define ‘temporal part’ (see  section 2),  and it raises a methodological issue: should ‘temporal part’ be defined in such a way that presentists can believe in temporal parts, or not?
• If eternalists accept temporal parts, they have a neat explanation at hand: your yesterday temporal part doesn't know about theories of persistence, but your tomorrow part does know about theories of persistence. But if eternalists reject temporal parts, then the two apparently-conflicting states are states of one and the same thing (you), and it's not obvious how to resolve the conflict. So perhaps eternalists should believe in temporal parts, and, conversely, those who reject temporal parts should be presentists. This argument succeeds only if eternalists really can't explain change without believing in temporal parts (see  section 3).
• First, should we attempt to establish a theory of persistence, and then let this dictate our theory of time? Or should we start with the theory of time?
• Second, tying the dispute about persistence to the dispute about time makes trouble for anyone who thinks that one of the disputes is genuine but the other is merely a verbal disagreement.
• And, third, since presentism and eternalism seem clearly to be incompatible, if each compels a different account of persistence, then there can't be ‘mixed’ worlds in which some things perdure and others endure (a peculiar consequence, since most endurantists think that processes perdure).
• Advocates of the ‘A-theory’ of time argue that the flow of time pushes events from one ontological status to another (presentists are usually taken to be A-theorists too). But advocates of the ‘B-theory’ of time think that there is no important ontological difference between past, present and future, and that there is no such thing as ‘the flow of time’. There is some tendency to think that the A-theory is more hospitable to endurantism, and the B-theory more hospitable to perdurantism, but there is no consensus on this matter.
• For our purposes, the key feature of STR is its claim that, for many pairs of events, there is no absolute fact of the matter as to which event, if either, happened first, or whether both occurred at the same time.
• This means that, for many events, there is no absolute fact of the matter as to whether they are occurring in the present, in the past or in the future. (If they were occurring now, they'd be occurring simultaneously with your reading this sentence, but there's no absolute fact of the matter about this simultaneity issue.)
• STR shows space to be much like time, objects extend in space by having spatial parts, so objects persist through time by having temporal parts.  But this argument is weak:
• According to STR, for many events there is no absolute fact of the matter as to whether those events are simultaneous with now. That's to say, at any moment, there is no absolute fact of the matter as to which events are present. This makes life difficult for presentists, who claim that only present events exist. If STR thereby rules out presentism, and if endurantism requires presentism in order to explain change (see  section 3),  then STR rules out endurantism: things have temporal parts. But not all endurantists agree that they must be presentists, and not all presentists agree that their view is undermined by STR.

• A third argument from STR to perdurantism does not rely on the claim that STR is out-and-out incompatible with endurantism. Instead, the claim is that STR highlights a phenomenon which can better be explained by perdurantists than by endurantists. To understand the phenomenon, imagine a three-dimensional cylindrical chocolate cake which you want to cut up into two-dimensional pieces (you've got a lot of friends). If you cut only at right angles to the length of the cake, then each piece will be circular. But if you cut at a different angle, then each piece will be oval. The cylindrical shape of the cake explains the shapes of the various pieces produced by cutting at various angles.

    

    Now imagine a four-dimensional object, cut into three-dimensional timeslices. In a non-relativistic world, there's only one way to do this, because there's only one way to divide up events into groups of simultaneous events: it's like cutting the cake at right-angles. But, by relativising simultaneity to reference frames, STR gives us lots of different ways to cut the four-dimensional object into three-dimensional slices, just as there are lots of different angles at which to cut the cake. The shape of the three-dimensional slices you get by cutting in different ways, from the perspective of different reference frames, can all be explained by the shape of the four-dimensional object you're cutting up.
• STR tells us that the persisting thing has different three-dimensional shapes with respect to different reference frames.
• The different shapes in different reference frames are correlated, but according to the endurance theorist there is no ‘underlying’ four-dimensional object to explain these correlations.
• Universalism is the view that any collection of objects whatsoever has a sum, an object they compose. Thinking just of the present moment, this entails that there is an object composed right now of your left ear, the front fork of your bicycle, and the Louvre.
• So there is an object made of your maternal grandmother's wedding ring on the day she was married, your right ear yesterday and a brief temporal part of an electron in the year 2020.
• (Universalism is sometimes called ‘unrestricted mereology’, ‘unrestricted composition’ or ‘unrestricted fusion’; ‘fusion’ means ‘sum’. For more on universalism, see the separate entry  on  mereology,  especially section 4.2.)
• it often seems that whether or not an object survives a certain kind of change is in some sense conventional, or up to us.
• This sounds mysterious: how could we have such powers? But the combination of universalism and perdurantism permits a less radical version of the view: there are lots of four-dimensional objects which share temporal parts with the wheeled thing in your bike shed, and it's up to us which one of those counts as a ‘bicycle’. Similarly, perhaps it's up to us which of the multitude of four-dimensional objects count as ‘people’. 
• Third, perdurantists who reject universalism seem committed to giving an account of the difference between collections of temporal parts which have a sum, and collections which do not. But such accounts seem to permit borderline cases, in which it's not clear whether a certain collection has a sum. And borderline cases look like cases in which it is not clear whether a certain object (the sum of those parts) exists or not. And many find such vagueness in existence unacceptable. Objections to this argument turn on whether non-universalists really have to give such an account, and on whether vague existence really is unacceptable.
• This third type of argument for universalism has also been used to argue directly for the existence of temporal parts.
• we ask which matter-filled regions exactly contain objects. Unless we agree that they all do, we will get into trouble with borderline cases, as in the previous paragraph.
• The other doctrine which usually goes along with perdurantism is Humean Supervenience. This is the claim that, roughly speaking, facts about which intrinsic properties are instantiated at which points determine all the facts there are. There are no irreducibly holistic facts. In conjunction with perdurantism, this entails that all the facts about a given persisting object supervene upon intrinsic facts about its briefest temporal parts. That's to say, if you fix what's happening at each moment, you've fixed everything. This sounds pretty plausible, but it turns out that it's rather difficult to reduce facts about motion, for example, to suitable moment-by-moment facts.
• People have various distinctive features: we have moral status, we have mental properties like reasoning and being conscious, and we are associated in an intimate but somewhat puzzling way with living organisms. 

• Moreover, most of us seem to have a special concern for our own future, and are willing to limit current pleasures like smoking, shopping, and not writing encyclopedia articles, because we believe that sacrifices made now will benefit us in the future. We also feel a distinctive kind of pride or shame about our own past actions, and are bound by our own past promises but not by those of other people.

    
• It has been suggested that only endurantists can justify our willingness to make sacrifices for our future selves, to act upon the plans formulated by our past selves, and to rely upon the evidence gathered by our past selves
• First, they may argue that it is the whole, identical, four-dimensional person who makes sacrifices, acts upon plans and reasons from evidence, via the activities of her temporal parts. Alternatively, they may accept that it is short-lived temporal parts which act, sacrifice and reason, but that past- and future-regarding actions can be justified by the intimate relations between distinct temporal parts of the same person.
• Stage theorists must take this second route, for they claim that the person just is a brief stage, who takes responsibility for the actions of her past counterparts, and acts to benefit her future counterparts.
• There are a number of issues about coincidence involving people. For example, it seems that we human people at least coincide with human organisms. You occupy the same location as a human organism right now, but it seems that you differ in various ways: the organism may have existed since conception, and will go on until biological death, but some believe that the person does not come into existence until the organism is relatively well-developed, and that the person may cease to exist before biological death, by entering a persistent vegetative state. You also seem to differ from the organism regarding what's possible: perhaps you could have been a robot, or a disembodied intelligence, whereas the organism could not.
• Certain puzzle cases also seem to suggest that a person might divide into two: suppose that, as a result of philosophical confusion on the hospital ethics committee, a doctor is permitted to remove the two halves of your brain and implant them into two different (brainless) bodies. On one understanding of this process, each of the resulting people has a good claim to be you. Is this a reason to think that two coincident people were walking around together before the operation, and that they have only now been separated?
• Finally, it seems that people are prone to indeterminacy, just like crumbling buildings and bicycles: some people have gradual endings, and sometimes, in stories at least, a person can undergo such a traumatic change that it's not clear whether the same person exists after the change.
• But any talk of either partial or total coincidence involving people can seem problematic, because of concerns about the use of first-person pronouns (who does your ‘I’ refer to before your brain-splitting operation, if there are two of you?), and about multiplying conscious entities (could two people have literally the same headache? if you merely coincide with a human organism, are you sure it's you who has the headache, and not the organism?)

93 more annotations...

• On this view, that proposition either has no truth value right now, or else has the  value indeterminate. When the relevant time comes, and you  either have lunch or don't, then, on the view in question, the  proposition that you have lunch on the relevant day will come to be  either true or false (as the case may be), and from then on that  proposition will forever retain its truth   value.^[2]
• The question of whether there could be time without change has  traditionally been thought to be closely tied to the question of  whether time exists independently of the events that occur in time.  For, the thinking goes, if there could be a period of time without  change, then it follows that time could exist without any events to  fill it; but if, on the other hand, there could not be a period of  time without change, then it must be that time exists only if there  are some events to fill it.

  • Surely the whole definition of time relates to change? So if nothing changes for a "period of time", then surely time isn't passing? So while time isn't passing.. what IS passing..? Hypertime?
• This view is typically called either “Reductionism with  Respect to Time” or “Relationism with Respect to  Time,” since according to this view, all talk that appears to  be about time can somehow be reduced to talk about temporal relations among things and events. The opposing view, normally referred to  either as “Platonism with Respect to Time” or as  “Substantivalism with Respect to Time” or as  “Absolutism with Respect to Time,” has been defended by  Plato, Newton, and others. On this view, time is like an empty  container into which things and events may be placed; but it is a  container that exists independently of what (if anything) is placed  in it.
• One is conceptual: time, according to this  argument, is by definition nothing more than a system of temporal  relations among things and events, so that the idea of a period of  time without change turns out to be incoherent.
• Here is a simplified version of Shoemaker's argument. Consider a  small, spatially finite possible world that is divided into three  zones, A, B, and C. In Zone A, there is a complete freeze — a  cessation of all change — for one hour every 2 years. These  local freezes in Zone A are preceded by a short period in which every object in A takes on a reddish glow (observable to the occupants of  all three zones), while at the same time a temporary force field  develops at the boundary of Zone A, preventing anything from entering or exiting that zone during the freeze. While the freeze in Zone A is taking place, Zone A appears to those in Zones B and C to be pitch  black, since no light can enter or exit the frozen zone; but as soon  as the local freeze in Zone A is over, the people in the other two  zones can again see everything in Zone A, and can in fact see those  things resuming their normal behaviors without missing a beat. To  those who remain in Zone A for the freeze, it appears that the  reddish glowing and the development of the force field are  immediately followed, not by any cessation of change, but, instead,  by a large number of sudden and discontinuous changes in the other  two zones.

• Meanwhile, In Zone B there is a similar freeze for one hour every 3  years, and in Zone C there is a freeze for one hour every 5 years.  The inhabitants of this strange world quickly become aware of the  local freezes, and they have no trouble calculating the “freeze function” for each of the three zones. What's more, they also  calculate that there is a global freeze — a period during which each one of the three zones undergoes a local freeze — exactly  once every 30 years. Whenever a global freeze occurs, of course, no  one is able to see any frozen objects or blacked-out zones, since  everyone and everything is frozen at the same time. But the reddish  glowing and the development of temporary force fields that precede  each world-wide freeze are observable to everyone; and so the global  freeze times come to be celebrated by “empty time  parties” all over the world.

    

    No doubt the inhabitants of this unusual world could come up with a  theory that explains the local freezes in a way that doesn't posit  any empty time. For they could theorize that in Zone A there is a  local freeze every two years, except for the 30th year, when there is no freeze; and similarly for the other zones. But such a theory would involve freezing functions that are more complicated than those that  entail a global freeze every 30 years.
• But for each of the  features attributed to time in the standard topology, two interesting questions arise: (a) does time in fact have that feature? and (b) if  time does have the feature in question, is this a necessary or a  contingent fact about time?
• Consider the question of whether time should be represented by a line without a beginning. Aristotle has argued (roughly) that time cannot  have a beginning on the grounds that in order for time to have a  beginning, there must be a first moment of time, but that in order to count as a moment of time, that allegedly first moment would have to  come between an earlier period of time and a later period of time,  which is inconsistent with its being the first moment of time.  (Aristotle argues in the same way that time cannot have an end.)
• or to a closed loop

  • this would answer the common objection to the A theorists view that time 'passes' or 'flows': where exactly does it flow TO? what direction? if time was a loop then it would just continuously flow round and round without any need for a direction.
• In a famous paper published in 1908, J.M.E. McTaggart argued that  there is in fact no such thing as time, and that the appearance of a  temporal order to the world is a mere appearance.
• First, he says, positions in time  can be ordered according to their possession of properties like  being two days future, being one day future,  being present, being one day past, etc. (These  properties are often referred to now as “A properties.”)  McTaggart calls the series of times ordered by these properties  “the A series.” But he says that positions in time can  also be ordered by two-place relations like two days earlier  than, one day earlier than, simultaneous with, etc.
• (These relations are now often called “B  relations.”) McTaggart calls the series of times ordered by  these relations “the B series.”

• In any case, McTaggart argues that the B series alone does not  constitute a proper time series. I.e., McTaggart says that the A  series is essential to time. His reason for this is that change (he  says) is essential to time, and the B series without the A series  does not involve genuine change (since B series positions are forever “fixed,” whereas A series positions are constantly  changing).

    

    McTaggart also argues that the A series is inherently contradictory.  For (he says) the different A properties are incompatible with one  another. (No time can be both future and past, for example.)  Nevertheless, he insists, each time in the A series must possess all  of the different A properties. (Since a time that is future will be  present and past, and so on.)
• One response to this argument that McTaggart anticipates involves  claiming that it's not true of any time, t, that t  is both future and past. Rather, the objection goes, we must say that t was future at some moment of past time and will be past at some moment of future time. But this objection fails, according to  McTaggart, because the additional times that are invoked in order to  explain t's possession of the incompatible A properties must themselves possess all of the same A properties (as must any further  times invoked on account of these additional times, and so on ad  infinitum). Thus, according to McTaggart, we never resolve the  original contradiction inherent in the A series, but, instead, merely generate an infinite regress of more and more contradictions.
• McTaggart concludes that time itself,  including both the A series and the B series, is unreal.
• That is, some philosophers have been  persuaded by McTaggart that the A series is not real, even though  they have not gone so far as to deny the reality of time itself.
• For example, when we say that the year 1900  has the property of being past, all we really mean is that 1900 is  earlier than the time at which we are speaking.
• According to The A Theory, the passage of time is a very  real and inexorable feature of the world, and not merely some  mind-dependent phenomenon.
• with A Theorists characterized as those who affirm the  reality of tense and B Theorists characterized as those who deny the  reality of tense.
• That is, she will deny  that it is true of any time, t, that t is  past, present, and future. Instead, she will insist, the closest  thing to this that can be true of a time, t, is (for  example) that t was future, is present,  and will be past, where the verbal tenses of the verb  ‘to be’ in this claim are not to be analyzed away (just  as the apparent references to the putative A properties pastness,  presentness, and futurity are not to be analyzed away in favor of  reference to B relations).
• In effect, then, the typical A Theorist makes exactly the move in  response to McTaggart's argument that McTaggart anticipated, and  explicitly rejected. Not surprisingly, then, many supporters of  McTaggart's argument feel that the A Theorist's response fails.
• Two other arguments against The A Theory (besides McTaggart's argument, that is) have  been especially influential. The first of these is an argument from  the special theory of relativity in physics.
• The second of the two other influential arguments against The A  Theory concerns the rate of the alleged passage of time. According to this argument, if it is true to say that time really passes, then it  makes sense to ask how fast time passes. But (the argument goes) if  it makes sense to ask how fast time passes, then it is possible for  there to be a coherent answer to that question. Yet, according to the argument, there is no rate that can be coherently assigned to the  passage of time. (“One hour per hour,” for example, is  said not to be a coherent answer to the question “How fast does time pass?”) Thus, the argument concludes, it cannot be true to say that time really passes.
• According to The B Theory, time is very much like the dimensions of  space. Just as there are no genuine spatial properties (like  being north), but, rather, only two-place, spatial relations (like north of), so too, according to the B Theorist, there  are no genuine A properties. According to The A Theory, on the other  hand, time is very different from the dimensions of space. For even  though there are no genuine spatial properties like being  north, there are, according to the A Theorist, genuine A  properties; and time, unlike space, can truly be said to pass,  according to The A Theory.
• But according to a somewhat less popular  version of Non-presentism, temporal location does matter when it  comes to ontology, because only objects that are either past or  present — but not objects that are future — exist. On  this view, which we can call “The Growing Universe  Theory,” the universe is always increasing in size, as more and more things are added on to the front end (temporally speaking).
• Hence, if time travel is impossible, then we should not even  be able to consider any story in which time travel occurs. And yet we do so all the time! One task facing the philosopher who claims that  time travel is impossible, then, is to explain the existence of a  huge number of well-known stories that appear to be specifically  about time travel.
• According to The 4D View, temporally extended objects have temporal  parts, temporal extension is perfectly analogous to spatial  extension, and time is one of four dimensions that are on a par, at  least with respect to the manner in which objects are spread out in  space-time. On The 3D View, however, temporally extended objects do  not have temporal parts, temporal extension is very different from  spatial extension, and time is unique among the four dimensions of  the world, at least with respect to the manner in which objects are  spread out in space-time.

25 more annotations...

• Special relativity (SR) (also known as the special theory of relativity or STR) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz and Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies".^[1] It generalizes Galileo's principle of relativity–that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)–from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be.^[2] Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.^[3]

• Einstein's special relativity was "special" because it dealt only with the specific case of intertial reference frames.  An inertial reference frame is a body that is either at rest or that moves with a constant velocity. In contrast, his general theory of relativity accounts not only for these, but also for bodies that accelerate (i.e., change their velocity).

• A-theorists deny that past, present and future are equally real, and maintain that the future is not fixed and determinate like the past. Those who wish to eliminate all talk of past, present and future in favour of a tenseless ordering of events are called B-theorists. B-theorists (such as D.H. Mellor and J.J.C. Smart) believe that the past the present and the future are equally real.
• It is often claimed that physical theories such as special relativity provide the B-theory with compelling support.
• A-theorists on the other hand believe that a satisfactory account of time must acknowledge a fundamental metaphysical difference between past, present and future (Prior 2003). The difference between A-theorists and B-theorists is often described as a dispute about temporal passage or 'becoming'. B-theorists argue that this notion embodies serious confusion about time, while many A-theorists argue that in rejecting temporal 'becoming', B-theorists reject time's most vital and distinctive characteristic. It is common (though not universal) to identify A-theorists' views with belief in temporal passage.
• It is also common (though not universal) for B-theorists to be four-dimensionalists, that is, to believe that objects are extended in time as well as in space and therefore have temporal as well as spatial parts. This is sometimes called a time-slice ontology.

2 more annotations...

• According to McTaggart, there are two distinct modes in which all events can be ordered in time. In the first mode, events are ordered by way of the non-relational singular predicates "is past", "is present" and "is future." When we speak of time in this way, we are speaking in terms of a series of positions which run from the remote past through the recent past to the present, and from the present through the near future all the way to the remote future. The essential characteristic of this descriptive modality is that one must think of the series of temporal positions as being in continual transformation, in the sense that an event is first part of the future, then part of the present, and then past. Moreover, the assertions made according to this modality imply the temporal perspective of the person who utters them. This is the A-series of temporal events.

   

  From a second point of view, one can order events according to a different series of temporal positions by way of two-term relations which are asymmetric, irreflexive and transitive: "comes before" (or precedes) and "comes after" (or follows). This is the B-series, and the philosophy which says all truths about time can be reduced to B-series statements is the B-Theory of time.