Metaphysics Study Guide - Space and Time

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Metaphysics – philosophy of space and time

Metaphysics is a traditional branch of philosophy concerned with explaining the fundamental nature of being and the world that encompasses it, although the term is not easily defined. Traditionally,

metaphysics attempts to answer two basic questions in the broadest possible terms:

1: What is ultimately there?2: What is it like?

etaphysics literally means before physics, showing that its meant to be the philosophy of the aspectsof reality that science cannot directly determine, which is actually a great deal. !"ote howe#er that this

does not mean that it is idle speculation without #alid means to approach it.$ %owe#er, being a meta

relation to physics, it is often directly informed by the sciences itself, and so closely ties to them. The

sciences actually grew out of natural philosophy, which at the time was seen as a double sided coin tometaphysics.

& central branch of metaphysics is ontology, the in#estigation into the basic categories of being andhow they relate to each other. ontology deals with questions concerning what entities exist or can be

said to exist, and how such entities can be grouped, related within a hierarchy, and subdi#ided

according to similarities and differences.

Philosophy of space and time

&n interesting thing to note about the concept of space, and especially time is that despite there being

seemingly intuiti#e ways that people imagine it as functioning, these ideas are not inherent. 'n some

sense, they were as ideas actually created, and before then people would ha#e only a general concept of it. (ome did not e#en ha#e names for it.

)hilosophy of space and time is a subset of metaphysics that tal*s about the bac*ground that items inthe uni#erse exist in. &lthough time and space used to be seen as separate by many, now they are seen

together as the single entity timespace that time and space are merely two types of dimensions of

measurement in. +b#iously this branch of metaphysics has a bit of crosso#er with regular physics, and

theoretical physics, since the theories are often de#eloped off of and interrelate with one another.%owe#er, we will not del#e much into physics, as that is its own topic.

Realism as regards time and space hold that time and space obecti#ely exist in some sense, although inwhat sense may be uncertain. (ome positions may s*irt the line between realism and anti realism, or

ma*e distinctions on what counts as -existence.

Anti-realists hold that in some sense time and or space are illusions. /or instance, all of reality could be some form of data system which includes data for what we consider spacial interaction or an arrow

of time, but which don0t actually exist. (ome forms of idealism hold that since nothing exists outside of

mind, that time and space are illusions in some sense created by it. (ome also hold that the concept ofe#en combined spacetime is a little #ague and needs to be better explained, although technically realist.

%ow realist such theories are depends on what the proposed solutions are. 't should be noted that

thin*ing that space time is imprecise and needs to be replaced with a new concept is actually amainstream belief in science now.





particles of light ha#e8percie#e no time. Things with mass can slow down their mo#ement through

space, and gain mo#ement through time instead. This is why speeding up slows the mo#ement of time

for them. 3ecause e#erything is mo#ing at the same speed at all times. 't ust changes how much of this

is through either the space or time dimensions. (ince our current model of quantum mechanics does notseem to account for relati#ity, an important issue of science is how to merge these theories together into

a form of relati#istic quantum mechanics.

!he hole argument is an argument against bac*ground dependance that says that if you ha#e two

distributions of metric and matter fields related by transformation, substanti#alists must maintain that

the they represent two ontologically distinct physical systems, e#en though you ha#e nothing withwhich to ustify this conclusion. &nd as such, occam0s ra9or would seem to imply bac*ground

independence.

"onventionalism states that there is no fact of the matter as to the geometry of space and time, but that

it is decided by con#ention. The first proponent of such a #iew, %enri )oincar, reacting to the creation

of the new non;uclidean geometry, argued that which geometry applied to a space was decided by

con#ention, since different geometries will describe a set of obects equally well, based onconsiderations from his sphereworld. 7ontemporary philosophy is still in disagreement as to the

correctness of the con#entionalist doctrine.

Sphere #orld is a description of a world which is ruled by hyperbolic geometry rather than ;uclidian

geometry. (uch that cur#ed lines !in geodesic form$ would appear to be straight in it. This world,

loo*ing normal to internal inhabitants, was used as an argument for con#entionalism and that space andtime0s arrangements are based on subecti#e mapping.

!he direction of time

!he arro# of time, or time's arro#, refers to the 5oneway direction5 or 5asymmetry5 of time. Why

should you be able to remember the past, but not the future? Time seems to mo#e in one direction, andmo#ing forward has different properties than mo#ing bac*wards. 'f indeed mo#ing bac*wards is a

coherent concept to begin with. There are a few arrows of time that describe different things. +ne of

the important questions to answer is whether these arrows are fundamentally the same thing in any

meaningful sense, or whether there isn0t some o#erarching arrow of time that the ones we see are mereresults of.

!-symmetry refers to the symmetry of physical laws under a timere#ersal scenario. &t themicroscopic le#el, it seems that if time were to re#erse, the theoretical statements that describe certain

physical processes would remain true. 4et at the macroscopic le#el it often appears that this is not the

case: there is an ob#ious direction !or flow$ of time. (ometimes #ariables that do not change upon time

re#ersal are referred to as even, and those that do are referred to as odd.

!he thermodynamic arro# of time is the arrow of entropy. This is considered the most importantarrow of time in physics, because ;ntropy is the only quantity in the physical sciences !apart from

certain rare interactions in particle physics$ that requires a particular direction for time. &s one goes

5forward5 in time, the second law of thermodynamics says, the entropy of an isolated system can

increase, but not decrease. %ence, from one perspecti#e, entropy measurement is a way ofdistinguishing the past from the future. %owe#er in thermodynamic systems that are not closed, entropy

can decrease with time: many systems, including li#ing systems, reduce local entropy at the expense of



an en#ironmental increase, resulting in a net increase in entropy. ;xamples of such systems and

phenomena include the formation of typical crystals, the wor*ings of a refrigerator and li#ing

organisms.

'n the most general sense, entropy itself refers to statistical distribution. 'f you were to throw thingsabout randomly, o#er time, you would expect them to e#en out, and thus lose order in the specific

sense, but become more statistically uniform in the o#erall sense. (ince entropic forces are emergent

effects resulting from systems tending towards maximum entropy some posit that entropy itself shouldnot necessarily be described as an arrow of time, but as a result from it.

Ma$#ell's demon refers to a demon wor*ing at a microscopic le#el that could operate a gate

!presumably of lowfriction construction$ allowing only swift molecules to pass through it. 'n this way,

the demon0s wor* would result in slow molecules !i.e. cold$ on one side of the gated barrier, and heaton the other side. 4et mo#ement from uniformity of temperature to a split of hot8cold #iolates the

(econd 6aw of thermodynamics, allowing it to beat entropy. (ince entropy is only a statistical law

there is nothing ma*ing it inherently impossible to o#ercome, howe#er unli*ely. What implications thishas for using it as an arrow of time are un*nown.

"ausality, or the causation arro# of time ta*es a metaphysical #iew, in which the direction of time

follows from an asymmetry of causation. We *now more about the past because the elements of the

past are causes for the effect that is our perception. We feel we can0t affect the past and can affect thefuture because we can0t affect the past and can affect the future. There are two main obections to this

#iew. /irst is the problem of distinguishing the cause from the effect in a nonarbitrary way. The use of

causation in constructing a temporal ordering could easily become circular. The second problem withthis #iew is its explanatory power. While the causation account, if successful, may account for some

timeasymmetric phenomena li*e perception and action, it does not account for many others.

%owe#er, asymmetry of causation can be obser#ed in a nonarbitrary way which is not metaphysical in

the case of a human hand dropping a cup of water which smashes into fragments on a hard floor,spilling the liquid. 'n this order, the causes of the resultant pattern of cup fragments and water spill is

easily attributable in terms of the traectory of the cup, irregularities in its structure, angle of its impact

on the floor, etc. %owe#er, applying the same e#ent in re#erse, it is difficult to explain why the #arious pieces of the cup should fly up into the human hand and reassemble precisely into the shape of a cup,or why the water should position itself entirely within the cup. The causes of the resultant structure and

shape of the cup and the encapsulation of the water by the hand within the cup are not easily

attributable, as neither hand nor floor can achie#e such formations of the cup or water. The questionthen is whether causation as we *now it dri#es the other forces, or in some sense is a result of them.

Retrocausality refers to the possibility of an effect ta*ing place earlier in time than its cause. &lthough

no *nown retrocausality has been pro#en to occur in the natural world, many models for it ha#e been

made which at least on the surface do not #iolate any physical laws. 'f it were possible, a question iswhat implications it has for #iewing causality as an arrow of time.

A light cone refers to the maximum speed information is able to tra#el in order to be causally related.

(ince if something is many light years away from eachother, causation will ta*e that amount of time to

reach one place from the other, that is said to be the boundary of its light cone at that gi#en amount ofyears. What this means is that anything outside something0s light cone is said to not in any meaningful

sense exist in the -past of that item until it enters it e#en if it intuiti#ely ta*es place earlier in how we

would see time. (ince this is according to relati#ity a real function of the uni#erse, and not a mereconstruct it is uncertain what that could mean for time and causality.

!he flo# of time refers to the idea that time in itself has an obecti#e present which need not be

explained in terms of internal laws, but which internal laws operate in relation to. &s such, whether



causality or thermodynamics operate as the main internal arrow of time in a gi#en uni#erse, that this as

a whole is not sufficient to explain time.

!he la#s solution refers to a subset of the theory of causality that posits that it is not cause and effect

themsel#es which generate this arrow, but merely that the laws of the uni#erse in themsel#es ha#e built

in an arrow of time that is nonre#ersible. Which though similar, is in some senses distinct.

!he cosmological arro# of time points in the direction of the uni#erse0s expansion. &n importantquestion is what causes this. 's it inherently related to the other arrows, and such time can only go

forward as we understand it while the uni#erse is expanding, and thus there will be a sudden -end of

time if it were to e#er begin contracting? +r is it merely an artifact of the fact that we ha#e only e#er

seen it expanding. (ome physicists assumed the first originally, although it should be noted that there islittle direct support.

!he #eak arro# of time refers to a few cases in particle physics which operate on a specific direction.

&lthough it is noted that the only one arrow in physics large enough that it accounts for most of what

we see is the arrow of entropy, the fact that a few other things, no matter how insignificant, seem tooperate in a similar manner is enough to gi#e e#idence that entropy itself may not be what causes the

subecti#e flow of time.!he %uantum arro# of time, refers to the fact that that according to the 7openhagen interpretation of

quantum mechanics, quantum e#olution is go#erned by the (chr<dinger equation, which is timesymmetric, and by wa#e function collapse, which is time irre#ersible. &s the mechanism of wa#e

function collapse is philosophically obscure, it is not completely clear how this arrow lin*s to the

others, and whether it is related in any sense to the thermodynamic arrow at all, or exists totallyseparately. 't should be noted that ha#ing a mathematical model for the process of something is not

equi#alent to understanding what causes that process to occur.

!he psychological arro# of time or the perceptual arro# of time refers to the human psychology of

remembering things from the past, but not from the future. 't should be noted that the fact that the

psychological time arrow goes in one specific direction does not inherently ustify the assumption of anobecti#e flow of time, but could merely be the results of physical processes which allow this. /or

instance, if a uni#erse physically had all the same e#ents at all the same times, but the flow of time

went bac*wards, but you still remembered forwards, then to you would there e#en be a difference?

;#en if your perceptions were undergone in re#erse, you wouldn0t *now that this was the case.

presentism and eternalism

+ne of the important questions in the philosophy of time is what obects one can say actually -exist.

Presentism is the philosophical doctrine that only e#ents and entities=and, in some #ersions of

presentism, timeless obects or ideas li*e numbers and sets=that occur in the present exist. &ccordingto presentism, e#ents and entities that are wholly past or wholly future do not exist at all. &lthough this

is the most intuiti#e sense of time, it is not inherently correct for that reason.

&ternalism, block universe, or block time is the position that the past, present, and future all existequally. &nd that what we percei#e as the present is not in any sense an actual flowing of time, but

merely that aspect of us that had that perception in any gi#en location of time. &lthough this theory is

suggested by the general theory of relati#ity, especially since relati#ity posits that time in some sensedoes not wor* at the same relation in all reference frames, it also seems to be contradicted by quantum



mechanics, !which suggests something closer to presentism$ posing an issue as to which should be

pri#ileged, if not one of the in between ones. 't has some implications for the mind, since it posits that

one is actually experiencing all e#ents simultaneously, e#en if the brain and causality order it to not

reali9e this. !"ote that this position does not necessarily inherently imply that time goes to infinity in both, or e#en one direction.$

't also has some implications for concepts such as death. /or instance, e#en if annihilationism !the ideathat people do not exist past death in any sense$ were true, all this would mean is that -death is one of

our temporal borders. 3ut if the ;ternalism is correct, there is no such property as ceasing to exist, or

certain e#ents being -done. They continue to exist timelessly, alongside eternal, unchanging momentsof each indi#idual point in time of life.

!he static interpretation of time is a subset of eternalism that posits that e#en if time is eternalist, thatan ontologically pri#ileged present of obser#ers mo#ing -through the bloc* uni#erse is the case. 't

describes it li*e a reel of film, where time is the film which in a real sense exists as an absolute single

bloc*, but which can be played through in a form of progression. 'n this sense, it can also be seen as a

form of middle ground between presentism and eternalism.

!he gro#ing block universe is another middle ground between presentism and eternalism, which

posits that although there is an ontologically pri#ileged -present, that the past also has obecti#eexistence, and thus while the past is ne#er destroyed, more time is always coming into being. Thus, the

past exists, but not the future. &lthough some critici9e this #iew, saying that if it were true we would

ha#e no way of *nowing whether what we see as the present is the true present, others argue thatalthough there exists a past, it is lifeless and inacti#e. 7onsciousness, as well as the flow of time is not

acti#e within the past and can only occur at the boundary of the bloc* uni#erse in which the present

exists.

A-series identifies positions in time as past, present, or future, and thus assumes that the 5present5 has

some obecti#e reality, as in presentism, the static interpretation, and the growing bloc* uni#erse.

-series defines a gi#en e#ent as earlier or later than another e#ent, but does not assume an obecti#e

present, as in fourdimensionalism.

od, or some interpretations of ultimate reality in many religions and beliefs is posited as being

timeless, and seeing time from an eternalist #iew, not e#en with subecti#ely #iewed ordering e#ents,

but all at once and equally. &lthough this might seem to posit that eternalism as a whole is necessarilythe case, it can also coexist with the static interpretation of time. Where >od would then see all the

aspects of the -reel of film e#en though its being played through with an ontologically pri#ileged

-present. &lthough there ha#e also been attempts to combine this possibility with presentism or the

growing bloc* theories, those are harder to ma*e a case for, since it seems at least on the surface to be acontradiction. !'n some of those beliefs, >od0s omniscience is instead of seeing the future posited as

seeing all possible futures.$

"ote that a >od seeing the future does not inherently imply fate or determinism, !nor does any form of

eternalism in general.$ since the future can simply be seen as being made up of the free choices people

will ha#e made. +n the surface this seems counterintuiti#e to people0s perceptions, but there0s nothingthat inherently indicates that it0s not possible.



&ndurantism and perdurantism;ndurantism #ersus perdurantism relates to obects as they exist throughout time. /or instance, do

obects ha#e extension in time the same way that they do in space? +r is there an obecti#e present

which denies the need for this? +r at each specific time, is the item there a wholly separate item fromthe one it is causally lin*ed to in the future? &lthough it might seem li*e the distinction has little in

terms of practical applications outside of understanding the endurance of the mind !since indeed, somemight wonder what practical effect it has to question whether their fan tomorrow is the same one astoday$ there is still a distinction.

&ndurantism or endurance theory is a philosophical theory of persistence and identity. &ccording tothe endurantist #iew material obects are persisting threedimensional indi#iduals wholly present at

e#ery moment of their existence. 'n other words, it holds that the past and future are not necessarily

-real or connected to the present, which exists independently. (ome argue that this #iew is not wellsupported by general relati#ity, although it is by quantum mechanics.

Perdurantism is the #iew is that an indi#idual obect has distinct temporal parts throughout its

existence. 't has two subgroups.

(orm theorists belie#e that a persisting obect is composed of the #arious temporal parts that it has.

Thus, they belie#e that all persisting obects are fourdimensional 5worms5 that stretch across spacetime, and that you are mista*en in belie#ing that obects or people are simply threedimensional. "ote

that at certain points, these worms can still undergo fission or fusion, and so entities can still be

connected to others in a branching latticeli*e !or fenceli*e$ pattern, and distinctions betweenindi#idual obects are merely describing how they are -currently situated in threedimensional space.

Stage theorists or e$durantists ta*e an item or particle to be identical with a particular temporal part

at any gi#en time. (o, in a manner of spea*ing, a subect only exists for an instantaneous period of

time. %owe#er there are other temporal parts at other times which that subect is related to in a certainway such that when someone says that they were a child, or that they will be an elderly person, these

things are still -true, because they bear a special 5identityli*e5 relation to these things.

&ndurance of time

+ne of the more simple aspects of philosophy of time is simply the question of how much time there is.

There are #arious answers.

!emporal finitism is the idea that time is finite. any early people, and some philosophers still today

posited that actual infinities are not possible, and by extension there could only be a certain amount of

time. (ome others posit that although there could be infinite time o#erall, in the multi#erse, that anygi#en uni#erse could only ha#e a specific amount.

"yclical time, )scillatory universe, cyclic model, or eternal return * eternal recurrence is the idea

that there is only a certain amount of time that loops bac* on itself and endlessly repeats. &lthough onemight at first glance assume that this means that each time it repeats would play out exactly the same,

some #ersions posit that this is not necessarily the case, and that it could play out differently each time.

&lthough the fact that each time could be different seems to ma*e it confusing how this differs from aneternal uni#erse, it is postulated in order to pre#ent an actual infinity of time. (ome #ersions howe#er,

are merely eternalist outright, and use cyclical time merely to refer to some process which may

endlessly repeat. !(uch as a big crunch and big bang cycle$



&ternal universe or infinite universe is the idea that time goes to infinity in both directions.

!&lthough since the creation of the big bang theory, it has been amended and some #ersions now posit

that time had a beginning, but goes to infinity in the future. 't should be noted though that some#ersions of the big bang posit it not as a true beginning of time, but merely a beginning of time for our

purposes.$ &lthough this leads bac*wards infinitely in terms of cause and effect !in ones with an

infinite past$ it should be noted that this does not alle#iate the need for an explanation of why it existsas a whole. (ince an infinite series inside the system going bac*wards isn0t an explanation for the

system as a whole existing.

Anti-realism being the group of theories that time does not exist has some which posit that all abo#e

theories are technically incorrect, time itself being an illusion. %owe#er, the abo#e models are not

necessarily all realist per say, since they could merely be describing relations rather than a tangible-bac*ground. &s such, further forms of anti realism which deny all of them e#en as descripti#e

de#ices are rather rare, although they do exist.

Multiverses

A multiverse is is the hypothetical set of infinite or finite possible uni#erses !including the historicaluni#erse we consistently experience$ that together comprise e#erything that exists: the entirety of

space, time, matter, and energy as well as the physical laws and constants that describe them. The

#arious uni#erses within the multi#erse are sometimes called parallel uni#erses. 't should be noted that

although this is not generally brought up in the discussion, ideas of the supernatural, or at the #ery leastthe preternatural are related to how one might see the properties of other higher ordered uni#erses.

't should be noted that while we ha#e no direct obser#ation of a multi#erse, !except arguably a type 1$and that by their #ery nature they would seem to be not directly obser#able, or at least not by anything

resembling current technology, that in a #ery real sense it ma*es more sense to err on the side of their

existence than on the side of their nonexistence. This is because we ha#e no means with with to udgethe absolute scale of reality, or how wide it might be, and with an infinite amount of possible si9es,

erring on the side of assuming there are unli*ely to be multi#erses means that we are pri#ileging the

smallest possible outcome merely because it matches most closely with our na#e obser#ations. 3ut

these obser#ations ha#e no real metaphysical significance.

There are seen as being four main -types or -le#els of multi#erse.

A +evel multiverse is a multi#erse which posits the existence of other regions of space which are

beyond our cosmological hori9on, but which ha#e the same physical laws and properties. This means

that the distance between them and us is so great that for all effecti#e purposes they are not in -our

uni#erse.

A cosmological horion is a measure of the distance from which one could possibly retrie#einformation.

A level . multiverse is a multi#erse which posits the existence of other uni#erses which ha#e different

laws. &lthough some posit that they ha#e some form of direct connection with us, where the distance,either through space, or some form of other connection is so great that the physical laws are different,

some other #ersions posit that these exist but may be totally unrelated to our uni#erse whatsoe#er. This



also includes multi#erse ideas which come from string theory and theory which posit different

uni#erses as ta*ing place on different branes. !"ote that due to the seeming order inherent in the

uni#erse, it is assumed that if it was not designed deliberately, that we must li#e in at least a type 2.$

Simulated multiverse refers to a subset of type 2 where in any gi#en uni#erse where the technology

gets good enough to simulate uni#erses with strong &' in them and this is done, it will result in a new

uni#erse that for the inhabitants is as real as the one it comes from. &nd that the people in this uni#ersemay ma*e their own with strong &' in it, and that this can go down for se#eral le#els until the point

where data simply cannot be compressed any further. 't should be noted that some theorists posit that if

this was possible, the simulated uni#erses would so #astly outnumber the -real ones that they comefrom that it would ma*e it almost a guarantee that we, or any obser#er who was questioning would in

fact be in a simulated uni#erse rather than a nonsimulated one.

/ictional realism is a more abstract #ersion of a type 2 uni#erse which is the idea that because fictions

exist, fictional characters exist in some sense as well. There are fictional entities, in the same sense in

which, setting aside philosophical disputes, there are people, ondays, numbers and planets. (ome

#ersions o#erlap with theories of mind, and posit that the indi#idual -self not being as concrete as oneli*es to imagine it, when a mind interacts with a story, relating with the characters in it, that in some

sense inside of itself, parts of itself gi#e some form of abstract life to those characters who then inhabit

their own -uni#erse as a subset of someone0s mind. &lthough this idea may seem patently absurd onthe surface, it should be noted that it is based on a #ery possibly correct notion that the idea that the self

represents -one single entity rather than a rearrangeable networ* of no determinate number is more

of a construct than a necessarily e#idenced reality. "onetheless it is seen as more abstract rather thantrue in a -literal way, and is more of a thought experiment on the wor*ing of the mind than it is

commonly considered a description of anything li*e a multi#erse.

A level 0 multiverse, or the -many worlds interpretation of quantum mechanics comes from one possible interpretation of quantum mechanics. This posits that since subatomic particles in

superpositions seem to ha#e no actual physical rules guiding which position they end up in in some

circumstances, that it may be true that this is because they end up in all of them, and each superpositionsplits off into its own equally real uni#erse. This is grossly counterintuiti#e to how most people see the

world, but at the current moment there seems to be no ob#ious answer to what guides quantum

mechanics, and this is #ery much a #alid one.

1uantum immortality is one possible implication of a le#el @ multi#erse. (ince e#ery possible

outcome exists in at least one uni#erse, this means that e#en the most improbable things happen in atleast one of them. Thus, no matter how unli*ely the chance is, in at least one uni#erse you may be

immortal, simply because anything that might de#iate from this will split into another uni#erse which

does not.

A level 2 multiverse, also *nown ultimate ensemble or mathematical uni#erse hypothesis is the idea

that not only is mathematical platonism true, but that e#ery uni#erse is nothing but mathematics in a

well defined sense, and that by extension e#ery possible uni#erse actually exists. (ome posit that thisidea seems unli*ely, since if e#erything exists equally in infinite amounts, then in any gi#en uni#erse it

seems uncertain why things which are li*ely should happen any more than some which are unli*ely.

(ome posit that the nature of differently si9ed infinities accounts for this though.

Modal realism is another type of le#el A multi#erse which posits that all -possible worlds as used in

the field of logic are in fact real worlds. The distinction between this and the mathematical uni#erse



hypothesis is merely that it posits logic as the primal dri#ing force rather than math, positing one or the

other as the true primal fundamental essence.

&schatology

)hilosophy of space and time o#erlaps with theoretical physics in many areas, including ;schatology,

which is theories on what the final e#ents of history will be. !although the word can also limit history tohuman history, or be used in #arious other ways$ This is important especially in philosophy of space

and time, since it in#ol#es questions such as whether there will always be entities in some sense, orwhether reality may permanently come to an end. "ote that in beliefs in #arious forms of

supernaturalism, descriptions of uni#erses coming to a final end are not a big deal, since they posit that

people will be preser#ed in some other fashion. "ote also that some of these descriptions refer only to

single uni#erses, and thus not to reality as a whole, so any multi#erse theory inherently pro#ides other!though often not well concei#able or understood$ options, and so worries about a permanent end to

reality are often seen as ill concei#ed.

ig crunch refers to a fate of the uni#erse in which the expansion of space e#entually slows and

re#erses resulting in a singularity near identical to one which the big bang came from. The two optionsfor what happens there are either that this is the end of time, or that it results in a big bounce.

"losed universe refers to a uni#erse with space that has elliptic !cur#ed in, or spherical$ geometry.

This elliptic geometry is seen as ma*ing it li*ely for it to end in a big crunch. !Though would not

inherently pro#e one to be the case.$

ig bounce refers to a cyclical model of the uni#erse where after the big crunch this singularity being

identical to the one the big bang came from leads to another big bang. &nd that this may be what the big bang we *now of so far came from.

!he heat death or big freee of the uni#erse refers to a point in the uni#erse where all energy has become dispersed so far from eachother that meaningful interactions can no longer occur in any sense.

't should note that this can only ta*e place if the uni#erse ne#er begins contracting in space.

)pen universe refers to a uni#erse with space that is hyperbolic !cur#ed out$. This is the type of

uni#erse that it would be said is li*ely to result in heat death.

/lat universe is a uni#erse which has flat geometry that is not cur#ed in either direction, and in which

the expansion of the uni#erse would be seen as li*ely to perpetually slow down without e#er fully

reaching the asymptote of 9ero. 't is noted that the geometry of the uni#erse appears to be #ery close toflat, but it is not able to be determined which side it comes down on if either. 't is also uncertain why it

is that the uni#erse would happen to ha#e nearly flat geometry.

Steady State theory refers to the idea that the uni#erse does not expand or contract, but maintains

itself at a relati#ely identical state eternally. This theory has been more or less effecti#ely renderedobsolete by the confirmation of the big bang, but was #ery popular before then.

!he ig Rip is the idea that the matter of the uni#erse, from stars and galaxies to atoms and subatomic

particles, will be progressi#ely torn apart by the expansion of the uni#erse at a certain time in the

future. &ccording to the hypothesis, the scale factor of the uni#erse and with it all distances in theuni#erse will become infinite at a finite time in the future.



&ternal 3nflation or chaotic inflation theory is the idea that the inflationary phase of the uni#erse0s

expansion lasts fore#er in at least some regions of the uni#erse. 3ecause these regions expand

exponentially rapidly, most of the #olume of the uni#erse at any gi#en time is inflating. &ll models of

eternal inflation produce an infinite multi#erse, typically a fractal. "ote howe#er that each indi#idualuni#erse could still undergo heat death after a finite amount of time, but the multi#erse would still ha#e

infinite time o#erall.

!he bubble universe model is a subset of eternal inflation that proposes that different regions of themulti#erse decayed to a true #acuum state at different times, with decaying regions corresponding to5sub5 uni#erses not in causal contact with each other and resulting in each of them ha#ing different

physical laws in different regions which are then subect to 5selection5, which determines each region0s

components based upon !dependent on$ the sur#i#ability of the quantum components within thatregion. The end result will be a finite number of uni#erses with physical laws consistent within each

region of spacetime.

!he Steinhardt–!urok model is a cyclic model of theory in which, two parallel branes collide

periodically in a higherdimensional space. The #isible fourdimensional uni#erse lies on one of these

branes. (ince the branes themsel#es are without beginning or end, while any indi#idual #isual uni#erse

ends, usually coming out of existence entirely, new ones will always be formed in a cyclical fashion.

!he aum–/rampton model is a model in which right before a big rip a turnaround occurs and only

one causal patch is retained as our uni#erse. The generic patch contains no quar*, lepton or forcecarrierB only dar* energy C and its entropy thereby #anishes, allowing the arising of a new uni#erse.

This borrows ideas from theory, but does not depend on it.

"onformal cyclic cosmology is a general relati#ity based theory in which the uni#erse expands untilall the matter decays and is turned to light so there is nothing in the uni#erse that has any time or

distance scale associated with it. This permits it to become identical with the 3ig 3ang, being a form of

singularity, and so starting the next cycle.

+oop %uantum cosmology !67$ is a finite, symmetryreduced model of loop quantum gra#ity that

predicts a 5quantum bridge5 between contracting and expanding cosmological branches. 'n short, thisresults in the big bang being replaced by a quantum bounce which begins a new uni#erse.

!he Poincar4 recurrence theorem states that certain systems will, after a sufficiently long but finite

time, return to a state #ery close to the initial state. &pplied to the uni#erse, this is seen as a possible

future in which something a*in to a cyclical #ersion of time is achie#ed.

5acuum metastability event is a theory on a possible e#ent in the far future which comes from the

fact that 'f the #acuum is not in its lowest energy state !a false #acuum$, it could tunnel into a lower

energy state spontaneously. This has the potential to fundamentally alter our uni#erseB in moreaudacious scenarios e#en the #arious physical constants could ha#e different #alues, se#erely affecting

the foundations of matter, energy, and spacetime. &s such, we ha#e no way to predict what this couldresult in, and it could include any number of #arious beginnings of a new uni#erse.

"osmic uncertainty is an unofficial title for the reali9ation that each possibility described so far is

based on a #ery simple form for the dar* energy equation of state. 3ut as the name is meant to imply,#ery little is actually currently *nown about the real physics of the dar* energy. 'f the dar* energy

equation of state is incorrect in any fashion, which by its nature is #ery li*ely, the possibilities of what

futures there might be shift so wildly as to be beyond our current predictions.

6yson's eternal intelligence concept !the 6yson Scenario$ states that intelligent beings would be able



to thin* an infinite number of thoughts in an open uni#erse. The intelligent beings would begin by

storing a finite amount of energy. They then use half !or any fraction$ of this energy to power their

thought. When the energy gradient created by unleashing this fraction of the stored fuel was exhausted,

the beings would enter a state of 9eroenergyconsumption until the uni#erse cooled. +nce the uni#ersehad cooled sufficiently, half of the remaining half !one quarter of the original energy$ of the intelligent

beings0 fuel reser#es would once again be released, powering a brief period of thought once more. This

would continue, with smaller and smaller amounts of energy being released. &s the uni#erse cooled, thethoughts would be slower and slower, but there would still be an infinite number of them.

'f the progress of the uni#erse was right, their energy use would match its changes ma*ing this a real

possibility. "ote howe#er that these particular conditions are quite rare, so this is more of a thought

experiment than a real description of a possible future. 'ndeed, since we ha#e no way of *nowing what possible future abilities to manipulate things there may me, the existence of a single subecti#e

ci#ili9ation indefinitely may happen under means we would ha#e no current way of understanding.

)mega point theory or posthumanism posits that in the uni#erse there may be no upper limit to the

complexity of structure that is able to be arranged, and that such in the far future intelligent life may beable to go beyond the limitations of the ending uni#erse in general. (pecifically, if there is no upper

limit to complexity that things such as infinite time could e#en be simulated inside of a uni#erse with

limited time, or a big crunch could result in a singularity which has its own simulated infinite time.Theories on this are rather #ague, by necessity, since it describes things which may be possible with

technology so far beyond human technology that we don0t e#en ha#e the means to comprehend its

arrangement. 'f this complexity changes shape enough, we may not e#en be able to recogni9e it as life.

Supernaturalism most simply is the idea that something !in context, referring to somethingspecifically conscious, although the word supernatural can also refer to non conscious things.$ outside

of the rules of our uni#erse may exist that, being not limited by it, may be in direct control of some

process which can ma*e new ones, sa#e entities from inside it, or other scenarios. "ote that none of thetheories abo#e necessarily inherently contradict supernaturalism, as e#en a uni#erse with no beginning

would not erase the need for a description of why it exists. (ome, howe#er are seen as wor*ing better

in certain contexts. /or instance, in a schema where only a single uni#erse would e#er exist, it seemsli*e it would ha#e more closure for it to end in a big crunch, rather than ha#ing an open endedexistence in heat death. %owe#er, in a schema where it would allow infinite uni#erses the second issue

is no problem, especially if it leads to other uni#erses.

6imensionsDimensions refer to a single line of measurement, usually in space or time. /or instance, we li#eexperiencing three spacial dimensions and one time dimension, and intuiti#ely ha#e a hard time

grasping the existence of more than that. !although it is not too difficult to grasp less spacial

dimensions$ /or instance, mathematically we ha#e no means to pro#e any logic to the existence ofexactly three spacial dimensions. (o an important question is whether dimensions are something that

actually exist independently, and are capable of existing in any number, or whether they are a meremathematical construct of ours which we mista*e for a description of possible reality. &nd if they existindependently, are there capable of being more time dimensions, or merely space?

"ote that the terms three dimensionalism and four dimensionalism are used mainly in the context of

tal*ing about timespace, and time as a fourth dimension, and so should not be mixed up hapha9ardly

with tal*ing about other dimensional ideas. "ote that in math there are many more hypothetical typesof space, but these are ust a few basics to discuss the concept as it relates to the physical world.

Spacial dimensions refer to dimensions that extend in space. "ote that when expressing three



dimensional space, we don0t necessarily *now that these extensions exist in any particular direction, nor

are they actually meaningfully numbered. They can be expressed in any direction, so long as the

directions are at right angles from eachother.

!emporal dimensions refer to dimensions that exist in time.

&uclidean space refers to a flat space of three spacial dimensions, and can sometimes be used as asynonym for the idea that in reality the only possible space is one of exactly three spacial dimensions.

"ote that for flat !or hyperbolic$ space, the space seems to stretch on to infinity. &s such, it may imply

e#en a specific uni#erse that is infinite in si9e. !and there may be infinite of these to boot$ ;ither that,or at some point space may ha#e to arbitrarily end, although we ha#e no understanding of how or why

it would, or what it would be li*e to see the -end of space. Whether space is infinite or not is another

important question.

Minko#ski space refers to the three spacial dimensions and one time dimension ta*en together as afour dimensional timespace. 't howe#er allows for the concept of cur#ed space, since it is generally

used to describe general relati#ity which includes this.

"urved Space or Riemannian geometry refers to spaces which while they may be three dimensional,

!though not necessarily$ are themsel#es cur#ed dimensions, and so #iolate traditional intuitions about

the functioning of space. 7ur#ed spaces play an essential role in >eneral Eelati#ity where gra#ity isoften #isuali9ed as cur#ed space, and so by modern intuitions the idea that space is necessarily

;uclidean is considered unli*ely.

7yperbolic space refers to space with geometry that is cur#ed outwards.

&lliptic space refers to space with geometry that is cur#ed inwards. &s such, one could set off in onedirection and may end up where they started e#en though they were doing straight. 3eing cur#ed

inwards, !spherical$ it implies that a limited amount of space exists at any gi#en time. !at least that is

theoretically directly connected to eachother.$

Rolled up dimension refers to an extra dimension that may exist in what we consider threedimensional space by being rolled up or cur#ed in a way that ma*es it in#isible to us.

n-dimensional space refers to space of an arbitrary amount of dimensions. (ometimes used in relation

to the idea that a gi#en uni#erse is capable of ha#ing any arbitrary amount. +r alternately implying that

we don0t *now what the allowable upper limit might be.

Additional time dimensions are concepts used in some theories such as the many worlds interpretationof quantum mechanics. &n important question in philosophy of space and time is why there should be

only able to be one time dimension if there can be multiple of space. 's it simply because humans

interpret it in this way, or is it inherent in reality, or is it possible for there to be other dimensions oftime? 'f the many worlds interpretation of quantum physics is two temporal dimensions, is it possible

for there to be three or more? What form would that ta*e?

6imensions #hich are neither space nor time refer to hypothetical dimensions which may besomething other than time or space entirely, yet still exist. 6ittle thought exists in this area, since thereis #ery little way to e#en comprehend what forms such dimensions would ta*e.

Supertasks

A supertask is a countably infinite sequence of operations that occur sequentially within a finite

inter#al of time. (ome question whether they are e#en theoretically able to be done at all, and others

say that it is a partially undefined idea, and the fact that laws of physics are not fully *nown ma*e it



hard to categori9e exactly what types of things are supertas*s. They relate to philosophy of space and

time in that whether some of them are possible in any gi#en uni#erse seems to relate in some sense to

how space and time wor* in general. %owe#er, since they are often confusing as to how they would

wor* e#en in a situation we *new had infinitely di#isible time and space, some see them as more of amathematical issue. !(ince at any rate certain sets of physical laws might ma*e them e#en theoretically

impossible to occur within them e#en if others allow them.$ We0ll gi#e a few examples.

An e%uisupertask is a tas* where each step of a supertas* must be completed in the same amount of

time. (ince many rely on tas*s which change time for each tas*, this gi#es different paramaters.

A hypertask is when the number of operations in a supertas* becomes uncountably infinite.

8eno's parado$es are a set of paradoxes that were formulated in gree* times, possibly by the philosopher Feno, which mostly focused on purporting to show that motion was an illusion. &lthough

there were an indeterminate number, mainly three are focused on. They are seen as the earliest time that

the concept of supertas*s was addressed.

Achilles and the tortoise refers to a thought experiment where a tortoise and &chilles are in a race.

The tortoise being slower is gi#e an 1GG meter head start. The tortoise howe#er can only mo#e half as

fast as him. (o by the time &chilles gets to 1GG meters, the tortoise will be at 1HG. 3y the time &chillesmo#es another HG, the tortoise will ha#e mo#ed another 2H. &nd so on and on. +n the surface, this

seemed to propose that each time they mo#e all they are doing is merely hal#ing the distance, and thus

an infinite number of tas*s would ha#e to be completed before &chilles gets out ahead. &nd so this being seen as impossible was posited as showing that motion as we understand it could not exist.

!he 6ichotomy parado$ is a more simple #ersion of the abo#e paradox. 't stated that any obect in

motion before getting to its goal must get half way. &nd before it gets there must get half way to halfway. &nd so on and on an infinite number of times.

The solutions to these paradoxes seem to rest on the assumption that time and space must then beinfinitely di#isible. 'f so, then infinitely small mo#ements would correspond to infinitely small times.

3ut at a rate which allows real mo#ement. &nd thus there is nothing inherently impossible incompleting this type of supertas*. There are more formal proofs which in#ol#e calculus, but many note

that pure math alone may not be enough to indicate possibility in the real world. &nd so there is

disagreement about whether it is a mathematical issue or also a metaphysical one. (ome also posit thatthe paradox arises from considering space and time as separate entities, and when considered as

spacetime it ceases to exist.

!he arro# parado$ is that if e#erything when it occupies a specific space is at rest, and if that which

is in locomotion is always occupying such a space at any moment, that a flying arrow is thereforemotionless. %owe#er, this is mainly answered with the argument that 'nstants are not parts of the flow

of time, as time is not made up of instants any more than a magnitude is made of points. %ence it doesnot follow that a thing is not in motion in a gi#en time, ust because it is not !arguably$ in motion in anyinstant of that time. &nd that what appears to be a paradox is merely begging the question by

implicating that obects that occupy the same space as they do at rest must be at rest.

!hompson's lamp is an attempt to show that a specific supertas* is impossible, which it purports

shows indirectly that all of them are. 'f you ha#e a lightswitch which can only either be on or off, and it

is one minute to midnight. &nd each time half of the time between now and midnight arri#es you

switch it, then what would its final state be? 'f you turn it on at @G seconds to midnight, then off at 1H,



then on at I.H, bac* and forth, it seems to arri#e at a contradiction by ha#ing neither step be a #alid

final stage. !Thompson belie#ed thus that regular motion itself was not a supertas*.$

"onetheless this is not seen as pro#ing that supertas*s are inherently impossible, and as a whole forsupertas*s, the contradictions that they supposedly gi#e rise to may be a#oided if one reects certain

unwarranted assumptions that are usually made. The main such assumption, responsible for the

apparent conceptual impossibility of supertas*s, is that properties which are preser#ed after a finitenumber of actions or operations will li*ewise be preser#ed after an infinite number of them. !Which

again is something shown as not necessarily correct by calculus.$ any supertas* thought experiments

ta*e a form similar to thompson0s lamp by being based on sequences which get or begin infinitelysmall.

Ross–+ittle#ood parado$ is another paradox regarding supertas*s9 suppose there is a ar capable ofcontaining infinitely many marbles. &t each time half of the amount of time between now and a minute

passes !@G sec, AH sec, H2.H sec, etc$ marbles are put in in order. /irst, marbles numbers 11G are put in

and 1 is ta*en out. Then next 112G are put in and J2 is ta*en out. +n and on through an infinite

number of steps. +ne argument states that there should be infinitely many marbles in the ar at the end, because at each step before the end of the minute the number of marbles increases from the pre#ious

step and does so unboundedly. & second argument, howe#er, shows that the ar is empty. 3ecause if the

ar is nonempty, then there must be a marble in the ar. 4et after infinite steps e#ery single numberedmarble has been ta*en out.

The Eoss6ittlewood paradox is that here we ha#e two seemingly perfectly good arguments withcompletely opposite conclusions. +ne ob#ious solution, then, is to simply say that supertas*s are

impossible. 'f supertas*s are impossible, then the #ery assumption that all of these scenarios had some

*ind of 0end result0 to them is mista*en, and thus there being no paradox.

enardete:s parado$ is another. & man wal*s a mile from a beginning point. 3ut there is an infinity of

gods, each of whom un*nown to the others intends to obstruct him. +ne of them will raise a barrier tostop his further ad#ance if he reaches the halfmile point, a second if he reaches the quartermile point,a third if he goes oneeighth of a mile, and so on ad infinitum. (o he cannot e#en get started, because

howe#er short a distance he tra#els he will already ha#e been stopped by a barrier. 3ut in that case no

barrier will rise, so that there is nothing to stop him setting off. %e has been forced to stay where he is by the mere unfulfilled intentions of the gods.

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Metaphysics Study Guide - Space and Time