Goddu_Time Travel and Changing the Past

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TIME TRAVEL AND CHANGING THE PAST:

(OR HOW TO KILL YOURSELF ANDLIVE TO TELL THE TALE)

G.C. Goddu

AbstractAccording to the prevailing sentiment, changing the past is logi-

cally impossible. The prevailing sentiment is wrong. In this paper, Iargue that the claim that changing the past entails a contradictionultimately rests upon an empirical assumption, and so the conclu-sion that changing the past is logically impossible is to be resisted. Ithen present and discuss a model of time which drops the empiri-cal assumption and coherently models changing the past. Finally, Idefend the model, and changing the past, against objections.

Oh, if you could but travel back in time, just think what you coulddo. You could provide advance warning and prevent the assassi-nation of Abraham Lincoln or the bombing of Pearl Harbor. Youcould prevent Caligula or Hitler or Pol Pot from ever being born.

You could bring back a cure for the Black Death and prevent thedecimation of Europe. You could play the stock market andbecome richer than Bill Gates. You could . . . .

According to almost all philosophers writing about time travel,however, these speculations about potential time travel exploitsare woefully misguided, for while time travel itself is logicallypossible, changing the past is not. For example, in Tips for TimeTravellers, Monte Cook provides the following advice for prospec-tive time travellers: Dont worry about changing the past. Youcant.1 John Hospers writes, Not all the kings horses or all thekings men could make what has happened not have happened,

for this is a logical impossibility.2

Gilbert Fulmer argues that theidea of changing the past is logically incoherent, and, therefore,the act logically impossible.3 According to Geoffrey Brown, not

1 Monte Cook, Tips for Time Travellers, in Philosophers Look At Science Fiction, ed.Nicholas Smith, (Chicago: Nelson-Hall, 1982), p. 49.

2 John Hospers, An Introduction to Philosophical Analysis, 2nd ed. (Englewood Cliffs, NJ:Prentice Hall, 1967), p. 177.

3 Gilbert Fulmer, Cosmological Implications of Time Travel, in The Intersection ofScience Fiction and Philosophy, ed. R.E. Meyers (Westport: Greenwood Press, 1983), p. 33.

Blackwell Publishing Ltd. 2003, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350Main Street, Malden, MA 02148, USA.Ratio (new series) XVI 1 March 2003 00340006


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even God has the ability to alter the past (which is admittedlysenseless).4 Numerous other authors also maintain the logicalimpossibility of changing the past.5 Hence, according to the

prevailing sentiment, while traveling to the past is perfectly coher-ent, changing it is not. You just could not prevent the bombing ofPearl Harbor or the birth of Hitler, even if you could travel backin time.

In this paper, I shall argue that the prevailing sentiment iswrong. Not only is time travel logically possible, but so is chang-ing the past. In section I, I shall argue that the claim that chang-ing the past entails a contradiction ultimately rests upon an

empirical assumption, and so the conclusion that changing thepast is logically impossible is to be resisted. In section II, I shallpresent my own model of time travel and argue that it coherentlymodels changing the past. In section III, I shall defend the modelagainst objections. Finally, I shall conclude, contra the prevailingview, that changing the past is logically possible.

I. Changing the past

What exactly is involved in changing the past? One might say thatthe past is all that has come before now. Hence, tomorrow thepast will be different. All that comes before tomorrow includesmore than all that comes before today. Hence, the past haschanged. What the past was today differs from what the past willbe tomorrow, or even one second from now. This sense of chang-ing the past is not at issue. At issue, rather is, can the past be

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Blackwell Publishing Ltd. 2003

4 Geoffrey Brown, Praying About the Past, Philosophical Quarterly35 (1985), p. 85.5 For example, see Bob Brier, Magicians, Alarm Clocks, and Backward Causation,

Southern Journal of Philosophy 11 (1973), p. 361; William Lane Craig, Tachyons, Time Traveland Divine Omniscience,Journal of Philosophy85 (1988), p. 147; Larry Dwyer, Time Traveland Changing the Past, Philosophical Studies27 (1975), p. 347; John Earman, Implicationsof Causal Propagation Outside the Null Cone, Australasian Journal of Philosophy50 (1972),p. 232; Antony Flew, Can A Cause Precede Its Effect?, Aristotelian Society SupplementaryVolume28 (1954), p. 48; Samuel Gorovitz, Leaving the Past Alone, Philosophical Review73(1964), p. 367; Richard Hanley, The Metaphysics of Star Trek(New York: Basic Books, 1997),

p. 205; Jonathan Harrison, Dr. Who and the Philosophers or Time Travel for Beginners,Aristotelian Society Supplementary Volume45 (1971), p. 7; Paul Horwich, On Some AllegedParadoxes of Time Travel,Journal of Philosophy72 (1975), pp. 43536; Murray MacBeath,Who Was Dr Whos Father?, Synthese51 (1982), p. 423; Paul J. Nahin, Time Machines,(New York: AIP, 1993), p. 181, p. 209; Larry Niven, The Theory and Practice of TimeTravel in All the Myriad Ways(Ballantine Books, 1971), p. 113, p. 121; Hilary Putnam, It

Aint Necessarily So,Journal of Philosophy59 (1962), p. 669; J.J.C. Smart, Is Time TravelPossible?,Journal of Philosophy60 (1963), p. 241; R. Swinburne, Space and Time(Macmillan& Co., 1968), p. 161.


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undone? Can some part or event of the past be made not to be apart or event of the past? Consider, for example, the followingtime travel scenarios:

Scenario 1: Paul, at the age of thirty, departs from February 12,1998, for the past and arrives on January 28, 1972. On this trip,in a fit of self-nihilism, he finds and kills his three-year-old self,after which he returns to 1998.

Scenario 2: Sarah has just completed building her timemachine. She decides to test the machine on herself tomorrowmorning at which time she intends to travel back one day. In

the meantime, she goes home, puts some salve on the burn shereceived that day, and goes to bed. In the morning, Sarah, withcoffee in hand, sits down to read the morning paper. She opensthe paper to the following headline: Famous physicist founddead. On the front page is a picture of her body, salved burnclearly visible on her arm, inside her pristine time machine.Underneath is the caption: Nobel-prize winning physicistfound dead yesterday in mysterious device that materializednear city hall. Extremely shaken, Sarah returns to the lab anddestroys the machine.

Are these scenarios logically coherent? Can the thirty-year-oldPaul, for example, make it such that he does not survive past theage of three? Can Sarah make it such that she does not appeardead in her time machine the previous day? The standard answerto these questions is no? But why?

According to R. Swinburne, To change something is to makeit different from what it was at another temporal instant. I cannotmake a thing at t1 different from what it is, was, or will be at t1 for this would imply that it both did and did not have some prop-erty at t1.

6 For example, assume that thirty-year-old Paul was neverkilled and resurrected. Paul cannot, therefore, at some time, say1998, change any instant of 1972 and make it such that thirty-year-old Paul kills his three-year-old self. To do so would make someinstant of 1972 such that Paul is both killed and not killed duringthat instant and make it the case that Paul both survives past theage of three and does not survive past the age of three. Similarly,since Sarah dies yesterday in her time machine, she cannot nowprevent herself from getting into her time machine and make it

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6 Swinburne, p. 161. See also, Dwyer, p. 348; Harrison, pp. 23; Horwich, p. 435;Hospers, p. 177; and Smart, p. 241.


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the case that she does not die yesterday, for then some instant ofyesterday would be such that both Sarah appears in her timemachine during that instant and Sarah does not appear in her

time machine during that instant. According to Swinburne,therefore, changing the past makes it the case that things simul-taneously have contradictory properties, which is logically impos-sible, and so changing the past must be logically impossible.

But consider again Swinburnes claim that to change some-thing is to make it different from what it was at another temporalinstant. According to Swinburnes claim, Paul changes if Paul isone way at one temporal instant and another way at a different

temporal instant. For example, Paul, at some temporal instant in1970 is under three feet tall. At some temporal instant in 1998,Paul is over five feet tall. Hence, Paul has changed from beingunder three feet tall at one temporal instant to being over fivefeet tall at another. But what is it for some instant of 1972, call iti1, to change? Presumably, at one temporal instant i1was one way,for example with Paul not killed, but at another temporal instanti1 was different, with Paul killed. But is the result of applying

Swinburnes claim to i1 a contradiction?To begin to see how to answer, consider David Lewis statementof why one cannot change the past. According to Lewis, Ifchange is qualitative difference between temporal parts of some-thing, then what doesnt have temporal parts cant change. Forinstance, numbers cant change; nor can the events of anymoment of time, since they cannot be divided into dissimilartemporal parts.7Why then can one make sense of Paul changing,

but apparently not the events of particular instants of 1972 chang-ing? Because instants or the events of particular instants are notthe sort of thing that have temporal parts in the same way thatPaul has temporal parts. Paul exists at many times, eg. the first dayof 1978, the first day of 1988, and the first day 1998. On the otherhand, neither i1 nor the events of i1 exist at many times. Neitheri1 nor the events of i1 exist during 2000 B.C.E or January 1, 1998,or any other instant. If i1 can be properly said to exist at a time at

all, then i1 exists at i1.But is the claim that the events of a temporal instant do not

themselves have temporal parts a logical truth? Isnt it possible,even physically, that the events of a particular temporal instant



7 David Lewis, The Paradoxes of Time Travel, in Philosophical Papers, vol II. (New York:Oxford University Press, 1986), p. 69.


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might have some kind of temporal part? Might not the best expla-nation of the nature of our universe ultimately involve two (ormore) temporal dimensions? Lewis himself explicitly restricts his

claim about the impossibility of changing temporal instants touniverses with a single temporal dimension and acknowledgesthat time could be two-dimensional and that an event might bemomentary along one time dimension but divisible along theother.8 Presumably the exact nature of the universe and time is amatter for empirical science to discover and so the claim that theevents of temporal instants do not have temporal parts is anempirical truth, not a logical one. Hence, the claim, At one time,

the temporal instant i1was one way, but at another time was differ-ent is meaningless or contradictory only given the empiricalassumption that temporal instants themselves lack temporalparts. Since Swinburne and others are claiming that changing thepast is logically impossible, empirical assumptions about thenature of time will not necessarily support their claim.

Drop then the assumption that temporal instants or events oftemporal instants do not themselves have temporal parts andsuppose for the moment that temporal instants do have temporalparts. Call the temporal parts of temporal instants hypertimes.Swinburnes claim should, in the case of events of particulartemporal moments, be rephrased as To change events of partic-ular temporal moments is to make them different from what they

were at another hypertemporalinstant. Suppose, therefore, that i1at hypertemporal instant h1, is such that Paul is not killed, but

that at some later hypertemporal instant, say h2000, Paul is killedduring i1. i1 has therefore changed from having Paul survive tohaving Paul not survive. At one hypertime, i1was such that Paul

was not killed, but at a later hypertime i1 is such that Paul is killed.Thus, even though at a particular instant, viz. i1, Paul is bothkilled and not killed, Swinburne is wrong to claim that a contra-diction results. A contradiction results only if one assumes thattemporal instants themselves do not have temporal parts.

Otherwise, i1 is one way at one hypertime and a different way atanother, just as Paul is under three feet tall at one time and overthree feet tall at another. Neither change entails a contradiction.

To reiterate: Introducing the, admittedly abstract, notion ofhypertimes allows one to make sense of the statement At onetime, the temporal instant i1was one way, but at another time was

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8 Lewis, p. 69.


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different. At one hypertemporal instant, the temporal instant i1was one way, but at another hypertemporal instant was different.Given that changing temporal instants does not entail that tempo-

ral instants or the events of temporal instants have contradictoryproperties at one and the same hypertemporal instant, changingtemporal instants or the events of temporal instants does notentail a contradiction. Hence, the standard claim that changingthe past is logicallyimpossible is to be resisted, since the basis forit is an empiricalassumption about the nature of time, viz. thattemporal instants do not themselves have temporal parts.

II. A consistent model of changing the past

Is there a way of coherently modeling a universe in which the pastchanges? I think there is. Consider first a standard video cassetterecorder and monitor set up. The VCR has a clock that displaysnormal, everyday time call this time clock-time. The monitor,on the other hand, displays how much time has elapsed on thevideo cassette being viewed call this time cassette-time. When

a cassette is played forward at normal speed, clock-time andcassette-time are synchronous, i.e. for every second of cassette-time that passes one second of clock-time passes. When a cassetteis rewound (or advanced), however, cassette-time decreases (orincreases) much more rapidly than clock-time. For example,suppose the clock reads 16:00:00 and the monitor, 0:00:00. Nowlet a cassette play the first twenty minutes of the Star Trekepisode,City on the Edge of Forever. At the end of twenty minutes the

clock reads 16:20:00 and the monitor displays 00:20:00. Now letthe cassette be rewound for fifteen (clock-time) seconds until themonitor display reads 0:05:00. The clock now reads 16:20:15. Nowlet the cassette record twenty minutes of the episode, YesterdaysEnterprise. When the cassette stops after twenty minutes theclock reads 16:40:15 and the display reads 0:25:00. The intervalbetween 0:05:00 and 0:20:00 has occurred twice, though at differ-ent clock-times. The images and sounds on the cassette during

that interval are now different from what they once were. Before16:20:15 the cassette-time interval between 0:05:00 and 0:20:00contained parts of The City on the Edge of Forever, but by16:35:15 that same temporal interval contains parts of YesterdaysEnterprise. The content of the cassette has been changed.

The VCR and monitor set up provides one conceptual basis forunderstanding time travel in a universe in which temporal




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moments have hypertemporal parts. Consider then a hypotheticaluniverse that has two temporal dimensions related much likeclock-time and cassette-time are related. Let the images and

sounds on the cassette over a particular interval be analogues ofthe events of the world over a particular interval. Since the inter-vals on the cassette are measured in cassette-time, cassette-timewill be an analogue of the time we live in; call this normal time.Clock-time is then an analogue of hypertime. If all proceedsnormally, i.e. no travelling in normal time occurs, then there willbe a one-to-one correspondence between hypertime and normaltime. January 1, 1978 in normal time will correspond to January

1, 1978 in hypertime. There will be no duplication of normal timepoints or intervals. Travelling backward in normal time will be ananalogue of rewinding the cassette. (Instantaneous travel wouldbe like a jump back on the tape.) If time travel into the pastoccurs, then the one-to-one correlation between hypertime andnormal time will fail to hold. Some points of normal time willcorrelate with two or more distinct points of hypertime. Just as, inthe case above, 0:10:00 of cassette-time corresponds with both16:10:00 and 16:25:15 of clock-time, so might January 1, 1978 ofnormal time correspond with both January 1, 1978 and January1, 2078 of hypertime. Finally, changing the events of previoustimes, i.e. changing the past, will be an analogue of recording newimages and sounds on the cassette.

Consider Paul from Scenario 1. On February 12, 1998 hedeparts for the past. Assume his trip takes one instant of hyper-

time. Paul arrives one hypertime instant later at normal timeJanuary 28, 1972. On this trip, he finds and kills his three-year-oldself, after which he returns to 1998. The following rough diagramcan be used to help explain Pauls travels in terms of normal timeand hypertime.

Hypertime: T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14T15 T16 T17 T18Normal time: t1 t2 t3 t4 t5 t6 t7 t8 t9 t3 t4 t5 t6 t7 t8 t9 t10 t11Universe State: e1 e2 e3 e4 e5 e6 e7 e8 e9 e3 e4 e5 e6 e7 e8 e9 e10 e11

Let t1 be February 12, 1968, t3 be the afternoon of January 28,1972, and t9 be February 12, 1998. Part of e1 includes Paulsbirth. e2e9 includes Pauls life until February 12, 1998; Paulgrows up, acquires his time machine and on February 12, 1998(T9) he departs. One instant rewind later he arrives at January28, 1972 (t3 at T10). His mere arrival changes the past. Before,the state of the universe associated with t3, viz. e3, included the

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presence of only one Paul. Now that state has changed andbecome e3 and includes the presence of two Pauls; a young oneand an older one who mysteriously appeared out of thin air. And

so the re-recording continues. At t4(T11) Paul kills the youngerversion of himself and returns to the future. Paul arrives att10(T17) and continues on with his life. E4 includes themurder/suicide of the three-year-old Paul and the subsequentdeparture of the thirty-year-old Paul. E5 perhaps includes thefutile search for the murderer and so on up to e10which includesthe appearance out of thin air of the thirty-year-old Paul.

Paul has changed the past from being one way, his younger self

living, to being another, his younger self not living. The fact thatsome of the es are italicized just means that those events have beenchanged and are no longer accessible (just as the recorded overvideo images are no longer accessible). They are not a part of theway the normal time world is, though there was a hypertime atwhich they were. A normal time historian at t11(T18) woulddescribe the order of events as, e1 e2 e3 e4 e5 etc, while a hyper-time historian, if there could be such a being, would describe events

as e1 e2, the way the interval t3t9 used to be, i.e. e3e9, the way t3t9is now, i.e. e3e9, e10, e11. Hence, a hypertime historian would beable to explain the origin of time travellers and the origin of thetime travellers memories while a normal time historian would not.

One significant divergence between the time travel case and theVCR set up requires mention. When one is done recording on anormal VCR one leaves all images and sound after the period ofre-recording untouched. Hence, a cassette could have five minutes

of one program, five minutes of another and then a sudden cutback to the first program. Pauls time travels, however, leave noth-ing after his arrival in the past, the moment re-recording starts,untouched. The reason for the divergence is that images andsounds on different parts of the tape are not causally related toeach other, but rather to the source of the recording. Events, onthe other hand, are causally related to each other through time.For example, the events of e4, the death of Paul, cause the inves-

tigation of e5, etc. Thus, Pauls brief appearance in the past sets inmotion a complete re-recording of everything he knew, e3e9.When Paul arrives back at t10 in the future he will have to live withthe consequences of the changes he has wrought.9



9 As a result of a choice concerning ease of diagramming, time travel into the future,given the current model, is not analogous to fast forwarding the tape in a less significant


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What of Sarah and her time machine? Sarah, when she exam-ines the paper, has not yet travelled in time, so the normal timeand hypertime lines should match perfectly. But if Sarah does not

get into her machine she changes the past even without time trav-elling, since she fails to appear in the past. How then will thecurrent model account for Sarah? The problem is easily resolvedonce one realizes which part of the normal time-line the Sarahstory actually describes. The Sarah story describes events happen-ing duringa re-recording. Consider again our diagram:

Hypertime: T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18Normal time: t1 t2 t3 t4 t5 t6 t7 t8 t9 t3 t4 t5 t6 t7 t8 t9 t10 t11Universe State: e1 e2 e3 e4 e5 e6 e7 e8 e9 e3 e4 e5 e6 e7 e8 e9 e10 e11

At t3(T3) Sarah does not appear dead in her machine in themiddle of town. Thus, the next morning [t6(T6)] when she readsthe paper, there is no front page story detailing such an eventbecause it did not happen. The same afternoon [t9/T9] Sarahtravels back in normal time to t3, somehow dying in the process.This event occurs at T10 in hypertime. The events of t3 have nowchanged because these events now, T10, include the arrival ofdead Sarah out of thin air, whereas previously, T3, they did not.Thus, at t6(T13) Sarah reads the paper and discovers to herhorror that if she gets into the machine she will die. Thus, att9(T16) Sarah, paradox free, destroys her time machine. No para-dox results because, hypertemporally at least, Sarah has alreadygotten into her machine and the consequences of that action tip

Sarah off not to get into her time machine at the later hypertime.Are Sarahs and Pauls escapades truly examples of changingthe past? Granted, neither Sarah nor Paul travel backwards inhypertime and hence never alter the hypertemporal past. ButSarah and Paul are perceivers of normal time and the only pastthey, or anyone else they interact with, care about is the normal-time past. All our history books are descriptions of the normal-time past. Therefore, given that before Pauls journey back to kill

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manner as well. Time travel into the future involves a jump in both hypertime and normaltime. One can avoid jumps in hypertime by one of at least two methods. Firstly, time travelinto the future, unlike the past, could be by standard relativistic methods. That is, in orderto get back to the future one does not just push the button and voila!, but rather themachine accelerates away from Earth at some significant fraction of light speed and thenreturns. Secondly, one could suppose that travel to the future, like travel to the past,requires at least one instant of hypertime, but during that instant all the interveningnormal time is played out. Hence, T12 might correspond to the entire period t5-t9. Othermethods, and hence other models, are most likely possible.


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his younger self the true description of the normal-time pastincluded Paul surviving past the age of three, but that after hissuccessful journey the true description of the normal-time past

does not, we must conclude that Paul can and does change thepast. Given that before Sarahs time travel the true description ofthe normal- time past did not include her appearing dead, but thatafter her travel it does, we must conclude that Sarah can and doeschange the past. Hence, changing the past is logically possible.

III. Objections and replies

Objection I: Two-dimensional time or the temporal slices ofobjects recurring just seems unimaginable. So how can any modelinvolving the recurrence of temporal instants or slices of objectsbe coherent?

Reply: Imagining two-dimensional time or imagining temporalslices enduring or recurring is admittedly difficult. So is imagin-ing a hypercube or imagining two straight lines in the same planethat are not a constant distance apart and yet never intersect.

Regardless, hypercubes are straightforward four-dimensionalobjects which can be described as follows: take a three-dimen-sional cube with edges of length one; project this cube one unitalong the spatial dimension at right angles to the normal three;connect the corresponding vertices of the original and projectedcubes; the result is a hypercube. Pre-Lobachevski, two straightlines in the same plane never intersecting and yet not a constantdistance apart, was thought absurd, unimaginable, impossible,

etc. Yet, even if difficult to truly imagine, such lines are a perfectlycoherent part of hyperbolic plane geometry. Similarly, whileimagining temporal slices of objects enduring or recurring isdifficult, there are perfectly coherent descriptions of theendurance or recurrence of temporal slices. For example, thingsendure or recur by existing at more than one time and sincetemporal slices of objects are momentary in normal time, for suchslices to endure or recur involves existing at more than one

moment of some kind of time other than normal time. On mymodel, for example, if time travel occurs, temporal slices ofobjects recur at later hypertimes.10



10 For other examples of descriptions of multi-dimensional time see, C.T.K. Chari, ANote on Multi-Dimensional Time, British Journal for the Philosophy of Science8, (1957): pp.155158; and T.E. Wilkerson, Time and Time Again, Philosophy48, (1973): pp. 173177.


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Objection II: Whatever the ts are in the model they are nottimes. The only real times are the hypertimes. Since the hyper-temporal past never changes, if the hypertemporal moments are

the only real temporal moments, then the model does not modelchanging the past.Reply: Why might one think that the hypertimes are the only

real times? Because one might think that e1 causes e2 and e2causes e3 and so on and when Paul pushes the button on his timemachine at e9 he causes the next state to be e3 and e3 causes e4and so on. If one holds that the ordering of causation determinesthe order of time, then one might think the universe being

described by my model is better represented and described asfollows:

Hypertime: T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18Universe State: e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 e16 e17 e18

Paul pushes the button on his time machine at T9. The result,however, is not time travel to 1972, i.e. T3, but rather a drastic,though instantaneous, change in the universe the universebecomes a duplicate of the state of the universe in 1972, with theexception that Paul and his time machine are present. (Thisduplicate is e10, for it is not a changed version of e3, but rather acompletely new state of the universe qualitatively very similar toe3). In other words, Pauls button pressing does not cause him totravel in time, but rather it causes the universe to become such

that at the very next instant, T10, the universe is almost in thesame state as it was in 1972.The world just described is a logically possible world.

Regardless, this world is notthe world my model is describing, forboth the causal and the temporal relations differ significantly. Inthe world of my model temporal slices of objects can becomehypertemporally extended. How so? By the activation of timemachines. When Paul pushes the button on his time machine at

T9 what happens is that (i) the temporal slice at t3 becomeshypertemporally extended and (ii) Paul and his time machineappear in the hypertemporal extension of the slice. The eventsof t2, viz. e2, are still the cause of (most of) the events of t3, butbecause the events of t3 are now(T10) also caused by e9, theevents of t3 at T10 are e10. Finally, because the events of t3 arehypertemporally extended, the events of each time up to Paulsoriginal departure become, in turn, hypertemporally extended.

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The universe-change world is not the world described by mymodel.11

Objection III: Of planar two-dimensional models of time, Lewis

writes:On closer inspection, however, this account seems not to giveus time travel as we know it from the stories. When the travellerrevisits the days of his childhood, will his playmates be there tomeet him? No; he has not reached the part of the plane of timewhere they are. He is no longer separated from them along oneof the two dimensions of time, but he is still separated fromthem along the other.12

Doesnt Lewis objection also apply to the new model? After all,the temporal part of the three-year-old Paul that leads to the timetraveller is the one in e4at t4(T4), but the temporal part that iskilled is the one in e4 at t4(T11). Hence, one might argue thatwe have yet to reach the relevant temporal part of the youngerPaul.

Reply: I cannot deny that different hypertemporal parts of

three-year-old Paul are involved in (i) Paul living past the age ofthree and (ii) dying at the age of three. After all, different hyper-temporal parts are necessary to avoid contradiction. Regardless, Iam not persuaded that Paul fails to reach the relevant part forthree reasons. Firstly, e4 is a hypertemporal extension of e4, justas thirty-year-old Paul is a temporal extension of three-year-oldPaul. Put another way, e4 is the way e4 is now (hypertemporally)just as thirty-year-old Paul is the way three-year-old Paul is now

(temporally). Secondly, e2, the state of the universe in which Paulturns three, is an immediate causal antecedent of both e3 and e3 and so a causal antecendent of both e4and e4. For e3, e2 is thesole immediate causal antecedent. e3, on the other hand has twoimmediate causal antecedents e2 and e9. Either way e2 is



11 The universe-change world, and other similar worlds, may raise epistemological prob-lems for any would-be time traveller. For example, how could Paul know whether he wasin a world in which he actually travelled in time or one in which the rest of the universe

changed? Note that the epistemological problem is not restricted merely to alleged casesof changing the past. For almost all purported time travel stories, regardless of whether ornot the story advocates changing the past, one could describe a universe in which there isno time travel at all, but merely a radical change in certain successive states of the universe.For a discussion of the problem of scepticism as it relates to time travellers, see Roy A.Sorenson, Time Travel, Parahistory, and Hume, Philosophy62 (1987): pp. 227236.

12 Lewis, p. 68. For an example of the sort of model Lewis is discussing, see JackMeiland, A Two Dimensional Passage Model of Time for Time Travel, PhilosophicalStudies26, (1974): pp. 153173.


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common to both and it is partly the fact that the state of theuniverse that Paul reaches, e4, is caused by e2, the state of theuniverse in which the one and only Paul turns three, which makes

it the relevant part of the universe. Thirdly, Paul has to live withthe consequences of all his actions. When Paul kills his youngerself, the future to which Paul returns will be one in which henever went to school or paid taxes or built a time machine.Hence, Paul has reached a relevant part of the past because e4 isthe hyptertemporal extension of e4 and e4 has both the rightcausal antecedents and the relevant causal consequences.

Objection IV: Consider a standard branching model, such as:

Time: t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 e16 e17

Universe State: e1 e2e31 e41 e51 e61 e71e81 e91 e101 e111 e121 e131 e141 e151 e161 e171

At t3, the afternoon of January 28, 1972, the universe branches.On the top branch no time traveller Paul appears and Paulsurvives past the age of three to build his time machine. At t9 onthe upper branch Paul departs for the past and arrives at e31 onthe bottom branch. At t4 Paul kills the younger version of himselfon the bottom branch and returns to the future, again on thebottom branch. Paul arrives at t10 and continues on with his life.e31 includes the murder/suicide of the three-year-old Paul andthe subsequent departure of the thirty-year-old Paul. e41 perhapsincludes the futile search for the murderer and so on up to e101

which includes the appearance out of thin air of the thirty-year-

old Paul. On this model the past never changes Paul merelymakes the bottom branch the way it always will be. At no time dothe events of t3 change the events of t3 are e3 and e31 and thoseevents remain unchanged.

So, the objection goes, (i) the scenarios can be accounted foron standard branching universe models13 and (ii) your model isonly a complicated branching universe model and the past doesnot change in branching universe models.14 Hence, your model

does not show that changing the past is logically possible.Reply: First, the fact that the scenarios can be accounted for or

shown consistent on a branching universe model is irrelevant tothe project at hand. The project is to produce one consistent

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13 See for example, Paul Sukys, Lifting the Scientific Veil, (New York: Rowman &Littlefield, 1999), p. 238.

14 Lewis, p. 80.


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model that both (a) accounts for all the events in the scenariosconsistently and (b) allows the past to change. The fact that thereare models that do (a), but not (b) is irrelevant.

Second, I deny at least one of the conjuncts of (ii). In otherwords, either my model is notjust a complicated branching modelor changing the past is possible on some (though clearly not all)branching models.

I take it that my model is complicated because it, unlike thestandard model presented above, (a) appeals to hypertimes and(b) has branches that terminate. So the objector might claim thatmy model is just the following branching model:

Time: t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16 t17e3 e4 e5 e6 e7 e8 e9

Universe State: e1 e2e31 e41 e51 e61 e71 e81 e91 e101 e111 e121 e131 e141 e151 e161 e171

Hypertemporal references have been suppressed, but eventse1e9 occur at hypertimes T1T9 respectively and eventse31e171 occur at hypertimes, T10T24 respectively. On thismodel e3 occurs at T3 and e31 at T10 even though both occur at

normal time t3. In addition, Pauls departure from e9 terminatesthe one branch and his arrival at e31 at hypertime T10 startsanother branch.

Is the complicated branching model my model? The answerhinges on whether e31 is a hypertemporal extension of e3. If thebranching on the complicated model is like the branching on thestandard model, then e31 is not a hypertemporal extension of e3.On the standard model e3 and e31 are not related as thirty-year-

old Paul and three-year-old Paul are related, but more like twoamoebas which result from the fission of one. On my model e3and e3 are hypertemporal parts of one event slice, the event sliceof t3, just as thirty-year-old Paul and three-year-old Paul aretemporal parts of one object, Paul. Hence, if e3 and e3 are notrelated in a manner similar to the manner in which thirty-year-oldand three-year-old Paul are related, then the complicated branch-ing model is not my model.

Suppose e31 is a hypertemporal extension of e3. In otherwords, not only do the hypertimes mark when the universebranches, but the universes branching just is e3 becoming hyper-temporally extended as e31. But then, regardless of whether themodel is my model or not, on the complicated branching modelthe past changes. At one time, T3, the events of t3 were one way,viz. e3, and at another, T10, the events of t3 are different, viz. e31.




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More generally, terminated branches just are the ways the pastused to be, and the unterminated branch is the way the past isnow.

Either my model is the complicated branching model or itisnt. If it isnt, then the complicated branching model is irrele-vant to the question of whether or not my model demonstratesthe logical possibility of changing the past. If it is, then there arebranching models, viz. the complicated one, on which the pastchanges.

Objection V: If Pauls surviving past the age of three is part ofthe universe, as it surely must be if Paul is to build his time

machine and travel in time, how can one say that the past hasbeen changed. If Pauls surviving past the age of three is alwayspart of the universe, isnt it always part of the past?

Reply: To change something, the thing must first beone way.For Paul to change from being under four feet tall to being overfour feet tall, he must first be under four feet tall. If one consid-ers the entire universe, i.e. the universe in all its spatial expansefrom the beginning of time to the end of time, part of thatuniverse will contain Paul being under four feet tall, while a laterpart will contain Paul being over four feet tall. Likewise, for thepast to change it must first be one way and then later another. Forexample, to change the events of t4 those events must first be one

way, in Pauls case e4at T4, and then later some other way, e4 atT11. If one considers the entire hypertemporal history of theuniverse, part of the universe, e4, will contain Paul surviving past

the age of three.Will Pauls surviving past the age of three always be part of thepast? Assuming no travel into the hypertime past occurs, e4willalways be part of the hypertemporal past when a hypertemporalhistorian at T18 looks back at what has come before, e4will be theevents that occured at T4. But e4 is not always a part of thenormal-time past the past that Pauls or Sarahs or our accuratehistory books describe. At hypertimes T4 and T5 e4is part of the

normal-time past, but by hypertime T11 it is not. So the events oft4 are at one hypertime the way the events of normal time were,i.e. part of the universe, and at some later hypertime not the waythe events of normal time are, i.e. not part of the normal-timepast, though still part of the universe. Thus, contrary to the objec-tion, even if the events of t4 are a part of the universe, as theymust be if they are to be changed, those events are not necessar-ily always a part of the past.

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Conclusion

According to Gilbert Fulmer, The idea that the past could bechanged by a time traveler is a confusion which stems from themistaken notion that time travel would cause a repetition of thepast.15 But it is Fulmer who is mistaken. The issue is not whethertime travel wouldcause a repetition of the past, but rather couldit.If temporal moments have temporal parts, then time travel mightcause temporal moments to hypertemporally occur again and bechanged.

In fact, once one admits that there are coherent models in

which the past can change, many of the traditional problems andparadoxes associated with time travel disappear. For example,suppose the prevailing sentiment is correct Paul can travel backin time, but he cannot kill his three-year-old self. But then,according to Samuel Gorovitz, Pauls murder weapon is notbehaving as the normal physical object we take it to be or thenotion of voluntary action does not apply in the usual way.16 Towhat degree Gorovitzs concerns are warranted, if changing the

past is logically impossible, is the source of tremendous debate.17

Regardless, Gorovitzs concerns are completely sidestepped onceone admits that Paul can change the past and kill his three-year-old self.

Does the hypertemporal model of time travel thereby rescuefrom incoherence all time travel stories that either take changingthe past for granted or make changing the past a fundamentalpart of the storyline? Not necessarily. The hypertemporal model

has certain consequences that rule out many such stories, espe-cially stories along the following lines. Paul and Sarah together goback in time and unknowingly change the past. They jumpforward and find a drastically altered future. They then go backinto the past and fix the problem and finally jump back into the



15 Gilbert Fulmer, Time Travel, Determinism and Fatalism, Philosophical Speculations inScience Fiction and Fantasy1, (1981): p. 41.

16 Gorovitz, p. 367.17 See, for example, Craig, pp. 140-141; Dwyer, p. 349; Paul Fitzgerald, Tachyons,

Backwards Causation, and Freedom, Boston Studies in the Philosophy of ScienceVIII, (1971):pp. 425434; Paul Fitzgerald, On Retrocausality, Philosophia 4, (1974): pp. 534547;Gilbert Fulmer, Understanding Time Travel, Southwestern Journal of Philosophy11 (1980):pp. 151153; Fulmer, Time Travel, Determinism, and Fatalism, pp. 4148; Horwich, pp.433437; Lewis, pp. 7580; Paul Thom, Time-travel and Non-fatal Suicide, PhilosophicalStudies27 (1975): pp. 211216; and Kadri Vihvelin, What Time Travellers Cannot Do,Philosophical Studies81 (1996): pp. 315330.


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original future. On the current hypertemporal model, however,there is no jumping back into the original future it is, after all,in the hypertemporal past. At most Paul and Sarah will jump into

a very similar future. The hypertemporal model allows changingthe past, but with the consequence that when one changes thepast one thereby sets in motion a new future.

Are there models that will allow one to get back to the originalfuture and still allow for changing the past? I do not know. Couldthere be models of time travel different from my own that consis-tently allow for changing the past? Probably. The argument thatchanging the past is logically impossible rests on the empirical

assumption that temporal moments do not have parts. Any modelof time that discards this assumption might produce an adequateexample of the past being changed.18 Do I think time is the way Ihave described it, i.e. that temporal moments in fact have hyper-temporal parts? I have no evidence that it is. Could temporalmoments have temporal parts? Could time be two-dimensional?No contradiction results by assuming that it is. If temporalmoments have hypertemporal parts, then time travel might causetemporal moments to hypertemporally occur again, in which casethe events of temporal moments changing over hypertime wouldbe no more contradictory than enduring objects changing overnormal time. Changing the past is logicallypossible.

University of RichmondRichmond, VA 23173

[email protected]

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18 At least some such models fail to model changing the past. For example, see Meiland,pp. 153173. On Meilands model what he is calling the past is notthe states of the universecausally responsible for the present state of the universe, and since the states causallyresponsible for the present state of the universe never change, Meilands model does notallow changing the past. See also, Objection III. For arguments against changing the pastin multi-dimensional relativistic models, see Alasdair M. Richmond, Plattners Arrow:Science and Multi-dimensional Time, RatioXIII (2000): pp. 256274.

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Goddu_Time Travel and Changing the Past