# Science shows why Doctor Who is so special

As Doctor Who's 50th anniversary looms, time travel is everywhere – on the screen, at least. Famously, the Doctor can whizz through the years using a "dimensionally transcendental" machine, the TARDIS, and make changes to the past as and when he likes. But what is time travel – and how much of "Doctor Who" might really be possible?

A handy definition of time travel comes from philosopher David Lewis. Lewis says time travel involves a journey having different durations viewed from outside (in "external time") or from inside (in "personal time"). Suppose you spend five minutes travelling aboard your machine, as measured by (e.g.) your watch and your memories. On arrival, you find 150 years have elapsed in the outside world. Congratulations, you have time-travelled. Five minutes of your personal time has covered 150 years of external time.

Odd as this sounds, Einstein's theory of Special Relativity introduced such possibilities to physics in 1905. The theory says: the duration of a process varies with the relative velocity of the observer. The closer that relative velocity gets to the speed of light, the longer the travelling process takes.

Suppose you want to see the Earth a billion years hence, but worry you have only about 50 personal years left. Special Relativity specifies that if you travel very close to the speed of light relative to the Earth, your 50 personal years can cover one billion Earth years.

In backward time travel, personal and external time differ in direction, so journeys end in external time before, not after, they begin; you spend five personal minutes travelling 150 years into the external past. General Relativity suggests that the universe is essentially curved spacetime, which might allow such divergences of external and .

Relativity treats space and time as aspects of a single entity: "spacetime". One of the more remarkable features of General Relativity is that it allows time and space axes to be interchanged, so one observer's space axis can be another observer's time axis.

In 1949, Austrian mathematician Kurt Gödel used General Relativity to describe a universe where intrepid voyagers can go anywhere in (past or future) time without travelling faster than light. Gödel's universe has no boundaries in space or time, and all the matter in it rotates. But our finite, non-rotating universe is not Gödel's. Despair not though – simply spin an ultradense, very (maybe infinitely) long cylinder very fast. Spacetime should curve around the cylinder so the direction of the local future partially points into the external past. Such devices are called "Tipler Cylinders", after physicist Frank Tipler.

Better yet, quantum theory suggests that "wormhole" connections between different spacetime points spontaneously form and break all the time. The chances are that natural wormholes are tiny - vastly smaller even than an electron, (and a billion trillion electrons can fit in a teaspoon). But you could perhaps find (or create) a wormhole big enough and durable enough to let you slip through into the past. Difficult, but theoretically possible.

No, you can't kill your physics teacher

So perhaps you could travel into the past. But what about paradoxes? What is to stop you assassinating your grandfather or yourself as infants? One answer says: logical consistency.

Classical logic says you cannot consistently kill in infancy someone who achieves adulthood. But, Lewis says, time travel need not involve doing the logically impossible – provided travellers' actions in the past are consistent with the history whence they come. So you could try killing your baby grandfather, but something would foil you – you would sneeze, or your gun would jam. Lewisian time travel is therefore (classically) consistent, but might look very strange, since seemingly possible actions (like shooting an unprotected infant) would prove impossible.

Another view says that backward time travel requires many worlds – that is, many different but equally real versions of physical reality. Physicist David Deutsch and philosopher Michael Lockwood argue that time travel must involve inter-world travel. If you travel backwards in time, you must arrive in a history different from your native one and so would be quite unfettered by your past once you get there. You could even kill this other history's counterparts of your grandfather and yourself.

Both these concepts of backwards time travel may disappoint anyone wanting to change the "one and only" past. Conventional logic says time travellers would either help make history what it was (Lewis) or create a different history (Deutsch/Lockwood). However, quantum logic might let travellers change the actual (one-and-only) past.

Suppose we hold that quantum measurements determine (or change) quantities measured, even if those quantities lie in the past. Someone could travel back and "observe" history turning out differently from how it originally was, thereby retrospectively making actuality different from what it had been. What would happen to travellers who rebooted history is not clear, but this model seems closer to the time travel familiar from "Doctor Who" and other fictions. Beware, though, because quantum theory allows no predicting, and still less controlling, of the outcomes of changing the past. There would be no way to foresee the effect you would have on the present.

So classical logic, General Relativity and all seem to permit . Classical logic plus General Relativity suggest backward travellers face weird consistency constraints. Many-worlds travellers face no constraints, but get displaced into different histories. Quantum-logic travellers could change the (one and only) past without constraints, but they couldn't predict or control what they would get.

So far, however, it seems only the Doctor knows how to change the past at will.

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Time travel may be possible but won't be economical

This story is published courtesy of The Conversation (under Creative Commons-Attribution/No derivatives).

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Nov 22, 2013
And how would one travel back to a specific point? The universe does not acknowldge our perception of time as it passes, that is, getting back to (Earth's) yesterday using a calendar wouldn't be much use if you time jumped from Mars. In a general case wouldn't one need to go back to the state of the universe as it was yesterday and then navigate to the desired location...but then yesterday would be...?
What we recognise as the passage of time (arrow of time etc) is just 'change' from one moment to the next and while we might know much about change (physics, reactions etc) we know very little about Time. Since SR suggests that a photon's (proper) time would always read zero is there such a thing as time at all?

Nov 22, 2013
Hello and thanks.
I take it the idea is that you don't 'time jump' as such but rather navigate by following the local future direction in a spacetime which is so curved that the local future will take you into the global past. So you can plot your destination as usual save in four dimensions instead of three. Interestingly Gödel concluded that the possibility of 'time travel' in his model universe actually proved that there is really no such thing as time as we normally think of it.
All best, Alasdair

Nov 22, 2013
What we recognise as the passage of time (arrow of time etc) is just 'change' from one moment to the next and while we might know much about change(physics, reactions etc)we know very little about Time.Since SR suggests that a photon's (proper)time would always read zero is there such a thing as time at all?

Strictly speaking, time is not a linear entity.But in the classical layperson sense, the perception of time passing tends to be separated into 3 main categories: That which has happened(past); that which will/could happen(future)& that which is happening(now).You talk about a 'moment'.I guess that this would equate to a piece of 'now'.(how long is that piece of now..?Nobody is quite sure..)The way you describe it as 'change from one moment to the next' conjures up an image of time as purely a series of 'now's'.That is an interesting way to think about it.Food for thought: if your photon experiences 0 passage of proper time,does that mean it never experiences a 'now'?DH66 :)

Nov 22, 2013
In case you are not sure about what I mean by 'never experiencing a now, think about it this way: the smallest unit of time is Planck time. Even that has a finite & existing duration. (But your photon would not experience even that):
http://en.wikiped...nck_time
http://www.univer...ck-time/
Hence it is PROBABLY the smallest possible piece of 'now'.
It is the 'change between the moments', that allow us to perceive that something has changed, ie to gain an awareness of the difference between the 'now' and 'not now', or (if you will) of the 'passing' of time.
Cheers, DH66

Nov 22, 2013
@DH66 '...It is the time required for light to travel, in a vacuum, a distance of 1 Planck length.≈ 5.39106(32) × 10−44 s...'
Note that in Planck Time we are still talking seconds and such is our terminology. Would ET (if exists) might determine the same length but maybe not the same idea of passage to traverse it.

@Al-Rich '...Gödel proved that there is really no such thing as time as we normally think of it.'
I'm not sure if say, the Gödel Metric would be appropriate because we are still using 'dt' in the equations but what if 'the now' had a analogous set of co-ordinate structures? However such would probably need 'new(?)' mathematics to determine progressing from one point to another. A 'cubical' matrix theory A(ijt) instead of A(ij)?

Nov 22, 2013
@Mimath:
I know. That was my point. I was enjoying questioning the definition (or rather, the existence) of a concept of 'now' for your photon, whose 'proper' time is equal to zero. Sometimes it is fun to think about such things. :)
Cheers, DH66
PS no before, after, or now. Is there a paradox here somewhere. How would you define it....

Nov 22, 2013
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Nov 22, 2013
Well I read the damn thing twice. Is this some kind of joke? It really sounds like some nouman's mumbo jumbo. Zephir might be able to explain it but Dr Who ever wrote the article sure did make a mess of it. Would it help if I read it again?

Yes, and take your time. ; )

Cheers, DH66

Nov 22, 2013
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Nov 22, 2013
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Nov 22, 2013
DarkHorse66, I'm not really suggesting there is no 'now' etc, I'm suggesting there is but not in the way we currently think of time. For example, it's rather pointless to think about time travel if yester-'nows' don't exist...nothing to go back to...not quite sure if I've expressed that properly but I'm sure you know what I mean. On the other hand if one could go into a future 'now' that would mean that future 'nows' would already exist. While QM could accept this in terms of probabilities perhaps the macro minded layman would see this as life already being mapped out so why bother.
Like you say DH66, fun to play around with. I think the paradox you were thinking of might be in the future rather than the past because the previous 'nows' might be 'frozen' and unchangeable but in your TARDIS going into the future you decide that a certain outcome is not to your liking so back to your 'present' you do things differently hoping to change that outcome.

Nov 22, 2013
But even this would suggest that all 'nows' are imprinted on, say, those '...analogous set of co-ordinate structures...', that is to say such structures would serve as memory too. So one would be working with an entity with an identity that is both covariant and contravariant (Tensor?) on the same side of the coin, as it were. That is, not as a dual tensor. Must admit my maths is woefully inadequate but maybe if I keep playing around...ha ha!
Maybe some up and coming Einsteins, Hawkins, etc will solve it one way or the other.
(By the way DH66 why 66? 66 is a special number to me and turns up in various ways in my figures...just thought I'd ask. Thanks in advance)

Nov 22, 2013
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Nov 23, 2013
Zephir_fan, never mind...as I remember it even Dr Who messed it up a bit. He never did fix the mechanism that always displayed the TARDIS as the English Police box. My bets are all on the Master where one never knew when he was going to turn up or what in. But in all that '...stuff...' maybe one should have have known that is, if the Master had been there in the first place....

Nov 23, 2013
But even this would suggest that all 'nows' are imprinted on, say, those '...analogous set of co-ordinate structures...', that is to say such structures would serve as memory too. So one would be working with an entity with an identity that is both covariant and contravariant (Tensor?) on the same side of the coin, as it were. That is, not as a dual tensor. Must admit my maths is woefully inadequate but maybe if I keep playing around...ha ha!
Maybe some up and coming Einsteins, Hawkins, etc will solve it one way or the other.
(By the way DH66 why 66? 66 is a special number to me and turns up in various ways in my figures...just thought I'd ask. Thanks in advance)

Perhaps ALL of those 'nows' are as malleable as each other. After all, what one calls the past or the future, or which 'now' moment one is actually standing in, is all relative to whatever perspective one is happening to choose. And the doctor can definitely choose which 'now' moment he wishes to take as his...cont

Nov 23, 2013
cont...'current' reference point. Perhaps the same potential is there for all of us, despite the fact that we are still constrained to travel in a single direction. Future (or past) 'now's' need not actually be fixed. Be careful not to see time as an absolute, nor the events that are unfurling within each sequence of 'now's'. If anything the LIKELIHOOD of an event occurring in a certain way, at a certain time (if at all) is only a probability (ie quantum in nature) & THAT level of likelihood will be influenced by other events that precede the final one. Nock any one of these out, & you might well have changed what was otherwise fairly certain to happen. It is not impossible that something might happen later again, to bring events back in balance (roughly back to how things would have panned out originally further down the sequence anyway) Effectively producing some kind of compensation. Just a different sequence of events to get there. My maths is not that great either. It's...cont

Nov 23, 2013
@DarkHorse66, [for previous cont] as in 'time and events of a individual create a unique individual'. Mmmm, the only problem I see with that is; wouldn't that uniqueness imply an absolute reality for that individual (absolute space-time). 'absolute' and 'relative' on the same side of the coin? in addition wouldn't that also create a problem with primitive assumptions (in any such system) being undefined and defined. Have to think about that one...ha.

Nov 23, 2013
cont...currently around 2nd year. But having probabilities does imply some kind of elasticity, at least with regard to possible outcomes. :)

That paradox would need to be around all 3(past,present, future) If our poor photon does not see time elapse, how does it even get to the future(even when defined as a part of a series of 'now' moments) if it can't have a 'now' moment to begin with?It can't speak of having experienced other 'now' moments either.That would imply a past 'now' moment too& that adds up to temporal progression...oh dear.Another hypothetical(!)possibility is that it does see the tiniest smidgin of passing time, that smidgin tending so tiny that it is at Planck level, ie ignorable at gravistic speeds)But that could mess up the tidy results that SR proclaims, too...
66has personal meaning on several levels, it is special for me too.What kinds of figures are you talking about?You are welcome to PM me instead, if it is private.Just click on my alias nexttomypostCheersDH66

Nov 23, 2013
DarkHorse66 [cont.] '...a single direction...' must be the arrow as in 4D spacetime since in 3D the arrow is proceeding similarly in all directions. Yes, my previous post mentions QM probability but let's take that a stage further, intuitively that is. Suppose someone, or some group finally find TOE, and in the present context, it turns out to be Time. 'Everything is made from bundles of Time'. Wouldn't that mean Time would then be absolute in the sense that no futher dichotomy was possible? If that were so then Dr. Who (or the other Time Lords of his kind) would then certainly (theoretically) be able to work out exactly where and when in the 'time continuum' he wanted to go. Ha! That would cause another problem, 'RD' part of the name TARDIS is 'relative dimensions'.

Nov 23, 2013
@DH66, [for previous cont] as in 'time and events of a individual create a unique individual'. Mmmm, the only problem I see with that is; wouldn't that uniqueness imply an absolute reality for that individual (absolute space-time). 'absolute' and 'relative' on the same side of the coin? in addition wouldn't that also create a problem with primitive assumptions (in any such system) being undefined and defined. Have to think about that one...ha.

Mmm, how do I answer that one..We are each unique individuals, shaped by many & varied elements. Change the elements, we are shaped differently, but just as unique. Uniqueness is simply a state of non-duplication & can take many forms. It is not required to be static or only of one form. So, no, no absolute reality; the form of uniqueness is relative to what it is being shaped by & what it shapes in turn. Cheers, DH66

Nov 23, 2013
@DH66, [for previous cont] as in 'time and events of a individual create a unique individual'. Mmmm, the only problem I see with that is; wouldn't that uniqueness imply an absolute reality for that individual (absolute space-time). 'absolute' and 'relative' on the same side of the coin? in addition wouldn't that also create a problem with primitive assumptions (in any such system) being undefined and defined. Have to think about that one...ha.

Mmm, how do I answer that one..We are each unique individuals, shaped by many & varied elements. Change the elements, we are shaped differently, but just as unique. Uniqueness is simply a state of non-duplication & can take many forms. It is not required to be static or only of one form. So, no, no absolute reality; the form of uniqueness is relative to what it is being shaped by & what it shapes in turn. Cheers, DH66

But would that make Dr. who relative [cont.]

Nov 23, 2013
3D vs 4D. Careful here, in 3D, we are talking purely in spatial dimensions (unless you mean 2Dspatial & 1D temporal) & this definition does NOT include time. In 4D, the 4thD IS time, & time does not have a physical/spatial direction at all. The arrow of time is only DESCRIBED as going in a forward direction, but this is purely a convention to describe a progression along a sequence of events. It does not actually go anywhere in physical sense. Strictly speaking, time can exist without space, but space cannot exist without time. Hence as soon as you have space, you have spacetime & the two are non-separable, if you want space to exist. But that does not make it absolute. The fact that a moving object perceives the elapsing of time differently, relative to a still one, should make that clear. No, I think the tardis' definition is still safe. :) Actually, he can go where he wants to. He is just not a very adept pilot (unlike River Song, who has a proper knack for it). And there...cont

Nov 23, 2013
[cont.] to who he was when he left A to B and then back to A again? What he was at A wouldn't be the same as when he returned to A which might then affect his decision to go to B. What I'm saying that there is something absolute about Dr. Who which enables him to retain his uniqueness as such (memory perhaps?). Have I expressed that properly?

Nov 23, 2013
DarkHorse66, Yes I did mean the latter as in 4D world line. However we are still talking of time in the 'conventional' sense and in that sense time travel (apart SR interpretation) I don't see as being possible.

Nov 23, 2013
cont..is also a period where the TARDIS is fitted with a Randomizer, while he is trying to avoid the Black Guardian (the 4th dr):
http://tardis.wik...ndomiser
http://io9.com/57...s-tardis
Cheers, DH66

Nov 23, 2013
Ha ha, you've got me there DarkHorse66. I managed only the 1st and part the 2nd Dr when they were on TV...a long time ago and I don't have access to later parts.

Nov 23, 2013
DarkHorse66, Yes I did mean the latter as in 4D world line. However we are still talking of time in the 'conventional' sense and in that sense time travel (apart SR interpretation) I don't see as being possible.

The time dilation that occurs for a moving entity relative to something at rest, IS a form of time travel. If you take a week to get wherever you are going (think twins paradox http://en.wikiped..._paradox ) and five years have passed for whoever stayed behind, then you have definitely taken a short-cut in time, relative to them. (& you have only aged the amount of time it took you to travel)
Cheers, DH66

Nov 23, 2013
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Nov 23, 2013
Ha ha, you've got me there DarkHorse66. I managed only the 1st & part the 2nd Dr when they were on TV...a long time ago and I don't have access to later parts.

You could go to 2nd hand bookshops & find the TV-tie-ins, ie the book versions written based on the episodes. Alternatively you could look online, eg:
https://www.googl...;bih=796
And here is some more news about lost & found episodes. There is a whole bunch of exciting news:
https://www.googl...episodes
(mmm, might have to repost that last link, if it does not post properly)
I think you are going to enjoy yourself...
Don't forget, the 50th anniversary episode (the day of the doctor) is going to be shown simultaneously around different countries in about 12 hours
link too long, see next post...cont

Nov 23, 2013
cont...see this for details:
https://www.googl...+episode
Just remember to allow for local time/date differences when working out if one is for you.
Or watch it here:
https://www.googl...treaming
For the Dr Who buffs
Best Regards to all, DH66

Nov 23, 2013
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Nov 23, 2013
DarkHorse66, yes am aware of this, such as at 0.999999999c p time is, say years, is about 24min as opposed 22367 years on Earth. So in this way a photon would not experience time while on Earth we are approaching infinity...theoretically speaking of course. If in the future v = 0.8c becomes possible perhaps the ill could take a trip and return to find medical science had progessed to enable a cure. One do but dream of such a world eh?
Nice debate, this, DarkHorse66 but I'll soon have to sign off for the day.

Nov 23, 2013
Before you go, I sent you a quick PM reply. So check your inbox.

Cheers, DH66

Nov 23, 2013
Thank you very much. Have a nice day.

Nov 23, 2013
Hi Walters1,
The time travel I have in mind is space-time travel and necessarily involves spatial displacement as well as movement in time. (Anyway if somehow you could move purely in time, i.e. with no spatial movement at all, presumably you'd run into other stages of yourself ...)
All best, Alasdair

Nov 23, 2013
Time travel backwards is impossible. Any change in the past would make us in the present disappear. If it was possible someone would have done it and we wouldn't be here.

And if changing the past doesn't make the present disappear, just creates a divergent path, that implies that every possible permutation of the universe from the beginning to end of time must exist side by side. An infinity of infinities, also BS.

Nov 23, 2013
You can easily prove that Photons are effected by Time using any number of tricks.

Lenses, Mirrors, double slit, etc.

All of those things can alter the properties of the Photon, thereby proving it is effected by Time the same as everything else.

Time exists as a real thing, else existing physics models wouldn't work as well as they do. If time did not exist, when do velocity equations and acceleration equations, and thermodynamics equations (rate loss of heat in an insulated room, for example,) always work to within margin of error of instrumentation?

Of course time is real.

We may not understand it much, but it can't be too unlike what we observe it to be, otherwise non of our machines would work.

Nov 23, 2013
Time is an inseparable function of space. Movement in space would be impossible without time.

Nov 23, 2013
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Nov 24, 2013
Hi folks,
Couple of things:

i) I might submit that time travel backward is logically possible provided what the traveller does in the past is consistent with the history whence the traveller comes. Here I follow David Lewis' paper "The Paradoxes of Time Travel", (The American Philosophical Quarterly, 13, 1976: 145-52).

ii) Why assume that many-worlds travel commits you to an infinity of worlds? (And of course many-worlds versions of QM include many well-founded empirical hypotheses.)

iii) Gödel, like many others, was perfectly well aware that there is a 't' co-ordinate in relativity – however, he believed this co-ordinate did not measure anything that really resembled the dynamic, flowing thing we ordinarily take to be time. See (e.g.) Palle Yourgrau, Gödel Meets Einstein: Time Travel in the Gödel Universe, (La Salle / Chicago, Open Court, 1999).

Thanks, Alasdair
(One doctor who isn't kidding ... Or posting anonymously incidentally.)

Nov 24, 2013
And if changing the past doesn't make the present disappear, just creates a divergent path, that implies that every possible permutation of the universe from the beginning to end of time must exist side by side. An infinity of infinities, also BS.
No, it simply means that reality is quantum and classical limits break beyond some degree

Nov 24, 2013
Hi again, folks,
Pardon the author sticking his nose back in again but if you are wondering how this piece ended up on physics.org then please note that I am wondering about that too.
I wrote the above for 'The Conversation UK', which is an online news and analysis publication written by academics from all sorts of fields. So I didn't write the above for a physics.org audience and if I'd known it was going to end up here, I'd probably have upped the physics more than a bit.
Anyway, I'm very glad to see you take an interest and I'll try to answer any questions as we go along.
Thanks to all and all best wishes,
Alasdair

Nov 24, 2013
And if changing the past doesn't make the present disappear, just creates a divergent path, that implies that every possible permutation of the universe from the beginning to end of time must exist side by side. An infinity of infinities, also BS.
No, it simply means that reality is quantum and classical limits break beyond some degree

That makes absolutely no sense.

If someone travels to the past and kills the progenitor of our species we will never exist in that timeline. If you think we are all going to disappear under those circumstances you're retarded and if you think that there are parallel timelines you're not even retarded because you believe that every possible permutation of every aspect of every particle in the universe exists simultaneously side by side in alternate dimensions.

If there is a third possibility I'd like to hear it.

Nov 24, 2013
If one assumes that the laws of physics don't change from one 'now' to the next then perhaps those same laws remain 'fixed' in the past too. If that were/is the case then entropy would have to be considered as part of the time travel 'equation'. The debate would then have to be whether the past would be a closed or open system. I'd be betting on the latter and 'scrambled eggs' would remain scrambled. That is to say one could view history but not change it. The alternative would be that if one prevented the eggs from being scrambled by one method the eggs would still get scrambled by some other procedure. In short, some type of conservation that would maintain a/the balance. Following this line would lead to QM (eigenstates?) and conservations therein.

Nov 24, 2013
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Nov 24, 2013
No, it simply means that reality is quantum and classical limits break beyond some degree

That makes absolutely no sense.

If someone travels to the past and kills the progenitor of our species we will never exist in that timeline. If you think we are all going to disappear under those circumstances you're retarded and if you think that there are parallel timelines you're not even retarded because you believe that every possible permutation of every aspect of every particle in the universe exists simultaneously side by side in alternate dimensions.

If there is a third possibility I'd like to hear it.
You assume there is only one past, when pasts are multivalued just as futures. If space is infinite but filled with matter then infinite copies of you will exist. In such a situation the question is not which past, but more fundamentally which you is in the past attempting to cause an intransitive causality mobius loop since you both are indistinguishable

Nov 25, 2013
Hi again, folks,
I really don't think I know what an "intransitive causality mobius loop" might be. (Although you hum it and I'll play it. You see, I can do requests.) I do agree though that there are versions of QM where pasts are multivariate too and that a present observation therein can select a past branch. Check out (e.g.) the view that Tim Maudlin calls 'quantum modal realism'.
However, I fear it does not follow from the mere infinity of space and matter that infinite copies of you must exist - you also need some kind of independent variation assumption.
I note too some examples of tiny troll and even (or do my eyes deceive me?) a sock puppet.
Hence my signing myself,
Yours respectfully,
Alasdair Richmond

Nov 25, 2013
Hi again, folks,
I really don't think I know what an "intransitive causality mobius loop" might be....
Yours respectfully,
Alasdair Richmond

Me too, Mr. Richmond, although I suspect it has something to with the so called 'bow tie loop' (more corectly cycling causality loops). There are various forms of the theory but all seem to end up with time becomming trapped and therefore ending...can't think that such would be considered by mainstream...do you know if Dr. Who ever faced this?

Nov 25, 2013
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Nov 25, 2013
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Nov 25, 2013
Zephir_fan, must admit I wondered why Al Rich would ask that question yet not know more than I did on the subject. I take people at face value but sometimes....well you know. Still I enjoy the 'chat'.
Also Al Rich mentioned David Lewis (above) but if memory serves then DL wrote intuitively and basically 'logic' of killing one's parents etc. and mostly in 1D. Unfortunately time, in the present context, should not be treated that way because it must cover all 3D's.