# Is an infinite past logically impossible? **URL:** \ **Category:** Factual Questions\ **Created:** [November 26, 2010, 8:06pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011 "2010-11-26T20:06:18Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![Spatial\_Rift\_47](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@Spatial\_Rift\_47](https://boards.straightdope.com/u/Spatial_Rift_47)\ **Post date:** [November 28, 2010, 10:29pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/61 "2010-11-28T22:29:37Z")
> [@Stratocaster](#): > > There is a “now” through which everything passes relative to a given position in space, which would amount to the same thing. No, even this is not necessarily true. Consider a particular location in space, like the Earth. For every event that is close enough to send light in our direction we can place it on a timeline. We observe the moon moving into the solar eclipse position. We observe a comet striking Jupiter. As long as we know the distance to some object we can account for the travel time of light. But there are events so far away that we will never observe them. We can never place them in a timeline. They will never pass through our Earth-now. We know this is true because of the continued expansion of the Universe. (Almost) everything is receding from our galaxy. The further out we look, the faster things recede. Because the expansion is being at least partly driven by spacetime itself, we know that objects out past a certain distance are receding from us _faster than light’s vacuum speed_. The light those objects emit can never catch up to us. See the wikipedia article: [Hubble sphere](http://en.wikipedia.org/wiki/Hubble_sphere). (The only way it could maybe catch up to us is if the expansion of the Universe at some point stopped and was dramatically reversed. But eternal expansion is a logically consistent theory of physics, so for the sake of arguing that an infinite past is consistent I’m going to assume eternal expansion.) For any particular location in the Universe, the accelerating expansion carves out things that can never intersect that location’s timeline. So even if every point in the Universe had its own “now”, not everything would have to pass through it. To put this back into the vocabulary of the infinite past idea: For any arbitrarily large value of “X years ago”, I can find a place in the Universe so distant that even if an event happened at that place X years ago, it would never pass through any “now” located here. That is a past without end. (I think this last step requires a Universe of infinite spatial extent, but that’s a well-accepted possibility.) > [@Stratocaster](#): > > Rather, relativity doesn’t destroy the flow of time, it just changes the rate of the flow (as compared between two different vantage points). All the same events occurred, **in the same sequence**. They just may have unfolded at a different pace, from my vantage point on my rocket ship. (Bolding mine). Again, no. Even if I choose a point in space and time, I can define different Nows by specifying reference frames of different velocities located at that point. Those reference frames, even though they exist at the same point, will disagree about the temporal ordering of observed events. See: [Relativity of simultaneity - Wikipedia](http://en.wikipedia.org/wiki/Relativity_of_simultaneity) . General Relativity makes it very difficult to define a “now” that even remotely resembles our intuitive experience of one. > [@Stratocaster](#): > > And anyway, even if it were a complete illusion. I’ve already acknowledged that the one possibility that permits an infinite past is that which demonstrates that time does not operate as we perceive it to, it’s a mirage; therefore, there’s no “infinity” to overcome logically. But if time does have the properties we perceive it to, then an infinite past still seems a non sequitur. So what if time doesn’t operate as we perceive it to? Lots of things don’t operate as the human brain likes to perceive them. Our perception could still exist. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 28, 2010, 11:11pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/62 "2010-11-28T23:11:35Z")
> [@](#): > > Well, that’s interesting. I think a never-ending future is possible in a way that an infinite past is not; the same non sequitur doesn’t exist here, I don’t think, in that there’s a starting point. OK, then, how much time is there after any given event? And how is it possible that there can be an infinite amount of time afterwards, since that would take an infinite amount of time? ---
**Author:** ![jackdavinci](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jackdavinci/32/3259_2.png) [@jackdavinci](https://boards.straightdope.com/u/jackdavinci)\ **Post date:** [November 29, 2010, 12:31am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/63 "2010-11-29T00:31:58Z")
> [@These are my own pants](#): > > However I think that it’s a red herring anyway as the normal kind of model of a universe “without beiginning” doesn’t have such infinite intervals of time in it anyway. Would you elaborate on that point? ---
**Author:** ![Stratocaster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/stratocaster/32/16393_2.png) [@Stratocaster](https://boards.straightdope.com/u/Stratocaster)\ **Post date:** [November 29, 2010, 10:45am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/64 "2010-11-29T10:45:54Z")
> [@Spatial\_Rift\_47](#): > > No, even this is not necessarily true. Consider a particular location in space, like the Earth. For every event that is close enough to send light in our direction we can place it on a timeline. We observe the moon moving into the solar eclipse position. We observe a comet striking Jupiter. As long as we know the distance to some object we can account for the travel time of light. But there are events so far away that we will never observe them. We can never place them in a timeline. They will never pass through our Earth-now. We know this is true because of the continued expansion of the Universe. (Almost) everything is receding from our galaxy. The further out we look, the faster things recede. Because the expansion is being at least partly driven by spacetime itself, we know that objects out past a certain distance are receding from us _faster than light’s vacuum speed_. The light those objects emit can never catch up to us. See the wikipedia article: [Hubble sphere](http://en.wikipedia.org/wiki/Hubble_sphere). The fact that we can’t observe the event doesn’t mean they aren’t subject to the constraints of time. Not sure why you think GR makes the non sequitur I describe non-existent. Can you clarify? The aspects you describe still don’t address the impossibility I described, I don’t think. ---
**Author:** ![Stratocaster](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/stratocaster/32/16393_2.png) [@Stratocaster](https://boards.straightdope.com/u/Stratocaster)\ **Post date:** [November 29, 2010, 10:46am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/65 "2010-11-29T10:46:56Z")
> [@Chronos](#): > > OK, then, how much time is there after any given event? And how is it possible that there can be an infinite amount of time afterwards, since that would take an infinite amount of time? Did you read the sentences after the ones you responded to? I think I answered this. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [November 29, 2010, 11:35am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/66 "2010-11-29T11:35:09Z")
> [@jackdavinci](#): > > …someone wrote the following comment at another website: > > > [@](#): > > > > It should be noted that an infinite regress of universes prior to this one is logically impossible; if the lifespan of universe has been repeating in an infinite cycle, there has not been, and never will be, enough time elapsed yet for us to reach this particular cycle we are observed to be on. Thus, even if there was a universe or numerous universes that preceded this one, there cannot be an infinite number of them. I’ve just realized that all this talk of an infinite past is not even necessary to address the question of the OP. If the universe before ours lasted for half as long as the the entire lifetime of ours, and the one previous to that last half the the time of is successor, and so on… Then we have an infinite regress of universes that have elapsed in a finite amount of time up to the present. This total amount of time is less than twice the entire lifetime of our universe. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [November 29, 2010, 11:38am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/67 "2010-11-29T11:38:33Z")
> [@Lance\_Turbo](#): > > I’ve just realized that all this talk of an infinite past is not even necessary to address the question of the OP. > > If the universe before ours lasted for half as long as the the entire lifetime of ours, and the one previous to that last half the the time of is successor, and so on… > > Then we have an infinite regress of universes that have elapsed in a finite amount of time up to the present. This total amount of time is less than twice the entire lifetime of our universe. And you can do that with plenty of other fractions as well. In fact, my sleep-deprived brain seems to think it would be possible with any fraction less than 1. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [November 29, 2010, 12:10pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/68 "2010-11-29T12:10:18Z")
> [@BigT](#): > > And you can do that with plenty of other fractions as well. In fact, my sleep-deprived brain seems to think it would be possible with any fraction less than 1. Sho 'nuff. ---
**Author:** ![KellyCriterion](https://avatars.discourse-cdn.com/v4/letter/k/b3f665/32.png) [@KellyCriterion](https://boards.straightdope.com/u/KellyCriterion)\ **Post date:** [November 29, 2010, 1:46pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/69 "2010-11-29T13:46:09Z")
> [@Lance\_Turbo](#): > > I’ve just realized that all this talk of an infinite past is not even necessary to address the question of the OP. > > If the universe before ours lasted for half as long as the the entire lifetime of ours, and the one previous to that last half the the time of is successor, and so on… > > Then we have an infinite regress of universes that have elapsed in a finite amount of time up to the present. This total amount of time is less than twice the entire lifetime of our universe. I’d say that’s a logical impossibility. Using experiments conducted in my mind (and I am not a mathematician or a physicist), I think you can “prove” there exists an indivisible unit of time, and an indivisible unit of length. Any real experiment replicating the scenario described in [Zeno’s paradox](http://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise) regarding the tortoise and Achilles, will show that Achilles will not only catch the tortoise, but pass it. I see this as a proof that there exists no paradox at all. The space between Achilles and the tortoise is, quite observably, _not_ infinitely divisible. ---
**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\ **Post date:** [November 29, 2010, 2:00pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/70 "2010-11-29T14:00:44Z")
> [@KellyCriterion](#): > > I’d say that’s a logical impossibility. > > Using experiments conducted in my mind (and I am not a mathematician or a physicist), I think you can “prove” there exists an indivisible unit of time, and an indivisible unit of length. > > Any real experiment replicating the scenario described in [Zeno’s paradox](http://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise) regarding the tortoise and Achilles, will show that Achilles will not only catch the tortoise, but pass it. > > I see this as a proof that there exists no paradox at all. The space between Achilles and the tortoise is, quite observably, _not_ infinitely divisible. But Achilles and the tortoise live in the same universe. Perhaps the indivisible amount of time and/or space is not the same in each universe. If it became half as big in each descent we wouldn’t run into a problem at all. ---
**Author:** ![Spatial\_Rift\_47](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@Spatial\_Rift\_47](https://boards.straightdope.com/u/Spatial_Rift_47)\ **Post date:** [November 29, 2010, 3:09pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/71 "2010-11-29T15:09:50Z")
> [@KellyCriterion](#): > > Any real experiment replicating the scenario described in [Zeno’s paradox](http://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Achilles_and_the_tortoise) regarding the tortoise and Achilles, will show that Achilles will not only catch the tortoise, but pass it. > > I see this as a proof that there exists no paradox at all. The space between Achilles and the tortoise is, quite observably, _not_ infinitely divisible. Sure it is. It’s just that the divisions quickly become infinitesimal. What this means for the infinite regress of universes in a finite time is that either almost all of them existed for a negligible amount of time, or (as **LanceTurbo** mentions) that the laws of physics changed as the chain of universes progressed such that all the universes way far back from ours did exist for considerable time, but compressed relative to ours somehow. **Strato** , what I was really talking about was causality. I think part of your objection is that given an infinite past, there would be an infinite chain of cause and effect leading up to us, etc etc. But that’s not the case. There can be an infinite past while still having us in a finite causal chain. I haven’t worked out any detailed mathematics on this, but it comes from what I said before: for any event some large amount of time ago, I can place it so far away that it never intercepts us. It never becomes a cause for anything here. I also think you’ve been thinking of “infinity” as an amount to be reached all along, but that’s just an intuition based on some of your language on page 2. As others have pointed out, that is a highly incorrect way of thinking about infinity. ---
**Author:** ![SCSimmons](https://avatars.discourse-cdn.com/v4/letter/s/e495f1/32.png) [@SCSimmons](https://boards.straightdope.com/u/SCSimmons)\ **Post date:** [November 29, 2010, 11:31pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/72 "2010-11-29T23:31:03Z")
> [@Stratocaster](#): > > An infinite amount of time can’t have already passed. A universe that comes into being with an already existing “infinite past” tortures the meaning of “past” into meaninglessness–how can something emerge with a past attached to it that stretches before the point of emergence? Conversely, how can something “always exist,” possessing an infinite past, except by arbitrary definition? The past is the ongoing “exhaust” of the present. The only infinite past that can exist is a past that defies any meaning–it’s something we call the past, but it has not, in fact, actually “passed.” It’s time that exists as a concept only, without the “clock ticks” that make any discussion of time meaningful. It’s a universe simultaneously bound by time and not bound by time. Or so it seems to me. There’s really no point in trying to reason intuitively about these, because either option leads you to a roadblock. If you say that time started at the Big Bang, then someone can complain that it doesn’t make sense that there was a first ‘event’ with nothing that came before it. As if an observer, watching the first instant of the explosions, couldn’t ask “What just happened?” because ‘just’ doesn’t have a meaning yet. The question of whether something is ‘logically possible’ isn’t about what we can intuitively make sense of, or express with our English concepts. I can make a set of consistent assumptions that include one that, given any event, there are events that preceded that event in time by any arbitrary amount. This meets any reasonable mathematical definition of ‘infinite past’, and the fact that this ‘tortures the meaning of “past” into meaninglessness’ really says more about the lack of applicability of our common-sense temporal language to ranges of time that far out of our experience. One can say the same about how the idea of a finite past tortures the meaning of ‘before’. But none of that is about logic, it’s about language. Before you start asking questions like this, you absolutely have to step away from our normal paradigms of thought, because in that context, nothing in this realm makes sense. We can make consistent mathematical models of time and space that do not include a beginning point. An infinite past is therefore logically possible, regardless of whether or not we’re able to intuitively make sense of those models. To the extent that these models agree with observed reality, they are not only logically, but actually possible as well. ---
**Author:** ![spenczar](https://avatars.discourse-cdn.com/v4/letter/s/858c86/32.png) [@spenczar](https://boards.straightdope.com/u/spenczar)\ **Post date:** [November 30, 2010, 12:22am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/73 "2010-11-30T00:22:21Z")
> [@KellyCriterion](#): > > Using experiments conducted in my mind (and I am not a mathematician or a physicist), I think you can “prove” there exists an indivisible unit of time, and an indivisible unit of length. If you can prove this, you will win a Nobel prize in physics and/or a Fields medal. ---
**Author:** ![Apollon](https://avatars.discourse-cdn.com/v4/letter/a/e47774/32.png) [@Apollon](https://boards.straightdope.com/u/Apollon)\ **Post date:** [November 30, 2010, 8:12am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/74 "2010-11-30T08:12:46Z")
> [@Stratocaster](#): > > Yes, that’s why it’s logically impossible. But it’s not “undefined,” it’s “infinite,” by definition. Remember the premise? “Is an infinite past logically impossible?” My response was to that premise. I don’t see how you conclude that this is logically impossible. You say that the elapsed time between the present and any point in the past must be finite. That is actually correct. No matter which point in the past you pick, you will always find that it is a finite amount of time away from now. That is because there doesn’t exist “a point inifinitely away” - not because infinite time is impossible, but because infinity cannot be contained between two points (it can, at the most, be limited in one direction by one single point, leaving the other direction unbounded). You can’t say something is illogical simply because it doesn’t conform to your mistake. At least half a dozen posters have already pointed out to you that an infinite past doesn’t have a starting point, yet you keep ignoring that, and pretend that it does have one. Then you continue arguing from that flawed premise that since t minus infinity is a defined point (which it really isn’t), and since infinity is infinite (which is probably true), then infinity cannot exist. This claim is unsound, because it assumes that infinity is bounded by two defined points. You cannot define the “starting point” of infinity, because that contradicts the very definition of infinity. You can only measure distances between defined points. T minus infinity is undefined - using that point to make any measurement at all, is meaningless. If you could find such a point, then you could always find another one that lies even further in the past. In truth, the universe (regardless of whether it’s of finite or infinite age) does not care about how much time elapsed since any arbitrary point in the past. It only cares about sequence of events, and the time between any two events is always finite. So, in an ageless universe, there would be an infinite number of events that have occured in the past, and each event needs only to “know” what happened immediately before it. It’s turtles, all the way down. Have you ever considered an infinite future? Would you say that it, too, is impossible, because if you started counting backwards from t plus infinity, then you never would reach the present? ---
**Author:** ![Apollon](https://avatars.discourse-cdn.com/v4/letter/a/e47774/32.png) [@Apollon](https://boards.straightdope.com/u/Apollon)\ **Post date:** [November 30, 2010, 8:19am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/75 "2010-11-30T08:19:55Z")
> [@spenczar](#): > > If you can prove this, you will win a Nobel prize in physics and/or a Fields medal. Hasn’t this already been established? It think that’s what the Planck Length and Planck Time are about. ---
**Author:** ![Apollon](https://avatars.discourse-cdn.com/v4/letter/a/e47774/32.png) [@Apollon](https://boards.straightdope.com/u/Apollon)\ **Post date:** [November 30, 2010, 8:45am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/76 "2010-11-30T08:45:24Z")
please delete ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [November 30, 2010, 9:02am UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/77 "2010-11-30T09:02:27Z")
> [@Apollon](#): > > Hasn’t this already been established? It think that’s what the Planck Length and Planck Time are about. A popular misconception; the Planck length isn’t actually known to have any particular physical significance. Seriously. It just happens to be the length that falls out from combining other physical constants in a certain way. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [November 30, 2010, 12:49pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/78 "2010-11-30T12:49:21Z")
The argument that if the universe has infinite age, we cannot define the current age, because that age is already infinite, looks a lot like a variation on the axiom of choice. You can argue until the end of time about the axiom of choice. So far as we know it can neither be proven or disproven. Like a lot of axioms, the fun comes in working out what happens with both possibilities. There isn’t a logical problem is talking about the universe as having an infinite past, but it helps to be quite clear about what is being said. How well this maps to any sort of reality is another matter. ---
**Author:** ![KellyCriterion](https://avatars.discourse-cdn.com/v4/letter/k/b3f665/32.png) [@KellyCriterion](https://boards.straightdope.com/u/KellyCriterion)\ **Post date:** [November 30, 2010, 2:05pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/79 "2010-11-30T14:05:33Z")
> [@Spatial\_Rift\_47](#): > > Sure it is. It’s just that the divisions quickly become infinitesimal. What does this mean in the real world? On the straight line that separates you and me , there’s either an infinite “amount” **(urgh!)** of positions that can be occupied by me, or there’s a finite amount. Explain how I might move “infinitesimally” closer to you along this line. ---
**Author:** ![Spatial\_Rift\_47](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@Spatial\_Rift\_47](https://boards.straightdope.com/u/Spatial_Rift_47)\ **Post date:** [November 30, 2010, 5:14pm UTC](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011/80 "2010-11-30T17:14:02Z")
You do it by moving an infinitely small distance. In better language, what that actually means is that the distance you move is less than some ϵ for an arbitrarily small choice of ϵ. [Previous page](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011.md?page=3) [Next page](https://boards.straightdope.com/t/is-an-infinite-past-logically-impossible/562011.md?page=5)