Q: In an infinite universe, does everything that’s possible have to happen somewhere?

The original question was: Lets say that we determine that an event is physically possible. So that means the probability of that event is greater than zero. Right? So my question is this. Is there any sense in saying that the event will NEVER happen even if it has a non-zero probability? In other words, if it can happen, will it happen given enough or infinite time? Does it have to happen eventually?

Physicist: There are a lot of subtleties in this question!  The answer is basically yes, but there are some sneaky assumptions worked into that.

Right off the bat, a probability is always based on “priors”.  For example, “the probability that it will rain today” or “the probability that a 4 will be rolled” are not, completely on their own, well-defined probabilities.

The probability of a particular event is dependent on “priors” or “conditions”.  In order to know the probability of getting a particular result, you must have prior knowledge of what die is being rolled.

Before you can find a probability that’s an actual number, you need to know something about the priors.  The probability that it will rain depends on the place, time, season, whether or not it rained yesterday, etc.  The probability that a 4 will be rolled depends on what kind of die is being rolled, if it’s weighted, or even if dice exist.

In this general case, you may have a tiny, non-zero probability, but if it’s based on priors that are themselves impossible, then the event itself may also be impossible.  You can generalize the priors a lot, but you can never quite get rid of all of them.  For example, it may be possible to prove, beyond a shadow of a doubt, that the probability that a unicorn is violent is 5%, given that unicorns exist (when a scientist says “given”, they’re about to spit out some priors).  However that doesn’t guarantee that a violent unicorn must exist, because it requires that unicorns (with their magic, and virgin sensing powers, and whatnot) must already exist in general.

But (and this may be more at the heart of the question), given an infinitely large universe that’s more or less homogeneous (lots of “stuff”, like the part of the universe we can see with telescopes, instead of just being empty forever), then pretty much anything that’s remotely possible, that could conceivably be the result of a string of remotely possible causes (e.g., horse begets unicorn begets violent unicorn), will happen somewhere.

As a slightly less fantastical example, we can imagine creating, say, an array of Tinker Toys™ linked together and spanning light-years of space.  If this could be instantaneously constructed, somehow teleported into existence, then it would continue to exist for a little while (its self-gravity would start to crush it in fairly short order).  It is not, by itself, an impossible configuration of stuff.

Light years of tinker toys. Its existence is possible, but there is no set of circumstances that would lead to it happening.

However, due to laws like the conservation of mass, the light-speed speed limit, and the nature of gravity, there’s no way to put together a structure this big and massive (or for it to form naturally).  Long before you even got to the business of connecting everything together you’d find that there was already far too much mass, far too close together.  No matter how fast you tried to get everything in place you’d find that the arrangement is smaller than its own Schwarzschild radius, which means that a Tinker Toy™ construction of this size and density is already a black hole (“teleporting it together” gives it a little time because no part of it would “know” that it was too big for a while).

So, we can sit back as say things like, “well, there are X many possible arrangements of atoms, or quantum states, or whatever, and this is one of them…” and can then calculate a ball-park estimate of the probability of this massive wooden grid existing (“1/X” maybe?).  Unfortunately, the answer we’d get would be incorrect, because the priors are messed up.  While it could exist, it could not be formed.  So simply knowing that something is “possible” doesn’t mean that the universe can ever be in a state that would eventually lead to that thing happening.

As far as happening eventually: if it’s not happening now (in an infinite universe), it almost certainly never will.

The tinker toy picture is of a “clockwork” tick-tac-toe playing computer.

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39 Responses to Q: In an infinite universe, does everything that’s possible have to happen somewhere?

1. Daniel Hazelton Waters says:

Yes if the universe expands forever creating space for events to occur then eventually a whole universe exactly like what we observe now will pop into existence. If you believe current theories that conclude that stuff just pops into existence given enough time in space. Usually it is just particles that constantly comes in and out of existence but it allows for any combination of particles by chance eventually. Don’t be surprised at any given event because as far as we now it is all possible.

Given an infinite universe, I would think that all of the Hilbert Hotel paradoxes would apply and that if a given configuration of the universe exists now, it will exist again an infinite number of times.

3. The Wonderer says:

Everything is possible if there are an infinite amount of universes. In smaller infinite amount of those our physics don’t work so anything can happen.

4. hateyou says:

Points of reference are destroyed when infinities come into play. IMAO there’s no place for infinities in physics yet its fun speculation.

Everything already has been, and is happening now(maybe).eg
1/infinite passed by as the light reached your eyes from your monitor, it occurred within those particles of light as they traveled to you, an infinite amount of times.
2/Infinite infinities occur an infinite amount of times within a single atom(and in all the infinitely small space between said atoms).
3/Wonder if we can help this local version of relativity we inhibit to merge our local universes and would we be causing something analogous as cancer on a being who’s atoms we might inhibit ?at what point would this cohesion of galaxies and universes cause problems to something’s existence ?

5. Samantha says:

My question is this:
If there is a chance that something can happen, and the exact same situation happens an infinite amount of times, will that possibility have to happen?

6. The Physicist says:

Yup!

7. james says:

In response to the first comment. That is quite an absurd stretch. First..things just dont pop into existence uncaused. Virtual Particles appear in an existing universe–not out of nothing.
You are buying the atheist line which is highly biased. Most went into the field of Origins as atheists–as University and Pew research polls show–they did not become atheist from what they learned from their field. They claimed the universe just “appeared designed” and set to prove the universe was not highly improbable. What they found was the math was a trillion times worse than just what we can see. The universe as a structure is 120 places right of the decimal point for just one of its parameters let alone all the others. Thats the opposite of what they expected. But again they retreat to the comic book multiverse.

So lets get this straight–an infinite universe maker machine that creates everything solves the problem of why we appear designed? The fact that a pinpoint of energy just happened to have the right laws and trajectories to build observers with consciousness who can comprehend that very pinpoint of energy is, Im sorry, far worse than a string of tinker toys.
Everything is not possible. Infinity itself is not possible and its even the more incoherent to propose an expanding infinity. No probabilities in all of reality get you to human beings popping out of nothing. The day that odds can build a code that lays out the precise spatial location of the 4 chamber heart, its electrical and pressure system, and build all the senses to observe and comprehend that reality could never come– no matter how much time and space were involved. The only reason it is even considered is the ones who propose it have a pathological bias toward naturalism.

8. Zebra says:

“If there is a chance that something can happen, and the exact same situation happens an infinite amount of times, will that possibility have to happen?”

Ask a statistician: no it doesn’t *have* to happen. A probabilist would say that it happens “almost always”. If I toss a fair coin the chance of a head is 50%. If I toss a fair coin an infinite number of times the probability of getting at least one head is 100%. However there is no physical or mathematical reason why I can’t toss an infinite number of tails, and no heads. In fact this is as equally likely as any other sequence of heads or tails. Take all sequence of length N (number=2^N) and then consider the number of them that have no heads(=1). Then the proportion with no heads =1/2^N which approaches 0 as N approaches infinity. But there is always 1 sequence of length N with no heads.

Hence 100% probability means “almost always”, it doesn’t mean “it has to happen”.

9. steve l says:

This is the most nonsensical meme floating around the Internet.

Consider the natural numbers 1, 2, 3, …

There are infinitely many of them … so 2 must show up more than once, right? Manifestly wrong.

But say we are talking about states of matter in a finite region. This would be modeled by using finitely many numbers, 1, 2, 3, say, and making an infinite list.

1, 2, 3, 1, 3, 1, 3, 1, 3, 1, 3, …

You say 2 must appear again … but it doesn’t. If you have finitely many states and infinitely many trials, all you can say for sure is that at least one state must reappear infinitely many times. But any particular state, such as the state that defines “you” or a pink elephant or a galaxy; might appear zero, one, 47, or infinitely many times.

It’s amazing how many otherwise smart people are fooled into thinking that “in an infinite universe, everything must happen.” This is manifestly false.

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11. Paul Czerner says:

No, impossible things can’t be possible, or they will no longer be impossible. There are some things that will be impossible because the infinity of possible things is infinitely greater than the infinity of the size or length of the universe.

12. Mariano Quiroga says:

Infinity is an awkward concept, we just can’t handle it extensively… Our minds can only imagine big things, “unimaginably big” things, but not infinity (in size, time, or may be multiple dimensions) . An infinite universe means that there must be other life sustaining planets, and given enough space and time, there should be another planet similar to the earth. There must even be an exact copy of our earth, not just somewhere, but everywhere, perhaps with subtle diferences between them, including some earth with the same country configuration, population, history, and even another “you” (aka the doppelganger), and being infinity that infinite, there must be infinite “yous” living in infinite earth like plan ets and at every moment of eternity. That bizarre seems to be probabilities at infinity, given enough space and time, if you could be possible once, then you could be possible many, infinite times

13. Stan says:

The number of possible events is infinite so it is practically impossible for any particular event to happen twice exactly in the same way. If we have an infinite universe and finite number of possible events, we can be sure that any particular event will happen somewhere sometimes. But the number of possible events is not finite.

14. Sean Hale says:

From a non scientific and perhaps a more philosophical viewpoint I would say when we use a term such as “everything possible,” we are putting a human viewpoint on something we as humans cannot possibly understand. Our reality is only determined by a chemical reaction in our brains based on our senses and years of evolution as human beings. What we perceive as possibilities may not even be real. If humans never came to be, then perhaps no one would ever imagine a unicorn and it would even be an option as a possibility.

15. Dale says:

Consider that nothingness is infinite and the “Universe” (something which is not nothing) resides in nothingness. One second after the Big Bang the Universe occupied a given amount of space surrounded by nothingness. At that point the Universe was measurable or finite, but expanding. Although we are incapable of comprehending its capacity today, it is still finite. Our inability to comprehend its size has given us license to label it as being infinite. Once that is done we lose the laws of logic and scientific proof and “anything” not only becomes possible, it becomes mandatory.

Then consider that if infinite means infinite we must concede that there are an infinite number of Big Bangs in various stages taking place throughout the infinite void. Some may expand and contract cyclically, while others may continue to expand and overlap others. If we are to loosely use the term infinite then yes, Samantha, there is someone out there who is exactly like you riding an unicorn off into the sunset(s)… an infinite number of times.

16. betaneptune says:

“Before you can find a probability that’s an actual number, you need to know something about the priors. The probability that it will rain depends on the place, time, season, whether or not it rained yesterday, etc. The probability that a 4 will be rolled depends on what kind of die is being rolled, if it’s weighted, or even if dice exist.”

The probability of an event is a function of what you know about the event, or what you choose to know. For example, life expectancy of humans is different from the life expectancy of males vs. the life expectancy of females. For any given person, it depends on what you know, or choose to know. You could, for example, ask what the life expectancy is of people living in a certain country. A more extreme case is having cancer.

So probability is simply the ratio of outcomes that satisfy your criteria for a certain event to the number of equally likely possibilities in the process (or more precisely, possibilities weight by how often you will encounter any given one) that you choose ot that can’t rule out.

Another example: Suppose there is a blood disease that kills 10% of all people. What are the odds that any give person dies? 10%. Now, suppose there is some agent in the blood of some people that reduces the likelihood of dying from this blood disease, and assume that 50% of those who have the agent are protected from the disease. The probability of any given person dying of this disease now depends on what you know! If you know a person has this agent in her blood, you will calculate different odds. So, if you don’t know about this agent, or don’t know who has the agent in her blood, all you can say is that there is a probability of 10% to die. If you know who has the agent, then the odds of those who do and those who don’t will be different. It depends on what you know. What you know determines the ensemble of equally likely possibilities that you choose or that you can’t rule out.

Another example: If you know a person just jumped out of an airplane, you would calculate a rather different life expectancy than for the general population. You can say that 100% of people who jump out of an airplane seven miles up will die rather soon. But you get different odds if you ask how many people will die before they reach 50.

There are only two situations I can think of where there are unique objective odds: quantum processes, and (perhaps only certain) simple games of chance. For quantum processes, the exact odds are calculable by the laws of quantum mechanics. Simple games of chance will have only one reasonably possible set of outcomes because only one ensemble of possible events is easy enough to work with.

OK, a third possibility: absurd possibilities. The probability of a human being able to jump to the moon is zero.

17. Floyd McMullen says:

Just the fact that the question has been asked is trully unbelievable.
Ive never really studied this before but I feel I have a better hold on
the fact of infinity. No number can be placed on it, and no difinitive word can
discribe it. Everything is possible and is being possible right now from word to word forever. Greay thing about itbis it makes us small but also puts above evrything else. We live in our own little bubble and will only see and feel this untillwe die in this life and become part of the next. But if we werent part of the whole which is another senario the whole wouldnt work. Want to talk. floydndakota at g and mayl.

18. Floyd McMullen says:

I keep going back and reading other post and just cant believe what Im reading.
Here is is a mindbender for you. Look at the a key and understand there is an infinite amount of times your finger has touched that key. An infinite number of timez you thought about touching it. An infinite time it has happened going to happen and is happaning at the time you did it. No number or word for it. Well yes there is.

19. Floyd McMullen says:

I tried my best in my last comment to explain not what I believe but what I know. I am going to give one example of that knowledge. Think of one blood cell in your body with the understanding that there are an infinite amount of infinite infinitys and come up with a scientific equation for that. Anything is and is happening right now. Even the electrical sparks that are flying through your mind as you read this have an infinite numbers of infinities in them. We are tought begining to end our whole human lives and dont even realize we are oart of the whole. I am really starting to understand this more every day. What power there must be inside this

20. Floyd McMullen says:

Sean you ard absolutly right. There are infinitys where hmans never came to be thats the fun part of it. Of course there are also infinities where Darth Vadar is as real as we are here. Sounds crazy but it is true. Mutiple universes, how small a thought.

21. Prakhar Raj says:

In an infinite universe it is mandatory for an event to continue infinite number of times.Now infinite means endless and since possibilities are finite it means that either
every event has to happen or there is a cycle that will continue before a particular possibility takes place.see suppose cycle happens then in an infinite universe every possibility in that cycle happens infinite number of times.So in a way there are finite cycles possible the probability of that cycle happening is finite.so imagine if a cycle takes place then the probability of other cycles is zero.it can only happen if there is only one possibility.so to take it like an event have zero probability there must be an event that is bound to happen no matter what.If we give no weightage then it is entirely impossible to have an evnt to have zero probability.It is bound to happen.
So either only one event takes place or every event takes place.if there are more than one possibility then no event can be impossible that is 0 probability

22. Prakhar Raj says:

Stan i would lke to say that had there been infinite possibility the probability of one event would be exactly zero.Think about it

23. Spencer says:

So if there’s an infinite possibility that something exists, isn’t there also an infinite possibility that something doesn’t/can’t exist?

24. Jeff says:

I have been experiencing happenings that I have already lived, truely. No matter whether back or forwards of where I am situated currently as in home or work life context. I happen to recognize straight-off what is about to occur as opposed to a memory of ‘oh that thing…’ . Does this mean there are two universes and due to my both acute and broader understanding of places and times and events mean I can be in tune with both of these? I’m speaking here of entire sections or chapters of life entering my daily time frame again for just a second time. Nothing major happens, but I would say one small change in any specific seems to put that area to rest. Other than that its becomes very boring watching it unfold again. At first I thought I may not have completed something the right way, a kind of second chance if you like. Sounds all to common a problem I realise. But I’d love to hear a few views from others please.

25. Jeff says:

If I may continue for a moment Moderator: To me deja vu would be just too simple an
explanation as I’m required to live through the exact wholeness of the situation for the
second time around. Daily life continues along eat sleep wake, but I also see things
happening or not for others also, that have absolutely nothing to do with my sphere, or
entanglements whatsoever howsoever. I can tell you the exact things that I have purchased recently, and how far I got with the item in the previous time frame. Did I have too much on my plate that time and was somehow transfered to complete at a later date? A sort of kindness to the here and now self via sorting through an entirety consciousness phenomena? ie a leahway of time to accomplish? Would it be okay to go as far as saying some entity organised this or is even writing this rather mad of a person? To dispute deja vu might be a way to relieve plain truth, or not. And indeed, what if something comes around twice, for real. How would we go about proving it did happen twice, certainly a first time, first. Then the second. If we take a photo of something, we store it on a hard drive, time goes by and new events take place, but then we take a photo of something, that you absolutely know and remember you have it on the hardrive but cannot be bothered to go and check. Or the very specific example I had some years ago of throwing out a magazine picture, only to see it
entirely as a brand new never before published page that very next day. It felt incredible, but it did happen. And thats where it all real lies actualy, I believe we may just possibly make our own realities appear again, not make our memories appear again, just because we’d like to have or see something all over again. Something metaphysical if you so like? There seems to be a very tight crunch moment in time where we get have or lose a chance at something appearing possibly based on us believing we’re about to lose something intrinsic or badly needed by our inner self/soul for that time stretch to complete normaly before going onto the next chapter. And it occurs. One could almost swear all things have come together for the event simply by overwhelming power of an almighty wish in the background of our self. And yet I have seen specific news broadcasts appear again over time as if a new item, to me it just appears at that moment as if, due to my pre-existing memory of it already, as quite boring and they shouldn’t put old stories back on tv. I had no real interest in that story, but there it was out in front of my eyes. I return to, how can find out its been twice for real? Do we want or need two of each thing?

26. floyd says:

Everyone is going to have to get used to the fact that they’re not 12345 universes multiverse doesn’t even sound right there are an infinite number of universes that have infinite number of infinities inside of them. I don’t need to be a mathematician to figure this out. As far as our understanding of that it just isn’t going to happen. We can only see so far with our human minds and instruments inward or outward. We live in a little bubble that we comprehend as beginning and end from birth till death. I feel lucky to have an opportunity to live within that bubble. If we were to ever understand infinity I believe we will become gods. Anybody ever watch Star Trek next generation? Pretty sure they’ll be somewhat like Q

27. Floyd says:

hateyou you you are so right. I haven’t seen anyone that understands this just like you do. I couldn’t of said it better myself. Please get back to me I’m so happy to have seen your post

28. Shawn E Dorney says:

in an infinity of all, there is neithor possible, probable, not possible etc… its a matter of infinate chances. example, there is the possibility of there being an infinate amount of planets, stars, moons, and other physical and prehaps non phisical things we cant even fathom. another example is to say life has an infinate amount of chances to occur somwhare under conditions familliar to us and also where we cant even understand how it could. If you truely beleive that the universe is infinate than there is a infinate amount of chances for anything to happen somewhere. has nothing to do with probability at all but a matter of where and when. I dont mean to say that aliens are going to land on earth some day because it is a matter of when, because the way things unfolded in our spec of wherever are the way they are and thats that. but if space is infinate we are also infinatly small and take up a amount of space that is infinatly small. if i spent all my time trying to drop a penny from hotel dubai and have it land on its side after bouncing 7 times its extreemly unlikley not to happen, but if i did it forever, for infinity, it would eventually happen an infinate amount of times

29. Kaol says:

There have been several comments here to the effect that the universe will last forever. But that isn’t the conclusion of modern physics, and neither does it reflect the natural world we see around us – where everything occurs in cycles of day and night, sunrise and sunset, spring summer and winter, waking and sleeping. Likewise the universe was said by the ancient Vedic seers of India 4 thousand years ago, to go through periods of rise and fall, or phases of creation and destruction if you like, with a fresh universe being created after the dissolution of the previous one. This model still allows for ‘everything that’s possible have to happen somewhere’, only extended over an infinite number of of universes that blink in and out of existence -one after the other- after billions of years. And given that those ancient seers of India correctly estimated the age of the (universe) thousands of years ago, they could well be correct in this instance too.

Science quote………………

“The Hindu religion is the only one of the world’s great faiths dedicated to the idea that the Cosmos itself undergoes an immense, indeed an infinite, number of deaths and rebirths. It is the only religion in which the time scales correspond to those of modern scientific cosmology. Its cycles run from our ordinary day and night to a ‘day and night of Brahma’, 8.64 billion years long. Longer than the age of the Earth or the Sun and about half the time since the Big Bang.”
― Carl Sagan, Cosmos

30. Paul S says:

An eternal universe in that it not having a beginning. Every possibility would already be true. And as we currently understand and observe the universe would be as it is. The universe being comprised of everything. And everything not being eternal too.

31. Chris says:

In a universe with a near infinite number of stars the most improbable things can happen. The most interesting being pure bliss and the absence of suffering. Every life that ever lived could be reanimated and returned .

32. Angel says:

@Chris

I am afraid that is not how probability works.

33. C.V says:

Everything has already happened and nothing can happen that has not already happened.There is no way that infinite does not exist , because it would mean that there is nothingness, but nothingness can not exist in real or not real world.
Now infinite can not exist in real world as we think of it, so it leaves us to face that nothing is real in a way we think it is and now we are back to the fact that everything is possible, but we are just one of the possibilities which again are infinite.
Think of it as rule set that is given to our reality, fact that there are infinite possibilities
does not mean that we can ignore our rule set.
What is interesting is , will we ever be able to connect to other realities trough this and most importantly, what are we in all of this.

34. Gary Kelnhofer says:

I like to use the Sun as an example. Imagine for a moment if you will, that we have unlimited computing powers and speed. Then input every bit of information about the Sun into it. This includes its exact size, weight, what its made of, including every particle. The information that will be input into our computer about the Sun will be beyond our human capabilities however, if we could actually input every bit of information including dust particles falling from space we would be able to calculate everything that the Sun does. If the input information was precise enough we should in my opinion be able to predict the individual heat waves radiating off the suns surface. Imagine isolating a particular wave of heat and being able to explain its existence with absolute precession. Now take all of that info and add it to say, Earth. Now we can predict our temperatures, storms and much much more. Now we need to inpute the moon’s info and all of the planet’s, Stars and cosmic dust into our computer. With the information collected we could calculate something so small as when and where a leaf will sprout on a specific tree or where each raindrop will land. I know our human minds cannot conceive such computing powers but we can’t rule out the possibility that it doesn’t exist somewhere in a galaxy far from us.

35. Floyd says:

Once you realize everything is possible, and everything is not possible I think you have a good grasp on infinity. We as humans in the middle of what I like to call the “Nowverse” have limited knowledge from this sphere outward. There are without question many species animal or vegetable on other planets in other galaxies in other universes in other infinities I’m sure even within our own bodies that ponder on these same questions. We have got to learn to live outside our box. The distance we’ve come this past century is only a drop of water in a endless sea of knowledge. Scientists are going to have to do the same. The great theorist that we’ve had in the past 2000 years have had some very good ideas many for which we’ve been given answers that mankind is always needed. But this is just human knowledge our own arrogance thinking. That’s why I love to hear it when people say that we are the only intelligent life it speaks volumes about them and their intelligence. We cannot be bottled up by ignorance. I’m no scientist I’m no scholar. I know a little bit about everything but not a lot about one specific thing. And I tend to ramble a lot. But I’m not going to limit my mind to what it can understand. And everybody has their own feelings about this. But as far as I’m concerned Anything is Possible everything is possible but an Infinity it’s also not possible does this make sense to anybody

36. Gary Kelnhofer says:

I believe everything is finite however, many believe in infinity because our minds and technology cannot see the end.

37. RR says:

Not everything is possible. There is not the possibility that my present self, within the next hour, could travel to Proxima Centauri or even to the moon for that matter. Therefore, though there is infinite space and time for the possibility for different circumstances there are finite parameters.

38. Floyd says:

Present self present Universe present time present place. I guess you’re forgetting about all the other universes and all the other universes that don’t exist and the ones that do exist within those universes Jesus Christ in order to understand Infinity you’ve got to think outside the box and that box is college I think everybody shouldn’t have an opportunity to go but as far as using it and practicality other than quoting theories to people it doesn’t mean anything to me it means a lot more it means that everything that I haven’t done here I’ve already done and will always be doing but for the answer to that question no you don’t have to be able to do everything but you can you already are you’re not you haven’t even heard this question and some universes times and places I’m going to stop rambling cuz there’s a lot of people to understand what I’m talking about here but there’s a lot to come in and Bash on me