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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23 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.

  2. Braden Flowers says:

    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 The Physicist says:


  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

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