(PhysOrg.com) -- As far as astrophysicists can tell, the universe is expanding at an accelerating rate, and will likely continue to do so indefinitely. But now some physicists are saying that this theory, called eternal inflation, and its implication that time is endless pose a problem for scientists calculating the probability of any event occurring. In a recent paper, they calculate that time is likely to end within the next 5 billion years due to some type of catastrophe that no one alive at the time will witness.

The physicists, Raphael Bousso from the University of California, Berkeley, and coauthors have posted a paper detailing their theory on arXiv.org. In their paper, they explain that in an eternal universe, even the most unlikely events will eventually occur -- and not only occur, but occur an infinite number of times. Since probabilities are defined in terms of the relative abundance of events, there would be no point in determining any probabilities because every event would be equally likely to happen.

"If it does occur in Nature, eternal inflation has profound implications," write Bousso and coauthors in their paper. "Any type of event that has nonzero probability will happen infinitely many times, usually in widely separated regions that remain forever outside of causal contact. This undermines the basis for probabilistic predictions of local experiments. If infinitely many observers throughout the universe win the lottery, on what grounds can one still claim that winning the lottery is unlikely? To be sure, there are also infinitely many observers who do not win, but in what sense are there more of them? In local experiments such as playing the lottery, we have clear rules for making predictions and testing theories. But if the universe is eternally inflating, we no longer know *why *these rules work.

"To see that this is not merely a philosophical point, it helps to consider cosmological experiments, where the rules are less clear. For example, one would like to predict or explain features of the CMB [cosmic microwave background]; or, in a theory with more than one vacuum, one might wish to predict the expected properties of the vacuum we find ourselves in, such as the Higgs mass. This requires computing the relative number of observations of different values for the Higgs mass, or of the CMB sky. There will be infinitely many instances of every possible observation, so what are the probabilities? This is known as the 'measure problem' of eternal inflation."

One solution to this problem, the physicists explain, is to conclude that time will eventually end. Then there would be a finite number of events that occur, with the improbable events occurring less often than the probable events.

The timing of this "cutoff" would define the set of allowed events. Thus, the physicists have attempted to calculate the probability of when time will end given five different cutoff measures. In two of these scenarios, time has a 50% chance of ending within 3.7 billion years. In two other scenarios, time has a 50% chance of ending within 3.3 billion years.

In the fifth and final scenario, the timescale is very short (on the order of the Planck time). In this scenario, the scientists calculated that "time would be overwhelmingly likely to end in the next second." Fortunately, this calculation predicts that most observers are "Boltzmann babies" who arise from quantum fluctuations in the early universe. Since most of us are not, the physicists could rule this scenario out "at a high level of confidence."

What would the end of time be like for observers around at the time? As the physicists explain, the observers would never see it coming. "The observer will necessarily run into the cutoff before observing the demise of any other system," the scientists write. They compare the boundary of the time cutoff to the horizon of a black hole.

"The boundary ... can be treated as an object with physical attributes, including temperature," the authors write in their paper. "Matter systems that encounter the end of time are thermalized at this horizon. This is similar to an outside observer's description of a matter system falling into a black hole. What is radically new, however, is the statement that we might experience thermalization upon crossing the black hole horizon." Yet the thermalizing "matter system" would still not notice anything unusual when crossing this horizon.

For those who feel uncomfortable about time ending, the physicists note that there are other solutions to the measure problem. They don't claim that their conclusion that time will end is correct, only that it follows logically from a set of assumptions. So perhaps one of the three assumptions underlying the conclusion is incorrect instead.

The first assumption is that the universe is eternally inflating, which is a consequence of general relativity and well supported by the experimental evidence so far observed. The second assumption is that the definition of probability is based on the relative frequency of an event, or what the scientists call the assumption of typicality. The third assumption is that, if spacetime is indeed infinite, then the only way to determine the probability of an event is to restrict one's attention to a finite subset of the infinite multiverse. Some other physicists have already looked into alternatives to this third assumption.

Whatever happens in the next 3.7 billion years, Bousso and his coauthors' paper will likely be spurring a variety of reactions in the near future.

**Explore further:**
Our universe at home within a larger universe? So suggests wormhole research

**More information:**
Raphael Bousso, et al. “Eternal inflation predicts that time will end.” arXiv:1009.4698v1

via: The Physics ArXiv Blog

## CTD1

http://www.dailyg...yes.html

and it's even attributed to string theory:

"Our calculations show that we would think that the expansion of the universe is accelerating," says Prof Senovilla. The theory bases it’s idea on one particular variant of superstring theory, in which our universe is confined to the surface of a membrane, or brane, floating in a higher-dimensional space, known as the "bulk". In billions of years, time would cease to be time altogether.

This model actually may be time symmetric in analogy with ripple spreading at the water surface - they're dispersing at both large, both small scales. For example, dark energy/quintessence models suggests frozen universe before 11.5 billion years or so.

http://www.futuri...universe

## dtxx

## ShotmanMaslo

Can someone explain where is teh problem?

## iWander

Bloody Cantor...the guy was crazy! An infinity is the perfect cancellation, it does not exist. If it did exist, there would not be multiple infinities, but a single infinity viewed from different perspectives. As you observe differences, we're not in an true infinity, but certain dimensions may have apparent infinite length. I say apparent as they will do what they do, until it reaches the end.

The article is saying that with an infinite amount of events, one of those events is bound to end time. As time passes, the probability of that happening increases.

The universe could end with the various forces and fields coming apart, just as they came together.

Everything ends, but it may mean something new will appear but as we are bound to time, we're dead.

## Skeptic_Heretic

Basically, if time is infinite, we should see reverses in entropy as they aren't restricted, simply unlikely.

That's the problem, we're not seeing enough weird stuff. Now I don't agree with the problem, I think it's philosophical ramblings based on a lack of understanding. No, you're not understanding the concept of infinity. There is no greater or lesser when comparing infinite quantities.

## frajo

One underlying assumption they forgot to mention is the inflation hypothesis itself.

One conceptual error is the mixing up of the inflation term of the inflation hypothesis (the nearly instantaneous expansion shortly after the BigBang) with the contemporary accelerating expansion of the universe which is a conclusion based mainly on SN Ia observations and the hypotheses of their inner workings.

I don't see any falsifiable predictions around here.

We need better SN Ia models.

## HoboWhisperer

## Skeptic_Heretic

## kasen

Right. You want less clarity to make something look less philosophic.

This seems to me like a misunderstanding and misuse of the mathematical infinity symbol and statistics. They did say they might be wrong, which is commendable, but won't appease the press. I am not looking forward to reading about this in the local tabloids.

## Noumenon

## HoboWhisperer

Read up on Georg Cantor's Set Theory.

## frajo

## Noumenon

Probability 'seems' like a relative concept so the error maybe expecting universal application from it (regarding infinite events).

## Skeptic_Heretic

Read up on the physical rammifications of infinity. ie: Hilbert's Hotel. You are right, but going a little bit OT we can prove that the set of real numbers has a higher cardinality, aleph-one or higher, than the set of natural numbers has, aleph-null. But without a conclusion there is no measure of cardinality.

You have two cars moving at different speeds for an infinite amount of time, which travels a greater distance? You can measure for a point in time, or for a given equal instance of like quantity, but at that point you create an upper boundary, thus reducing infinity to non-infinity. That is the only measure of how you can create cardinality, by instituting a boundary condition.

## Skeptic_Heretic

## Noumenon

## KevinPEdwards

However, that doesn't change what you're chances are to win the lottery in that one instance. Yes if you were to play the lottery indefinitely you would win an infinite number of times and lose an infinite number of times. You're conception would be that you lost a larger amount of times, but for every instance you lost someone could point to a unique instance you won.

## getgoa

For all practical purposes the only human thing here is the meteorological read of 50% and all else is basing more or less on the assumption that inifinity is finite and that could be very well a philosophical argument.

Its philosophy because man invented time on earth it is not infinite nor expansive but as the assumption was applied finite.

This develops into distances and man does not know time without distance, for all practical purposes in this argument you could get away with saying the world is flat and all man got off the ark the day before yesterday? its very wicked in the bible but the time is shown with disrespect for light and distance.

And so this shows how the bible can return a philosophical argument into a light argument just from knowing very basic phrases in the bible.

## ShotmanMaslo

Not if the probability of such event is zero. Then it wont happen, even in infinite time.

## Skeptic_Heretic

## ShotmanMaslo

No, if the probability to violate causality is zero. You may eventually get some macroscopic manifestation of quantum effects (like walking through a wall..) because probability of such thing is not zero (altrough extremely small), but what does it have in common with ending time? There is no quantum process that can end time..

Why should we see reverses in entropy and weird stuff? Given infinite time, they will eventually happen (maybe even happened?), but they will be so rare that probability of us observing them is virtually zero. I dont see how lack of "weird stuff" implies finite time.

## KevinPEdwards

## Pkunk_

## KevinPEdwards

I believe it's if you can find an injective map from your set to the set of natural numbers or not.

## joefarah

Given his track record, I'll bet the end (of time) is a lot sooner than even a hundred thousand years before I subject myself to this lunacy. Come on now... for lack of a better measure, the universe would be as likely to last another 13 billion years than as not. I'm tired of simulations that are not well grounded.

## Gawad

Eh. Well the hyperreals are designed for that (*R). Although I have no idea if they would help in this case they do let you work with and comapare infinites.

Anyway, I have the destinct feeling those reactions "Bousso and his coauthors' paper will likely be spurring...in the near future" are going to be mostly giggles from the back of the room. Please, this is a rediculous paper. "Brousso! The math doesn't work!" "O.k., what if, say, time were to end in 5GY?" "Oh yeah, o.k. now the math works"...long silence..."OH MY GOD THE WORLD IS GOING TO END IN 5GY!!!" ...stares..."You're not serious!?!" Releaved exhale. "Well, no, not really..."

## Gawad

## baudrunner

In this universe, existence is a finite band in the three-dimensional spectrum of an expanding entity. What is being created at the periphery is new, we are old, and what has been is no more, but the creation front will continue to expand beyond into incomprehensible depths, beginning the process toward an eventual demise.

## otto1932

## DoubleD

In an infinte universe, it seems that both events (time ending vs. time not ending) are equally probable.

Am I missing something here ?

## Gawad

http://motls.blog...tml#more

Anyway, it a hilarious read to boot.

## A_Paradox

1/ it wont be a "bang" but a whimper with no echo

2/ seems like it will favour borrowers more than lenders

## Quantum_Conundrum

"My sheep hear my voice, and a stranger they will not follow..."

## A_Paradox

1/ it wont be a "bang" but a whimper with no echo

2/ seems like it will favour borrowers more than lenders

## AAhhzz01

Of course...

Time could have ended since I started reading this article. Paused for an indefinite, but non infinite period, reversed direction, wound all the way back to the big bang, rebounded from that event and wound forward again to let me finish this post.

I, with a conciousness only attuned to a forward motion in time, would never notice the changes would I?

## no1nose

## Mr_Man

Thus, the universe expands and time goes on infinitely until "infinite" ceases to have any meaning.

If the universe "stops expanding" or if "time stops", that is it - there is no way for an outside observer to exist, no way to measure it.

This also means that anything we consider to be infinite also is not possible for it to really be infinite.

I always thought of time ending as heat death of the universe - all matter decaying into the lowest level of energy until the universe consists only of that, all particles cooling until the universe has all mater symmetrically smeared through out, perhaps at this point there is no energy left to excel expansion?

## droid001

## Husky

## Husky

## MathieuHamaekers

## mrlewish

## RobertKarlStonjek

In other words the infinities cancel out. If we include an observer then the infinite universe starts to make sense ~ the maximum observable interval and spatial extension are finite for any one observation (snapshot). If we ask about possible events in the Milky Way then we first observe that total interval for the existence of the Milky Way is finite, as is the existence of any body or particle. With these finite parameters one can then model probabilities on a per-frequency-per-interval-per-space-time region and the infinities are overcome. It makes far more sense than the Big Bang Model...

## RobertKarlStonjek

In other words the infinities cancel out. If we include an observer then the infinite universe starts to make sense ~ the maximum observable interval and spatial extension are finite for any one observation (snapshot). If we ask about possible events in the Milky Way then we first observe that total interval for the existence of the Milky Way is finite, as is the existence of any body or particle. With these finite parameters one can then model probabilities on a per-frequency-per-interval-per-space-time region and the infinities are overcome. It makes far more sense than the BB Model

## daywalk3r

So trying to "calculate" the probability of "time ending" for various future "points in time", while in fact understanding so little about the subject (and feel free to quote me on that), is about as perfect of an exercise in futility as it ever gets.. Almost as good as guessing the result of 1+1, while knowing numbers, but "not being so sure" how to add or substract them..

---

To me, it seems like the authors could use some lectures in basic logic, and then they might realise, that:

Probabilities do NOT define reality, but it is REALITY which defines the probabilities!

And if some people think, that "there is a probability of it being the other way around", it is hardly surprising that they actually believe (and claim to be able to explain):

## daywalk3r

Action/re-action, cause/effect, every event has a specific reason as to "why" it is actually happening..

There is no such thing as "everything will eventually occur within an infinite time frame". As long as it does not meet the very basic rules of consistence (and so existence) within its local environment (the local universe), it's just NOT going to happen. Period.

So far, most of the events which were ever observed or studied by mankind, had (sooner-or-later) allways a cause/reason attributed to it.

And the evidence is so crushing, that we have very little reason to believe, that there would be no cause/reason behind events currently not so well (or not fully) understood - ergo phenomena (I hate that word, it's being abused too much.. :)

So running around and spouting pearls like "everything will happen within an infinity, no matter how ridiculous it is.." and then even pulling conclusions from that, is ridiculous, to say the least..

## daywalk3r

Even time itself has to be treated "relatively", and therefor it does not matter at all wether it stretches or contracts ad infinitum. It will never reach the point of "infinitely small" or "infinitely large" within a refference frame of the "in situ" observer - ergo, IT WILL NEVER STOP.

Time could be considered nearing a stand-still (or the opposite), but only if you compare 2 different "points of view" - like, for example, when an external observer observes the time "slowing down" for another observer, which is closing in towards a black hole. The relative "time-flow" delta between them will at some point be so large, it could practically be considered as "infinite", though in reality, this point will never be reached..

## Pyle

I wonder if we knew the exact improbability of being somewhere else that we couldn't actually be there?

If he had one left, DA would be laughing his ass off about now.

## daywalk3r

And yes, seeing as probability is used to model reality, which actually gives some pointers as to from what "village" (or should I say "camp"?)

they are comming from, it's safe to assume, that there is quite a big "missing link" between what they believe in (QM/CI), and what you base your arguments on (GR/SR).

Although they are not directly saying, that what you wrote is wrong, there is reason to believe that they probably don't believe that what you wrote, is true :)

## chandram

## trekgeek1

So you are talking about Jesus' track record and his coming back and you are refusing to lend yourself to the "lunacy" of this article? You are sick of simulations that are not well grounded but you are a Christian? You've based your entire belief system on accepting without evidence or simulation. Get your head out of your........... well, you know.

## Benbenben

I flip coins: 50/50 head/tail

In fact, there are an infinite number of me(s) flipping coins,

1 per second,

from this time, forward

without cease.

The chance is large that, as 'me-all' continue to flip,

each of me will, on an individual basis, eventually have a flip result of 'head'.

There IS also an extremely small chance

that at least one of me

will never flip and get 'head'

(but instead will always get 'tail'...so don't feel too bad for this possible-me).

The chance of a me continuing to only get 'tail' and never any 'head' far all time, is so small

it might (correctly) be called infinitesimal but is still nonzero.

>>>Every possibility of infinitesimal probability,

must have at least an infinitesimal probability of never occurring.

## nuge

## oliverrp

## TDK

## Benbenben

I flip coins: 50/50 head/tail

In fact, there are an infinite number of me(s) flipping coins,

1 per second,

from this time, forward

without cease.

The chance is large that, as 'me-all' continue to flip,

each of me will, on an individual basis, eventually have a flip result of 'head'.

There IS also an extremely small chance

that at least one of me

will never flip and get 'head'

(but instead will always get 'tail'...so don't feel too bad for this possible-me).

The chance of a me continuing to only get 'tail' and never any 'head' far all time, is so small

it might (correctly) be called infinitesimal but is still nonzero.

>>>Every possibility of infinitesimal probability,

must have at least an infinitesimal probability of never occurring.

## A_Paradox

1/ it wont be a "bang" but a whimper with no echo

2/ seems like it will favour borrowers more than lenders

## plasticpower

I keep wondering, is the number of things that the human mind simply cannot comprehend and explain at this moment finite or infinite? Can we even comprehend infinity? Have humans ever observed true infinity in nature? Is it possible to say something for certain IS infinite with our current existing bank of knowledge?

As far as I can tell, the only things truly "infinite" are numbers, which is a concept us humans (who have not yet PROVED that anything is truly infinite), have come up with. Is the concept of infinity some kind of a glitch in our intelligence?

Are we forever bound to have incomplete theories to explain our world? We can't tie quantum mechanics with the standard model, our math allows for infinite sets and "imaginary" numbers that cancel each other out, we don't know if we can compute Pi to its last digit.. We don't have a complete picture of any part of this world. But we're good estimators.

## Skeptic_Heretic

## genastropsychicallst

## Noumenon

Hmm interesting, could you elaborate? [bot check]

(SH, thks for the laugh.)

## otto1932

## Husky

Also the theory implies that anything can happen and given enough time/space, WILL happen, so its inescapable conclusion that there must be a planet out there made out of swiss cheese and spare tires?

## Glen_Lincoln

## Noumenon

Not necessarily, it may merely mean that an infinite universe is not intelligible.

Given the nature of mind, an understanding of some aspect of Reality implies subjecting it to intrinsic a-priori conditions, ...an a-priori conceptual framework necessarily involving the intuitions of Time and Causality. Reality is not intelligible apart from being conceptualized by mind (truism)....

## Noumenon

## Noumenon

I think they define 'event' as one that occurs within the realm of possibility given the known laws of physics.

## Quantum_Conundrum

## MorituriMax

## dtxx

Suppose you do go 99.999999...% of c and after a day's time for the astronaut 5GY years has passed on earth. Time would obstensibly "end" for those on earth, but the astronaut would have only experienced 1 day of time. How long it will be until "time ends" depends on your frame of reference. Not every piece of matter in the universe is moving at the same speed or through the same intensity gravity well as we are on earth.

## Empyre

## 5thabove

John^^

## 5thabove

John^^

## Bob_B

## Sirandar

If the universe was going to end in 4 billion years because of an infinately improbable event it probably would have already. My bets are on a probable event that just hasn't happened yet.

## jsa09

Doesn't matter to me what the number is 5 billion or 25 billion or 5,000 billion a number from infinity is just plain wrong.

What is a fun experiment is thinking of buying an infinite number of lottery tickets in an infinite number of lotteries. I find it difficult to enter a lottery twice a year and bemoan the loss of money those tickets cost.

Even when I know I will win the lottery one day (If I lived that long).

## Quantum_Conundrum

The odds of winning the lottery are small enough, and the prizes small enough that you would have a net negative if you played the lottery infinite times, even if you won infinite times.

## Kingsix

Lets make a theory and form assumptions to support that theory. Sometimes it makes about as much sense as mythology.

Here is my new theory of everything.

I am going to assume that something cannot exist in nothing, so.. The universe is on the back of a very large slug moving across another dimension. Currently the universe is expanding because the slug is stretching out as it moves, pretty soon, lets say 3 billion years from now, so I cannot be proven wrong, the next phase in the slugs movement will start and the universe will begin to contract.

Oh and how did it all start? The universe is a glob of the slime that the slug excretes to move easier, so there are many universes, and dark matter is what is holding us to the slug.

There you go, modify your beliefs accordingly.

## brizzadizza

But if I played an infinite amount of lottery tickets and won an infinite amount of times, for every one of my losses I could find a unique win. Clearly that would mean that my bank roll would be vastly increased.

Or what about long strings of wins? With a sufficiently long series of games I am guaranteed to have a string of winnings, the sum of which is greater than the sum of all the losses before it.

## derphysiker

I'm sorry, but this is exactly the kind of article that gives science a bad name. The theory is highly speculative and has already falsified itself to a certain extent (or I wouldn't be writing this), yet it still is presented as if it has any impact on the world as we know it. It has not. It is pure theory and the authors should have balls enough to say "we don't know how to deal with this infinity mathematically so we have to let time end in our theory to get results".

Having said that I'd like to comment that due to the infinite thinning of matter and energy I don't see a problem with infinite time. Long before infinite time becomes a problem all physical activity will stop. No need to calculate further. No problem.

## derphysiker

Oh, and if you really want to speculate about "Boltzmann babies" popping into existence, then also speculate about a nearly infinitely dense seed of matter and energy popping into existence with a bang. Maybe that's how this universe started in the first place...

## derphysiker

This is definitely the time when you want to stop playing... :-)

Yes, and this will happen an infinite number of times. But for the (energy) balance of the (universe) casino it is essential that you continue playing so it can reap its losses. Which leads to the conclusion that you will not be able to overcome your gaming addiction. Or else the universe has to end.

I hope this reasoning shows the problems that you fall into when dealing with infinities. Simply stated, every bet is off when you introduce something infinite into an argument. The church already lost with their claim of their god being of infinite power... and of infinite mercy.

## toocool

## georgert

## Damon_Hastings

This sounds like sophistry to me, or at least bad math. Just because two sets are both infinite doesn't mean they're incomparable. For example, if you pick a uniformly random number between 1 and 10 (including fractions), are you more likely to choose a number between 1 and 2 or a number between 2 and 10? Just because there are an infinite number of fractions in both ranges doesn't mean you can't answer the question. (The answer is that you're more likely to choose a number between 2 and 10.) Mathematicians compare infinite sets all the time. It's not that spooky. (Well, not until you progress beyond aleph naught, anyway.)

## KomMaelstrom

If I were to where blue tint glasses, white paper will appear blue, but the paper is not blue. Merely that the medium by which I am viewing the paper attributes a blue quality to all light that it allows through. In other words, by understanding a perspective, all information perceived through such is structured by the functions of the perspective.

## TheobromaCacao

derphysiker gets it. Given infinite time, any non-zero probability event, such as (say) the big bang, will occur infinite times. I'll be typing this an infinite number of times. In fact, I'll be Master of the Universe an infinite number of times. Just apparently not this time. Oh well.

Infinity is fun! Collect the whole set!

## Deuterium2H

It is NOT necessarily true (or to be more exact, sufficient) that given an infinite amount of time... "Any type of event that has nonzero probability will happen infinitely many times". The Set of Even numbers has the same size (cardinality) as the Set of Intergers (or Rational Numbers). However, every member of the Set of Integers is NOT in the Set of Even numbers, even though they both constitute a denumerably infinite set, and have an exact one to one correspondence.

Discrete events in Space-Time may also be "countably" infinite and have a cardinality equal to Aleph Nought. In which case they may be infinite, but not necessarily exhaustive, just like the Even numbers

## stealthc

## Skeptic_Heretic

## Noumenon

## jsa09

It may be non-zero probability that I will get up out of my chair and walk out to front lawn without opening the door in between. It may have already happened. I would put it down to being absent minded.

Does that mean I should introduce a spontaneous "end of all time" just to make it easier for me to do calculations that I don't understand? I don't think so.

Can use the unlimited funds and unlimited time rule and always walk away with a profit from playing roulette. Just bet on red or black and keep increasing your bet until you win.

Trouble with real world is that I don't have infinite funds.

## abhishekbt

How come the author of the article reached 5 billion years in the title of this article? That's too much of rounding I'd say!

## derphysiker

I think this will happen in reality. Due to the thinning out of matter and energy during the final fade many now merely improbable events will become impossible, leaving only the improbable high-energy events... like a new big bang.

reading this my own text over again strikes me with the feeling that this cosmology is simple enough to be the real truth... quick, lets start a religion! :-)