
Time Likely To End Within Earth's Lifespan, Say Physicists - lotusleaf1987
http://www.technologyreview.com/blog/arxiv/25807/?ref=rss
======
zeteo
"If the universe lasts forever, then any event that can happen, will happen,
no matter how unlikely."

That's just plain mathematically wrong. There are many kinds of infinity
(<http://en.wikipedia.org/wiki/Aleph_number>), and the set of all possible
events has a much, much higher cardinality than an infinite axis of time. This
is similar to saying that, since the set of integers is infinite, it must
contain Pi.

~~~
hugh3
_the set of all possible events has a much, much higher cardinality than an
infinite axis of time._

Are you sure of that? How would you prove it?

It seems intuitively right, but intuition has a habit of being wrong, when it
comes to infinities.

~~~
Robin_Message
I have a machine that flashes a light on or off once a second, at random. You
can view streams of output from the machine as possible events. Now, suppose
an infinite amount of time has passed (aleph-null, by definition). Have I seen
every possible sequence?

Well, take the set of aleph-null length sequences (all aleph-null of them [1])
and put them in an order. Now construct the following sequence: invert bit 1
from sequence 1, invert bit 2 from sequence 2, ... etc.

Note that this sequence was never produced by the machine, since we enumerated
all the sequences it produced, but they are all different to this one. So, by
a standard diagonalisation, the set of events is higher cardinality.

[1] How many aleph-null length sequences come out of the machine? Well, they
have to be continuous, so the only obvious aleph-null length sequence is the
_total_ sequence the machine produces. However, you can drop an entry from the
beginning of the sequence to get another aleph-null length sequence. And so
on, making a total of aleph-null.

~~~
hugh3
Interesting attempt, but I'm not convinced by the part of the argument where
you divide the complete output of the flashy light box into aleph-null
sequences, each of length aleph-null.

Mostly, I'm unconvinced that an "event" which takes an infinitely long time to
complete actually counts as an event. Usually when we talk about events
they're localised in space and time.

~~~
theli0nheart
Well, it's kind of a Catch-22.

This proof is dependent upon the lemma that time is infinite. On the other
hand, the set of events we're looking for is the one where time ends.
Therefore by assuming the lemma we have no need for the proof.

OTOH, if we're looking at another event that's not so confusing (one that's
not the end of time), the proof holds water. It's a pretty sweet proof that I
think is similarly used to prove that the set of real numbers is uncountable.

~~~
hugh3
No, what I'm saying is that an event which takes an infinitely long time to
happen (ie an infinite series of one-second flashes) isn't a proper "event",
which as used at least in relativity, is something that happens in finite
space and time.

But there's no need to argue about the definition of event. I'll say instead
that I'm interested in knowing whether infinite time implies that all _finite-
length_ events must eventually happen (and indeed, happen an infinite number
of times as the paper claims).

~~~
Robin_Message
Yes, sorry, there is definitely a theorem that if you have an infinite
sequence, uniformly distributed over an alphabet, then the probability of
seeing any finite sequence is 1. I think that, given some assumptions, you can
model the universe as an infinite numerical sequence, so you should see all
finite events.

However, the assumptions here seem tricky. Uniform distribution of probability
seems unlikely, and if the universe is anything like the game of life, there
are garden of Eden states with no predecessor state, which an evolving system
cannot reach, even in infinite time.

Cardinality is indeed tricky. I had thought that all finite sequences would be
greater than aleph-null, but apparently it isn't.

------
ZachPruckowski
From the sounds of it, this is a far from accepted idea that's just now coming
out in like it's first paper or something, so don't start planning your End of
Time Party. There's still a lot of verification and research and math between
this being published and it becoming the consensus among physicists.

~~~
hugh3
It's not even a paper, it's just a manuscript on the arXiv, yet to pass peer
review, if indeed it ever will.

I had a quick skim of the manuscript, and remain skeptical... a bunch of it
doesn't even seem to make sense:

 _If it does occur in Nature, eternal inflation has profound implications. 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._

------
Maro
Woit's take on the Not Even Wrong blog:

<http://www.math.columbia.edu/~woit/wordpress/?p=3185>

~~~
hugh3
And linked from that, Lubos Motl's even less charitable take:

[http://motls.blogspot.com/2010/09/bousso-et-al-
catastrophe-i...](http://motls.blogspot.com/2010/09/bousso-et-al-catastrophe-
imminent-time.html)

 _Much like most other doomsday prophets and other kinds of crackpots, the
authors are completely unable to understand the point and the arguments that
they're assuming something fundamentally wrong in their very first axioms -
and that's why everything they write down has to end up being a complete
nonsense.

Instead, they obviously expect a long sequence of follow-up papers that will
discuss whether the Universe will cease to exist in 5.31 or 5.32 billion years
and worship the amazing prophets, Bousso et al., who have predicted this
amazing doomsday. This is also clear from a staged dialogue included in the
paper where a semi-dumb person asks various questions about the doomsday that
the authors would clearly like to be discussed in other people's papers._

------
crazyjimbo
I've skimmed the paper and it's quite readable. The problem arises because
probability doesn't make sense in an infinite universe. To make sense of it
the authors consider a small patch of finite size and then let that finite
size go arbitrarily large. In this picture probability is well defined but our
space and time will always have an edge. However this is just a model, not an
expected version of reality. The same thing happens in quantum field theory
where the theory doesn't make sense at arbitrarily high energy so we just
impose a cut off and ignore energies above a certain scale. This doesn't mean
we think physics just stops there. Instead, it's just a way to parameterise
our ignorance about what comes beyond.

------
asmithmd1
This theory is well across the line from science and into religion.

How is this: "we'll run headlong into this catastrophe before we can observe
its effects on anything else."

any different than this:

"But of that day and hour knows no man, no, not the angels of heaven, but my
Father only." <http://bible.cc/matthew/24-36.htm>

~~~
j_baker
The difference is "Father knows".

------
paulitex
"Earth's lifespan" is slightly misleading if we're talking about inevitable
future catastrophes of physics. What's more important is the lifespan of earth
as a hospitable planet and that's significantly less time (since the sun is
heating up). From <http://en.wikipedia.org/wiki/Sun#Life_cycle> "...the Sun is
gradually becoming more luminous (about 10% every 1 billion years), and its
surface temperature is slowly rising. ... The increase in solar temperatures
is such that already in about a billion years, the surface of the Earth will
become too hot for liquid water to exist, ending all terrestrial life". So
(using the numbers from this article) we have about 1 billion years to get off
this rock, leaving another 2.7 billion on other planets before time ends. Not
a bad run if we can make it. :)

~~~
hugh3
_We have about 1 billion years to get off this rock_

Or we could just _move_ this rock.

------
alphaBetaGamma
"Any type of event that has nonzero probability will happen infnitely many
times(...). This undermines the basis for probabilistic predictions of local
experiments. If infnitely 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 infnitely many observers who do not win,
but in what sense are there more of them?"

The first sentence is wrong, as pointed out by zeteo, but the rest does not
make any sense either.

Take continuous random walk starting at zero at t=0. There are an infinite
number of paths that reach each value at time t=1. Yet we can say the the
probability that the random walk is positive at t=1 is one half. And by "say"
I mean give a solid mathematical definition of this fact, not some hand waving
argument.

------
markkat
This is based upon a false assumption. Not every possible thing need happen
given infinite time. There's an infinite number of things that can happen, and
each thing that happens takes a finite amount of time to happen. Infinite time
is not enough for infinite things to happen.

------
tkeller
> If the universe lasts forever, then any event that can happen, will happen,
> no matter how unlikely. In fact, this event will happen an infinite number
> of times.

Umm... this does not follow. Their argument surely must be more convincing
than this nonsense.

------
ellyagg
I'm not a physicist and I'm baffled. Doesn't entropy imply that all events
cannot happen? Wouldn't an event happening infinite times clearly and
unambiguously violate the effects of entropy?

------
jakerocheleau
This doesn't really affect anything here at all. It may be neat that they're
predicting time to end over 3 billion years from now, but I can guarantee
we'll all be long dead by then.

------
gwern
Well, that makes sense. <i>Time</i>'s circulation has been dropping for years
anyway.

------
frisco
Less arXiv on HN, please.

~~~
hugh3
Less of the whole arXiv, or just the subset of the arXiv which is crazy?

~~~
frisco
The problem is that you need to be a domain expert to tell which parts are
crazy. It's not a general consumption resource.

~~~
hugh3
True. Though the best heuristic that a non-physicist can apply is that if
something on the arXiv sounds interesting, it's probably crazy.

Non-crazy papers have titles like _Universal quantum control of two-electron
spin quantum bits using dynamic nuclear polarization_ and _Towards finite
density QCD with Taylor expansions_ and tend to be of interest to around four
people in the world, of whom three may or may not be the authors.

~~~
frisco
Right, and "Eternal Inflation Predicts That Time Will End" totally fails that
test. (I don't mean to sound like I'm attacking you -- I agree with you. This
is re: the OP)

------
qntm
This can be easily averted. Destroy the Earth.

------
rick_2047
I will leave the validation arguments to the people who know something more
than the highschool physics I know. But "End of Time" wtf can that mean?

Take a shot sci-fi fans.

------
zeynel1
Time Likely To End Within Earth's Lifespan, Say Astrologers

There is a 50 per cent chance that time will end within the next 3.7 billion
years, according to a new astrological model of the zodiac.

Look out into space and the signs are plain to see. According to a certain
reading of our tarot cards; Cronos created Heaven and Earth when he sneezed
for the first time 13 billion years ago; therefore; Heaven and Earth have been
expanding ever since. And the best evidence of the expansion of the Cronos'
sneeze comes from observation of the Cronos' germs in distance reaches of the
cosmos; therefore; cosmos' expansion is accelerating.

That has an important but unavoidable consequence: it means that the cosmos
will expand forever. And a cosmos that expands forever is infinite and
eternal. This is obviously because the creator of the cosmos the eternal and
infinite god Cronos is infinite and eternal.

Today, a group of astronologist rebel against this idea. They say an
infinitely expanding cosmos cannot be so because the laws of astrology do not
work in an infinite cosmos. For these laws to make any sense, the cosmos must
end, say the Trimagistus Nuovo Raphaello Bousso at the University of
California, Berkeley and few pals. And they have divined when that is most
likely to happen.

Their divination is deceptively simple and surprisingly powerful. Here's how
it goes. If the cosmos lasts forever, then any event that can happen, will
happen, no matter how unlikely. In fact, this event will happen an infinite
number of times.

This leads to a problem. When there are an infinite number of instances of
every possible divination, it becomes impossible to determine the
probabilities of any of these divined events to occur. And when that happens,
the laws of astrology simply don't apply; the absurd laws of physics take
over. "This is known as the "measure problem" of eternal inflation," say
Bousso and buddies.

In effect, these guys are saying that the laws of astrology abhor an eternal
universe.

The only way out of this conundrum is to divine some kind of divine
intervention that brings an end to the cosmos. Then all the probabilities make
sense again and the laws of astrology regain their power to divine.

When might this be? Bousso and co have consulted Cronos' assistant in charge
of human affairs, a Mr. Prometheus, and this is the reply they got: "Time is
unlikely to end in our lifetime, but there is a 50% chance that time will end
within the next 3.7 billion years," said Mr. Prometheus who started it all
when he stole the light from Gods to give it to humans and that was about 3.7
billion years ago. So if no symmetry breaking occurs; Bousso and Co's 3.7
billion year prediction for the end of time is as good as proved by Einstein's
General Relativity.

But Mr. Prometheus had one cautionary statement: "The time will end for
humans; not for gods. I am sorry" said Mr. Prometheus, a good friend of
humanity since the beginning.

3.7 billion years is not so long! It means that the end of the time is likely
to happen within the lifetime of the Gaea and the Hyperion.

But Buosso and co have some comforting news too. They don't know what kind of
divine intervention will cause the end of time for humanity but they do say
that we won't see it coming. They point out that if we were to observe the end
of time in any other part of the cosmos where the authority of Cronos has been
usurped; we would have to be causally ahead of it, which is unlikely because
the God Mnemosyne hates to remember what she had not forgotten.

In other words we'll run headlong into this divine intervention before we can
observe its effects on anything else.

The imminent end of time is a little unsettling but the argument is by no
means astronologically sound. Among other things it depends crucially on an
important assumption about the laws of astrology: that we ought to be able to
understand why they work, not just observe that they do work. And that's a
physical point of view rather than an astrological argument. And you cannot
trust physicists to explain anything; because for them if it is Wednesday it
must be a wave; if it is thursday it must be a particle.

So Buosso and buddies raise some interesting questions but nothing to lose any
sleep over. At least, not for another 3.7 billion years Cronos will not bother
to end time for human beings.

Ref: arxiv.org/abs/1009.4698: Eternal Inflation Predicts That Time Will End

