Is the Past Infinite?

This attachment is a possible dark energy model developed decades ago. Just to see what comments(if any)are generatedAttachment #1: possible_candidate_for_dark_energy.doc

That's a great question about whether the past could be infinite. We often consider the future to be infinite but I think what we mean is that for any fixed time T1 we can find later events than T1. It doesn't mean that we expect that there would be a time T2 in the future such that for any finite time T1 from the present, T2 is later than T1 - in other words, that there would be times an actual infinity later than the present.

Some of the same considerations could apply to an infinite past. Do we mean that for any finite time T1 in the past, there would be events before that? Or do we mean that there is a time T2 in the past such that for any finite time T1 in the past, T2 is before T1? Times an actual infinity earlier than the present?

We might call these the potentially infinite past (PIP) and the actually infinite past (AIP). As implied above, the same considerations apply to the future, since the future and past are relative.

The AIP is certainly more interesting and challenging. It raises the question, could there be objects that are infinitely old, whose creation time is before any finite time in the past? Black holes can last forever, if their inflow is faster than their Hawking radiation. However over an infinite time period we might expect random fluctuations in inflow rate which could eventually cause the size to drop to zero, whereby the hole would disappear.

We could model the size of the black hole as a 1 dimensional biased random walk where the hole disappears if the path ever crosses zero. If the probability of getting smaller is >= 1/2 then eventually the path will cross zero. If the probability is < 1/2 then the hole can avoid this fate. However in that case the size will grow without limit and the hole will be infinitely large after an infinite time. I think the probability of finding a finite-size, infinitely old black hole would be zero.

William:

I'm hopeless biased in favor of past-eternal universes being possible, based on some work I've done on the subject with Steven Gratton.

What I love about applying physics to 'philosophical' questions is how they can sometimes be resolved in a way that you would never have guessed based on pure thought. For example, anyone before general relativity (or really Riemannian geometry) would have been utterly baffled at how the universe could be finite, yet have no boundary. But it's utterly simple once you understand the geometry of a 3-sphere.

I think this may be another case, particularly in terms of what you

nicely called the 'endless chain of causation'. What Steven and I found is that if you try to really understand a fully steady-state model (like the classic steady-state cosmology, or an eternally-inflating cosmology that is statistically independent of time), then there are indeed boundary conditions that define the cosmology, but that these are not applied at any particular *time* -- rather, they are placed on a 'null' spacetime surface that is 'earlier' than all times -- even through times go arbitrarily early. It's a bit hard to explain this without the mathematics, I'm afraid, and in some sense that's precisely the point -- the structure of these models is something I at least would never have come up with any way other than following the mathematics where it went.

That being said, I also think 'philosophical' thinking is quite important. What led Steven and I (or at least I, he can speak for himself) to do this project at all was the conviction that if we can define a cosmology that approaches a steady-state (as eternal inflation does), then we should be able to make that steady-state exact, which is to say past-eternal.

Hal:

I think you're probably right that any given object will be impermanent, even if the universe goes on forever.

I think the 'bias' that it is reasonable for the universe to be future-infinite but not past infinite is that we can easily imagine the universe continuing infinitely into the future -- what would stop it?

But actually I think it's a bit tricker than this. If we were to take a finite system, it could indeed go on 'forever' but by attaining equilibrium. After that, the system would become *timeless* in that there would be no thermodynamic arrow of time defined by entropy increase. Thus I don't think it's quite right to say it is 'continuing into the future'.

Going toward the past we can also worry about entropy. Very crudely: if we go into the past, entropy must decrease. What happens when it hits zero? There is nowhere to go. This leaves the possibilities that:

(a) we change the rules (this is the standard approach, wherein we invoke a strong gravitational singularity, which our theories cannot treat), or

(b) entropy starts to increase again (i.e. the arrow of time 'reverses'), or

(c) entropy was always infinite, so that no matter how far back we go, we never run out.

The past-eternal models I've studied have some aspects of both (b) and (c).

The question of an infinite past or future relies on what is ultimately possible of configurations or states. Is the space of all possibilities definite, bounded by extremes, or indefinite. Big bang or not, an expanding universe in reverse eventually collapses into a singularity (Alpha). As the previous post remarks, once at Alpha there is no where to go (but expansion). In the future of expansion, even more evident with accelerating expansion, conditions move ever nearer toward a physical state of absolute zero, or a perfectly flat and empty universe. One can claim the big bang didn't happen in the past or that time can never reach zero in the future, but the two extremes are plainly boundaries in the space of all possibilities. Like fractions between 0 and 1, the space of all possible configurations is infinite, but it is bounded by extremes, and therefore not indefinite. Consequently neither the past or future can be infinite without eventual repetition. Time could oscillate between the two extremes forever but eventually all the possible arrangements of configurations would be used up, and the course of time would have to repeat. In an infinitely extended flat universe they could all be used up in one journey from Alpha to zero. Fortunately for us it appears time is more selective than that.

I don't believe past or future is infinite, and agree that once an equilibrium is reached there is no meaning to the idea of ordinary time. What I don't agree with is the notion that an equilibrium exists somewhere between Alpha and zero. Zero is the equilibrium. Just as time begins at Alpha, time ends at zero.

http://everythingforever.com

Challenging the Standard Model of the origin of the universe could be difficult because many people are attempting to use science as a substitute for religion. Religion has tradionally attempted to explain the origin of the universe. Religious concepts are doctrines which are to be accepted without question. Those who claim a "scientific" explanation for the origen of the universe want the same certainty that they have the one and only possible explanation as those who rely on traditional religion. They ignore the fact that empirical science concepts are always subject to change as more information becomes available.

For these individuals, the idea that the universe began with a perfect linear explosion of a black hole with matter moving away at or above the speed of light. Then this matter supposedly changed its mind and decided to clump together to form stars and planets. I don't see any way the universe could have begun in this fashion without the intervention of some higher dimension intelligence (ie, God).

They ignore the possibility that the idea that the universe has always existed would be more consistent with a theology that the universe exists because of natural processes than the Standard Model.

If there was a Big Bang resulting from a natural process it is more likely that it would have involved a spinning black hole releasing jets of material in a spiral fashion. I support this particular model, but the idea of an infinite past is a possibility. The two might even be combined with galaxies collapsing and coming back with Little Bangs.

I though of the following just after I hit the submit post button.

Are you aware of the flaw in the reasoning that claims that the universe is expanding at an increasing rate? This claim falsely suggests that the greater red shifts in light from the more distant galaxies indicates that the universe is expanding at an increasing rate. In fact, it would indicate the exact opposite if the red shift isn't a result of what some have called "lazy light".

The flaw becomes apparent by looking at the information in four dimensions. Light left a distant galaxy at time "T" when the galaxy's relative velocity in respect to earth was "V". At time T 1 light left a closer galaxy at V - x. At time T 2 light left an even closer glaxy at V - x - y. Examined in this fashion it is obvious that the rate of expansion slowed over time rather than increased.

Images of distant galaxies moving toward each other would tend to support some form of "lazy light" theory.

William it depends what you mean by infinite past. The time embedded observer evaluates time as duration, as a series, as change. For time to regress infinitely without repetition there would have to exist an absolutely indefinite measure of unique configurations to match the infinite regress of time. However, our collapsing past reveals that the space of possible configurations is bounded by the extreme of collapse or the point of the big bang. If we turn to the question of the future being infinite, again we run into the extreme of absolute zero. The space of all possibilities is not indefinite or unbounded.

The angel observer outside of time evaluates the time of existence itself, not change, which is one enormous moment. It doesn't have a past or future. It just is. The angel sees all possibilities simultaneously, and only can evaluate time as something embedded in the whole of existence, like a direction in space. The angel sees any repetition of states as the same series of time. So the angel's question is, why does this direction in space follow a particular path or course through the space of possibilities? If possibilities were bounded in only one direction, say the future, then the reason could be that time is searching for a balance that doesn't exist, moving away from the definite group of possibilities in its past toward the forever larger group of possibilities in its future. But if the space of possibilities is bounded in both directions by extremes, then a direction in space that is guided by a computation of what is probable would only be able to travel away from imbalance toward a distinct overall position of balance in state space. Time (probabilistic space) would begin at the extreme of imbalance, such as positive or negative, and end at an extreme of balance, such as absolute zero. The positive or negative states would be seen as two halves of the balanced whole.Attachment #1: allpossiblestates.jpg

William:

Thanks for bringing up this interesting idea of the 'block universe'. Probably that deserves its own whole blog and thread (maybe I'll work on one). But briefly, and in relation to past-infinite universes, yes, I think there is a sense in which the 'eternal' boundary conditions suggest a block universe at some fundamental level. (Amusingly, my early talks on this even included an Angel that could move backward in time:)

But at the same time I'm not convinced this is really any different than any other cosmological model, in which you assume that at some early time the universe was in a precise physical state. My opinion is that questions surrounding the meaning of time, 'now' or free will could all be asked in either context equally easily (and answered with equal difficulty!).

Gevin:

I don't think we have to assume that there a finite number of elements of the configuration space. And as I've said above, I also don't think we have to believe in an initial singularity, especially if inflation occurred. In particular, the classical 'singularity theorems' all make assumptions that either (a) simply do not apply to inflating universes, or (b) apply, but nevertheless allow models in which there is no singularity.

Much of people's thinking about this question relies on the classic big-bang model. But if inflation happened (and there is good reason to think that it did), then this thinking just does not apply.

Having only recently read paper by Anthony, I need to digest some of it's content further, but I do believe on what is basically the concept of descriptive "finite" size, embedded into an "infinity" Time, relatively speaking of course. One can arrive at a continuum 2-d mobius pathway, but then one asks which is "inside" and which is "outside"?

Asking the question:is the past smaller (size) than the future?, the same as asking, is the past_time equivilent to the future_time, regarding "timescales"?

A finite "length" can be bounded across in an infinity amount of "time" (one can cross a road at different speeds?), but a finite "time" cannot be circumvented by an infinity speed length, or particle?

William:

My father (Sam) has looked through the posts and wanted me to throw this up there to add to the discussion.

Up until the 1960s there was a conflict between those who maintained that, in some way, the universe always was and always will be, worlds without end. These were the steady state boys (and some girls.) There were those, who since the late 1920s, believed that some sort of gigantic explosion generated the universe. Given the lack of hard data, the conflict simmered R.W. Wilson and Arno Penzias, accidentally in one of those bits of serendipity came up with an important bit of evidence (for which they later received the Nobel Prize). While cleaning up a radio telescope--literally removing bat guano and pigeon excrement which they thought had corrupted the data--they kept on hearing the same noise. The pigeons were short, though each denies doing the deed. The noise was steady and coming from all areas of the universe. New York, oddly enough, was ruled out as the source. There was also measurable heat which couldn't be accounted for. What could account for this steady noise? They decided that it was the left over sound of an explosion. The term "Big Bang," which laypersons could glaum on to easily, was coined. Thus, the Big Bang theory replaced or rather out-competed the Steady State theorists. The Big Bang is the standard version of the origins of the universe. Further research--over 20+years--revealed that the best date for this explosion was 13.8 billion years ago. So, the standard version is that the Big Bang occurred 13.8 billion years ago and accounts for the totality of the universe as we now know and see it.

However, the half-life of any theory, no matter how well thought-out, how much data support it, is not long. Individuals kept on coming up with both logical and empirical questions, which, they felt, were not answered by proponents of the standard version. In easy terms, What came before the Big Bang? One answer, created by some guys with one foot in quantum mechanics is this: an event created by another universe accidentally brought this universe into existence. This presupposed not one universe but many--separated by what? An infinity of space-time? But how can you have an infinity of space time with finite universes? Aha!

Meanwhile, let me work on the problem that is raised by the concept of infinity and its relation to the space-time continuum, i.e., if space and time end, so does infinity, no matter how defined. If infinity ends, so does space-time.

So more later...

Michael

Dear William,

The main problem for all cosmological theories is whether or not there exists quantum gravity. It is believed that this problem is related to the cosmological constant problem i.e. the dark energy problem, as well as the problem of time arrow, etc.... Now, there is no fully satisfactory quantum theory of gravity and one of the candidates (string/M-theory) has a lot of problems to predict known facts as well as to solve the above mentioned problems. It is true that the Standard model or the GUT coupled with classical gravity does not predict the observational value of the cosmological constant because SM is put in classical curved space-time background where there the problem of its vacuum energy i.e. unitarity, is evident. Therefore, wedding between QFT and clasical gravity produces a bad marridge. Because of that, it is very important to marry quantum mechanics and gravity in sence of noncommutative (quantum) geometry of space-time which is an old physical arena of the Universe. Philosophically, even QFT possesses classical space-time background as well as string theory so that the main problem for me is to find such theory of the Universe which will be background free and free parameter independent i.e. without the put-by-hand assumptions. It seems that such kind of theory (quantum loop gravity) already exists but it has a free parameter and its relationship with well known facts is tiny (see literature about relationship between loop gravity and entropy of black hole). Historically, our progress to understand misteries of the Universe is so far closely connected with our knowledge of the structure of space-time i.e. geometry from Euclid to Einstein and I think that future progress still lies there.

Best regards,

aca

Looking for the Big-Bang in our distant past, is analogous to an observer trying to locate a single Electron, using a single Eye as the only detection impliment!

It is Here, There and Everywhere.

It first occurred to me that the BBT might not be the best explanation upon reading that Omega=1. If the force of gravity and the expansion of space are in equilibrium, where is the additional expansion for the universe as a whole to beexpanding? It seems like a big convective cycle of expanding radiation and collpsing mass. This suggests black holes are the eye of gravitational storms and the CMBR is the dew point of radiation in space. To the extent gravity curves space in and mass radiates its energy back out, does radiation effectively curve space back out? There are hills between those gravity wells? That way, the further light travels, the more it's spectrum is stretched and the faster the source appears to be receding, but this doesn't account for all that does fall into gravitational wells, keeping the pressure from actually causing the galaxies to be moving apart. This external pressure might also account for the effect on the Pioneer spacecraft, as well as causing the outer rims of galaxies to spin faster then is accounted for by the amount of mass in them, thus solving the need for dark matter.

Also redshifting appears to equate to a cosmological constant, which is fixed to balance gravity, so this would explain why the redshift doesn't slow as standard BBT assumed and hense needed dark energy to fill in the gap.

Inflation Theory was added to make BBT work, yet it assumes that space itself is expanding, not just that the galaxies are moving apart in space. If this is so, why doesn't the speed of light increase proportionally, since it is our most stable measure of space?

I thought it might be of interest to add that the Alternative Cosmology Group has another conference coming up;

http://www.cosmology.info/2008conference/

I think time can be best understood as a consequence of motion, rather than a dimensional projection.

While physical reality goes from past events to future ones, the information of these events goes the other way. First it is future potential, then past circumstance. If time is a fundamental dimension, then physical reality proceeds along it, from past events to future ones, but if time is a consequence of motion, then physical reality is simply energy in space and the events, once created, are replaced by the next and recede into the past. It isn't presentism because time as a point would be meaningless as a measure of motion. The only absolute time would be like absolute temperature; the complete absence of it. Of course most motion is at the speed of light, but we cannot process it in real time, so our minds create flashes of perception, like frames of film. Thus to us, time does seem like a series of instants. So the physical brain moves forward in time, but the mind is a record of the events receding into the past.

Consider a thermal medium, say a pot of hot water, with lots of water molecules moving about. To construct a timekeeping device out of this we would measure the motion of one of these points of reference against the medium it is moving through. The point is the hand and the medium is the face of the clock. Obviously all the other points are hands of their own clocks, but are medium/face for all other clocks. The motion of any point/hand is balanced by the reaction of the medium/face of the clock. So to the hand of the clock, the face goes counterclockwise. At any one moment, the positions of all these points constitute an event, so while any and all of them go from past events to future ones, the medium against which any point is being judged is the overall context, which once created, is displaced by the next, as all these individual points move around, so the events go from future potential to past circumstance. The illusion of direction is created because the reference point moves through the series of circumstances, though these events go the other way. There are innumerable points of reference describing their own narrative, so every potential clock constitutes its own measure of time. Whether the earth rotating and creating days, or a cesium atom going through transitions, or strings and vibrations, conserved energy goes toward the future, as the information defining it recedes into the past. As a measure of motion, it would be meaningless to ascribe a dimensionless point to time, as that would be a total lack of motion, like a temperature of absolute zero, so any description requiring time has an inherently fuzzy position.

If time is simply a measure of the motion of energy, what does it say for the model of the universe that describes it as a unit of time that internally goes from beginning to end, as it externally goes from being in the future to being in the past?

We do perceive gravity as curving the measure of space around a body, yet radiation climbs directly out of this gravity well. Could it be that radiation does effectively have the opposite effect on space, since it does expand, just as mass contracts? Since it would be a far more gradual effect and effectively hidden in the vicinity of a gravity field, with no point of reference around which it curves, the only viable proof would be the redshift of light from distant galaxies. When the effect first described as proof of dark energy was first discovered by Perlmutter, et al, in 1998, it was that the supposed rate of expansion wasn't being slowed by gravity, since the assumption was that it was all a consequence of the initial singularity and should be cooling off. On the other hand, if redshift is an optical effect on light crossing enormous expanses of space, with the effect compounded, so that redshift is multiplied the further light travels, so that eventually the source appears to recede at the speed of light and beyond which it is no longer visible, then we have the signature of a cosmological constant that balances gravity, not the afterglow of a singularity with dark energy tacked on to explain the observation of continuing expansion. Since this is an optical effect, the actual sources are no more receding then a gravitationally lensed object moves around in space because an intervening gravity field makes it appear that way. Therefore the energy to make these objects actually move away is unnecessary. A possible analogy would be running up a down escalator, with the increased space falling into gravity wells,increasing the external pressure on them and providing a cause for the effect attributed to dark matter.

One of the main reasons to require a direction of time is that entropy is increasing and usable energy is decreasing, eventually to reach thermal equilibrium, but what if a complete thermal equilibrium, given the level of energy present, is just not stable. The cosmic microwave background radiation seems to be the energy closest to equilibrium, but there is a definite phase transition at 2.7k. Space doesn't seem able to hold energy above that in a stable, uniform state, so it is constantly collapsing and expanding around equilibrium, creating a perpetual convective cycle of gravity sinks balancing a sea of expanding space defined by radiating energy. So there would be no need for a singularity as uncaused cause of low entropy state.

These opposing effects would also describe the two directions of time, with mass as the discrete units of measure that go from being in the future to being in the past, while they go from start to finish, as the hand of the clock is the expanding energy that is constantly leaving the old forms and going on to create new ones. An analogy of this would be of a factory, where the units go from beginning to end, as the process moves on, consuming more raw material and expelling finished product.

hi all,

I had an idea about the infinite past. Suppose the following thought experiment with a Markov chain: each day there is a random variable x_i (for example the position of an electron) which depends only on the previous day's variable x_(i-1). Assuming that there are infinite random variables before this day x_i, x(i-1), x_(i-2). The question that arises is what is the probability of a configuration of the variables. It is

p(x_i,x_(i-1),x_(i-2))=p(x_i|x_(i-1))p(x_(i-1))p(x_(i-2))...

The result is the product of infinite terms smaller than one (and positive), so the result is always zero!

What is the problem with that? It is impossible for the electron to be at any time at any place given that there was inifinite time before that.

I am looking forward for comments

Sorry for the mistake, the equation is p(x_i,x_(i-1),x_(i-2))=p(x_i|x_(i-1))p(x_(i-1)|x_(i-2))p(x_(i-2)|x_(i-3))...