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### Author Topic: How reasonable is the logic of Borde, Guth and Vilenkin?  (Read 6149 times)

#### Bill S

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##### How reasonable is the logic of Borde, Guth and Vilenkin?
« on: 10/01/2015 19:04:51 »
I recently read the article at:

http://discovermagazine.com/2013/september/13-starting-point

This is an extract from that article, and I would appreciate comments on it, especially on the argument against inflation being “eternal” into the past.

“In Vilenkin’s bubbling universe, inflation was, by definition, eternal into the future. Once initiated, it would not stop. But was it also eternal into the past? Was there ever a time when the universe was not inflating? And if the universe were always inflating, and always expanding, would that imply that the universe itself was eternal and had no beginning?

To address this question, Vilenkin joined forces with Guth and Long Island University mathematician Arvind Borde. Using a mathematical proof, they argued that any expanding universe like ours had to have a beginning. The thought experiment they posed went like this: Imagine a universe filled with particles. As it steadily expands, the distance between particles grows. It follows that observers sprinkled throughout this expanding universe would be moving away from each other until, eventually, they occupied widely scattered regions of space. If you happened to be one of those observers, the farther an object was from you, the faster it would be moving away.

Now throw into the mix a space traveler moving through space at a fixed speed: He zooms past Earth at 100,000 kilometers per second. But when he reaches the next galaxy, which is moving away from us at, say, 20,000 kilometers per second, he will appear to be moving only 80,000 kilometers per second to observers there. As he continues on his outward journey, the space traveler’s speed will appear smaller and smaller to the observers he passes. Now we’ll run the movie backward. This time, the space traveler’s velocity will appear faster and faster at each successive galaxy.

If we assume inflation is eternal into the past — that it had no beginning — the space traveler will eventually reach and overtake the speed of light. A calculation by Borde, Guth and Vilenkin showed that this would happen in a finite amount of time. But according to the laws of relativity, it is impossible for any massive object to reach the speed of light, let alone exceed it. “This cannot happen,” says Vilenkin. “So when you follow this space traveler’s history back in time, you find that his history must come to an end.”

The fact that the traveler’s journey backward in time hits an impasse means that there’s a problem, from a logical standpoint, with the assumption of an ever-expanding universe upon which this whole scenario is based. The universe, in other words, could not always have been expanding. Its expansion must have had a beginning, and inflation — a particularly explosive form of cosmic expansion — must have had a beginning, too. By this logic, our universe also had a beginning since it was spawned by an inflationary process that is eternal into the future but not the past.”

Surely, the argument that if you "...run the movie backward. This time, the space traveler’s velocity will appear faster and faster at each successive galaxy” applies only up to the astronaut’s point of origin.  Beyond that point successive galaxies would once again be receding at successively greater rates, so the astronaut's speed would be decreasing relative to each successive galaxy.

No one would perceive the astronaut as travelling at above 100,000 kps.
« Last Edit: 10/01/2015 19:15:38 by Bill S »

#### jeffreyH

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #1 on: 10/01/2015 19:44:59 »
Remember that the movie running backwards involves a negative time dimension. As we move forward in time things appear to be moving away faster, therefore in the past things would appear to be moving away more slowly. The observer has a constant velocity in his local frame but as spacetime contracts going back in time this velocity WILL appear to increase. Remember you are in a moving frame within a succession of other moving frames relative to yourself. The proper question is have they neglected the effects of time dilation in their thought experiment?

#### Bill S

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #2 on: 10/01/2015 20:05:26 »
Quote from: Jeffrey
…. question is have they neglected the effects of time dilation in their thought experiment?

That was my first thought, then I ran into problems wondering what running the movie backwards actually meant in the real world.  A negative time dimension is all very well in a thought experiment, but can you apply it to the Universe?

Of course, my final comment that “No one would perceive the astronaut as travelling at above 100,000 kps.” is not justifiable, as we are told no more than that that was the first detected velocity in the thought experiment.

#### dlorde

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #3 on: 11/01/2015 20:40:54 »
I'm no relativist mathematician, but it doesn't make sense to me; they throw in a traveller moving at a 'fixed speed' - relative to what - some arbitrary set point and time? they now compare the speed of that traveller relative to observers in galaxies whose speed has increased (relative every other galaxy) due to the expansion of spacetime itself (of course, the traveller's speed relative to every other galaxy would also be affected by the expansion). I'd think, reversing time, the traveller's speed relative to other galaxies would decrease as the universe shrinks, just as the speed of the galaxies does, relative to each other.

It seems to me that their argument for the traveller should also apply to any galaxy that is moving relative to another in addition to the expansion of spacetime (with the exception of a few galaxies that just happen to have identical speeds).

There just feels to be something wrong with setting an arbitrary stationary reference frame, then making an argument based on switching frames between multiple observers...

Also, I can't help feel that even if their reverse time argument did appear to increase the traveller's speed without limit (but not that of any galaxy(?), I would expect any observers to measure his speed as approaching ever closer to the speed of light, rather than to exceed it.

It may be that you can prove that eternal past expansion isn't possible, but I don't see why you need to introduce a special traveller moving at some 'fixed speed' relative to some unspecified frame.

#### jeffreyH

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #4 on: 11/01/2015 21:55:03 »
The time reversed movie will break simply because it will eventually reach the inflationary era. This is after all the whole point; to validate the big bang hypothesis. Unless I am mistaken.

#### dlorde

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #5 on: 12/01/2015 20:30:04 »
The time reversed movie will break simply because it will eventually reach the inflationary era. This is after all the whole point; to validate the big bang hypothesis. Unless I am mistaken.
But the argument wasn't about inflation, it was that the traveller would appear to moving > c.

Also, inflation is a consequence or requirement of the big bang theory... if you posit eternal expansion without big bang or inflation, you won't reach the inflationary era (though there are probably plenty of other reasons to reject eternal expansion in favour of the big bang - such as the CBR).

#### JohnDuffield

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #6 on: 12/01/2015 20:54:32 »
Bill: it's a popscience argument that doesn't hold water. Like dlorde said, the space traveller moving through space at a fixed speed is a contradiction in terms. A stationary observer here will appear to be moving at 20,000 kilometers per second to stationary observers in the next galaxy. And vice versa. And there are galaxies out there moving away from us at a speed greater than the speed of light. Which we can see, see http://arxiv.org/abs/astro-ph/0310808, it's a caterpillar on a rope thing. Yes, the expansion of the universe started 13.8 billion years back, but that's nothing to do with their thought experiment. And then there's this:

"“The way the universe gets around that problem is that gravitational energy is negative,” Vilenkin says. That’s a consequence of the fact, mathematically proven, that the energy of a closed universe is zero: The energy of matter is positive, the energy of gravitation is negative, and they always add up to zero. “Therefore, creating a closed universe out of nothing does not violate any conservation laws.”

That's another popscience myth. Gravitational field energy is positive. When you drop a brick, potential energy is converted into kinetic energy. Conservation of energy applies. There isn't less energy in this universe when the brick hits the ground.

dlorde: see John Horgan's blog where "Physicist Paul Steinhardt Slams Inflation, [the] Cosmic Theory He Helped Conceive". I don't think inflation is an essential part of big-bang cosmology myself. Expansion yes, but not inflation. IMHO it's a solution for a problem that doesn't exist.
« Last Edit: 12/01/2015 20:56:29 by JohnDuffield »

#### dlorde

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #7 on: 12/01/2015 23:41:38 »
dlorde: see John Horgan's blog where "Physicist Paul Steinhardt Slams Inflation, [the] Cosmic Theory He Helped Conceive". I don't think inflation is an essential part of big-bang cosmology myself. Expansion yes, but not inflation. IMHO it's a solution for a problem that doesn't exist.
Yes, I understand that, and I also have some doubts about inflation; my point was that I don't think you can validate the big bang hypothesis by an assertion of inflation (i.e. that the traveller would reach the inflationary era) - it's affirming the consequent. At least it looks that way from here.

But it was just a minor point of logic - I have no dog in this race; I'm sceptical, but happy to wait and see what the consensus is on Borde, Guth and Vilenkin. I don't have the maths for a proper critique of my own.

#### JohnDuffield

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #8 on: 14/01/2015 10:12:51 »
...my point was that I don't think you can validate the big bang hypothesis by an assertion of inflation
Noted and agreed!

I don't have the maths for a proper critique of my own.
IMHO you can often point out a flaw regardless of any maths. In fact I'd go so far as to say that sometimes people get "lost in maths" and don't see an obvious problem, like the one you pointed out in post #4.
« Last Edit: 14/01/2015 10:14:34 by JohnDuffield »

#### jeffreyH

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #9 on: 15/01/2015 20:15:27 »
The time reversed movie will break simply because it will eventually reach the inflationary era. This is after all the whole point; to validate the big bang hypothesis. Unless I am mistaken.
But the argument wasn't about inflation, it was that the traveller would appear to moving > c.

Also, inflation is a consequence or requirement of the big bang theory... if you posit eternal expansion without big bang or inflation, you won't reach the inflationary era (though there are probably plenty of other reasons to reject eternal expansion in favour of the big bang - such as the CBR).

They would ultimately travel faster than c if they weren't all heading towards each other. Reverse expansion and it only has one way to go, inwards to a point in space. It may not have been a point at all though but simply a density increase generally.

#### yor_on

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #10 on: 26/01/2015 17:48:46 »
Don't get it? The problem seems the same as with no light reaching us from some limit of expansion. As far as I can see there is no problem with 'space' expanding as long as light continue to be a local constant in it. Seems to me Vilenkin loses context reasoning as he does. A inflation can be defined as a 'space' doing 'ftl', although I would avoid making that kind of comparisons I think.
=

Ok I think? I might get how he means. He's considering a time reversal
https://en.wikipedia.org/wiki/T-symmetry

But that isn't what we see, even though you can find a symmetry. Myself I would call the symmetry a result of causality's demands. It gives us a logic that will hold for events, even when observer dependent, as well as when playing the movie backward (time reversal). Without that we can forget physics, at least as they look now. If causality disappear you will need some new and totally weird type of logic connecting us, communicating.
=

But I'm not sure that really was it? Rereading the citation above? My first statement about it being equivalent to the idea of us watching all galaxies around us disappear can then be used. Assuming that one really could play the movie backwards should then turn the guy traveling into a singularity of some 'invisible' sort as it seems to me. But it falls as a suggestion as it presume the guy time traveling without a beginning. It's more of a logical trap to me as what defines this universe is causality, and this causality is bound by constants, 'c' one of the most important to me. Unless someone has a proof to the opposite?
« Last Edit: 27/01/2015 11:45:35 by yor_on »

#### yor_on

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #11 on: 26/01/2015 17:55:02 »
Maybe one can think of it this way? Think of a wave in a expanding space, assume it to 'elongate', that also means that for a observer observing light 'propagating' in some defined portion of a inflating space, he will find the light to redshift, to then ultimately 'disappear' from observation. It won't mean that he will measure different speeds though.
=

what it might ask about though is the relation of energy, as represented by that light increasingly red shifted due to a expansion, and a 'space'? And there it depends on how you define it, as a 'field'? How then will conservation laws describe it? I prefer one where communication builds a universe myself, and defines what exist, in such a universe 'space' is a weird idea and a secondary to energy, or 'light'. Because that is what communicates as it seems to me. That one in its turn can then be related to if you define light as 'propagating' or not? Assume it to be a 'flickering' field for example, 'flickering' in the way all 'observers', animate or inanimate, observe communication between them, as well as inside, because that is also 'light communicating'. Doing so the duality is real, dependent on type of 'experiment/observation'.

also, doing so we can find the limits in 'c', that both represent a speed, added together from a local definition of lights 'propagation' of a length, as timed by a clock. And there we then if we prefer, which I do, can define two local constants, or three. We can define 'time' as a local constant equivalent to 'c', we can define a length as a local constant equivalent to 'c', we can define any choice of clock as equivalent to 'time' too, when split into even chunks. That makes the clock equivalent to time, to 'c'. Actually, what it really do is to simplify time, time is 'c' through such a definition. And that is what clocks measure.

So there you have a constant 'flickering'. and in two different ways :) The most important to me is if you think of Planck scale as the one defining a 'microscopic limit'? If you do the 'flickering of time' starts there, over the whole field. And that one is unnoticeable for us. The second description is the one in where 'observers' experiment, or if you like 'observe' those signals. That one is a result of the 'flickering field' existing if so :) as without it nothing would happen. That then would make 'time' what makes things happen, which pleases me :)

What this describes is a 'field' as a clock, the clock keeps a constant 'flickering' defining a 'time', as a metronome of sorts. The other side of this field is 'mass' and 'motion', creating observer dependencies, as it 'measures/observes/experiment' (pick thy choice). But it gives the metronome (field) a even steady rhythm, as locally measured, and when comparing that local rhythm over a 'space' to some other 'rhythm' , give us observer dependencies. But it doesn't explain what 'space' is. What it assumes though is that observer dependencies is something related to how we treat that space separating you from what you observe, as well as how that space treats you, as your constituents communicating with each other. Meaning that a moving lightclock is indeed a different thing from a comoving, being at rest with you. Space exist, so do motion, and mass.

As a very outlandish idea, think of the field as a plane. Think of everything 'mass' as those able to measurably communicating in between themselves, and as nodes, existing in this plane. Dimensionally, and observer dependently, I guess that those nodes also could be defined as adding further dimensions by us 'observers', having the ability to communicate in between. As I said, outlandish idea.

Also one need to see how I define a observer there. Animate (life) or inanimate (rock) doesn't matter. What I'm after is the ability to communicate, receive and leave 'information'.
« Last Edit: 26/01/2015 20:29:56 by yor_on »

#### yor_on

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #12 on: 27/01/2015 11:45:57 »
==

"The universe, in other words, could not always have been expanding. Its expansion must have had a beginning, and inflation — a particularly explosive form of cosmic expansion — must have had a beginning, too. By this logic, our universe also had a beginning since it was spawned by an inflationary process that is eternal into the future but not the past.” "

Assume the universe to be a symmetry break. Assume it to gain a 'clock' through it, actually unable to be a symmetry break without a clock existing. The universe becoming 'time'. Time is what we use constantly. You might be able to use 'emergences' defining it, the 'beat' existing but maybe the 'beat' came 'first'. In that case the whole universe is a emergence created through that beat existing.

It won't matter to you, or to me, what exist outside 'time'. And I doubt we will find ways to explore such a situation in person. That's not a 'outside' btw, that's a symmetry. And you can find it lurking in the ideas of quantum mechanics too. It's at that QM plane, using scaling, that we will find 'time disappear'. And there Planck scale is of a immense interest to me.

So yea, the universe has a beginning, but how will you define it? The best we can do is to use astronomy, using lights constant to define a sphere of observation, defining a age. That only tells you what you see from here. But assuming that it is a isotropic homogeneous universe you now can draw conclusions telling you that it will look the same, everywhere. So, 'time' may have a start, but that one we already can proof astronomically. But that doesn't tell us anything, except as defined inside. A infinite amount of 'points' inflating, from time 'zero', leaves us a 'infinite universe' today, in a accelerating expansion.

And it doesn't matter for this how you want to define a universal 'size', from its inside. Easier to think of it as undefinable. That way you also learn to separate the idea of 'dimensions' from our definitions of length and a clock. We use local definitions, always, and they should hold true everywhere inside. We so much want the universe to be count able, but I don't expect it to be. It's a symmetry and a relation.

You need to put it together. 'Time disappearing' at some quantum scale, with astronomical evidence of a infinite universe coming from 'time zero'. Time is a matter of the scale you use.
==

Think of it this way, how do you define a size?
How do you define a time
A length?

And then there comes the idea of 'dimensions'.

You also need to see that any definition of some 'original point' of departure for a universe only makes sense from Victorian associations. In a universe of undefinable 'size', finding a accelerating expansion in each 'point' (SpaceTime position), being isotropic and homogeneous, meaning that all places you go to will present you a same SpaceTime looking out at the universe.  In such a universe you will find astronomical proofs for a 'start of time' everywhere you go, as you will find the exact same 'light sphere' of observation meeting you. But as each position also can be translated into a 'origin', locally defined, you now have a infinite set of 'points' starting this universe. It's simple, if you accept the assumptions. If you don't, you better be Victorian :)
« Last Edit: 27/01/2015 12:23:57 by yor_on »

#### Bill S

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #13 on: 27/01/2015 18:05:29 »
Quote
In such a universe you will find astronomical proofs for a 'start of time'

How can there be a start of time?  Surely, if there were no time there could be no change, so how could time come into existence?

#### yor_on

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #14 on: 27/01/2015 20:55:43 »
That's a really good one, and one reason for the idea of 'emergences' I guess? What we see astronomically is a 'finite beginning' called the Big Bang. And if we then assume a isotropic and homogeneous universe we will see that same beginning everywhere you go. No limits to it and no place where the universe 'ends' as in turning you back to some origin, the way I think that is :)

the proofs are there astronomically, but how it could start? If you find a way to explain that one I think you will get several Nobel prizes.
==

One way might be to define our 'symmetry break' as becoming a symmetry of its own, possibly? We have Quantum logic, and mechanics, statistics we use to define most probable 'paths', etc. In the idea of many paths as well as in the idea of Planck scale, lies an assumption of there existing a grainy universe that taken to its end also dissolves into logic and statistics. Scaling down you (might) meet a 'field', that field (might) travel many paths simultaneously for each outcome, as for example per Feynman's description. Or you can define it as if it just 'knows' the most probable outcome. If it didn't statistics would be a joke. How it knows is interesting because you could see that as a 'time less' function. And it's part of what makes this universe tick. But I won't swear to it, and I don't think you will either :)

The real point is assuming time to be the 'symmetry break' here. And the mirror to that is something where time, at least the one we measure, doesn't exist. There is a difference between a temporal direction as we have locally defined, causality that join our universe into one thing, and a 'ground beat'. Don't know if it's possible, but maybe there can be a 'beat' behind 'time', without that temporal direction.

(we do have a ground beat, it's your local time, and it works everywhere, for every one, when it comes to physics, and repeatable experiments. We all share that one. If we didn't repeatable experiments wouldn't be repeatable.)
==

Try this one Time Really Passes. for one argument :)

« Last Edit: 27/01/2015 22:01:27 by yor_on »

#### yor_on

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #15 on: 28/01/2015 14:48:54 »
If you read that link, I find this most interesting "When we use a Geiger counter to detect whether a radioactive atom has decayed or not, we register a click, according to whether the decay occurred. Either there is a click or not, but not both. In the many worlds theory, both do indeed happen, but just in different worlds. We are to dismiss the apparent uniqueness of the experimental outcome as an illusion."

you can apply it, keeping a uniqueness to what we experience, by assuming that what's existing is a result of this symmetry break, forcing a causality and local clock upon us. It doesn't need to be so that every path is taken, just that every path is available for 'testing', and then allowing the one that fits our situation. There's a lot of logic to the way we're built, a lot of laws and rules to this universe. In that case this 'timelessness' existing somewhere else also can be seen as something containing more 'dimensions' than what we have as it allows for 'everything', then 'choosing' a outcome. And classical physics also must have to do with it, as well as the idea behind Mach's principle, that everything communicates with everything. Like a four dimensional puzzle, built according to the classical and other physics, chemistry, you name it. That leaves only a few outcomes most probable each time, following the rules set up, which also makes for repeatable experiments. Somewhat making us into a sub set, to something 'more', defining this universe.
=

And that one we then can turn upon its head :) defining it such as you first need those rules, then creating 'one' creating the rest. Like the way we're backtracking suns, creating new types of suns, creating planets, creating life. it shrinks and become simpler as you back track it, more and more complex as you follow it the other way into a 'now'. It's in a complex plane creation, and it covers a lot more than just physics, that one is easy to see looking at the way we act. It doesn't matter if we think 'ethics' are our invention, that wouldn't be here without us. To me it's a inevitable outcome of intelligent life. And if you accept many origins, then it happened all over.

Also :) And this one some won't like quite possibly. Turning the idea of dimensions on its head, instead defining it such that the existence of dimensions imply a symmetry break :)
=

So, where would that leave a universe, many origins, each one traceable to a simple beginning, a Big Bang. What is a universe? And 'dimensions'? If it now would be communication that create a universe then? The ability to exchange information between 'points'? What would they need? Similar rules, the exact same rules? Could they compromise? Would such an ability also create dimensions?
« Last Edit: 28/01/2015 16:11:30 by yor_on »

#### yor_on

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #16 on: 29/01/2015 15:07:05 »
John, you can also think of it this way. both arguments, mine as well as yours can be thought to work. It depends on how you set your expectations. I use 'c', and treat gravity as something impending on it, using 'paths'. You define it as 'c' only is 'c' in SR and loses its definitions in GR. Myself I prefer 'c' to be 'c' in both cases, and use it as a origin. That also means, (to me then:), that the universe started 'simple'. It had a constant that it used and from that, with transformations we get to the gravity we find practically today. I don't mean that gravity, as a rule, didn't exist in a Big Bang, just that  the 'rule of constants' was 'c'.

Gravity is a result of matter, acceleration and 'energy' http://physics.bu.edu/~duffy/py105/Energy.html over a SpaceTime. 'c' on the other hand, is communication to me. It's what communicates inside you, outside of you, everywhere, and it adapt to a geometry. but it has to be 'c'. From 'c', backtracking our universe to its simplest constituents you can see that 'c' is a 'flat representation' of a Space Time. The way I think of it is as a local definition, to be perfectly simple defined for SR. SR fits that first instant of a Big Bang, to me (again), as I use a definition where a inflation has 'many origins', thinking of it as if communication is what upholds, and create, a 'commonly agreed on SpaceTime'.  SpaceTime is the commonly agreed on concept, of local constants 'running rampant all over', in my thoughts sort of (and that's a joke, even if containing a grain of truth:). so my universe should be a simple one, where communication gets raise to complexity. And 'complexity' does not end in matter and 'energy', it's also what give us thoughts, ethics, morals etc etc. It's about information to me. Communication is what is needed to exchange information. Using 'c' as information, also defining it as equivalent to a local time keeping (clock) it's the speed of information for us macroscopically. Whether that can be circumstanced through entanglements I'm of two minds. Maybe it can? On the other tentacle, using my definitions, we then would have access to something else than this SpaceTime we observe, as it would break the speed of information. QM is the way to go.

Using my definitions you also can define it as 'time dissolves' in a entanglement. It does not seem to obey 'c'. that is unless we start to differ between what is useful information, versus non-useful. It doesn't help us to 'know' of a entanglement falling out, unless we can use it to exchange information. and this exchange seems still to be defined to 'c'.  But, it's about 'time' and it's about 'c'. There might be a limit to entanglement though, if you consider Planck scale to be of importance, or maybe it's more correct to define as outside of Planck scale? Using those units 'times' shortest step is one Planck length, as well as 'c' is. the equivalence is there, but if we assume a entanglement to be instantaneous, then it's also outside what I define as a exchange of 'useful information' .So the most interesting thing I can think of, for the moment :) is whether there is a way go around the limit of information using entanglements.
« Last Edit: 29/01/2015 16:04:59 by yor_on »

#### jeffreyH

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #17 on: 29/01/2015 22:23:29 »
This can all be cleared up by looking at it in one way. Think of a highway and you are in the fast lane traveling at 100 mph. The first car you pass is traveling at 40 mph so you pass him easily and your speed compared to him is relatively fast. The next car you pass is traveling at 50 mph and so your speed relative to him is slower than when you passed the first car. This can continue until perhaps the last car you pass is traveling at 99 mph. You speed relative to his is a crawl compared to the first encounter and your speed hasn't changed. Wind this all backwards and all the vehicles may have started in a traffic jam way way back along the road. That is the big bang. Why is this so difficult to understand?

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##### Re: How reasonable is the logic of Borde, Guth and Vilenkin?
« Reply #17 on: 29/01/2015 22:23:29 »