# Inflation and causality

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Several things I don't get:

1. Can we say that every event in the universe is causally connected to the big bang?

2. Can inflation cause 2 time-like events to become space-like?

In a flat universe, inflation could cause 2 locations to not be in any single light cone*, right? And thus there is no single event that could be causally related to both.

So does that mean that inflation prevents various locations in the universe from having a common causal source (and thus the answer to question 1 would be "no")?

Or does it mean that inflation allows 2 events that are not in any single light cone, to have a common causal source?

I think what I'm asking is "Does inflation destroy causal relationships, or does it preserve them?"

* If spacetime is open, it might be possible to have an infinite inflating region of space contained within an earlier light cone... if I got that right. See http://edge.org/conversation/next-step-infinity

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Several things I don't get:

1. Can we say that every event in the universe is causally connected to the big bang?

yes

. Can inflation cause 2 time-like events to become space-like?

No

Events are spacetime points vand are neither timelike nor spacelike. Vectors are timelike or bspacelike and smooth curves are timelike or spacelike if their tangent vectors are everywhere timelike orb spacelike.

Moreover, in general relativity, the spacetime manifold is fixed an neither inflation nor anything changes it.

. In a flat universe, inflation could cause 2 locations to not be in any single light cone*, right? And thus there is no single event that could be causally related to both.

This makes no sense. "Locations" would usually be interpreted as spacelike related points (not joinable by any timelike curve) and hence even in the flat case no two "locations would be in any single light cone.

. So does that mean that inflation prevents various locations in the universe from having a common causal source (and thus the answer to question 1 would be "no")?

Or does it mean that inflation allows 2 events that are not in any single light cone, to have a common causal source?

I think what I'm asking is "Does inflation destroy causal relationships, or does it preserve them?"

neither

. * If spacetime is open, it might be possible to have an infinite inflating region of space contained within an earlier light cone... if I got that right. See http://edge.org/conv...t-step-infinity

This site is interesting, but in trying to express everything without using mathematics, also introduces misconceptions and distortions.

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I read in Brian Green's The Fabric of the Cosmos that inflation "created" the matter and energy particles that exist today. Per quantum mechanics, in "empty" space, virtual particles pop into existence in matter/ antimatter pairs. They then collide and annihilate each other.

Per Greene, inflation just after the big bang expanded space at such a stupendous rate that it separated virtual particles before they could find each other and annihilate. Thus they became real particles.

Edited by IM Egdall
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I read in Brian Green's The Fabric of the Cosmos that inflation "created" the matter and energy particles that exist today. Per quantum mechanics, in "empty" space, virtual particles pop into existence in matter/ antimatter pairs. They then collide and annihilate each other.

Per Greene, inflation just after the big bang expanded space at such a stupendous rate that it separated virtual particles before they could find each other and annihilate. Thus they became real particles.

This amounts to speculation about speculation.

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Events are spacetime points vand are neither timelike nor spacelike.

[...]

This makes no sense. "Locations" would usually be interpreted as spacelike related points (not joinable by any timelike curve) and hence even in the flat case no two "locations would be in any single light cone.

I'll try to fix my wording...

Can inflation cause a time-like interval between 2 events to become space-like? Or does "the spacetime manifold is fixed" mean that nothing can change whether an interval is space-like, time-like, or light-like?

and

If our universe is flat, is it possible to find 2 points in spacetime such that no single lightcone (of any 3rd spacetime point) contains both, given inflation?

Addendum: Can the BB be considered an event, with spacetime coordinates and a light cone? Treating it as a normal event might be the source of my confusion...

Edited by md65536
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Well I hate to disagree with the good Doctor, but its my understanding that the post-inflation universe has causally disconnected observable universes, which, because of the finite speed of light, cannot freely pass information to each other.

Guth's inflation then, adds a pre-inflation period where the distances between regions were small enough for light to reach all parts and therefore insure isotropy.

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I'll try to fix my wording...

Can inflation cause a time-like interval between 2 events to become space-like? Or does "the spacetime manifold is fixed" mean that nothing can change whether an interval is space-like, time-like, or light-like?

"The spacetime manifold is fixed" means just that. It embodies ALL of "time" and ALL of "space". Nothing changes it. That is one reason for the giant incompatibility between general relativity and quantum theory.

and

If our universe is flat, is it possible to find 2 points in spacetime such that no single lightcone (of any 3rd spacetime point) contains both, given inflation?

No single light cone can contain any two spacelike separated points. This has nothing to do with inflation. So, there are lots of such points -- the tip of your nose and the tip of your right index finger at any single moment in time for instance.

Edit: This is not correct. What is true is that neither are in the forward light cone of the other. If you go far enough back in time you may and probably will find a light cone that contains both points. In special relativity you will be able to do this. When you throw in the big bang then a lot depends on the nature of the associated singularity.

Addendum: Can the BB be considered an event, with spacetime coordinates and a light cone? Treating it as a normal event might be the source of my confusion...

The big bang can be considered to be any Cauchy surface (if you don't understand this Google "Cauchy surface") near t=0. But it is not a single event. VERY imprecisely you can think of it as a point with the entire universe in its light cone, but this is so imprecise that you should not try to draw conclusions from this picture. The big bang itself is not well understood. We have theories that do a pretty good job from say t+10^-33 sec (this perhaps optimistic), but t=0 is essentially a complete mystery.

Despite the impression that you may get from popularizations, expressions such as "the moment of the big bang" are not well-defined. Moreover the singularity associated with the big bang is not a point or even a set of points in spacetime itself. By definition, there are no singular points in the spacetme manifold. Singularities in general relativity are very subtle and technical things.

Edited by DrRocket
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Well I hate to disagree with the good Doctor, but its my understanding that the post-inflation universe has causally disconnected observable universes, which, because of the finite speed of light, cannot freely pass information to each other.

My feeble understanding of inflation is that just because 2 regions are causally disconnected now doesn't mean they always were.

As with Guth's pre-inflation period that you mention, if regions are close enough together for enough time, they can share information, and still then be separated by inflation faster than c and become causally disconnected.

So I guess that without Guth's inflation, this would not happen. Even if these regions were once a fraction of a meter away from each other in the first conceivable moments after the big bang, inflation separated them early enough and fast enough that light didn't have enough time to cross even those small distances.

This would allow those 2 disconnected regions to "never" (in all well-defined time) have been causally connected with a common causal parent event, and yet still have a common cause in the BB singularity.

No single light cone can contain any two spacelike separated points. This has nothing to do with inflation. So, there are lots of such points -- the tip of your nose and the tip of your right index finger at any single moment in time for instance.

Yes, but I would say that the tip of my nose and the tip of my right index finger at a single moment one second after noon are within the light cone of my belly button at noon.

Am I not using the terms correctly?

I guess what you're saying is that 2 objects might be separated by a time-like interval at one pair of times, and be separated by a space-like interval at another. It doesn't require inflation or even for the objects to move. My fingertip yesterday and my nose today are connected by a time-like interval, but my fingertip now and nose now are connected by a space-like interval. All these events have fixed coordinates on the spacetime manifold. I was in error in trying to reason about spacetime intervals as somethings that move or evolve in space or time.

Edited by md65536
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If you think about causal disconnection, you realise that as you 'wind the film backwards' in time the disconnection becomes larger, not smaller. So without inflation, there would never have been a time where causal connectivity ensured isotropy.

But maybe what DrR means is that all parts and times of the universe are causally connected to the Big Bang event, although all parts and times of the universe are no longer ( post inflation ) causally connected to each other.

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But maybe what DrR means is that all parts and times of the universe are causally connected to the Big Bang event, although all parts and times of the universe are no longer ( post inflation ) causally connected to each other.

Right.

And this does not require inflation. But inflation does help to explain why regions that might not otherwise be expected to have been causally connected in the distant past actually were in communication -- the "horizon problem".

I guess what you're saying is that 2 objects might be separated by a time-like interval at one pair of times, and be separated by a space-like interval at another. It doesn't require inflation or even for the objects to move. My fingertip yesterday and my nose today are connected by a time-like interval, but my fingertip now and nose now are connected by a space-like interval. All these events have fixed coordinates on the spacetime manifold. I was in error in trying to reason about spacetime intervals as somethings that move or evolve in space or time.

Right.

"objects" are not events. Spacetime points are events. Spacelike and timelike separation applies to events. Events don't move so neither do the intervals that connect them.

Note the correction added in edit to that earlier post of mine. I hope I did not confuse you too much.

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What is true is that neither are in the forward light cone of the other. If you go far enough back in time you may and probably will find a light cone that contains both points. In special relativity you will be able to do this. When you throw in the big bang then a lot depends on the nature of the associated singularity.

Thanks, this helps.

Is it fair to say that causality is simple in SR (any two causally related events are within each other's light cone (one's future and the other's past cone unless the events share a point in spacetime)), but that it's not always that simple with GR?

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Moreover, in general relativity, the spacetime manifold is fixed an neither inflation nor anything changes it.

Wait, if those like, calabi-yao manifolds are always fixed, what's actually expanding when the fabric of space expands, and why do some scientists suspect the possibility of a "big rip"?

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Wait, if those like, calabi-yao manifolds are always fixed, what's actually expanding when the fabric of space expands, and why do some scientists suspect the possibility of a "big rip"?

I'm going to take a stab at this to see how well I get this.

I would not consider this post as an answer until it is approved or corrected by someone who knows!

The expansion is equivalent to the larger spacetime intervals between pairs of objects on a Cauchy surface, relative to the spacetime intervals of the same objects on past Cauchy surfaces.

If you imagine a plane in space-time that is the set of all points where t=0, for all clocks that have been synchronized to some arbitrary single clock that has arbitrarily been set to 0 (sorry if I'm unnecessarily obfuscating this!), then you'll be imagining one possible Cauchy surface.

Now if you sweep this plane forward through time*, you'll be sweeping it through the fixed spacetime manifold. The spacetime intervals between expanding regions will be larger on subsequent future Cauchy surfaces that you sweep through.

* My guess is that there are many ways to do this, and some ways but not all will result in new Cauchy surfaces.

Edited by md65536
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This amounts to speculation about speculation.

I thought iinflation answered the Big Bang theory's horizon and flatness problem. And per Greene's book, its predictions agree with CMB anisotropy. I understand inflation theory is still "a work in progress," as Greene put it. But saying it is mere speculation seems a bit too strong here.

And virtual particles also have supporting evidence like Lamb shift.

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Wait, if those like, calabi-yao manifolds are always fixed, what's actually expanding when the fabric of space expands, and why do some scientists suspect the possibility of a "big rip"?

What is "expanding" are spacelike hypersurfaces corresponding to a one-parameter foliation of spacetime by a timelike parameter. This requires homogeneity and isotropy. See the thread on cosmo basics.

Calabi-yau manifolds are irrelevant to this.

I thought iinflation answered the Big Bang theory's horizon and flatness problem. And per Greene's book, its predictions agree with CMB anisotropy. I understand inflation theory is still "a work in progress," as Greene put it. But saying it is mere speculation seems a bit too strong here.

And virtual particles also have supporting evidence like Lamb shift.

Inflation is one explanation for the horizon and flatness problem, but the post to which I responded said nothing about those problems.

Greene's books are very good, very entertaining, and very speculative. He tends to put the caveats in inconspicuous places, but at least he puts them in. You should read all books on string theory with a grain of salt. If it is a Kaku or Susskind book, a train car load is needed.

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What is "expanding" are spacelike hypersurfaces corresponding to a one-parameter foliation of spacetime by a timelike parameter. This requires homogeneity and isotropy. See the thread on cosmo basics.

Calabi-yau manifolds are irrelevant to this.

There's virtually no way to even test some a lot of the theoretical stuff. We can't test tiny 4 dimensional fold in the fabric of space, that's like string theory or an educated guess, there isn't even a way to prove there's an actual fabric of space, it could just be how force carrier particle's act in a vacuum or some other unknown forces.

Also, I thought calabi yau space was a part of the whole "what is the fabric of space?" thing anyway

http://en.wikipedia....%93Yau_manifold

Edited by questionposter
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What is "expanding" are spacelike hypersurfaces corresponding to a one-parameter foliation of spacetime by a timelike parameter. This requires homogeneity and isotropy. See the thread on cosmo basics.

Calabi-yau manifolds are irrelevant to this.

Inflation is one explanation for the horizon and flatness problem, but the post to which I responded said nothing about those problems.

Greene's books are very good, very entertaining, and very speculative. He tends to put the caveats in inconspicuous places, but at least he puts them in. You should read all books on string theory with a grain of salt. If it is a Kaku or Susskind book, a train car load is needed.

I totally agree, especially with respect to string theory, which is highly speculative. No compelling evidence to date supports (or contradicts) it.

I thought you were saying that inflation theory is also highly speculative. Perhaps I misunderstood.

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