Did cosmic inflation happen everywhere in the Universe?

[PeterDonis]

A condensation of an energy point, into matter, can change the reference parameters in an isotopic way.

I have no idea what you are talking about here. Can you give a reference?

 

[RobertSpencer]

Sure there is. The inflating region and the bubble universes do not occupy the same spacetime. You are trying to apply intuitions that simply don't apply here.
That's one way to do it, but not the only way. There is no requirement that the different bubble universes lie "in the same space" even in a higher dimension.

So, they reside in 2 different dimensions?

Is this the String Theory extra dimensions you are talking about?

 

[PeterDonis]

So, they reside in 2 different dimensions?

No. The idea of "same dimension" or "different dimension" doesn't apply at all. Again, you are trying to use intuitions that simply don't apply to this model.

 

[Ibix]

Imagine a 2d universe on a sheet of paper. Now imagine another one and another. You could imagine them stacked on top of each other. Unfortunately that's wrong. What you've done is taken the 2d universes and "embedded" them in a 3d space, and there's a direction from one universe to the next. As soon as you try to visualise that it's wrong.

The best analogy I can come up with for what (I think!) @PeterDonis is saying is an Excel workbook. You have a universe on each worksheet, and there's a collection of worksheets, but there's no spatial relationship between the sheets. They're not next to each other, and they're not underneath each other. You just click the tab to select the one you want to see.

 

[RobertSpencer]

Can you pls elaborate a bit further how 2 spacetime

Sure there is. The inflating region and the bubble universes do not occupy the same spacetime. You are trying to apply intuitions that simply don't apply here.
That's one way to do it, but not the only way. There is no requirement that the different bubble universes lie "in the same space" even in a higher dimension.

Can you pls elaborate a bit further what this means? I thought that space-time was just a mathematical concept created by Einstein to explain Relativity.

I always thought that there is no such thing as space-time, like there is something called space.

What would 2 different spacetimes look like??

 

[weirdoguy]

I thought that space-time was just a mathematical concept created by Einstein to explain Relativity.

Both theories of relativity teaches us that spacetime is as "real" (whatever that means) as space.

 

[PeroK]

Can you pls elaborate a bit further how 2 spacetime

Can you pls elaborate a bit further what this means? I thought that space-time was just a mathematical concept created by Einstein to explain Relativity.

I always thought that there is no such thing as space-time, like there is something called space.

What would 2 different spacetimes look like??

Space and time or spacetime are both a) some physical, measurable aspect of our universe; and b) a well-defined mathematical object to which the physical thing is mapped in a mathematical model.

The other thing you are missing, although it can be a difficult concept, is that two universes may have absolutely no relation to each other. In one sense, there's no point in even talking about things outside our universe, as, by definition, we cannot observe them in any way. But, we can imagine that there might be completely separate universes. In this case, however, asking "where" or "when" they exist makes little sense. As does asking what they "look" like.

 

[PeterDonis]

I thought that space-time was just a mathematical concept created by Einstein to explain Relativity.

I could just as well say that "space" was just a mathematical concept created by Euclid (or Kant, or Galileo, or Newton) to explain geometry and Newtonian physics. See further comments below.

I always thought that there is no such thing as space-time, like there is something called space.

You have it backwards. As far as GR is concerned, spacetime is more "real" than space, since spacetime is an invariant 4-dimensional geometry, whereas "space" is an artificial construct that depends on your choice of coordinates. Note that this basic concept is taken from special relativity and has nothing to do with gravity or cosmology in particular; it is necessary, as Minkowski showed in 1907, because the Lorentz transformations between reference frames mix up space and time; there is no way to keep them separate, as they are in Newtonian mechanics. If you don't understand this basic point, I strongly suggest taking the time to learn SR properly, from a textbook like Taylor & Wheeler that explains how spacetime works.

What would 2 different spacetimes look like??

Like two different 4-dimensional geometries, which have no connection with each other.

 

[nikkkom]

If inflation did not stop everywhere then wont' those inflating bubbles squish into other inflating bubbles and non-inflating bubbles (like our observable universae) thus destroying things or creating a catastrophic event?

Imagine a 2-dimensional analogy: an ever-stretching "rubber" sheet.

Inflation would be a case where the relative recession rate increases for any two chosen comoving observers, and remains constant if you choose two points at a fixed distance from each other and measure how fast comoving observers move past.

If inflation stops in a bounded region of this "rubber" sheet, it means that this patch becomes more rigid and less able to stretch: relative recession rate of comoving observers no longer increases. (It even slows down).

If you imagine how real rubber behaves, it's obvious that the "faster expanding" remainder of the sheet is _not_ squishing our "more rigid" patch: if anything, it tries to pull on its edges a bit: "why aren't you keeping up?"

 

[nikkkom]

The only thing I don't get is how some of those bubble universes cannot bump into one another?

The "black/empty" volume in that picture expands much, much, MUCH faster than bubbles do.

 

[JMz]

Problem is this. Matter and energy are the same thing.

Setting aside the question of mass and energy being "the same thing", matter and mass are certainly not. As conventionally phrased, matter is simply the densest form of energy (or mass). Other forms existed, but matter did not.

 

[RobertSpencer]

The "black/empty" volume in that picture expands much, much, MUCH faster than bubbles do.

I can believe this. But PeterDonis says that those bubbles are spatially infinite.

So, I don't see how even more than one bubble can exist anyway.

I don't get the 4-dimensional geometries thing. I majored in biology not physics.

When you mean 4-dimensional geometries, do you mean 3 spatial + 1 time dimension??

Is this 4-dimensional geometries a thing, like the the sun is a thing?

 

[PeterDonis]

PeterDonis says that those bubbles are spatially infinite.

Yes.

So, I don't see how even more than one bubble can exist anyway.

That's because you're making an assumption that is not valid: that all of the bubbles have to share the same "space". They don't. This has been stated several times in this thread, and it's going to stay the same no matter how many times you say you don't believe it. You asked a question and that's the answer.

When you mean 4-dimensional geometries, do you mean 3 spatial + 1 time dimension?

Yes.

Is this 4-dimensional geometries a thing, like the the sun is a thing?

Yes.

 

[RobertSpencer]

Yes.
That's because you're making an assumption that is not valid: that all of the bubbles have to share the same "space". They don't. This has been stated several times in this thread, and it's going to stay the same no matter how many times you say you don't believe it. You asked a question and that's the answer.
Yes.
Yes.

So, in the above multiverse picture, what is the black stuff, the stuff outside the bubble?? What is that? Is that 'space' or the 'inflation field'??

The 'inflation field' resides in 'space', right?? So, is the black area 'space'?

Is it another 4-dimensional geometric which is spatially infinite?

 

[JLowe]

View attachment 224051

So, in the above multiverse picture, what is the black stuff, the stuff outside the bubble??

That's not a picture of any "multiverse." It's nothing but artist conception. It has no literal value whatsoever.

 

[JMz]

I don't get the 4-dimensional geometries thing. I majored in biology not physics.

Perfectly acceptable. But PF deals with the most mathematical science, and mathematical physics has existed for at least 100 years longer than mathematical bio has. We have a responsibility to look for common language with you, but it's not always possible to give you the extra 100 years of math background in an online forum. If you want to understand beyond the level of metaphors, as you seem to, then you have a responsibility to do some serious reading. We can suggest good sources.

 

[PeterDonis]

in the above multiverse picture, what is the black stuff, the stuff outside the bubble?

Meaningless. The response from @JLowe is correct.

The 'inflation field' resides in 'space', right?

It depends on which model of inflation you are talking about. In the "eternal inflation" model, which appears to be the closest one to the one you have in mind, the spacetime in which the inflation is occurring is separate from each of the "bubble universe" spacetimes that come into being. So from the viewpoint of any of those bubble universes, no, the inflaton field is not in their "space" (actually spacetime) at all. (More precisely, it doesn't have a nonzero value anywhere in their spacetime.)

 

[rootone]

Can you pls elaborate a bit further how 2 spacetime

There is not is not two spacetimes, who said that?

 

[PeterDonis]

There is not is not two spacetimes, who said that?

I think he was referring to a number of my posts in this thread. I was trying my best to express in ordinary language how an eternal inflation model can have multiple "bubble universes" that are spatially infinite (as we think ours is). Any attempt to describe this in ordinary language is going to distort something.

 

[rootone]

OK Peter. Thanks for the explanation.
Yes there are multiverse theories.
To be fair I need to sharpen my Occam's razor a bit.
and see a dentist as well.

 

[RobertSpencer]

Is Inflation a theory which is supported by lots of experimental evidence, or is it still a hypothesis?

 

[PeterDonis]

Is Inflation a theory which is supported by lots of experimental evidence, or is it still a hypothesis?

Both. We have evidence that our universe had an inflationary epoch (though not all cosmologists assign the same weight to it), but we don't have any real evidence for a multiverse or models like eternal inflation; discussion about the different possible inflation models are just theoretical at this point.

 

[RobertSpencer]

I think I am getting a little bit idea of what is going on.

Inflation's mathematical physics gives equations which shows that there can be bubble universe which are in different space-times.

Suppose there are 2 people in Bubble universe A and B, one in A and the other in B.

If A takes a spaceship and travels in any direction for any amount of time, you are saying that he will not meet the person in Bubble universe B.

So, this type of scenario is possible only if the 2 space-times are in 2 different dimensions I presume?

Are 2 4D spacetimes both having infinite space is a purely mathematical construct?

It's just on paper but no evidence exist for it?

Is it the maths that tells us that both can exist with infinite space in different space-times??

 

[PeroK]

I think I am getting a little bit idea of what is going on.

Inflation's mathematical physics gives equations which shows that there can be bubble universe which are in different space-times.

Suppose there are 2 people in Bubble universe A and B, one in A and the other in B.

If A takes a spaceship and travels in any direction for any amount of time, you are saying that he will not meet the person in Bubble universe B.

So, this type of scenario is possible only if the 2 space-times are in 2 different dimensions I presume?

Are 2 4D spacetimes both having infinite space is a purely mathematical construct?

It's just on paper but no evidence exist for it?

Is it the maths that tells us that both can exist with infinite space in different space-times??

Here's a different mathematical analogy. Suppose you are on the real number line. Given any positive number, if you go far enough to the right you will reach it. And, given any negative number, if you go far enough to the left you will reach it.

But, at what point do you encounter the function ##f(x) = \sin x##?

The mathematical space of continuous functions is not connected to the number line, or to the space of 3D vectors. You could ask, if the space of 3D vectors takes up all of 3D space, then "where" are all these continuous functions? And, where is the set of nxn matrices? But, these are fruitless questions. Mathematically these sets of objects are separate. They belong in separate sets, each of which may be finite or infnite dimensional - the set of continuous functions is infinite dimensional.

You need to free up your mind a little. At the moment, it appears you cannot conceive anything outside a single 3D + 1T universe. There's almost no point in reading about multiverses if you can't think beyond this!

Try to imagine that there might be other universes with no spatial or temporal connection to our universe at all. Completely separate universes, with nothing in common with each other - not even the same laws of physics. As separate as the set of continuous functions is from the set of 3D vectors.

 

[jbriggs444]

2 space-times are in 2 different dimensions I presume?

The term "dimension" does not mean what you think it means.

 

[PeterDonis]

If A takes a spaceship and travels in any direction for any amount of time, you are saying that he will not meet the person in Bubble universe B.

That's correct.

his type of scenario is possible only if the 2 space-times are in 2 different dimensions I presume?

No, it just means the 2 spacetimes are not connected. In other words, when you say what you said in the first quote above, you've said all that needs to be said. There is no more.

It's just on paper but no evidence exist for it?

See post #57.

 

[nikkkom]

I can believe this. But PeterDonis says that those bubbles are spatially infinite.

Then we interpret the same pic differently. I see it as a depiction of inflationary model where more than one region of space underwent transition to the lower-energy vacuum.

 

[PeterDonis]

I see it as a depiction of inflationary model where more than one region of space underwent transition to the lower-energy vacuum.

Yes, but the "depiction" is obviously not accurate since it's not showing the "bubbles" of true vacuum as spatially infinite, whereas our best current model says the one we actually live in is spatially infinite.

 

[nikkkom]

Yes, but the "depiction" is obviously not accurate since it's not showing the "bubbles" of true vacuum as spatially infinite, whereas our best current model says the one we actually live in is spatially infinite.

I don't think so. Our observations only tell us that the size of our low-energy vacuum bubble is likely to be much bigger than observable Universe.

 

[PeterDonis]

Our observations only tell us that the size of our low-energy vacuum bubble is likely to be much bigger than observable Universe.

Our current best fit model is that our universe is spatially flat. That is based on combining a number of different observations. A 3-sphere with an extremely small curvature (so its 3-volume is much larger than that of our observable universe) is within the current margin of error, yes, but is considered unlikely.

However, the key point for this discussion is that, as far as I know, an "eternal inflation" model with multiple "bubble universes" is compatible with each bubble being spatially infinite. So whichever our own universe turns out to be, it would not rule out an "eternal inflation" model.

 

[nikkkom]

However, the key point for this discussion is that, as far as I know, an "eternal inflation" model with multiple "bubble universes" is compatible with each bubble being spatially infinite.

Well, this would only be possible if the Universe is more than 3-dimensional spatially, if it to contain infinite multiple 3-dimensional objects. I never heard that eternal inflation models assume that.

 

[PeterDonis]

this would only be possible if the Universe is more than 3-dimensional spatially, if it to contain infinite multiple 3-dimensional objects.

You're making the same assumption @RobertSpencer is making: that all of the bubble universes need to be in the same "space". As I understand the "eternal inflation" models, that is not the case.

 

[RobertSpencer]

Well, this would only be possible if the Universe is more than 3-dimensional spatially, if it to contain infinite multiple 3-dimensional objects. I never heard that eternal inflation models assume that.

I totally get this. This is talked about in Brian Greene's book Hidden Reality.

The only problem is, since that 4th spatial dimension is so small, I don't see how an entire universe can reside in it.

 

[PeroK]

I totally get this. This is talked about in Brian Greene's book Hidden Reality.

The only problem is, since that 4th spatial dimension is so small, I don't see how an entire universe can reside in it.

Perhaps it's a small universe!

 

[PeterDonis]

This is talked about in Brian Greene's book Hidden Reality.

Please note that this is a pop science book and you should not try to learn actual science from it. (Brian Greene's pop science books, in particular, seem to cause a lot of misunderstandings.)