Welcome to this week’s installment of the From Eternity to Here book club. We’re on to Chapter Fourteen, “Inflation and the Multiverse.” Only one more episode to go! It’s like the upcoming finale of Lost, with a slightly lower level of message-board frenzy.
Excerpt:
There is a lot to say about eternal inflation, but let’s just focus on one consequence: While the universe we see looks very smooth on large scales, on even larger (unobservable) scales the universe would be very far from smooth. The large-scale uniformity of our observed universe sometimes tempts cosmologists into assuming that it must keep going like that infinitely far in every direction. But that was always an assumption that made our lives easier, not a conclusion from any rigorous chain of reasoning. The scenario of eternal inflation predicts that the universe does not continue on smoothly as far as it goes; far beyond our observable horizon, things eventually begin to look very different. Indeed, somewhere out there, inflation is still going on. This scenario is obviously very speculative at this point, but it’s important to keep in mind that the universe on ultra-large scales is, if anything, likely to be very different than the tiny patch of universe to which we have immediate access.
This is a fairly straightforward chapter, trying to explain how inflation works. Given that by this point the reader already is familiar with dark energy making the universe accelerate, and with the fine-tuning problem represented by the low entropy of the early universe, the basic case isn’t that hard to put together. Of course we have an additional non-traditional goal as well: to illuminate the tension between the usual story we tell about inflation and the “information-conserving evolution of our comoving patch” story we told in the last chapter. Here’s where I argue that inflation is not the panacea it’s sometimes presented as, primarily because it’s not that easy to take all the degrees of freedom within the universe we observe and pack them delicately into a tiny patch dominated by false vacuum energy. Put that way, it doesn’t seem all that surprising, but too many people don’t want to get the message.
This is also the chapter where we first introduce the idea of the multiverse. (The multiverse occupies less than 15 pages or so in the entire book, but to read some reactions you would think it was the dominant theme. The publicists and I must share some of the blame for that perspective, as it is an irresistible thing to mention when talking about the book.) Mostly I wanted to demystify the idea of the multiverse, presenting it as a perfectly natural outgrowth of the idea of inflation. What we’re supposed to make of it is of course a different story.
Looking back, I think the chapter is a mixed success. I like the gripping narrative of the opening pages. But the actual explanation of inflation is kind of workmanlike and uninspiring. I really put a lot of effort into coming up with novel explanations of entropy and quantum mechanics, which didn’t simply rehash the expositions found in other books; but for inflation I didn’t try as hard. Partly simply because of looming deadlines, partly because I was eager to get to the rest of the book. Hopefully the basic points are more or less clear.
To Juan,
you confirmed my suspicion that you confound the ket |Psi> in the general N-particle case, with the special case described by wavefunctions as Y(x,t). Nowhere in the absoluteastronomy link that you gave above appears the word “field”, even once!
As explained to you before, it is only the last special case of Y(x,t), which can be interpreted as a field and next quantized using the formalism of second quantization.
You are right that “In any general sense, since real numbers are a subset of complex numbers, I can most certainly tell you that any number you produce has a complex number representation.” But this is a straw-man. Evidently the complex extensions of the Schrödinger equation used to explain some of the phenomenology of irreversible systems and of the arrow of time are those where purely real observables are extended by adding a non-zero imaginary part. If you read my messages with care, you would find the part where I gave the dissipation condition. I repeat it now: “In standard literature, the dissipativity condition is then defined as Im{H} =< 0”. When the imaginary part is zero, dissipation is zero and one recovers time symmetry.
I fail again to follow parts of your message. You did not reply to my questions for clarifications and it seems that you are rejecting the well-known fact that the Schrödinger equation is Markovian with your “since you don’t understand the general use of the word Markovian”.
The Schrödinger equation is valid only as approximation, when one ignores non-Markovian corrections, mixed states, random terms f… In the more general cases we use more general equations: from simple Ito-Schrödinger equations to more developed expression as Lindblad equation, Eu equation, the Brussels-Austin equation, etc.
An introduction to the Lindblad equation is given in the above Wikipedia link linked in my previous message.
I want just to add that the Brussels-Austin equation is based in a complex extension of the Liouville space and the condition for dissipativity is Im{Z} =< 0, where Z is an eigenvalue of the Liouvillian in a generalized space (beyond the Hilbert space of ordinary quantum mechanics). The applications to instable systems: particles, fields, etc. are found in standard literature in mainstream journals
http://order.ph.utexas.edu/people/Petrosky.htm
Hi Sean,
(I have a strange problem using chrome: each time I try to comment I’m redirected to Petrosky’s web page. It’s seems ok using explorer.)
Thx for your answer, although I’m not sure to understand. You seem to say that what happens in a flat matter-dominated universe has nothing to do with inflation. Then I was unclear: my question is about whether the “to any observer the size of the observable universe is the size of a black hole”? assertion may also hold in a universe with a big vacuum energy, or cosmological constant.
“the universe isn’t a black hole; if anything, it’s a white hole.”
What if white holes were black holes seen from the inside?
I don’t disagree with you Juan. I think that you are entirely right. I can insert an arbitrary variable into any equation and make it behave in a way that makes us happy. The question is whether the variable is used for an ad hoc approximation or whether it has real physical significance.
In any case when it comes to states, we run into the same general questions of orthogonality, independence, exclusion, variance, collinearity, interaction, etc. These general issues are what we are trying to address when we build our models, and there is a growing proscriptive way of how to deal with these things when building a theory.
In any case, putting aside the physical meaning of the word emergence, we see that how our equations behave emerges from our general use of the properties of numbers and how we construct more complex mathematical structures that incorporate those behaviors. The beauty and frustration of modern physics is that the real world almost behaves as objects we can define mathematical, but not quite. This is why I keep telling you that our disagreement is a semantical one and completely detached from the specifics of the application of math to particular problems.
That we can model certain systems using a particular approach is useful, but whether it reveals a deeper physical understanding and linkage to fundamental behavior of mathematical objects is another issue.
Also you need to be more careful with your use of onclick and urchinTracker
You know what Juan. I want to apologize for my behavior.
I’m very late coming to the book club (I was #7 on the library’s wait list). Ch.2’s comment option is long closed so I am posting here.
Top of pg 39, If I read correctly, you are stating the apparent angular size of the Sun is about 1 degree across. If that were true, there would be more frequent lunar eclipses, but no total solar eclipses. I believe the value is about half that value, around 0.5 degrees or 32 arc minutes, approximately the same size as the disk of the moon.
Yes; that was a typo.