April 2, 1999 NEW!

Some reading.

I've spent most of the last few days at the library.

I started with labyrinths again. Found a book with plans of old mazes and passages about the Cretan labyrinth, then followed the references into stories about people going underground. Somewhere along the way I ended up reading the sixth book of the Aeneid. There's a passage about how easy it is to go down and how difficult it is to get back out. I copied the reference, though I hardly needed reminding.^[1]^[2]

Then I asked about books on time travel.

I had trouble getting the words out. I wanted to explain that I meant the physics, but the librarian hadn't suggested otherwise. She just asked what I'd already read.

I also looked up delusions, dissociation, and experiences around sleep. Things people see while they believe they're awake. I sat with a psychiatric manual open beside my notebook for most of one afternoon.^[3] Some descriptions sounded familiar until I read further. Others frightened me enough that I stopped taking notes.

I don't know how to assess any of that. I can recognize something I've felt in a paragraph without knowing whether the rest applies to me.

By the time I got home, I had a stack of photocopies and no useful answer. Each explanation seemed reasonable while I was reading it. Then I'd think about the kitchen in that other house, or try to put my leg into the socket again.

I've mentioned the doctorate before. Theoretical physics. I ought to be able to make a better attempt at this than looking for a story that resembles what happened to me.

The phrase I kept coming back to was Einstein-Rosen bridge.^[4]

I knew it before any of this. I also know that the original bridge isn't a passage you can simply walk through. Calling the opening downstairs a wormhole would already be assuming something I haven't established.

Still, I've started working through the equations again.

Ignoring the cosmological constant for the model I'm considering:

G_{μ ν} = R_{μ ν} - \frac{1}{2} R g_{μ ν} = \frac{8 π G}{c^{4}} T_{μ ν}

I wrote that across a clean page and sat looking at it. I know what the symbols mean. I have no measurements from downstairs that would let me put anything useful into them.

There are mathematical models of traversable wormholes. Morris and Thorne worked through some of them years ago.^[5] The difficulty goes beyond finding an enormous supply of energy. Their throats require stresses that violate an energy condition satisfied by ordinary classical matter. I can't turn that requirement into a list of things to buy.

I caught myself writing “no solution” in the margin.

That's careless. There are solutions under particular assumptions. Whether anything physically available could support them is another question. Nobody has demonstrated a traversable wormhole. These papers study the mathematics; they don't describe an experiment I can repeat.

The time-travel paper is worse to read now. I remember being interested in this sort of thing when it was safely hypothetical. Under the conditions Morris, Thorne and Yurtsever discuss, a traversable wormhole could acquire a time shift between its mouths.^[6] Hawking gives reasons to suspect that quantum effects would prevent the formation of a time machine.^[7]

I've been going back and forth between them, checking what each argument assumes.

None of this accounts for my knee. Even if I accepted the date on that receipt, moving between two dates wouldn't explain why part of my leg has grown back.

I still don't believe I've traveled through time. I realize how that sounds after what I've written here. I don't know what I believe. I've described what I remember, and now I'm trying to find a way to check it.

I used to be much more comfortable deciding that something was impossible. At the moment I can't even give a reliable account of how long I spent underground.

I've asked the library to get Visser's book and copies of several papers I couldn't find.^[8] There are references in the references, so the list keeps getting longer. I'm going to work through them properly. Write down the assumptions, check the calculations, see whether any of it suggests something I can actually measure.

I've cleared the kitchen table for the papers. The groceries are still in the bag on the other chair.

- me, Daniel

References and notes

W. H. Matthews, Mazes and Labyrinths: A General Account of Their History and Developments. Longmans, Green and Co., 1922. Plans, historical accounts and mythology. Nothing I found in it explains the changing distances in my notes.
Text of the book. Back to text
Virgil, Aeneid, Book VI, particularly lines 126–129. The Sibyl's warning concerns the return from the underworld. I have copied the reference without treating the resemblance as evidence.
Book VI. Back to text
American Psychiatric Association, Diagnostic and Statistical Manual of Mental Disorders, fourth edition, 1994. I haven't diagnosed myself from this. I wrote down some questions to bring to my therapist.
DSM-IV. Back to text
A. Einstein and N. Rosen, “The Particle Problem in the General Theory of Relativity,” Physical Review 48, 73–77 (1935). The bridge construction must not be confused with a demonstrated, traversable connection between two places.
Original paper. Back to text
M. S. Morris and K. S. Thorne, “Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity,” American Journal of Physics 56, 395–412 (1988).
For a static, spherically symmetric model:
$d s^{2} = - e^{2 Φ (r)} c^{2} d t^{2} + \frac{d r^{2}}{1 - \frac{b (r)}{r}} + r^{2} d Ω^{2}$ $d Ω^{2} = d θ^{2} + \sin^{2} θ d φ^{2}$
At a regular throat, b(r₀) = r₀. The flaring condition requires b′(r₀) < 1; Φ must remain finite to avoid a horizon. With ε denoting local energy density and pᵣ radial pressure, the field equations give, at the throat,
${(ε + p_{r}) |}_{r_{0}} = \frac{c^{4}}{8 π G {r_{0}}^{2}} [b^{'} (r_{0}) - 1] < 0$
This violates the null energy condition. Spherical symmetry is a simplifying assumption here, not something I've observed downstairs.
Paper. Back to text
M. S. Morris, K. S. Thorne and U. Yurtsever, “Wormholes, Time Machines, and the Weak Energy Condition,” Physical Review Letters 61, 1446–1449 (1988).
Their analysis includes null geodesics for which
$\int T_{μ ν} k^{μ} k^{ν} d λ < 0$
where $k^{μ} = \frac{d x^{μ}}{d λ}$ and λ is an affine parameter. This is an averaged energy-condition violation. The time-machine argument is conditional on creating and maintaining a traversable wormhole; it does not establish that either is physically achievable.
Paper. Back to text
S. W. Hawking, “Chronology protection conjecture,” Physical Review D 46, 603–611 (1992). Quantum stress-energy near an emerging chronology horizon may produce backreaction that prevents closed timelike curves from forming. A conjecture supported by calculations under stated assumptions, not a general experimental verdict.
Paper. Back to text
Matt Visser, Lorentzian Wormholes: From Einstein to Hawking. American Institute of Physics Press, 1995. Requested through the library. I haven't read it yet.
Author's bibliography. Back to text

Comments (2)

Comments

Jackson wrote:

I went back to the junction pages after reading the wormhole references. Before distance can go into an equation, you have to say which two points you measured between. You could do that when your numbers were still on the walls. I'm trying to imagine what you'd use now.

al_73 wrote:

I can't follow the equations, but I don't think a wrong date on a receipt gets you this far. Have you tried the phone number on it, if there is one?

References and notes

Comments

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