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(For the purposes of a science-fiction story where the author is attempting to have as much basis in fact as possible) if one were to create or make use of a Morris-Thorne or similar traversable wormhole and accelerate one end to modify it to be a "time machine", would one simply be able to step through? Would the transition, in theory, be safe or deadly? Would some kind of life-support gear be in order? Would this apply also if one stepped back to the younger end (from the point of view of the person travelling through).

For the purposes of this I'm assuming that both ends of the wormhole are on the Earth's surface and at points in time where the atmospheric, surface, etc. conditions are suitable for a human to live normally.

I apologise if this should be in the Science Fiction site, but I wish to look at this from the point of view of a scientist with the sense of wonder of, say, Hawking. Any information and thoughts on this would be amazingly helpful.

EDIT: I don't feel this question is a duplicate of the question: Would there be forces acting on a body as it traverses space near a wormhole?; as I seek to understand the effects of passing through the wormhole to a human's life and health by "stepping" through, not an ambiguous body in space.

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There are quite a variety of concerns here. For a full overview you can check "Lorentzian wormholes" by Visser. For now we'll consider wormholes defined by the thin-shell formalism, where the matter propping up the wormhole is on a very thin shell on the wormhole mouth.

First, there's the tidal forces. As the tidal stress induced by gravitational forces depends on the Riemann tensor, we can consider the Riemann tensor of a thin-shell spacetime :

$$R_{abcd} = - \delta(r) \tau_{abcd} + \Theta(r) R^+_{abcd} + \Theta(-r) R^-_{abcd}$$

with $\tau_{abcd}$ a tensor depending on the discontinuity of the extrinsic curvature $K$. Since this is the most important part in propping the wormhole open, let's assume (without any good reasons) that we can neglect the curvature outside of the wormhole mouth.

The extrinsic curvature tensor locally looks roughly like

\begin{equation} K = \begin{pmatrix} 1/R_t & 0 & 0 & 0 \\ 0 & 1/R_1 & 0 & 0 \\ 0 & 0 & 1/R_2 & 0 \\ 0 & 0 & 0 & 0 & 0 \end{pmatrix} \end{equation}

$R_t$ is the radius of the timelike curve described by that point (it's related to the wormhole's acceleration), while $R_1$, $R_2$ are the principal radii of the surface. Hence by making the radii as large as possible (that is, making the surface as flat as possible), we can make the tidal effects arbitrarily small.

In other words, if the wormhole mouth has at least one part of it that is flat, then one can pass through it unmolested by tidal forces.

Then there's the matter of the matter itself propping the wormhole open. As there isn't really any realistic model of matter that can prop up a people-sized wormhole (or even one large enough to get one electron to go through), it's hard to say exactly what are the possible risks (the matter involved might not even couple to ordinary matter), but considering a rough estimate of the order of magnitude for the (absolute) energy is about $10^{27} kg$, in an area of a few cubic meter, it's safe to say that it's probably not a great idea to approach it too much.

There again, flat faces are a benefit : the stress-energy tensor for the thin-shell part is again zero if the surface is flat. This does not mean still that this is a good idea : such very dense matter is likely to radiate in the vicinity.

Another issue is the throat length and time : if we drop the thin-shell assumption, which isn't terribly realistic, there is still some way to travel between the two mouthes. The length of the throat is related to the amount of negative energy required (long throats require less negative energy), which means that a more reasonable worhole may have very long travel times to actually cross. The perceived time is also an issue, as the travel time could be very short for the person crossing it but very long from the outside perspective (this is related to the redshift function which brings up a whole bunch of other potential problems).

Then if we actually assume a time machine scenario, things get much much worse. To simplify matters somewhat, you might be aware that you can describe the quantum vacuum as a gallore of virtual particles (wrong yes, but let's go with that for now). As a wormhole approaches time machine formation, there are more and more virtual particles forming almost-loops, which has the bad side effect of blue-shifting them, increasing their energy. Those become actual loops when the time machine is actually formed, which has the result of making the stress-energy tensor diverge : the quantum vacuum has infinite energy, which probably bad results if this was possible.

It's quite likely that the wormhole collapses before this happens.

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  • $\begingroup$ Great answer! This is going to reveal my lack of knowledge; I'm having difficulty putting the order of magnitude of absolute energy from the exotic matter shell into context, due to the use of kg in the answer. Is this erroneous or can you provide clarification? I find orders of magnitude of energy is typically measured in J. $\endgroup$ – Johnny Kirk Mar 2 '18 at 18:16
  • $\begingroup$ You can convert to joules by the usual $E = mc^2$. Wormholes are usually about $10^{44} J$ of energy for an opening on the human scale. If you wish for something a bit less harrowing math-wise you can try "The physics of Stargates" by Enrico Rodrigo, which is fairly complete and not very math-heavy. $\endgroup$ – Slereah Mar 2 '18 at 18:19
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I'll divide this up into two categories: hard constraints and slightly less hard constraints.

Hard constraints

There are pretty general arguments to the effect that the throat of a wormhole is likely to be an environment of hard radiation. This would probably kill you.

The structure of general relativity is such that if a being wants to artificially create any object whose gravity is strongly non-newtonian, it needs to have godlike mastery of absurd amounts of mass and energy. It's hard to imagine such a being as having anything in common with humans.

Exotic matter is required in order to stabilize a wormhole. Even if exotic matter exists (which it probably doesn't), the Ford-Roman quantum inequality is a hard constraint on what you can do with it.

Slightly less hard constraints

Each mouth of the wormhole basically acts like an object with some mass, within its own part of the universe. Therefore by default we just expect it to travel along some orbit. It is not possible for it to orbit while remaining stationary with respect to the earth's surface. If you wanted it to sit in someone's house, for example, you would need to have some way to exert a force to support its weight. Otherwise it would sink to the center of the earth, probably with catastrophic consequences for the earth.

Generically, we expect exotic matter to be deadly to humans, since atoms are the only form of matter that can come in contact with humans in kilogram quantities without annihilating them.

By default we expect a wormhole to be a region of intense gravitational fields, very much like a black hole. Stepping through a wormhole is likely to kill you through tidal forces, just as in the case of falling into a black hole, where you will probably be spaghettified before you hit the singularity. As with black holes, the intensity of these tidal forces decreases with the size of the object. A very small wormhole like the one you describe is likely to be more deadly.

As pointed out by John Rennie in a comment, Visser has described a class of wormholes that theoretically allow a human to pass through without touching any exotic matter or experiencing any tidal forces. However, they require matter with even more exotic properties than other wormholes. It is generically true that general relativity lets you have any spacetime geometry you want, but it then requires you to have matter distributed in a certain way and having certain characteristics in order to support that geometry. The types of matter Visser talks about are so different from anything we know of that IMO his calculations are tantamount to saying that you can't actually have the geometry he describes.

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  • $\begingroup$ Thanks for your answer! I know when discussing wormholes in the scope of GR you do require a shell of exotic matter with negative mass to keep the wormhole open for someone to travel through without exceeding the speed of light, but I hadn't considered the effects of the exotic matter on life in itself; I'm curious if you could please elaborate on the effects of exotic matter with negative mass itself on life and also the hard radiation from the wormhole? I feel the effects of the wormhole on Earth itself and it falling in is beyond the scope of the question, but it's certainly interesting. $\endgroup$ – Johnny Kirk Mar 2 '18 at 17:16
  • $\begingroup$ I apologise, to avoid misunderstanding I didn't mean the effects of the hard radiation on life, I meant more information on the nature of this radiation. $\endgroup$ – Johnny Kirk Mar 2 '18 at 17:23
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    $\begingroup$ Ben, is that always true? The sort of polyhedral wormholes Matt Visser described have no tidal forces except very near to the edges, and I think (but wouldn't swear to it) that the Ellis wormhole has at most minimal tidal forces. $\endgroup$ – John Rennie Mar 2 '18 at 17:23
  • $\begingroup$ @JohnRennie: I'm claiming that it's just generically to be expected that for any situation where Newtonian gravity is a poor approximation, curvature is strong. A human stepping through a wormhole is passing through a region of vacuum, so the only type of curvature we can have is tidal curvature (i.e., Weyl tensor, not Ricci tensor). I don't claim that this is a rigorous proof, just a statement of what we should generically expect. The WP article on the Ellis wormhole doesn't appear to contradict this. If you can point me to info on Visser's wormholes, I'd be interested to take a look. $\endgroup$ – Ben Crowell Mar 2 '18 at 21:08
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    $\begingroup$ @BenCrowell info on Matt Visser's wormholes here, and see also Do polyhedral wormholes make sense? $\endgroup$ – John Rennie Mar 3 '18 at 5:49

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