## Monday, October 23, 2017

### Murder by slowdown?

Zeno wants Alice dead and he has the following plan. He slows down Alice’s functioning—say, by cooling her or by sending her around the earth on a spaceship so fast that relativistic time dilation does the job—so much that each second of Alice’s internal time takes a billion years of external time. In six seconds of Alice’s internal time, she’s dead, because the sun runs out of hydrogen and turns into a red giant.

Did Zeno kill Alice or did the sun kill Alice? Both: Zeno kills Alice by shifting her future life into a spatiotemporal position where that life would be destroyed by the sun. This is akin to sending Alice now into the sun on a speeding rocket.

(I am not a lawyer, but I expect Zeno could only be convicted of attempted murder, since a conviction for murder requires the victim to be dead; similarly, I assume that an 80-year-old person who gives someone a poison that takes forty years to work can only be convicted of attempted murder, because by the time the poison does its work, the murderer will be dead.)

But now imagine that Zeno lives in a universe where the earth will be habitable forever. He sets up an automated system that slows down Alice’s internal time to such a degree that in the first year of external time, Alice’s internal time moves ahead only 3 seconds; in the next external year, it moves ahead by 1.5 seconds; in the next year, it moves ahead by 0.75 seconds; and so on. What happens? Well, Alice still cannot have more than six seconds of life ahead of him. In n years of external time, she will have had 6 − 6/2n seconds of internal time.

So just as in the first scenario, Zeno has ensured that Alice has less than six seconds of internal time left. It sure sounds like murder. But wait! In the second scenario, it seems that Alice never dies: she is alive this year, just sluggish; she will be alive next year, though even more sluggish; and so on.

But Alice will be dead in exactly six seconds of internal time. So what will be the cause of death? The unfortunate misalignment between Alice’s internal time and the external time of the universe, together with the universe running out of time “once year ω rolls around”? Maybe. I am not sure. This is paradoxical.

There is a way of getting out of this paradox. Suppose internal time must be discrete. Then to slow down Alice’s time means to space out the discrete ticks of her time. Suppose for simplicity that Alice has a hundred ticks per internal second. Then in the next year, she will have 300 ticks. Some time in year ten, the 599th tick of Alice’s future life happens. And the 600th tick will never happen. So, the gradual slowdown story is is impossible. The speed hits zero after the tenth year. The best (or worst?) Zeno can do is ensure that the 599th tick of Alice’s life is the last one. But if that’s what he does, then he causes her death by ensuring that the 600th tick never happens. But if that’s what he does, there is no gradual slowdown paradox.

IanS said...

Something like this is almost physically possible. Suppose Zeno drops Alice into a supermassive black hole. She is wearing a space suit (so she won’t be killed by the exposure). She carries a clock that shows her proper time and a radio transmitter that broadcasts it. Zeno hovers (maybe by using thrusters) and watches Alice fall.

Note: the following is based on my understanding of popular accounts. I’m no expert. Quantum effects are ignored.

What does Zeno see? As Alice approaches the event horizon, her fall seems to slow down, her radio is red-shifted, and her clock (and everything with her) seems to run slower. The closer Alice comes to the event horizon, the greater the slowing. Zeno never sees Alice cross the event horizon, no matter how long he waits. She is gradually red-shifted to invisibility. No matter how long he waits, Zeno never receives a broadcast time later than (say) T1.

How does Alice see it? She falls through the event horizon at time T1 without noticing anything dramatic. She dies some time later (say at tine T2) when tidal forces pull her apart. Alice is doomed at time T1 (once inside the event horizon, she can never escape), but she does not die until time T2.

The moral? From Zeno’s point of view, this setup is just as in your post. T1 (Alice’s proper time) corresponds to infinity (external time). But it does not follow, and in fact it is not true, that Alice dies at time T1.

Alexander R Pruss said...
This comment has been removed by the author.
Alexander R Pruss said...
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Alexander R Pruss said...

But what if one does it through accelerating motion in a straight line, with the acceleration increasing appropriately? Hmm. I suppose eventually as the acceleration rises, you get the equivalent of a black hole. But what happens, then? I don't know.

That said, perhaps for the thought experiment it doesn't have to be a literal speed-up of all processes, just the larger scale electrochemical processes that are involved in life?

IanS said...

It is implicit in the post that Zeno can make Alice’s vital functions work normally but arbitrarily slowly. I think that if you accept this, you have to accept that her life can end, from her point of view, without her ‘dying’ in the usual sense (i.e. by irreversible disruption of her vital functions).

To take an extreme case, suppose Zeno puts Alice into fully reversible cryogenic storage. Suppose that while she is in storage, her internal time stops completely relative to external time. (This is fantasy of course, but surely no more fantastic than your scenario.) I think it would be wrong to say that she ‘dies’ in the usual sense when she is put into storage. (If you say this, what will you say when she is revived?) But suppose Zeno puts her into storage and somehow ensures that she will remain viable for ever but never actually be revived. Then, on the view I am suggesting, she will not have died, but her life will have ended (from her point of view) when she was put into storage.

Alexander R Pruss said...

I am inclined to think that complete freezing is death, and revival is resurrection, but I am not sure.

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