Suppose I raise my right hand. As a result, light reflects off that hand differently than it otherwise would have. Of the many, many photons flying speedily away, a portion of them will escape Earth’s atmosphere into interstellar space. Let’s follow one of these photons.
The photon will eventually interact with something — a hydrogen atom, a chunk of interstellar dust, a star, the surface of a planet. Something. Let’s call that something a system. The photon might be absorbed, reflected, or refracted. (If the photon passes through a system without changing or being changed in any way, ignore that system and just keep following the photon.) If it interacts with a system, it will change the system, maybe increasing its energy if it’s absorbed or altering the trajectory of another particle if it’s reflected or refracted. Consequently, the system will behave differently over time. The system will, for example, emit, reflect, refract, or gravitationally bend another photon differently than it otherwise would have. Choose one such successor photon, heading off now on Trajectory A instead of Trajectory B or no trajectory.
This successor photon will in turn perturb another system, generating another successor photon traveling along another trajectory that it would not otherwise have taken. In this way, we can imagine a series of successor photons, one after the next, perturbing one system after another after another. Let’s call this series of photons and perturbances a ripple.
Might some ripples be infinite? I see three ways in which they could fail to be.
First, the universe might have finite duration or after a finite period of time it might settle into some unfluctuating state that fails to contain systems capable of perturbation by photons. However, there is no particular reason to think so. Even after the “heat death” of the universe into thin, boring chaos, there should still be occasional fluctuations by freak chance, giving rise to systems with which a photon might interact — some fluctations even large enough, with extremely minuscule but still finite probility, to birth whole new usually solitary and usually very widely spaced post-heat-death star systems. (This follows from standard physical theory as I understand it, though of course it is disputable and highly speculative. If there are nucleations of Big Bangs in ways that are sensitive to small variations in initial conditions, that could also work.)
Second, successor photons could have ever-decreasing expected energy, gaining longer and longer wavelengths on average, until eventually one is so low energy that it could not be expected to perturb any system even given infinite time. Again, there is no particular reason to think this is true, even if considerations of entropy suggest that successor photons should tend toward decreasing energy. Also, such an expected decrease in energy can be at least partly and possibly wholly counteracted by specifying that each successor should be the highest energy photon reflected, refracted, emitted, or gravitationally bent differently from the perturbed system within some finite timeframe, such as a million years.
Third, some photons might be absorbed by some systems without perturbing those systems in a way that has any effect on future photons, thus ending the ripple. Once again, this appears unlikely on standard physical theory. Even a photon that strikes a black hole will slightly increase the black hole’s mass, which should slightly alter how the black hole bends the light around it. And even if photons occasionally do vanish without a trace, such rare events could presumably be cancelled in expectation by always choosing two successor photons, leading to 2^n successors per ripple after n interactions, minus a small proportion of vanished ones.
It is thus not terribly implausible, I hope you’ll agree, to suppose that when I raise my hand now — and I have just done it — I launch successions of photons rippling infinitely through the universe, perturbing an infinite series of systems. If the universe is infinite, this conclusion is perhaps more natural and physically plausible than its negation (though see here for an alternative view).
Such infinitudes generate weirdness. With infinitude to play with, we can wait for any event of finite probability, no matter how tiny that finite probability is, and eventually it will occur. A successor photon from my hand-raising just now will eventually hit a system it will perturb in such a way that a person will live who otherwise would have died. Long after the heat death of the universe, a freak star system will fluctuate into existence containing a radio telescope which my successor photon hits, causing a bit of information to appear on a sensitive device. This bit of information pushes the device over the threshold needed to trigger an alert to a waiting scientist, who now pauses to study that device rather than send the email she was working on. Because she didn’t send the email, a certain fateful hiking trip was postponed and the scientist does not fall to her death, which she would have done but for my ripple. However vastly improbable all this is, one thing stacked on another on another, there is no reason to think it less than finitely probable. Thus, given the assumptions above, it will occur. I saved her! I raise my glass and take a celebratory sip.
Of course, there is another scientist I killed. There are wars I started and peaces I precipitated. There are great acts of heroism I enabled, children I brought into existence, plagues I caused, great works of poetry that would never have been written but for my intervention, and so on. It would be bizarre to think I deserve any credit or blame for all of this. But if the goodness or badness of my actions is measured by their positive or negative effects (as standard consequentialist ethics would have it), it’s a good bet that the utility of every action I do is ꝏ + -ꝏ.
My Boltzmann Continuants (Jun 6, 2013).
How Everything You Do Might Have Huge Cosmic Significance (Nov 29, 2016).
And Part 4 of A Theory of Jerks and Other Philosophical Misadventures.
[image source, cropped]