# Utilitarianism and Relativity Realism

## Introduction

Most people on less wrong seem to be some kind of hedonic consequentialist. They think states with less suffering and more joy are better. Moreover, it is intuitive that if you can cause some improvement in human well-being to be achieved then (other things being equal) it is better to realize that improvement as soon as possible. Also, most people on this site seem to be realists about special relativity. That is they assume that any inertial reference frame is an equally valid point from which to describe reality rather than believing there is one true reference which offers a preferred description of reality. I will point out that these beliefs (plus some innocuous assumptions) lead quickly to paradox.

## Relativity Realism

Before I continue I want to point out that empirical observations really are agnostic about the existence of a preferred reference frame. Indeed, it’s a consequence of the theory of relativity itself that it’s predictions are equally well explained by postulating a single true inertial reference frame and simply using the Lorentz contraction and time dilation equations to compute behavior for all moving objects. To see that this must be true not that if we take relativity seriously the laws of physics must work correctly in any reference frame. In particular, if we imagine designating one reference frame to be the true reference frame then, relativity itself, tells us that applying the laws of physics in that reference frame has to give us the correct results.

In other words once we accept Einstein’s equations for length contraction and time dilation with velocity we can interpret those equations as either undermining the idea of a fixed ether against which objects move (any reference frame is equally valid) or that there really is a fixed ether but objects in motion behave in such a manner that we can’t empirically distinguish what is at rest.

At first blush this second result seems so jury rigged that surely the simpler assumption is that there is no preferred reference frame. This relies on a false description of the situation. The question isn’t, “do we assign a low prior probability to the laws of physics conspiring to hide the true rest frame from us?” Presumably we do. The question should be, “given that the laws of physics do conspire to make a special rest frame empirically indistinguishable from any other inertial frames what probability do we assign to such a frame existing?” After all it is a mathematical truth that the time dilation and length contraction do perfectly conspire to prevent us from measuring motion relative to some true rest frame (if it existed) so in deciding whether to believe in a preferred rest frame we aren’t deciding between laws that would and wouldn’t hide such a frame from us. We are only deciding whether, given we have such laws, whether we think such an undetectable true rest frame exists.

To make it even more plausible that there is some true rest frame I will remark (but not argue) that relativity is a pretty general phenomena that can be derived from any model that conserves momentum, where the forces obey the inverse square law and all propagate at a constant speed relative to some fixed background, matter is held together in equilibrium states of these forces and time is implicitly measured via the rate it takes these forces to propagate. In other words if you have atoms held together by EM forces and the time it takes physical processes to happen is governed by the time it takes either forces or matter to cross certain distances then relativity comes for free. So it isn’t amazing that we might have a true prefered reference frame and yet it be impossible to experimentally determine that frame.

(As an aside this interpretation of relativity, fully consistent with all observables so far, makes for much better scifi since FTL travel doesn’t allow anyone to go back in time).

## A Paradox Resulting From Relativity Realism

Suppose we have two different brain implants that will be implanted in two different conscious but coma bound individuals. After a delay of 10 minutes after implantation the first device delivers an instantaneous burst of euphoria every second. The other delivers an instantaneous burst of discomfort every second. I assume we would all agree that (with sufficient additional assumptions) the world is a better place if we implant just a device of the euphoria inducing kind and a worse place if we just implant a device of the second kind. So assume the devices are appropriately calibrated so that the effect of implanting both is neutral (or very very nearly so). So far so good.

I think we can all agree that the world would be better off if we delayed implanting the discomforting device by 10 minutes (or equivalently implanted the pleasurable device 10 minutes earlier). If you dispute this conclusion then you get absurd results if you even admit the possibility of a universe that exists forever as in such a universe it is no better to permanently increase human welfare now than to delay that increase by 10 minutes or 10 centuries.

Now assume that the two individuals receiving the transplants are actually on spaceships moving in opposite directions at high rates of speed and the implantation is done at the instant they pass by each other. For simplicity we assume everyone else dies at this instant (or add an irrelevance of identical outcomes assumption and note that the two ships are moving at the same velocity relative to everyone else).

From the reference frame of the individual who received the beneficial implant we can analyze the situation as follows. Without loss of generality we can assume the ships are traveling at an appropriate speed so that for every second that pases in our reference frame only ^{1}⁄_{2} a second passes on the other ship. Thus in this reference frame the first experience of discomfort is delayed by 10 minutes and then only occurs every other second. Now surely the world is no worse off because the discomfort occurs less frequently. But ignoring the fact that the discomforting device fires less frequently this is exactly equivalent to implanting the desirable device 10 minutes before the undesirable one. Thus, since implanting both in the same reference frame was neutral, it is actually favorable (better than not implanting them) to do so when the recipients are in fast moving reference frames moving in opposite directions. Note the same result holds if we assume the device only creates discomfort or euphoria a single time with the minor assumption that if two worlds only differ in events before time t then what happens after time t is irrelevant to which one is preferable.

However, the same analysis done in the reference frame of the unpleasant implant gives the exact opposite conclusion.

## Avoiding the Paradox

Perhaps one might try and avoid the paradox by insisting that no experience truly occurs instantaneously. However, this is easily seen to be futile.

Assume that each device inflicts pleasure or discomfort for duration epsilon << 1 second. If you assume that the total badness of the uncomfortable experience is somehow mediated by changes in neurochemistry or other physical properties you are lead to the assumption that even described from the reference frame of the desirable implant the experience of 2*epsilon seconds of discomfort by the time dilated individual is really no worse than the experience of epsilon seconds of discomfort would be for someone with that implant in your reference frame. In other words when time is dilated the experience of pain per unit time is diluted. This leads to the exact same result as above.

On the other hand if we really do increase the weight we give to pain experienced by those undergoing time dilation an even simpler set of implants leads to paradox. These implants start working immediately, one generating a pleasant experience for 5 minutes the other an unpleasant experience for 5 minutes again calibrated so that installing both is overall neutral. Now by assumption from the reference frame of the beneficial implant things are overall worse (the longer duration of discomfort experienced by the other individual is overall worse than someone in the same reference frame getting the undesirable implant) and vice versa from the other reference frame.

The use of instantaneous experiences was merely a way to simplify the example but irrelevant to the underlying inequalities. Those inequalities are a result of the implicit time discounting forced by the assumption that other things being equal it is better for improvements to occur now rather than later combined with the fact that realism about relativity renders facts about simultaneity incoherent.

Personally, I think the only decent way of avoiding this paradox is to deny realism about relativity. Sure, it’s a radical move. However, it’s also a radical move to say it’s not true that it’s better to cure cancer now than in 10 centuries even if the human race will continue to exist forever. Indeed, even if you don’t assume literally infinite duration of effects even an unbounded potential length of effect with probabilities that decrease sufficiently slowly is equally problematic.

## Responses

I’ve deliberately avoided phrasing this dilemma in terms of a formal paradox and listing the assumptions necessary to generate the paradox. Partly this is laziness but it’s also a desire to see how people are inclined to respond before I attempt to draw up formal conditions. After all I ultimately want to capture common views in the assumptions and if I don’t know what people’s reactions are I can’t pick the right assumptions.

You cannot possibly gain new knowledge about physics by doing moral philosophy. At best, you have shown that any version of utilitarianism which adheres to your assumptions must specify a privileged reference frame in order to be coherent, but this does not imply that this reference frame is the true one in any physical sense.

This seems untrue. If you have high credence in the two premisses:

If X were a correct physical theory, then Y.

Not Y.

then that should decrease your credence in X. It doesn’t matter whether Y is a proposition about the behaviour of gases or about moral philosophy (although the implication is likely to be weaker in the latter case).

Instead of measuring “bad events per unit of time measured from the other person’s point of view”, wouldn’t “bad events per unit of subjective time” be a much better metric which doesn’t fall prey to this paradox?

And why are you bothering to distinguish between “there is no true preferred rest frame” and “there is a true rest frame which is perfectly indistinguishable from all the other moving ones”? They both make the exact same predictions, so why not just fold them into one hypothesis? What does that little epiphenominal tag hanging off one of them get you? Just because relativity is derivable from some fairly basic starting conditions doesn’t seem to imply that there is an indistinguishable true rest frame to me, though I may be missing something obvious.

Indeed it would. Otherwise, any simulated human universe could be significantly ethically improved by adding a simple code that would make it run

slowly(from our point of view; inside the simulation it would be the same) when the humans inside the simulation are happy.Don’t mix physics and ethics. They are completely different levels of abstraction. Also, learn more about each before making hasty conclusions.

This should be your clue that you did something wrong. Most likely that you misunderstand realism, relativity or both. One standard suggestion is to draw a spacetime diagram of what you are describing in each frame you care about. This tends to elucidate the usual confusion about relativity of simultaneity.

If you figure that your confidence in any prediction decreases exponentially in the future because each second is an independent opportunity for weird things to happen, then the preference to cure cancer now falls out with no need for additional time-based preferences. You then need special confidence calculations when relativity is involved, but that’s reasonable.

To phrase your result in terms a physicist would use: an all-time integral of a scalar function (happiness) is not Lorentz-invariant. But rather than draw a philosophical conclusion from this I would suggest modifying the equation for total happiness. If I recall correctly the standard method is defining a happiness density (over space), so rather than state “There is X amount of happiness at this point in time” you would state “At this point in time and space there is Y amount of happiness being created/destroyed”, and then define the total happiness as an all universe integral (so you integrate over spacetime).

I do hope that I’m not making some elementary mistake (imagine the embarrasment), but this thread seems to fall in the general category of ‘attempting to draw philosophical conclusions from a limited understanding of modern physics’. I remember reading material here on LessWrong that warns about this, such as adding up to normality.

Yes it is, since Lorentz-transformations have determinant 1, i,e., are measure-preserving. The issue in the example is that happiness isn’t a function on all of space-time, it is a function on the world lines of being capable of experiencing it.

You can integrate happiness over the proper time along those world lines; I suspect that’s equivalent to integrating a happiness density that looks like SUM_i h_i(t) delta(x—x_i(t)) over spacetime.

Ah. It’s about time the assumptions were made clear. I thought that ‘creation of happiness’ was a function defined on spacetime, and the proposed definition defines the total happiness to be only the happiness created on the observers world line. I believe this is not Lorentz-invariant—while a scalar H(x,t) might be invariant under such a transformation we are interested in H(x,t)dt, which messes up the invariance. And I think your remark about the determinant is just a rewording of my point: the determinant of a matrix describes the change in volume of a (in this case) 4-dimensional volume, but if we integrate only in one direction our result can still change (almost) arbitrarily. And therefore introducing an all-space integral solves the problem—this quantity does deal with all four dimensions.

Another way to avoid the paradox is to care about other people’s satisfaction (more complicated than that, but that’s not the point) from

theirpoint of view, which encompasses their frame of reference.Another way perhaps is to restate implementing improvements as soon as possible as maximizing total goodness in (the future of) the universe. Particularly, if an improvement could only be implemented once, but it would be twice as effective tomorrow instead of today, do it tomorrow.

I don’t see why you

wouldn’tdo it this way, since that’s the basic, fundamental moral intuition we derive from our faculty of empathy.I guess I didn’t make myself at all clear on that point, I ascribe to both of the above!

Relatively also implies the lack of absolute time—it doesn’t make sense to speak of “before” or “faster” or “now” in absolute. What matters for pleasure/pain of sentient entity is relative to

theirframe of reference, their subjective time.And while observers in different frames will disagree on “what time is it ?” they will agree on the subjective experience each person has. And the only way to “sum” the pain/happiness between difference frames of inertia is considering when they can mutually agree on something—when the signal from one can reach the other.

If person A is on Earth suffering and person B is on a spaceship in happiness, it only matters to sum the suffering of one with the happiness of the other when a signal from Earth towards the ship (or vice-versa) can reach its destination, and you’ll find that doing all the calculation the prediction of the two frames will be the same.

The only point where this can be tricky is if the ship goes beyond our event horizon—if due to expanding universe it reach the point where it can’t reach Earth anymore because it’s going away from it faster than light. There I’ve to admit it makes knots in my head.

So utilitarianism has known paradoxes if you allow infinite positive/negative utilities (basically because infinite sums don’t always behave well). On the other hand, if you restrict yourself, say to situations that only last finitely long all these paradoxes go away. If both devices last for the same amount of subjective time, this holds true in all reference frames, and thus in all reference frames you can say that the situations are equally good.

If you restrict to finitely long situations, you wind up with weird effects at the cutoff window.

This isn’t a problem if you believe that there will only ever be finitely many people. Or if you exponentially discount (in some relativistically consistent manner) at an appropriate rate.

Caring about times within some time limit in a single reference frame is sufficient.

The problem with a time limit is that it encourages you to not care what happens afterwards.

Hm, I think any integrable time-discounting function would also work. And the trouble with an AI that doesn’t time-discount is that it gets Pascal’s mugged by literally any chance of eternity.

I really suspect we’d care more about the total number of times that both of these events occur, rather than the rate. That is a quantity preserved under Lorentz transformation.

Moved to Discussion.

What? Did we really have an article disproving the theory of relativity using moral argumentation in Main, without it getting immediately heavily downvoted?

I can’t even

One man’s modus ponens is another man’s modus tollens.

In other words, even if this is completely correct, it doesn’t disprove relativity. Rather, it disproves either relativity or most versions of utilitarianism—pick one.

It seems like all it shows is that we ought to keep our utility functions Lorentz-invariant. Or, more generally, when we talk about consequentialist ethics, we should only consider consequences that don’t depend on aspects of the observer that we consider irrelevant.

You must even!

What does it mean that this preferred reference frame “exists”? What about general relativity? I don’t even understand what a “preferred reference frame” means there mathematically.

I have no idea what you’re talking about. Generally speaking, I would refrain from inventing new physics before understanding the physics already invented in the last 100 years.

Regarding the paradox, the correct thing is summing over different reference frames weighted by 2^-{Kolmogorov complexity}. See also this and discussion here.

No to both. Delaying eutopia seems bad because we’ll experience something bad in the meantime. Pausing all of reality for 10 centuries is not even meaningful, and pausing only humanity seems neutral if (implausibly) it does not affect the total subjective duration nor the quality.

Why do you assume that the observers don’t correct for the Lorentz time dilation to get out the happiness in the rest frame of the experiencer?

Make the modus ponens a modus tollens and I like the article.

One approach is to only care[1] about future events that you can influence. Any actions you take will necessarily be in your frame of reference, why wouldn’t your judgment of the state of the universe also be in this frame? That takes care of part of the paradox.

The other part of the paradox comes from “I think we can all agree that the world would be better off if we delayed implanting the discomforting device”. I think actually getting that agreement will dissolve the paradox: you’ll have to find agreement on reasons to discount future suffering. For me, it’s a mix of time-sensitive uncertainty and a (somewhat unconventional) belief that empathy that varies over time/distance[2].

[1] “care” used here in a narrower sense than usual. something along the lines of “make judgments about state of the universe for decision purposes”.

[2] I personally find that my own empathy[3] varies with expected future interactions, and I see most humans acting as if that were true for them as well. If I torture the anecdotal data enough, I can make it fit an inverse-square rule with “emotional distance”, which I find elegant but not particularly rigorous.

[3] empathy here used to mean roughly of “in my utility function, the coefficient of the term for my perception [4] of another’s happiness”

[4] perception to include expectation and projections, not only direct experience.