## Saturday, October 22, 2022

### What If the Effect Comes Before the Cause?

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

The cause comes before the effect. And I’m glad it does because it’d be awkward if my emails arrived before I’d written them. If that ever happens, it’ll be a case of “retrocausality.” What does that mean? What’s it got to do with quantum mechanics and what is the “transactional interpretation”? That’s what we’ll talk about today.

Causality is a relation between events in space and time, so I’ll be using space-time diagrams again. In such a diagram, the vertical axis is time and the horizontal axis is one dimension of space. Anything that moves with constant velocity is a straight line at some angle. By convention, a 45 degree angle depicts the speed of light.

According to Einstein, yes that guy again, the speed of light is an upper limit for the transmission of information. This means if you take any one point in space-time, then you can only send or receive information from points within cones of less than 45 degrees to the vertical through the point. The boundaries of those areas are called the forward light cone and the backward light cone.

Every philosopher in existence had something to say about causality, so there are many different definitions, but luckily today we’ll need only need two. The first one is space-time causality. Suppose you have two events that are causally related, then each must be inside the other’s light cone, and the one in the past is the cause. It’s as simple as that. This is the notion of causality that’s used in General Relativity. One direction is forward, that’s the future, one direction is backward, that’s the past.

But it turns out that not all space-times allow you to tell apart past from future. This is much like on a Moebius strip you can’t tell the front from the back because they’re the same! In some space-times you can’t tell the past from the future because they’re the same.

Normally this doesn’t happen because you can’t turn around in time. If you wanted to do that, you’d have to go faster than light. But some space-times allow you to go back in time and visit your own past without moving faster than light. It’s called a time-like closed curve. That it’s time-like means you can travel along it below the speed of light, and that it’s closed means it’s a loop.

The simplest example of this is a space-time with a wormhole. Let’s say if you enter the wormhole it transports you from this point A to this point B. From where you started, the wormhole entrance is in your future. But it’s also in your past.

This is weird and it creates some causality problems that we’ll talk about in a bit. However, for all we know time-like closed curves don’t exist on our space-time which is a little bit disappointing because I know you really want to go back and revisit all your Latin exams. This is why I first want to talk about another notion of causality which makes going back in time a little easier. It’s called “interventionist causality”. It’s all about what you can “intervene” with, and it works without a time-order.

To understand interventionist causality you ask which event depends on another one. Think back of the example of writing an email and someone receiving it. If I intervene with you writing the email, for example by distracting you with jokes about retrocausality, then the other person won’t receive it. So neither of the two events happen. But if I intervene with them receiving the email, for example by boring them to death with jokes about retrocausality, you’ll still write the email. According to interventionist causality, the event that you can intervene with to stop both from happening is the cause. In general you don’t have to actually prevent an event from happening, you look at what affects its probability.

Normally the causal order you get from the interventionist approach agrees with the order you get from the space-time approach. So then why use it at all? It’s because in practice we often have correlations in data, but we don’t know the time order, so we need another method to infer causality. We encountered many examples for this in our recent video on obesity. What came first, the obesity or the change in the microbiome? Interventionist causality is really popular in the life sciences, where longitudinal studies are rare, because it gives you an alternative way to analyze data to infer causality.

But back to physics. This notion of interventionist causality is implicitly based on entropy increase. Let me illustrate that with another example. Suppose you flip a switch and the light turns on. If I stop you from flipping the switch, the light doesn’t turn on. But if I stop the light from turning on that doesn’t stop you from flipping the switch. Interventionist causality then tells us that flipping the switch is the cause and the light turning on the effect.

However, from a purely mathematical perspective, there exists some configuration of atoms and photons in which the light stays off in just exactly the right way so that you don’t flip the switch. But such an “intervention” would have to place photons so that they go back into the bulb and the electric signal back into the cable and all the neural signals in your brain go in reverse. And this may be mathematically possible, but it would require an enormous amount of entropy decrease, so it’s not practically possible.

This is why the two notions of causality usually agree. Forward in space-time is the same direction as the arrow of time from entropy increase. But what if that wasn’t the case? What if there’d be places in the universe where the arrow of time went in the other direction than it does here? Then you could have effects coming before their causes, even without wormholes or some other weird space-time geometry. You’d have retrocausality.

As you have probably noticed, emails don’t arrive before you’ve written them, and lights don’t normally cause people to flip switches. So, if retrocausality exists, it’s subtle or it’s rare or it’s elsewhere.

In addition, most physicists don’t like retrocausality because going back and time can create inconsistencies, that’s situations where something both happens and doesn’t happen. The common example is the grandfather paradox, in which you go back in time and kill your own grandfather, accidentally we hope, so you are never born and can’t go back in time to kill him. I guess we could call that a retrocasualty.

The movie industry deals with those causal paradoxes in one of three ways. The first one is that if you go back in time, you don’t go back into your own time, but into a parallel universe which has a similar but slightly different history. Then there’s no inconsistency, but you have the problem that you don’t know how to get back to where you came from. This happens for example in the movie “The Butterfly Effect” in which the protagonist repeatedly travels to the past only to end up in a future that is less and less like what he was hoping to achieve.

Another way of dealing with time-travel paradoxes is that you allow temporary inconsistencies, they just have to be fixed so that everything works out in the end. An example of this is Back to the Future, where Marty accidentally prevents his parents from meeting. He has to somehow fix that issue before he can go back into his own future.

These two ways of dealing with time travel inconsistencies are good for story-telling, but they’re hard to make sense of scientifically. We don’t have any theoretical framework that includes multiple pasts that may join back to the same future.

The option that’s the easiest to make sense of scientifically is to just pick a story that’s consistent in the first place. An example for this is the Time Traveler’s Wife, in which the time traveler meets his future wife the first time when she is a child but he already an adult, and then he meets her again when they’re both the same age. It makes for a really depressing story though.

But even if time travel is consistent, it can still have funny consequences.

Imagine for example you open your microwave and find a notebook in it. The notebook contains instructions for how to turn your microwave into a time machine. But it takes you ten years to figure out how to make it work, and by the time you’re finished the notebook is really worn out. So, you copy its content into a new notebook, put it into the microwave, and send it back in time to your younger self. Where did the notebook come from?

It's often called the “bootstrap paradox” but there’s nothing paradoxical about it in the sense that nothing is inconsistent. We’re just surprised there was nothing before the appearance of the notebook that could have given rise to it, but it can have consequences later on. For starters, you’ll have to buy a new microwave. This means that in the presence of causal loops the past no longer determines the future.

Hmm, indeterminism. Where have we heard that before? In quantum mechanics, right! Could retrocausality have something to do with quantum mechanics?

Indeed, that retrocausality could explain the seemingly strange features of quantum mechanics was proposed by John Cramer in the 1980s. It’s called the Transactional Interpretation. It was further developed by Ruth Kastner but Cramer seems to not be particularly enchanted by Kastner’s version. In a 2015 paper he called it “not incorrect, but we consider it to be unnecessarily abstract.” That’s academia. Nothing quite like being dissed in the 1st person plural.

Kramer’s idea goes back to Wheeler and Feynman who were trying to find a new way to think about electrodynamics. Suppose you have light going from a sender to a receiver. If we draw this into a space-time diagram, we just get this line at a 45 degree angle from the event of emission to the absorption.

Those waves of the light oscillate in the direction of the two dimensions that we didn’t draw. That’s because I can’t afford a graphic designer who works in 4 dimensions, so we’ll just draw another graph down here that shows the phase of the wave as a function of the coordinate. This is how we normally think of light being emitted and absorbed.

But in this case we have to tell the emitter what is the forward direction of time. Wheeler and Feynman didn’t like this. They wanted a version that would treat the future and past the same way. So, they said, suppose the wave that comes from the emitter actually goes into both directions in time but the wave that goes backward in time has the opposite phase. When it arrives at the absorber, it sends back an answer wave. In the range between the emitter and absorber, the answer wave has the same phase as the one that came from the emitter. But it has the opposite phase going forward in time. Because of this, there’s constructive interference between the event of emission and that of absorption, but destructive interference before the emission and after the absorption.

The result looks exactly the same as the normal version of electrodynamics where the wave just starts at the emitter and ends at the absorber. Indeed, it turned out that Wheeler and Feynman’s reinterpretation of electrodynamics was identical to the normal version and they didn’t pursue it any further. However, I want to draw your attention here already to an odd feature of this interpretation. It’s that it suggests a second notion of time which doesn’t exist in the physics.

When we say something like: when the wave from the emitter arrives at the absorber, the absorber returns a wave, that doesn’t play out in time. Because time is the axis on this diagram. If you illustrate the physical process, then both the emission and absorption are in this diagram in the final version, period. They don’t get drawn into it, that’d be a second notion of time.

That said, let’s look at Cramer’s Transactional Interpretation. In this case, we use wave-functions instead of electromagnetic waves, and there isn’t one absorber, but several different ones. The several different absorbers are different possible measurement outcomes.

Suppose for example you emit a single quantum of light, a photon, from a source. You know where the photon came from but you don’t know where it’s going. That’s not because the photon has lost its internet connection and now can’t find a tube entrance, it’s because of the uncertainty principle. This means that its wave-function spreads into all directions. If you then measure the photon at one particular place, the wave-function instantaneously collapses, everywhere. This brings up the question: How did the wave-function on one side know about the measurement on the other side. That’s what Einstein referred to as “spooky action at a distance,” which I talked about in my earlier video.

Let us draw this into our space-time diagram. We have only one direction of space, so the photon wave-function goes left and right with probability ½. If you measure it on one side, say the right side, the probability there jumps to 1 and that on the other side to 0.

Cramer’s transactional interpretation now says that this isn’t what happens. Instead, what happens is this. The source sends out an offer wave, both forward and backward in time. In the forward direction, that approaches the detectors. Again down here we have drawn the phase of that wave. It’s now a probability amplitude rather than the amplitude of an electromagnetic field.

When the offer wave arrives at the detectors, they both send back a confirmation wave. When those waves arrive at the source, the source randomly picks one. Then the waves to that one detection event enter a back-and-forth echoing process, until the probability for that outcome is 1 and that for the other possible outcomes is zero. That reproduces the collapse of the wave-function.

Cramer calls this a “transaction” between the source and the detector. He claims it makes more sense than the usual Copenhagen Interpretation with the collapse, because in the transactional interpretation all causes all propagate locally and in agreement with Einstein’s speed of light limit. You “just” have to accept that some of those causes go back in time.

Take for example the bomb experiment in which you want to find out whether a bomb is live or a dud, but without exploding it because last time that happened, Ken spilled his coffee, and it was a mess. If the bomb is live, a single photon will blow it up. If it’s a dud, the photon just goes through. What you do is that you put the bomb into an interferometer. You send a single photon through and measure it down here. If you measure the photon in this detector, you can tell the bomb is live even though the photon didn’t interact with the bomb because otherwise it’d have blown up. For a more detailed explanation, please watch my earlier video on the bomb experiment.

In Cramer’s interpretation of the bomb experiment an offer wave goes over both paths. But if there’s a live bomb on that path, the offer wave is aborted and can’t go through. The other offer wave still reaches the detector. The detector sends answer waves, and again the answer wave that goes along the bomb path doesn’t pass through. This means the only transaction that can happen is along the other path. This is the same as in quantum mechanics. But in the transactional interpretation the path with the bomb is probed by both the offer wave and the answer wave, so that’s why the measurement can contain information about it.

Great! So quantum mechanics is just a little bit of reverse causality. Does that finally explain it? Not quite. The issue with Cramer’s interpretation is the same as with the Wheeler-Feynman idea. This notion of time with the wave propagating this way and back seems to be a second time, internal to the wave, that has no physical relevance. And the outcome in the end is just the same as in normal quantum mechanics. Indeed, if you use the interventionist notion of causality, then emitting the particle is still the cause of its eventual detection and not the other way round.

Personally I don’t really see why bother with all that sending back and forth if it walks and talks like the usual Copenhagen Interpretation? But if it makes you feel better, I think it’s a consistent way to think of quantum mechanics.

In conclusion, I’m afraid I have to report that physicists have not found a way to travel into the past, at least not yet. But watch out for that notebook in the microwave.