Also, if MWI hypothesis is true, there’s no way for one branch to interact with another later, right? If there are two worlds that are different based on some quantum event that occurred in 1000 CE, those two worlds will never interact, in principle, right?
“Acausal” is used as a contrast to Causal Decision Theory (CDT). CDT states that decisions should be evaluated with respect to their causal consequences; ie if there’s no way for a decision to have a causal impact on something, then it is ignored. (More precisely, in terms of Pearl’s Causality, CDT is equivalent to having your decision conduct a counterfactual surgery on a Directed Acyclic Graph that represents the world, with the directions representing causality, then updating nodes affected by the decision.) However, there is a class of decisions for which your decision literally does have an acausal impact. The classic example is Newcomb’s Problem, in which another agent uses a simulation of your decision to decide whether or not to put money in a box; however, the simulation took place before your actual decision, and so the money is already in the box or not by the time you’re making your decision.
“Acausal” refers to anything falling in this category of decisions that have impacts that do not result causally from your decisions or actions. One example is, as above, Newcomb’s Problem; other examples include:
The Prisoner’s Dilemma, or any other symmetrical game, when played against the same algorithm you are running. You know that the other player will make the same choice as you, but your choice has no causal impact on their choice.
In EDT, which originates in academia, casuality is completely ignored, and only correlations are used. This leads to the correct answer on Newscomb’s Problem, but fails on others- for example, the Smoking Lesion. UDT is essentially EDT, but with an agent that has access to its own code. (There’s a video and transcript explaining this in more detail here).
TDT, like CDT, relies on causality instead of correlation; however, instead of having agents chose a decision that is implemented, it has agents first chose a platonic computation that is instantiated in, among other things, the actual decision maker; however, is is also instantiated in every other algorithm is equal, acausally, to the decision maker’s algorithm, including simulations, other agents, etc. And, given all of these instantiations, the agent then choses the utility-maximizing algorithm.
One must distinguish different varieties of MWI. There is an old version of the interpretation (which, I think, is basically what most informed laypeople think of when they hear “MWI”) according to which worlds cannot interact. This is because “world-splitting” is a postulate that is added to the Schrodinger dynamics. Whenever a quantum measurement occurs, the entire universe (the ordinary 3+1-dimensional universe we are all familiar with) duplicates (except that the two versions have different outcomes for the measurement). It’s basically as mysterious a process as collapse, perhaps even more mysterious.
This is different from the MWI most contemporary proponents accept. This MWI (also called “Everettianism” or “The Theory of the Universal Wavefunction” or...) does not actually have full-fledged separate universes. The fundamental ontology is just a single wavefunction. When macroscopic branches of the wavefunction are sufficiently separate in configuration space, one can loosely describe it as world-splitting. But there is nothing preventing these branches from interfering in principle, just as microscopic branches interfere in the two-slit experiment. There is no magical threshold of branch size/separation where the Schrodinger equation no longer permits interference. And in MWI understood this way, the Schrodinger equation is all the dynamics there are. So yeah, MWI does allow for the interaction of “worlds” in principle. The reason we never see this happening at a macroscopic scale is usually explained by appeal to special initial conditions (just like the thermodynamic arrow of time).
ETA: And in some sense, all the separate worlds are actually interacting all the time, just at a scale that is impossible for our instruments to detect.
Suppose I use the luck of Mat Cauthon to pick a random direction to fly my perfect spaceship. Assuming I live forever, do I eventually end up in a world that split from this world?
No. The splitting is not in physical space (the space through which you travel in a spaceship), but in configuration space. Each point in configuration space represents a particular arrangement of fundamental particles in real space.
Moving in real space changes your position in configuration space of course, but this doesn’t mean you’ll eventually move out of your old branch into a new one. After all, the branches aren’t static. You moving in real space is a particular aspect of the evolution of the universal wavefunction. Specifically, your branch (your world) is moving in configuration space.
Don’t think of the “worlds” in MWI as places. It’s more accurate to think of them as different (evolving) narratives or histories. Splitting of worlds is a bifurcation of narratives. Moving around in real space doesn’t change the narrative you’re a part of, it just adds a little more to it. Narratives can collide, as in the double slit experiment, which leads to things appearing as if both (apparently incompatible) narratives are true—the particle went through both slits. But we don’t see this collision of narratives at the macroscopic level.
Also, if MWI hypothesis is true, there’s no way for one branch to interact with another later, right? If there are two worlds that are different based on some quantum event that occurred in 1000 CE, those two worlds will never interact, in principle, right?
To expand on what pragmatist said: The wavefunction started off concentrated in a tiny corner of a ridiculously high-dimensional space (configuration space has several dimensions for every particle), and then spread out in a very non-uniform way as time passed.
In many cases, the wavefunction’s rule for spreading out (the Schrödinger equation) allows for two “blobs” to “separate” and then “collide again” (thus the two-split experiment, Feynman paths and all sorts of wavelike behavior). The quote marks around these are because it’s not ever like perfect physical separation, more like the way that the pointwise sum of two Gaussian functions with very different means looks like two “separated” blobs.
But certain kinds of interactions (especially those that lead to a cascade of other interactions) correspond to those blobs “losing” each other. And if they do so, then it’s highly unlikely they’ll accidentally “collide” again later. (A random walk in a high-dimensional space never finds its way back, heuristically speaking.)
So, as long as the universe has relatively low entropy (as it will until what we would call the end of the universe), significant interference with “blobs” of wavefunction that “split off of our blob” in macroscopic ways a long time ago would be fantastically unlikely. Not impossible, just “a whale and a petunia spontaneously appear out of quantum noise” degree of improbability.
As I understand it: If you draw out events as a DAG with arrows representing causality, then A acausally effects B in the case that there is no path from A to B, and yet a change to A necessitates a change to B, normally because of either a shared ancestor or a logical property.
I most often use it informally to mean “contrary to our intuitive notions of causality, such as the idea that causality must run forward in time”, instead of something formal having to do with DAGs. Because from what I understand, causality theorists still disagree on how to formalize causality (e.g., what constitutes a DAG that correctly represents causality in a given situation), and it seems possible to have a decision theory (like UDT) that doesn’t make use of any formal definition of causality at all.
Having seen the exchange that probably motivated this, one note: in my opinion, events can be linked both causally and acausally. The linked post gives an example. I don’t think that’s an abuse of language; we can say that people are simultaneously communicating verbally and non-verbally.
Broadly, branches become less likely to interact as they become more dissimilar; dissimilarity tends to bring about dissimilarity, so they can quickly diverge to a point where the probability of further interaction is negligible. Note that at least as Eliezer tells it, branches aren’t ontologically basic objects in MWI any more than chairs are; they’re rough high-level abstractions we imagine when we think about MWI. If you want a less confused understanding than this, I don’t have a better suggestion than actually reading the quantum physics sequence!
Also, if MWI hypothesis is true, there’s no way for one branch to interact with another later, right? If there are two worlds that are different based on some quantum event that occurred in 1000 CE, those two worlds will never interact, in principle, right?
I think it depends on perspective. We notice worlds interfering with each other in the double slit experiment. I think that maybe once you are in a world you no longer see evidence of it interfering with other worlds? I’m not really sure.
Also, if MWI hypothesis is true, there’s no way for one branch to interact with another later, right?
Basically, if two of them evolve into the same “world”, they interfere. It could be constructive or destructive. It averages out to be that it occurs as often as you’d expect, so outside of stuff like the double-slit experiment, they won’t really interact.
They are evidence against wave-form collapse, in that they give a lower bound as to when it must occur. Since, if it does exist, it’s fairly likely that waveform collapse happens at a really extreme point, there’s really only a fairly small amount of evidence you can get against waveform collapse without something that disproves MWI too. The reason MWI is more likely is Occam’s razor, not evidence.
Well, I tried to understand some double-slit corner-cases. If I read some classical Copenhagen-approach quantum physics textbook, it is hard to describe what happens if you install a non-precise particle detector securely protected from experimenter’s attempts to ever read it.
Of course, in some cases Penrose model and MWI are hard to distinguish, because gravitons are hard to screen off and can cause entanglement over large distances.
Philosophy sources, eg the online Stanford Encyclopedia thereof or some work on Aristotle. But I don’t recommend you bother. “Formal” means a logical implication. “Final” suggests a purpose, which makes sense in the context of decision theory.
Aristotelian tradition. I’m sure you could find a lot of similarly motivated classifications in the cybernetics and complex systems literature if you’re not into old school metaphysics.
What do people mean here when they say “acausal”?
Also, if MWI hypothesis is true, there’s no way for one branch to interact with another later, right? If there are two worlds that are different based on some quantum event that occurred in 1000 CE, those two worlds will never interact, in principle, right?
“Acausal” is used as a contrast to Causal Decision Theory (CDT). CDT states that decisions should be evaluated with respect to their causal consequences; ie if there’s no way for a decision to have a causal impact on something, then it is ignored. (More precisely, in terms of Pearl’s Causality, CDT is equivalent to having your decision conduct a counterfactual surgery on a Directed Acyclic Graph that represents the world, with the directions representing causality, then updating nodes affected by the decision.) However, there is a class of decisions for which your decision literally does have an acausal impact. The classic example is Newcomb’s Problem, in which another agent uses a simulation of your decision to decide whether or not to put money in a box; however, the simulation took place before your actual decision, and so the money is already in the box or not by the time you’re making your decision.
“Acausal” refers to anything falling in this category of decisions that have impacts that do not result causally from your decisions or actions. One example is, as above, Newcomb’s Problem; other examples include:
Acausal romance: romances where interaction is impossible
The Prisoner’s Dilemma, or any other symmetrical game, when played against the same algorithm you are running. You know that the other player will make the same choice as you, but your choice has no causal impact on their choice.
There are a number of acausal decision theories: Evidential Decision Theory (EDT), Updateless Decision Theory (UDT), Timeless Decision Theory (TDT), and Ambient Decision Theory (ADT).
In EDT, which originates in academia, casuality is completely ignored, and only correlations are used. This leads to the correct answer on Newscomb’s Problem, but fails on others- for example, the Smoking Lesion. UDT is essentially EDT, but with an agent that has access to its own code. (There’s a video and transcript explaining this in more detail here).
TDT, like CDT, relies on causality instead of correlation; however, instead of having agents chose a decision that is implemented, it has agents first chose a platonic computation that is instantiated in, among other things, the actual decision maker; however, is is also instantiated in every other algorithm is equal, acausally, to the decision maker’s algorithm, including simulations, other agents, etc. And, given all of these instantiations, the agent then choses the utility-maximizing algorithm.
ADT...I don’t really know, although the wiki says that it is “variant of updateless decision theory that uses first order logic instead of mathematical intuition module (MIM), emphasizing the way an agent can control which mathematical structure a fixed definition defines, an aspect of UDT separate from its own emphasis on not making the mistake of updating away things one can still acausally control.”
One must distinguish different varieties of MWI. There is an old version of the interpretation (which, I think, is basically what most informed laypeople think of when they hear “MWI”) according to which worlds cannot interact. This is because “world-splitting” is a postulate that is added to the Schrodinger dynamics. Whenever a quantum measurement occurs, the entire universe (the ordinary 3+1-dimensional universe we are all familiar with) duplicates (except that the two versions have different outcomes for the measurement). It’s basically as mysterious a process as collapse, perhaps even more mysterious.
This is different from the MWI most contemporary proponents accept. This MWI (also called “Everettianism” or “The Theory of the Universal Wavefunction” or...) does not actually have full-fledged separate universes. The fundamental ontology is just a single wavefunction. When macroscopic branches of the wavefunction are sufficiently separate in configuration space, one can loosely describe it as world-splitting. But there is nothing preventing these branches from interfering in principle, just as microscopic branches interfere in the two-slit experiment. There is no magical threshold of branch size/separation where the Schrodinger equation no longer permits interference. And in MWI understood this way, the Schrodinger equation is all the dynamics there are. So yeah, MWI does allow for the interaction of “worlds” in principle. The reason we never see this happening at a macroscopic scale is usually explained by appeal to special initial conditions (just like the thermodynamic arrow of time).
ETA: And in some sense, all the separate worlds are actually interacting all the time, just at a scale that is impossible for our instruments to detect.
Suppose I use the luck of Mat Cauthon to pick a random direction to fly my perfect spaceship. Assuming I live forever, do I eventually end up in a world that split from this world?
No. The splitting is not in physical space (the space through which you travel in a spaceship), but in configuration space. Each point in configuration space represents a particular arrangement of fundamental particles in real space.
Moving in real space changes your position in configuration space of course, but this doesn’t mean you’ll eventually move out of your old branch into a new one. After all, the branches aren’t static. You moving in real space is a particular aspect of the evolution of the universal wavefunction. Specifically, your branch (your world) is moving in configuration space.
Don’t think of the “worlds” in MWI as places. It’s more accurate to think of them as different (evolving) narratives or histories. Splitting of worlds is a bifurcation of narratives. Moving around in real space doesn’t change the narrative you’re a part of, it just adds a little more to it. Narratives can collide, as in the double slit experiment, which leads to things appearing as if both (apparently incompatible) narratives are true—the particle went through both slits. But we don’t see this collision of narratives at the macroscopic level.
To expand on what pragmatist said: The wavefunction started off concentrated in a tiny corner of a ridiculously high-dimensional space (configuration space has several dimensions for every particle), and then spread out in a very non-uniform way as time passed.
In many cases, the wavefunction’s rule for spreading out (the Schrödinger equation) allows for two “blobs” to “separate” and then “collide again” (thus the two-split experiment, Feynman paths and all sorts of wavelike behavior). The quote marks around these are because it’s not ever like perfect physical separation, more like the way that the pointwise sum of two Gaussian functions with very different means looks like two “separated” blobs.
But certain kinds of interactions (especially those that lead to a cascade of other interactions) correspond to those blobs “losing” each other. And if they do so, then it’s highly unlikely they’ll accidentally “collide” again later. (A random walk in a high-dimensional space never finds its way back, heuristically speaking.)
So, as long as the universe has relatively low entropy (as it will until what we would call the end of the universe), significant interference with “blobs” of wavefunction that “split off of our blob” in macroscopic ways a long time ago would be fantastically unlikely. Not impossible, just “a whale and a petunia spontaneously appear out of quantum noise” degree of improbability.
As I understand it: If you draw out events as a DAG with arrows representing causality, then A acausally effects B in the case that there is no path from A to B, and yet a change to A necessitates a change to B, normally because of either a shared ancestor or a logical property.
I most often use it informally to mean “contrary to our intuitive notions of causality, such as the idea that causality must run forward in time”, instead of something formal having to do with DAGs. Because from what I understand, causality theorists still disagree on how to formalize causality (e.g., what constitutes a DAG that correctly represents causality in a given situation), and it seems possible to have a decision theory (like UDT) that doesn’t make use of any formal definition of causality at all.
Having seen the exchange that probably motivated this, one note: in my opinion, events can be linked both causally and acausally. The linked post gives an example. I don’t think that’s an abuse of language; we can say that people are simultaneously communicating verbally and non-verbally.
Broadly, branches become less likely to interact as they become more dissimilar; dissimilarity tends to bring about dissimilarity, so they can quickly diverge to a point where the probability of further interaction is negligible. Note that at least as Eliezer tells it, branches aren’t ontologically basic objects in MWI any more than chairs are; they’re rough high-level abstractions we imagine when we think about MWI. If you want a less confused understanding than this, I don’t have a better suggestion than actually reading the quantum physics sequence!
I found an excellent answer here
I think it depends on perspective. We notice worlds interfering with each other in the double slit experiment. I think that maybe once you are in a world you no longer see evidence of it interfering with other worlds? I’m not really sure.
Pretty sure double slit stuff is an effect of wave-particle duality, which is just as consistent with MWI as with waveform collapse.
Basically, if two of them evolve into the same “world”, they interfere. It could be constructive or destructive. It averages out to be that it occurs as often as you’d expect, so outside of stuff like the double-slit experiment, they won’t really interact.
Hmm. I’m also pretty sure that the double-slit experiments are not evidence of MWI vs. waveform collapse.
They are evidence against wave-form collapse, in that they give a lower bound as to when it must occur. Since, if it does exist, it’s fairly likely that waveform collapse happens at a really extreme point, there’s really only a fairly small amount of evidence you can get against waveform collapse without something that disproves MWI too. The reason MWI is more likely is Occam’s razor, not evidence.
Well, I tried to understand some double-slit corner-cases. If I read some classical Copenhagen-approach quantum physics textbook, it is hard to describe what happens if you install a non-precise particle detector securely protected from experimenter’s attempts to ever read it.
Of course, in some cases Penrose model and MWI are hard to distinguish, because gravitons are hard to screen off and can cause entanglement over large distances.
Non-traditional notions of causality as in TDT such as causality that runs backwards in time.
“Acausal” means formal or final as opposed to efficient causality.
Also, a monad is just a monoid in the category of endofunctors.
That looks like precise jargon. Where should I look up the words you just used?
Philosophy sources, eg the online Stanford Encyclopedia thereof or some work on Aristotle. But I don’t recommend you bother. “Formal” means a logical implication. “Final” suggests a purpose, which makes sense in the context of decision theory.
Aristotelian tradition. I’m sure you could find a lot of similarly motivated classifications in the cybernetics and complex systems literature if you’re not into old school metaphysics.