It’s true, but not testable, to say that a spaceship going over the cosmological horizon of an expanding universe does not suddenly blink out of existence
This example has been used by Eliezer before in the Sequences, and it is a bit problematic under the latest physical theories. Assuming cosmological horizons behave like black hole event horizons, the theories say the following:
The spaceship doesn’t “blink out of existence”; instead it becomes more and more red-shifted, and never crosses the horizon from our own point of view.
Further, in a quantum mechanical picture, the state of the spaceship eventually returns from the horizon, greatly scrambled, in the form of Hawking radiation. This happens within a finite proper time, as measured by the spaceship’s clocks.
Worse, if the spaceship also manages to cross the horizon (i.e, the clocks keep ticking from its own point of view) and continues to exist in some region “outside”, then its informational state becomes duplicated. But this is a violation of unitary evolution in quantum mechanics. It’s sometimes called the “xeroxing” paradox.
Accordingly, anyone taking a trip on that spaceship shouldn’t be at all confident they’ll reach anywhere!
But there is an interesting (and rather worrying) follow-through to this reasoning. In cosmology, we observe something very like a positive cosmological constant (lambda term) pushing galaxies apart at an accelerating rate. If it continues to behave like a cosmological constant, then every galaxy in the universe is exactly like the spaceship, and will eventually red-shift into a cosmological horizon with respect to every other galaxy. It apparently follows from this that every galaxy in the universe (including our own) can only continue to exist for a finite proper time before getting scrambled into Hawking radiation. So we’re not actually any safer staying on Earth than going off in the spaceship! This “end-of-time” effect has been discussed in a number of recent papers including this one by Raphael Bousso: the predicted end is in about 5 billion years. Needless to say, the effect is extremely controversial, as is the chain of reasoning leading to it. But if there is something wrong with the reasoning, it’s not clear where...
Assuming cosmological horizons behave like black hole event horizons
Why on Earth would they?
Edit: Also that paper does not say anything about cosmological horizons converting anything into Hawking radiation! It’s an entirely different and stranger argument.
In asymptotically flat spacetimes, the event horizon of a black hole is defined (roughly) as the boundary of the region of spacetime that can be seen by an immortal observer (more precisely, it’s the boundary of the causal past of future null infinity). If you extend this definition to generic spacetimes, then it applies to the cosmological event horizon in a spacetime with positive cosmological constant. Because of this formal similarity, a number of results in black hole thermodynamics (specifically, the laws of black hole mechanics) can be generalized to the cosmological horizon.
Anyway, one response (Susskind’s) to the sort of thing drnickbone brings up, in the case of black holes, is black hole complementarity. We seem to have this paradox when something falls into a black hole. On the one hand, we don’t want information to disappear beyond the event horizon, so the information must be absorbed into the event horizon itself, theoretically readable off the structure of the horizon (or off Hawking radiation). On the other hand, from the perspective of an infalling observer, nothing special happens as she passes through the horizon. It certainly doesn’t seem to her as if the information she carries has been smeared over the event horizon. Susskind’s response is essentially that both of these things happen. The information is both reflected and transmitted by the event horizon. But the no-cloning theorem rules out the possibility that the reflected and transmitted information are two separate things. Instead, they are the same event described from different perspectives.
From an outside observer’s perspective, the information is painted onto the horizon. From an infalling observer’s perspective, the information passes right through the horizon. Extending this idea to the cosmological horizon and a spaceship leaving my horizon: From the perspective of the spaceship nothing special has happened. After all, why should they care about my horizon. From my perspective, once the spaceship hits the horizon, all the information constituting the spaceship is now smeared over the horizon. And of course, if I am to abide by the no-cloning theorem, I cannot simultaneously maintain that the spaceship continues to travel past the horizon. From my perspective, the spaceship does cease to exist (except as information encoded in the structure of the 2-dimensional cosmological horizon).
[ETA: I should have mentioned that this isn’t just completely baseless speculation on Susskind’s part. He bases his claim on an argument from string theory. The basic idea is this: The spatial extent of a string’s wave function depends on the “resolution time”, which is the time scale over which observations are made. As this time scale gets smaller and smaller, i.e. as our observations get faster, the spatial extent of the string gets larger. As long as the resolution time is significantly larger than the Planck time, the effect of this phenomenon is negligible. Now think of someone falling into a black hole while making measurements on a string. Another observer is outside the black hole looking on. The infalling observer’s resolution time won’t change as she falls. But the outside observer’s resolution time will effectively get smaller and smaller, due to gravitational time dilation. As a consequence, the string gets bigger and bigger from his perspective. As the falling observer hits the event horizon, the string is big enough to be spread across the entire horizon, which means the information it contains is now spread across the event horizon. So from the outside observer’s perspective, the string never falls into the black hole; it gets smeared across the horizon and the information is eventually radiated out. And since the infalling observer is also made of strings, she unfortunately gets spread across the horizon too. But none of this holds in the infalling observer’s perspective. The string doesn’t grow in size—it remains localized and falls through the event horizon into the singularity. So, very speculative, but not baselessly so.]
On the one hand, we don’t want information to disappear beyond the event horizon, so the information must be absorbed into the event horizon itself, theoretically readable off the structure of the horizon (or off Hawking radiation). On the other hand, from the perspective of an infalling observer, nothing special happens as she passes through the horizon. It certainly doesn’t seem to her as if the information she carries has been smeared over the event horizon. Susskind’s response is essentially that both of these things happen.
An update. I didn’t realise this a couple of months ago, but it seems there has been a big controversy brewing recently about black hole complementarity, and whether it is consistent. There was a key paper by Polchinski and three others in August Complementarity or Firewalls?; see also his guest post in Discover.
The basic argument is that there is a new black hole paradox: quantum states on the edge of a horizon have to be fully entangled BOTH with Hawking radiation that has already emerged from the black hole AND with neighbouring states that are just inside the black hole. And that is not possible, because there is a “monogamy” of quantum entanglement. Further, complementarity doesn’t help, because an observer could in principle collect the entangled radiation that had already emerged from the black hole, distill it, and then bring it into the black hole to meet its duplicate entangled state inside, which would lead to quantum cloning. Oops. Instead Polchinksi et al propose that there is a “firewall” at the black hole event horizon which would destroy the second entanglement, and also destroy any observers going into the black hole.
There seems to have been a big fight on the high energy physics archive, with lots of authors drafting papers in an attempt to refute Polchinski et al, then withdrawing them or heavily editing them. Bousso also had a go, claiming that they had misunderstood complementarity, then retracted; his latest version argues that they’ve found a genuine paradox after all.
To be fair, not many of these physicists/cosmologists agree with the firewall solution, probably because it can leads to observers suddenly disappearing into flame without warning (it is possible to reach an event horizon around a very large black hole in otherwise normal space, with no outward-sign that is coming, then smash into the firewall and die). That violates the same sorts of physical intuitions that Eliezer raises in the main article (and which I challenged). It’s also not clear exactly when a firewall forms (if it does) or if there are firewalls at cosmological horizons.
P.S. I found the following interesting paragraph in Bousso et al which considers Susskind’s complementarity proposal. It seems to make a big difference whether you define an observer first (and then consider his causal horizon), or define a causal patch first (together with its horizon) and then consider where the observer might be:
In the traditional discussion of black hole complementarity, one picks an observer and constructs the associated causal patch. It is impossible, by construction, for an observer to leave his own patch. In other words, time cannot end if we live in a causal patch centered on our own worldline. In eternal inflation, however, one first picks a causal patch; then one looks for observers in it. Some of these observers will be closer to the boundary and leave the patch sooner than others, who happen to stay in the patch longer. Equivalently, suppose we do want to begin by considering observers of a given type, such as an observer falling towards a black hole. To compute probabilities, we must average over all causal patches that contain such an observer. In some patches the observer will be initially far from the boundary, in others he will hit the boundary very soon. This yields a probability distribution for the rate at which time ends
If we consider it in “many worlds” terms, then the wave function over the causal patch contains many different branches, and human observers (indeed our whole Milky Way galaxy) get to exist in lots of those branches. But in only a very few of the branches is our galaxy near the centre of the patch and able to continue to survive for 100s of billions of years; in most of the other branches we are somewhere off-centre, and will be smeared out against the horizon very much sooner. The fact that the Milky Way will continue to exist in some branches does not mean we should expect to survive in our branch. This reminds me somewhat of the discussions on quantum suicide.
Thanks for this, though in a way, Susskind’s interpretation seems to be even weirder than that of Bousso et al.
In Susskind’s view, we would have to say that every galaxy apart from ours has an end-of-time experience, and gets smeared out on the horizon (or thermalized by de Sitter radiation), still in an average of about 5 billion years. But our own doesn’t… so in 100 billion years or so we will be the lucky sole survivors in a universe containing a single remaining galaxy. Yet we are not really “lucky” because every other galaxy is experiencing the same thing from its own galacto-centric viewpoint. And while these individual amazing survivor stories are all consistent, there is no globally consistent story where all the galaxies continue to survive, just moving further and further apart. Strange...
Well horizons might not behave exactly the same (this is all theoretical physics) but there is quite a long chain of papers arguing that Hawking radiation arises from all sorts of causal horizons, and for the same sorts of reasons that motivate it for black hole horizons. See Gibbons-Hawking effect or look up “de Sitter radiation” on Google scholar. Here’s just one paper.
With regard to your edit, the paper by Bousso et al does in fact discuss physical interpretations of the “end of time” effect, and scrambling into radiation appears to be the authors’ preferred interpretation. See Section 5.3 on “causal patch measure” and this paragraph:
We now see that there is a different, more satisfying interpretation: the inside observer is thermalized at the horizon. This interpretation invokes a relatively conventional physical process to explain why the inside observer ceases to exist. Time does not stop, but rather, the observer is thermalized. His degrees of freedom are merged with those already existing at the boundary of the causal patch, the horizon.
That question sprung to mind too, right before “How could that even make sense?” and a few hundred milliseconds later “What are the precise engineering details required for me to use this effect (and the implied possibility for FTL communication) to go back and sink the first fleet, thereby preventing my own existence?”.
Edit: Also that paper does not say anything about cosmological horizons converting anything into Hawking radiation! It’s an entirely different and stranger argument.
(My reply is to the version conveyed within the grandparent, not to the strange argument. It is probably best for me to hold off reading said strange argument until is confirmed as reasonable by a sufficiently trusted source. Given the complexity of the subject I may forget to not-believe something I read.)
“What are the precise engineering details required for me to use this effect (and the implied possibility for FTL communication) to go back and sink the first fleet, thereby preventing my own existence?”.
Well there’s nothing in the Gibbons-Hawking effect (all causal horizons have a temperature and emit thermal radiation), or in the referenced paper of Bousso et al to imply FTL travel. Where did you get that idea? The “end-of-time” papers may be wrong but they’re not that wrong...
This example has been used by Eliezer before in the Sequences, and it is a bit problematic under the latest physical theories. Assuming cosmological horizons behave like black hole event horizons, the theories say the following:
The spaceship doesn’t “blink out of existence”; instead it becomes more and more red-shifted, and never crosses the horizon from our own point of view.
Further, in a quantum mechanical picture, the state of the spaceship eventually returns from the horizon, greatly scrambled, in the form of Hawking radiation. This happens within a finite proper time, as measured by the spaceship’s clocks.
Worse, if the spaceship also manages to cross the horizon (i.e, the clocks keep ticking from its own point of view) and continues to exist in some region “outside”, then its informational state becomes duplicated. But this is a violation of unitary evolution in quantum mechanics. It’s sometimes called the “xeroxing” paradox.
Accordingly, anyone taking a trip on that spaceship shouldn’t be at all confident they’ll reach anywhere!
But there is an interesting (and rather worrying) follow-through to this reasoning. In cosmology, we observe something very like a positive cosmological constant (lambda term) pushing galaxies apart at an accelerating rate. If it continues to behave like a cosmological constant, then every galaxy in the universe is exactly like the spaceship, and will eventually red-shift into a cosmological horizon with respect to every other galaxy. It apparently follows from this that every galaxy in the universe (including our own) can only continue to exist for a finite proper time before getting scrambled into Hawking radiation. So we’re not actually any safer staying on Earth than going off in the spaceship! This “end-of-time” effect has been discussed in a number of recent papers including this one by Raphael Bousso: the predicted end is in about 5 billion years. Needless to say, the effect is extremely controversial, as is the chain of reasoning leading to it. But if there is something wrong with the reasoning, it’s not clear where...
Why on Earth would they?
Edit: Also that paper does not say anything about cosmological horizons converting anything into Hawking radiation! It’s an entirely different and stranger argument.
In asymptotically flat spacetimes, the event horizon of a black hole is defined (roughly) as the boundary of the region of spacetime that can be seen by an immortal observer (more precisely, it’s the boundary of the causal past of future null infinity). If you extend this definition to generic spacetimes, then it applies to the cosmological event horizon in a spacetime with positive cosmological constant. Because of this formal similarity, a number of results in black hole thermodynamics (specifically, the laws of black hole mechanics) can be generalized to the cosmological horizon.
Anyway, one response (Susskind’s) to the sort of thing drnickbone brings up, in the case of black holes, is black hole complementarity. We seem to have this paradox when something falls into a black hole. On the one hand, we don’t want information to disappear beyond the event horizon, so the information must be absorbed into the event horizon itself, theoretically readable off the structure of the horizon (or off Hawking radiation). On the other hand, from the perspective of an infalling observer, nothing special happens as she passes through the horizon. It certainly doesn’t seem to her as if the information she carries has been smeared over the event horizon. Susskind’s response is essentially that both of these things happen. The information is both reflected and transmitted by the event horizon. But the no-cloning theorem rules out the possibility that the reflected and transmitted information are two separate things. Instead, they are the same event described from different perspectives.
From an outside observer’s perspective, the information is painted onto the horizon. From an infalling observer’s perspective, the information passes right through the horizon. Extending this idea to the cosmological horizon and a spaceship leaving my horizon: From the perspective of the spaceship nothing special has happened. After all, why should they care about my horizon. From my perspective, once the spaceship hits the horizon, all the information constituting the spaceship is now smeared over the horizon. And of course, if I am to abide by the no-cloning theorem, I cannot simultaneously maintain that the spaceship continues to travel past the horizon. From my perspective, the spaceship does cease to exist (except as information encoded in the structure of the 2-dimensional cosmological horizon).
[ETA: I should have mentioned that this isn’t just completely baseless speculation on Susskind’s part. He bases his claim on an argument from string theory. The basic idea is this: The spatial extent of a string’s wave function depends on the “resolution time”, which is the time scale over which observations are made. As this time scale gets smaller and smaller, i.e. as our observations get faster, the spatial extent of the string gets larger. As long as the resolution time is significantly larger than the Planck time, the effect of this phenomenon is negligible. Now think of someone falling into a black hole while making measurements on a string. Another observer is outside the black hole looking on. The infalling observer’s resolution time won’t change as she falls. But the outside observer’s resolution time will effectively get smaller and smaller, due to gravitational time dilation. As a consequence, the string gets bigger and bigger from his perspective. As the falling observer hits the event horizon, the string is big enough to be spread across the entire horizon, which means the information it contains is now spread across the event horizon. So from the outside observer’s perspective, the string never falls into the black hole; it gets smeared across the horizon and the information is eventually radiated out. And since the infalling observer is also made of strings, she unfortunately gets spread across the horizon too. But none of this holds in the infalling observer’s perspective. The string doesn’t grow in size—it remains localized and falls through the event horizon into the singularity. So, very speculative, but not baselessly so.]
An update. I didn’t realise this a couple of months ago, but it seems there has been a big controversy brewing recently about black hole complementarity, and whether it is consistent. There was a key paper by Polchinski and three others in August Complementarity or Firewalls?; see also his guest post in Discover.
The basic argument is that there is a new black hole paradox: quantum states on the edge of a horizon have to be fully entangled BOTH with Hawking radiation that has already emerged from the black hole AND with neighbouring states that are just inside the black hole. And that is not possible, because there is a “monogamy” of quantum entanglement. Further, complementarity doesn’t help, because an observer could in principle collect the entangled radiation that had already emerged from the black hole, distill it, and then bring it into the black hole to meet its duplicate entangled state inside, which would lead to quantum cloning. Oops. Instead Polchinksi et al propose that there is a “firewall” at the black hole event horizon which would destroy the second entanglement, and also destroy any observers going into the black hole.
There seems to have been a big fight on the high energy physics archive, with lots of authors drafting papers in an attempt to refute Polchinski et al, then withdrawing them or heavily editing them. Bousso also had a go, claiming that they had misunderstood complementarity, then retracted; his latest version argues that they’ve found a genuine paradox after all.
To be fair, not many of these physicists/cosmologists agree with the firewall solution, probably because it can leads to observers suddenly disappearing into flame without warning (it is possible to reach an event horizon around a very large black hole in otherwise normal space, with no outward-sign that is coming, then smash into the firewall and die). That violates the same sorts of physical intuitions that Eliezer raises in the main article (and which I challenged). It’s also not clear exactly when a firewall forms (if it does) or if there are firewalls at cosmological horizons.
Worth watching for more developments.
P.S. I found the following interesting paragraph in Bousso et al which considers Susskind’s complementarity proposal. It seems to make a big difference whether you define an observer first (and then consider his causal horizon), or define a causal patch first (together with its horizon) and then consider where the observer might be:
If we consider it in “many worlds” terms, then the wave function over the causal patch contains many different branches, and human observers (indeed our whole Milky Way galaxy) get to exist in lots of those branches. But in only a very few of the branches is our galaxy near the centre of the patch and able to continue to survive for 100s of billions of years; in most of the other branches we are somewhere off-centre, and will be smeared out against the horizon very much sooner. The fact that the Milky Way will continue to exist in some branches does not mean we should expect to survive in our branch. This reminds me somewhat of the discussions on quantum suicide.
Thanks for this, though in a way, Susskind’s interpretation seems to be even weirder than that of Bousso et al.
In Susskind’s view, we would have to say that every galaxy apart from ours has an end-of-time experience, and gets smeared out on the horizon (or thermalized by de Sitter radiation), still in an average of about 5 billion years. But our own doesn’t… so in 100 billion years or so we will be the lucky sole survivors in a universe containing a single remaining galaxy. Yet we are not really “lucky” because every other galaxy is experiencing the same thing from its own galacto-centric viewpoint. And while these individual amazing survivor stories are all consistent, there is no globally consistent story where all the galaxies continue to survive, just moving further and further apart. Strange...
Well horizons might not behave exactly the same (this is all theoretical physics) but there is quite a long chain of papers arguing that Hawking radiation arises from all sorts of causal horizons, and for the same sorts of reasons that motivate it for black hole horizons. See Gibbons-Hawking effect or look up “de Sitter radiation” on Google scholar. Here’s just one paper.
With regard to your edit, the paper by Bousso et al does in fact discuss physical interpretations of the “end of time” effect, and scrambling into radiation appears to be the authors’ preferred interpretation. See Section 5.3 on “causal patch measure” and this paragraph:
Because they’re both horizons, of course!
That question sprung to mind too, right before “How could that even make sense?” and a few hundred milliseconds later “What are the precise engineering details required for me to use this effect (and the implied possibility for FTL communication) to go back and sink the first fleet, thereby preventing my own existence?”.
(My reply is to the version conveyed within the grandparent, not to the strange argument. It is probably best for me to hold off reading said strange argument until is confirmed as reasonable by a sufficiently trusted source. Given the complexity of the subject I may forget to not-believe something I read.)
Well there’s nothing in the Gibbons-Hawking effect (all causal horizons have a temperature and emit thermal radiation), or in the referenced paper of Bousso et al to imply FTL travel. Where did you get that idea? The “end-of-time” papers may be wrong but they’re not that wrong...