The “New Rules for Time Travel ” and Sean Carroll’s Gate
Marshall Barnes, R&D Eng
United States of America
February 16, 2010
(NEW! As of 3/4/2010, see special *note about Sean Carroll after References at the bottom...)
This paper will deconstruct and analyze the closed time-like curve examples of Sean Carroll as he wrote them in the March 2010 cover story for Discover Magazine in relation to issues of entropy, determinism, and time travel paradoxes. I will then reveal the actual nature of how those space-time geometries would function, in contrast to they way in which they were described in the article. Topics include wormholes, black holes, Riemann slits, causality, and parallel universes.
The cover story of the March 2010 edition of Discover Magazine contains the screaming headline—The New Rules for Time Travel: What to know before you go! with a huge picture of a clock with the glass cover exploding from across its face. As the nature of time, and in particular - time travel, is one of my main areas of fundamental study, I took particular interest and wasted no time in finding the article inside which I discovered to actually be called How To Travel Through Time. I quickly scanned through it looking for some new information concerning a breakthrough, perhaps on par with the University of Connecticut’s Ronald Mallet PhD , but instead I was confronted with what appeared to be the same tired cliché subjects derived from time travel theories. Or so I thought. To my delight, I saw the basis for a new paper and a chance to do some fresh work in response, as well as reintroduce some research results that I have explained before in a number of my lectures.
The article was written by Sean Carroll, PhD and was an excerpt from his just released book, From Eternity to Here. Early on he reduces the whole issue of time travel to a matter of paradoxes and the question of “what happened at the vicinity of this particular event in space-time?”, and but seemingly fails to comprehend the somewhat obvious implications of that very same question and its logical conclusion. The logic and the obviousness will become apparent later.
Next he focuses on the issue of free will and how consistent stories are still possible even in space-times with closed time-like curves. He then introduces a plot device — a gate that will allow you to go one day into the past if you walk through the front, and one day into the future if you walk through the opposite side. Sean suggests a hypothetical situation to make this more interesting. He has us assigned as the guardians of this gate device to monitor closely who comes and goes. One day we see a guy leave from the back of the gate, which according to Sean, “It just means that you will see that person enter the front of the gate tomorrow.” When tomorrow comes, however, the guy is still hanging around the gate and when it has been 24 hours since he exited the back of the device, he walks around and disappears through the front. This signals to Sean that the guy came from nowhere and that the entire life of this time traveler consists of nothing else but this closed time-like loop that his action implies. Sean uses this to emphasize a link between the increase of entropy over time since the time traveler must align “every single atom in his body...” “in precisely the right place to join up smoothly with his past self”. This insistence reveals that Sean doesn’t understand his time traveler, or the space-time geometry that he has constructed with his gate apparatus, beyond anything but the most pedestrian level, as I will prove later. However, let me note now that the idea that the time traveler must line-up with his “past self” indicates that there must be more than one of him or else what is he to line-up with? This will also become problematic later. You should note that this is the first and last time in the article that Sean mentions the idea of duplicates of anything that would result from this time travel scenario involving the time traveler who seems to be on the CTC. I will also reveal why that is important.
Another disturbing thing about this time traveler/CTC scenario is Sean's claim that the time traveler will not accumulate new memories. It's as if Sean believes that going through the gate wipes out your memories when in fact, it wouldn't. Part of this is because, as he has already indicated, he's trying connect the time traveler to his past self and, by doing so, would rid the time traveler of any continuation of existence beyond that point except as a repeat of his past self. We'll see, in excruciating detail, why this wouldn't be the case, later.
Next, he attempts to bring some validity to this whole affair by giving a detailed description of what closed time-like curves are but it is not surprising that he only makes things worse when he actually states that “In the usual way of thinking, the laws of physics function like a computer. You give as input the present state, and the laws return as output what the state will be one instant later (or earlier, if we wish). By repeating the process many times, we can build up the entire history of the universe from start to finish. In that sense, complete knowledge of the present implies complete knowledge of all history.”
Of course, I was stunned at this statement. It’s as if there's no uncertainty principle from quantum mechanics limiting how much we can know, or how physicists, knowing full well the rules of general relativity, rejected the notion of the implied reality of black holes, or even everyone’s lack of certainty, despite all we know about particle physics, of what will happen when the Large Hadron Collider is turned on all the way at Cern. Scientists are still debating on whether or not there will be a big crunch for the universe, let alone feeling certain about how it all began, and Sean is talking about building up the entire history of the universe from start to finish? After some consideration it would appear that Sean was actually trying to convey the determinism described by solutions derived from the space-like Cauchy surface, where space-time is completely at rest. From that, it can be argued (not by me) that CTCs arise wherein causality breaks down and can allow for events which are their own cause, thus creating a Cauchy horizon . As you will read later, it is clear that I do not subscribe to this interpretation - of events that are their own cause, and I am encouraged in that position by the numerous incongruities that I have found in the work of those who just blindly accept the idea without serious reconsideration.
Sean argues that CTCs actually prevent knowledge of the future (again, based on determinism), which is actually quite funny in one aspect when you consider that CTCs, especially the way that he describes them, would actually do the opposite—they repeat history so that you know exactly what to expect—a repeat of what has happened before. Remember? His insistence on the time traveler aligning his body up exactly with his earlier self at the right moment? Yet Sean claims that CTCs make predictions impossible. He actually insists that CTCs make the universe “unpredictable” because “mysterious strangers and random objects can then appear and disappear out of thin air…” Sounds like a very good description, actually, of any number of discoveries from quantum mechanics — virtual particles, quantum tunneling...Need I say more?
In reality, what Sean is trying to say is that the CTC prevents future knowledge of a region of space-time from being predicted by prior knowledge. It really has nothing to do with the knowledge of the entire universe in a literal sense, but in the parlance of general relativity. However, with this distinction unclear, it is writing like this - with sweeping generalities, that perpetuates a state of misinformation among the scientifically interested lay public as well as a reliance on false assumptions among physicists. In the wake of such statements I am not surprised then when he states further that CTCs would prevent the ability to “divide all of space-time into distinct moments”. He thinks so because CTCs curve space-time back on itself, which is true, however it is equally untrue that such a geometry would prevent the former division from taking place. A CTC doesn't replicate everything exactly (in fact Sean states that "Closed time-like curves make the future resemble the past" - emphasis mine) but takes a region of space-time and curves it back through time. That doesn't mean that going through it is an exact repeat of what happened before (thus dividing distinct moments in time is still possible) . Again, we see why later. At this point I'm merely setting up Sean's positions. I will do a full deconstruction and resolution in due time.
The problem here can be summed up with this quote from Sean, “Some of our understanding of time is based on logic and the known laws of physics, but some of it is based purely on convenience and reasonable-sounding assumptions”. The later is exactly why Sean Carroll has so many problems with his article. I gave a presentation at the 2004 International Mars Society conference titled, Avoiding Hidden Assumption Traps When Thinking Outside of the Box where I showed that it is exactly this tendency to assume that has led to what I call the train wreck in physics when it comes to these kind of advanced concept subjects. Especially when it comes to time. I will now reveal the solutions to the various problems stemming from this in Sean's article.
Let’s begin by revisiting the space-time geometry of Sean’s gate. This is something that I am very familiar with, to the point that I will sometimes refer to such configurations as Riemann slits, which is the mathematical term for an opening that takes you from one plane to another. The term was invented by German mathematician Bernhard Riemann  back in the mid-1800s. I prefer that term when discussing said geometries in general and not speaking specifically about wormholes, black holes, etc. which have a variety of specific and mutually exclusive properties that preclude generalization for discussions of non-trivial space-times. Figure 1 shows such an opening within a cube of space with vector lines in a light cone-like arrangement that define the spatial direction one is viewing when looking through opposite sides of the Riemann slit. The vector lines are both indicating a region outside of the light cone of a typical space-time diagram but also light coming from within the slit from the destination it opens to. The correlation with the light cone of a space-time diagram is due to the region inside the slit being a destination that would exist outside the light cone on a space-time diagram in that area that is usually referred to as Elsewhere and would only be reachable via traveling faster than light, time travel or transversable wormhole (i.e. a Riemann slit). It should be remembered that although the slit occupies the place where Now usually appears on a space-time diagram, this is not a space-time diagram and the vector lines are indicating directions from within the slit, directions that exist in a region that would normally be considered outside the light cone of the space indicated by the cube. The contrasting dashed arrows indicate each line of sight to that region.
Now, the unique nature of Sean’s gate is it doesn’t open up to another space-time but to two — a day in the past on one side and a day in the future via the other. In this case, when applied to my diagrams, if you look through the front (or right side) you will be looking to the past by one day. If you walk around and look through the left (or back) you will be seeing the future by one day. He has indicated that this gate is a time machine that we discover, so we are left to understand that we are talking about a physical construct of some type and not just a natural wormhole that we have discovered. He uses the word “gate” and never mentions wormhole, and he also indicates that it is a time machine. I emphasize this because it is not unknown for physicists to call wormholes, or CTCs, time machines because they fear writing about time travel in any other form. So I want to hold Sean to his words and by doing so, point out that if the gate is a time machine, somebody built it, which means that you could keep going backward in time to when it was first placed there, which is the point where the first inconsistency shows up—the fact that there is a time machine at all.
First let me explain this important point and I will then move on to how it relates to CTCs. When discussing time travel to the past, in particular, and paradoxes, nearly everyone focuses in on some inconsistent plot element like murdering your grandfather or your teenage mother falling in love with you so she never weds your dad (the same paradoxical result ). Because of this, the idea is that some event creates a paradox that would be illogical and so indicates that time travel is impossible or that some mysterious force of coincidences comes together to prevent such things from occurring in the first place. Hence, Discover magazine's claim that Sean's article constitutes new rules for time travel because Sean's initial premise is that CTCs could provide time travel without inconsistency. What is constantly ignored here is that the first, initial inconsistency, as in all time travel scenarios, is the arrival of the time traveler to begin with.
It's October 1914, on the Western Front and suddenly, during the Battle of Ypres, amongst the drifting smoke and explosions, a glowing ring of light opens up on the trenches and out steps a determined looking young man, armed with an Uzi. Just then, a mustached German Gefreiter, acting as a runner, races by but not noticing the phenomena that is happening just above him and to his right. The man fires his Uzi at the soldier, gunning him down in a hail of bullets, and then just as suddenly vanishes into the portal of light, which blinks out. Stunned, near-by soldiers of the Barvarian Regiment List , scramble to his side.
"Gott im Himmel! Adolf ist durch den Engel des Todes getötet worden! "
Of course this is the classic, "what if you went back and killed Hitler..." scenario, albeit with a unique twist, but the importance here is not that it is inconsistent with the historical record but the mere act of opening a path to the past, in most cases, would be inconsistent with the historical record. What you do isn't the determining factor, its the mere act of changing space-time to enable you to do anything, that is the determining, inconsistent factor. This simple fact renders all other arguments, concerning paradoxes and keeping stories consistent within CTCs, moot.
Now the idea that CTCs simply repeat the same thing over and over ignores the fact that there is a starting point. After all, if the CTC is truly closed then you can’t get into it in the first place. It’s similar to Stephen Hawking’s chronology protection conjecture , which is also wrong (and which he has since abandoned so I won't waste space going into all the obvious reasons it was never right, here) but it is correct on this one angle - if you do produce a causal link to the past then that link will be destroyed by the sudden eruption of feedback. If a space-time were to actually go back and curve to an exact previous point, in time and space, then any energy from that time, and near that region, could flow through that CTC back to where it began, repeatedly, and destroy the CTC in an explosion. I am reminded of galactic jets that are seen erupting from the center of supermassive black holes and wonder, since time and space are said to break down inside of black holes, could these jets in some instances be the result of brute force CTCs being created and exploding?
It used to be believed that you might be able to fly into a black hole and avoid the singularity but we know now, from Hubble Space Telescope photography, that the tremendous gravitational forces and radiation exceed the tolerances for any technology that we could imagine. I pointed this out in my 2009 article Space Shuttle Endeavor Crew Flunk Kid's Youtube Question  (the short title) concerning how a member of the shuttle crew answered that "We don't know" when a British kid asked via Youtube what would happen if you flew into a black hole. The right answer is that, due to the conditions that I cited, there is no flying into a black hole. If the forces just near the accretion disc are powerful and hot enough to turn matter into gas, a flight even past the accretion disc is impossible, let alone into the hole itself. But it cannot be disallowed that such rampant and brutal forces, that are exerted within such a celestial body, could be capable of tearing CTCs into existence which would violate causality and explode as Hawking predicted. I am differentiating between the type of CTC that allows for time travel and that which would result from the out of control forces stemming from a black hole, thus my use of the term brute force.
However, outside of topic of black holes, descriptions of CTCs encounter the problem of describing what happens to that entry point. Any CTC must have an initial beginning. If it pinches off soon after it is formed, there may not be enough energy to destroy the loop. If it does remain open too long, the energy would be joined by more and more, and eventually the CTC would be destroyed as it would be inside a black hole.
But such ideas ignore quantum mechanics which tells us that you only get one outcome per measurement which means there is no going back to the same exact moment in the same exact time, in the same exact space, at least not in the exact same space-time, which means that we must be talking about parallel universes here and, in fact, all discussions on time travel lead to that simply by the act of the time machine being switched on. Arguments that parallel universe time travel isn't really time travel are inconsequential inside a physics discussion. The point is to discuss physics and not sheer fantasy. Whether they are mentioned outright or left unspoken, as Sean has done, the point at which parallel universes come into play can be seen in every physics time travel scenario. Despite being mute on the subject, Sean's own design betrays his silence, as I will illustrate.
Figure 3 shows how Sean's gate is set-up. The top illustration shows Today with the right side of the gate leading to Yes. (yesterday) and the left leading to Tom. (tomorrow). Yes. leads to the space-time Yes.Today where yesterday is the current day and the day you came from is in the future. Likewise, Tom. leads to the space-time Tom.Today where that future day is current and the day you came from is in the past. Each time I go through the opening in the same direction, I go further by one day into the past or future, depending on my direction. I have corresponding arrows that point directly to the space-time configuration that each path through the gate would lead to.
So, I can keep going backward in time by going through the front of the gate, over and over again. Before I proceed I want make a clarification. He specifically states that "When you pass through it in one direction, it takes you exactly one day into the past; if you pass through in the other direction, it takes you exactly one day into the future." There is no mention of having to wait before you go through the gate, although he mentions waiting later as part of his scenario with a time traveler. That being the case, that every time you pass through the gate you arrive the day before in the one direction and the next day in the other, then it is possible to go back to the gate's beginning. That means I can finally arrive the day before the gate was put there, but if I’m there the day before, how did I emerge to that past and can I get back? The answers to those questions simultaneously reveal another aspect of Sean’s gate that he failed to see, but I will answer the questions first. When I go through the opening and arrive the day before the gate was there, there will obviously be an opening through which to walk through because the purpose of the gate is to open up to the past in one direction and the future in the other. But I arrive before the gate is in place, how did I get there? Obviously there was an opening to pass through. Notice I said opening and not gate?
Let’s put you in my place instead. Imagine that you are about to go through the gate and arrive the day before it was put in place. You’re standing there and you see this door frame looking device (an arbitrary shape since Sean describes none) and inside the device, just as Sean described, is the day before. Note, he says that you have to pass through, but what happens when you turn around and look at the gate? Do you actually see the gate? If you’re arriving the day before it was created , how could you? There is no gate there on that day. Do we have a paradox here? No, we don't.
There are no paradoxes in time travel. What we have is the discovery of a long series of assumptions that are in Sean’s article. First of all, how does this gate function? This is an important question because as a research and development engineer I want to know how things work or if they can be built. British physicist John Gribbin, in his article, Why Time Travel Is Possible  closed it by saying, "self-consistency is a consequence of the Principle of least action, and nature can be seen to abhor a time travel paradox. Which removes the last objection of physicists to time travel in principle -- and leaves it up to the engineers to get on with the job of building a time machine." If we engineers are going have the job of building a time machine we have to understand intimately how such a device could be possible. That means we have to understand the physics. As a conceptual theorist that is also my job. So if a physicist like Sean is going to suggest such a device, the first thing I'm looking at is how it's supposed to operate. Because I have an intense interest in the nature of time and temporal mechanics, my scrutiny will be on a different level than that of a casual reader or your typical PhD physicist, who treats the subject more as a curiosity that arises from certain applications of general or special relativity, instead of being an integral part of the next step in Man's understanding the universe.
Now, Sean's gate functions by opening a hole in space-time to one day in the past in one direction and one day in the future in the other. Notice, we’re talking about a hole that you pass through. Ever walk through a doorway into another room and, on one side of the doorway, there is this ornate frame but on the opposite side, there is just a plain wall? Sure you have. If nothing else, the front entrance to most homes is like that. Well, that ornate door frame is like the gate. When you pass through and turn around you wouldn’t see the gate because it wouldn’t exist in that space-time of the day before it was created, but the opening that it caused would. This situation also reveals something else—that we’re talking about parallel universes here, automatically. Why? Because if the gate opens up to the day before it was created and yet it didn’t exist the day before it was created —that’s a paradox itself unless it opens to a parallel day before it was created. From an engineering point of view, the gate is generating some kind of field that has created this hole is space-time, and in some way has stabilized it.
This revelation creates a whole new state of affairs. For example, the way that Sean describes the gate, it would be possible to go through the openings that it caused, not only past the time it was created (something that most physicists refrain from suggesting because they only like to consider time travel via CTCs or CTLs when not derived from time dilation on speeding rockets through space) but into infinity in either direction. Those familiar with the theoretical aspects of rotating black holes will recognize this concept of being able to travel to an infinity of parallel universes as depicted in certain Penrose maps .
So Sean’s gate would actually open to a parallel past where the gate itself didn’t exist. Even if you began the day after and went back to the first day that it was operational, you still wouldn’t see it on that day because the day that the gate first connects to is the day before it existed and that is only possible in a parallel universe. In other words, the past timeline is never linked to the one where we see the gate first being activated.
I'll explain a different way. Going through the gate the day it is activated and you arrive in the space the day before it is activated, imagine just hanging out there for 24 hours. What happens then? The hole will still be there but, will the gate suddenly materialize around it? No. Here's why - you are in a space-time where a hole opened where there had never been one before. The day that hole opened by the activation of the gate is not the same day and place as the original day before the gate was activated because on that day there was no hole. No hole, no linear link to the exact day that the gate was activated, no ever seeing the gate suddenly appear on that side. Ever.
But what about the future side? Now that’s a different story but only in as far as the appearance of the gate. Going to the future you would be able to turn around and see the actual gate because it could exist in the future. However, it would also be a parallel future. Why? Because of something that Sean seemed so concerned about—free will. Determinism. If the gate takes you one day into the future it is also possible to visit the future and then return and destroy the gate. If you do, how could you have visited the future? By now, you know the answer
So to review before going further -
1. The front of the gate actually leads to parallel paths where the opening exits but not the gate itself.
2. The back of the gate leads to parallel futures where the gate does exist.
The way Sean wrote it is that you go through the gate and you see another one as if it has a copy in each version of space-time in the same exact spot. However it can't be in the exact same spot without adhering to the arrangement that I just described which in turn would not allow for Sean's exact scenario. You can see now why that wouldn't work. The reason he wrote it that way is because he was trying to figure out a way to write a CTC into his story to prove a point. We'll see later that this was even more problematic than I've revealed so far. It also leads to all kinds of false assumptions and erroneous results, as you are seeing now.
Another element that Sean missed is the issue of copies. You’ll remember that he mentioned the time traveler aligning himself with his past self. In the future direction you could see a copy of you because the day that the time machine was switched on it connected to the future next day. Unless something changes that future, you could be there as well to greet yourself coming through from the past. He only briefly mentions it when he first introduces the gate idea, but not in as far as when the time traveler comes along. However, the idea of the time traveler aligning himself with his past self is wrong because there is no past self that we see of the time traveler.
Again, the futures are parallel because of free-will. Someone could cause the gate to shutdown cutting off access to the future but then how could the future have been there with the gate? All time travel involves parallel universes. You have to finish doing the work to see them, but the presence of paradoxical solutions is indicative of your not being finished with the work. And unlike what Sean says, it's not just free-will but randomness that can be introduced. Any type of random event could alter the future that was connected through the gate. For a better understanding of this it is important to notice this other unknown element of Sean's model - the three clocks.
There's essentially a clock running at all times on the gate, the yesterday side and the tomorrow side. You can cheat time in either direction by going through the gate but you can also just wait like the time traveler did before he went through again. Multiple clocks (of this nature) means multiple universes because they could lead to multiple outcomes that are not consistent. There's nothing in physics that rules time travel out, and we know, at least from the Copenhagen interpretation of quantum mechanics, that there's only one outcome observed per measurement. If time travel isn't ruled out then, but there is a constraint on multiple outcomes, those alternate outcomes must only be possible in parallel universes. There's no escaping it.
So what about the time traveler and his closed CTC? First of all, unlike what Sean stated, the time traveler's life is not and could not only be made up of his going back and forth through the gate. Biology alone prevents that, another indication of not doing the work this subject requires. What I mean is the the time traveler was obviously born, raised, etc. Also, each time he goes through the gate he's doing it again, but for the first time. Let me explain.
According to Sean, the first time we see the time traveler is when he is existing the backside of the gate, returning from one day in the future. Sean has us decide to wait 24 hrs and then be surprised when the time traveler, who has spent this whole time loitering around the gate, just walks around and enters the front to go back to the past. What does this really mean? Remember those clocks I was talking about? When we saw the time traveler first arrive from the future there was a future version of ourselves that had just seen him enter the front of the gate to exit when we saw him. 24 hrs later, those versions of ourselves are on their next day in the future, 48 hours ahead of where we were when we saw the time traveler first pull his stunt. Sean makes the mistake of assuming that we will see the very same event repeat, and we will be the original witnesses, but we aren't. The original witnesses, ourselves 24 hours ahead, are then 48 hrs ahead of where we were when we first saw the time traveler. I can prove it easily - if we first saw the time traveler when he came from the future, then we can't be the same ones that saw him leave the future. I can prove that too - when Sean has us see him exit the next day and go to the past, we already knew he had done that before but were surprised to see how he had done it. Once you have space-time geometries that introduce copies you have parallel universes in the mix. We know those copies of ourselves are real because that's where the time traveler came from. This also raises an additional issue - if anyone is a copy in this scenario, it's not him. After all, he's the one time traveling. We saw him come from the future and we saw him go to the past the next day and at any point along that timeline of events he was without a duplicate of himself, the way that Sean wrote it. When he was in the future, he was with our copies. Then he leaves and comes to the past to be with us. Then the next day, he returns to the past. Unlike Sean's characterization, the time traveler isn't aligning himself with any copy - he's the constant original.
This is where we get to the next level of erroneous assumptions. Sean says that the time traveler must align with his past self, but that would be impossible. Sean also says that we see only one time traveler. In reality, that would not be true either. At some point, the time traveler must have arrived at the gate for the first time. He goes through to the past and hangs out. Depending on when he returns, to the future, if he would, he could run into a copy of himself. For example, if he returns at the same instant that he left, he would pass himself. Then if he turned back around he could hang out in the past with himself, at least using the logic that Sean uses, he could. Guess what? That would be yet another erroneous assumption. The reason is that it is easy to think of going back and forth from past to future through this gate but what that neglects is the attention to the fact about those clocks I mentioned and the fact that the gate is always open and not selecting specific dates. It's an engineering thing and here's how it works -
1. It's Tuesday. Time traveler goes through gate to Monday for the first time and stays for 24 hours.
2. The opening to the gate stays open during that time. 24 hours passes on the other side as well.
3. On that other side of the gate it is now Wednesday and he is not on that other side.
4. Sean would say that if the time traveler walked around and went through the gate on the past side, he would merge with his past self, who had been through the gate the first time. However, this is where his copy shows up to go through the gate for its first time. There is no merging, and we also see that now the time traveler has a copy because I didn't forget to add that first event of time travel for him.
Another mistake in this scenario is the whole issue that the time traveler has created some kind of CTC. Remember what Sean said about determining the nature of time by making assumptions? This is where specifically, such an approach goes awry. In fact, as you will see later, this whole affair has gone terribly awry (yes, it gets worse). Sean assumed that the time traveler would leave the gate area and then we would see him on the next day to make his entrance through the front. Instead he hung around the gate until the next day and then went through at the exact time that we saw him emerge through the other side, the day before. Because of this, Sean says there is a CTC. What's the difference between his hanging around and going, say a mile down the street and waiting to the next day, and then coming back? Nothing. OK, the difference is a mile trip in either direction, but we still have the same individual doing the same act. The reason why it is the same individual is because we don't see another version of him showing up to go through to the past. The idea of him hanging around the gate to go through again isn't the point. The point is that we never see another version of him showing up to go through first. As a result, the description only appears to suggest a CTC but it is only the world-line of the time traveler that suggests this, and not the space-time geometry of the gate itself. Just as the paradoxical etchings of M.C. Escher  prove, an idea on paper doesn't make it real.
I understand fully that there are going to be those who will protest and insist that CTCs cause causality to break down, but I would argue back that the point is what caused the CTC in the first place? Causality can't be broken before there is an alleged cause.
As I've already pointed out that a CTC must have an entry way or it's of no consequence, and probably couldn't exist anyway, allow me to reiterate that the gate is the thing that is manipulating space-time, not the time traveler. In other words, you, as the guardian, could simply run the time traveler off and prevent him from using the gate. No more CTC effect. At all. Sean was attempting to use this feature of the story to create a case for some unnamed force that would prevent such actions that would lead to inconsistencies. He claimed that there was a vexing problem to figuring out what it was that forces us to make consistent choices in time travel scenarios. The reason that it is such a vexing problem is that there is no such thing. The solution is the many-worlds model. Logic dictates it. The math reveals it and the geometries describe it. It is impossible to construct, design, conceive or imagine a time travel scenario where parallel universes do not emerge as a solution.
CTCs themselves are the obvious elements of such a solution. Where is everyone else when someone amongst us decides to go into a CTC? The same place we were before. Where are they? Are they in the same space-time continuum as we are? No? Well, what would you call it then? That's right. And as for what a CTC actually is, it is a curved region of space-time that returns to a point in its past, but in a parallel universe. How can I say this with such certainty? By introducing a video camera.
Upon approaching the CTC, if a person begins to video their experience, when they arrive in the so-called point of origin, back in time, they may very well run into themselves but that encounter will not be recorded in the video when they first entered the curve if they play it back. It will be for their copy's video but not the original person. I'm imagining a region where it takes some time to complete the journey back, even if it's only minutes. Once they hit that point that they had entered before, they will see themselves but of course that moment will not be recorded when the video is played back, showing their initial entry, because when they first entered they didn't see themselves. Meanwhile, because of free-will, i.e. randomness, this time traveling person can do something else once they arrive back at that entry to the CTC because it is connected to a point in space-time which is also connected to another space-time. In other words, if there's a way in, there is also a way out and that way out will lead to an actual parallel universe. Imagine a roundabout on a street and you will see what I mean if you then imagine it rotating (to imitate the curvature in space-time) so that you end up at the same point that you entered but now, instead of in the future (at the normal rate of elapsed time) you are in the past and seeing yourself entering the roundabout. Again, you didn't see yourself doing that when you first entered and so…well, you know the answer by now.
Now, what if it's like walking up to a mirror - a configuration where the travelers would see themselves approaching the point of entry as if they were about to leave, just as they were actually entering? That one, because the connection or gate or what have you, could be blocked or the travelers prevented from going all the way in, which would leave a different kind of paradox (where did the copies of the travelers come from then?) and would be the result of travelers from a parallel universe initiating the action first, instead of the other way around.
Now, I will reveal the biggest error, one that completely destroys everything about Sean's example. It even invalidates the things that I've said about how the Sean's gate would work. Why? Because on closer inspection I realized that under no circumstances could a gate configuration, as he describes, work. I left the previous deconstructions and analysis in because I am also trying to show the kind of thought processes and scrutiny that temporal mechanics demand if you want serious, accurate solutions. It just turns out that in double checking my work I saw the fatal flaw that killed the entire idea, and it goes right back to the way that I described Riemann slits working in Figure 1&2.
Sean describes a single gate performing double duty - linking a day in the future on one side and a day in the past on the other. A single gate would not be able to perform this function. A single gate would appear as it does in Figures 1 & 2. When creating a Riemann slit in space-time there is a front and back to it. In other words, you can walk around it, 360 degrees, at its destination point, as well as its point of origin. That means that an opening to the past must be an opening to the past on both sides of the gate in in the space of its origin only. Sean's gate functions like a spiral through time. If you keep walking through the right side, you keep going back a day in time. If you walk through the left, you go to the future by a day each time. In reality, regardless of which way you walk, you can only go in one temporal direction and once you go there you can only return from whence you came. There is no going further in either direction.
In order to have the type of geometry indicated by Sean, you must have two gates - the second which would connect to the future, and to accomplish the type of operation Sean describes. These two gates must be separated by some distance, so that their separate operations don't interfere, but could still function as a single gate and, in fact, fit perfectly into Sean's basic design. Or so I thought... I've already given you a clue as to the ultimate dead end to this idea.
Placing the two gates close together results in the following configuration in regards to space-time linkages:
1. The past gate has a face that allows you to enter from the front. The face on the opposite side is not seen and faces the hidden face of the other gate.
2. The future gate has a face that allows you to enter from the back of this arrangement. As already stated, its opposing side is hidden and faces the hidden side of the past gate.
3. Entry into either gate places you in exactly the type of configuration as Sean describes as when you are in the past or future and walk around to the opposite side of where you entered - you will be able to look through and see beyond the hidden side of the gate through which you came and see the space between it and the second gate. For easier understanding, take two exact coins and place their opposing sides together, with some space between them. Heads is the front/past side, and tales is the back/future side.
Like I said, or so I thought. What won't work is the repetitious going back and forth, from past to future. Let me explain. Sean's configuration allows you to go to the past and then return the next day. Or even keep going to the past. The reality is that it won't work, not even with the version I created, because each gate only allows you to go the past by one day or the future by one day but not both. The problem is that Sean just arbitrarily came up with this idea without working out the details of the space-time geometry he was actually describing. Remember how I said that a Riemann slit connects to the other destination so that you can walk around it and look back through? So if our time traveler walks out the past gate, he can return through that gate just as described - back to the future because that's what's in the interior of that gate. In other words, as far as the story goes, you only need one gate - but it won't work both ways like Sean has it - it will just work the way a Riemann slit would. For a trip to the future, you would use the future gate and the return would obviously allow you to go back to the past but there would be no going further either. The time traveler scenario would then work like this:
1. We see the time traveler exit the past gate opening.
2. He waits around 24 hours and then goes back through the past opening and arrives a day in the future.
Huh? Right. Remember the clocks? 24 hours has gone by both outside and inside the gate. By going through again he only returns to the future he came from which is now 24 hours ahead. He can't go back to the past again by going back through the gate - he's already in the past it connects to. The same would hold true if he were to try a trip to the future through the future gate. Each gate opens to mutually exclusive space-times. So that means there is not even the chance to describe a CTC in any form using Sean's idea. At least not as anything more than a rhetorical exercise. But physics, especially trying to explain advanced concepts, should be more than merely rhetorical. It should be accurate, especially when being used to describe "new rules".
Sean closes his article by saying, "The alternative answer to the puzzles raised by closed time-like curves is probably that they simply cannot exist".
I would suggest, instead, that the puzzles cease to exist once you truly understand CTCs.
 S. Carroll, How Time Travel Works, Discover Magazine, March 2010
 R. L. Mallett, Weak gravitational field of the electromagnetic radiation in a ring laser, Phys. Lett. A 269, 2000
 P.K. Townsend, Black Holes, Lecture Notes 1992 ArXiv http://arxiv.org/pdf/gr-qc/9707012v1
 M. Barnes, Avoiding Hidden Assumption Traps When Thinking Outside the Box, Mars Society Convention Proceedings August 2004
 M. Kaku, Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension, Anchor Books Doubleday 1994
 D. Gordan Smith, Eyewitness Account of Hitler's WWI Years Found, Spiegel Online International
 S.W. Hawking, The chronology protection conjecture. Phys. Rev. D46, 603-611. (1992)
 M. Barnes, Answering A Kid's Question that the Shuttle STS-127 Astronauts Couldn't:"Here's what happens Cameron, if you fly into a black hole July 23, 2009
 J. Gribbin, Why Time Travel Is Possible http://www.lifesci.sussex.ac.uk/home/John_Gribbin/welcome.html School of Life Sciences, University of Sussex
 A.J.S. Hamilton, Black Holes, http://casa.colorado.edu/~ajsh/phys5770_08/bh.pdf Center for Astrophysics and Space Astronomy, University of Colorado at Boulder
 Schattschneider, Doris. M.C. Escher: Visions of Symmetry, New York, N.Y. : Harry N. Abrams, 2004
Although so far I have not been accused of being biased against
Sean Carroll, I would point out that such is not the case. In fact,
I am personally amused to recall that May 23, 2008, I vigorously defended
the choice of Scientific American to run an article of his concerning
time running backwards in other universes (in relation to ours). You
can read it yourselves at
http://www.scientificamerican.com/article.cfm?id=the-cosmic-origins-of-t... beginning with Befell's comment at
02:29 AM on 05/23/08 (the next section of comments) , and then mine under the firm's name AET RaDAL, directly
below that. The point is that I care more about the subject of time and
time travel than I do about personalities. The subject deserves rigorous
analysis and vigorous debate. What prompted my defense of Sean
was the suggestion that his article in Scientific American was offensive
to "rational-minded people" and should not have been published.
That kind of attack, quite frankly, I will never let go unanswered.