Time in Jewish Law 2

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[Rabbi Michael Abraham] Why “from among the Kutim”? That’s what the Mishnah says; it’s a Mishnah. “One who buys wine from among the Kutim” — that’s a Mishnah. The Mishnah deals with this, so I’m saying: how did they drink the wine when they bought it from among the Kutim? Sealed with a seal — “recognize, please, your seal, your cord, and your staff.” So this going back in time in the halakhic context — true, it’s indifferent to physics. Even if physics forbids going back in time, in the halakhic or legal world, a condition exists in the legal world as well. I don’t know whether retroactive clarification exists in the legal world; I need to check that sometime. Why define this as going back in time and not define it as tithing with deferred tithing, the way there’s deferred tax? No, because it takes effect now. You can’t drink. You’re drinking the wine now — how are you drinking if there still isn’t any tithe? The tithe will take effect when the wine remains at the end. That’s exactly the definition. The rule says that when I buy an apartment I have to pay purchase tax, but I can reach an arrangement with the tax authorities that I’ll pay in a few months. You defer it, but it doesn’t take effect now; nothing retroactive is happening here. But with terumah it has to be there, it has to happen retroactively. Why? Because if the terumah is defined now as terumah, then you’ve exempted the rest. If it’s defined in Jewish law that I can also separate at the end on such a barrel, then that’s the definition. No, that’s not a definition. But you don’t separate at the end retroactively. Beyond the obligation to give it to the priest, the obligation to give it to the priest can be delayed. But the status of terumah — what does it take hold on? Separating terumah does two things: first, it permits the pile, exempts the pile — meaning once you separate terumah, only then are you allowed to eat. After that you also have to take what is terumah and give it to the priest. Okay? So that can be delayed. But maybe that’s exactly the novelty here in the Mishnah? What? There’s no terumah right now — just that you can separate it later? So I’m saying: there is something here right now that is terumah. What? There is something in the barrel right now that is terumah. If there isn’t, then everything is untithed produce. In law, paying the tax doesn’t permit entry into the apartment; you owe tax. They tell you: fine, right now you owe me a hundred shekels; defer it, pay it in another month — but you already owe me the hundred shekels now. I’m asking whether I don’t owe the tax at all right now. How can I buy an apartment? The law says that if I buy an apartment, I owe tax. So the parallel in Jewish law is the obligation, not the payment. If we rule that on the Torah level there is no retroactive clarification, does that mean we’re saying the law can’t take effect that way? Yes, but when we rule that on the Torah level there is no retroactive clarification, we’re not ruling that the concept of retroactive clarification is undefined. Otherwise, the one who says there is no retroactive clarification would have to argue against the one who says there is retroactive clarification: what are you even talking about? I’m not saying there is no retroactive clarification; I’m just saying blah blah blah blah blah. You’re not saying anything. What is retroactive clarification? The concept of retroactive clarification is contradictory. Even the view that says there is no retroactive clarification defines the concept; it just claims there is no retroactive clarification. He says: there isn’t such a thing; in Jewish law you can’t do this. That’s a halakhic determination, not a logical one. At least that’s what it sounds like. The one who says there is retroactive clarification says there is such a thing. They’re arguing about logic. As I said, everyone is subject to logic, and if it’s logically defined then it’s defined. Now the question is whether such a thing can be done — that’s already a halakhic question. But without its being logically defined, you couldn’t argue halakhically, because what are you arguing about? You’re arguing about something that doesn’t even exist, that isn’t defined. The Ran says: why is there no retroactive clarification? Because it is not fitting for something to take effect on the basis of doubt. Okay. This definition of the Ran — maybe we’ll discuss it later when we get to retroactive clarification — is a definition that may actually disconnect it from going back in time. There is a whole dispute among medieval authorities (Rishonim) who understand the concept of no retroactive clarification as having nothing to do with going back in time. It’s something entirely different. Rashi, other medieval authorities — we’ll see. But at the moment I’m still far from Jewish law; we’ll get to Jewish law later. That’ll still take us some time. Right now I’m in a general introduction to the concept of time before we enter these halakhic topics. And what I basically want to say is that in order to discuss the halakhic questions, first of all we have to assume the concept is defined — the concept of going back in time. And then ask whether it’s possible. Right now I’m speaking halakhically, not physically. Is it possible or not possible? If it isn’t defined, then the problem is not that physically you can’t go back in time; the problem is that it isn’t defined, so what are you talking about? Even if I’m free of physical constraints, I’m not free of logical constraints. No one is free of logical constraints. “The dead are free.” Therefore we have to check whether the concept itself is well-defined. Good. So I really want to begin this issue of defining going back in time by looking at the concept of time in general. There’s a book, by the way — a little book I recommend that you read, in the Open University broadcast series, by Avshalom Elitzur, called Time and Consciousness. And he’s an interesting fellow; we knew each other at the Weizmann Institute. He has several things in that series. Oh, he has more? That’s the one I know. He gave it to me. I know him from the Weizmann Institute; we sat there for some years. An interesting guy. He’s also connected to this issue in another way. He never did matriculation exams, never went to school — from Bat Yam or something like that. He did none of that, no bachelor’s degree, no master’s degree, and was accepted directly to do a doctorate in physics. They recognized him for a doctorate. He’s self-taught. There was a huge controversy about it; also at Bar-Ilan, on his website, he’s full of bitterness about it. Doesn’t matter. In any case, he wrote a book about the nature of time, and he begins by saying that there are actually several kinds of timelines. He speaks about seven — seven different timelines. A physical timeline, a thermodynamic timeline, a psychological timeline — all kinds. A collection of different timelines, each with its own characteristics. Sometimes that’s only a mode of expression, by the way. That’s why I’m not sure I accept his approach, because he turns it into — like logic, what I said earlier about quantum logic — it’s a mode of expression; they call it quantum logic. It isn’t logic. It’s the structure of that theory. But logic — there’s only one logic. So here too, I think the timeline is one, or maybe composed of several components. And in different contexts it can appear in different forms. I’ll give you just one example: they talk about, say, the psychological timeline. The psychological timeline can flow at different rates. Meaning, if you’re depressed, time can flow slowly or quickly. “And they seemed to him but a few days because of his love for her.” Right. So “because of his love for her” — yes, these are the famous questions about this issue; I won’t get into them — but in his love for Rachel, in Jacob’s eyes the seven years passed like a few days. So the psychological timeline sped up. That is, it ran faster than the real, physical timeline. But of course that’s not true. It’s not that the timeline ran faster; rather, I passed more quickly along the timeline, and my sensations — the way I perceived time — sped up. But it’s not that anything actually happened to time. So to call that a psychological timeline, as though it were another timeline — I don’t think so. I think that’s more a manner of speaking. Once there was some program — they invited me to a radio program about time, on Friday evening, one of those relaxed Friday-evening programs. So it was about time, and they did an hour with me there. And I was speaking exactly about this issue. They’d done a little homework and were talking about several timelines. I told them I don’t think it has to do with the question of how many timelines there are; it’s a question of how you perceive time. Is that not on Matzat, I think? Right? I don’t know where it is or what it was called. Do you remember which station? Yeah, I don’t remember anymore. Don’t remember. I think Sarah Beck did it; she was the interviewer. But anyway. So there are, however, at least two timelines worth noticing. The ordinary timeline, when you look at it from a physical perspective, seems reversible — in the sense that every physical process, say if you film something physical happening, then you can film it and afterward project the film backward. Fine? Now the question is whether someone watching the film can know whether this is a backward projection or a forward one. For any basic physical process, you won’t be able to tell. Say I do something like billiard balls, okay? I send one billiard ball or hit others — collisions and all those things. If you go to a system, then yes, entropy. Entropy has to keep increasing. No, apart from entropy, even in a system it’s like that unless the temperature is not zero. But I’m saying in a basic process, say a single particle or two particles or whatever, some basic thing — the microscopic laws of physics are all time-reversible. Therefore whatever happens forward can also happen backward. Meaning physics permits it to happen backward. Physics does not mark a direction on the timeline. That’s the point, and that follows from this — think about it: suppose time in all the laws of physics always appeared squared. Everything dependent on time would depend on t squared, not on t. Then you understand that it makes no difference whether it’s t or minus t. If you substitute minus t for t there — meaning time flowing backward — it doesn’t matter, because squaring won’t change it. Or a second-order differential equation, which is the same thing. Then too the direction of time doesn’t change the equation, and therefore it’s basically lawful. The basic equations in physics are second-order, and therefore they are time-reversible. But there is a puzzle, which I think to this day hasn’t really been solved, even though people talk about it in various ways. It seems to me, if I understand correctly — maybe I’m not up to date enough — but I think to this day it hasn’t really been solved, and that is that in thermodynamics, what Shmuel mentioned earlier, time flows only forward. Meaning, there a direction exists for processes. For example, suppose we place — say a flowerpot falls from the roof and smashes below. Fine? Now I’ll show the movie backward. Will any of you have any doubt that you’re seeing a backward movie? Meaning, the shards rise upward like in cartoons, right? Rise upward, arrange themselves, and become a whole flowerpot on the roof. Everyone understands that this is not a physical process. Hot water and cold water — you take two things and separate them. Right, you can mix them; you can’t unmix them. Even before the shards, it rises upward; that’s against gravity. Against gravity is also something against time. No, because if you give it an initial velocity, then it can go upward. If you give it an initial velocity it can rise upward; you throw something. At the end, when it reaches the bottom in the forward movie, it will reach the bottom at high speed. So in the backward movie it starts with high speed and loses speed as it goes up. That’s a physically permitted process. Say it’s an elastic collision. Fine? Yes. But it’s still obvious — or I don’t know what I’m seeing. Take a container of gas; that’s always the example they give in this context. Take a gas container where all the gas is concentrated in one corner, one of the eight corners of, say, a box-shaped container. Fine? And all the gas is concentrated in the upper-left-front corner. Okay. Now leave it alone, and the gas will spread through the whole container. But it won’t happen that you start with gas spread throughout the container and suddenly see it all concentrated in some corner. Fine? That means these processes suddenly have a direction. The question is: how can that be? Every particle — gas is a collection of particles, right? That’s all it is. There’s nothing there beyond a collection of particles. So how can it be that for each particle its physics is reversible — meaning everything that happens to it can happen forward and backward — but for the gas of particles there is a direction to its physical behavior? Meaning what happens in one direction cannot happen in the other direction. Okay, that’s basically the question. So they speak there perhaps of the thermodynamic timeline and the physical timeline, and in that sense even within physics there are several timelines — at least two: the physical timeline and the thermodynamic timeline, and the timeline of microscopic physics. Now let’s look for a moment at the microscopic timeline, yes — the reversible one. When we talk about these two timelines — actually both of them — we’re basically asking: what is the direction of the flow of time? She asked me that too. So I told her that the direction of the flow of time also is not necessarily a characteristic of time but a characteristic of our sensation relative to time. Meaning, we flow along time. That doesn’t mean the timeline itself flows in some way. We say, we use the expression “time flows.” Fine, what does “time flows” mean? It means that when I’m alive, or sitting, studying, or something like that, I experience the passage of time. But it could be that I pass along the timeline, and not that the timeline is traveling in any sense. Also when I walk through space, I change my location across space; space does not flow. There was some statement by Einstein like that, that time is what prevents everything from happening all at once. So the claim is that space is static. Okay, there’s something that separates time from space. In Richard Taylor’s book Metaphysics — I think I’ve mentioned it here and there in the past — another nice book, an introduction to basic issues in metaphysics. An American philosopher who wrote it in a very accessible, clear, and beautiful way. In one of the chapters there he talks about the equivalence of time and place and space, and he says that this feeling that the timeline has a different character from space is an illusion. It has no different character. It’s exactly the same thing. It doesn’t flow in any sense. Meaning, there are no things you can say about time that you can’t say about space, and vice versa. So he takes an example. He says: let’s see — why is there this illusion regarding time and not regarding space? Right, and that’s already a property of us, of our psychology, not of time itself. As I said before, after all time exists, so first I ask what the nature of time is, not how I perceive it. If I perceive it differently from space, maybe — but that’s already in me, not in physics. Fine. To change place you need to invest energy, but you can’t change time. Okay, nice example. What? The example the Rabbi gave is that I can be in the same place at two different times; I can’t be at the same time in two different places. Yes, so we’ll get to that in a moment. So indeed Richard Taylor tries to show there logically that everything you can say about space, you can say about time and vice versa. Why? Because there is a very basic paradox in saying that time flows. Think for a moment: when I say, for example, that place changes, that I change place — what does that mean? It means that at some time, t equals one, I’m in one place, and at t equals two — yes, a second has passed — I’m in another place. That is called changing place. Meaning my place changed along the timeline. Time changed, so I’m also in a different place. That means I changed place. Or alternatively, that I grew, okay? A child who grows. What does it mean that he grows? It means that at a certain time he was of one height, and at a later time he is of another height. Every process of change is a process that occurs along the timeline. Anything you say changed, that flows — basically it flows along what? What does time itself flow along? How can you say that time itself flows? Flows over what? Everything that flows, flows along the timeline. But when you say the timeline itself flows, that means — say you’re saying quantity x flows. What does that mean? That there is a function x of t; x is a function of t. At some t there is one x; at another t there is another x. We also touched on this a bit in the previous class — commandments explicitly dependent on time and commandments indirectly dependent on time. So now I’m speaking about a certain quantity’s dependence on time. I say: the quantity changes as a function of time. Time changes, so x also receives different values. But when you say that t itself flows, then it flows over what? You can’t define it at all in those terms. t as a function of t never flows. Given t, I’ll tell you what t is — and then there is no… what does it even mean to flow? Fine? It lacks meaning. Therefore he says that when we speak of time flowing, it’s probably over space, just as when space flows it’s over time. But if so, then there is no difference at all between the language of place in space and the language of place in time. Let’s take an example, a sample sentence. I want to describe that I traveled from Haifa to Tel Aviv. Fine? I changed place over time. So I say: at t equals eight in the morning — say in hours — at t equals eight in the morning I was in Tel Aviv. At t equals nine I was in Haifa. Fine? So there, I described motion from Tel Aviv to Haifa across the timeline — which apparently you can’t do with time itself but only with space. He says: but when people who know a little mathematics seek symmetry between time and space, then you have to exchange all the concepts of time with space, and all the concepts of space with time. You have to make a full exchange. So let’s make a full exchange and see that we get a completely lawful sentence. Fine? In Haifa, at x equals Tel Aviv, I was at t equals eight, and at x equals Haifa I am at t equals nine. If you like, let’s formulate it the other way around: at x equals nine I was in Haifa, and at x equals eight I was in Tel Aviv. I even went backward in time, if you like. Right? Meaning from x equals nine, from t equals nine to t equals eight. So basically, whatever you can say when the place-axis is such-and-such and the time-axis is such-and-such, if you switch their roles — the place concepts and the time concepts — you’ll still get a lawful statement. There’s no problem. You see the reversibility, like the reversibility of physics. Film the movie differently, switch the place of time and space, and you get a perfectly lawful statement. There’s no problem with it. Therefore basically his claim is that even what Yossi said earlier — yes, he also deals with the argument that apparently you can’t be in two different places at the same time, but you can be in the same place at two different times. So he says that’s not true. Being in the same place at two different times is simply being an entity extended in time. So if there’s an entity extended in space, then it can be in several different places at the same time. It’s simply long enough, so it can be in several different places at the same time. Well, about that one can argue a little, I think, because you can’t be, say, in two different places without being in between. Fine? But you can be in two different times. Yes, well, here one can begin to argue a little, because an object extended through space — I don’t know to what extent. Even in two different times you can’t without being in between, because you had to move from place to place. Why? I can disappear and then come back. That’s only a physical limitation; it’s not a logical limitation. Disappear? Yes. Not in the same space. That I can’t do because the laws of physics forbid it, but there’s no logical limitation here. Logically I can define a process like that, where you disappear from one place and arrive in another place, in the same place at another time. Fine. So you were — but through all that time you were. No, I disappeared in the middle. We talked in the previous class about how you can teleport in the middle, right? The sukkah disappears from space after a certain time. So he says the same thing on the principled level. True, in physics this usually doesn’t happen, but the laws of physics aren’t logic. On the logical level there can be a body that disappears and returns by a continuous route of platform nine and three quarters, and it returns. My son has now gone to Hogwarts under Harry Potter’s influence. If it disappears and returns, is it the same body? Defining it as the same body isn’t simple. Fine, okay, fair enough. In any case, his claim is that everything you can say about time you can say about space; just switch the roles coherently and you’ll see that every sentence you formulate about time and space, if you switch the roles, you can still say it. That means it is basically completely equivalent. Now, what he assumes there, by the way — around relativity too there was the same discussion. Say, the formulation of relativity, the conventional formulation of relativity, really does see space and time as parameters that function in the same way, that play the same role. Right, this is Einstein, whose claim basically is that this is a coordinate system that does not have three axes but four axes. It isn’t x, y, and z, the three axes of space, but x, y, z, and t. But fine, you can always do that; people don’t understand. Okay, so I can define it as a system — what does that mean? It means that you can rotate within this four-axis system. Meaning, they can exchange roles. When you rotate, then what counts for you as time will count for him as space, and vice versa. Meaning, they really function as a single coordinate system. It’s not just that I describe it as a function of four variables — that’s no great insight; for that you don’t need relativity. In any case, but there too let me just draw your attention — whoever knows a bit, Shmuel certainly knows, and you too, mathematics? physics? — the metric of relativity, time doesn’t appear there the same way as space. There is an i there, right? There is that imaginary unit, and therefore there is a difference even though it’s one coordinate system. There is still a difference between time and space. Meaning, it’s not correct to look at it completely that way. After you’ve defined the metric you can already do what you want, but within the metric there is indeed a distinction between time and space. In any case, the claim is that this whole change — the debate between Einstein and Bergson, the whole business of whether time really flows — Bergson argued in Creative Evolution, the French philosopher, half-Jewish, I don’t know — I think the wrong half, I’m not sure. His claim was that time flows; time is duration; it is different from space. And Einstein kept saying: nonsense, it isn’t. They didn’t really debate each other, but it was perceived as a debate between Einstein and Bergson, where Einstein says it is exactly the same thing; there is no difference between time and space. And Taylor shows Einstein’s conception very beautifully from a philosophical standpoint. But because Bergson didn’t have Einstein’s physical and mathematical abilities, he lost that debate even though he was right. Meaning, he was right and lost; that’s always the problem. Very often scientists have an advantage over other people because they have very strong tools, and other people can’t contend with them using those tools. So even though someone feels he is right and knows he is right, he can’t — he doesn’t have the tools to explain or show where the scientist arguing with him is mistaken, and so he loses the argument even though he was right. I think that happens a lot, because scientists always think they’re right because they have good tools to show that they’re right. But you have to be careful, because often the problem is in the tools — not in what you do with the tools, but in the question of what the tools themselves say. Now what does this actually mean? The problem, the point where the debate seems to have gotten stuck — that is, where Bergson got stuck and missed the whole issue — is the problem I mentioned before. Because the concept that time flows is a concept that is apparently paradoxical. Flows over what? Do you understand that in this view, where I see time and space as the same thing, time doesn’t really flow? Time flows over space just as space flows over time? That has no meaning. Nothing here flows — neither space flows nor time flows. This is some kind of system that, even if I say it exists — I spoke about that last time — but it is completely static. I can change place, I can change time; we, bodies in the world, can change place and time. But place and time do not change and do not flow and nothing of the sort; it’s only a manner of speaking. So the point, basically, is how to define at all the concept of time flowing. And again, their mistake in that debate was that they immediately started arguing about whether time flows or not, and did not define the concept — what does the flow of time mean? Not whether time flows or not, but first define the concept, show that you understand what you’re talking about. After that, claim that time doesn’t flow or does flow. But first explain what it means that time flows. And I think because he didn’t explain it but only described sensations, he was doomed to lose that debate. Now here there really is a very difficult problem. Think about going back in time. When I speak about going back in time, I’m basically saying that suppose now I’m on Thursday and I want to go back to last Tuesday, right? That’s called going back in time. What’s the problem in doing that? There’s no problem at all; two days ago I was there. Two days ago I was on Tuesday, now I’m on Thursday — what, can’t you go back in time? What’s the problem? Why isn’t that going back in time? Or I want, on Thursday, to be on Tuesday. I didn’t understand that sentence. If you’re on Thursday, then you’re on Thursday, not on Tuesday. How do you want on Thursday to be on Tuesday? Or I want to be a round square. Or to be in Haifa when I’m in Tel Aviv. Yes, exactly. It’s just words. Words that mean nothing. I want my causal sequence from Thursday — not causal, chronological. Causal is already too strong; we’ll talk about that later. There is a very important point missing here. I want to be on Tuesday after Thursday. Meaning that Tuesday should come after it, not before it. If it comes before it, that’s not called going back in time. Going back in time means that after I experienced Thursday, or after I was on Thursday, I will be on Tuesday. But even here there is a problem. Because even here, on the logical level, what difference does it make? It’s saying the same thing. Tuesday by definition is two days before Thursday. What does it mean that I want to be on Tuesday after Thursday? Tuesday by definition is two days before Thursday. When I’m on Tuesday, I’ll be there two days before Thursday. So what does it mean to be on Tuesday after I was on Thursday? It’s not after. If I’m on Tuesday then I’m before. You understand that this expresses everything I said earlier — that for time there is no “over what” to flow. Flows are along the timeline. When I ask how the timeline itself flows, I can’t ask that question; it’s just nonsense. The timeline flows means that I change time along the timeline. I don’t change time along the timeline. At t equals one I’m at t equals one. And at t equals two, by definition I’m at t equals two. There’s no… And if you like, as I said before, if you want to speak about the flow of time over space — which is of course well-defined, no problem — that’s what we call velocity. Right? Velocity is change of place over time. You can look at velocity itself the other way around: change of time over place. It makes no difference; it’s only a way of looking at things. Okay? It’s exactly the same. A body has velocity, so it changes place according to time, or you can say it changes time according to place. It’s only a question of which way you look at it. But then it isn’t really called that the timeline moves. Therefore I say: when I speak of the timeline flowing, there is some problem of definition here. What does it mean to go back in time? Is it even defined? Before the question whether it’s possible — what is the definition at all? Once I sent — I wrote some post once. I wrote a post because there was some article about some guy from Herzliya — what’s it called? the Interdisciplinary Center. The Interdisciplinary Center in Herzliya. He published an article, and the popular headline was: “He solved the problem of going back in time using a computer,” in software. I was stunned. There’s a conceptual problem here. What does software have to do with it? The question is what he assumed when he wrote the software. An inflated headline. What? First time the Rabbi has seen an inflated headline? No, an infantile headline, not an inflated one. Meaning, it says nothing. Yes. So I looked to see whether the fellow himself was an idiot or whether the reporter was an idiot. And I looked, and indeed the fellow himself expressed himself more moderately. But once you understand what he did, you don’t really understand what value there is in it. Fine, okay. He certainly didn’t solve any problem; that’s obvious. There’s the twin paradox, where one travels close to the speed of light and then he supposedly ages at a different rate. So can one see in that a kind of… Yes, right. As if his rate of time is different. So what is a rate of time? It depends on acceleration. The question is whether it’s time or whether his biology works differently. It’s a law in physics that if you travel fast your biology works differently. So what happened? Fine, that’s a law in physics; it’s not… You can’t go backward, say; outside the light cone you can’t get out. Yes. Not even just backward. You can’t exceed the speed of light. Meaning, from the standpoint of physics it’s not only that you can’t go backward in time, you also can’t even go forward in time too quickly — outside the light cone. You also can’t. You can’t do anything beyond the speed of light. Unless it changes. What? Now they want — there’s a new article saying that the speed of light changed at the beginning of the universe. It either accelerated or decelerated. One of the two. Doesn’t matter, but still, the speed of light today is the maximum according to which one can… today. The fact that this quantity is a function of time is fine, but it’s still a physical limitation on the velocities possible there. Yes, but then if you catch it exactly when it changes, and then you want to leave the light cone, maybe it’s possible? I haven’t thought it through to the end. It’s a dynamic light cone. Meaning, it’s a light cone that expands over time. Fine, but still you won’t be able to leave it, I assume, in a dynamic way. Anyway. I once saw that it’s like a supersonic cone. You exceed the speed of sound, which changes depending on the temperature of the atmosphere. But still that cone exists. Everything — sounds can’t pass the supersonic cone. Yes, but there it’s not exactly a cone, it’s not parallel. The plane can pass, but there yes — but there it’s not exactly… it’s not parallel. The speed of sound and the speed of light are two different things. The speed of sound depends on a medium; the speed of light is something a bit different, because the speed of sound really is something that propagates in a medium. Without a medium there is no sound. And the medium is what generates the sound. Therefore there it’s not a cone. It’s not a limitation of sound that it can’t exceed the speed; that is its speed. When I say that light can’t exceed the speed of light, that’s not a limitation of the light cone; that is the speed of light, it’s a law in physics. The cone means that nothing can exceed that speed. There is an a priori limitation on every physical process — not just on light — that you cannot move faster than the speed of light. There’s no parallel to that in sound. Right, so the claim that time flows, basically, it seems to me — or going back in time — I was at the question of how to define at all this concept of going back in time. It seems to me this requires assuming that there are two timelines. In saying that I am not solving the problem; I haven’t solved any problem in physics. I’m simply proposing a model within which the concept of going back in time would be defined. Within that framework one can at least define it consistently, and now we can talk about whether it’s true or not true, whether physics allows it or doesn’t allow it. As long as you don’t propose some model that enables us to understand the concepts within it, there’s no point discussing whether these concepts are possible or not. Therefore I’m not claiming that there really are two timelines; I’m offering an interpretation of the concept of going back in time. For the concept of going back in time to have meaning, I need to assume there are two timelines — that one timeline moves along the second timeline. Okay? Therefore only within that framework can I talk about the timeline, about going back in time. And then what I’m saying is this: what is going back in time? There is a certain time — let’s say time flows; I’ll use the conventional terminology. There is one timeline that constantly flows forward. You can’t do anything about it. There is another timeline over which it flows; or maybe it doesn’t flow forward at all but is fixed, fine? And there is a timeline that flows over it. Fine? Now the question is whether the timeline that flows over it can change direction and flow backward. Then what this basically means is that I can speak of going back in time in the sense of being on Tuesday after I was on Thursday. “After” not in the axis of the days of the week, because in the days of the week by definition, when I’m on Tuesday I’m two days before Thursday. Rather, there is some timeline upon which the week is created, or revealed to us. First Sunday, then Monday, then Tuesday. Those days appear on some other timeline — they themselves are not the timeline. And now I ask: can I be on Tuesday after Thursday? Where “after” here is of course not after in the week, because Tuesday is before Thursday in the week, but after in the sense of the lower timeline. Like place: I can flow forward in place, increase position with time, or decrease position with time. Fine? In this sense it behaves, functions, exactly like place if there are two timelines. Then one can talk about going back in time. Now one can discuss: does physics really have two timelines or not? Even if there are two timelines, does physics permit going back in time or not permit it? All those are questions in physics. But I can ask those questions only after I have given meaning to the concepts. Why is this important? Because from a legal standpoint there is no limitation. I’m coming back to retroactive clarification and conditions. From a legal standpoint I can define that in my legal world it is possible to go back in time — as long as the concept is defined. Meaning, as long as there is a model within which I can speak consistently about this concept of going back in time. Otherwise, even in the legal world I couldn’t speak about such things. Therefore for me it is important to define this concept, first, so that physicists will have something to do, because after all they too need to publish articles. And second, so that in the halakhic world — I’m flipping the picture, do you see? People always look at the Talmudic analysts as these idlers dealing with nonsense. Look what physicists deal with. The question is: two timelines — what, like you say two timelines, so set up two place-axes. What, same thing, right? Same thing. It’s nonsense. What is two place-axes, that you are in…? Set up two place-axes. If you have some feeling that space moves, then fine, maybe it moves over another space if that helps you somehow. I don’t have the feeling that space moves. So what — I don’t understand what you gained. I gained this: I can now define the concept that time flows in a consistent way. There is, after all, a very strong feeling that time flows. The question is how to define something that flows — over what? That’s the question. Flows over what? That is exactly the question. What does “flows” mean? You have a feeling, but that feeling has no meaning; it’s just words. Maybe it’s simply because we only grow older and don’t become younger? So time flows. I’m saying again: I’m not claiming there are two timelines. I’m offering an interpretation of the concept of going back in time, or of the flow of the timeline, if we adopt a model in which there are two timelines. Then the concept has meaning. Now we can ask whether it’s possible or not in the context of physics, but in the legal context everything is fine, because there we are like the Holy One, blessed be He — above time. There we can do whatever we want, as long as it is well-defined. Because if it were not defined, then even on the legal level we couldn’t do it, because then we could derive from it a result and its opposite. A contradiction. There is a rule in logic that from a contradiction you can derive both x and not-x. Therefore a contradiction cannot sit inside a system, because otherwise from that same system I can derive two opposite conclusions. Okay? Therefore I need it to be well-defined within the system, not contradictory. So even in the legal world it is very important to define the concepts consistently. When you speak about a condition that operates backward in time — if you say: I am making this transaction on condition that tomorrow it will be springlike and won’t rain. Fine? But I concluded the transaction today. Fine? So I say: this is a condition in which the future determines what happens today. Okay? So I’m doing a going-back-in-time move on the legal plane. Going back in time on the legal plane is no problem. Even if Yakir Aharonov discovers that you can’t go back in time, lawyers don’t care — they can define it. If the law defines that this is a possible process, then it is possible. Retroactive legislation — they say it’s not appropriate to do it, but there’s no problem in the definition of retroactive legislation. But if what you’re saying is correct, then I don’t need the physical story. I can do it without the two timelines you just mentioned. Because I, as a jurist, can make the model. You need to define for me what that means. What? But you as a jurist need to define for me what that means. To define for me what it means, you need the model. But it means in legal terms, not physical ones. No — what does it mean? That’s why I’m asking what it means. In physical terms it means that if it rains tomorrow, then right now the transaction was concluded. So all you’re really telling me is that it was concluded. Right, exactly. So you’re not telling me… If so, then it lacks meaning. You’re only saying that only tomorrow will I know whether the transaction was concluded today — tomorrow, when it rains. Correct. But that is only… we’ll get to that in a moment; that isn’t going back in time. Going back in time means that what you’re really telling me is that information is revealed to me that was already true today; it was only revealed to me tomorrow. Today I don’t know it. From a legal standpoint it doesn’t bother me that I can’t manage to define going back in time. You don’t see that as a problem. No, it’s a very big problem. It doesn’t bother many jurists, but I had arguments about this when I wrote the book. There’s a chapter there about law. Because jurists don’t understand that there is a problem here — and there is a problem. Their concepts are not defined, or include contradictions. Therefore the whole issue of a suspensive condition and a resolutive condition, which everyone gets tangled up in — what exactly is the difference between a suspensive condition and a resolutive condition? Ask jurists; I don’t know what… Ask jurists — nobody will know how to define it for you. Why? Everyone thinks they understand, but when you ask them very… they won’t know whether it’s a resolutive condition or a suspensive one. Read Daniel Friedman’s book on contracts, I think — right? Does he have a book on contracts? He has one on insurance law. No, I think he has a book — perhaps his main book, I think — on contracts. Now he… there’s a book in which he does — I refer to it here, I think, you can look — where he shows how complicated it is. There really isn’t a sharp distinction between a resolutive condition and a suspensive condition. And therefore — why? Because none of the jurists did the work of conceptual definition. By the way, in Jewish law they did. Rabbi Shimon Shkop did, for example. But in the legal world they didn’t, and therefore they get tangled up in the definitions because they don’t have a model within which they… It’s not really going back in time; they’re not speaking about going back in time. I’ll get to it when I discuss it; then we’ll see. In any case: so what’s wrong with defining it the way you defined it earlier — that the information only arrives at a later stage and we only know it retroactively? Because that’s not the correct definition; it has implications. I’ll talk about the implications of this. There are different legal implications if I see it one way or the other. That’s the difference between retroactive and retrospective. Meaning, a retroactive process is something that truly goes back in time or affects the past. A retrospective process means that the future does not affect the past; rather, from a certain point in the future I see the past differently, but not that something in the past itself changed. And that has enormous practical significance. What? Meaning that in practice it really is only retrospective. No, here, I’ll give you a practical difference. In Jewish law there are practical differences because Jewish law dealt with this. In Jewish law, “one who buys wine from among the Kutim” — we mentioned earlier retroactive clarification, okay? You can’t see that as retrospective. Rabbi Amiel in Middot LeCheker HaHalakhah talks about this: that there is a distinction between retroactive and retrospective in this context, and he wants to claim that there is a difference in the laws of retroactive clarification between a retroactive case and a retrospective case. In my opinion he’s mistaken; there’s no difference. The Talmud itself, the Talmud itself connects them; it does not distinguish between retroactive and retrospective. I’ll give you an example. In the context of, say, the Talmud in Eruvin discusses the question: suppose I place… a sage will come to town on the Sabbath, and I want to go hear his lecture. I don’t know whether he’ll come from the east or the west. I need to place an eruv; I can’t go outside the city. So at twilight — because the eruv has to take effect at twilight — I place an eruv at twilight in the east and another eruv in the west, and I say this: if the sage arrives in the west, then the eruv on the west side will be the eruv that allows me to go westward; and if the sage arrives in the east, then the eruv on the east side will be the eruv. This assumes that you can’t make eruvin in both directions; you have to choose your two-thousand cubits. You can’t make an eruv in both directions, but one of the two, and I make it depend on the sage’s arrival. If the sage arrives here, this is the eruv; if the sage arrives there, that is the eruv. That is retrospective, not retroactive. Why? Because ultimately, when do I need to know which eruv is the correct one? When the sage arrives. No — when the sage arrives. When the sage arrives I need to know whether I’m allowed to go in that direction or not. By the time the sage arrives, the direction is already defined. So why does this belong at all to the topic of retroactive clarification? Why is it retrospective? So then it’s not even retrospective; it’s just forward. No, it’s retrospective because the eruv has to be acquired at twilight. An eruv that wasn’t acquired at twilight doesn’t take effect. But its practical consequences — that is, when do I make use of the fact that this is the eruv? Only after it has already been clarified. That’s retrospective. Why? Because after the sage has arrived there, it becomes clear to me retroactively that the eruv on that side was the correct eruv, and now I can use it. But I make use of it only after it has been clarified. Theoretically I need it to be clarified backward in order for it to take effect, because only at twilight does it take effect. But in terms of my use, I use it only after it has become clear. In “one who buys wine from among the Kutim,” it’s not like that. Because in “one who buys wine from among the Kutim,” I am making use of it now; I am drinking the wine. I’m drinking the wine now. That means there is terumah here now, not that in two days I will look at it as though today there was terumah. If it were retrospective, they would have to flog me now, or it would be death at the hands of Heaven. It depends — it depends on a dispute among medieval authorities as to whether what I violated here was untithed produce or terumah, but we’ll discuss that later. So the claim is that I can’t drink wine if this is retrospective. Rather what? It could be that if I went ahead and drank the wine, then after two days, once it becomes clear which two logs are the terumah, now when people look backward in time they say: no, he drank ordinary wine, non-sacred wine. It was permitted to drink it. But now, at the time when I’m drinking, that’s not true. And if a religious court comes and flogs me, it can flog me too, because I really did a prohibition, right? Only afterward, say two days have passed, and those two logs remain — now the religious court can no longer flog me, because now I look at the past differently. Fine? I look at it differently, not backward. I see it differently, but it didn’t really change backward. But if in that interval of time he is standing trial? Then he gets flogged. Then he gets flogged. No, I’m saying that’s in the retrospective view. And whoever claims and says: but tomorrow it’ll be fine. Correct. That’s what Rabbi Shimon Shkop says, for example, right? Although again, in “one who buys wine from among the Kutim” that’s not correct. Because in “one who buys wine from among the Kutim,” the Talmud itself says that if there is retroactive clarification, I’m allowed to drink. He uses it as a trick for separating terumah on the Sabbath and a Jewish holiday, when it is forbidden to do so. It’s fixing something, right. So I’ll do it in this way, and then it will solve the problem because it will take effect only on a weekday, but it will already permit me to drink today. So there it is truly retroactive; it’s not retrospective. If it were retrospective, it would only exempt from punishment in two more days. Now it wouldn’t even exempt from punishment; but in two more days people would view the matter differently. Fine? But if it’s retroactive, then it permits me to drink now, because there really was terumah here now. True, I’ll know that only tomorrow, but it already was so now. Okay? Another example of the difference between retroactive and retrospective: there is Rabbi Shem Tov Gafni. He was an interesting Jew. I think I mentioned him once before, right? The ancestor of all the Avivs and Yehonatan Gefen — not the father, the great-grandfather or something like that — and Moshe Dayan and Uzi Dayan and all that crowd. Finkelstein clarified for me through Uzi Dayan exactly what the family tree is. In any case, he wrote a book called The Dimensions of Prophecy and Geology. “Geology” there is in somewhat archaic language; we’re talking, I think, about the beginning of the twentieth century when he lived. There he wants to claim, following Kant, who says that space and time are only forms of perception — so there he wants to claim, following Kant, that since space and time are only forms of our perception, then it makes no sense to ask the question of how old the world is, or these dilemmas, right? Is it six thousand years as we count, or five thousand seven hundred, or is it fifteen billion years as they estimate today in the most scientific way? Why? Because if time really is only a form of human perception, then before there was a human being there was no time. Yes, but if there was more than a human and there was more than five thousand… Fine, but that’s already an easier question, because the question is who counts as a human. You know, humans also evolved. Homo sapiens is what they define today as human, and even there it’s unclear how much that can shift you on the scale by a few thousand years. Meaning, eight thousand years, ten thousand years — that already gets very close to the relevant scale. It depends what you define as a human. Maybe you define a technologically developed human, but why not…? No, not technologically. A human different in itself too, not only technologically developed. A human whose own capacities of perception and relation to the concepts of time and space are different. But there are skeletons a million years old or more where they can’t find the slightest difference at all… So the question is what you define as a difference. There’s also no difference between an ape and a human in DNA except some, I don’t know, some few tenths of a percent of the DNA. So the question is what you define as a difference. Do you understand? It’s all a matter of definition here. It’s like — I think I mentioned this once — once I was sitting in the Kollel Chazon Ish where I studied, and some avrekh came over to me and said — he knew I’m a physicist — so he said to me: tell me, is glass a liquid or a solid? So I said to him: if you want to heat it on the Sabbath, it’s a solid. Meaning, physicists define it as a liquid because its crystalline structure is disordered. When the crystalline structure is disordered, it is not defined as a solid. But that is a definition for the purposes of physics. What does that have to do with the halakhic context? Concepts are defined differently in the halakhic context than in the physical context. Therefore very often transferring concepts from one field to another is done very carelessly, because what we’re really copying are definitions, not findings. And that’s a very well-known disease in the legal world too, by the way: they bring a psychiatrist’s evaluation of a defendant’s condition, but it’s not clear that what the psychiatrist defines as “not responsible for his actions,” the jurist will define as “not responsible for his actions,” and vice versa. The jurist — the psychiatrist — does not always give expert testimony; sometimes he gives an expert definition. And one has to be very careful about that. I don’t remember whether I spoke about this here once; I think maybe in classes I once gave on issues of Jewish law, where I brought an example. One of my lecturers in electrical engineering — one of the lecturers from whom I studied electrical engineering, Frankenthal at Tel Aviv University — taught us electromagnetic fields. It was a wonderful course. He told us there that there was a federal law in the United States that any two states that transfer something through an intervening state have to pay that state. But that’s only if the thing passes through wires. If it passes through the air, then not — for example, radio waves or something like that, then not. Fine. So states A and C passed an electric line through state B and didn’t pay. State B sued them. So they brought a physicist to explain to the judge that there is something called Poynting’s theorem. Poynting’s theorem says that the power doesn’t actually flow inside the wire but in the electromagnetic field around the wire. Therefore it isn’t flowing in the wire at all; it’s flowing through the air, and everything is fine — no need to pay for that. It flows through the air, or one can describe it in a… “Electricity is in the air” — there’s a song like that, no? I’m saying it flows through the air and no, no, no — that’s a song. It’s just that you’re intelligent enough to ask that question. The judge — I don’t know whether he was… Ah, okay. In any case, a judge who sees expert testimony is only asked to say: okay, if the expert says so — he’s a physicist, he knows — and he exempted them from payment. Now he doesn’t understand that these are simply two equivalent modes of description. You can describe the power as though it passes through the wire, and Poynting’s theorem says that an equivalent description can be that the power passes through the electromagnetic field around the wire. The wire of course creates the electromagnetic field, so these are two ways of looking at it. Okay? It isn’t really that the power passes here or there; these are two physical ways of looking at it. In the plain, commonsense way a jurist should look at it, it passes through the wire. What do I care now about physicists’ equivalence theorems? But when you look at a definition as a claim, that is exactly the problem. The physicist brings you a definition. As a physicist you can define whatever you want, but the jurist is looking for a claim, not a definition. Definitions, leave to me — I’m responsible for definitions here, not the physicist. Okay? I once read a very… And did they really exempt them from payment? I don’t know, I don’t remember whether he told us or not, but he told this anecdote. I’ll give you another example I once encountered. Before my doctorate… a friend of mine showed me an article about a Vizhnitz Hasid from Haifa who developed an alternative theory of relativity to Einstein’s. Shefler — Chaim Shefler was his name — who, like everyone else, was at some point a teacher in Midrasha, as it later turned out to me. In any case, he says to me: listen, maybe it’s interesting, because professionals say the man is talking sense. There was some Giora something — I don’t remember — someone from the Technion who checked it out and really said that he says sensible things and it’s worth examining. Fine. So I went, traveled to him in Haifa, because I was just before my doctorate. I said maybe I’ll do a doctorate on this; it sounded interesting. And the man does integrals and everything. He’s not one of those who just babble and talk in the air. The man really does mathematics properly. He’s a very impressive autodidact. In any case, fine — I thought about it, debated whether to do it or not. There I discovered, to my astonishment, that every year several alternative theories of relativity to Einstein’s come out, also by physicists, that solve many problems left open in relativity. Nobody cares about any of it. I mean, go check all these theories of relativity — they probably get stuck on other problems too — so nobody checks them at all. In connection with time? Ah yes, exactly. Every outsider suffers from the same issue. Anyway, I spoke with that fellow from the Technion, and he referred me to the literature, and I thought maybe I’d work with him — that he would be my doctoral advisor. So he gave me some articles to read. Among them was an article by someone named Salomon, I think, an American, who argued — we look, say, at Coulomb’s law. Coulomb’s law is a law that says, for example, that if there is a point charge in some place, then it exerts a force on another point charge proportional inversely to the distance. Like with mass? Yes. Inversely proportional to the distance between them. Fine, say the force is one over the distance or something like that — over the square of the distance, yes. The energy — the potential — is one over the distance. What was the law again? The law says that the force between two point charges decreases with distance like the square of the distance — meaning, say, if the distance is one then it’s one over one; if the distance is two then one over four, and so on. Fine, that’s a law of one over the square of the distance. In gravitation too it’s the same thing. Now what happens is that when we calculate the energy of such a particle, that particle creates a field around it, fine? Like Poynting’s theorem. So it creates a field around it. Now what happens is that the energy of an electric field is calculated by multiplying charge by field. You have to take the charge at a point times the field at that point and sum over all space — integrate over all space. Never mind, this is only to demonstrate; you don’t need to understand the physics, only to follow the claim. Now what happens is that in field theory it’s known that there are always blowups — you reach infinities and remove them in all sorts of mathematically illegitimate ways. Physicists do all sorts of bending of mathematics, what’s sometimes called renormalization and things like that. Now this Salomon argued: why does this happen? It happens because we are summing the product of the charge and the field of that same particle. Meaning, that particle induces some field around itself, right? It exerts forces on all kinds of particles around it, so another particle will feel a field acting on it, a force will act on it, will give it energy and all kinds of things. But what about this particle itself? This particle itself together with the field that it itself creates. To say that this particle feels the force that it itself induces around itself is nonsense, because the force it induces around itself and the charge are simply two equivalent ways of relating to the particle. A particle in space — you can say there’s a point charge here, and you can say there’s a Coulomb field around it — that is saying the same thing. But those aren’t two things; they are two ways of looking at the same thing. Now do you understand what happens when we treat these two things as two separate things? We multiply the field that exists at that place by the charge that exists at that place — and what is the distance? Zero. So we divide by zero squared. If the charge is truly pointlike, yes, yes — in the integral we get infinity, in short. We get infinity, divide by zero. Even if it’s not pointlike? That doesn’t matter; we’re summing. Is there some internal division here? Yes, but we’re still summing in the integral. At every point in space we have only part of the particle’s charge. Never mind — I’m still talking about a point charge. So the particle is a collection of charges, but I’m talking about the point charge. If it’s a collection of charges, then between every point, every part and every part… Right, but not point with itself. But at that same point, no. That same point that composes it — the field it makes with its own charge — you can’t do that. Break it down into point charges; it doesn’t matter. In short, why am I saying this? It doesn’t matter. I’m only trying to illustrate the problems that can arise from treating one thing that has two equivalent modes of description as two things. Meaning, if they are two things, then there is also interaction between them. But it’s not interaction between them; it’s simply two ways of looking at the same object. An object cannot generate interaction with itself. Yes — I, you know, I am my own brother. We have the same parents. Right — both I and myself have the same parents, so I am my own brother. That’s roughly the same thing, you see? That is, I refer to myself and refer to someone else — the sentence is true, both I and myself have the same parents — but it is not correct to say that I am my own brother. I and myself are the same thing, therefore we have the same parents. That is not a claim; it is a definition that we have the same parents. Okay, so that is exactly the same mistake. How did I get to all this? About people who transfer…? Definition.