The reign of King Henry VIII of England, for instance, included six weddings of Henry, and a huge number of beheadings of unfortunate others. So again: Does.
WHAT WOULD TIME HAVE TO BE LIKE IN ORDER TO BE LIKE SPACE? [This essay is a lecture given in 2012 to a group of students at the University of Hawaii. Its ideas having been published academically years before, it has not itself been published. But it can serve as an introduction to my book (1993) Space-Like Time. --FC] You have all heard the idea that time is in some sense like space. You have heard time referred to as “the fourth dimension”, and heard the word ‘spacetime’--as if time were enough like space for one to speak sensibly of some sort of combination of the two. But what, exactly, does this mean? After all, in some way or other, everything is like everything else. To say simply that time is like space, with no further explication, is hopelessly vague. My purpose today is to lay out for you what I regard as the most significant thing that one might mean by saying it--most significant in the following sense. First consider what time and space are like as each of them is ordinarily conceived, and consider the very biggest difference between those two ordinary concepts. Then the most significant thing one might mean by the phrase ‘time is like space’ is that this difference does not exist in reality. This feature of time as it is ordinarily conceived to be does not really apply to time after all. In other words, the ordinary concept of time is wrong--instead of being as it is ordinarily conceived to be, actual time is in this respect the way space is ordinarily conceived to be. Let me repeat that. Instead of being as it is ordinarily conceived to be, actual time is in this respect the way space is ordinarily conceived of as being. That is what I’ll be referring to here as the claim that time is like space. This description is so abstract that you won’t yet know what I’m getting at. I’ll have to spell out, as much as I can today, that difference between time and space as they are ordinarily conceived. The reason I will have to do this is that, even though you already have the ordinary concept of time, you have it largely unconsciously. Editorial comment: This is the wonderful thing about analytic philosophy. It takes ideas that people already have (including ideas that scientists already have, in the case of philosophy of science) and digs into them far more deeply than the people themselves normally do. Analytic philosophy digs into concepts and beliefs that are normally understood just unconsciously and superficially--hence very unclearly. So when it works, analytic philosophy makes clear for the first time things that before were familiar but very unclear. This brings me back to what I will claim is the biggest difference between time and space as each is ordinarily conceived. If we revise the ordinary concept of time in such a way as to remove that difference, we will get a new concept of time that seems very strange to ordinary people. I will label this new concept “space-like” time. You may wonder, “Why would Dr. Christensen want a new concept of time?’ The reason it is so interesting is that arguably--I stress the word ‘arguably’ --this new concept is required by Einstein’s Theories of Relativity that you’ve all heard about. That makes this concept extremely important to science. But here is what makes it really important to physics for physicists to understand this new concept of space-like time. The vast majority of physicists casually label time “the fourth dimension”, and casually talk as if they understand what it would have to mean for time to be like space. But many of them seem not to understand it. They do not understand the concept of spacelike time, it seems to me, because they read into it something from the ordinary concept of time.
Now, just how seriously the work of physicists is affected by this unwitting reading in is a topic I cannot even begin to discuss here. I will just say that if more physicists realized it, they might feel forced into profoundly transforming Einstein’s theories. I have published an entire book on the subject--one which has not taken the world of physics by storm. So I can’t blame you for thinking that I’m awfully arrogant to take on the whole world of modern physics like this. What I can do today, however, is to demonstrate to you what time would have to be like, in order to be anything remotely like space. Once you have seen that for the first time, you will perhaps understand how a lot of very intelligent people could have missed it. Just as an aside, I have a couple of degrees in physics myself. ***** To begin, consider a couple of things that one might use the phrase ‘time is like space’ to mean. Well, space is conceived as being 3-dimensional while time is considered one-dimensional. But no one who uses this phrase has in mind that time really has three dimensions. Another way in which time and space are ordinarily considered to differ is that time is conceived as having an intrinsic directionality, the earlier-later asymmetry, whereas space is considered to be the same in all directions. But this is still a pretty minor difference all by itself. After all, little children begin with a concept of space that has an intrinsic directionality to it, the up-down asymmetry. When they first learn that the world is round, they are apt to ask “Then why don’t people on the other side fall off?” So the earlier-later asymmetry doesn’t make the ordinary concept of time hugely different from that of space--though it is related to the difference I’m aiming to explicate here. For reasons I hope will be clearer later on, it is extremely difficult to explicate that difference. Because of that fact, I am first going to introduce a conceptual tool we will need for the task: the idea of a conceptual fiction. Perhaps some of you have heard the phrase ‘mathematical fiction’. In any case, you all know what a fiction is: something such that we talk as if it is real, even though we don’t actually believe it exists. For example, there is Santa Claus and the Land of Oz. Now, a conceptual fiction is a little different. We don’t pretend it is real for entertainment or for societal reasons, but for intellectual reasons: in some way or other, it aids us in thinking about subjects that would otherwise be more difficult to comprehend or to manipulate in our minds. For an example, if you’ve had any physics or chemistry, you may have heard of a “perfect gas”. (How many have heard this phrase?) No scientist believes that any perfect gases really exist. But under certain conditions, the formula defining a perfect gas approximates those describing real gases; and because that formula is mathematically so simple, it can be conveniently used in those conditions to describe the behavior of real gases approximately. I hope you can see how useful this fiction could be, in circumstances where one doesn’t need answers that are exactly correct. For another example of a conceptual fiction, consider “the average man”. Now, I’m sure you’ve all heard of the average man. But ask yourself: have you ever met the average man? In fact, could you ever meet the average man on the street--shake his hand, pat his 1-2/3 children on the head, and so on? (At first I was going to use as my example the average person, so I could point out that the average person is a hermaphrodite. …But that would’ve been silly, so I didn’t do it.) I hope you feel you understand this example. There is no such man as the average man. There are many men who have, to some approximation, the features that the average man is said to have. (Average height, average income, etc.) But “the average man” himself is a conceptual fiction, not
a real being of any kind. Then why do we talk just as if such a person did exist? The answer is that doing so helps us to mentally manipulate certain information which otherwise we could not, or could not nearly so easily, “wrap our minds around”. Talk of the average man--or the average thing of any kind that you care to choose--helps us to codify a huge amount of information about an entire population of real things. To see how this works more clearly, consider the following pair of sentences [write on the board]: The height of the average man is 5 feet, 8 inches. ≈ The average height of all men is 5 feet, 8 inches.
Without getting too technical, I suggest that the second sentence provides the real “cash value” of the first one. (I’m not claiming that the second sentence is true--it’s merely an illustration.) Pay special note to the fact that I have not put an “equals” sign between these two sentences. Instead I have used a symbol which I employ in these contexts to mean something like “is equivalent for certain non-literal purposes”. I must stress the fact that these two sentences do not mean literally the same thing. The first sentence speaks of an entity that does not exist, hence it must be false, whereas the second one at least could be true. For convenience I often use the word ‘paraphrase’ in this special sense, in order to stress that the two sentences in question do not mean the same. And that is an interesting fact about very many conceptual fictions: They can, so to speak, be “paraphrased away”, when we need to stress that a sentence seemingly referring to one of them is not literally true. Or, to be more precise, to stress that we talk as if the sentence is true only for reasons of conceptual convenience. We will later look at some especially revealing paraphrases (in this sense) involving our concept of time. I am slowly moving in that direction. But first I must make one more general point about conceptual fictions. Chances are, until now you have never realized that you have been employing these critters all your lives. They are so convenient, and our language use is so habitual and automatic, that we rarely think consciously about what we “really mean”, at the deepest level of our understanding, when we say something that is thoroughly ingrained in our conscious and unconscious thought. But I hold that ordinary thought and speech are absolutely loaded with conceptual fictions. And the one I am about to talk about here is a really big one, one that is extremely valuable to finally become conscious of. ***** That conceptual fiction is the passage of time. Note well that I am not calling time itself a conceptual fiction. It is the passage of time that I insist does not exist. But I also think that, by careful introspection, we can all come to realize that it is just a conceptually convenient add-on to our concept of time. Indeed, we can come to realize that, despite all its convenience, the passage of time is an absurd or even downright self-contradictory notion--that it could not be part of any coherent concept of time. Until one does realize this, moreover, it is very difficult to grasp the topic of this lecture: what time would have to be like if it were to be like space. To begin, let us ask ourselves a couple of puzzling questions. In general when we speak of something as passing by, we can ask the question of how fast it is moving. How fast, for example, is a certain car passing along the street? And we can in principle give an answer: a particular car is passing by at the rate of 30 miles per hour. Now let us ask this question: How fast does time pass? (Well? Can somebody tell us?)
To clarify the situation a bit, consider some specific examples of passage-of-time talk, such as ‘Valentine’s Day is approaching’ and ‘Christmas is receding into the past’. Then the question is, just how fast is Valentine’s Day approaching? And the answer quickly becomes clear: With every day that passes, Valentine’s Day becomes a day closer. So Valentine’s Day is approaching at the rate of one day per day! Or one hour per hour, one second per second, etc. So when you stop and think about it for the first time, there is something very odd about our familiar concept that time passes. Ordinary motion, or any other ordinary type of change, takes time to happen. Again, we can measure ordinary change in such units as miles per hour. So for time itself to move, or for some chunk of time such as Valentine’s Day to move, would also take time to happen. And this appears to mean that time must in some sense be “given twice over”. There must be, not just “regular” time, but some sort of hyper-time as well: the time that it takes for “regular” time to pass. But does this make any sense, literally? To find out, let us dig deeper. Let us do so with this question: If Valentine’s Day is approaching, exactly what is it approaching? Again a little introspection can reveal the answer: it is approaching…us! When we say that time is passing, we mean that it is going past us! (Not so?) But I will have to expand on that word ‘us’, and to do so I will have to make a highly important distinction between two very different types of entity that we commonsensically talk and think about. I refer to the difference between objects, on the one hand, and the events or situations that happen to objects, on the other. Now, in the category of objects I include both material objects, including our own bodies, and also such immaterial objects, if there are any, as souls or minds. (A big philosophical issue, but one that is irrelevant here.) So the category of objects is a very large one. Prima facie, it includes everything from the physicist’s photons and electrons, to molecules and bacteria and books and mountains and planets and galaxies and the whole darned universe. But it does not include any of the things I have spoken of as events and situations. In this category are included such entities as cases of the falling of an object, cases of the decomposing of an object, cases of the being round of an object, and so on and so on. Again, us people are a special category of objects. So we can contrast people themselves with things that are said to happen to people: We can contrast, say, weddings and beheadings, on the one hand, with the people who are wedded or beheaded on the other. Is this distinction more or less clear? Often the events and situations we speak of are vastly more complex than this. Take wars and reigns of monarchs, for example. Wars are composed of shootings and bombings and holdings or losings of territory, and many other things. Reigns of monarchs are composed of such simple situations as holdings of territory and the monarch’s merely being alive, as well as a lot of very complex situations and events. The reign of King Henry VIII of England, for instance, included six weddings of Henry, and a huge number of beheadings of unfortunate others. So again: Does this category-difference, between objects, and the events or situations that happen to objects, seem at least crudely clear? Again, chances are it is a distinction you’ve never before thought consciously about, though it should become clearer as you do introspect your own concepts more thoroughly. We have to rush on and apply this important distinction to our present topic. Returning to the idea of the passage of time, then, I will now use a diagram to show you exactly what it is. This line I have drawn is meant to represent a period of time. Segments of the line represent shorter periods, while points on the line represent instants of time. It is standard to call this simple figure a “time diagram”. Now let me add a further feature, oblong rectangles along the time-line to represent temporally extended events. This one, to be concrete, is meant to represent
the reign of Henry VIII, and this one to represent the reign of Elizabeth II. Speculatively, I am even representing the presumed reign of Charles III, now spoken of as Prince Charles. I draw this to illustrate that events and situations are supposed to be located in time. Still all familiar? Now I will add a further feature to the time-diagram. This small circle I mean to represent the universe of objects. And these arrows are meant to signify that all objects together are thought of as moving through time. Or, alternatively, time is thought of as moving past all objects as a single collection. We sometimes say that time is passing--passing us, to repeat--and sometimes say that we are constantly moving forward into the future. Either way, what I have just drawn represents the familiar concept of “the passage of time”. (Unfortunately, I don’t have a video-projector, or I could display to you even more clearly just how we conceive the passage of time. You will have to imagine the circle on the diagram and the rest of the diagram as moving past one another.) We don’t always speak in terms of the whole universe of objects, of course. Sometimes we single out particular objects, as when we say something like ‘I have just passed through a bad situation’. But in its essence, this is what all of our passage-of-time talk amounts to. See? Does this all seem familiar, now that I have laid out the details? But again, I hope that it is also beginning to seem very odd. To repeat, ordinary motion takes time to happen. Then for time itself to move past the universe of objects would likewise take time. Evidently, to repeat, it takes one day of hyper-time for a day of regular time to go past us. While you’re reflecting on that I’ll keep going. Pay special attention to the very different ways in which those two categories of things are treated in this picture. Events and situations are fixed in time and move rigidly along with it, while the objects that they happen to change their temporal locations and go on to new events and situations. For example, it would be said that my putting my shoe on my foot this morning is several hours earlier than a certain lecture of mine; but my shoe and my foot and I myself am in the midst of that lecture. There is an event, my putting of a shoe on my foot, that is no longer attached to any objects--the objects have left it behind. In fact, in this concept, gazillions of events and situations exist that are no longer attached to the objects they happened to. (Former lectures, for example.) They’re just sort of ghosts, ever moving farther and farther away from us. And similarly for events and situations not yet attached to their objects. Because this picture of reality is so ingrained in your thinking, you may well not yet be convinced that the passage of time cannot be real. But perhaps you will become more convinced after I present an alternative. To see the alternative, consider these two pairs of sentences. The reign of Henry VIII has gone into the past. ≈ The reign of Henry VIII no longer exists. Henry’s reign is receding ever farther into the past. ≈ It is ever longer ago that Henry’s reign existed.
This is one of those points at which the subject at hand is so subtle and complex that I would have to write entire book chapters to even begin to adequately explain and justify what I want to say. (Come to think of it, I have written entire book chapters on it.) But I hope that, at least intuitively, you can grasp my conclusion, which is this: At the core of the ordinary concept of time, after the conceptual fictions are stripped away, the events and situations we speak of as being past have not gone anywhere. They have not gone anywhen. They have merely ceased to occur or to exist. They do not go on existing, moving away at that relentless pace of one day per day or any other pace; they just stop existing. Alternatively, us objects do not move serially from one pre-existing situation to the next; rather, one situation involving us exists and then a different situation exists.
Next let me present a consequence of this claim of mine that may be especially helpful. As some of you may already have noticed, in fact we do not always talk as if time forever passes at that same speed of one second per second. We often say things like this: “Time really dragged during Christensen’s lecture”. Or on the other hand “The time went by really fast during that fun party.” These statements are very familiar--ordinarily they wouldn’t sound odd to anyone. But they would certainly sound odd if you made them more precise, as in: ‘At the party, time flew so fast that it took only15 minutes for a whole hour to go past!’ I submit that when we express subjective feelings of this variety, we do not literally mean that time seemed to move at a different rate than the usual one minute per minute. We mean that events and situations seem to exist for a different amount of time than they actually do. We could say instead, ‘That one-hour party seemed to last only 15 minutes’ And when we say that, I submit, we eliminate talk about the passage of time. We replace it with talk of events and situations beginning, continuing, and then ceasing to exist. At the deep core of our unconscious thinking, I suggest, we don’t really believe that time passes. ***** This new idea requires a lot of absorbing. One thing that may help you absorb it is my answer to the following question: If the passage of time is merely a conceptual fiction, why is it so firmly embedded in all of our thinking? What is so dang useful about it that we just think of it as real? To begin to answer this question, let me point out some basic facts about human experience. First, human beings are highly visual creatures. With our stereoscopic color vision, we may be the most visual mammals of all. Other mammals have auditory and olfactory and tactile senses far superior to ours, but we excel in vision. And with the thinking capacities of our large brains, we are very apt to be the most visualizing animals of all. Our very word ‘imagination’ reflects this: When we think of conceiving something in our minds, we usually think first of creating a mental image of it, not mental sounds or smells or something else. The importance of visualization to us is especially obvious (oops, there’s a vision-word) when we consider the ubiquitous use of graphs and other diagrams in modern life. Do we want to understand a relationship between temperature and pressure, or between population size and average wealth, more clearly? (Oops, another vision word.) Then we’re apt to diagram it. I’m sure you can think up oodles of your own examples. This leads naturally to my next point: diagrams are inherently spatial entities. They involve sizes and shapes, not tones and fragrances and such. So whenever we use a diagram to represent tone or force or temperature or wealth or population size or what have you, we are “spatializing” it. We are using size and shape to represent something which in itself is non-spatial. And, to repeat, we do this because we are so good at perceiving and conceiving in a visual way, relative to our abilities to perceive and conceive in ways that involve our other senses. Of course, our spatial abilities involve tactile and sensorimotor aspects as well as visual ones. But in terms of vividness and precision, as my examples illustrate (oops, another vision-word), our visual sense dominates. And this leads to a second point about our nature: that we have no visual experience of temporal facts or features of reality. We can see or visualize the spatial features known as size and shape. We cannot see or visualize, say, having been the case or being yet to be the case. We can’t even visualize the temporal relationship of one entity being earlier than another one. We can let spatial features represent temporal ones, and then imagine or diagram the spatial features. That is in fact what I have already done by drawing a line on the board to represent time: it employs the spatial relationship of one point on the board being higher than another as a proxy for one time or event or situation being later than another. I hope you have some glimmering of where all this is going.
Well, it may be asked, if we don’t see any temporal facts or features of things, where do we get the idea that there are any temporal features or facts in the first place? This is one excellent question…but it is far too deep and complicated for me to try to answer it here. I believe that our temporal concepts are tied into, among other things, the contrast between all of our sensory experiences, on the one hand, and our memories and anticipations of sensory experiences on the other. But my key point here is the one I have just made: that we have direct visual experience of spatial features and facts, but no direct sensory experience of temporal ones. Correspondingly, we have no ability to understand temporal features or facts in the way we understand best, namely by seeing or by visualization, except by employing spatial facts or features as a proxy or surrogate. We start with something like that line on the board, with the up-down spatial relationship between points (or, if you prefer, the left-right relationship) standing in for the earlier-later relationship. But then we run into a problem. A crucial part of the ordinary concept of time, I’ve been pointing out, is that events and situations come into and go out of existence. They don’t exist, and then they do exist, and then they don’t exist again. But those spatial points on the diagram do not come into and go out of existence--they all just sit there. They have different spatial locations, but they do not differ from one another in regard to their existence. Woe is us. We want to be able to visualize temporal information, but the spatial picture we have begun with has let us down. It makes it appear as if all the events and situations of all time are equally existent. How might we correct for that? What could we possibly [at this point I roll my eyes heavenward] put into the diagram…as a proxy…for events and situations going into and out of existence? I hope you’ve seen my answer coming. We could add to the diagram something representing the universe of objects, and let its coinciding with one event or situation after another stand in for the serial existing of each event or situation. Or we could focus on individual objects instead of the whole universe, visualizing each object as moving from one already-existing event or situation to the next. Either way, by adding the moving universe of objects to the time-line, we get that surrogate we need to stand in for the coming into and going out existence of events and situations. We get to eat our cake and have it too. Ta-daa! I have dumped my story of the origins of time’s passage on you pretty fast. And to repeat, I have had to leave out huge numbers of crucial details. So if you still have many doubts, I understand. I believe it will be yet easier for you to see the passage of time as a fiction after I have finally given my answer to the question this talk is about: what time would have to be like to be like space. But I think this long excursion into passage-of-time talk has helped pave the way for that discussion. ***** Let me start by again comparing two sentences, one of them “spatial” and one “temporal”: Honolulu is here, Kailua is there, and Hilo is over yonder. Christensen’s lecture is in the present, World War II is past and Armageddon is in the future. On the surface, the spatial sentence and the temporal one have a lot in common. But when we look closer, we realize that, at least as they are ordinarily meant, the two are extremely different. The words ‘here’, ‘there’ and ‘yonder’ express a difference in location between the three cities, a difference relative to the location of the speaker. Relative to someone in Kailua, that place counts as “here” while it is Honolulu that is “there”. But--this is absolutely crucial--these spatial terms
do not signify any difference regarding existence among Honolulu, Kailua and Hilo. The three places are thought of as all equally existing. To repeat: words in ordinary speech such as ‘here’, ‘there’ and ‘yonder’ express differences in location only, not differences regarding existence, From things I have already said today, I hope you see where I’m going next. Just as this first sentence involves spatial locations, this second sentence, the one carrying temporal information, is thought of as involving temporal locations. But in addition, the temporal sentence expresses a difference in regard to existence involving the three catastrophes. (That was a joke.) A lecture by Christensen is occurring, it exists; but World War II merely did exist and Armageddon merely (allegedly) will exist. I hope you agree with me that the difference between existing and not existing is a big difference. (For that matter, the difference between having existed and being going to exist is also a big one, but I won’t be discussing it here.) Correspondingly, as I claimed at the start of this lecture, there is a huge difference between space as it is ordinarily conceived and time as it is ordinarily conceived. I have just pointed out a key part of the difference. But wait. What about space and time in themselves, not the way we conceive them? Maybe they are actually different from what we commonsensically take them to be. Finally, we are on the verge of answering the question I began with. Consider the following idea: that what we really should do is understand this second sentence as being fully analogous to the first one. In other words, we should use words such as ‘past’ and ‘formerly’ and ‘present’ and ‘will be’ and so on as expressing, not differences in existential status, but differences in temporal location only. This idea has seemed plausible to a lot of people--including a lot of physicists in particular. But what I am about to reveal is that it results in a lot bigger change in our concept of reality than one might suppose at first glance. Most people who make this suggestion, I maintain, do not realize that. Look back at the time-diagram I began with, and consider the monarchial reigns represented on it. On the view that time is like space (as I have now defined that view), the reigns of Henry VIII, Elizabeth II and (presumably) Charles III differ from one another only in temporal location, not in regard to existence. In whatever sense any one of them exists, so do the other two. But to see what this really means, consider more closely the logical relationship between events or situations and the objects they involve or happen to. With no such difference in existence for the moving universe of objects to stand proxy for, it no longer makes sense in this concept of time, so I will now erase it. To see concretely what is to replace it, consider next the following sentences: The reign of Henry VIII over England exists --> Henry VIII is reigning over England -->Henry VIII exists
The arrows represent the relationship of logical implication. If the reign of Henry VIII over England exists, it follows that Henry VIII himself exists and is reigning over England. And when I say ‘Henry VIII exists’, I’m not referring to his bones moldering in Westminster Abbey. I mean the flesh-and-blood and famously corpulent (that means fat) Henry VIII. And now it really hits the fan. Henry VIII is reigning over England, and Elizabeth II is reigning over England? Isn’t that some sort of contradiction? It would be, but there is a way out. In fact, it is the only possible way out, and it really reveals what it would mean for time to be like space. Notice again that, under the ordinary concept of time, only events and situations are thought of as being temporally extended--as being spread out along the time-line. The sole way for both Henry VIII and Elizabeth II to be reigning over England, then, is for them to be reigning over different parts of England. That is, different parts of England in a temporal sense, not in the usual spatial sense of ‘part’ and ‘whole’. In other words, just like events and situations, objects are to be seen
as temporally extended. This is one reason why it was important for me to make clear earlier that on the ordinary view of time, objects (such as England) are not treated as being spread out across time. If they have a location in time at all, on the ordinary concept, it is at just one instant of time, and it is forever changing that position. (Then, of course, I insisted that even that isn’t literally meant.) But now we have a concept of time in which both events and situations, and the objects they happen to, are spread out over time. Indeed, each object, and each temporal part of an object, is at the same temporal location as the events and situations that happen to it. For you to really get a grasp on this new idea, I must now introduce another sort of diagram. For obvious reasons, I will call it a space-and-time diagram. Since the chalkboard surface is only twodimensional, and since I’m already using one of those dimensions to represent time, it can portray just one of the three dimensions of space. But it should help. Allow me to introduce…Henry VIII! Of course, I can portray only one of his spatial dimensions. I had to pick one over the other two; I picked his famous girth. As you can see, the part of Henry that is located back here in late 1490 (the time of his conception) is pretty small. Later temporal parts of him are spatially wider, and temporal parts of him after 1535 are ever wider. That’s when he falls from a horse and suffers a compound fracture of his leg. The theory is that the resulting permanent disability leaves him so immobile that he really puts on the pounds. (Clearly, this drawing is not “to scale”--please forgive my artwork.) This “time-slice” of Henry VIII is wedding (a time-slice of) Catherine of Aragon, and this slice of him is marrying (a time-slice of) Catherine Parr. I have drawn a sharp edge for Henry here in 1547 on the controversial assumption that death is the end of a person, though it is obviously not the end of (i.e., the latest temporal part of) the person’s body. I hope it is clear to you that this concept of objects--let’s call them “four-dimensional” objects--is not the concept of ordinary thought and ordinary language. But let me be more explicit regarding the nature of the difference. Consider my little finger. As we normally speak and think, my little finger now is one and the same thing as my little finger now. Oh, in modern times we may think of it as having gained and lost a few gazillion molecules in the time it took me to say that. But my little finger now and my little finger now is regarded as overwhelmingly composed of the same matter. Not just the same amount of matter, or the same kind of matter; the very same matter. In contrast, under the concept of time as being like space, this temporal part of Henry VIII is considered to be composed of entirely different matter than this part. Instead, these two temporal parts of Henry VIII are considered to be just like these two spatial parts of the table I’m sitting on. We refer to the two as different parts of the same thing, largely because they are connected more or less continuously by other matter lying between them. Yet this and this are regarded as being composed of entirely different matter. They are composed of the same kind of matter, but it is totally different matter. See? This idea is hard to wrap your head around. It is emphatically not the ordinary concept of objects. And space-like time is emphatically not the ordinary concept of time. I often use the following terms: under the ordinary concept of time, objects “persist’ or “continue” through time; under the concept of time as being like space, as I’ve already said, objects “extend” or “spread” across time. What I have said about this subject here is about as much as I can say in a short period to explain the difference. So I hope that at least you have a rough intuitive grasp of what is at stake. Now, a concept’s being different from the ordinary one doesn’t mean it is wrong. Which concept of time is correct, if either, is another complex subject about which I have a lot to say. But the final thing I want to say here is one I hinted at back at the beginning. An awful lot of people, including an awful lot of physicists, have not grasped even roughly what I have tried to prove to
this class today. Many talk casually, as I said earlier, about time as being like space. But they do not understand what it means. I have often heard physicists and others say things like this: “Why of course time is like space. Things move through space, and things move through time”. Or else they may draw a space-and-time diagram like this next one, and say something like the following: “This represents an electron moving along its path in spacetime”. Do you now see what they’re doing when they say these things? They are reading the passage of time, from the ordinary concept of time, into the concept that time is like space. For an object to move through spacetime, it has to move through time. And that is passage-of-time talk. I’ve tried hard to convince you that even in the ordinary concept of time, the passage of time is a fiction. The passage of time makes no literal sense under any concept of time. And it certainly makes no sense in the concept of time as being like space. Now, you might realize that scientists who talk this way may not mean it as it sounds--that they are merely “speaking with the vulgar’, talking in terms that would be familiar to their audience but which they themselves do not take literally. I would be satisfied to think that this is the case. When I said earlier that many physicists read back into space-like time something from the ordinary concept of time, I had in mind something much more serious than “passage”. What I meant is what I have now labeled the persistence through time of objects. I hold that many, if not all, physicists do not realize that space-like time requires “4-dimensional” objects. They recognize “4-dimensional” events and situations (say, wave-packets spread across Minkowski spacetime). But they talk constantly of 3-dimensinal objects—be they seen as having an ever-changing location in time or not. They talk of one and the same entire electron as moving in space (not of different temporal parts of it that bear different spatial relationships), and indeed of one and the same scientist (not a wholly different temporal chunk of him or her) making temporally separated measurements on that same electron. I cannot today explain how this leads to profound difficulties and even contradictions, for everything from Einstein’s epistemology to solving the problem of inertia. The last two chapters of my book are all about this. Alas, demonstrating this profound misunderstanding is way beyond the scope of my talk today. And I have just, so to speak, run out of time. Thank you for your attention.
