pmb Posted July 4, 2012 Share Posted July 4, 2012 (edited) Of course it is a type of spatial dimension, I've told you more than once now, .. I know what you believe. Now I want to know why you believe it. What do you think it means to say that time is a dimension in space, i.e. a spatial dimension? What I don't get is why don't you think that space is a temporal dimension? Taylor and Wheeler write on page 18 of Spacetime Physics Today we have learned not to overstate Minkowski's argument. It is right to say that time and space are inseperable parts of a larger unity. It is wrong to say that time is identical in quality with space. You know what space is, right? Loosely stated, it's the totality of "points." Each point in space is identified by exactly three numbers, i.e. it takes three numbers to specify the position vetor R = (x, y, z). Time is what we read on a clock. A time reading is not used to identify a point in space. An event is the conflation of a clock reading and the position vector and expressed as X = (ct, r). The collection of all events is called spacetime. Nothing about this indicates that time is a spatial dimension. In fact all the literature I've quoted states that time is not physically the same thing as space. Edited July 4, 2012 by pmb Link to comment Share on other sites More sharing options...
Aethelwulf Posted July 4, 2012 Share Posted July 4, 2012 I know what you believe. Now I want to know why you believe it. What do you think it means to say that time is a dimension in space, i.e. a spatial dimension? I actually don't even believe time exists. What I know is that time makes up the forth dimension of the metric; ie. it is a type of spatial dimension. In relativity, time is called ''imaginary space'' and space is called ''imaginary time''. http://www3.plala.or.jp/MiTiempo/former/supplement/s-1.html Link to comment Share on other sites More sharing options...
pmb Posted July 4, 2012 Share Posted July 4, 2012 I actually don't even believe time exists. What I know is that time makes up the forth dimension of the metric; ie. it is a type of spatial dimension. Yes. Time is very much the fourth dimension of spacetime. I explained all of this above. Spacetime is also known as Minkowski space. But this is a different use of the term "space" than the typical physical meaning. Its a mathematical space. Mathematical spaces don't neccesarily represent space as in the "spatial" kind of space. Minkowski space is a good example of that. Its not the "spatial" kind of space but a mathematical space. And its quite true that time is a dimension in that mathematical space. But you shouldn't be confusing the two kinds of meanings of the term space and it seems likeits what you're doing. In relativity, time is called ''imaginary space'' and space is called ''imaginary time''. Not really. One can use an imaginary coordinate but this is exceptionally rare thing to do. Almost nobody uses that concept anymore. Link to comment Share on other sites More sharing options...
Aethelwulf Posted July 4, 2012 Share Posted July 4, 2012 (edited) Yes. Time is very much the fourth dimension of spacetime. I explained all of this above. Spacetime is also known as Minkowski space. But this is a different use of the term "space" than the typical physical meaning. Its a mathematical space. Mathematical spaces don't neccesarily represent space as in the "spatial" kind of space. Minkowski space is a good example of that. Its not the "spatial" kind of space but a mathematical space. And its quite true that time is a dimension in that mathematical space. But you shouldn't be confusing the two kinds of meanings of the term space and it seems likeits what you're doing. Not really. One can use an imaginary coordinate but this is exceptionally rare thing to do. Almost nobody uses that concept anymore. I said it was a type of spatial dimension, unto which you have tried to argue its not, but now you seem to be agreeing that it is the fourth dimension of space. Contradictory much? And of course it's mathematical. It's an abstraction which defined both space and time as part of the same metric. What time is in that metric is defined under imaginary space and space itself is defined as an imaginary time. The link I showed you, explained all this. It also explained time was the 1st degree of freedom and as I explained to you before, if by ''change'' you means something which happens within the degree of freedom known as time, then I would agree. However, this does not mean change and time are synonymous, because that is patently wrong. Edited July 4, 2012 by Aethelwulf Link to comment Share on other sites More sharing options...
studiot Posted July 4, 2012 Share Posted July 4, 2012 It's an abstraction which defined both space and time as part of the same metric. This is mathematical rubbish. Link to comment Share on other sites More sharing options...
Aethelwulf Posted July 4, 2012 Share Posted July 4, 2012 This is mathematical rubbish. All mathematics is an abstraction. I don't see why you would say it is rubbish. Link to comment Share on other sites More sharing options...
studiot Posted July 4, 2012 Share Posted July 4, 2012 It is not the abstraction that is nonsense it is your view of metrics. Metrics are a precisely defined mathematical term (as are manifolds you used earlier). Link to comment Share on other sites More sharing options...
Aethelwulf Posted July 4, 2012 Share Posted July 4, 2012 It is not the abstraction that is nonsense it is your view of metrics. Metrics are a precisely defined mathematical term (as are manifolds you used earlier). I view all math as abstractions. Oh well, I'm hardly going to nit-pick over this. My real quarrel is that time is a dimension, a spatial dimension and one which is imaginary in the theory. Link to comment Share on other sites More sharing options...
studiot Posted July 4, 2012 Share Posted July 4, 2012 Well how about discussing my post#25 in the light of your views? It was a response to one of your earlier comments. Link to comment Share on other sites More sharing options...
pmb Posted July 4, 2012 Share Posted July 4, 2012 (edited) I said it was a type of spatial dimension, unto which you have tried to argue its not, but now you seem to be agreeing that it is the fourth dimension of space. Contradictory much? I can't tell what you know or don't know. However it seems to me that you don't know what a space is in the mathematical sense of the term. You seem to keep confusing it with the familiar meaning of the word as in the set of all spatial locations. For example: (1) Let p = pressure and v = volume. The pv diagram used in thermodynamics is a type of space whose points are (p, v) which have nothing to do with the normal meaning of space. But the (p, v) are elements of that space. (2) We call a set of values x1, x2, ..., xN a point. The variables x1, x2, ..., xN are called coordinates. The totality of points corresponding to all values of the coordinates within certain ranges constitute a space of N dimensions. Other words, such as hyperspace, manifold, or variety are also used to avoid confusion with the familiar meaning of the word "space." The space Rn is the usual n-dimensional space of vector algebra. (3) A vector space is a set V with operations of addition and scalar multiplication. The elements of V are called vectors. The operaion of addition combines two vectors in the vector space to produce another vector which is also in the vector space. The operation of scalar multiplication combines any real number a and any vector v to produce another vector in the space can labeled av. The operators must the following eight axoims (1) commutative law of addition (2) associtive law of addition (3) additive identity law (4) additive inverse law (5) distribution law (vecetors) (6) distribution law (scalars) (7) associateve law of multiplication (8) scalar identity law (4) Hilbert space is a function space (set of functions) which has the following properties (1) The space is linear (2) There is an inner produt defined on the space (3) The space is complete. Every Cauchy sequence of functions in the Hilbert space converges to an element of the Hilbert space The vectors in an abstract vector space can be matrices. They don't always have to be geometrical vectors. Elements of Hilbert space are quantum states and can be something as simple as a stationary state such as [math]\Psi(x) = A e^{ikx}[/math]. These are what I mean by mathematical spaces. The examples of spaces that I gave are not related to Cartesian 3-space but to something abstract such as a collection of vectors to form a vector space. Spacetime is a kind of space. It too is a mathematical space in that its not a Cartesian 3-space which has only spatial elements in it. Spacetime is the space which consists of 4-positions X which are events in spacetime. As I said earlier an event is the conflation of Cartesian 3-space with time to make something altogether new, i.e. spacetime. When you've been using the term spatial it appears to be in the sense of pertaining to Cartesian space. Its not. Its about spacetime which is of a different nature than Cartesian space. The metrics in Eucliean space and Minkowski space are even different. Edited July 4, 2012 by pmb Link to comment Share on other sites More sharing options...
studiot Posted July 4, 2012 Share Posted July 4, 2012 (edited) Talking of metrics here is an interesting one that declares that every point is the same distance from every other point. This is (almost) equivalent to the old geocentric view of the universe that projected all the universe onto the celestial sphere. For any two points r, s in 4D Minkowski space [math]d(r,s) = \left\{ \begin{array}{l} 1,\quad r \ne s \\ 0,\quad r = s \\ \end{array} \right\}[/math] Remember that for a metric function to be valid d must be non negative. Edited July 4, 2012 by studiot Link to comment Share on other sites More sharing options...
pmb Posted July 4, 2012 Share Posted July 4, 2012 (edited) Talking of metrics here is an interesting one that declares that every point is the same distance from every other point. This is (almost) equivalent to the old geocentric view of the universe that projected all the universe onto the celestial sphere. For any two points r, s in 4D Minkowski space [math]d(r,s) = \left\{ \begin{array}{l} 1,\quad r \ne s \\ 0,\quad r = s \\ \end{array} \right\}[/math] Remember that for a metric function to be valid d must be non negative. The Minkoski metric is defined as the tensor g in [math]dX*dX = g_{\alpha\beta}dx^{\alpha}dx^{\beta}[/math] where g = diag(1, -1, -1, -1) or [math]dX*dX = ds^2 = c^2dt^2 - dx^2 - dy^2 - dz^2[/math] This metric does not say that every point is the same distance from every other point though. This is the metric used in flat spacetime. In the early history of relativity they used to use ict as the temporal component of an event, not just ct. That's what Aethelwulf was talking about when he referred to the imaginary space dimension. But the term "space" as used here is in the abstract sense as I've explained about in quite a lot of detail. Nobody uses that nowadays though so that point is moot. Edited July 4, 2012 by pmb Link to comment Share on other sites More sharing options...
anotherfilthyape Posted July 4, 2012 Share Posted July 4, 2012 This question is not a scientific question, it is a philosophical question, it must be addressed without science because you cannot falsify your conclusions... I had say that time is change, which can happen in any level of matter. Link to comment Share on other sites More sharing options...
pmb Posted July 5, 2012 Share Posted July 5, 2012 This question is not a scientific question, it is a philosophical question, it must be addressed without science because you cannot falsify your conclusions... I had say that time is change, which can happen in any level of matter. I dissagree in the sense that this is a topic in the philosophy of science. We're discussing the definitions of t basic terms used in science. Definitions don't need to be falsifiable, oinly hyopotheses do. E.g. if I said that the electric field is defined as force per unit mass then it can't be falsified, but that doesn't mean that its wrong. The same with the concept of time. Link to comment Share on other sites More sharing options...
studiot Posted July 5, 2012 Share Posted July 5, 2012 (edited) This metric does not say that every point is the same distance from every other point though. This is the metric used in flat spacetime. Thank you, I am aware of the usual metric and its properties. I was just concerned that it is all too easy to transfer results from mathematics into physics and forget to transfer the conditions of validity. In particular you have to be very careful if you introduce i into the distance function because d cannot be imaginary or complex. Edited July 5, 2012 by studiot Link to comment Share on other sites More sharing options...
pmb Posted July 5, 2012 Share Posted July 5, 2012 (edited) Edit: Sorry. I think I was asleep when I wrote that! Edited July 5, 2012 by pmb Link to comment Share on other sites More sharing options...
Alan McDougall Posted July 5, 2012 Author Share Posted July 5, 2012 Some great posts guys, What about a "Moment in Time" do we ever reach one?, my point being once you think you have reached a point in time it is already gone. A sort of a paradox if you like. Link to comment Share on other sites More sharing options...
studiot Posted July 5, 2012 Share Posted July 5, 2012 What about a "Moment in Time" do we ever reach one?, my point being once you think you have reached a point in time it is already gone. A sort of a paradox if you like. Hello Alan, what did you make of my post#25? One of the consequences of the Minkowski spacetime continuum has profound implications for your last question which is bound up with existence. If we accept (for the moment) this view then take my computer. It has no existence on the moon. It is on earth. This may be obvious but consider it has space coordinates (a,b,c) (on earth) but not (m,n,p) on the moon. So what about time? Well it existed yesterday and today so it has time coordinates (y,t) So it has 4D coordinates (a,b,c,d,ct) and (a,b,c,d,cy) and everything in between. All this is a roundabout way of saying that in spacetime view time does not flow ie my computer does not cease existing yesterday because it exists today. Link to comment Share on other sites More sharing options...
pmb Posted July 5, 2012 Share Posted July 5, 2012 Well it existed yesterday and today so it has time coordinates (y,t) I don't understand what you mean by this. The letter "y" usually refers to a spatial variable, not a temporal one. And here you have two variables when a time coorinate only uses one. So what does (y, t) mean? So it has 4D coordinates (a,b,c,d,ct) and (a,b,c,d,cy) and everything in between. Again, you seem to be using a spatial coordinat, y, where a temporal one is usually used. All this is a roundabout way of saying that in spacetime view time does not flow ie my computer does not cease existing yesterday because it exists today. Time does pertain to your computer though. I don't know why you say that in spacetime view time does not flow . Can you elaborate for me? Some great posts guys, What about a "Moment in Time" do we ever reach one?, my point being once you think you have reached a point in time it is already gone. A sort of a paradox if you like. We can record moments in time. Its just that being human we don't experience moments in time very well. But its not a paradox in any sense of the term. Link to comment Share on other sites More sharing options...
studiot Posted July 5, 2012 Share Posted July 5, 2012 Using a,b, c as spatial coordinates was a mistake thanks. I have corrected it. All the letters are just numbers in some arbitrary coordinate system except c. Their values do not matter. They are not really variables. c is of course the necessary transformation constant to convert time to distance. What I am trying to explain is the notion that we cannot say "my computer no longer exists yesterday my computer exists today my computer does not exist tomorrow because time flows from past to future" In other words we cannot use 'the present' as a definition of existance within 'spacetime'. It already encompasses the past and future. Sorry if this is a bit rambling but I'm rushing. Link to comment Share on other sites More sharing options...
Aethelwulf Posted July 5, 2012 Share Posted July 5, 2012 I can't tell what you know or don't know. However it seems to me that you don't know what a space is in the mathematical sense of the term. You seem to keep confusing it with the familiar meaning of the word as in the set of all spatial locations. When staying over at my partners last night, I found myself thinking about ways I could explain myself better. I don't believe time actually points out spatial locations, but the notion that space is inseparable to time is fundamentally unique. Time was just another space dimension, an imaginary space dimension in the Minkowski understanding. It's certainly not a ''real space dimension'' (using real as in the mathematical sense), because when people often talk about the spacetime continuum, is that it has three space dimensions and one temporal dimension. This is true, but time if a very special type of imaginary space dimension. What could be throwing you off my statements, is that I am saying it is a dimension of space - well, what I really am saying it is an ''imaginary space dimension''. As I tried to explain, all time is for the spacetime metric is that time is simply an imaginary leg off the real legs of the spacetime triangle. It's an added dimension which many have dubbed ''the imaginary space dimension.'' Using a,b, c as spatial coordinates was a mistake thanks. I have corrected it. All the letters are just numbers in some arbitrary coordinate system except c. Their values do not matter. They are not really variables. c is of course the necessary transformation constant to convert time to distance. What I am trying to explain is the notion that we cannot say "my computer no longer exists yesterday my computer exists today my computer does not exist tomorrow because time flows from past to future" In other words we cannot use 'the present' as a definition of existance within 'spacetime'. It already encompasses the past and future. Sorry if this is a bit rambling but I'm rushing. Time isn't linear ( in the sense that there is some extension from a past to future as in an arrow of time) nor does time flow. Link to comment Share on other sites More sharing options...
studiot Posted July 5, 2012 Share Posted July 5, 2012 What does linearity have to do with it? Link to comment Share on other sites More sharing options...
pmb Posted July 5, 2012 Share Posted July 5, 2012 When staying over at my partners last night, I found myself thinking about ways I could explain myself better. I don't believe time actually points out spatial locations, but the notion that space is inseparable to time is fundamentally unique. Time was just another space dimension, an imaginary space dimension in the Minkowski understanding. It's certainly not a ''real space dimension'' (using real as in the mathematical sense), because when people often talk about the spacetime continuum, is that it has three space dimensions and one temporal dimension. This is true, but time if a very special type of imaginary space dimension. What could be throwing you off my statements, is that I am saying it is a dimension of space - well, what I really am saying it is an ''imaginary space dimension''. As I tried to explain, all time is for the spacetime metric is that time is simply an imaginary leg off the real legs of the spacetime triangle. It's an added dimension which many have dubbed ''the imaginary space dimension.'' Yes. And as I've been trying to say is that time is a dimension of the spacetime manifold. A manifold is a collection of elements which satisfies certain properties. It is a space in the mathematical sense of the term, not as space as in "position of something inside my living room." It's a space in the abstract sense as I've given examples for in the post above. I'm glad we got that cleared up. Link to comment Share on other sites More sharing options...
Aethelwulf Posted July 5, 2012 Share Posted July 5, 2012 In fact, I think I will write up a thread on time, because it is an interesting subject. Link to comment Share on other sites More sharing options...
pmb Posted July 5, 2012 Share Posted July 5, 2012 (edited) In fact, I think I will write up a thread on time, because it is an interesting subject. I'm curious about something so please bear with me. Have you never heard the term space used in any other sense than "place inside a room"? For example when you hear the term Hilbert Space as being a function space, what did the term space mean to you? Wikipedia defines Space in the mathematical sense as follows http://en.wikipedia.org/wiki/Space_(mathematics) In mathematics, a space is a set with some added structure. Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space. For instance, all inner product spaces are also normed vector spaces, because the inner product induces a norm on the inner product space such that: [math]||x|| = \sqrt{<x, x>}[/math] Modern mathematics treats "space" quite differently compared to classical mathematics. Edited July 5, 2012 by pmb Link to comment Share on other sites More sharing options...
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