Strange Posted February 23, 2014 Posted February 23, 2014 "Science" doesn't develop "practical quantitative models", people do. Of course. But there is a difference between the models produced by people doing science and people just thinking about concepts. And the difference is that they are quantitative and productive (unlike "mmm... time is change, man"). The cool thing about scientific models is that they can be communicated very precisely, and thus shared. The really cool thing about scientific models is that they are mathematical and hence practically useful. Well, can you give me an example of a mathematical model of time that doesn't use units of time? General Relativity. (Although I don't really now what you mean by "units of time"; I assume it means anything you can claim is defined by change.)
Lizzie L Posted February 23, 2014 Posted February 23, 2014 What we call "physical reality" is inside the past light cone. All the rest, especially the so-called "Present" is knowable through duration. As time passes by, the observer translates higher on the time axis (he moves up) and operates a "scanning" of the world around him. Just to push things a little further - you could argue that "physical reality" - is inside both cones. And we can infer what that reality is by fitting models to data. It won't be perfect in either case, but depending in the kind of data we are talking about, some future models will be more accurate than past ones. Some past histories will have no single solution, given the data, whereas some present states will have a single future. That would be true of some kinds of deterministic worlds, wouldn't it? Of course. But there is a difference between the models produced by people doing science and people just thinking about concepts. And the difference is that they are quantitative and productive (unlike "mmm... time is change, man"). Yes. You are preaching to the choir here I actually teach quantitative methodology! And I never said "time is change". That's something of a straw woman. The really cool thing about scientific models is that they are mathematical and hence practically useful. Well, I'm not sure that it's their mathyness that makes them practically useful. But I agree (well I would assert!) that the criterion by which we evaluate a model is its usefulness, and for scientific models, that's often quantitative accuracy. Well, can you give me an example of a mathematical model of time that doesn't use units of time? General Relativity. Isn't c in there somewhere? (Although I don't really now what you mean by "units of time"; I assume it means anything you can claim is defined by change.) I mean that the parameters in the equations include time in units - e.g. seconds.
michel123456 Posted February 23, 2014 Posted February 23, 2014 You absolutely are. When you look at your feet, you see them the way they were a split-split-split second before, because of the time it takes light to travel from your feet and to your eyes. Which raises yet another interesting question: The way we observe time clearly depends on what we're looking at (which is the point of relativity) -- but it "changes" the rules of the game of observation: When we look at the world close to us, we technically see the present but not the future or past When we look at the sky, we see the past and are unable to see the present or future. When we look at rotating galaxies, we see some starts more farther into the past as some others, which means we have a distorted view not only of space, but of time as well. That cone is a way to make sense of something I don't quite think we are hardwired to make complete sense of. Sure. But why can I not observe directly myself as I was a second ago? Or a minute ago?, Or an hour ago? All those points lie inside the past light cone and I cannot directly observe them. (...) When we look at the sky, we see the past and are unable to see the present or future.(...) We can see the past, yes. But not ALL the past. i mean: the part of the past that we can observe is a direct function of the distance.
Endercreeper01 Posted February 23, 2014 Posted February 23, 2014 (edited) Sure. But why can I not observe directly myself as I was a second ago? Or a minute ago?, Or an hour ago? All those points lie inside the past light cone and I cannot directly observe them. You cannot observe these things directly because you have to be at a distance equal to [latex]c\tau[/latex] in order to observe it a time [latex]t[/latex] ago. Edited February 23, 2014 by Endercreeper01
Lizzie L Posted February 23, 2014 Posted February 23, 2014 I guess you could if you had a mirror far enough away.
Schneibster Posted February 23, 2014 Posted February 23, 2014 (edited) I think Schneibster's point about hyperbolic time is essentially about light cones. No. It's about the shape of time relative to space, as shown by the hyperbolic trig version of the Lorentz transform. This is based on the math, Lizzie. Do you not believe the math? Because there's no questioning it. This is basic relativity math. Not even any scary integrals. Just hyperbolic trig. t → (cosh s)t + (sinh s)x x → (sinh s)t + (cosh s)x y → y z → z Or, if you prefer, t → √(1 - (v2/c2)) * (t - vx)/c2 x → √(1 - (v2/c2)) * (x - vt) y → y z → z they are equal. BTW, see that c2 in the t transform? Remember I said we're moving forward in time at the speed of light? There's the mathematical proof. One last point: the traditional light cone is at precisely 45 degrees, and the units are c=1. Making 3d pictures misses the point; it should be t on the vertical axis and x on the horizontal, to make a Feynman diagram. The angle is 45 degrees because in the traditional Feynman diagram the speed of light and the speed of time are equal. Edited February 23, 2014 by Schneibster
michel123456 Posted February 23, 2014 Posted February 23, 2014 You cannot observe these things directly because you have to be at a distance equal to [latex]c\tau[/latex] in order to observe it a time [latex]t[/latex] ago. That is correct. What does that mean concerning the content of the past light cone? Can I directly observe the inside part of the past light cone?
Schneibster Posted February 23, 2014 Posted February 23, 2014 Relativity tells us that Space & Time form a continuuum, IOW that Space & Time are 2 sides of a same thing. If Space can be rotated in time, and reversely, and if as you say "It's its relations to the space dimensions that make it temporal or spatial", doesn't that mean that, in the end, Time and Space are exactly the same thing. But that doesn't mean they behave the same. They may be the same basically, but their relations to one another are what determines how we see them. When we transform them, we don't actually change any basic quantities.
studiot Posted February 23, 2014 Posted February 23, 2014 Michael123456, thank you posting a light cone pic. (post#139) But you have the basic deductive sequence back to front. We note (observe) that we cannot observe the future and posit the light cone explanation. Not the other way round. That is the scientific method. Schneibster, yes it is in the maths. So do you understand what you have posted? If so what is v?
Lizzie L Posted February 23, 2014 Posted February 23, 2014 In "the math" we have 4 axes - x, y, z and t. As John Baez says in Schneibster's link, we can set the speed of light to 1. That means that if the spatial axes are measured off in light-seconds, the time axis will be measured off in seconds, and the cone will have an angle of pi/4. And my fairly simple point is that those time units are defined in terms of some kind of clock, or oscillator, whether it's the orbit of the earth round the sun, the rotation of the earth, or some property of cesium.
studiot Posted February 23, 2014 Posted February 23, 2014 (edited) In "the math" we have 4 axes - x, y, z and t. With respect, I thought you had picked up the point that we don't. Two independent sets of axes are required. Because as I said we require at least two entities for the comparison The 'transformation' in schneibster's post#158 refers to the mathematical link between them. I await his explanation of v Edited February 23, 2014 by studiot
Schneibster Posted February 23, 2014 Posted February 23, 2014 (edited) Lizzie, if you go down all the tracks what you're going to find is that spacetime is a postulate of relativity. And that space and time are postulates of Galilean and Newtonian physics, as well as Aristotelian. The reason you keep getting stuck on time is because you learned Newtonian physics, not relativity. Special relativity shows the shape of time. In mathematics terms, you're endlessly repeating, "but you haven't defined zero!!!" With respect, I thought you had picked up the point that we don't. Two independent sets of axes are required. Because as I said we require at least two entities for the comparison The 'transformation' in schneibster's post#158 refers to the mathematical link between them. I await his explanation of v That mathematical link shows both time's essential sameness to space, as well as the difference in its relations to space dimensions from the way they relate to one another. This is as much of "the character of dimension" as we know. A transform doesn't link two things that are different. It can't. You can't define a transform that turns time into water, or love into electricity. You can define a transform that turns time into space, and vice versa. And it really works that way. So in fact, your claim the transforms don't prove anything is wrong. They do prove something: time and space are, essentially, the same. So, you can actually see space. OK, well, time is no different. It's only difference is in its relation to space. To another time dimension, as uncool pointed out, it appears right circular, just as the space dimensions all appear to one another. It's only when we start having rotations-- in the case of time, that means velocities, or rapidities-- that we have to transform things from time into space, and vice versa, this way. In fact, those transforms are pretty much the most information we have about time and space themselves. Edited February 23, 2014 by Schneibster
Lizzie L Posted February 23, 2014 Posted February 23, 2014 With respect, I thought you had picked up the point that we don't. Well, no I hadn't, but I appreciate the respect Two independent sets of axes are required. Because as I said we require at least two entities for the comparison That's fine. But we still have spatial axes and time axes, don't we? The 'transformation' in schneibster's post#158 refers to the mathematical link between them. Yes indeed. So explain to me the units on the two types of axes, or explain to me why there aren't two types of axes, or why we don't need units for them. I await his explanation of v Well, I don't understand his claim that we're moving forward in time at the speed of light I don't see how we can move forward in time at the speed of light i.e. at distance per time interval 1
studiot Posted February 23, 2014 Posted February 23, 2014 (edited) That's fine. But we still have spatial axes and time axes, don't we? The 'transformation' in schneibster's post#158 refers to the mathematical link between them. Yes indeed. So explain to me the units on the two types of axes, or explain to me why there aren't two types of axes, or why we don't need units for them. Yes we still have x,y,z,t but remember that there is no absolute coordinate system. That one refers to that entity and that light cone. All measurements in xyzt are as observed by the entity at the apex of the cone. Any other entity will have her own cone with coordinate system x'y'z't' Roger Penrose didn't realise the confusion his beautiful diagram would cause. I still await the explanation of v Edited February 23, 2014 by studiot
Schneibster Posted February 23, 2014 Posted February 23, 2014 In "the math" we have 4 axes - x, y, z and t. As John Baez says in Schneibster's link, we can set the speed of light to 1. That means that if the spatial axes are measured off in light-seconds, the time axis will be measured off in seconds, and the cone will have an angle of pi/4. And my fairly simple point is that those time units are defined in terms of some kind of clock, or oscillator, whether it's the orbit of the earth round the sun, the rotation of the earth, or some property of cesium. No, actually they're defined by the speed of light, which is a constant for all observers in all frames.
Lizzie L Posted February 23, 2014 Posted February 23, 2014 Yes we still have x,y,z,t but remember that there is no absolute coordinate system. That one refers to that entity and that light cone. I get that. My point is really not very profound and it is simply that along the spatial axes, relative or not, we have units of light-seconds (or whatever time unit you want to use) and on the t axis you will have units of seconds (ditto, if you are setting c at 1). So we need a definition of seconds (or years or whatever). For which we need to refer to an oscillator, no? All measurements in xyzt are as observed by the entity at the apex of the cone. Sure. I get that. I didn't not Any other entity will have her own cone with coordinate system x'y'z't' Absolutely. But it's orthogonal to my point, as it were Roger Penrose didn't realise the confusion his beautiful diagram would cause. It's a beautiful diagram.
Schneibster Posted February 23, 2014 Posted February 23, 2014 (edited) Well, I don't understand his claim that I don't see how we can move forward in time at the speed of light i.e. at distance per time interval Did you read the traditional Lorentz transform in post 158 156? Read the BTW part at the end. That's what the necessity of that factor of 1/c2 is. That's why it's there. If we were (impossibly) accelerated to the speed of light, we would be rotated so that what appears to everyone not sharing our velocity to be x, appeared to us to be our future or t, and what appears to everyone not sharing our velocity to be t to be the direction we're moving, or x. This is not a matter of perception. It is a matter of the actual character of time and space. Edited February 23, 2014 by Schneibster
Lizzie L Posted February 23, 2014 Posted February 23, 2014 No, actually they're defined by the speed of light, which is a constant for all observers in all frames. Well, no, you can't define the time by the speed of light. You can express distance and time in terms of the speed of light, so that distance is measured in, say light-seconds, as you suggested, and if you want to keep your conic angle at pi/2 then you can measure your time in seconds. But that won't help you define the seconds.
Schneibster Posted February 23, 2014 Posted February 23, 2014 (edited) Let's try another angle: Why is the speed of light constant? Well, no, you can't define the time by the speed of light. You can express distance and time in terms of the speed of light, so that distance is measured in, say light-seconds, as you suggested, and if you want to keep your conic angle at pi/2 then you can measure your time in seconds. But that won't help you define the seconds. I am most very sorry to directly contradict you but in fact the speed of time is defined by the speed of light. You are totally ignoring the math, Lizzie. Go back and look at the Lorentz transforms again. Post 158.156. Studiot used the wrong post number above, I think. Edited February 23, 2014 by Schneibster
studiot Posted February 23, 2014 Posted February 23, 2014 Time is measured in seconds, distance in metres. Both by international convention I have no problem with either and no wish to develop alternative units based on c or 'plank' dimensions etc. There is another current thread here where a GCSE student was led to make the classic units mix up because too many non standard units were used in his question. Consistency of units is a big thing of mine. Perhaps swansont will tell us about an old particle physics unit - the barn.
Schneibster Posted February 23, 2014 Posted February 23, 2014 What do you mean by "the speed of time"? The speed at which future seconds become past seconds. It's one second per second. Which is c.
Lizzie L Posted February 23, 2014 Posted February 23, 2014 Well, if we are going to measure time in seconds, that's fine by me, and by using the speed of light we can readily get a distance measure from that e.g. light-seconds (we don't need metres as well). But in that case I rest my case: time is measured in terms of change - if you don't have a changing thing, you can't measure time. And if you can't measure time, you don't have a way of putting anything on a t axis. QED *harrumph*
Schneibster Posted February 23, 2014 Posted February 23, 2014 (edited) Time is measured in seconds, distance in metres. Both by international convention I have no problem with either and no wish to develop alternative units based on c or 'plank' dimensions etc. There is another current thread here where a GCSE student was led to make the classic units mix up because too many non standard units were used in his question. Consistency of units is a big thing of mine. Perhaps swansont will tell us about an old particle physics unit - the barn. I'm familiar with dimensional analysis (which is what that's called). Please explain why the Lorentz transform can change time into space and vice versa if they are "different things." It's only a transform; no more, basically, than (for example) changing the angle your x y and z point to, or changing the location of the origin. That's all transforms can do. They can't alter the basic character of things; if you "turn the corner" you won't "turn into a penguin." At least not via a transform. Well, if we are going to measure time in seconds, that's fine by me, and by using the speed of light we can readily get a distance measure from that e.g. light-seconds (we don't need metres as well). But in that case I rest my case: time is measured in terms of change - if you don't have a changing thing, you can't measure time. And if you can't measure time, you don't have a way of putting anything on a t axis. QED *harrumph* No. The shape of time forms the speed of light; the speed of light defines the shape of time. They are effects of a single cause: our universe obeys special relativity. I can put light-seconds on the t axis if I like. It will work fine. We can update all our time measurements to use light-seconds. And Lizzy, if we do, it will all work. All of science, all of engineering. No problem. Just gotta make all the unit conversions. Of course, having the unit of time be 2.997925x108 might be a bit unwieldy, we've got computers, it's no biggie. Edited February 23, 2014 by Schneibster
Lizzie L Posted February 23, 2014 Posted February 23, 2014 What do you mean by "the speed of time"? The speed at which future seconds become past seconds. It's one second per second. Which is c. Really?
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