Iggy

I am treating them differently because they are different. One is time and the other three are space. You don't have 4 spatial coordinates. You have three of space and one of time. Regular motion is defined as a change in space per a change in time. You aren't addressing the problems of using two variables of time. Particularly, that we can only measure one. That is untrue. The spacetime metric recognizes the difference between space and time. It does so by having space and time carry a different sign. If treating space and time differently were a real objection you would object to measuring one with a ruler and the other with a clock. It isn't a real objection. You're trying to direct the conversation away from yet another problem. I asked specifically if you could graph it as a dot moving in the x-y plane or as a line in the x-y plane. The answer is that it is a line in the x-y plane. As a mathematical description, that is correct. Similarly, a space-time diagram with a metric, for example, of ds=dt-dx shows a line in the x-t plane. If you want to show or consider it to be a dot moving in the x-t plane (like your diagrams do and as your description says) you need another variable of time. That is the correct mathematical description. It is not a matter of opinion.

A dictionary could solve any disagreement. In an effort to make your argument work you are complicating things greatly. You have just described regular motion. As t changes, the spatial position of things change. At t=0 the spatial potion of the pencil is 0,0,0. At t=1 the spatial position is 1,1,1. That is good old fashion, regular, motion. A change in spatial position per a change in time. The speed is dx/dt. With only 4 coordinates the description "the pencil changed coordinates in spacetime" is not right. You could say "the pencil changed coordinates in space". Regular spacetime diagrams show a change in spatial position with respect to time -- three spatial dimensions and one time dimension. Your animated diagrams show a change in space-time position with respect to an additional variable of time. 4 spacetime dimensions and an additional variable of time. If you want to say *first* one object occupies 0,0,0,0 *then* another object occupies 0,0,0,0 you need an additional variable that represents "the first object..." and "the second object..." etc. You've ended up with 5 variables. Your diagrams show 5 variables. Do you know how to graph x=y? Do you think it is a dot moving in the x,y plane or do you think it is a line in the x,y plane?

Space is measured with a ruler and time with a clock. Space and time are mixed between frames when one person measures the distance between events entirely with a ruler (for example) and another measures the distance with some combination of a ruler and clock. In other words, some amount of space in one frame has become some amount of time in another frame. Your question is if some amount of space in one frame can become some amount of time in another frame then why can't some amount of motion through space in one frame become some amount of motion through time in another. The answer is simply that motion requires two dimensions. Time requires one dimension. Space requires one. Motion requires two. If you mix space and time between frames you are mixing one dimension for another. If you mix motion between frames you are mixing two dimensions with two others. It isn't the same thing. Does that make sense?

I suspect both black dots are meant to represent the same object but that the diagrams function differently. Motion requires two dimensions. We can only talk about motion through space because there is a detectable time dimension. Motion through time would require another time dimension which the frames in your animations provide. Your diagrams have two different "durations" because there is no other way to show or express the motion of a dot through space-time. The distance along the t axis is one variable of duration and the length of the animation (i.e. the number of frames) is another variable of duration. Only one variable of time is detectable. Motion through space is different from motion through time for that reason alone. Only one of them is measurable.

I agreed that C is the location of the event of the emission of light. The problem is not the location of point C on the diagram, but the frame number of the animation in which point C is at that location. In one animation you have the black dot and the red dot at the same t coordinate in the same frame. In another animation you have the black dot and the red dot at different t coordinates in the same frame. They cannot both be correct. Let's also be clear, adding a variable of time in the form of animation to a spacetime diagram is not standard and it does not give standard results. I disagree with the practice entirely, and I believe it is the reason you are having to draw inconsistent diagrams.

I would hope that we could agree that a space-time diagram which cannot include light cannot be correct.

I have consistently asked, since post 202, for you to add light to this diagram, I have told you that I do not understand it without the addition of light. If you could provide me with a version of that diagram with light or tell me how to correctly add light to the diagram I would be happy to answer all four questions.

Allow me to be more clear. You have frequently accused me of mixing up your two diagrams, but I believe adding light to the one diagram, would give the equivalent of the other diagram, except that the black dot is displaced which is something that your worldview doesn't allow because you've said that dots are objects which do not exist at multiple t values. For that reason I believe you are prevented from adding light to the first diagram. In other words, as Spyman pointed out, I don't think you can square the diagram immediately above (the one with light on it) with the following statement, I believe you made the first diagram in this post to explain that statement and that point of view and made the second diagram to explain a different statement and a different point of view, and that the two cannot be reconciled.

I believe you are correct about sticking to the less confusing quoting, and I freakin' love cheese nips! Honestly, Michel, I don't mean to be playing or to be anything but sincere. I'm curious how you would put light on this diagram. It's fine if you think I've done it wrong or if you want to explain some other reason or some other way of doing it. I just mean to ask how you would get light on that diagram.

Excuse me? I am quoting this: No, no, no. I filled in the ellipsis points that you added. I did that for context so as to not make things confusing. Please, I am not playing, If I have added the light incorrectly, can you please do it, or tell me how to do it so that I can understand the diagram?

No, no, no. Then you do it. Please, either put light on the diagram or tell me how to correctly do it.

If I draw a light ray from the black dot in this diagram, it will never reach the red dot. Like this: That is the correct way to put light on it? That is the same as this diagram with the addition of light?

Yes... Can you add the light or tell me how to add it please,

If we see it then its light reaches us, yes?

You have said these two things: "yes, the black dot is seen by the red dot" "Yes, the green dot is not observable from the red dot" Do you know what a contradiction is? You have to do something to fix these contradictions. They are your diagrams and your statements about them. Right now, the best that can be said is that you have an inconsistent interpretation of spacetime.

Yes!!! That's what I'm saying. You are saying the exact opposite: Yes. Have you changed your mind now? Or, do "yes, the black dot is seen by the red dot" and "Yes, the green dot is not observable from the red dot" make perfectly consistent sense, but I'm mixing and matching sentences talking about two different things like chili sauce with chocolate. Honestly?

I have mixed? I have mixed? They are your diagrams. You drew them both and made contradictory claims about them! If I draw light from the green dot it doesn't reach the red dot: I think you could have figured that out without me drawing it. It is the same as your diagram: In YOUR diagram the red dot doesn't see the green dot. A moving line between the green dot and the red dot *does not* make a light cone according to this diagram. Can you admit this please? The light ray hitting you in your eye can't be mixed with what you see? You say the light from an object hitting you in the eye has nothing to do with what you see. Are you serious with this? Point C, frame unknown. I can't give x and t values because you haven't labeled them and don't know at which frame it is because we've lost that information. You could never see an object comoving at point C. A triangle that looks like a past light cone fixed to point A (as in your other diagram) is not a past light cone.

If the black dot in this diagram is seen by the red dot, then the green dot in this diagram is seen by the red dot, But, that is clearly not what you said before and it clearly isn't what happens. You keep saying very contradictory things. It is nobody's fault that we are unable to square the contradictions you are telling us. You say that the black dot in the first diagram above is seen by the red dot... that is absolutely wrong according to the second diagram and everything you've said about it. You don't realize this, but the problem is that you have two different variables of time represented in these diagrams... one represented with the t axis and the other represented by the diagram's animation. This leads to contradictions because some aspects of time are being attributed to a change in vertical position on the t axis and others as changes between frames in the animation. I'm trying to explain why you are saying contradictions. That your views are contradictory is indisputable. We need to focus on why that is or how to fix it.

yes. Imagine more blue dots. You have the same problem with Spyman. Excuse me? Are you saying that the blue dots *are* seen by the red dot? Are you saying that the black dot is seen by the red dot? Please answer directly.

If you maintain what you said then we need to change your current diagrams. A past light cone consists of all the things you see at one moment in time. The things on this line: are *not* all seen at once. It is not a past light cone. It is, in fact, called a particle horizon. It is traveling through time, it is not a past light cone. I said the *positive* dx/dt section. That is the upper half of the thin black line on this diagram: The line that traces out the path of the light ray. The top section of that line has a positive slope, dx/dt. The lower half has a negative slope -dx/dt. Calling that section of line the "positive dx/dt section" was an easy way to identify the section that makes a past light cone for the red object. The black line has a slope that changes from -1/1 on the lower half to 1/1 on the top half. On a typical spacetime diagram the slope of a line is the speed of the particle in space over time. For example, light is sloped at 45 degrees because the line rises one unit of time for every one unit of space. Its speed is dx/dt or (1/1) or one. One lightyear per year for example. Slower objects make lines that are closer to 90 degrees. 90 degrees is at rest. The slope in the case of this line on this diagram changes from -1/1 (or, -1) to 1/1 (or, 1) between the bottom half and the top half

You aren't explaining the very obvious contradiction. You are talking around it. In your latest diagrams the past light cone is not "traveling with us in time". The triangle in this diagram is not the past light cone: In the following diagram the positive dx/dt section of the black line is a past light cone, but it is not "traveling with us in time". Have you changed your mind about your previous statement (please indicate), or would you like to change the present diagram?

But their observation will be different. By definition. Their observations will be different, but will be consistent. In your previous interpretation the observations were not consistent. But, that no longer matters because you have now completely changed your approach to diagramming spacetime in order to avoid this inconsistency. All I can do now is appreciate that you changed your mind and repeat Spyman in an effort to get you to admit it. You previously said that the surface of the past light cone is populated with objects that move through spacetime. This leads to some inconsistencies one of which I've been harping at. In your new interpretation: The past light cone does not move through time with the observer. In an effort to fix this you've created the same problem you previously had... But, according to your first diagram in this post light moves like so: The blue dot is therefore not the "point where the observer looks at". The problem is that the universe has one dimension of time and you are trying to show that one dimension as both a t axis and an animation. In other words, this is true in our universe: Objects move through space over time You are trying to make both of these things true: Objects move through space over time Objects move through time over time It isn't a position that is consistent with physics.

Same here. Let's re-read and I'll get some sleep and we'll get back together subsequent.

You can put as many observers as you want in space-time using relativity. It is not constrained by inconsistencies the way yours is. I understand your belief that Marion moved from 12:00:09 to 12:00:10. It means that if Marion is at 12:00:10 (if she is the black dot) then she cannot be at 12:00:09 (she cannot be the red dot) But, at 12:00:10, by your interpretation, according to Paul the red dot is Marion. This means that Marion is two different dots at the same time. You say that she can't be two different dots at the same time, and you say that she is two different dots at the same time depending on perspective. That is internally inconsistent... a serious problem that you haven't answered. Two different people can observe the world at the same time. This is a fact of the real world and space-time diagrams need to reflect that fact. There is nothing unsafe about simultaneous observations in a typical diagram and there is no reason for it to be unsafe. No space-time diagram has ever had a problem with comparing the observations of multiple observers. This appears to be something that you have made up (invented) because of the specific problem your worldview has, and you haven't done anything to support such a strange notion. If you didn't model objects in space-time in a manner inconsistent with reality you wouldn't have this problem. What is surprising is that you refuse to complete or consider both Paul and Marion's observations in the same diagram. This is surprising because, First, because that has never been a condition of space-time diagrams of any type. Diagrams have always included multiple observers. Second, because more than one observer exists between -2 < x < 1. They are both located in the area diagrammed so they both belong on the diagram. The problem with your interpretation is more than just diagramming. Regardless of the diagram, you say that Marion moves from 00:09 s to 00:10 s and that she can't exist at both times 'simultaneously'. At 00:10 s Marion is at 00:10 s according to Marion and 00:09 s according to Paul. Both observers, you say, are correct. At 00:10 s Marion exists at two locations in space-time. This fundamentally disagrees with your statements. Your 'solution' is to say that Marion cannot compare observations with Paul. But, in reality people compare observations all the time. One person's truth needs to agree with the truth of another. If Marion is a single dot on a spacetime diagram then either she is the red dot or the black dot. Yes, I have. According to the normal scientific interpretation and method, where is the object? A hint: the object does not exist at only one specific point along a world-line. Mass is a property of objects so the answer to "where is mass" is the same as the answer above. I have a feeling you will only accept an answer that gives the location of mass somewhere (some single specific location) along the world-line of the object because you presume that mass should multiply beyond its correct value if it exists at more than one time. I wish you understood that your presumption concerning mass comes from trying to fit the typical understanding of space-time (in which objects and mass are not dots moving on the manifold) into your understanding of space-time where they are. For the typical scientific functionality and interpretation of space time to make sense it would require a completely different view and understanding than the one you have... you don't appear to be able to think outside the box your views have put you in.

A few decades ago I heard CO2 lasted for a few decades or up to a century, but these days I hear numbers for the minimum "half life" for CO2 as at least 120 years and up to several centuries. Wow, that really is long term and relatively permanent. That surprises me -- and worries me!