michel123456

Thank you DH, it was a very clean explanation. I see no divergence between your text and my understanding. Your explanation is valid for a still frame of the diagram. When the diagram gets dynamic, it becomes weird, since "dynamic" means "time" and I suppose it is not so correct to have 2 times, one under "dynamic representation" and one under T axis. So you agree that the right part of the diagram is not visible. (sorry but I would like a clear answer about the black zones). Besides (a little bit out of subject) I don't understand how the Great Army progressed about 200 km in a single day between 6th & 7th of December, and gained 2000 soldiers in the meanwhile. (related to Minard's diagram).

No. It is a moving diagram. Time is already there.

If you replace kinetic energy with money, saying that the bus has kinetic energy is like to say the bus is full of money. The problem is that the amount of money is 10 dollars for you, 1000 dollars for another, 10 billions dollars for another observer. But when you step on the bus searching for the pactole, what do you find? No money. Kinetic energy is not on the bus. Kinetic energy is somewhere else, hidden by a trick in spacetime, that makes it relative to motion. So, if you want to understand kinetic energy, I mean understand, not only calculate, you must understand motion. If you want to understand motion, you must understand space and time. That is where I focus.

Following your definition of events, the small dots in the moving diagram can only be objects. When you draw a still spacetime diagram on a sheet of paper, objects are lines, and events are dots. But when the diagram is moving, the lines become dots, and dots become flashes.

I guess so. ??????????????? Events that last in time (like the event of N. Armstrong broadcasting for thousands of years?)......and they are distincts from underlying objects ? (like the event of the sun shining for thousands of years but distinct from ...the sun?). That makes no sense to me. Yes, Déjà vu, Spyman. Do you agree at least with the black zones?

I am trying to figure what you say. ........ This is how i understand it, see below: The black zones we cannot see. The white diagonals we can see. When an event cross the line, it comes from a black zone and vanishes in another black zone.

Don't worry, AJB is thinking about it.

Anyway, the interior part that is visible will remain very close to the diagonal, technically speaking. Then, if you erase all parts that are not visible on this diagram, you will remain only with the 2 diagonals going from the center to the lower part. And then (my question #2) an accelerated observator should observe events popping from nowhere (look carefully near the diagonals at what happens). Is that correct?

At least we agree on something. Under the same assumption, can we now see an event that is inside the past cone?

I am talking about observable through light or EM radiation. Do you disagree with the following DH's statement?

That is not the question. O.K. I'll bite. The bus has no kinetic energy. But the infinite set of FOR that move around the bus observe & measure that relatively to them, the bus has kinetic energy. You have an infinite set of FOR that measure a set of values from infinite to zero (not to minus infinite). What do you choose?

No, that is the broadcast, not the event. I mean, if you look into your telescope, can you observe the physical event of N.A. on the Moon?

You are messing things IMHO. The smash between the bus & me will have to do with acceleration. The bus will produce a force on me in order to make me change velocity. This change will be done in a too small period of time, and that will kill me. Sorry Iggy, I don't answer to your kinetic energy question because I want to remain on space contraction question. That's the question.

Do you mean the diagram is wrong? Or simply that it involves "concepts in advanced physics that dive into the deep end of the trivial minutia pool of knowledge". Anyway, you seem to have a really good understanding of this diagram (@ DH). You wrote (and I agree 100%): and And now the stupid question: Can we observe today the event of Neil Armstrong broadcasting "That was one small step ..."? Can we observe anything that is inside our past light cone?

I see you whish to introduce gravity by the means of the equivalence principle. Why do I ask? Because it is a starting point. An object observed at rest can never be observed longer, no matter the state of motion (underlined for Spyman). In other words, it exists an infinite set of FOR that will measure an infinite set of dimensions for a specific object, dimensions going from from infinitely small to D. (not to infinitely big) D is the dimension of the object as measured at rest. What do you think ? That all FOR are equal beween them? or that there is something special in D ?

There will be something missing. That's the reason he has to draw a diagram first. He may understand why there is only one solution to the problem, and how to put that into equation.

I was asking for an example where the shuttle is larger than 37,19 meters long.

Obviously, that didn't help. where is your problem? 1. understanding the parameters of the question? 2. which equations to use? 3. or the resolution (the math)?

Looks like homework to me. I always take a sheet of paper,a pencil, and put the question into a small diagram, that helps a lot.

This comes from a Spyman's post#49 in another thread. Here is a diagram from the wikipedia article on Special Relativity under "Reference frames, coordinates and the Lorentz transformation" title : "Diagram 1. Changing views of spacetime along the world line of a rapidly accelerating observer. In this animation, the vertical direction indicates time and the horizontal direction indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The lower quarter of the diagram shows the events that are visible to the observer, and the upper quarter shows the light cone- those that will be able to see the observer. The small dots are arbitrary events in spacetime. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the view of spacetime changes when the observer accelerates." I have 3 questions: 1. It is said in the explanation that "The lower quarter of the diagram shows the events that are visible to the observer" which gives the impression that the observer can look at his own word line. Is that so? 2. The upper part of the diagram is the observer's future, so he cannot observe it. The left part is out of the light cone, so it is also unobservable. The right part of unobservable for the same reason. So if this diagram is correct, there should be events that pop up from nowhere when they enter the lower part of the diagram. Is that correct? 3. If you look carefully, they are some moments when events (little dots dancing everywhere) are going back in time (time is the vertival axis). Is that compatible with observation? see picture below:

Can you show me a concrete example of such a coordinate system? How is it possible to decelerate from an "at rest" situation?

Wait. When you have meters (m) you get one dimension. When you have meters by meters (m^2) you get 2 dimensions. But when you have seconds by seconds (s^2) you don't? Where is the difference?

Interesting comment. The curve is one dimensional. The graph is 2 dimensional. And if you put units on X (say meters), then Y are square meters: 2 dimensional. I guess the growing graph of increasing surfaces can be represented 3D (a pyramid).

I don't know if I am allowed to answer, but if you read carefully SMF's post, the answer is hidden there.

Take a cube, slide it, or rotate it, and you get the 4th dimension through motion. If you take the cube and let it fall down, you are in fact using twice the time dimension because a free falling body is accelerating (m/s^2). It could be considered as a 4 dimensional event taking place in time: in other words maybe a 5 dimensional event.