# Event Space

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#### Woody

I have been toying with an idea, and thought I would share it, to see if anyone else wants to play...

We can describe positions in spacetime as events.
Observers in different reference frames, travelling at different velocities, will disagree about the relative positioning of these events.
However they will not disagree about the causal connections between these events.
So we can construct a structure of events and the causal links between them, which will be agreed by all observers.

Does this then imply a some how "more fundamental" level of "event space" and it is our view of this event space and how we interpret it in terms of space and time that changes due to our respective reference frames?

#### donglebox

This is a very natural and intuitive idea.
I don't know the advantages of this structure for solving the problem of multi node traffic flow,
It's also possible that if you're referring to more essential interactions, everyone has different mapping methods.
That is a powerful way of thinking to construct these models directly in ideas, rather than through formal combinations. It can be called the school of intuitionism.
To express these models, May be it is necessary to describe them accurately.
There are many indescribable problems, which are called Uncomputable problems.
For existing methods,
There are some similar graph node models, or corresponding relationships in group theory structure, which may be able to describe your ideas by analogy.
There are practical models from the production consumer model to the more complex models in the engineering method.
Some problems can be described by general equation, ODE, PDE equation according to complexity level,
But for most complex problems of more than three objects, what I know is that mathematicians can only approximate the solution without exact form.

#### Woody

You seem to be talking about the classic NP problem of the "travelling salesman"
I was looking toward the issues of the 4 dimensional spacetime and relativity
which cause different observers moving at different velocities to give different interpretations of distance in both space and time.
I am suggesting that there is an underlying structure of events and causes, which will be the same for all observers,
but that that travelling at different velocities causes different observers to view this underlying structure from different "angles"
and thus make different measurements of the space and time distances between events.
I do however see that group theory could be a way of approaching the connection between an event/causality structure and observed spacetime.

#### donglebox

Yes, TSP problem. I'm too far away. Please forgive me for my statement.

I just don't know the subject

You mentioned that there is an existing structure, even if it is a group operation, can this structure be described by a matrix? For example, the conclusions and recognition patterns of observers can be reduced to a digital field sieve (matrix) equivalently,

#### Woody

I have been trying to decide what the dimensionality of event space might be.
One dimension is obviously the causal dimension (similar to the time dimension)

However, each event can have causal links to multiple subsequent events.
I think that in addition each event can have causal links to multiple preceding events
(preceding events which have caused this event to occur)

I am imagining causality "cones" of events that caused the chosen event,
and of events that will be caused by the chosen event.
These would correspond to the light cones of a Minkowski diagram.

What happens to this event/causality network when we throw the QM probability spanner into the works?

#### Farsight

Does this then imply a some how "more fundamental" level of "event space" and it is our view of this event space and how we interpret it in terms of space and time that changes due to our respective reference frames?
I don't think so. Space is real, motion is real, and the things that happen are real. But a reference frame is an abstract thing. You can't look up to the clear night sky and point out a reference frame. Your reference frame is little more than your state of motion. In similar vein whilst space is real and events are real, "event space" is an abstract thing too.

#### neila9876

@ Woody:
I suggest that a better idea is to distinguish "event" from position of space time."Event" is something happens in space time and always concerns a "course" or say a series of positions of space time.
I always say that I have a bad habit that I sometimes even try to put aside time t for simplicity.
Actually people have to "seperate variants" in calculations, e.g. motion of electron in Coulomb field in QM.
There are two kinds of "play": play more and more complicated and play more and more simple...The local dark force of Jiangmen city belongs to the former one.haha...to the degree of the most complicated in cosmos.

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#### donglebox

There may be several situations in selecting which causal variable
1，We can construct a variable that mirrors itself. When it sees its own state at the last moment, it determines whether the current state is T or F
2，We can also construct a variable that is numerical, only related to its last moment, so it may become divergent and infinite. Or it may be locked in a value.
We need to consider avoiding those values in the model
3，We can also construct variables that are related to the original time and have a positive weighting relationship with the QM probability of the previous time,
In the case 3 of only one variable, QM probability wrench may not be negative, 0 < r < 1,
This scale of growth sometimes collapses, but it still grows in the long run.
But it may not be true.
The real situation may be like the stock market index. People will depend on the last moment of joy or panic,And expectations for fantasy
until the big external forces play an end role.
This may be a good analysis object

In these analyses, we can divide the current value by the above one to obtain a random numerical sequence

Cellular automata has demonstrated that in an incomplete observation process (discrete time and space),
Random looking sequences can also be constructed from regular transformation directions
In a complete system process, once all paths in the space are traversed completely,
These sequences will restart the previous path

Replay everything. (I've experimented with this in one complete cellular automata.)
I think the probability in QM may also have this rule.

In other words, probability itself exists in causality.

When we do not consider the above, we can also regard QM wrench as a variable.
If so, it will continuously change the tensor matrix of time and space, and pass on the changes,

From a global perspective, this is no different.

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#### Woody

The point of my eventspace is that all observers will agree on its structure, regardless of their reference frames.

If an observer sees that event A causes event B, then all observers will agree that event A caused event B.
This requires that all observers must agree that event A happens before event B
but if they are moving at different velocities, they will disagree about the timing and positions of events A and B.

However if we have an event C that is not (directly) causally connected with events A and B
some observers might see it as occurring before event A, while other observers might see it as happening after event B.
If we introduce event D (say an electron emitting a photon)
and have the photon interacting with a second electron at event C, while the electron interacts with another particle at event A
then all observers will agree that event D occurs before event A (and B) and also before event C
but they need not agree on the order of occurrence of event C relative to A and B.

Perhaps "causallity-space" might be a better term than "eventspace"
(I just liked the slight pun of an event space also being a term that might be applied to, for example, a theater).

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#### Woody

I guess what I am saying is that there is an underlying topological structure, determined by causal connections, which will be agreed by all observers.
However, how that underlying topological structure is translated into spacetime will differ depending on the relative reference frames of the observers.

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