How do we measure the degree of "change" between 2 systems?

[geordief]

Suppose we have 2 systems ,one of which derives from the other how can  one measure the difference between them (the amount of "change")?

Can we assume that the first system is comprised of n constituent parts and the other m constituent parts since these parts can interact and destroy/create  themselves?

Do we have to connect the two systems with an array of "lines of causality "?

[studiot]

30 minutes ago, geordief said:

Suppose we have 2 systems ,one of which derives from the other how can  one measure the difference between them (the amount of "change")?

Can we assume that the first system is comprised of n constituent parts and the other m constituent parts since these parts can interact and destroy/create  themselves?

Do we have to connect the two systems with an array of "lines of causality "?

Can you provide a bit more detail perhaps a simple example of the change ?

Traditionally we use the Calculus to measure change as in velocity is rate of change of position and acceleration is rate of change velocity etc.

But I am not sure if that is what you mean.

 

 

[geordief]

35 minutes ago, studiot said:

Can you provide a bit more detail perhaps a simple example of the change ?

Traditionally we use the Calculus to measure change as in velocity is rate of change of position and acceleration is rate of change velocity etc.

But I am not sure if that is what you mean.

 

 

It could be ,on the macro level  the arrangement of the solar system (discounting its position in the galaxy)

We have some 10(?) main objects-planets (let's discount the Sun for simplicity )

At 12 midday our time the various planets are set out in an arrangement and 12 midnight we have a new arrangement

At  12 midday the next day  there is a third arrangement

 

Calling the arrangents 1,2,3   can we measure how much 2 is changed from 1 and does 3 change from 1 to a greater degree?

I am not sure whether or not the lapse of time enters into any calculation or whether the configurations "stand alone" as it were.

I think it is unarguble that changes have happened  but can we measure that change for the system as a whole or  just by comparing individual  components of one system against  individual components  of the other system.

 

[KJW]

1 hour ago, geordief said:

Suppose we have 2 systems ,one of which derives from the other how can  one measure the difference between them (the amount of "change")?

Can we assume that the first system is comprised of n constituent parts and the other m constituent parts since these parts can interact and destroy/create  themselves?

Do we have to connect the two systems with an array of "lines of causality "?

This is a big question. I don't think there are any general answers, with the answer depending on the particular situation. For example, let the two systems be two different points in some abstract space. Then does the measure of difference between the two points depend on the path between them? In thermodynamics, functions of state such as entropy are defined explicitly such that the differences are independent of the path between the initial and final states in state space. By contrast, distances between points in ordinary space or spacetime do depend on the path between them.
 

 

[Halc]

Well, you posted this in relativity, so it needs to be stated that you seem to be referencing states at times relative to some inertial frame, say the frame of the center of mass of the collection of objects, which is stable in isolation.

The question seems to be how to express the states 1,2,3

34 minutes ago, geordief said:

I think it is unarguble that changes have happened  but can we measure that change for the system as a whole or  just by comparing individual  components of one system against  individual components  of the other system.

Sure, in state 2 the Earth object has rotated just over 180 degrees and is facing the other way. It has also moved around the solar system just like all the other objects.  I referenced the solar system center of mass, so given that reference, each of the objects has a position relative to that at each of the times 1,2,3.  It's a stable point of reference, so nobody is worrying about saying where Earth is relative to Jupiter since both have moved.

Measuring it is another thing, but measuring doesn't seem to be your question.

Edited Thursday at 09:11 PM by Halc

[geordief]

9 minutes ago, KJW said:

This is a big question. I don't think there are any general answers, with the answer depending on the particular situation. For example, let the two systems be two different points in some abstract space. Then does the measure of difference between the two points depend on the path between them? In thermodynamics, functions of state such as entropy are defined explicitly such that the differences are independent of the path between the initial and final states in state space. By contrast, distances between points in ordinary space or spacetime do depend on the path between them.
 

 

Your "abstract space" is  that a timeless  concept?

Is my question ,then connected to entropy?

Another  example of two differing systems  could be a shuffled pack of cards  and ,in these cases I have  feeling that  entropy   might be a method  of comparing one arrangement of the cards versus another.

Still ,my initial example  specified that one arrangement derived  from the other...so  I think time entered the frame,unlike the pack of cards.

[studiot]

1 hour ago, geordief said:

It could be ,on the macro level  the arrangement of the solar system (discounting its position in the galaxy)

We have some 10(?) main objects-planets (let's discount the Sun for simplicity )

At 12 midday our time the various planets are set out in an arrangement and 12 midnight we have a new arrangement

At  12 midday the next day  there is a third arrangement

OK so this is definitely not a Calculus problem that we can solve.

It is called the many body problem in Calculus gravitation.

The point of traditional calculation is the we assume a system passes from on point (or state in KJW's case) to another in a smoothe continuous fashion so that each following point is somehpow close to the previous one.

Such an assumption allows us to plot a path from one state, condition, place or whatever to another with infinitesimal intervening steps and never jumping.

 

This whole centuries old assumption was shattered in the mid 20th century with the discovery of chaotic systems that do not follow such a predictable path.

We do not know if a multiplanet system is long term chaotic or not but many very much simpler systems are.

 

33 minutes ago, Halc said:

Measuring it is another thing, but measuring doesn't seem to be your question.

That is a good question.

There is a difference between measuring after the event and prediction before the event.

Edited Thursday at 09:42 PM by studiot
spelling

[geordief]

15 minutes ago, Halc said:

It's a stable point of reference, so nobody is worrying about saying where Earth is relative to Jupiter since both have moved.

I wasn't sure where to post really but I often post in relativity  and thought it might be quite  close

 

I am indeed worrying about where Earth is relative to Jupiter  but I think you may be saying that the Sun's reference  frame "includes" that information .

Can we say that for a complete system it is possible to describe it  by using any chosen reference point and that all the individual  relationships can be bound up  in that one reference point?

From my lowly  knowledge  status  I wonder whether I can doubt it (or if I have expressed  myself at all cogently)

Edited Thursday at 09:26 PM by geordief

[studiot]

24 minutes ago, geordief said:

I wasn't sure where to post really but I often post in relativity  and thought it might be quite  close

 

I am indeed worrying about where Earth is relative to Jupiter  but I think you may be saying that the Sun's reference  frame "includes" that information .

Can we say that for a complete system it is possible to describe it  by using any chosen reference point and that all the individual  relationships can be bound up  in that one reference point?

From my lowly  knowledge  status  I wonder whether I can doubt it (or if I have expressed  myself at all cogently)

You need more than one reference point.

You also need a direction, at minimum.

 

A typical example would be how we measure compass bearings.

Compass bearings are measured clockwise from a chosen line called North.

 

A second system of measurement of the same thing is the cartographers and surveyors easting and northings you get on an OS map.

Bearings here are measured anticlockwise from a chosen line called East.

This second system is the normal mathematical method of measuring angles in polar coordinates.

[swansont]

2 hours ago, geordief said:

Suppose we have 2 systems ,one of which derives from the other how can  one measure the difference between them (the amount of "change")?

Change in what? It’s going to depend on the variable. The question is too vague.

[geordief]

13 minutes ago, swansont said:

Change in what? It’s going to depend on the variable. The question is too vague.

Yes ,I think I was  perhaps thinking along those lines.

I seem to want to describe or measure a "system as a whole" and am coming to the realization that a system may be the  "sum" of its internal relationships and moreover   the concept seems to run foul of the  idea that there is no absolute time or space.

Any system cannot be fixed  -only approximated  as such.

Still ,with my solar system  example of 1,2,3 states  if the third system was disturbed by a massive black hole would we have no hesitation in agreeing that the change between 3 and 1 was greater than that between 2 and 1?

We would have  to show that  one variable at a time  and then stick them all together to  model the system "as a whole"?

Edited Thursday at 10:09 PM by geordief

[Halc]

3 hours ago, geordief said:

how can  one measure the difference between them

OK, it does seem to be a measurement topic, and not one of expressability or predictability

Measurement of planets is hard due to the long delay between where it is and where you see it.

1 hour ago, studiot said:

There is a difference between measuring after the event and prediction before the event.

The OP didn't seem to reference prediction

 

1 hour ago, geordief said:

Is my question ,then connected to entropy?

Your OP seemed to have little to do with entropy. Your card shuffle example was one of a chaotic function, but the deck seems no more entropic before or after the shuffle, as opposed to if you play 52 pickup.

1 hour ago, geordief said:

I wasn't sure where to post really but I often post in relativity  and thought it might be quite  close

This seem to have nothing to do with relativity theory. Choice of coordinate system was necessary even in Newton's physics.

1 hour ago, geordief said:

but I think you may be saying that the Sun's reference  frame "includes" that information

The sun's frame is an accelerating one, more complicated.  I chose an inertial frame, but I didn't compute many numbers in it. Just >180 and 'faces the other way'.

38 minutes ago, studiot said:

You also need a direction, at minimum.

This is true, and you need two of them, not just one.  Given distant stars not in the system, we have that reference. The OP said to ignore the gravitational influence of the rest of the galaxy, but that doesn't mean we don't have external references.  Without it, picking a stable reference is possible (since rotation is absolute), but not as easy.

19 minutes ago, geordief said:

the concept seems to run foul of the  idea that there is no absolute time or space.

But I chose the CoM as the reference. That's not an absolute reference, sure, but the relationships between the planets can be derived from each planet's coordinate relative to that CoM.  Measuring it all is another problem since there's nowhere to be that sees where everything is at a given time since the distances are so large.

Edited Thursday at 10:28 PM by Halc

[swansont]

4 hours ago, geordief said:

Yes ,I think I was  perhaps thinking along those lines.

I seem to want to describe or measure a "system as a whole" and am coming to the realization that a system may be the  "sum" of its internal relationships and moreover   the concept seems to run foul of the  idea that there is no absolute time or space.

Any system cannot be fixed  -only approximated  as such.

Still ,with my solar system  example of 1,2,3 states  if the third system was disturbed by a massive black hole would we have no hesitation in agreeing that the change between 3 and 1 was greater than that between 2 and 1?

We would have  to show that  one variable at a time  and then stick them all together to  model the system "as a whole"?

There are directly measurable variables, though some are not (like entropy); you need to specify.

“system as a whole” doesn’t work, as there’s no way to guarantee a way of combining individual changes of variables of different quantities that makes any sense. (e.g. a change in position and temperature)