# playing with 4D coordinates

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The position of an object (or an event) in spacetime can be described with a set of 4 coordinates:

3 spatial coordinates and 1 temporal.

(x,y,z,t)

Say we have event A with coordinates (0,0,0,0)

That represents something that happens at the origin right now.

Then some other random event B.

Say event B has coordinates (x,y,z,t) .

One can choose a set of spatial axes so that x axis is aligned to the direction between the observer and event B, so that we get simplified coordinates (x',0,0,t).

Now:

1.If B has coordinates (0,0,0,0) we can safely conclude that A=B (= sign meaning that A & B are 2 events that took place at the same place at the same time). If A & B are objects (and not events), then A & B are the same object. (or 2 objects that have collided).

2. If B has coordinates (1,0,0,0) we can safely conclude that A & b are different events, because they happened at different spatial coordinates at the same time. If A & B are objects then they are not the same object.

That's what happens when we change the spatial coordinate.

If we change the temporal coordinate, things are different.

3. If B has coordinates (0,0,0,1) we should safely conclude that A & B are different events, because they happened at the same spatial coordinates at a different time. If A & B are objects then we should conclude that they are not the same object (see point 2 above). But that is not what we conclude.

What we conclude is that objects A & B are the same object at 2 different time coordinates.

Why do we incorporate different properties to spatial & temporal coordinates? Why aren't they simple numbers ?

Edited by michel123456
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Events A & B in scenario 3 don't necessarily correspond to the location of the same object. Say an object is traveling along the x-axis with velocity v. We mark event A as the object crossing the origin. Event B, which is at the same location but later in time, will obviously NOT correspond to the location of the object because the object is currently located at the event (v,0,0,1).

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Events A & B in scenario 3 don't necessarily correspond to the location of the same object. Say an object is traveling along the x-axis with velocity v. We mark event A as the object crossing the origin. Event B, which is at the same location but later in time, will obviously NOT correspond to the location of the object because the object is currently located at the event (v,0,0,1).

Standed corrected.

But in scenario 3 we can conclude that A & B are the same object (as one possibility) while in scenario 2 it is impossible to be the same object.

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Standed corrected.

But in scenario 3 we can conclude that A & B are the same object (as one possibility) while in scenario 2 it is impossible to be the same object.

Sure, because in scenario 3 the events are separated by a timelike geodesic, whereas in scenario 2 they're connected by a spacelike geodesic. Events connected by spacelike geodesics can't possibly be causally related because light hasn't had enough time to go from A to B, and information can't travel faster than c.

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So, why are we putting such kind of different properties to space coordinates against time coordinate ?

Another example:

an objetc makes the following transformation:

A. from (0,0,0,0) to (1,0,0,0)

This is considered impossible, because the object cannot change spatial coordinates in zero time.

we must consider this:

B. from (0,0,0,0) to (1,0,0,1)

This transformation is what we call: "motion". The object changed coordinates, the object moved.

To be compared to the following transformation:

C. from (0,0,0,0) to (0,0,0,1)

This last transformation is what we call: "standing at rest". The object changed coordinates, but only the temporal one has changed. Here it seems that 'nothing happened" because only "time passes by".

It is not impossible (comparing to A). Which is a monumental difference.

Further, the common understanding of this change of coordinates is that the object did not "moved in time", but occupies both coordinates.

The object was at (0,0,0,0), now it is at (0,0,0,1).

As a matter of consequence, one must reconsider transformation B and make a corrective statement: that the object did not "move" from coordinates (0,0,0,0) to (1,0,0,1) but litteraly occupies both coordinates.

That is our common understanding.

I wish everybody a Merry Christmas.

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Merry Christmas, my guess is that because it's better than doing (x,y,z) with a notation presumably and also might be more suitable for radio since now in more of a linear algebra form.

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So, why are we putting such kind of different properties to space coordinates against time coordinate ?

Because that's how time works, vs how space works.

Another example:

an objetc makes the following transformation:

A. from (0,0,0,0) to (1,0,0,0)

This is considered impossible, because the object cannot change spatial coordinates in zero time.

we must consider this:

B. from (0,0,0,0) to (1,0,0,1)

This transformation is what we call: "motion". The object changed coordinates, the object moved.

To be compared to the following transformation:

C. from (0,0,0,0) to (0,0,0,1)

This last transformation is what we call: "standing at rest". The object changed coordinates, but only the temporal one has changed. Here it seems that 'nothing happened" because only "time passes by".

It is not impossible (comparing to A). Which is a monumental difference.

Further, the common understanding of this change of coordinates is that the object did not "moved in time", but occupies both coordinates.

The object was at (0,0,0,0), now it is at (0,0,0,1).

That's not the common understanding from a physics perspective, and as this is a discussion of physics, that's really the only perspective that matters.

As a matter of consequence, one must reconsider transformation B and make a corrective statement: that the object did not "move" from coordinates (0,0,0,0) to (1,0,0,1) but litteraly occupies both coordinates.

That is our common understanding.

Our speed through spacetime is constant, when measured a certain way. If the spatial component gets larger, the time component gets smaller.

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Because that's how time works, vs how space works.

That's not the common understanding from a physics perspective, and as this is a discussion of physics, that's really the only perspective that matters.

What is then the common understanding?

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What is then the common understanding?

That's a leading question. It's a misunderstanding because you aren't applying physics to the problem. Instead, you are trying to dictate to nature how it should behave.

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Too much math..

Objects are NEVER the same objects.

Take for example yourself - you're breathing, oxygen is absorbed from air, changed to co2 etc. etc.

Even if object is not alive it's constantly hit by photons, 65 billion neutrinos per cm3 per second from Sun. Air is heating it and cooling all the time by little fractions.

Constant change.

Edited by Przemyslaw.Gruchala
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That's a leading question. It's a misunderstanding because you aren't applying physics to the problem. Instead, you are trying to dictate to nature how it should behave.

The common understanding is a leading question?

In a spacetime diagram, an object is represented by its world line. So, if i understand correctly, an object is considered as occupying more than one set of 4D coordinates. Otherwise an object wouldn't be a line but a point.

Isn'it the common understanding?

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The common understanding is a leading question?

Sorry, I misread that as misunderstanding.

I gave you the common understanding. The four-velocity is constant: c

In a spacetime diagram, an object is represented by its world line. So, if i understand correctly, an object is considered as occupying more than one set of 4D coordinates. Otherwise an object wouldn't be a line but a point.

Isn'it the common understanding?

It's a trajectory. Not position.

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Sorry, I misread that as misunderstanding.

I gave you the common understanding. The four-velocity is constant: c

It's a trajectory. Not position.

What does that mean?

That objects change coordinates in spacetime ?

Because if that's the common interpretation, I agree with that. I thought that common understanding was different.

--------------------------------------------------------------

The question I am debating for so long with Iggy is the following:

_do you believe the object is static in spacetime, "existing" all the way long, represented in a spacetime diagram by its world line?

or

_do you believe that the object changed coordinates in spacetime?

And what I gathered from md65536

Events are static in spacetime, not objects. The objects change coordinates.

I thank him for that.

Edited by michel123456
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What does that mean?

That objects change coordinates in spacetime ?

Yes. You move through spacetime at c.

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Yes. You move through spacetime at c.

If i move, if i change coordinate, that means that the coordinate i leave remains empty. Correct?

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If i move, if i change coordinate, that means that the coordinate i leave remains empty. Correct?

Yes. You only occupy one set of coordinates.

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Yes. You only occupy one set of coordinates.

...on A Theory.

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Yes. You only occupy one set of coordinates.

So the common interpretation is that I am moving through spacetime, leaving empty the coordinates I left.

And also we know that this last coordinate is not directly observable.(i cannot directly observe my own past)

IOW in a spacetime diagram, the Observable Universe is entirely collated along the diagonals that pass through the observer. And the entire rest of the diagram is empty of objects.

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So the common interpretation is that I am moving through spacetime, leaving empty the coordinates I left.

And also we know that this last coordinate is not directly observable.(i cannot directly observe my own past)

IOW in a spacetime diagram, the Observable Universe is entirely collated along the diagonals that pass through the observer. And the entire rest of the diagram is empty of objects.

Not sure how you conclude that there are no other objects.

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Not sure how you conclude that there are no other objects.

Correct.

i should have stated:

if there are objects that fill the entire rest of the diagram, these objects are directly unobservable.

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Correct.

i should have stated:

if there are objects that fill the entire rest of the diagram, these objects are directly unobservable.

No, other objects are observable, but only at one location at a time.

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No, other objects are observable, but only at one location at a time.

At one time (say t=00), you pin in a spacetime diagram all the observable objects around you, what do you obtain?

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At one time (say t=00), you pin in a spacetime diagram all the observable objects around you, what do you obtain?

Their location at a time d/c in the past.

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Their location at a time d/c in the past.

O.K. that gives you a diagonal.

And at this same t=o, what can you plot on the rest of the diagram ?

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O.K. that gives you a diagonal.

And at this same t=o, what can you plot on the rest of the diagram ?

What else is there to plot?

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