Understanding common displacement

[michel123456]

In this simple diagram I am representing the displacement of an object from point a to point b (see below very short video explaining the concept)

 

I have put the axis X & Y, so the displacement takes place in the two-dimensional space of a sheet of paper. The sheet of paper is in orange colour

Since we are talking about an “object”  it is commonly understood that during the displacement, the object will go from a to b following the path [a,b]. When the object will reach point b, it will have gone from a (that looks evident but wait & see). The line ab is a path.

 

Now, it is also known from the laws of physics that this displacement could not take place without time. So let’s introduce the 3^rd dimension T.

The vertical axis is Time. We see that the path from a to b has been transformed from a path from a to c.

 

The projection of c upon the sheet of paper is point b and the projection of the same point c upon the XT plane is the point t.

My question is:

Why is it commonly understood that the line [a,b]represents a path contrarily to the line [a,t] that we do not commonly understand as a path?

The question arises because it seems to me that the commonly accepted representation of the line [a,t] is that it represents the object itself along TIME, i.e. that the object literally IS at all points of the line [a,t] .

 My interpretation is that it is not the case. To me the line [a,t] is a path (to be more precise, it is the projection of the path [a,c] ). It means that when the object is at point c, it is NOT at point a altogether.

When the coordinates of point c are occupied, the coordinates of point a are free & available for another object.

Thank you for your inputs.

 

This last diagram is the perpendicular projection as seen from the right side. We see the horizontal Y axis (of Space) & the vertical axis of Time. The blue line is the projection of the path [a,c].

Edited May 24, 2019 by Strange
Changed X to Y in last line (see next post)

[michel123456]

Sorry, it is the Y axis.

[swansont]

3 hours ago, michel123456 said:

ISince we are talking about an “object”  it is commonly understood that during the displacement, the object will go from a to b following the path [a,b]. When the object will reach point b, it will have gone from a (that looks evident but wait & see). The line ab is a path.

 

 

 

The projection of c upon the sheet of paper is point b and the projection of the same point c upon the XT plane is the point t.

My question is:

Why is it commonly understood that the line [a,b]represents a path contrarily to the line [a,t] that we do not commonly understand as a path?

What do you mean "we"?

It's not necessarily called a path, since there is only one way to arrive at that point (unlike any 2D or 3D space), but there is certainly a notion in physics that we travel through time to get there.

(I'm assuming here that "common displacement" means we can discuss this in terms of Newtonian kinematics)

 

Quote

The question arises because it seems to me that the commonly accepted representation of the line [a,t] is that it represents the object itself along TIME, i.e. that the object literally IS at all points of the line [a,t] .

Not as you've drawn it. The representation along time would be the projection of the line [a,c] onto the time axis. IOW, t should be on the T axis

And the object is at only one point for any value of time t (t is usually the variable here, but you are using at a value. So t will be the variable)

Quote

 My interpretation is that it is not the case. To me the line [a,t] is a path (to be more precise, it is the projection of the path [a,c] ). It means that when the object is at point c, it is NOT at point a altogether.

The particle is point a only at t=0 and it's also the case that x=0 and y=0 (assuming that a is at the origin, as shown)

Quote

When the coordinates of point c are occupied, the coordinates of point a are free & available for another object.

False and irrelevant. Multiple particles can occupy the same space and same time, but that's another part of physics. If you want to say that only one particle can exist per point, the statement is still false. A new particle can arrive at a as long as the initial particle is not at a. It does not specifically have to be at c.

 

 

[michel123456]

1 hour ago, swansont said:

What do you mean "we"?

The Human Beings generally.

 

1 hour ago, swansont said:

And the object is at only one point for any value of time t (t is usually the variable here, but you are using at a value. So t will be the variable)

Yes we agree.

 

1 hour ago, swansont said:

The particle is point a only at t=0 and it's also the case that x=0 and y=0 (assuming that a is at the origin, as shown)

Yes.

 

1 hour ago, swansont said:

A new particle can arrive at a as long as the initial particle is not at a. It does not specifically have to be at c.

Yes (I wonder if we are talking about the same concept)

Resuming:

Say that object C starts at point a and t=0.

What I say is that when the object C is at c (or anywhere else) the point a is free for another object (coordinate t=0 is free, C is not there any more)

Conventional explanation say that no other object Q can be at a because a was once occupied by the object C (coordinate t=0 is constantly occupied by C)

I hope you follow the concept & see the difference.

Edited May 23, 2019 by michel123456

[swansont]

12 minutes ago, michel123456 said:

The Human Beings generally.

Well, I disagree that that was the general view.

12 minutes ago, michel123456 said:

Resuming:

Say that object C starts at point a and t=0.

What I say is that when the object C is at c (or anywhere else) the point a is free for another object (coordinate t=0 is free, C is not there any more)

Conventional explanation say that no other object Q can be at a because a was once occupied by the object C (coordinate t=0 is constantly occupied by C)

I hope you follow the concept & see the difference.

You are using point a and point c as defined by spatial coordinates (e.g. when you say "at point a and t=0"), but occasionally it seems you are using them to define them with both spatial and temporal coordinates. This will lead to inconsistencies and confusion.

A new particle can be at spatial point a at any time after t=0, but under no circumstance will it have a temporal coordinate value of 0 if it is at that point.

[michel123456]

51 minutes ago, swansont said:

You are using point a and point c as defined by spatial coordinates (e.g. when you say "at point a and t=0"), but occasionally it seems you are using them to define them with both spatial and temporal coordinates. This will lead to inconsistencies and confusion.

Yes I use the points a & c as defined by both spatial & temporal coordinates. Why inconsistencies & confusion? Isn't that what you are doing in a spacetime diagram?

 

51 minutes ago, swansont said:

A new particle can be at spatial point a at any time after t=0, but under no circumstance will it have a temporal coordinate value of 0 if it is at that point.

Why? Take a look at the diagram again.

.

If the blue line [a,c] is a path, then its projection is also a path. Why would it be treated differently in one direction (the XY plane) than the other (the YT plane)?

 

Edited May 23, 2019 by michel123456

[studiot]

From what I can see you are running smack into the difference between the way Mathematics and Physics treats graphs in general and multiaxial graphs in particular.

In Mathematics scales along (all) the axes are just numbers.

Physics adds units to these numbers to give them meaning.

So either you can say that physics allows you to endow meaning that is not inherent (there) in the Mathematics,

Or you can say that in Mathematics you can do things you can't do in Physics.

[michel123456]

2 minutes ago, studiot said:

From what I can see you are running smack into the difference between the way Mathematics and Physics treats graphs in general and multiaxial graphs in particular.

In Mathematics scales along (all) the axes are just numbers.

Physics adds units to these numbers to give them meaning.

So either you can say that physics allows you to endow meaning that is not inherent (there) in the Mathematics,

Or you can say that in Mathematics you can do things you can't do in Physics.

Well I suspect that we  (the human beings) have given properties to Time that do not come out from a simple but rigorous geometric treatment.

I should have said "axiomatic properties".

 

[studiot]

4 minutes ago, michel123456 said:

Well I suspect that we  (the human beings) have given properties to Time that do not come out from a simple but rigorous geometric treatment.

It's good to bear that in mind.

 

[swansont]

1 hour ago, michel123456 said:

Yes I use the points a & c as defined by both spatial & temporal coordinates. Why inconsistencies & confusion? Isn't that what you are doing in a spacetime diagram?

No, you are not, and that’s why it’s confusing.

1 hour ago, michel123456 said:

 

Why? Take a look at the diagram again.

.

If the blue line [a,c] is a path, then its projection is also a path. Why would it be treated differently in one direction (the XY plane) than the other (the YT plane)?

 

Only one particle can be on that blue line. It can’t intersect any other trajectory without violating your condition of not having two particles occupy the same space.

The projection onto the xy plane can overlap.

[michel123456]

17 hours ago, swansont said:

Only one particle can be on that blue line. It can’t intersect any other trajectory without violating your condition of not having two particles occupy the same space.

The projection onto the xy plane can overlap.

Why do you say that?

I guess it is because the axis is labelled T.

If I had labelled Z, you would'nt have any problem, right? You would agree that the blue line is a path & that multiple points can be placed on it.

[Strange]

On 5/23/2019 at 8:10 AM, michel123456 said:

Why is it commonly understood that the line [a,b]represents a path contrarily to the line [a,t] that we do not commonly understand as a path?

These are both paths (to me). The first is a path through space, the second is a path through spacetime (a 2D projection of the path [a,c]).

 

On 5/23/2019 at 8:10 AM, michel123456 said:

The question arises because it seems to me that the commonly accepted representation of the line [a,t] is that it represents the object itself along TIME, i.e. that the object literally IS at all points of the line [a,t] .

 My interpretation is that it is not the case. To me the line [a,t] is a path (to be more precise, it is the projection of the path [a,c] ). It means that when the object is at point c, it is NOT at point a altogether.

I'm not sure what the difference is.

The graph represents that at time a, the object is at position a. At time t it is at position c. You could animate that and show the object moving between the two points. Or you can just consider it as a path showing the position at each time. These are just different views of the same thing.

In other words, the question as to whether the particle IS at all points on the timeline depends on what you mean by "IS". So, really, this is a philosophical question (see also "block time").

However, there is a difference between animating a path through space and one through spacetime. In that latter case you are implicitly introducing another measure of time - the external one that passes in our world. So it could be considered "cheating" a bit.

[swansont]

2 hours ago, michel123456 said:

Why do you say that?

I guess it is because the axis is labelled T.

If I had labelled Z, you would'nt have any problem, right? You would agree that the blue line is a path & that multiple points can be placed on it.

No two particles can have identical coordinates of (x,y,t).  This is YOUR stipulation, that two particles can't occupy a point.

 

[michel123456]

I never mentioned the word "particle" because I din't want to enter this part of physics.

I am talking about pedestrians & busses if you like, I called "objects" in my OP.

And the question is whether the blue line is a path or not, and whether its projection is still a path.

 

2 hours ago, Strange said:

These are both paths (to me). The first is a path through space, the second is a path through spacetime (a 2D projection of the path [a,c]).

 

I'm not sure what the difference is.

The graph represents that at time a, the object is at position a. At time t it is at position c. You could animate that and show the object moving between the two points. Or you can just consider it as a path showing the position at each time. These are just different views of the same thing.

In other words, the question as to whether the particle IS at all points on the timeline depends on what you mean by "IS". So, really, this is a philosophical question (see also "block time").

However, there is a difference between animating a path through space and one through spacetime. In that latter case you are implicitly introducing another measure of time - the external one that passes in our world. So it could be considered "cheating" a bit.

I could animate the 2D graph (this one below)

But since I introduce time as a vertical axis, I cannot animate it any more, that would be introducing a second time (cheating as you said). So I will refrain to do that ( I have learned from previous experience).

Now you wrote

2 hours ago, Strange said:

The graph represents that at time a, the object is at position a. At time t it is at position c. You could animate that and show the object moving between the two points.

No. I could animate the point going from a to b. The path [a,c] is in spacetime.

The question is: in the 3D diagram , can I say that the blue line [a,c] is a path and thus consider that at t=1, when an object C is at c it means that the point a is a free coordinate and receive another object Q.

The common reaction to that would be "Bogus, Q cannot be there because Q belongs to the past of C and as we (human beings) know the past cannot change."

But if I (myself) stick to the diagram, I can put Q & C altogether without any conflict. Q will be at a and C will be at c. No problem, no issue. The problem arises only when we (H.B.) give to the T axis this extraordinary faculty of "never change". As i said earlier, if I label the vertical axis Z, we have no problem. The problem comes from some axiomatic property that we input to the T axis.

The next step would be to say, whathever, if Q existed I would see the past change. Would I ?

 

The common conception is that Q is an ancient event of C, that the blue line represents the "life line" of C. It is a solid object that does not allow another object Q enter inside.

And that is thus my question: why do we consider things that way?

Edited May 24, 2019 by michel123456

[swansont]

46 minutes ago, michel123456 said:

I never mentioned the word "particle" because I din't want to enter this part of physics.

I am talking about pedestrians & busses if you like, I called "objects" in my OP.

And the question is whether the blue line is a path or not, and whether its projection is still a path.

“Path” does not have a strict definition in physics, AFAIK. So there is no justification in physics to say it is or is not a “path”. That would be a lay description, and I don’t see the importance of the name we attach to it. Perhaps you could clarify why this matters.

50 minutes ago, michel123456 said:

The question is: in the 3D diagram , can I say that the blue line [a,c] is a path and thus consider that at t=1, when an object C is at c it means that the point a is a free coordinate and receive another object Q.

The common reaction to that would be "Bogus, Q cannot be there because Q belongs to the past of C and as we (human beings) know the past cannot change."

That right. 

50 minutes ago, michel123456 said:

But if I (myself) stick to the diagram, I can put Q & C altogether without any conflict. Q will be at a and C will be at c. No problem, no issue.

The map is not the same as what is mapped.

50 minutes ago, michel123456 said:

The problem arises only when we (H.B.) give to the T axis this extraordinary faculty of "never change". As i said earlier, if I label the vertical axis Z, we have no problem. The problem comes from some axiomatic property that we input to the T axis.

Axiomatic? Or observed? (Not that it matters) The rule exists, and you aren’t following it. That’s why the problem arises.

 

50 minutes ago, michel123456 said:

The next step would be to say, whathever, if Q existed I would see the past change. Would I ?

That’s not a physics question. 

 

[ag400002]

Perhaps as you pass through and change position in relative time, you coordinate with absolute time when absolute time passes through you. 

   

[swansont]

31 minutes ago, ag400002 said:

Perhaps as you pass through and change position in relative time, you coordinate with absolute time when absolute time passes through you. 

Relative vs absolute doesn’t enter into the discussion.

[michel123456]

On 5/24/2019 at 1:51 PM, swansont said:

“Path” does not have a strict definition in physics, AFAIK. So there is no justification in physics to say it is or is not a “path”. That would be a lay description, and I don’t see the importance of the name we attach to it. Perhaps you could clarify why this matters.

Definition of "path" = a route or track between one place and another. (taken from https://dictionary.cambridge.org/dictionary/english/path )

I was also thinking to the word "trajectory" but the definition does not match exactly (it has already another meaning)

The concept is similar: on a path (or a trajectory) there is a single "object" traveling. The path itself is simply a set of coordinates, and the object C occupies only one of these, no matter its state of motion. it is a situation of multiple exclusive: if one coordinate is occupied the others are not.

In other words, my concept can be reduced to this: IF you exist today, you don't exist yesterday (anymore), and you don't exist tomorrow (yet). There is no "other yourself" in the past when you were born because the Time dimension has basically the same properties with the spatial ones. Time should not have any "special property" that freezes everything in it.

In this case, Spacetime should not be considered as a block, the past is free to evolve, the future also.

And the past & future can contain other objects than those we are currently observing. Which means that the Universe is much more filled than previously thought.

 

[swansont]

2 hours ago, michel123456 said:

Definition of "path" = a route or track between one place and another. (taken from https://dictionary.cambridge.org/dictionary/english/path )

I said definition in physics. There are words that in a particular science do not mean what they do in common use.

2 hours ago, michel123456 said:

I was also thinking to the word "trajectory" but the definition does not match exactly (it has already another meaning)

The concept is similar: on a path (or a trajectory) there is a single "object" traveling. The path itself is simply a set of coordinates, and the object C occupies only one of these, no matter its state of motion. it is a situation of multiple exclusive: if one coordinate is occupied the others are not.

That's fine, and consistent with what I have said.

2 hours ago, michel123456 said:

In other words, my concept can be reduced to this: IF you exist today, you don't exist yesterday (anymore), and you don't exist tomorrow (yet). There is no "other yourself" in the past when you were born because the Time dimension has basically the same properties with the spatial ones. Time should not have any "special property" that freezes everything in it.

OK. What does this have to do with physics?

2 hours ago, michel123456 said:

In this case, Spacetime should not be considered as a block, the past is free to evolve, the future also.

How does the past evolve? Causality is a real thing.

2 hours ago, michel123456 said:

And the past & future can contain other objects than those we are currently observing. Which means that the Universe is much more filled than previously thought.

Again, causality is a real thing. So is conservation of energy.

[michel123456]

1 hour ago, swansont said:

How does the past evolve? Causality is a real thing.

Like the present evolves. Exactly in the same way.

[swansont]

1 hour ago, michel123456 said:

Like the present evolves. Exactly in the same way.

Is there any evidence that the past evolves? Remembering that in physics, one must define the present as some value of t, and in an inertial frame of reference, all points are assigned that value (Einstein clock synchronization). Other than that, “past” and “present” are not rigorously defined. Their common use is inconsistent with special relativity.

So if there is a snapshot taken at t=0, under what condition at some time t>0 would the t=0 situation be different?

[michel123456]

18 hours ago, swansont said:

Is there any evidence that the past evolves?

Basically, everything we are observing with our telescopes belongs to the past, and it is evolving.

To me it shouldn't matter whether things are in the past, the present, the future: everything is evolving (reminding Heraclitus).

Simply it happens that the things of the Universe that cross our line of sight are the one we observe (looks like a tautology). And since our line of sight is dictated by the Speed Of light, we are observing the objects that lie on the diagonals of a spacetime diagram. All the other objects are not directly observable, so we consider they don't exist.

The regular way to look at a spacetime diag. representing the Universe is something like this:

We (the human beings) are on planet Earth at point A. What we are observing at t=0 lies on  the blue thick lines. That is the image we get from the Universe in which we recognize Galaxy G1. I will call it +G1 because it is real thing we are actually observing (a reality solid as the desk in front of you). We are figuring that "today at T=0" the galaxy +G1 is not there anymore but has moved to point G1 where our calculations give us some new coordinates. We have no contact with point G1 and we must imagine that Galaxy G1 is there. At some time in the future the galaxy will be in point -G1 (the negative shows simply the future). In our current understanding, G1 is one and single Galaxy that traveled through time. The diagram is full of such galaxies that completely fill the diagram. In this diagram nothing moves (not even us). It is the Block Universe, frozen. For showing the passage of time, we must slide point A upwards. And Galaxy +G1 is sliding upwards at the same pace.

Now, I (myself) am considering that this is a bizarre way of thinking, because the Time dimension does not behave the same way as the other 3 spatial dimensions (see argumentation above).

What happens when we are taking back from Time this peculiar power to freeze everything?

Well, the result still works.

The observable Universe is still exactly on the blue thick lines. And as we are sliding upwards in the diagram, so is the Observable Universe.

The only bizarre element is that the diagram is strangely void. How in the hell is it possible that the O.U. corresponds exactly to our diagonal?

The next step is to fill the diagram (the entire sheet of paper) with galaxies. That doesn't change much to the situation: as we slide above in the diagram, so are all the galaxies, so is the O.U. Simply, as I stated before, it happens that the things of the Universe that cross our line of sight are the one we observe.

After that I will return the question: what is the evidence that the past doesn't evolve?

 

Edited May 29, 2019 by michel123456

[swansont]

2 hours ago, michel123456 said:

Basically, everything we are observing with our telescopes belongs to the past, and it is evolving.

This light travel delay is known and accounted for in physics, and is one example of why physics tends not to use such vague terminology as past and present.

2 hours ago, michel123456 said:

To me it shouldn't matter whether things are in the past, the present, the future: everything is evolving (reminding Heraclitus).

Stricter definitions are required to discuss this.

2 hours ago, michel123456 said:

Simply it happens that the things of the Universe that cross our line of sight are the one we observe (looks like a tautology). And since our line of sight is dictated by the Speed Of light, we are observing the objects that lie on the diagonals of a spacetime diagram. All the other objects are not directly observable, so we consider they don't exist.

The regular way to look at a spacetime diag. representing the Universe is something like this:

We (the human beings) are on planet Earth at point A. What we are observing at t=0 lies on  the blue thick lines. That is the image we get from the Universe in which we recognize Galaxy G1. I will call it +G1 because it is real thing we are actually observing (a reality solid as the desk in front of you). We are figuring that "today at T=0" the galaxy +G1 is not there anymore but has moved to point G1 where our calculations give us some new coordinates. We have no contact with point G1 and we must imagine that Galaxy G1 is there. At some time in the future the galaxy will be in point -G1 (the negative shows simply the future). In our current understanding, G1 is one and single Galaxy that traveled through time. The diagram is full of such galaxies that completely fill the diagram. In this diagram nothing moves (not even us). It is the Block Universe, frozen. For showing the passage of time, we must slide point A upwards. And Galaxy +G1 is sliding upwards at the same pace.

Block universe 1) does not preclude motion, and 2) is an interpretation of physics. They are a way (as with QM interpretations) for people to make sense of the physics, but are not, by themselves, physics.

2 hours ago, michel123456 said:

Now, I (myself) am considering that this is a bizarre way of thinking, because the Time dimension does not behave the same way as the other 3 spatial dimensions (see argumentation above).

What happens when we are taking back from Time this peculiar power to freeze everything?

Well, the result still works.

The observable Universe is still exactly on the blue thick lines. And as we are sliding upwards in the diagram, so is the Observable Universe.

The only bizarre element is that the diagram is strangely void. How in the hell is it possible that the O.U. corresponds exactly to our diagonal?

The next step is to fill the diagram (the entire sheet of paper) with galaxies. That doesn't change much to the situation: as we slide above in the diagram, so are all the galaxies, so is the O.U. Simply, as I stated before, it happens that the things of the Universe that cross our line of sight are the one we observe.

After that I will return the question: what is the evidence that the past doesn't evolve?

As I said, causality and conservation of energy.

It is part of special relativity as well — times and distances are relative, but events are not. If an event is seen to happen in my frame, it happens in all frames. There are no circumstances where a collision between two objects is observed and at some later time, the collision didn't happen. Or, as with your earlier example, which I was using as a guide for what you meant: if an object is at point a (at 0,0,0), then there cannot be a different object at that point in our reckoning of the past. It is impossible that Q is at that point. The past does not evolve in that way.

[michel123456]

1 hour ago, swansont said:

(...)Or, as with your earlier example, which I was using as a guide for what you meant: if an object is at point a (at 0,0,0), then there cannot be a different object at that point in our reckoning of the past.(...)

Yes, the restrictions of Relativity are counting.

What I am proposing is that our reckoning of the past is relative. An event in our past will be perceived  as immutable, and there is no physical way to "jump" into a FOR that would see otherwise (that would need an override of SOL). In the diagram it is represented as a "jump in time" along the life line: it is not physically allowed.

In my POV we are sliding into the time dimension without knowing what is in our front or in our back because of Relativity. Relativity forbids us to have any direct knowledge of these objects.

But we should have indirect indications that those objects exist.

One of the indication would be that the Observable Universe is too empty (that there is not enough matter in it).

[swansont]

3 minutes ago, michel123456 said:

In my POV we are sliding into the time dimension without knowing what is in our front or in our back because of Relativity. Relativity forbids us to have any direct knowledge of these objects.

But we should have indirect indications that those objects exist.

What does that have to do with changing past events? Not knowing is not the same thing as changing.