The Illusion of Time

[studiot]

 

but what I read was that you wanted to know if we occupied multiple time coordinates. And we do.

 

No, that was not the question posed.

 

I stated that as a fact, with some backing reasoning.

 

Given that statement as true I posed a question concerning the effect of that on movement of physical bodies.

This question has nothing to do directly with special relativity.

 

Your grid presentations are interesting though, as I have not thought in those diagonal terms.

Thank you.

 

However your (1+1) or (x, t) grid does beg the question

 

Where would the the second observer be travelling?

Since there is only one x axis and it is already occupied by michael and myself, how would she get past?

[MigL]

Haven't you ever read Flatland, Studiot ?

 

Not sure I understand your question in post #59 either.

But if you were a sphere your world line would be a world TUBE.

Or have I misunderstood ?

[studiot]

 

Haven't you ever read Flatland, Studiot ?

 

Or have I misunderstood ?

 

 

Good evening , MigL

 

Yes

 

and

 

Yes

 

But were your comments with reference to my post#59, that allowed 3/4 D continua (x,y,z,t) or with reference to mypost about Elfmotat's (x,t) continua?

[elfmotat]

 

No, that was not the question posed.

 

I stated that as a fact, with some backing reasoning.

 

Given that statement as true I posed a question concerning the effect of that on movement of physical bodies.

This question has nothing to do directly with special relativity.

 

Then I really have absolutely no idea what you're asking. Could you try rephrasing your question?

 

Your grid presentations are interesting though, as I have not thought in those diagonal terms.

Thank you.

However your (1+1) or (x, t) grid does beg the question

Where would the the second observer be travelling?

Since there is only one x axis and it is already occupied by michael and myself, how would she get past?

 

 

I never said that spacetime was (1+1)-dimensional in that scenario, I said that you were. This is also completely irrelevant to the rest of the thread.

[studiot]

 

Edit: to expand on this to make it easier to visualize, pretend for a moment that you're a (1+1)-dimensional creature. You have some finite length. In your rest frame, if you were to plot your location as a function of time, it would appear as a series of straight lines with each line occupying exactly one time coordinate

 

I never said that spacetime was (1+1)-dimensional in that scenario, I said that you were

 

Forgive me, but I assumed you were restricting the discussion to a single (1+1) dimension contimuum by the above statement, not (1+1) embedded in a continuum of greater dimensions, which obviously contains many such restricted subcontinua.

Please clarify.

 

 

 

 

This is also completely irrelevant to the rest of the thread.

 

This is unfair.

Of course it is relevent since it was (and still is) a legitimate question about the conditions of validity of your statement.

Where is your second observer?

 

In terms of your slant diagram the slanted lines still have a projection on the x axis, which I call their x coordinate.

I agree that this projection will vary with the slant.

 

 

Then I really have absolutely no idea what you're asking. Could you try rephrasing your question?

 

If I zero a coordinate system at the left hand edge of my desk and align one end of my ruler with it, my ruler extends in space from x=0 to x=300, and occupies all points between continuously.

 

If I now move it to the other end it extends from x = 1200 to x = 1500 and occupies all of the points between continuopusly and none of the original points.

 

I am am inviting you to comment on the situation along the time axis, given that the ruler was manufactured in 2010 and will be destroyed in 2015.

 

This is a thread about time so this is entirely relevent.

[elfmotat]

 

Forgive me, but I assumed you were restricting the discussion to a single (1+1) dimension contimuum by the above statement, not (1+1) embedded in a continuum of greater dimensions, which obviously contains many such restricted subcontinua.

Please clarify.

 

This is unfair.

Of course it is relevent since it was (and still is) a legitimate question about the conditions of validity of your statement.

Where is your second observer?

 

I don't know what "restricted subcontinua" means, but I made no claims about the dimensions of the space in my post. I made the object in question 1-dimensional so that I could draw it on a 2-d plot. Would you prefer that I make all my diagrams 4-dimensional?

 

What do you mean by "where is your observer?" The word "observer" means "coordinate system," not "material object."

 

 

 

In terms of your slant diagram the slanted lines still have a projection on the x axis, which I call their x coordinate.

I agree that this projection will vary with the slant.

 

 

If I zero a coordinate system at the left hand edge of my desk and align one end of my ruler with it, my ruler extends in space from x=0 to x=300, and occupies all points between continuously.

 

If I now move it to the other end it extends from x = 1200 to x = 1500 and occupies all of the points between continuopusly and none of the original points.

 

I am am inviting you to comment on the situation along the time axis, given that the ruler was manufactured in 2010 and will be destroyed in 2015.

 

This is a thread about time so this is entirely relevent.

 

I still don't know what your question is. What am I supposed to comment on?

[studiot]

This is a discussion forum and I made the point that physical objects are not points, they have physical sizes which show up as multiple coordinates referred to all axes.

They have beginning and and end points and solid ones also occupy all points between.

 

 

(I think it was Michael) made the point that he considers timelike and spacelike axes are not exactly the same and I was exploring the differences, in relation to my point above and also in relation to his comment about movement.

 

You introduced simplified coordinate systems with (I think) one time and one space axis. Any such are continua and could be considered subcontinua of a space having a greater number of dimensions.

(I think it was Jon) introduced Flatland, which is a larger subcontuum than yours, but still smaller than our 3 or 4 D world.

 

I found this interesting and tried to incorporate this point in my discussion as well.

 

Perhaps I have brought too many points together and we should consider them one at a time?

[MigL]

One more stab at it...

All physical objects extend in space across multiple co-ordinates like your ruler does.

But if Michel123456 is wrong about previous ( in time ) co-ordinates being vacated, then...

No specific object can extend in time across multiple co-ordinates because the previous same object would occupy some of those co-ordinates.

 

But do objects extend in time across multiple co-ordinates in the same sense that your ruler extends across the 300 space co-ordinates ?

[studiot]

 

But do objects extend in time across multiple co-ordinates in the same sense that your ruler extends across the 300 space co-ordinates ?

 

 

A pretty good rendition from my Hymn sheet.

[JonG]

No specific object can extend in time across multiple co-ordinates because the previous same object would occupy some of those co-ordinates.

 

But do objects extend in time across multiple co-ordinates in the same sense that your ruler extends across the 300 space co-ordinates ?

I admit to being a bit lost here. I can't see why different atoms in an object can't occupy a set of spatial points at time t₁ and also occupy the same set of spatial points at a later time t₂. None of the atoms at the later time would occupy the same points (in 4D spacetime) as those at the earlier time because they would have different time coordinates.

 

But perhaps that isn't what you are implying.

[michel123456]

But do objects extend in time across multiple co-ordinates in the same sense that your ruler extends across the 300 space co-ordinates ?

I would say yes. If an object extends through space, it must also extend through time. But the time interval would be restricted by the dimension of the object. I cannot see how an object could extend infinitely through time. The same way an object occupies a specific section of space, the same object must occupy a specific section of time. Not a point.

Studiot and michel: snap your fingers at the same time. For a moving observer, your snaps are not simultaneous. Instead there is a finite period of time between them. You may feel like you're only occupying one time coordinate, but that's only because you're trapped in your own rest frame!

 

Edit: to expand on this to make it easier to visualize, pretend for a moment that you're a (1+1)-dimensional creature. You have some finite length. In your rest frame, if you were to plot your location as a function of time, it would appear as a series of straight lines with each line occupying exactly one time coordinate:

 

 

 

But if a moving observer were to plot your position over time, they would plot something like this:

 

 

Notice how you occupy a finite interval of time. Your body is "smeared out" over time for a moving observer due to relativity of simultaneity.

You said it.

 

In fact your diagrams show that time & space are not so different.

[studiot]

OK so let us return to not just Flatland where there is (x,y,t), but Lineland, where there is only (x,t).

 

Now on the above grids, studiot and michael 'occupy' the space between x=-1 and x+1.

 

So my question as to where is the alternative observer amounts to

 

How can an observer in motion pass the physical obstructions posed by studiot and Michael as she translates along the x axis?

 

or

 

Why does she not bump into the obstruction and stop?

Edited October 7, 2014 by studiot

[MigL]

I don't do laTex so bear with me...

 

Lets assume an object does extend in time like it does inspace.

In effect we measure the object to occupy spatial co-ordinates ( Xi, Yj, Zk ) for i,j,k=1 to n. We again measure it at a later time to occupy the co-ordinates ( Xi, Yj, Zk ) for i=10 to n+10. It has moved 10units along the x axis. Now lets apply the same argument to the temporal dimension.

Say at time Tn the object extends through time by ten units equally spaced about Tn, i.e. from n-5 to n+5. Now we repeat the procedure at Tn+5 such that the object now extends fom n to n+10. It has moved into the future by 5 units.

 

The temporal co-ordinates between Tn and Tn+5 are now double booked, an impossibility.

Either objects cannot extend through time, or Michel123456 is right,and previous times vacate their co-ordinates.

 

I choose to believe that objects don't extend through time, and past co-ordinates are not vacated.

 

Sorry, studiot posted before I did and abandoned the temporal extension question and went back to the role/validity of the observer in a spatially reduced model.

Edited October 7, 2014 by MigL

[studiot]

This discussion is going somewhere.

 

Let me throw something else into the mix.

 

 

The temporal co-ordinates between Tn and Tn+5 are now double booked, an impossibility.

 

 

If you only have one spatial dimension you can get 'double booking'

 

But we can count at least 3.

 

So a physical object can sidestep around something on say the x axis by moving up the y axis,

then past the object on the x axis,

Then back down to the x axis.

[elfmotat]

This is a discussion forum and I made the point that physical objects are not points, they have physical sizes which show up as multiple coordinates referred to all axes.

They have beginning and and end points and solid ones also occupy all points between.

 

 

(I think it was Michael) made the point that he considers timelike and spacelike axes are not exactly the same and I was exploring the differences, in relation to my point above and also in relation to his comment about movement.

 

You introduced simplified coordinate systems with (I think) one time and one space axis. Any such are continua and could be considered subcontinua of a space having a greater number of dimensions.

(I think it was Jon) introduced Flatland, which is a larger subcontuum than yours, but still smaller than our 3 or 4 D world.

 

I found this interesting and tried to incorporate this point in my discussion as well.

 

Perhaps I have brought too many points together and we should consider them one at a time?

 

So you're wondering whether or not worldlines terminate? Sure: the particles that make up an object can be created and annihilated, meaning there are endpoints on a particle's worldline. The length of the worldline from one endpoint to another is the particle's lifetime.

 

 

One more stab at it...

All physical objects extend in space across multiple co-ordinates like your ruler does.

But if Michel123456 is wrong about previous ( in time ) co-ordinates being vacated, then...

No specific object can extend in time across multiple co-ordinates because the previous same object would occupy some of those co-ordinates.

 

But do objects extend in time across multiple co-ordinates in the same sense that your ruler extends across the 300 space co-ordinates ?

 

It depends on what you mean by "objects." If we're talking about point particles, then the particle's worldline goes through each time coordinate exactly once. Particles extend in time the same way they do in space, with the length of their worldline representing their lifetime. Extended objects will be cross each time coordinate at a finite length (i.e. a bunch of points) instead of at a single point, this length is shorter than the object's length than in its rest frame (I accidentally drew that second plot so that they appear longer - disregard this) due to the object's world-volume being rotated.

 

 

I don't do laTex so bear with me...

 

Lets assume an object does extend in time like it does inspace.

In effect we measure the object to occupy spatial co-ordinates ( Xi, Yj, Zk ) for i,j,k=1 to n. We again measure it at a later time to occupy the co-ordinates ( Xi, Yj, Zk ) for i=10 to n+10. It has moved 10units along the x axis. Now lets apply the same argument to the temporal dimension.

Say at time Tn the object extends through time by ten units equally spaced about Tn, i.e. from n-5 to n+5. Now we repeat the procedure at Tn+5 such that the object now extends fom n to n+10. It has moved into the future by 5 units.

 

The temporal co-ordinates between Tn and Tn+5 are now double booked, an impossibility.

Either objects cannot extend through time, or Michel123456 is right,and previous times vacate their co-ordinates.

 

I choose to believe that objects don't extend through time, and past co-ordinates are not vacated.

 

Sorry, studiot posted before I did and abandoned the temporal extension question and went back to the role/validity of the observer in a spatially reduced model.

 

This makes no sense. You can't simultaneously hold t constant and not hold it constant.

 

 

This discussion is going somewhere.

 

Let me throw something else into the mix.

 

 

 

If you only have one spatial dimension you can get 'double booking'

 

But we can count at least 3.

 

So a physical object can sidestep around something on say the x axis by moving up the y axis,

then past the object on the x axis,

Then back down to the x axis.

 

I see no problems with "double booking" in spacial coordinates. We never stated how the objects we're considering will interact. Let's say they're neutrinos: they could pass right through each other with no interaction.

Edited October 7, 2014 by elfmotat

[studiot]

 

I see no problems with "double booking" in spacial coordinates

 

When I see you running through a brick wall or better a 38" Devon Cobb wall, I will believe it.

 

BTW have you seen any of the 'Dynamo' productions?

They are almost believable.

 

Edited October 7, 2014 by studiot

[JonG]

Befuddled as I might be, it seems to me that the apparent conflict arises because it is being assumed that to extend through time means something similar to the phrase to extend through space. But it doesn't. Points on an object can extend through space at the same time but they cannot extend through different points in time at the same time.

 

If an object is said to extend from x,y,z,t₁ to x,y,z,t₂ all that means is that all points in spacetime between x,y,z,t₁ and x,y,z,t₂ are* occupied. I can't see what other meaning it could have. Nor can I see that it gives rise to any conflict.

 

*There is a problem in writing this down in a consistent way because these points are not all occupied now, but that's simply because the language we use has evolved to cater for our twisted view that the only time which actually exists is the present. But there isn't an objective present.

Edited October 8, 2014 by JonG

[studiot]

 

Points on an object can extend through space at the same time

 

Surely that is prohibited by special relativity of simultaneity?

[JonG]

 

Surely that is prohibited by special relativity of simultaneity?

I'm sorry. I wrote it badly. What I meant was that different points on an object can exist at different points in space at the same time. That is what we mean when we say that an object is extended in space. However, points on an object can't have different temporal coordinates at the same time, but they can have different temporal coordinates, so the object can extend in time. They simply can't have different temporal coordinates "now". Edited October 8, 2014 by JonG

[studiot]

No offence but this is still rather contorted?

 

 

However, points on an object can't have different temporal coordinates at the same time,

 

Agreed, but what is the same time?

 

 

but they can have different temporal coordinates, so the object can extend in time.

 

Which makes the point, Mig and I were trying to put and explore the significance of this statement, given this is a thread about time.

 

 

 

So you're wondering whether or not worldlines terminate? Sure: the particles that make up an object can be created and annihilated, meaning there are endpoints on a particle's worldline. The length of the worldline from one endpoint to another is the particle's lifetime.

 

That's not actually what I said, but since you introduce world lines, do you consider it necessary to move the entire wordline in time for time travel to occur?

[JonG]

No offence but this is still rather contorted?

 

 

Agreed, but what is the same time?

 

 

 

By the same time I simply mean sharing the same time coordinate as denoted by the time axis.

 

With regard to objects being extended in time, if we agree on that, then - we agree! (I'm finding it difficult to recall what stance contributers have taken earlier on in the thread!)

Edited October 8, 2014 by JonG

[studiot]

 

By the same time I simply mean sharing the same time coordinate as denoted by the time axis.

 

 

 

But, as elfmotat has pointed out that implies simultaneity, which depends upon the observer.

[MigL]

Sorry studiot but what I was trying to do was, start from a false premise, and show that it leads to inconsistencies.

And I would say, on second reading and as elfmotat pointed out in a previous post, made a 'dog's breakfast' out of it.

JonG is also right in stating that it is language that fails us as it is open to interpretation.

In the example I used, I was trying to define an object which exists simultaneously in the past ( 5 units ), present, and future ( 5 units ), but that is already inconsistent as simultaneously means 'at the same time'.

[studiot]

I agree language is a problem.

 

But there is also an underlying problem in our analysis. In using (x,y,z,t) we are implicitly accepting the 'block universe' concept.

 

To be precise there is something missing. What is missing is that which connects parts of a physical object and makes it an entity.

[JonG]

What I wrote:

 

By the same time I simply mean sharing the same time coordinate as denoted by the time axis.

 

 

 

But, as elfmotat has pointed out that implies simultaneity, which depends upon the observer.

 

 

I am not sure that elfmotat did point that out, but I do disagree that it implies simultaneity. Several different spatial points sharing the same time coordinate simply means that they do, indeed, have the same value for t as their time coordinate. It only implies simultaneity if it is also asserted that these points are observable at the same time.

 

If we consider the x-axis in a spacetime diagram, it is clearly possible for different events to have different x coordinates but have the same time coordinate. What we can't do is observe them all at the same time, so it contains no implication of simultaneity.