What does "depends on time" mean? — Luke

It means:

Motion is change in spatial position over change in temporal position. — Luke

i.e. that where something is depends on when.

I've taken great pains to explain myself and present my argument, which you continue to ignore. — Luke

I have answered every question you have asked. You have not done the same.

What does "depends on time" mean?
— Luke

It means:

Motion is change in spatial position over change in temporal position.
— Luke

i.e. that where something is depends on when. — Kenosha Kid

What comes before and after the "i.e" is not equivalent. Motion is not defined as merely having a spatiotemporal position.

I have answered every question you have asked. You have not done the same. — Kenosha Kid

Did you have questions? I thought you were just telling me what's what.

What comes before and after the "i.e" is not equivalent. Motion is not defined as merely having a spatiotemporal position. — Luke

The passage you quoted did not state that motion is defined merely as having a spatiotemporal position, making yours an overtly fallacious argument. It states that the spatial part of the spatiotemporal position depends on the temporal part, that is: for each time, the object has a position. Assuming continuity.

Did you have questions? I thought you were just telling me what's what. — Luke

I have asked you lots of questions, yes. Here's one I'd really like an answer to if you're sure of your position:

What is it then that changes spatial position?
— Kenosha Kid

In Eternalism? Nothing. That's what I'm arguing. Nothing moves; nothing changes.
— Luke

No. What is it that changes position at all? Forget eternalism. Just a mountain at a given moment in time, an aerial photograph if you will. The summit is in one place. The foot is far away from it. It exists in more than one position. By your argument, radius is impossible because what changes spatial position? — Kenosha Kid

You will recall that your response was yet again evasive:

I'm not going to argue with you by analogy. There is no long-standing debate about whether altitude of a mountain can change with position. This is about time and motion. — Luke

Given that, in eternalism, time is laid out like space, I would like an answer.

...the spatial part of the spatiotemporal position depends on the temporal part, that is: for each time, the object has a position. Assuming continuity. — Kenosha Kid

Is this different for Presentism?

What is it that changes position at all? Forget eternalism. Just a mountain at a given moment in time, an aerial photograph if you will. The summit is in one place. The foot is far away from it. It exists in more than one position. By your argument, radius is impossible because what changes spatial position? — Kenosha Kid

I've answered this, but perhaps it depends on what you mean by "exist in more than one position". The position of the mountain as a whole object doesn't "exist in more than one position". The 3D mountain exists in the spatial position of the 3D mountain. It would need to be displaced from that position in order to change position. However, if what you mean by "exist in more than one position" is to have a part of the mountain existing at one spatial position and another part of the mountain existing at another spatial position, then I agree that different parts of the mountain "exist in more than one position". I don't follow how this implies that "radius is impossible". Perhaps you mean something else by "exist in more than one position"?

Is this different for Presentism? — Luke

Yes, it holds whether the past and future are real or not.

However, if what you mean by "exist in more than one position" is to have a part of the mountain existing at one spatial position and another part of the mountain existing at another spatial position, then I agree that different parts of the mountain "exist in more than one position". — Luke

:up: Then you understand perfectly well what is meant by "existing at more than one point in time". In 4D, it is the same thing. Time is not special in this respect.

Proceeding hierarchically, stop me when I presume incorrectly:

If you are happy that a 4D object exists at more than one time to the extent that it exists in more than one position (i.e. has length), you are presumably happy with the concept of duration in 4D, which is a length of time between two points in time.

And if you're happy with time intervals in 4D, and you are happy that the spatial position at one end of the interval may be different to that over the othet end, the you are presumably happy that a 4D object's position changes with with respect to time, i.e. it's position at one time (x, y, z, t) maybe different at another.

There is the kinematic definition of motion. Nothing needs to be bolted on or derived further if you stick to that definition of motion, other than the assumption of continuity. There is no version of the above that can be held and motion not pop out gratis.

If you are happy that a 4D object exists at more than one time — Kenosha Kid

Just as I am not happy that a 3D object exists at more than one space (the object fills the space), I am equally not happy that a 4D object exists at more than one time (the object fills the time). And just as I agree that different parts of a 3D object exist at more than one space, I agree that different parts of a 4D object exist at more than one time.

And if you're happy with time intervals in 4D, and you are happy that the spatial position at one end of the interval may be different to that over the othet end, you are presumably happy that a 4D object's position changes with with respect to time, i.e. it's position at one time (x, y, z, t) maybe different at another. — Kenosha Kid

I have no qualms with saying that different parts of the 4D object have different spatial positions at different times. I disagree that the 4D object as a whole has different spatial positions at different times.

There is the kinematic definition of motion — Kenosha Kid

Following your reasoning above, this would imply that the 4D object as a whole moves.

This is leading us back around to my argument.

I have no qualms with saying that different parts of the 4D object have different spatial positions at different times. I disagree that the 4D object as a whole has different spatial positions at different times. — Luke

Do you agree that even a part of a 4D object, such as an atom in the window of a car, has different spatial positions at different times?

There is the kinematic definition of motion
— Kenosha Kid

Following your reasoning above, this would imply that the 4D object as a whole moves. — Luke

No, it does not. A body at a spatial coordinate (x,y,z) at time t may have a different spatial coordinate (x',y',z') at time t' (a path). This does not mean that the body at coordinate (x,y,z,t) moves. That is not shown, nor is it sensible.

The gradient of the mountainside is not a change in the spatial position of the mountain, as you implied earlier. The mountain hasn't moved. — Luke

It may help to imagine a pipe going down the mountainside. The answer to where the pipe is on the 2D surface of the Earth depends on which altitude you’re asking about: the pipe changes 2D location with altitude. If the pipe is on the east side of the mountain, for instance, it gets further east the lower down the mountain it goes. It’s not moving over time, but the relevant segment of it at a given altitude is further east the lower the altitude. Yet at every altitude, it is still the same pipe.

Do you agree that even a part of a 4D object, such as an atom in the window of a car, has different spatial positions at different times? — Kenosha Kid

I get the sense this could be a trick question, but yes, I think so.

A body at a spatial coordinate (x,y,z) at time t may have a different spatial coordinate (x',y',z') at time t' (a path). This does not mean that the body at coordinate (x,y,z,t) moves. That is not shown, nor is it sensible. — Kenosha Kid

A body at (x,y,z) at t or at (x', y', z') at t' is not a 4D object; it is part of a 4D object. I was countering this statement:

you are presumably happy that a 4D object's position changes with with respect to time — Kenosha Kid

The gradient of the mountainside is not a change in the spatial position of the mountain, as you implied earlier. The mountain hasn't moved.
— Luke

It may help to imagine a pipe going down the mountainside. The answer to where the pipe is on the 2D surface of the Earth depends on which altitude you’re asking about: the pipe changes 2D location with altitude. If the pipe is on the east aide of the mountain, for instance, it gets further east the lower down the mountain it goes. It’s not moving over time, but the relevant segment of it at a given altitude is further east the lower the altitude. Yet at every altitude, it is still the same pipe. — Pfhorrest

Sorry, I don't understand what you're getting at. I didn't claim that it wasn't the same mountain.

Do you agree that even a part of a 4D object, such as an atom in the window of a car, has different spatial positions at different times?
— Kenosha Kid

I get the sense this could be a trick question, but yes, I think so. — Luke

Fine fine fine. Not a trick at all. We only need consider an atom. This is also kinematic motion: different spatial positions at different times, i.e. time-dependent positions.

I actually thought you were going to say, "No, the atom at one time is not the same atom as the atom at another time" or something. Fortunately:

I didn't claim that it wasn't the same mountain. — Luke

:up:

So in eternalism, the entire history of the atom is all laid out, right? The whole 4D object is the entire history atom. This describes a path in the block, such as the path of the Moon in Huw Price's image. At different times, the atom may be in different positions, i.e. the path of the atom in the block may be wiggly. This wiggliness is identically motion: time-dependent position. You don't need to look any further than wiggles (or slants).

That is my argument.

Fine fine fine. Not a trick at all. We only need consider an atom. This is also kinematic motion: different spatial positions at different times, i.e. time-dependent positions. — Kenosha Kid

Hold on. You said the atom was "part of a 4D object", not a 4D object. It depends on Presentism or Eternalism whether this remains the same object at different times.

[EDIT: I see now that I should have clarified this earlier. Sorry, it's 3am here.]

I didn't claim that it wasn't the same mountain — Luke

Don't read anything into this comment. I'm just trying to figure out how @Pfhorrest's response relates to what he quoted.

Sorry, I don't understand what you're getting at. I didn't claim that it wasn't the same mountain. — Luke

What I’m getting at is that the latitude and longitude of the same one single pipe changes with altitude, the pipe moves east the lower down the mountain it goes, even though in a full 3D picture the pipe is just laying there, not changing or moving at all. When we say its latitude and longitude “change” or it “moves”, we mean with respect to altitude, not with respect to time. If we consider altitude just another dimension like latitude and longitude, in that 3D picture nothing is changing or moving, but when just looking at a 2D picture with respect to a third dimension, we see change and movement.

Likewise when we look at a 4D picture, or at a 3D picture with respect to a fourth dimension of time.

Sorry but I find your analogy confusing. You've got latitude, longitude, altitude, cardinal directions and a (3D?) pipe all happening in 2D?

Hold on. You said the atom was "part of a 4D object", not a 4D object. It depends on Presentism or Eternalism whether this remains the same object at different times. — Luke

Oh, you are going that route. Explain? Continuity is assumed in kinematics.

What difference will continuity make?

Sorry, need sleep. I'll revisit this in the morning.

What difference will continuity make? — Luke

Kinematics assumes a continuum. If an atom at one instant does not exist any preceding or succeeding instant, it's kinematic velocity is undefined.

The eternalist view of the atom is that its entire history exists. If you do not assume continuity, even over a tiny interval of time, the eternalist view is different to the picture I've been referring to: the atom has no history to exist. It would appear as a single point in the block, not a path.

We all gotta sleep. Have a good one.

Back to physics!
I might have missed it, but what is 'present' has not been defined in the course of the long debate.
Presentism can make sense only if time is pixelized. (Planck's Constant??)

Couldn't sleep. Here goes:

Let's say there's a mug sitting on my desk (x, y, z) at time t, and I pick it up, walk over and put it in the dishwasher (x', y', z'), where it ends up at time t'.

Most people, who are Presentists, would say that it's the same object at t as it is at t' (and at all points in between).

Eternalists, however, know that the mug at t and at t' are two different parts of a 4D object. They know that all parts of the 4D object exist, and that the part at t must be different to the part at t'. The 4D object consists of these different parts.

Presentists find it unproblematic to say that the mug sitting on my desk was moved to the dishwasher. The same object was carried from (x,y,z) at t, to (x', y', z') at t'.

However, different objects exists at these two locations in Eternalism - the different parts of the 4D object. It is not possible that the part moves from t to t' in Eternalism, because a different part already exists there (and at all points in between).

However, different objects exists at these two locations in Eternalism - the different parts of the 4D object. — Luke

"different objects exists at these two locations in Eternalism" is such a assumption. My counter would be that this is not generally held to be true by eternalists, nor is it a component of any typical definition of eternalism, i.e. this is now a special kind of eternalism.

That said, motion may still be recovered in this eternalism, even if we assume the object at t' to be different to the object at t, so long as there exists another continuity connecting the objects at t and t'. This is at least sensible: we do not see an object disappear then be replaced by a different but indistingushable object.

Then we can define a new kinematics over that continuity, identical in mathematical form to the previous kinematics except maybe from some replacement of dummy variables (e.g. t -> i), and giving exactly the same net result. This thing would look identical to what motion looks like in normal eternalism, where the object at t' is just another part of the same object at t. It would allow you to calculate velocities as gradients with respect to some continuous labeling system for identity, i.

Which is a complicated way of changing some labels at the end of the day.

Couldn't sleep. — Luke

I have a remedy. Lie back, close your eyes, and in your mind say... "Motion is possible in eternalism. Motion is possible in eternalism. Motion is possible in eternalism..." You'll be out like a light, I promise.

Try this instead then:

You have a line drawn on a grid with axes labelled x and y.

The y-position of the line changes with respect to the x-position. It’s not changing over time as you experience it, you’re just looking at the line sitting there, but when you talk about where the line is on the y-axis, you have to specify which part of the x-axis you mean it in respect to, because the line isn’t just a point, it’s a continuous line.

Now relabel that same graph so instead of “x” it says “longitude” and instead of “y” it says “altitude”. The line is exactly the same, we’re just talking about it in terms of longitude and altitude instead. The line gains altitude as it crosses longitude. It’s still not moving in respect to your experience of time, but still the line changes in altitude with respect to latitude. This is like the pipe on the mountainside I was taking about.

Now relabel the graph again, so that “latitude” is now “time” and “altitude” is now “space”. The line is unchanged, only the labels are different. But now, the line is changing its position in space with respect to its position in time. Not its actual position in space as you experience it over time as you experience it, but changing its space-coordinates relative to its time-coordinates.

Eternalism says that if you could somehow step outside of our normal space and time, you would see thing still in it like that line. The things change their position in space relative to their position in time. But you are now outside of space and time, so nothing seems to be changing relative to your experience of time, because you now have no experience of time. Time is only down there in the universe that you’re looking at from outside. But still, you can see in that universe that at different places in the time dimension, the same things are at different places in the various space dimensions. That means they’re moving, changing, with respect to time. You are just outside of time now, so you don’t experience time in a timelike way. But the things down there in the universe still do.

"different objects exists at these two locations in Eternalism" is such a assumption. My counter would be that this is not generally held to be true by eternalists, nor is it a component of any typical definition of eternalism, i.e. this is now a special kind of eternalism. — Kenosha Kid

What's to disagree with? The 4D object is the entire spatiotemporal existence of the mug. Or, as I said earlier:

Just as I am not happy that a 3D object exists at more than one space (the object fills the space), I am equally not happy that a 4D object exists at more than one time (the object fills the time). And just as I agree that different parts of a 3D object exist at more than one space, I agree that different parts of a 4D object exist at more than one time. — Luke

The 4D object can be broken into its constituent parts, just like a mountain can. You referred to the same thing earlier and I mimicked your example, when you said:

A body at a spatial coordinate (x,y,z) at time t may have a different spatial coordinate (x',y',z') at time t' — Kenosha Kid

If the 4D object is the entire spatiotemporal existence of the mug, and if the 4D mug is made up of its constituent parts, then how are the two parts you mention above not different and co-existing parts? They are different objects (i.e. parts) existing in two spatiotemporal locations. The co-existence of all parts of the 4D object is just Eternalism. What's the point of disagreement?

That said, motion may still be recovered in this eternalism, even if we assume the object at t' to be different to the object at t, so long as there exists another continuity connecting the objects at t and t'. This is at least sensible: we do not see an object disappear then be replaced by a different but indistingushable object. — Kenosha Kid

In that case, how do you intend to calculate your Eternalist motion between one part and another? You will need to pick out these two different parts in order to do so.

Which is a complicated way of changing some labels at the end of the day. — Kenosha Kid

And this has been your mistaken assumption all along: that the existence of time automatically implies the existence of motion. But that's exactly the difference between Presentism and Eternalism. Eternalism is a motionless existence. Of course the existence of the 4D mug over its ...er, lifespan(?)... will be the same in either case at the end of the day. Or consider it in MST terms instead; a combination of both views.

Eternalism says that if you could somehow step outside of our normal space and time, you would see thing still in it like that line. — Pfhorrest

No, it doesn't. It says time is really static (inside spacetime).

Sorry Jacob, but the discussion is focused on Eternalism, not Presentism. But Presentism has its share of problems, I agree.

The 4D object can be broken into its constituent parts, just like a mountain can. — Luke

It's an interesting idea. We could consider something like the object over one Planck time as a sort of temporal "atom". We're far from classical kinematics then. Moving to QM, you don't even need time to have momentum: it is a purely spatial geometric feature.

If the 4D object is the entire spatiotemporal existence of the mug, and if the 4D mug is made up of its constituent parts, then how are the two parts you mention above not different and co-existing parts? — Luke

They are, but now we can consider the 4D geometry of the part, see that it has one, and motion again falls out.

In that case, how do you intend to calculate your Eternalist motion between one part and another? You will need to pick out these two different parts in order to do so. — Luke

You'd need some information about what parts exist where and when. This would replace a history of one object in 4D with a history of different 3D objects transforming into one another, building up the worldline that you say is not one object but different parts at different times. Then it's the same story: 4D geometry = motion.

And this has been your mistaken assumption all along: that the existence of time automatically implies the existence of motion. — Luke

No, the existence of time-dependent positions necessitates motion, by definition. You can have an eternalist universe without motion, but then the temporal dimension would be redundant.

But that's exactly the difference between Presentism and Eternalism. — Luke

No, the difference between presentism and eternalism is down to whether the past and future exist, not whether motion exists. Your OP attempts to derive a stationary universe from eternalism, but you have to put that in by hand, viz:

Eternalism is a motionless existence. — Luke

Moving to QM, you don't even need time to have momentum: it is a purely spatial geometric feature. — Kenosha Kid

This underlies my whole view of the matter (although somewhat vaguely): that Eternalism is all position and Presentism is all momentum.

They are, but now we can consider the 4D geometry of the part, see that it has one, and motion again falls out. — Kenosha Kid

Motion implies that the same object moves from t to t'. This is a Presentist assumption which makes no sense in Eternalism.

You'd need some information about what parts exist where and when. This would replace a history of one object in 4D with a history of different 3D objects transforming into one another, building up the worldline that you say is not one object but different parts at different times. — Kenosha Kid

A 4D object consists of different 3D parts. A 3D part in Eternalism is equivalent to a 3D object at a time in Presentism. Both describe the mug on my desk at time t. I don't see how this is problematic.

[EDIT: There seems to be no equivalent concern with stitching the different parts of a mountain back together to make the whole mountain.]

You can have an eternalist universe without motion, but then the temporal dimension would be redundant. — Kenosha Kid

I don't understand your use of the word "redundant" here. The temporal dimension is the entire spatiotemporal existence of an object. Eternalism concerns existence, not motion, although such an existence logically precludes motion, as I have argued.

No, it doesn't. It says time is really static (inside spacetime). — Luke

If that’s what you think eternalism is, then you’re arguing against a strawman that nobody else is arguing for.