Doesn't the interval of time represent some change of temporal location? — Luke

Does a distance represent some change in spatial location? It's the same thing.

I don't see what difference it would make to my arguments, but I'm happy to discuss them. — Luke

Just that, in relativity, an object is said to be moving through time. This is a feature of relativity, though, not eternalism generally. The kinematics in relativity are complex in practise, but basically amount to rotations in 4D instead of accelerations. Everything has the same 4D velocity: the speed of light. A body at rest is moving forward through time at this speed. When it is accelerated, its velocity is rotated away from the temporal direction (called time dilation) toward a spatial direction.

One of the complications is that, if you imagine two observers moving with respect to one another, the velocity of Observer B as seen by Observer A is the change of 4D position seen by Observer A with respect to the change in 4D position of Observer B as seen by Observer B. Graphically it makes a lot if sense but it can make your head spin.

Does a distance represent some change in spatial location? It's the same thing. — Kenosha Kid

It can, can't it? I'm not sure I understand your point. Do you think I should have asked instead: doesn't the temporal distance represent a change in the temporal location of an object? I thought the context of my reply would have made this clear enough, given your statement:

A "change" in temporal position, as referred to by myself, meant nothing more than an interval of time over which we can consider different positions of the same object — Kenosha Kid

Am I missing something?

It can, can't it? — Luke

It can, yes, e.g. the distance travelled by a hiker. But does that necessitate a hiker in order to have some concept of distance? No. So does something need to change temporal location in order for us to have a concept of duration?

does something need to change temporal location in order for us to have a concept of duration? — Kenosha Kid

I'm trying to understand. You said that "change in temporal position" is only a length and "not something an object does." So is an object's change in spatial position, or its motion, at different times also "not something an object does"?

I'm trying to understand. You said that "change in temporal position" is only a length and "not something an object does." So is an object's change in spatial position, or its motion, at different times also "not something an object does"? — Luke

Yes. We might colloquially say that a ruler goes from one end to another, but nothing is really going anywhere: it just occupies that space. It is a spatial distance. Likewise in 4D, we don't need something to "go" in order to have the concept of temporal distance. A 4D object just occupies a 4D space. The "change" in position between two points on it is just a consideration of its geometry, e.g. what is the change in gradient from point A to point B? What is the change in in altitude between the foot and the summit? Likewise what is the change in position between time t and t'?

So is an object's change in spatial position, or its motion, at different times also "not something an object does"?
— Luke

Yes. — Kenosha Kid

I see. So you concede that, in terms of classical kinematics at least, objects do not move?

I see. So you concede that, in terms of classical kinematics at least, objects do not move? — Luke

Okay you kinda edited out the bit that was clearly talking about lengths. A ruler does not change in position between one end and the other. A mountain does not change in position between the foot and the apex. A body does not move temporal position from one point to another.

That does not mean one end of the ruler cannot change position as I throw it, or the apex of the mountain cannot move as the Earth rotates. That, in 4D, is gradient in its geometry with respect to time.

You're approaching this as an exercise in catching someone out, taking a response out of context if necessary. At the end of the day, it doesn't matter how I explain it to you: the gradient of a 4D object with respect to the time dimension is motion. That is inescapable. There's no space to wiggle into there, no clever angle from the outside that changes it. You're still left with v = dx/dt, and as long as you have that, you have motion.

Okay you kinda edited out the bit that was clearly talking about lengths. — Kenosha Kid

My bad. You said:

Yes. We might colloquially say that a ruler goes from one end to another, but nothing is really going anywhere: it just occupies that space. — Kenosha Kid

You're still left with v = dx/dt, and as long as you have that, you have motion. — Kenosha Kid

Well, either "dt" represents a length/duration for comparison purposes only (is "not something an object does"), or else it represents a change in temporal position. You can't have it both ways.

Well, either "dt" represents a length/duration for comparison purposes only (is "not something an object does"), or else it represents a change in temporal position. You can't have it both ways. — Luke

dt represents a duration: the difference between one temporal position and another. dx represents a normal spatial length: the difference between one spatial position and another. If something is at one position at one time, and at a different position at a different time, that is motion. From "outside of time", viewing time as just another dimension like space, that looks like an object that spans time and space, geometrically, changing where it is in space over time. But it's not "changing where it is in time" as you watch it from outside of time. That would require there be some meta-time over which its place in time could change, which is nonsense.

Well, either "dt" represents a length/duration for comparison purposes only (is "not something an object does"), or else it represents a change in temporal position. You can't have it both ways. — Luke

This seems more an objection to terminology than the necessity of motion arising from 4D geometry. I think the point is well covered, quite circularly, in our preceding conversation.

This seems more an objection to terminology than the necessity of motion arising from 4D geometry. — Kenosha Kid

"dt" (and with it "dx") is or isn't something an object does? Which is it?

As I've said a few times, I don't doubt that you can obtain a value for motion, but that doesn't mean that anything really moves. Motion is a Presentist notion.

Motion is a Presentist notion. — Luke

How can anything move through time if there is only one time, the present? That sounds like getting taller in flat world.

From "outside of time", viewing time as just another dimension like space, that looks like an object that spans time and space, geometrically, changing where it is in space over time. — Pfhorrest

Again, if you're arguing that time passes "inside" of time but not "outside", then you're saying that temporal passage is real. You only imply it above, but you've explicitly stated it elsewhere, such as:

If you're looking at a 4D object, where one of the four dimensions is time, then you're standing outside of time, and there is no dimension that seems timelike to you in which for the 4D object to move.

An object moving in three dimensions with respect to the fourth will just look like a 4D object to you, though. — Pfhorrest

Your view that time really passes makes you an A-theorist, not a B-theorist. I am attempting to demonstrate that B-theory Eternalism precludes motion. This was all covered in the OP. See the section and links on the B-theory of time.

I also described temporal passage (A-theory) earlier on the previous page:

If you stare at a clock for one minute, you will have changed your temporal location by one minute. Of course, you don't need to stare at a clock in order to change your temporal location, you can do whatever you like. You only need to age and experience life as you always do. Apparently, you have no choice but to do this. Taking this (literally) everyday aspect of the experience of time's passing to be reflective of something real in the world, this is known as temporal passage (aka the passage of time, time passing, etc.). — Luke

Is this sort of experience terribly unfamiliar to you? The B-theory of time states that the experience of time's passing is not reflective of something real in the world; i.e. temporal passage is not real and is some kind of illusion.

How can anything move through time if there is only one time, the present? — Pfhorrest

I'm not here to defend Presentism. Additionally, although they are related, temporal passage (A-theory) is distinct from Presentism.

To reiterate what's at stake here:

Motion has been defined as change in spatial position over change in temporal position (or dx/dt)

@Kenosha Kid states that: "A "change" in temporal position, as referred to by myself, meant nothing more than an interval of time over which we can consider different positions of the same object, i.e. it is a length of a section of the 4D object. It is not something the object does in classical kinematics."

@Kenosha Kid needs to remain consistent with B-theory Eternalism, in which the entire (4D) object exists at all times and time does not pass. Objects do not really travel through time according to the B-theory. Therefore, @Kenosha Kid does not want to say that the object actually moves from t to t'. So he maintains that a change in temporal position is no more than "an interval of time over which we can consider different positions of the same object".

However, if an object does not actually change its temporal position, then it cannot actually change its spatial position either. And if an object does not actually change its spatial position, then it doesn't actually move. According to the above definition of motion, that is.

@Kenosha Kid appears to be saying that an object both does and does not change its temporal position.

However, if an object does not actually change its temporal position, then it cannot actually change its spatial position either. And if an object does not actually change its spatial position, then it doesn't actually move. According to the above definition of motion, that is. — Luke

And that is why secretly you're a presentist. It is not a condition in eternalism that a 4D object need move within a 4D space to have motion, since that would be a new kind of motion (hypermotion, I guess) in an even higher-dimensional space that would be hard to conceive of. All that matters is that the geometry of a slice at time t' differs from the geometry of a slice at t of the same 4D object. This, by definition, gives the object a gradient in space with respect to time, which means it moves. According to the above definition of motion, that is.

As I stated ages ago, you need to show that nothing is time-dependent in eternalism in order to disprove motion. Figuring out different ways of verbally forcing presentist ideas into eternalism isn't going to cut it.

It is not a condition in eternalism that a 4D object need move within a 4D space to have motion, since that would be a new kind of motion (hypermotion, I guess) in an even higher-dimensional space that would be hard to conceive of. — Kenosha Kid

No. I've only ever been talking about the motion of 3D objects in the 4th dimension; that is, 3D parts of the 4D object. This is what you consider with your temporal interval and this is what we mean when we talk about the motion of an object. I have not been talking about anything different.

I've only ever been talking about the motion of 3D objects in the 4th dimension; that is, 3D parts of the 4D object. — Luke

If so, are you satisfied that a 3D part at time t' may differ from the 3D part a time t? If so, that is motion.

If so, are you satisfied that a 3D part at time t' may differ from the 3D part a time t? — Kenosha Kid

Yes, representing a change in temporal position of the object. That is, the object has changed its temporal position.

Yes, representing a change in temporal position of the object. That is, the object has changed its temporal position. — Luke

That's it! You've described motion!

And you've agreed that the object has moved from t to t'.

And you've agreed that the object has moved from t to t'. — Luke

No. The above does not depend on anything moving from one time to another, merely that the position at t' differs from that at t.

How can a change in the temporal position of the object from t to t' not mean that the object has moved from t to t'?

And if the object has not moved in time, then the object has not moved.

You keep oscillating between these.

Either the object moves from t to t' and there is temporal passage (not B-theory).
Or the object does not move from t to t' and there is no motion.

Either the object moves from t to t' and there is temporal passage (not B-theory).
Or the object does not move from t to t' and there is no motion. — Luke

Then your definition of motion depends on temporal passage, which kinematics does not. As I have said many times, motion in 4D is straight geometry. If you are happy with a ruler having length without changing position, you have no reasonable objection to a 4D object having duration without changing temporal position. Simply insisting it is different is itself contra to eternalism.

Then your definition of motion depends on temporal passage, which kinematics does not. — Kenosha Kid

If time is continuous, what else could change in temporal position of the object mean except that the object moves from one time to the next , i.e., temporal passage?

If you are happy with a ruler having length without changing position, you have no reasonable objection to a 4D object having duration without changing temporal position. — Kenosha Kid

If it doesn't change temporal position then it can't change spatial position. Motion = 0.

If time is continuous, what else could change in temporal position of the object mean except that the object moves from one time to the next , i.e., temporal passage? — Luke

Ask yourself the same thing about the length of a ruler? Does it rely on the concept of a 'here' that moves from one end to another? In which case why treat time differently?

If time is like a ruler, as per Eternalism, then there is no motion.

If time is like a ruler, as per Eternalism, then there is no motion. — Luke

If <insert literally anything here>, then there is no motion. All you're proving is that you will assert the same thing no matter the course of the conversation. That wasn't even a rational statement.

Motion is an inevitable consequence of the geometry of 4D objects. Unless you address that, you're not even close to disproving motion.

Again, if you're arguing that time passes "inside" of time but not "outside", then you're saying that temporal passage is real. — Luke

I’m saying that the very question of whether time moves / things move through time is confused. Things change in space with respect to time. Some things, like humans, have memories of the past and expectations of the future, and so even at a given instant have a picture of the changes that happen over time in their minds; that is our perception of time. But thinking of either of those things as time changing where it is relative to an observer, or an observer changing where it is relative to time, is confused nonsense. Because, as I’ve repeatedly asked, over what could that change of temporal position occur, and how would you measure the rate at which it occurs? What per what? Time per time?