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.

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.

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?

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.

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?

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"?

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?

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

I'm a little confused by this. Doesn't the interval of time represent some change of temporal location? Doesn't an object occasionally move during this interval, and wouldn't that be something the object does?

However, in relativistic kinematics, an object does have a velocity in the temporal direction and so can be thought of, at any given time, as changing temporal position in a reference frame with respect to temporal position in its own rest frame. This is true at all times and requires no particular 'now'. Nor does motion completely depend on it, since photons have no temporal velocity and yet move pretty nippily.

We have been discussing the former, but happy to discuss the latter, or QM. — Kenosha Kid

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

You just don't understand what motion means — Pfhorrest

What does it mean, then?

No I'm pretty sure Kenosha Kid will deny as much as I do that objects change their temporal position. — Pfhorrest

I hope so, then I will have demonstrated that Eternalism logically precludes motion.

What would a "change in temporal position" even be — Pfhorrest

It forms part of the definition of motion that @Kenosha Kid and I have agreed upon, for starters.

Kinematics holds in eternalism and presentism. That is, it doesn't care how you conceive of a change in time, whether it's a length or an evolving 'now'. Eternalism is more general and complete insofar as it both allows for and does not require motion forward in time to have motion in space. Presentism has a more tenuous position because it does need such a thing, be it a spotlight or whatever. — Kenosha Kid

Okay, but I am asking how temporal change is conceived, and whether a change in time is possible, in Eternalism, not in kinematics.

My counterarguments:

1a. All times exist - no part can change temporal location

A rehash of my mug/dishwasher example: Basically, if all 3D parts of an object exist at all times of a 4D object, then no part can change its temporal location. Similarly:

1b. The 3D-4D analogy - nothing changes

You and @Pfhorrest have presented a 3D-4D analogy in which:

position has a gradient with respect to time in the exact same way altitude has a gradient with respect to radius — Kenosha Kid

"altitude has a gradient with respect to radius"
This tells us only that altitude changes with respect to radius. However, the altitude of the mountain does not change (in 3D; at a given 4D location), and neither does the radius of the mountain change at any of its different cross sections. By analogy, the same holds true for time (4D):

"[spatial] position has a gradient with respect to time [temporal position]"
This tells us only that spatial position changes with respect to temporal position. However, the spatial position of the object does not change (in 4D; at a given 5D location), and neither does the temporal position of the object change at any of its different cross sections.

2a. What makes change in temporal location possible in Eternalism?

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.).

I believe that the experience of temporal passage informs most people's (if not everyone's) understanding of what time is. If Eternalism has no such "propagator" as temporal passage, then how is change in temporal location possible? Similarly:

2b. How can I visualise change in temporal location without temporal passage?

What does a change in time look like without temporal passage? Can such a change be experienced? If time does not pass, how can I possibly get to, or find myself at, different temporal locations?

It is the definition of velocity in kinematics. If position depends on time, position has a gradient with respect to time in the exact same way altitude has a gradient with respect to radius (and angle, for non-isotropic mountains :) ). In eternalism, position does depend on time, et voila: motion. — Kenosha Kid

Firstly, thank you for taking the time to try and clarify this matter for me.

I understand that the relationships or functions of position and time are present in the gradient. I think that my argument is really more to do with the change in time that underpins motion. I don't understand what difference there is between the change in time found in Eternalism and the temporal passage of Presentism. More precisely, I don't understand what a change in time (or time itself) could mean in the absence of temporal passage. Does anything change temporal location in Eternalism, and, if so, how?

You didn't answer the question: do you believe that temporal passage is real?

If so, then I don't consider you to be an Eternalist (or, more specifically, a B-theory Eternalist or block theorist). It would be pointless to argue with you if your view allows for temporal passage, because I believe that there is change and motion if there is temporal passage. That's just a hybrid view with Presentism.

Moving Spotlight is nonsense; if something "moved" to give the perception of time, it would have to be over time, and so would appear static from a perspective outside of time — Pfhorrest

Sorry, I can't make sense of this.

Nothing moves through time, and time itself doesn't move past anything. Saying that either of those things happens is nonsense. Things move through space over time. — Pfhorrest

What's the difference between moving "through time" and moving "over time"?

They can also move through one dimension of space over another dimension of space, without bring time into anything at all. — Pfhorrest

How?

All change is comparative. Something changes in one dimension with respect to another dimension. The road to my house changes its altitude in respect to its latitude (it gets higher the further north it goes). — Pfhorrest

How does it "get higher" or "go further north" irrespective of time? All change requires time.

That I see it happen, and nobody's presented a good reason to doubt that. I remember things being different at earlier times than they are now. That's what change over time is. — Pfhorrest

You believe that temporal passage is real? Perhaps you are a Moving Spotlight Theorist instead of an Eternalist.

A change in diameter over altitude. — Pfhorrest

The virgule was intended to signify "or", not division.

The mountain isn't changing its altitude. Over the dimension of altitude, the mountain changes its diameter. — Pfhorrest

So nothing actually changes? It's merely comparative? Then your analogy has no implications for actual change in Eternalism.

I am an eternalist, I've read the views of other eternalists plenty, and none of us deny that change or motion happen. — Pfhorrest

And I'm asking what justifies your assumption that such change/motion does happen?

How can you give the diameter of a mountain without specifying at which altitude you mean? The mountain has different diameters at different altitudes. — Pfhorrest

You've been talking about a change in altitude/diameter. That's part of your 3D to 4D analogy.

You (and MU) seem to think that that sign is lying. "The road doesn't actually get narrower. — Pfhorrest

I don't deny that it "gets" narrower over time, assuming change. I just don't find such change to be consistent with an Eternalist universe.

Allow me to fix the ambiguity:

Motion in (3D + time) = geometry in 4D. — Kenosha Kid

Some measure in the first n-1 dimensions changes over the last dimension. In the case of the mountain it’s diameter over altitude. — Pfhorrest

How is change possible in 3D? Looks like the analogy is breaking down...

In the case of the mountain it’s diameter over altitude. In the case of me it’s height over time. — Pfhorrest

You're saying that if you change altitude then diameter changes, and if you change time then height changes. But this is based on the assumption that something can or does change in time (in 4D) or in altitude (in 3D). You can't just assume this when it's what's in question here. I've provided arguments for why Eternalism precludes change/motion. What justifies your assumption that Eternalism includes change/motion?

Hence the mountain that gets smaller with altitude even though it stays the same size with time; the pipe along its side that gains altitude as it moves westward, even though it’s not moving with respect to time; the abstract line that moves in a y-ward direction over the x-ward direction, even though it too doesn’t move with respect to time. — Pfhorrest

The abstract line does not move at all. How does the pipe gain altitude as it "moves" westward? If it's not moving with respect to time, then what is it moving with respect to? How does the mountain "get" smaller with altitude? Why do you assume altitude moves upwards rather than down? You are comparing one width/radius of the mountain with another width/radius. The mountain doesn't change at all. Your comparison of one part of the mountain to another assumes a change in altitude. What is actually changing?

No, not at all, as per the mountain example. You don't need a hiker to have a gradient. You don't need a temporal hiker to have a gradient either. — Kenosha Kid

What does a gradient have to do with motion? It's just an assumption that there is motion in the gradient. A universe without change or motion is equally conceivable, so why do you get to assume your gradient has motion rather than doesn't? Again, what does motion mean without a change from t to t'?

doesn't the very concept of motion assume that a 3D object moves from t to t' in some fashion akin to temporal passage?
— Luke

No, it just depends on position being a continuous function of time. What you're talking about is a kind of propagator. That can be made consistent with kinematics, but not derived from it. — Kenosha Kid

How is continuity sufficient? What does change/motion mean without temporal passage? Isn't such a "propagator" being implicitly assumed when you talk about deriving motion from the geometry? Surely any concept of motion assumes that something gets from t to t'. Otherwise, what else could motion be? Change has no meaning in a static world.

As I've said before, motion is the geometry of the 4D object. Any point on that object will have a coordinate (x, y, z, t). If two points (x, y, z, t) and (x', y', z', t') on the same 4D object have different time coordinates (t' != t) but the same spatial coordinates (x'=x, y'=y, z'=z), the object is not in motion. Otherwise it must be by definition, since its position is different at different times — Kenosha Kid

I'm attempting to argue that motion is a Presentist notion. I don't doubt that you can calculate a value for motion for a given section of a 4D object (i.e. in Eternalism), but doesn't the very concept of motion assume that a 3D object moves from t to t' in some fashion akin to temporal passage? You can say that there's motion in Eternalist geometry, but the concept of motion is based on Presentist assumptions, I would argue.

Motion in 3D + time = geometry in 4D. — Kenosha Kid

What is motion in 3D? How does that work without time?

The continuity of 4D objects purely as geometric objects is sufficient, and that geometry is sufficient for motion. — Kenosha Kid

Why is it sufficient?

No you don't, that is precisely what the eternalist viewpoint doesn't need. You don't need to account for how you get from an event at time t to one at time t', because it's all just laid out there and real. The continuity of 4D objects purely as geometric objects is sufficient, and that geometry is sufficient for motion. — Kenosha Kid

Are you denying that we "get from an event at time t to one at time t'"? Or are you saying that "history is laid out there and real" somehow provides this motion? If so, how?

Unless you main one must account for the subjective human experience of presentism in an eternalist universe. But understand that is not needed for motion: motion is geometric in 4D just as shape is in 4D. — Kenosha Kid

You introduced this aspect into the discussion:

"there needs to be some explanation for why, if I stare at a cup for a given interval of time, the cup at the end not only appears indistinguishable from the cup at the start, but appears continuously" — Kenosha Kid

The impression of presentism when you are laid out in 4D is a different question that does not bear on whether or not motion is possible. — Kenosha Kid

If you're just going to assume that motion is possible because it's "in the model", then I suppose there's nothing to discuss. I guess your model contains no assumptions.

There's no "you" to get from one point to the other (presentism). — Kenosha Kid

So it's the same cup from t to t', but not the same you?

I'll come back to the rest later.

The momentum of a quantum mechanical body at a particular time is a feature of its wavefunction's geometry at that time. Precisely, it is, in a given direction, proportional to the number of wave peaks per metre in that direction. It is still related to time, but indirectly, via something called the dispersion relation, which is energetics not kinematics. — Kenosha Kid

I'll have to take your word for it.

If it is irrelevant in eternalism whether consider the cup at time t' to be the same cup as the cup at time t, then it cannot form part of your argument one way or the other. (So here we agree.) — Kenosha Kid

I never meant to imply that it was irrelevant. They are different parts. If you want to refer to them as the same part, then you are ignoring the Eternalist reality and may as well be a Presentist. Hence, "you can also say that time passes if you want".

No, just whatever it is that connects the cup at t' to the cup at t. It's not something I postulate. — Kenosha Kid

In Presentism, what connects the cup at t' to the cup at t is temporal passage. An Eternalist can just reject that and attribute it to something else with an identical effect?

I know the cup at t' is the same as the cup at t, that they are different cross sections of the same 4D object. But if you want to postulate they are not, then there needs to be some explanation for why, if I stare at a cup for a given interval of time, the cup at the end not only appears indistinguishable from the cup at the start, but appears continuously. — Kenosha Kid

As an Eternalist, you know they are different 3D cross sections of the same 4D cup, but for a Presentist there is just one 3D cross section of the same 3D cup moving through time. What you need to account for as an Eternalist, which you have simply assumed here, is how you, or your consciousness, moves from one temporal cross section to another. As I said earlier: "Motion implies that the same object moves from t to t'. This is a Presentist assumption which makes no sense in Eternalism." So how is it that the same object moves from t to t'?

Space is present in both, so therefore momentum is possible in both. — Kenosha Kid

Momentum requires only space?

If motion were impossible, then x(t) = x, which a constant. We could write a position as (x, y, z, m, n, t). But since (x, y, z, t) fully determine position, i.e. (m, n) don't do anything, this is merely describing a 4D something in a 6D space for no reason: it is still 4D. Likewise if nothing moved, (x, y, z) cannot change thus those coordinates define everything. — Kenosha Kid

Those co-ordinates might define everything for a 3D part. What about the rest of the 4D object?

1) Eternalism does not say that the cup at time t is a different cup at time t', so the above is unnecessary — Kenosha Kid

Eternalism logically entails that the cup at time t and the cup at time t' both co-exist as separate objects/parts. They exist as different 3D parts of the same 4D cup, but always as different parts. You can call them the same cup if you like, but you can also say that time passes if you like.

2) Is still yields motion, just via an additional variable.

There is something that turns the cup at t into the cup at t'. — Kenosha Kid

The additional variable is motion? That is, what is this "something"?

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

As defined, yes. — Kenosha Kid

Wait... Are you saying you are satisfied that Eternalism logically precludes motion (according to our agreed upon definition of motion)?

You're arguing against something that nobody is defending. — Pfhorrest

I'm not arguing against anything. I'm trying to demonstrate the logical implications of the concept of Eternalism.

Eternalists don't think that the universe is motionless. — Pfhorrest

I think that some do, actually.

They think motion has to be with respect to something. 3D objects move with respect to a fourth dimension of time, tracing out a 4D shape as they do so. — Pfhorrest

I'm pretty sure Eternalist objects have 4D existence, rather than "tracing out a 4D shape".

not the motion of 4D objects with respect to... what exactly? — Pfhorrest

Again, I wasn't arguing for this. I was checking whether you wanted to.

Moves with respect to what? Time is one of the four dimensions. — Pfhorrest

I know. I was wondering whether you wanted to follow that problematic route.

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

Sorry, but this has all been covered previously. I don't wish to rehash it again here. Is there something you think I failed to address earlier in the discussion?

Edit: Basically, I've been arguing that Eternalism logically precludes motion throughout the thread. If correct, this implies that an Eternalist universe is motionless (inside and out). I can't really condense that into a few sentences to try and convince you. Take a look at the last 2-3 pages.

But they are nevertheless still parts of the same object. — Pfhorrest

Parts of the same 4D object, certainly. Are you wanting to argue that the 4D object moves?

Edit: Or are you implying that these different parts (e.g. of the mountain) are all the same part?

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. — Luke

To anticipate a possible objection, it may be argued that, given the above equivalence, my argument against motion in Eternalism will allow for the same argument to be made against motion in Presentism, thus making motion also impossible in Presentism.

My response is that there is no difference between the Eternalist part at t and the Presentist object at t, or between the Eternalist part at t' and the Presentist object at t'. As I said, a 3D Presentist object at a time is equivalent to a 3D Eternalist part. The reason that motion is possible in Presentism, and what distinguishes this view from Eternalism, is that the Presentist object at t and the Presentist object at t' are considered to be the same object (by Presentists). However, the Eternalist part at t and the Eternalist part at t' cannot be considered to be the same part (by Eternalists). When talking about motion, it is presumed that the same 3D object/part moves through time (i.e. travels) from t to t'. This is a Presentist assumption which only makes sense in Presentism.

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.

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

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).

"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.

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).

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

What difference will continuity make?

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