You "need another concept of movement" for what? — Luke

Yeah that was worded badly maybe, I was just getting off the train and had to hurry. You need to adjust the concept of motion to the 4D frame, because...

Put simply, 3D objects move; 4D objects don't. — Luke

... saying a 4D object doesn't move, doesn't make sense because there is no 5th dimension in relation to which it could move. The term movement just doesn't apply, because motion is change in position over time. There is no 'over time' for a 4D object as a whole.

But at this point i'm starting to repeat myself again.

Like, what is the height of a 2D square in a flat 2D universe? The answer is not 0... the answer is that height doesn't apply because there is no dimension wherein you can measure it.

↪Luke
I'm done with the thread, I said what I have to say. — ChatteringMonkey

But at this point i'm starting to repeat myself again. — ChatteringMonkey

You could say that again... and again... ;)


What's ironic about the argument that there is no motion in eternalism is that Zeno's famous arrow thought experiment argues exactly the opposite (and just as badly):

"Everything, when it is behaving in a uniform manner, is continually either moving or at rest, but what is moving is always in the now, hence the moving arrow is motionless."

Nothing can change in an instant of time. Zeno, who apparently embraces presentism, says that since only the now exists, change cannot happen.

You need to adjust the concept of motion to the 4D frame, — ChatteringMonkey

What is this adjustment?

... saying a 4D object doesn't move, doesn't make sense because there is no 5th dimension in relation to which it could move. The term movement just doesn't apply, because motion is change in position over time. There is no 'over time' for a 4D object as a whole. — ChatteringMonkey

Exactly. This supports my claim that B-theory Eternalism precludes motion. All objects are 4D in Eternalism, whereas motion only makes sense with 3D objects.

What changes position over time? You seem to be saying that it's not a 4D object, but a 3D part of it. But no 3D part actually moves; there's one 3D part at one position and another 3D part at another position. It's not the same 3D part moving through time or changing position over time. So again: what changes position over time?

To recap:

- Motion is defined (by you) as change in position over time
- 4D objects don't change position over time - because this would require a higher dimension
- 3D parts of a 4D object don't change position over time - because each 3D part exists at its own fixed spatiotemporal position

So where is the motion? What changes position over time? Anyone?

Do you have anything of substance to add - any argument for motion in a block universe - or just hand waving and eye rolling?

This is likely my ignorance, but the MST seems to imply a privileged history. The whole point of spacetime is that it is invariant. The passage of time for a woman flying to a neighbouring solar system at 0.1c is not that of her Earthbound twin, and no objective duration for comparison is necessary or possible. So either the MS adds nothing, or it adds something that makes a nonsense of the world around us. Or does every observer have her own spotlight?

I'm not sure how it could possibly make sense to have a spotlight "moving" through spacetime either. Or, to put it another way, what is the worldline of the spotlight?

, why would that be smuggling in religion?

This is likely my ignorance, but the MST seems to imply a privileged history. — Kenosha Kid

MST is a hybrid of Presentism and Eternalism. Presentism does indeed entail a "privileged history". However, I'm not here to defend Presentism, but to point out the nature of the (block) universe according to (B-theory) Eternalism, which, by definition, contains no temporal passage.

The whole point of spacetime is that it is invariant. — Kenosha Kid

I'm not sure whether that's the "whole point of spacetime", but the laws of physics are considered to be invariant in spacetime, yes.

The passage of time for a woman flying to a neighbouring solar system at 0.1c is not that of her Earthbound twin, and no objective duration for comparison is necessary or possible. — Kenosha Kid

That only makes sense if there is a passage of time. However, there is no passage of time according to B-theory Eternalism. Furthermore, if the absence of temporal passage implies the absence of motion, as I am arguing, then nothing - including light - can travel.

So either the MS adds nothing, or it adds something that makes a nonsense of the world around us. — Kenosha Kid

That's a little hyperbolic. A common criticism of Presentism is that it is inconsistent with special relativity. I don't claim to have the answers on how to make Presentism consistent with special relativity. Maybe light is travelling at the leading edge of the present moment and everything else is travelling relative to it. At least, this seems to make more sense to me than everything at all times (including all past and future times) somehow being in motion. Anyway, I'm merely trying to point out the logical implications of Eternalism, such as its preclusion of temporal passage and motion.

Or does every observer have her own spotlight? — Kenosha Kid

According to special relativity, I think so.

why would that be smuggling in religion? — jorndoe

I don't see how one can give "special metaphysical status" any meaning without referring to religious principles.

MST is a hybrid of Presentism and Eternalism. Presentism does indeed entail a "privileged history". However, I'm not here to defend Presentism, but to point out the nature of the (block) universe according to (B-theory) Eternalism, which, by definition, contains no temporal passage. — Luke

Yes, I watched the video you linked (thanks) and realised you seem to lean toward the pure eternalism it discussed. But you are presenting MST for consideration. My point was that there is no concept of absolute simultaneity. There is no "now" that you and I share, unless we're co-moving. So I was wondering how a spotlight illuminates "now" across many bodies moving at different speeds. Is there a basis for choosing?

I'm not sure whether that's the "whole point of spacetime", but the laws of physics are considered to be invariant in spacetime, yes. — Luke

It absolutely is. (I used to teach this stuff at uni, so I'm not totally pulling this out of the air.) The point was to come up with a way of doing mechanics that dealt with invariants rather than frame-dependents. In spacetime, the invariant is the interval, the 4D equivalent of distance/displacement/duration.

That only makes sense if there is a passage of time. — Luke

Yes, that's the problem. The MST seems to reintroduce a passage of time, not for worldlines but for the spotlight tracing them. I think we're as one on this, that just wasn't clear to me at the start.

Now I'm caught up (thanks for waiting)...

when does motion occur according to Eternalism? — Luke

Simplest of kinematics is velocity: change in position / change in time. This, and all higher orders of motion, are retained in four dimensions. It's just that "change in time" is not special. Let's say you're due south of the summit of a mountain. As you move toward the summit, you're moving north. But you're also moving upwards as you ascend. There's a relationship there: the gradient change in altitude / change in latitude. "Motion" in the usual 3D+1 way of thinking is now just equivalent to that.

My point was that there is no concept of absolute simultaneity. There is no "now" that you and I share, unless we're co-moving. — Kenosha Kid

According to the principle of relativity, laws of physics don't privilege any reference frame. But that doesn't mean that a reference frame cannot be privileged in some other sense - like in the sense of indicating the absolute now. The absolute now would not be part of the known laws of physics if it existed; it would come as an extra fact about the world. But that's old news - it was as true for Galileo and Newton as it is for Einstein.

Science and common sense have pretty much always operated under the assumption that the laws of nature are time translation invariant, and that assumption has borne out well in practice. But the laws of nature (assuming that they exist) do not fix everything about the universe, and they certainly do not rule out additional facts that are not time translation invariant - otherwise the universe would have been static in every sense.

But you are presenting MST for consideration. — Kenosha Kid

I presented the MST mainly for comparison with the block universe. Perhaps that was an error on my part. It was intended to demonstrate that if you want Eternalism with temporal passage, then the MST appears to be the only available option (rejected by most Eternalists), unless someone can present an alternative option. Otherwise, you must acknowledge that Eternalism (i.e. the block universe) does not contain temporal passage - that is, if you didn't already believe the definition.

My point was that there is no concept of absolute simultaneity. There is no "now" that you and I share, unless we're co-moving. So I was wondering how a spotlight illuminates "now" across many bodies moving at different speeds. Is there a basis for choosing? — Kenosha Kid

Yes, these are all well documented problems for Presentism. My concern in this discussion, however, is with whether or not Eternalism precludes motion.

It absolutely is. (I used to teach this stuff at uni, so I'm not totally pulling this out of the air.) — Kenosha Kid

Great! I hope you can help to clarify some of these matters (particularly if I am wrong about all of this).

That only makes sense if there is a passage of time.
— Luke

Yes, that's the problem. The MST seems to reintroduce a passage of time — Kenosha Kid

You find it problematic that MST reintroduces a passage of time? Does this imply that you acknowledge and find it unproblematic that Eternalism (i.e. the block universe) has no passage of time?

Simplest of kinematics is velocity: change in position / change in time. This, and all higher orders of motion, are retained in four dimensions. It's just that "change in time" is not special. Let's say you're due south of the summit of a mountain. As you move toward the summit, you're moving north. But you're also moving upwards as you ascend. There's a relationship there: the gradient change in altitude / change in latitude. "Motion" in the usual 3D+1 way of thinking is now just equivalent to that. — Kenosha Kid

I get that it could be viewed and used like a model in that way. But are you referring here to Eternalism (i.e. the block universe)? If so, then how do you answer my question of what it is that changes position over time if 4D objects (and/or their subdivided 3D parts) remain fixed at their spatiotemporal locations according to Eternalism?

I presented the MST mainly for comparison with the block universe. Perhaps that was an error on my part. — Luke

Well, it was a good one then, I'd never heard of it. I'm just playing catch-up.

Does this imply that you acknowledge and find it unproblematic that Eternalism (i.e. the block universe) has no passage of time? — Luke

In the sense of a 'now' that moves through time? Yes, I find that unproblematic. There are questions about how we account for experience, but those questions don't arise out of the block universe picture.

If so, then how do you answer my question of what it is that changes position over time if 4D objects (and/or their subdivided 3D parts) remain fixed at their spatiotemporal locations according to Eternalism? — Luke

When you say "changes... over time", in the block universe that means "what changes in the rest of the worldline as we move along the time axis in a particular direction". It's probably easiest to convey diagrammatically. If we just consider one spatial and one temporal dimension for the moment, imagine a helix oscillating about a line parallel to the time axis. This could represent a given spatial coordinate in a given frame as the Earth orbits the Sun. Pick a random point on that helix, then follow its path. As the time coordinate increases, the spatial coordinate changes. That is motion as we mean motion to be, which is a 3D + time concept, everyday experience if you like. The "change" is the gradient of the worldline. An unchanging thing would be a straight line parallel to the time axis.

According to the principle of relativity, laws of physics don't privilege any reference frame. But that doesn't mean that a reference frame cannot be privileged in some other sense - like in the sense of indicating the absolute now. The absolute now would not be part of the known laws of physics if it existed; it would come as an extra fact about the world. But that's old news - it was as true for Galileo and Newton as it is for Einstein. — SophistiCat

Taking the broader point, I agree that the existence of things that cannot even be indirectly observed is possible. I'm less convinced that it's meaningful to talk about them. Which I guess is what I was saying earlier: what is the explanatory power of the spotlight? If we accept that a) it is a privileged frame, not shared by all of us, and b) makes no difference to observable phenomena, it can't explain, say, the psychological passage of time, which is subjective, i.e. relative.

Taking the point further, there is nothing to say that a privileged frame mightn't be necessary in future physics, although I think that would have to entail an abandonment of much of relativity, replaced by something that predicts the verified phenomena relativity predicts plus some additional stuff.

An "absolute now" is not a concept that makes sense to me though. "Now" now is not "now" exactly a year ago: it is not absolute. But a privileged moment (e.g. 13.7 billion years ago) wrt which "now" can be referred and seen to change would be absolute and sensible, even if it has no obvious descriptive power.

When you say "changes... over time", in the block universe that means "what changes in the rest of the worldline as we move along the time axis in a particular direction". — Kenosha Kid

What do you mean when you say "as we move along the time axis"? Do you mean simply tracing out a path on a map, or is it that we actually pass through time?

Do you mean simply tracing out a path on a map — Luke

Yes, just this. It would be easier if I could draw it, or write equations. But if you can imagine it, groovy. The question is: what changes (other than the time coordinate) as you follow the path of the helix? The answer is the spatial coordinate of the helix.

To anticipate the follow-up question, or the similarity of what I'm suggesting to the spotlight, it is not necessary to do this for the "change" with time to be there. It's merely a means of illustrating that the change is already encoded in the worldline. You can look at the helix as a whole and see that it is changing in space and time together, i.e. as one coordinate changes, so does the other.

Yes, just this. It would be easier if I could draw it, or write equations. But if you can imagine it, groovy. The question is: what changes (other than the time coordinate) as you follow the path of the helix? The answer is the spatial coordinate of the helix.

To anticipate the follow-up question, or the similarity of what I'm suggesting to the spotlight, it is not necessary to do this for the "change" with time to be there. — Kenosha Kid

Okay, but the Presentism/Eternalism debate is a metaphysical, ontological concern, in which it is argued that the nature of time and existence is best described by one (or a hybrid) of either Presentism or Eternalism. To say that Eternalism precludes motion means that there is no motion in reality. You're saying that motion is no more than tracing out a line on a map? What does the map represent?

It's merely a means of illustrating that the change is already encoded in the worldline. — Kenosha Kid

If Eternalism implies that motion is impossible in the universe, how can it be that motion is "already encoded in the worldline"? Isn't that just an assumption - an assumption which is contradicted by Eternalism?

Yes, I came at this with a kinematic idea of 'motion' and a geometric approach to the block universe. The latter seems justified given the video link you posted, which also presented a geometric picture of the block. I don't have any understanding of a non-kinematic definition of motion tbh, which is my ignorance.

Is 'motion' in the sense that you use defined to rely on the existence of a passing 'present', i.e. is this something different from a conventional kinematic definition of 'motion'? If so, then it's a truism that motion does not exist in a universe without such a present, so long as 'motion' in that sense is not then confused with 'motion' as in the movement of bodies over time generally, which requires no present. I see then the use of re-introducing such a present by means of something like the spotlight.

My preference would be to not add ontological features to satisfy strange definitions. Such a definition would be a presentist definition applicable to presentist descriptions. Time exists in the block (as an axis). Motion is conventionally defined as change in position wrt time (which also works for presentism). Motion exists in the block (if anything exists whose spatial position changes as its time position changes). The answer is inevitably geometric, since the block universe is geometric, and inevitably kinematic given the (imo only sensible) kinematic definition of motion.

Motion is conventionally defined as change in position wrt time (which also works for presentism). Motion exists in the block (if anything exists whose spatial position changes as its time position changes). The answer is inevitably geometric, since the block universe is geometric, and inevitably kinematic given the (imo only sensible) kinematic definition of motion. — Kenosha Kid

I'm not disagreeing with this definition of motion or suggesting any "non-kinematic definition" of motion. However, what I believe Eternalism entails is that there is not "anything [that] exists whose...time position changes". Eternalism posits a universe in which all things (commonly thought of as being past, present and future) have equal existence. That is, everything exists at all times. This implies that all things have a four-dimensional existence and therefore nothing moves through time. Instead, everything exists at its own (fixed) temporal location. The block universe in this case is not a model along which you can trace time with your finger, but the actual universe in which nothing changes its spatiotemporal location.

That is, everything exists at all times. — Luke

Caveat to follow, but: everything exists at all times, but not necessarily at the same place at all times. This variance of position with time is motion.

(Caveat: in reality, not everything necessarily exists at all times.)

The block universe in this case is not a model along which you can trace time with your finger — Luke

As I said:

To anticipate the follow-up question, or the similarity of what I'm suggesting to the spotlight, it is not necessary to do this for the "change" with time to be there. It's merely a means of illustrating that the change is already encoded in the worldline. — Kenosha Kid

The block universe in this case is ... the actual universe in which nothing changes its spatiotemporal location. — Luke

I was speaking of things in the universe, not the universe itself, but that does work too. Imagine a 3D universe consisting only of an eternal stationary ball. In the block universe depiction, this is a straight line parallel to the time axis. Now boost to a frame of reference in which the straight line now has a gradient. i.e. is no longer parallel to the time axis. There's your motion: I just moved the whole universe for you, Luke, and you're still not happy!!! :grin:

You cannot unambiguously say the ball "is moving" because that's present tense and there is no present: just a straight line through the block at some angle from the time axis. The ball has motion, though. In that sense (the kinematic sense) the ball is moving, i.e. if instead the worldline of the ball is sometimes parallel to the time axis and sometimes not, I could say "the ball is sometimes moving" and you'd understand me, right?

Caveat to follow, but: everything exists at all times, but not necessarily at the same place at all times. This variance of position with time is motion. — Kenosha Kid

You still seem to be presuming that an object can change its temporal position (i.e. move through time). Eternalism rejects this.

Imagine a 3D universe consisting only of an eternal stationary ball. In the block universe depiction, this is a straight line parallel to the time axis. Now boost to a frame of reference in which the straight line now has a gradient. i.e. is no longer parallel to the time axis. There's your motion: I just moved the whole universe for you, Luke, and you're still not happy!!! — Kenosha Kid

Why does a 3D universe need a time axis? You seem to be imagining a stationary ball that does not change its spatial position over time, but which still changes its temporal position.

The ball has motion, though. Informally, the ball "is moving", i.e. if instead the worldline of the ball is sometimes parallel to the time axis and sometimes not, I could say "the ball is sometimes moving" and you'd understand me, right? — Kenosha Kid

Unless I've misunderstood you here, you seem to be talking about a ball that changes or doesn't change its spatial position, despite all the while changing its temporal position.

Thank you all for helping me to clarify my argument that the block universe precludes motion:

The block universe (or B-theory Eternalism) has no temporal passage - that's just the B-theory
Temporal passage is (typically sequential) change in temporal position - no passage = no change
Motion is change in spatial position over change in temporal position - no change = no motion

You still seem to be presuming that an object can change its temporal position (i.e. move through time). Eternalism rejects this. — Luke

Yes and no. The no first. Imagine we never heard of the block or spacetime or relativity, and we're stuck with old-fashioned Gallilean kinematics. A thing is, in my frame of reference, stationary if I measure it's positional coordinates r=(x,y,z) over time t and they don't change. A thing is sometimes moving if I measure r over t and they sometimes change. A bouncing ball's height changes over time. I can describe its position at any given time as r(t) = some value.

I can calculate its velocity at all times from these measurements of position. v(t) = some change in r(t) / some corresponding change in t. Allow the change in t to become infinitely small, you get calculus and kinematics. You do not object to the standard kinematic definition of motion.

Now it turns out we've been living in a block universe the whole time. The ball in the block appears as a wiggly line. Sometimes (at some times) that wiggly line is parallel to the time axis of the block, sometimes not. For simplicity, at each time t, the wiggly line has only one positional coordinate, so r(t) still fully describes the path of the ball. (In quantum mechanics, this is not true, and we have to switch from calculus to vector calculus to describe velocities.) The velocity of the ball is still v(t) = some change in r(t) / some corresponding change in t.

"change in t" does not mean "some passage of some objective present moment from the first value of t to the last". Duration is just a length in the block. If you're happy with the idea that a mountain surface's altitude increases closer to its summit, you're happy with the idea that altitude is a functional of radius from the summit, and that you have a gradient: a change in altitude(radius) / a corresponding change in radius. There is no logical exception then to a change in position(time) / a corresponding change in time. We do not ask, "but what is moving toward the summit such the radius can vary?" That would be meaningless. It's equally meaningless to ask "but what is moving through time such that the time can vary?"

The yes: When we say something is "moving through time", they're speaking of a worldline with a nonzero length that is not at right angles to the time axis of the block. Everything real "moves through time", i.e. it exists for more than one value of t and is continuous. That does not mean that the worldline itself, which we may write as a function of (z,y,z,t) is moving with respect to some other time t2. And whatever meaning one might derived from: "how does a path over space and time move through time?" is equivalent to that derived from: "how does a ruler of 12" length move from one end to the other?"

Taking the broader point, I agree that the existence of things that cannot even be indirectly observed is possible. I'm less convinced that it's meaningful to talk about them. Which I guess is what I was saying earlier: what is the explanatory power of the spotlight? If we accept that a) it is a privileged frame, not shared by all of us, and b) makes no difference to observable phenomena, it can't explain, say, the psychological passage of time, which is subjective, i.e. relative. — Kenosha Kid

Yes, the choice of a privileged frame in the sense that is required here cannot be dictated by any physical observations. Although, digressing a bit, there are other considerations that can lead us to single out a "preferred" frame. The division between laws and that which the laws leave out - boundary conditions and such - is conventional to a degree. While relativistic laws are reference frame invariant (up to coordinate transformation), the same cannot be said about those things that the laws do not fix, such as the distribution of matter and radiation in the universe. If we take those other things into account, we can identify reference frames that are special in some way, such as the frame in which the cosmic microwave background radiation has the same energy profile in all directions.

None of which is relevant to the hypothetical frame of absolute simultaneity that would be required for presentism though; there is no particular reason, other than perhaps considerations of symmetry, to identify this frame with the isotropy of the CMB or any other observable feature of the universe. All the same,the need for a privileged frame is not fatal to presentism, although as you point out, no observation can help us identify this frame. Physics doesn't rule out this requirement, but if one is of a positivist disposition, one should find this situation disturbing.

An "absolute now" is not a concept that makes sense to me though. "Now" now is not "now" exactly a year ago: it is not absolute. But a privileged moment (e.g. 13.7 billion years ago) wrt which "now" can be referred and seen to change would be absolute and sensible, even if it has no obvious descriptive power. — Kenosha Kid

Right, there is no fact that you can add to the objective scientific description of the universe that could establish an absolute present. You could say "Now is X seconds from the Big Bang in the comoving frame" or something like that, but that could only be right in the same way in which a stopped clock can be right. So how do you establish a constantly moving now without a reference? You would need a second time axis. And then a third time axis to perform the same function for the second. And then a fourth, fifth, etc.

"change in t" does not mean "some passage of some objective present moment from the first value of t to the last".

That does not mean that the worldline itself, which we may write as a function of (z,y,z,t) is moving with respect to some other time t2. — Kenosha Kid

You seem keen to saddle me with Presentist assumptions. I have not mentioned an objective present moment or a second time dimension. I am using the same definition of motion as you.

What I am arguing is this:
Eternalism has no passage of time. I believe we agreed to this earlier.
Passage of time means that time passes, or that objects pass through time, which means that objects change their temporal position (in a given direction, if you prefer).
Without passage of time, then objects do not change their temporal position.
If an object does not change its temporal position, then it cannot change its spatial position, and therefore it cannot move. Since this applies universally, then there is no motion in the block universe.

While relativistic laws are reference frame invariant (up to coordinate transformation), the same cannot be said about those things that the laws do not fix, such as the distribution of matter and radiation in the universe. — SophistiCat

Right, only insofar as they are denoted by us as functions of coordinates, e.g. as fields, so that we can deal with them.

If we take those other things into account, we can identify reference frames that are special in some way, such as the frame in which the cosmic microwave background radiation has the same energy profile in all directions. — SophistiCat

I am no astronomer, but to my knowledge, the distribution is a uniform, isotropic black body spectrum. Statistically, for every photon red-shifted by change from one frame to another, there is a photon blue-shifted the other way. Since the point of relativistic physics is that phenomena are invariant even if the way we denote them is wrt coordinate systems, it's difficult to imagine what special universal features might be yielded simply by judicious choice of inertial frame. Moving to non-inertial frames, if, say, the universe was found to have net spin, you could call the frame it which it doesn't 'special'. A very novel physics explaining pseudoforces would be required.

All the same,the need for a privileged frame is not fatal to presentism, although as you point out, no observation can help us identify this frame. — SophistiCat

I suppose if we discovered some kind of cosmic pole, that would do it, but yeah I'm not sure how we'd recognise it. I agree, it's not fatal, but it's not justifiable either. All it explains is how much the idea relies on seemingly nonreal things. Other than a fear of a slippery slope back to eternalism, what recommends a single privileged frame over everything having its own 'now', like the spotlight theory? At least those frames aren't special, so need no justification.

You seem keen to saddle me with Presentist assumptions. I have not mentioned an objective present moment or a second time dimension. I am using the same definition of motion as you. — Luke

But that's the problem, you're clearly not. Motion is a gradient of position over time. Position exists in the block. Time exists in the block. As long as objects are a) continuous and b) not parallel to the time axis of the block, you get motion from that and that alone. There's nothing else needed, it's there in the geometry of the object. The fact that when you represent this block the line doesn't move within it is irrelevant because that's not what motion is. Motion in 4D is exactly the same thing as motion in 3D + time, not a 4D + time version of it.

To state that kinematics is impossible in the block, do one of the following:
1. Demonstrate that spatial positions do not exist in the block (the numerator)
2. Demonstrate that temporal positions do not exist in the block (the denominator)
3. Demonstrate that the block contains no continuous worldlines (requirement of continuity).
If any if those are true, then yes, motion cannot exist in the block. But if any of those were true, you wouldn't be talking about the block.

It probably helps not to call it "change in position" or "change in time". If you're happy flipping between 4D and 3D + time representations, that's perfectly sensible, but it's clear the word "change" implies a passage of time to some. The correct word would be "distance" in 4D.

A point object appears in the block as a continuous wiggly line such that, at each time t in the block, the other coordinates of the object are defined. A point on this wiggly line is an event, Event A. Another is Event B. If the spatial coordinates at B differ from A, then between A and B the line has a gradient in those spatial coordinates with respect to time. That gradient is called velocity.

Or you can reintroduce the terminology "change in time" uncontroversially by imagining clocks at Event A and Event B.