What does "depends on time" mean? — Luke
Motion is change in spatial position over change in temporal position. — Luke
I've taken great pains to explain myself and present my argument, which you continue to ignore. — Luke
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
I have answered every question you have asked. You have not done the same. — Kenosha Kid
What comes before and after the "i.e" is not equivalent. Motion is not defined as merely having a spatiotemporal position. — Luke
Did you have questions? I thought you were just telling me what's what. — Luke
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
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
...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
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
Is this different for Presentism? — Luke
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
If you are happy that a 4D object exists at more than one time — Kenosha Kid
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
There is the kinematic definition of motion — 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. — Luke
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
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
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
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
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
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
I didn't claim that it wasn't the same mountain. — 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. — Kenosha Kid
I didn't claim that it wasn't the same mountain — Luke
Sorry, I don't understand what you're getting at. I didn't claim that it wasn't the same mountain. — Luke
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
What difference will continuity make? — Luke
However, different objects exists at these two locations in Eternalism - the different parts of the 4D object. — Luke
Couldn't sleep. — 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. — 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. — Luke
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
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
Which is a complicated way of changing some labels at the end of the day. — Kenosha Kid
The 4D object can be broken into its constituent parts, just like a mountain can. — Luke
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
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
And this has been your mistaken assumption all along: that the existence of time automatically implies the existence of motion. — Luke
But that's exactly the difference between Presentism and Eternalism. — Luke
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
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
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
You can have an eternalist universe without motion, but then the temporal dimension would be redundant. — Kenosha Kid
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