Time and movement paradox

[Someone here]

Grandson :"Grandpa, Grandpa. I'm all confused."

Grandpa: (groan) "Yes, what is it?"

Grandson: "In today's class we analyzed the flight of an arrow with snapshots. Now the arrow moves in flight towards its target, but those snapshots don't show any movement which is a paradox. And I know none of those snapshots will show any movement no matter how many snapshots are taken. And if you say that all you need to do is measure the time between snapshots, that will mean there are gaps between snapshots and there are no movements in those gaps. Grandpa, grandpa I'm so confused."

Grandpa: "Why don't you ask your teacher these questions? That's what he gets paid for."

Can you help Grandpa out of this jam?

[LastThursday]

Three things come immediately to mind:

1. The snapshot has an exposure time which is unavoidable. So there will always be motion blur on the snapshot (no matter how small). Ok, motion blur isn't movement, but it is evidence of it. If you keep decreasing the exposure time, the image will get darker an darker. A zero exposure time will capture the arrow perfectly still, but there will be no image.

If you were thinking of it scientfically you might even conclude that the arrow becomes partially transparent when it moves through the air.

2. And a lesser more philosphical point: is a snapshot of an arrow an arrow? Can it be trusted as a representation of the real thing? A representation necessarily throws away a lot of information - including in this case most evidence of movement (and the back of the arrow etc). Can you even trust the person showing you the snapshots that they are all of the same arrow?

3. This story shows that the mind thinks platonically as it were: where snapshots are perfect; motion is composed of a series of perfectly still arrows; the snaphots all go "together" in a series and are of the same arrow, taken close in time together etc. But reality is always a lot messier and less clear cut.

[Someone here]

19 minutes ago, LastThursday said:

Three things come immediately to mind:

1. The snapshot has an exposure time which is unavoidable. So there will always be motion blur on the snapshot (no matter how small). Ok, motion blur isn't movement, but it is evidence of it. If you keep decreasing the exposure time, the image will get darker an darker. A zero exposure time will capture the arrow perfectly still, but there will be no image.

If you were thinking of it scientfically you might even conclude that the arrow becomes partially transparent when it moves through the air.

2. And a lesser more philosphical point: is a snapshot of an arrow an arrow? Can it be trusted as a representation of the real thing? A representation necessarily throws away a lot of information - including in this case most evidence of movement (and the back of the arrow etc). Can you even trust the person showing you the snapshots that they are all of the same arrow?

3. This story shows that the mind thinks platonically as it were: where snapshots are perfect; motion is composed of a series of perfectly still arrows; the snaphots all go "together" in a series and are of the same arrow, taken close in time together etc. But reality is always a lot messier and less clear cut.

@LastThursday always appreciate your mind 

However, The paradox still stands because the gaps still remain between the snapshots. You would need to take an infinity of snapshots to eliminate those gaps between snapshots which is impossible to do in this scenario. So we have a situation of movement and nonmovement in this scenario, a paradox.

 maybe I should explain why I titled this thread " time and movement paradox" instead of "A movement paradox." Well time is a good eyecatcher and it is intricately tied up with movement. You should compare this thread with Zeno's paradoxes, i.e. the one about the arrow (the significant difference is that in Zeno's day, there were no cameras to take snapshots).

Could the problem be overcomed by simply using a video recorder, with a continuous filming motion. The premise is logically sound, gaps in time are excepted between frames due the nature of snapshots, without a point of reference, the theory of relativity specifically states the moving objects will appear motionless.

[DocWatts]

Grandpa could begin by pointing out that time and space are high level abstractions that we use to make sense of our experience.

He could also explain that paradoxes are the borne out of the way that we use high level abstractions to frame problems that we come across

In this case by thinking of an arrow as a discreet object with fixed boundaries, and by thinking that discreet objects occupy a position in something called space that's continuous (non-atomistic).

And while we have good reasons for thinking this way in our day to day lives, science has shown that on a fundamental level what we think of as matter doesn't behave in the way we would expect from our interactions with macroscopic objects in our day to day lives. Particles are closer to possibility clouds with no definitive boundaries or position, then they are to billiard balls or anything else you can relate to in your normal life.

Because our minds conceive of these two things (objects and space) as having different axiomatic assumptions, we run in to paradox.

...then grandson nods non-comprehensively, and Grandpa remembers that he's talking to a ten year old who doesn't have a frame of reference for Construct awareness 

Edited May 8, 2022 by DocWatts

[LastThursday]

On 08/05/2022 at 9:39 PM, Someone here said:

@LastThursday always appreciate your mind 

And I always appreciate your questions.

On 08/05/2022 at 9:39 PM, Someone here said:

However, The paradox still stands because the gaps still remain between the snapshots. You would need to take an infinity of snapshots to eliminate those gaps between snapshots which is impossible to do in this scenario. So we have a situation of movement and nonmovement in this scenario, a paradox.

Nah, just have two cameras timed so that they shoot snapshots alternately and so there are no gaps - since each camera has a finite exposure time.

On 08/05/2022 at 9:39 PM, Someone here said:

Could the problem be overcomed by simply using a video recorder, with a continuous filming motion.

Even video cameras have frames (snapshots) or more likely a rolling shutter. There is never any continuity as such, it's always static frames.

On 08/05/2022 at 9:39 PM, Someone here said:

the theory of relativity specifically states the moving objects will appear motionless.

More precisely that movement is relative to the observer. An object can be motionless in one POV (frame of reference) and moving in another (at the same time). My mug is motionless on my table, but moving at thousands of miles an hour relative to the centre of the galaxy.

Being motionless is just a special case of movement.

If instead of a camera you used a Doppler gun, you could most definitely get a measurement of movement, because of the absolute shift in the wavelength of the returning light. So the paradox is only manifested by the equipment you use to measure movement with.

Notice that with a Doppler gun you can't measure position, unlike with a camera. So you have the opposite paradox, where you know the arrow is moving, but not what path it takes through the air.