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The Impossible Physics Problem

PhantomWolf

Penultimate Amazing
PhantomWolf
Joined
Mar 6, 2007
Messages
21,203
Here's a simple appearing and yet impossible physics problem that you can give to people that have trouble understanding that all motion is relative.

You awake to find yourself in a box. Inside the box with you are a stopwatch, a compass, and a laser range finder. The box has a small slit set halfway up and in the centre of each of the four walls. Peering through these slits you can see that you are adrift on an ocean, with nothing in sight except for another four boxes, each one only visible through one of the four slits.

Using your compass you are able to determine that the box is orientated so that the walls are to your north, south, east, and west. Using the stopwatch and rangefinder you are about to determine your change in distance to each of the other boxes over the course of a minute. These are as follows. Multiple checks show that this change is consistent.

The north box -3m
The south box +2m
The west box +4m
The east box +1m

Using the above information, determine how fast your box is drifting through the ocean, and in which direction.
 
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If the box doesn't contain any food or water, it's rather a moot point.
 
It doesn't seem simple to me. It seems self-evidently impossible since we can know nothing about the movement of the other boxes.
 
In fact, it's the kind of problem that's more like "if John has 2 apples and Marry has 3, determine the temperature of the Sun." It sounds really smart to come up with an unsolvable problem, but it really isn't when it's just that the information provided has nothing to do with what you need to solve it. Any silly person can come up with one, and apparently some feel a need to.

The fact is, you can add the same ∆v to all 5 boxes (e.g., they're all in the gulf stream which moves them all about 4 miles per hour or 6.4 kilometers per hour in the same direction) or have them in a still lake, and nothing changes in their relative motion.

Essentially all you're seeing there is just Galilean invariance, sometimes known as Galilean relativity. As long as your system is inertial, relative to another (e.g., to the 0 latitude and longitude point), it doesn't matter what speed you move at, you'll see the same things happening.
 
Robin said:
It doesn't seem simple to me. It seems self-evidently impossible since we can know nothing about the movement of the other boxes.
Click to expand...

Well, that's not entirely true, in fact, we can easily determine all of their velocities relative to our own box. We can always determine the velocities of four of the boxes relative to the remaining one, but never determine an absolute velocity of all five boxes because we cannot use the information from the five boxes to determine their velocities against a fixed point outside of the boxes.

And that's kinda the point. That all velocities and thus all movement is relative, and never absolute. Hence why it is a question to give people that can't understand that movement is relative.
 
PhantomWolf said:
Using the above information, determine how fast your box is drifting through the ocean, and in which direction.
Click to expand...


My box is not drifting through the ocean at all in any direction. It might be moving with respect to distant land masses or with respect to some other portion of the same ocean, but it's stationary with respect to the water immediately around it. Unless it's being propelled through the water by some force, such as wind or a powered prop or being pushed by dolphins, but then it's not drifting.

That might just be playing games with the wording, but it suggests that floating on an ocean isn't a very good metaphor for outer space.
 
Myriad said:
My box is not drifting through the ocean at all in any direction. It might be moving with respect to distant land masses or with respect to some other portion of the same ocean, but it's stationary with respect to the water immediately around it. Unless it's being propelled through the water by some force, such as wind or a powered prop or being pushed by dolphins, but then it's not drifting.

That might just be playing games with the wording, but it suggests that floating on an ocean isn't a very good metaphor for outer space.
Click to expand...

All of the boxes could be drifting, but in different currents. But they'd still be drifting (or not) relative to the center of mass of the ocean as a whole.
 
Robin said:
It doesn't seem simple to me. It seems self-evidently impossible since we can know nothing about the movement of the other boxes.
Click to expand...

PhantomWolf said:
Well, that's not entirely true, in fact, we can easily determine all of their velocities relative to our own box. We can always determine the velocities of four of the boxes relative to the remaining one, but never determine an absolute velocity of all five boxes because we cannot use the information from the five boxes to determine their velocities against a fixed point outside of the boxes.

And that's kinda the point. That all velocities and thus all movement is relative, and never absolute. Hence why it is a question to give people that can't understand that movement is relative.
Click to expand...

It seems to me that you and Robin are saying the same thing, just replace 'movement' with 'drift' in Robin's post.
 
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Impossible? Or just boring? Seems like a story problem meant to change the minds of people who don't believe in relativity, but have the math to trivially prove relativity from a simple story problem.
 
Myriad said:
That might just be playing games with the wording, but it suggests that floating on an ocean isn't a very good metaphor for outer space.
Click to expand...

While using space ships would work far better I agree, most of those that this would be useful for showing that there is no such thing as absolute motion also are likely to try and claim that space isn't real because you can't have gas pressure next to a vacuum.
 
alfaniner said:
With respect to... what? The premise is incomplete.
Click to expand...

This is the exact point you need to come to. That motion needs to be relative. In the question though, with respect to the ocean. The objective is to show people that believe in absolute motion that it doesn't exist and in fact all motion is only relative to other objects.
 
The way in which the boxes drift apart would be characteristic of the local ocean currents.
So in theory, you could get your position and with the change in that your speed.
 
I don't understand the puzzle.

Let's simplify it. Get rid of the North and South because that causes terrible triangulation trigonometry tribulations terminating in terrible tristeza. And get rid of the West as well.

Two boxes, Box A and Box B, start at set positions and can travel on in a straight line to the right at any speed. Box moves at 4 units per minute away from Box A.

Question: How fast is Box A moving?

Answer: Not enough information. Box A could be moving at 0 units per minute or up to infinite units per minute. Both boxes can move at any speed. All we know is that Box B moves at 4 units per minute faster than Box A, which is what the question already told us.

Perhaps the intent of the puzzle is trick people into attempting to solve it without considering a simplification and then realizing that determining the possible relative positions at different velocities are endless and, I would hope, realizing that the problem can be greatly simplified to prove that it is unsolvable, which is the best way to solve problems.

Or perhaps it is an attempt to trick us into goin beyond the question and creating massive trigonometric functions that calculate the angles of the box relative to the other boxes to satisfy the requirements that I suspect would result in a maximum velocity relative to the box system (or at least a specific box) before the geometry becomes impossible and probably a maximus possible acceleration.

I would have fallen for it in my younger days. But these days I am more wise and tired. Mostly tired.

Oh, yeah. I forgot to mention that even though the other boxes are moving relative the box at a consistent velocity that doesn't necessarily mean that all the individual boxes are moving at a consistent velocity. They could be accelerating, or even accelerating at different rates. I think. I have not done the calculations to prove whether or not that is possible. I'm just trying to trick someone else into doing that proof.
 
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