The Impossible Physics Problem

[PhantomWolf]

So you're just throwing us the same old relativity problem and solution we're already well familiar with. What's next? A tutorial on how to suck eggs?

Did you read this part...

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.
Are you having trouble with accepting relativity? If not, then it's not a problem for you to try to solve.

 

[PhantomWolf]

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.

There is no attempt to trick here at all, it's an attempt to show that there is no such thing as absolute motion and that you can't solve a velocity without that velocity being relative to something else. It doesn't matter if you simplify it or not, you can change it to one box and the one you are in and you still will be unable to determine your box's velocity in regards to the Ocean, all you can do is determine it relative to the other box. The question is not for people that understand physics and provides some trick to catch them out, it is purely for people who refuse to accept relativity and believe that there is such a thing as absolute motion.

 

[theprestige]

Did you read this part...

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.
Are you having trouble with accepting relativity? If not, then it's not a problem for you to try to solve.

People who have trouble with that concept are going to have trouble working your physics problem. People who can work your physics problem have already worked out that all motion is relative.

Who exactly is this problem directed at? Anyone who can work it already knows the truth. Or, they have already decided to reject the truth regardless of the problems that work out to the truth.

 

[PhantomWolf]

People who have trouble with that concept are going to have trouble working your physics problem. People who can work your physics problem have already worked out that all motion is relative.

Who exactly is this problem directed at? Anyone who can work it already knows the truth. Or, they have already decided to reject the truth regardless of the problems that work out to the truth.

Seriously, I have only answered this question about six times now.

 

[theprestige]

Seriously, I have only answered this question about six times now.

You've answered it maybe once, and that answer is lacking. The people who can work the problem aren't your audience. The people who are you audience can't work the problem. Or won't work the problem. Or won't acknowledge the working.

And none of the people who can work the problem and will change their minds after working the problem are here on this forum. So what's the point of you posting this problem? Are you just trying to signal your virtue in knowing the problem and its solution? A virtue that was never in doubt, here?

 

[PhantomWolf]

You've answered it maybe once, and that answer is lacking. The people who can work the problem aren't your audience. The people who are you audience can't work the problem. Or won't work the problem. Or won't acknowledge the working.

And none of the people who can work the problem and will change their minds after working the problem are here on this forum. So what's the point of you posting this problem? Are you just trying to signal your virtue in knowing the problem and its solution? A virtue that was never in doubt, here?

To my knowledge, many of the people on this forum deal with debunking people that think they understand physics and come up with crazy ideas, such as absolute motion. The reason for posting was in the very first part of the first post, the bit I just quoted for you again. It's a problem that can be given to people who aren't accepting that motion is relative and not absolute. Most of those people do think that they are smart enough to solve such a problem, the idea is to show them that they can't. If you don't have those sort of people in your life, good for you, then this thread has nothing for you. If you do deal with people that reject relativity, then feel free to borrow and modify as you see fit.

 

[DevilsAdvocate]

Dang it. I told myself I would stop thinking about this problem and now I keep thinking about it.

I think I may have the means to a solution.

The North Box is moving at -3M per minute. That means it is moving at 3M per minute closer to our box. That means it must eventually come to and go South of our box. At that point it would be moving at +3M per minute. But the "change is consistent" so it can never be anything but -3M.

That puts a time limit on how far away the North Box can be at the starting configuration. We obviously have a problem with infinity here, because that messes everything up.

But this is in an ocean. Considering that our compass (and stopwatch for that matter, but that gets into more complicated matters of relativity) works the way a compass works on Earth, I will presume that the ocean is on Earth.

That sets limits. We are measuring with a laser. We know how far the North Box is at the start. Due to the curvature of the Earth, we can calculate the maximum distance of the North Box. That also sets the maximum time that the change can be consistent.

The maximum distance (and therefore time) is also regulated by how far away the boxes are from shore. Once they hit shore, they will cease that consistent change of movement.

The minimum distance is 4M off shore. The maximum distance is the lesser of the furthest place on Earth from the shore or the longest distance for a laser to hit a distant box. Well, not actually really the actual middle of the ocean, because our system of boxes will be moving at different velocities in different directions, but somewhere sort of middleish.

The West Box is moving away at +4. The East Box is moving away at +1. In order to maintain the measurement of consistent change for the maximum time before one of those boxes moves beyond the horizon, our box would have to be moving west. More than zero. The maximum depends on our position.

See where I am going? To maintain maximum consistent change before the system breaks, we can determine what direction we are moving and to some degree how fast.

To do this mathematically, we should scrap the problems of using the Earth. The ocean is a circle. For that, I think we would need to set either the size of the circle or the distance that our box can detect another box. I think that with either of those parameters, it should be possible to calculate the other.

It may be possible to calculate the time and distance traveled by our box. I suspect we would get a range of possible values rather than an absolute. An interesting question would be whether given such a scenario any result in a singular rather than a range value.

 

[PhantomWolf]

The North Box is moving at -3M per minute. That means it is moving at 3M per minute closer to our box. That means it must eventually come to and go South of our box. At that point it would be moving at +3M per minute. But the "change is consistent" so it can never be anything but -3M.

Well, I'd say that when the box passes us it would be consistent that the speed would become +3. If it remained +3 all the time then it would be constant rather than consistent.

As to the rest of it, I swear you have given it waaaaaaaaaaaaaaaaaay too much thought DA.

 

[HansMustermann]

The problems that led to relativity are different, though. The main problem is specifically that your laser range finder actually works in both the N-S and E-W directions just the same. That's not even remotely the same if you used, say, an echo locator instead.

So essentially it's the wrong problem for relativity deniers in the first place.

 

[Puppycow]

It seems like one possible solution is that our box is stationary and the other four boxes are moving at different rates in different directions. I don't think there's enough info there to really be certain of anything. I guess that's why you called it "impossible"?

 

[DevilsAdvocate]

Well, I'd say that when the box passes us it would be consistent that the speed would become +3. If it remained +3 all the time then it would be constant rather than consistent.

As to the rest of it, I swear you have given it waaaaaaaaaaaaaaaaaay too much thought DA.

In order to accomplish teaching someone about relativity, your puzzle requires someone to give it waaaaaaaaaaaaaaaaaay too much thought. The simplified approach is that the different boxes don't matter. Just work it out for one box. Or just skip to the basic idea that the whole system of boxes may be moving at one million meter per second to the south and the whole question is meaningless rubbish.

Your puzzle is basically that there are a bunch of boxes that can move at any speed and what speed is this box moving at. Well, it can move at any speed because that is what it says right there in the question. The speed or distance away of any other boxes are entirely irrelevant.

The whole system of the boxes could be staying basically in the same place or be whizzing off to the South at the rate of 1 million miles per hour. All the stuff about compasses and lasers and stop watches and how far one box is from anther box does not matter at all.

The relative positions of the boxes don't matter at all. It is basically just saying that a box can move at any speed; what speed is the box? The directions and compasses and stopwatches and other boxes and given distance measurements and relativity and everything doesn't matter.

The only thing that matters is that the box can move at any velocity and that means the box can move at any velocity.

 

[Robin]

The problem is, if you give this to someone who doesn't yet buy any sort of relativity, even Galilean relativity, then they will just respond that the scenario tells us nothing because we are only short of information. That if only we had a little more information then we could tell quite easily how we are drifting through the ocean.

Then they might conclude that I was making an argument from ignorance towards the relativity of motion.

 

[PhantomWolf]

In order to accomplish teaching someone about relativity, your puzzle requires someone to give it waaaaaaaaaaaaaaaaaay too much thought. The simplified approach is that the different boxes don't matter. Just work it out for one box. Or just skip to the basic idea that the whole system of boxes may be moving at one million meter per second to the south and the whole question is meaningless rubbish.

Your puzzle is basically that there are a bunch of boxes that can move at any speed and what speed is this box moving at. Well, it can move at any speed because that is what it says right there in the question. The speed or distance away of any other boxes are entirely irrelevant.

The whole system of the boxes could be staying basically in the same place or be whizzing off to the South at the rate of 1 million miles per hour. All the stuff about compasses and lasers and stop watches and how far one box is from anther box does not matter at all.

The relative positions of the boxes don't matter at all. It is basically just saying that a box can move at any speed; what speed is the box? The directions and compasses and stopwatches and other boxes and given distance measurements and relativity and everything doesn't matter.

The only thing that matters is that the box can move at any velocity and that means the box can move at any velocity.

You could have boiled that down to "The boxes could be moving at any speed because we can only determine how fast they are moving relative to each other" which of course is the right answer.

 

[PhantomWolf]

The problem is, if you give this to someone who doesn't yet buy any sort of relativity, even Galilean relativity, then they will just respond that the scenario tells us nothing because we are only short of information. That if only we had a little more information then we could tell quite easily how we are drifting through the ocean.

Then they might conclude that I was making an argument from ignorance towards the relativity of motion.

Well once they determine that we don't have enough information, then you introduce more questions, such as "what other information do you need, and why do you need it?"

 

[erlando]

Using the above information, determine how fast your box is drifting through the ocean, and in which direction.

In what frame of reference?

 

[a_unique_person]

Well once they determine that we don't have enough information, then you introduce more questions, such as "what other information do you need, and why do you need it?"

You won't be starting another thread like this. Just saying.

 

[rjh01]

At least 3 other boxes are moving. The North and South boxes will eventually meet as they are coming together at speed 1. The east and west boxes are moving apart from each other at speed 5.

 

[sphenisc]

Dang it. I told myself I would stop thinking about this problem and now I keep thinking about it.

I think I may have the means to a solution.

The North Box is moving at -3M per minute. That means it is moving at 3M per minute closer to our box. That means it must eventually come to and go South of our box. At that point it would be moving at +3M per minute. But the "change is consistent" so it can never be anything but -3M.

That puts a time limit on how far away the North Box can be at the starting configuration. We obviously have a problem with infinity here, because that messes everything up.

But this is in an ocean. Considering that our compass (and stopwatch for that matter, but that gets into more complicated matters of relativity) works the way a compass works on Earth, I will presume that the ocean is on Earth.

That sets limits. We are measuring with a laser. We know how far the North Box is at the start. Due to the curvature of the Earth, we can calculate the maximum distance of the North Box. That also sets the maximum time that the change can be consistent.

The maximum distance (and therefore time) is also regulated by how far away the boxes are from shore. Once they hit shore, they will cease that consistent change of movement.

The minimum distance is 4M off shore. The maximum distance is the lesser of the furthest place on Earth from the shore or the longest distance for a laser to hit a distant box. Well, not actually really the actual middle of the ocean, because our system of boxes will be moving at different velocities in different directions, but somewhere sort of middleish.

The West Box is moving away at +4. The East Box is moving away at +1. In order to maintain the measurement of consistent change for the maximum time before one of those boxes moves beyond the horizon, our box would have to be moving west. More than zero. The maximum depends on our position.


See where I am going? To maintain maximum consistent change before the system breaks, we can determine what direction we are moving and to some degree how fast.

To do this mathematically, we should scrap the problems of using the Earth. The ocean is a circle. For that, I think we would need to set either the size of the circle or the distance that our box can detect another box. I think that with either of those parameters, it should be possible to calculate the other.

It may be possible to calculate the time and distance traveled by our box. I suspect we would get a range of possible values rather than an absolute. An interesting question would be whether given such a scenario any result in a singular rather than a range value.

I don't think you've thought about this enough. Clearly boxes don't pass through each other, they bounce of each other,so the North box will switch from -3M from the north to +3M to the north. And obviously they also bounce of the coastlines. What you've got here is a rudimentary four directional range-finder system. By timing the return time of each of the boxes you'll either get each box having a constant return time, in which case your stationary*. Or at least one pair of boxes will show some variation. Over time the varying boxes can be used to map out the the distance to surrounding coastlines, and by comparing the compression/skewing of the derived coastal map to an actual map it should be possible to determine one's velocity.

* There's a region in the Southern Ocean between 55° and 63° S where the E and W boxes may each complete a hemicircumnavigation before bouncing off each other and returning. This will also give constant values, but the values should be large enough to distinguish them from the stationary situation anywhere else except the widest part of the Pacific. If this is the case then the the ability to identify Galapagos Penguins from Fairy Blues would be helpful.

 

[DevilsAdvocate]

You could have boiled that down to "The boxes could be moving at any speed because we can only determine how fast they are moving relative to each other" which of course is the right answer.

No. I could have and did boil it down to "A box is moving at an unknown velocity. What is the velocity of the box?"

The velocity of the box is unknown, which of course is the right answer, because it tells you that right there in the question.

If you take you puzzle and eliminate all factors relevant to the velocity of the box, you end up with no factors relevant to the velocity of the box. Everything in the puzzle is completely irrelevant. It is just a box that could have any velocity and therefore could have any velocity.

That is the bottom of the boil.

 

[3point14]

This is all the fault of Star Trek, you know.

Arriving at a destination and saying "Full stop" or some such. It gives people terrible ideas about relative motion and orbital mechanics.