Hypothetical: let’s say I have a magic space gun. When you fire it, it goes in a straight line forever.
So I fire the gun, move it one plank length to the right and fire it again.
For the longest time it will appear as if the two bullets are on the same trajectory. But they are not. They will eventually split apart. My question is: If my target is between these two trajectories, how do I shoot it?
Depends upon how you view space - Continuous (smooth slide) or discrete (pixelated grid). Regardless, the Heisenberg Uncertainty Principle, would indicate that you would not be able to hit the target.
Generally, you can’t.
This problem is similar to wave propagation through anisotropic media. The simplest example is an object behind a mirror. Shine the flashlight just to the left of the mirror and the beam misses the object. Move it a little to the right and the beam gets reflected away from the object.
If space is quantized such that positions are limited, then it is anisotropic.
I don’t see the issue. If you fire, move slightly right, and then fire again, then you’ll have two parallel beams, which will always stay the same distance apart.
Or, if you change your direction, instead of your position, then they’re two intersecting lines, at whatever angle you changed your aim by. To hit something between those two lines, you change your angle by half as much.
You can’t because a plank length is the shortest length possible.
Why would they eventually split apart if the beams are perfectly parallel and 1 plank length apart?
Are we talking expansion of the universe stuff?
But the second part - why can’t you change positions entirely (more than a Planck length) and change the angle of the gun to hit the target?
If you move the gun a plank length but keep the gun parallel with the previous shot the tragectories won’t diverge. The problem only manifests itself if you need to keep the start of the lines at the same point in space.
The Planck length is a length defined in terms of physical constants but that doesn’t mean it’s the smallest possible length. After all the Planck mass is way bigger than the mass of an electron
Who said anything about parallel?. I’m standing in one position. I point the gun. And then I move it one plank ength to the right.
You make your bullet two plank lengths in diameter.
So it’s like a gun on a spinning wheel with the center point fixed? And you fire, spin the wheel a fixed arc distance, and fire again. It doesn’t seem like it matters whether it’s a plank length or 5 degrees, you’ll end up with a space between the bullets at any arbitrary distance.
If the bullets were traveling in space (for the longest time) might their mass eventually draw them together, hitting the target?
It seems like the OP is asking, how can I hit a target I don’t aim correctly at. Rather than firing then rotating the gun, just move it parallel.
But if you aimed the (magic) gun at the target in the first place, this would not matter.
To me (and apparently to others in this thread), that means that you’re leaving the gun pointing in the same direction and sliding the whole thing one Planck length to the right. But I don’t think that’s what you mean. I think what you’re saying is you leave the butt end of the gun fixed, and rotate the gun so that the end of the barrel moves one Planck length to the right. Is that what you mean?
If space is quantized so that a Planck length is the smallest possible length, then you can’t hit the target by rotating the gun. If space is not quantized, then you rotate it so the barrel moves a half Planck length. There’s no particular reason to think that the Planck length is the smallest possible length. BTW, if that were indeed true, and you moved the gun as you describe, how far does a point half way down the barrel move?
Things that make you go hmmm.
Yes. Because people don’t typically move to the right when they’re trying to hit a target. They just point the gun more to the right from where they’re standing.
Why complicate the basic question, which is: if the universe is quantized and if the Planck length is indeed the basic unit, what meaning does a smaller distance have?
The answer will depend solely on a framework that doesn’t yet exist, so I can’t understand how there can be a current answer. Please correct me if I’m wrong. (Not that you wouldn’t if I didn’t ask.)
The question I’m trying to ask is there always a straight line between two points.
From my hypothetical in the OP, I don’t think there is. Hence the question.
Mathematically, of course there is. And then between them and between them and on infinitely. What you’re asking is if there is a physical manifestation of that given certain constraints, which is not answerable with current understanding.
That plus conceptually that the universe is not some flavor of non-Euclidean where truly parallel lines cannot actually exist.