When do we know where an object is

[Daniel Huren]

soo i might have asked this poorly but the question i have is to long for the actual title of the thread also not shure if this is quantum physics of actual physics but the nature of the question seems closer to quantum physics also not shure if the prefix is right but this seems like a pretty advanced question and isent something i think high school physics can answer

at what point does the probability that an object of any size is going to be were you expect it to be 100% of the time

 

[DarkBabylon]

Welcome to the physics forums!
For starters I would like to clarify that what you refer to as "actual physics" is more commonly known as "classical physics", as quantum mechanics is (a huge) part of physics. (not to demean the classical physics, as it is still useful in many applications)

Now to address the question: One of the things that was sort of guessed, but is a very good and based guess, that particles obey wave mechanics. This is the point where a wave equation was needed to describe a particles. Once you introduce that, we imply that many of the behaviours of wave mechanics apply in particles small enough and light enough. One of them, that turns out to apply, is the uncertainty principle.
The uncertainty principle states that if we were to multiply the standard deviations (closely related to how spread out the wave function) of momentum and position they must always obey:
Δx*Δp≥ħ/2
where Δp, Δx are the standard deviations of momentum and position respectively.
In laymen's terms it basically means that should you at any point know the momentum with more certainty, you'll lose certainty over the position and vice versa. In the scales of quantum mechanics, it can mean huge changes on the certainty should one be spread out more or less.

Lesson here is, at no singular point can you be sure with 100% certainty that the particle is there. Otherwise it implies the particle went *everywhere in the universe* ever since you measured it. However, you could start bargaining with the universe. If you are completely fine with the particle be just in a certain region (say, 2<x<5), it is possible for you to make its wave function in space be in that region with near 100% success, and although it wouldn't sit quietly there (after all it has a not-exactly-zero momentum), you can be sure enough it'll stay around that region. It is done with changing the potential energy in space.

Indeed to get any further, math that is not normally taught in high school is involved, in particular Differential Equations and integrals, but with enough patience, good book and enough interest one could learn it.

 

[Daniel Huren]

so i think i get what you explained there and it helps a little well trying to reconcile this in my head but the 2<x<5 thing is the part i want to understand more though since i feel like its the part i don't fully understand and probably pertains most to what my question is getting at is and if we don't have an answer for it yet I am fine with that but what i really want to know is if i let's say i take a o sphere of size x and some were in that sphere is a single particle how small can that sphere be before you can't be a hundred percent certain that that particle you stuck in that sphere is not longer certain to be were you expect it to be

 

[Daniel Huren]

so i think i get what you explained there and it helps a little well trying to reconcile this in my head but the 2<x<5 thing is the part i want to understand more though since i feel like its the part i don't fully understand and probably pertains most to what my question is getting at is and if we don't have an answer for it yet I am fine with that but what i really want to know is if i let's say i take a o sphere of size x and some were in that sphere is a single particle how small can that sphere be before you can't be a hundred percent certain that that particle you stuck in that sphere is not longer certain to be were you expect it to be

i mean would it be easier if i imagine the particle as a bump in space like we do for gravity and its some were on that bump cause what i really want is to be able to picture this in my head would the center of that bump then be the most likely spot its at but it could technically be anywhere on said bump and how big would that bump be if that's the case

 

[Mark44]

so i think i get what you explained there and it helps a little well trying to reconcile this in my head but the 2<x<5 thing is the part i want to understand more though since i feel like its the part i don't fully understand and probably pertains most to what my question is getting at is and if we don't have an answer for it yet I am fine with that but what i really want to know is if i let's say i take a o sphere of size x and some were in that sphere is a single particle how small can that sphere be before you can't be a hundred percent certain that that particle you stuck in that sphere is not longer certain to be were you expect it to be

2 < x < 5 means that x is somewhere between 2 and 5.

To make your posts more readable, please use at least a minimal amount of punctuation, like a period at the end of a sentence, and start the next sentence with a capital letter.

When you say "i take a o sphere of size x", is the o significant or is that a typo?
If you have a particle in a sphere of radius r, you are more certain about where the particle is if r is a small number. If I have one particle in a sphere of radius .001 cm and another particle in a sphere of radius 100 km, I can get a better estimate of the position of the first particle because it's in a smaller region.

 

[Daniel Huren]

i get that but I am asking about what's the difference between the 2 something being a area of space to small for us be certain of its location an 5 being an area of space big enough to be certain of its location is somewhere in that 5

what i want to know is how big is that space were you can be certain of its location is it even measurable?

or am i missing something that was explained already?

also the o is a typo i apologize

 

[DarkBabylon]

When I wrote the '2<x<5' thing, I gave an example of a region you check if there are any particles there, rather than a width of measurement. The width in that case would be 3.

Our only limit is the standard deviations, so now the question is how percise you want the momentum and position measurements. But their multiplication must never decrease from a certain value. It reallt varies from system to system.