Uncertainty principle in Quantum mechanics: Why can’t you just measure the position first ignoring the momentum for now, and then after finding the position, just restart from scratch to measure the momentum accurately?

 You cannot measure position and momentum simultaneously because particles do not HAVE absolute position and momentum simultaneously.

When you think of a “particle,” I’m betting you are picturing a little round ball in your mind, like a marble but very tiny.

You’re wrong.

It’s not your fault you’re wrong. Science communication to non-scientists shows particles as hard round balls, like this:

This is wrong. Particles are not little hard balls, and atoms do not have electrons orbiting in circles around a nucleus.

Subatomic particles are fuzzy, smeared out in space, and can do things that little hard balls can’t do. For example, they can pass through something without traveling through the space it occupies. (This is called “tunneling,” and it’s how the flash memory in your SSD and your smartphone works.)

As long as you think of particles as hard balls like marbles only smaller, you won’t be able to understand a whole lot of physics, beginning with uncertainty.

Theres no analogy to describe what they’re really like because they are not like any macroscopic objects. Nothing in your intuitive understanding of the world is remotely like what they are.

For example, mass-bearing particles like electrons and protons have a wavelength. They aren’t located in one area of space; they can, in a sense, “be” anywhere in that wavelength. But they aren’t like ripples on a pond either.

That’s why people say the language of quantum physics is math. Normal language that describes things in the macroscopic world, like marbles and springs and such, don’t work. Particles are not like anything you can picture in your brain.

And as weird as it sounds, they don’t have absolute momentum and position at the same time.

There is a bound, a limit on how smeared out they are; we can know generally where they are and how much momentum they have. That limit is expressed mathematically in terms of $\hslash$, the reduced Planck constant, and the total uncertainty is given as

$\Delta x\Delta p\ge \frac{\hslash }{2}$

You can reduce the wavelength of the particle you’re measuring, which will confine it to a smaller space and give you more precision in its location, but doing this makes its momentum more uncertain. You can do the same the other way, reducing the uncertainty in its momentum, at the cost of increasing its uncertainty in location.

This isn’t because you aren’t clever enough to build a device that measures both. It’s because particles are not hard balls, they don’t act like hard balls, and they don’t have absolute position and momentum.