8
$\begingroup$

A water molecule is made of 1 oxygen atom and 2 hydrogen atoms, so it is very small, like quantum scale small. So if I accelerate a bunch of these water molecules through the double slit using a spray then would I see an interference pattern on the screen? Intuition tells me no but my gut feeling is saying otherwise...

$\endgroup$
0

4 Answers 4

30
$\begingroup$

No, not with a spray.

The reason for this is that "sprays" are not isolated molecules. They are fine droplets, and the individual droplets are still vastly larger than a molecule - a molecule is on order of 0.2 nm in size, but a droplet is >1000 nm. Hence, the droplets will not display sensible quantum behaviors of the type you are looking for.

Now you might ask about vapor or steam, i.e. water gas, which truly is separated to a molecular level. The problem there is that the molecular motions are randomized, by which I don't mean the "quantum-random" sense but the "thermal-random" sense. In terms of the position wave functions for the centers of mass of the molecules, which is what you want to try to get to behave nontrivially, they will be essentially waves of random and incoherent shape and direction(*). To get the double-slit pattern, you need coherent waves - same shape, same direction, synchronized phases. This means you need a molecular gun that is capable of regulating speed, direction, and timing accordingly - just as to do it with electrons, you need an electron gun.


(*) Technically, we don't really want to even talk "wave functions" at all here, because there is going to (almost surely) be entanglement due to molecular collisions (which thermalize the gas), which is how we can treat the gas as a classical gas for the purposes of, say, the ideal gas law. The entanglement means an individual molecule's kinematics are "decohered" with regard to the rest and can be treated as though it has an unknown, but actually much more localized, positional wave function. In a sense, the quantum "fuzziness" has been sucked from the molecule and transferred onto the surrounding gas. This is called a "mixed state"; mathematically it is represented via a density operator and not a Hilbert vector (those "$|\psi\rangle$" things) or a wave function. The analogue of a wave function for density operators is the density matrix, which is a function of two parameters. A more "physical" version of this is the Wigner function, which gives a "never-localizable" distribution where the two parameters are position and momentum simultaneously. We can still take the marginal for either, of course, which will be a probability density function or pdf, but this is not the same as a "wave function", because the wave function includes phase information.

$\endgroup$
9
  • $\begingroup$ @Jirka Hanika: If the gas is thermalized, as we can usually approximate, it will almost surely have gotten that way by molecules colliding with each other. $\endgroup$ Dec 11, 2023 at 8:29
  • $\begingroup$ Wouldn't the slits behave rather like a pair of nozzles? $\endgroup$
    – MikeB
    Dec 11, 2023 at 16:57
  • $\begingroup$ @MikeB: Hmm. You're right, I'd think so. When I first answered this, I remembered some diffraction experiments had been done using "buckyballs" which are actually considerably bigger than water molecules, but not the details. I just decided to look it up, and there's a schematic here: quantumnano.at/research/universal-matter-waves/… which kinda suggests the experiment is not too different from this! But note though you also need a velocity selector - I forgot to mention that the wavelength also matters. $\endgroup$ Dec 11, 2023 at 18:28
  • 1
    $\begingroup$ Given that interference patterns can be created with much larger molecules than H2O such as bucky-balls, I'm not sure how you can assert that an electron gun is required. $\endgroup$
    – JimmyJames
    Dec 12, 2023 at 16:26
  • 1
    $\begingroup$ @JimmyJames : Yes. Note my link which describes the Buckyball experiment explicitly. You will need more than a slit though, you will also need some way to ensure the velocities and so wavelengths are about equal. Remember you're picking molecules out of a Maxwellian (or approximately so, at least) distribution. So you need to ensure only molecules of similar velocities make it to the screen, while turning away those of substantially different velocity. That's also why I mentioned a gun: a gun lets you control the velocity directly, which is more efficient. $\endgroup$ Dec 12, 2023 at 17:26
11
$\begingroup$

The deBroglie wavelength of a droplet of water can be calculated like any other particle:

$$\lambda = \frac{h}{mv}$$

Where $h = 6.62607015×10^{-34} \frac{J}{Hz}$ - at $100 \frac{m}{s}$ a 1000 nm radius sphere of water has a mass of $2.4 * 10^{-15}$ grams.

This gives a wavelength of about 3 nm.

As the wavelength is much smaller than the droplet, it will be hard to generate an interference pattern.

Dropping the speed down to 0.1 m/s makes the wavelength longer than the particle size.

The next hard part is not having the droplet self destruct, and avoiding it from accidentally being measured by interacting with photons and thus the environment. Objects that are not extremely cold emit a LOT of photons (thermal heat), which makes them difficult to keep isolated.

So, super cool the droplet, send it at extremely slow speeds in a vacuum, super cool the environment, and you could get a quantum interference pattern.

I don't think we have the engineering capabilities to do this.

$\endgroup$
1
  • 2
    $\begingroup$ I feel like it is worth pointing out here that the typical problem for more massive molecules is actually wavelengths that are too small. As you increase the mass of the particle, the wavelength actually decreases. This wavelength is only unmeasurably large because the velocity of the droplet is non-relativistic (reasonable, since otherwise it would evaporate or turn to plasma), not because of the droplet being too massive. $\endgroup$
    – Obie 2.0
    Dec 11, 2023 at 1:39
5
$\begingroup$

They have performed interference experiments with big molecules, but not in forms of sprays, since then collisions and interactions between the particles would lead to their decoherence and loss of quantum effects. But if you shoot one molecule through the double-slit setup, yes, it would interfere (if the length scales are properly sized).

$\endgroup$
2
1
$\begingroup$

Every "entity" with mass has an associated deBroglie wavelength λ = h/mv. But because m is (relatively) large for droplets, λ becomes very small. But if you squint, even relatively large masses we'd normally treat classically expose "quantum-ness".

The limit of the quantum model for ever larger masses is the familiar, seemingly continuous behavior of macroscopic objects. Quantum effects are still there, but they become vanishingly small, and hence irrelevant. This resembles other improvements of classical physics for scales beyond everyday experience, notably relativity where the limit for slow velocities consists, unsurprisingly, of the laws of classical mechanics.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.