# Will tennis ball produce same interference pattern in double slit experiment if everything was scaled up?

Assume the same experimental setup as double slit experiment with electron but everything is exactly scaled up in size so that electron is replaced with tennis ball. Now we throw tennis balls at double slits, instead of electrons. Will tennis ball produce interference pattern same as electron when looked from similarly scaled distance?

You see the interference when the De Broglie wavelength of the object is comparable or larger than the distance between the slits. The De Broglie wavelength is $$\lambda= {h \over m v}$$. Since the electron has a very low mass $$m$$, it can have a "large" wavelength (say some nanometers), and therefore it is possible to show its interference pattern using a crystal lattice, in the same way it is done for X-rays.

A tennis ball, on the other hand, has a very large mass compared to the electron. Its wavelength will be incomparably smaller. So the problem is not scaling up the experiment, but scaling it down. There is of course some difficulty when trying to squeeze a tennis ball into a slit smaller then the Planck length.

Ok but, imagine that somebody could hypothetically arrange such experiment. Do we believe that we would see the interference pattern? The answer is that we don't know. The largest things we have measured the interference pattern of are some macro molecules. We don't know whether quantum mechanics holds up to the tennis ball scale or if some modification of the theory (quantum gravity?) is needed to describe large objects.

• About the last statement, we do understand how quantum mechanics can be approximated to usual Newtonian mechanics at length scale comparable to tennis ball scale. Do you think quantum gravity is relevant for describing large objects like tennis ball?
– KP99
Oct 5, 2021 at 7:04
• @KP99 it may be, or it may be not. The fact is that we don't know because we have no experimental verification. What we do know is that naively extending quantum mechanics to large objects leads to weird paradoxes. On the other hand, we have many modified theories of QM, that predict a different behaviour for macroscopic objects, such as objective collapse theories Oct 6, 2021 at 5:17

Macroscopic object vs. elementary particle
The main difference between a tennis ball and an electron is that the former is a complex object consisting of many atoms (and hence of many electrons, protons and neutrons), whereas the latter is an elementary particle. The collision between a complex object and slits will likely excite low energy modes in the object (i.e., the ball) - that is the collision will be inelastic, and this will result in partial or complete destruction of the interference picture. To bypass this obstacle the ball has to be cooled to very low temperature and have a small velocity. Note that the same could happen, if we consider screen as a macroscopic object, which is plausible even in the case when the experiment is done with electrons - see this answer on a related question.

Buckyballs interference
Another thing to point out is that a double-slit experiment has been done with C60 molecules (buckyballs): Wave–particle duality of C60 molecules (see also here). This is somewhat similar to the tennis balle xperiment, although still on a much smaller scale.

Wavelength of a tennis ball
The other answers (correctly) pointed out the difficulties associated with a very short wave length of a macroscopic object. However, it is necessary to point out that such a composite object is not characterized by a single wavelength - what is meant here is the wave length of its center-of-mass. As long as the object does not interact with anything, the momentum of the center-of-mass is conserved and the object can be treated as a de Broglie wave, but this is manifestly not the case when it interacts with the screen/slits.

Launching the ball
Another difficulty is putting a ball in a state with a well-defined momentum. For electrons this is easily achieved by electrical means, for they are charged particles. E.g., in semiconductor realizations of the double-slit experiment one simply uses the lack of balance between right- and left-moving electrons when an electric potential is applied.

Launching a tennis ball by usual mechanical means is a very incoherent process. One could envisage something like cooling the ball to micro-Kelvin temeratures, giving it an excess electric charge and accelerating it with electric field.

The answer is an emphatic no.

For noticeable diffraction to occur, the width of the slits needs to be of the same order of magnitude as the wavelength associated with the object passing through them. In the case of a tennis ball, the wavelength would be extremely small compared to the ball itself, so a slit narrow enough to cause diffraction would be too small to allow the ball to pass.

Another reason why you would not see anything in your proposed experiment is that a tennis ball is vastly larger than an electron, so if you scaled up the viewing distance by the same factor, you would be standing around 1,000,000,000,000 kilometres from your apparatus, or about a light year.

YES, but the interference pattern will be of different shape.

https://www.desmos.com/calculator/hxjhr3eiyd

Look at this graph and change the l value. It is the wavelength of the wave.

Since the mass of a tennis ball is large compared that of an electron, its wavelength is very small according to the de-broglie equation. So the interference pattern is, as you can see from the graph, the pattern we observe.