Why do scientists do particle collision experiments more than once?

Why are the particle collision experiments involving the same particles are done more than once. Shouldn't the collision of the same particles with the same velocity as the experiment before give out the same results. If they don't why so? How does the same values give out different outputs?

• So you want just one collision? Please clarify your question, perhaps with a specific example. – Jon Custer Aug 15 '17 at 19:50
• @JonCuster Say electron-positron collision. Large Electron–Positron Collider. – user165955 Aug 15 '17 at 19:52
• But what are you measuring in the collision? Total cross section? Angular variation? Spectrum of generated particles? Unpolarized vs polarized beams? Gamma spectrum? Many many things to measure, and you want good statistics too... – Jon Custer Aug 15 '17 at 19:59
• When they are trying to detect the particle that they have theorized. The spectrum of generated particles. – user165955 Aug 15 '17 at 20:04
• The point is that you are not able to set up the exact same initial conditions for every particle. Even if you were able to, Nature at that level is probabilistic. Finally, even in macroscopic classical physics, experimental physics is based on statistical analysis. – Diracology Aug 15 '17 at 20:21

The results of a collision are not deterministic in quantum mechanics/quantum field theory, which is the relevant theory to describe what happens in colliders. Just like other observables are uncertain in quantum mechanics and measuring the same observable on identically prepared states may yield different outcomes, the results of a collision in a collider are likewise uncertain until measured by the detectors. All that QFT predicts are scattering amplitudes, from which you can predict the probability of a particular outcome of a particular collision.

Therefore, in order to be able to compare experimental results with the theoretical predictions, we need to measure the very same collision often enough to be confident that the frequency with which we observed a particular outcome approximates the actual probability, i.e. essentially an exercise in applying the law of large numbers.

• How are those scattering amplitudes calculated? – user165955 Aug 15 '17 at 21:22
• @Черенки Uh...with quantum field theory, that's a pretty broad question. To answer that question in any detail I would have to reproduce an introductory textbook on QFT, for which this is not the place. – ACuriousMind Aug 15 '17 at 21:27
• Can you recommend any? – user165955 Aug 15 '17 at 21:34
• @Черенки See e.g physics.stackexchange.com/q/11878/50583 and its linked questions. – ACuriousMind Aug 15 '17 at 21:38
• Given that you can't control the impact parameter at atomic/nuclear scales the results of a collision aren't—as a practical matter—deterministic classically either. – dmckee Mar 25 '18 at 17:15

Any measurement has uncertainty. You can reduce your uncertainty in the measurement by making many uncorrelated observations. If the initial error is $\sigma$, then $N$ observations will reduce the error to $\frac{\sigma}{\sqrt{N}}$.

That is true for all experiments that have any randomness associated with them; but it is particularly true for particle physics. As particles get smaller, you leave the world of determinism and find yourself firmly in the field of probability. For example, if you hit matter with a photon, there is a finite probability of Compton scatter. The scattered photon will have a certain energy and momentum that depends on exactly how it interacted with the electron (classical analog: did you hit the electron head-on, or with glancing impact? And what the momentum of the electron was at the time of interaction?). You can then detect the scattered photon - but since you don't know the exact point of interaction, you can only estimate the angle of scatter. Then, when you measure the energy of the scattered photon, you once again add uncertainty.

If you want to prove anything about the nature of matter on the subatomic scale, you have to accept that you can only derive probability distributions; and that you need to probe the probability many times to gain accurate knowledge.

If I flip a coin once, and it comes up "heads", do I conclude that the coin is unfair (or even, do I conclude that both sides of the coin have "heads" on them?). How many flips do you need to be sure?