CSinUK said:Fairly simple question but it's been bugging me for a while:
Particle accelerators such as the LHC publish some impressive images of the tracks of particles in their detectors. Can someone explain why that is possible considering the uncertainty principle?
Bill_K said:You're thinking the appearance of the track depends somehow on the width of the particle's wavepacket, but it doesn't. The track is marked by the aftermath of a series of atomic collisions, which in the old days produced bubbles, or developed the granules on a photographic plate. Nowadays the innermost detectors in CMS and ATLAS are silicon chips about 100 microns in diameter. The resolution is the same regardless of the particle's energy.
High energy is relevant in the collision itself but not the track.
Bill_K said:The question in this thread, Lapidus, was about the track. I said that high energy is relevant in the collision itself but not the track.
As an illustration of your own question, consider the electron scattering experiments that determine the size ("charge radius") of a nucleus. At low energy the differential scattering cross section σ(θ) doesn't change much as you vary the energy, it's known as the Mott cross section σM(θ). However as you raise the energy, to the point where the electron's deBroglie wavelength q approaches the size of the nucleus, σ(θ) begins to decrease: σ(θ) = σM(θ) |F(q)|2 where F(q) is the Fourier transform of the nuclear charge density, it's known as the form factor. Approximately, F(q) = 1 - (qa)2/6 where a is the charge radius. So you can see the effect of the finite size of the nuclear charge distribution, but only if the electron's deBroglie wavelength is small enough, i.e. a comparable size.
The need for the much higher energy used in LHC collisions is simply to provide enough energy to create the particles.
The Uncertainty Principle, also known as Heisenberg's Uncertainty Principle, is a fundamental concept in quantum mechanics that states that it is impossible to know with absolute certainty both the position and momentum of a particle at the same time. This is due to the wave-particle duality of matter, where particles can behave as both waves and discrete particles at the same time.
The Uncertainty Principle is relevant in the study and use of particle accelerators because these machines operate on a very small scale, where the effects of quantum mechanics are significant. As particles are accelerated to high speeds, their position and momentum become more uncertain, making it difficult to predict their exact behavior and interactions.
No, the Uncertainty Principle is a fundamental principle of quantum mechanics and cannot be overcome. However, scientists have developed techniques and technology to minimize the effects of uncertainty in particle accelerators, allowing for more precise measurements and experiments.
Particle accelerators are powerful tools for studying the behavior of particles and their interactions. By manipulating and accelerating particles to high speeds, scientists can observe and measure their behavior, which can provide insights into the principles of quantum mechanics, including the Uncertainty Principle.
Yes, there are many practical applications of the Uncertainty Principle and particle accelerators. These include medical applications such as cancer treatment through proton therapy, industrial applications such as materials testing and analysis, and research in fields such as particle physics and cosmology to better understand the fundamental nature of our universe.