# De Broglie wavelength of a massive particle as v approaches c

We understand that from a relativistic version of De Broglie's wavelength-momentum relation that as velocity approaches 0 the wavelength trends to infinity and as velocity approaches the speed of light wavelength tends to 0. What does a de Broglie wavelength of 0 imply, other than infinite kinetic energy (Theoretically)?

• Massive particles can not achieve that velocity. We don't have to ignore the uncertainty relation to conclude that relativistic particles will behave very much like classical particles if we perform only weak measurements on them. This is the principle on which high energy physics particle detectors rely: given the large momentum of the particles they detect the position uncertainty is of absolutely no consequence for the operation of the detector and the trajectories look very much like classical particle trajectories would. – CuriousOne Sep 12 '15 at 8:04
• This entire question is hypothetical. I said that. The question here in fact is what is absolute particle character, and is it even theoretically possible. – Tamoghna Chowdhury Sep 12 '15 at 8:06
• Even hypothetically it is impossible. Physics only deals with what is allowed within the laws of nature. It can't make predictions that would violate the ones we know, already. Having said that, the universe produces cosmic ray particles that have roughly the energy of a golf ball... that's about as classical for your purposes as one can get! If these things would race photons over distances of millions of light years, the photons would only win by a fraction of a second, I believe. – CuriousOne Sep 12 '15 at 8:11
• A massive particle cannot reach $c$ so the hypothetical is impossible. – Rob Jeffries Sep 12 '15 at 8:11
• Does my answer provide an appreciable counter-logic? – Tamoghna Chowdhury Sep 12 '15 at 8:12

The smallest possible length being the Planck length, and an absolute particle being 0 - dimensional, the kinetic + rest mass-energy of the particle would cause near-instantaneous gravitational collapse, and the resulting black hole will also nearly immediately evaporate by Hawking radiation, erasing the particle from existence at v=c. So if even a massive particle became an absolute particle, its existence would not be measurable at all (an existential period of approximately 2 Planck times, which is not measurable given the uncertainty principle), and for all practical and theoretical purposes it might not exist.

• We have plenty of posts which explain why this wouldn't happen. The particle has to have sufficient rest mass in the observer rest system to form a microscopic black hole. Your idea of particles having a size is also wrong. An elementary particle does not have a size. It only has a position uncertainty, but that's not the same as size. – CuriousOne Sep 12 '15 at 8:14
• I just said that an elementary particles has zero size. That is my basic justification. Also, the particle does have a rest mass, already provided in the question – Tamoghna Chowdhury Sep 12 '15 at 8:17
• As the answers to this question explain you cannot turn an object into black hole simply by making it travel fast. – John Rennie Sep 12 '15 at 10:21
• Thanks for your explanations, but the character of an absolute particle still remains unclear. – Tamoghna Chowdhury Sep 12 '15 at 12:08
• That's because neither he word "absolute" nor "particle" make the least sense in this context. You invented something that physicists simply don't care about. – CuriousOne Sep 12 '15 at 14:49