0

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)?

Qmechanic
  • 201,751
Tamoghna Chowdhury
  • 1,111
  • 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 08:04
  • 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 08:06
  • 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 08:11
  • A massive particle cannot reach $c$ so the hypothetical is impossible. – ProfRob Sep 12 '15 at 08:11
  • Does my answer provide an appreciable counter-logic? – Tamoghna Chowdhury Sep 12 '15 at 08:12
  • No, I am afraid not. – CuriousOne Sep 12 '15 at 08:15
  • "What does a de Broglie wavelength of 0 imply,..." As we talk about "massive" particles, intuitively, it might imply that the object is "always there", i.e. is "no wave" (paradoxically, refering to wave length). As energy correlates to frequency, any "massive" particle would attain endlessly plenty of energy, which is some Einstein standard? In that context, I'd like to know what acceleration to speed of light implies for "massive particles" which are no elementary particles. If they do why do they fall apart? That's your question? – Peter Bernhard Oct 06 '22 at 20:08
  • Honesty, I asked this question way back in high school when I didn't understand this well enough to formulate a good question myself. Now, of course, massless particles have momentum, and the de Broglie wavelength can approach 0 as the momentum tends to infinity, which works as though the velocity of a massive particle is capped below c, the particle itself can just be more massive. So, in conclusion, a de Broglie wavelength of (close to) 0, just implies extremely large kinetic energy. – Tamoghna Chowdhury Oct 08 '22 at 11:17
  • @PeterBernhard as for your second question, that would be better as a separate question. However, the particles don't just fall apart because they're moving very fast, they fall apart because they collide with other particles, giving the constituents enough energy to overcome the binding energy of the composite state. And no, that was not my question. – Tamoghna Chowdhury Oct 08 '22 at 11:20
  • Does the photon have such "composite state"? - There is a real situation for what you assume in your question! Some photon approaching some black hole will (funny German: Mößbauer-Effekt) augments its frequency, presumably to some infinite short length of wave and infinite momentum. According to Einstein, energy is mass, Contrary to atomic explosions, energy might be re-converted to mass. This is being serious (what happens when an electron absorbs a photon?). From a very large momentum there might derive very tiny bits of "massive" mass, as some grams are enough to build a bomb. – Peter Bernhard Oct 10 '22 at 09:15
  • Are there related questions concerning photons, as they might be the only particles that are not "massive", and the question - actually, like yours - would focus on assuming frequency of such un-massive photon being infinite, kinetic energy infinite? Is there some school book answer I should know? – Peter Bernhard Oct 10 '22 at 09:29
  • @PeterBernhard, as far as we know, photons do not have composite state, i.e., they are elementary particles. As I've said before, your questions are better off as actual questions than comments on really old posts - there are other users of this site who are more qualified to answer these questions than I am. – Tamoghna Chowdhury Oct 10 '22 at 09:36

0 Answers0