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W.L.Bragg, the pioneer in x-ray diffraction, gave this lucid but vivid interpretation:"The dividing line between the wave & particle nature of matter & radiation is the moment now. As this moment steadily advances through time, it coagulates a wavy future into a particle past.. . . . Everything in the future is a wave, everything in the past is a particle." If "the moment 'now' " is understood to be the time a measurement is performed, this is a reasonable way to think about the situation.( The philosopher Søren Kierkegaard may have been anticipating this aspect of modern physics when he wrote, "Life can only be understood backwards, but it must be lived forwards.") $^\text{1}$

What is meant by now? What does the statement actually mean?

$^\text{1}$ Concepts of Modern Physics by Arthur Beiser, Shobhit Mahajan , S Rai Choudhury.

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    $\begingroup$ It means that Bragg didn't understand quantum field theory. Wave/particle duality is fully explained by quantum field theory and you should ignore all other attempts to obfuscate it. Search this site for more. $\endgroup$ – John Rennie Feb 26 '15 at 12:27
  • $\begingroup$ @John Rennie: Greetings, Sir. I was actually studying the above book's section "Waves of What? - Waves of Probability". $\endgroup$ – user36790 Feb 26 '15 at 12:32
  • $\begingroup$ This is primarily opinion based as it amounts to guessing what someone who was confused about quantum mechanics meant by a handwavy statement. A word of advice: Quantum mechanics is best understood through mastering the mathematical formalism, not through words. $\endgroup$ – ACuriousMind Feb 27 '15 at 0:07
  • $\begingroup$ @user36790 I don't understand why are you mocking John Rennie. If you don't understand, you can ask. Bragg studied the X-ray diffraction in the early years of the past century, when the quantum theory was in infancy and the wave-particle duality wasn't clear at all. $\endgroup$ – Sofia Feb 27 '15 at 2:35
  • $\begingroup$ @Sofia: What let you think that I'm mocking Rennie??? Ridiculous! When he posted the comment, I didn't completely write the whole quotation from the book; after writting it & adding the source, I addressed him about what I was reading. And just formally used "greetings" as I talked to him after a very long time. If that is bothering, then pardon me. I apologize. Sorry:) $\endgroup$ – user36790 Feb 27 '15 at 3:14
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Bragg appears to to try to explain wave-particle duality by waving his hands rapidly.

The moment of observation (the present) is now. Extrapolating backwards in time from that moment (when I observe a particle) I can deduce that this thing I observed was a particle in the past. But I cannot deduce much about its future - the further out you try to predict, the more uncertain that future looks. Knowing about the past is not very helpful - that's the point of the Kierkegaard quote.

This is how some people thought about uncertainty and wave-particle duality a long time ago when this whole science was in its infancy. I wouldn't get too hung up about it.

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  • $\begingroup$ Sir, does matter wave carry energy & transport it? As is written by Resnick & Halliday "We should expect wave function to be more complicated than the corresponding quantity for a light wave because a matter wave, in addition to energy & momentum, transports mass & electric charge. Is it true? Can you please help? $\endgroup$ – user36790 Mar 8 '15 at 12:48
  • $\begingroup$ You need to distinguish between a "wave" and a "wave function". A wave can carry matter, charge, etc. a wave function is just a mathematical description of the probability of finding a particle in a certain location. But when you describe the wave function of an electron you do in fact show how that electron (and thus its mass and charge) can be "moving" so that there is a net current (displacement of charge). $\endgroup$ – Floris Mar 8 '15 at 14:14
  • $\begingroup$ Thanks sir, for the pretty good reply! So, the matter wave transports energy, mass, charge. But is there any mathematical treatment that proves that it carries energy, mass & charge? $\endgroup$ – user36790 Mar 9 '15 at 3:12
  • $\begingroup$ There may well be but I can't think how to do it - that is not my strong area sorry. $\endgroup$ – Floris Mar 9 '15 at 3:20
  • $\begingroup$ Thanks,nevertheless . Your help with quick reply is enough! From Newtonian mechanics to Quantum arena, you've always helped me. I'll really owe to you if I become anything in my life:) $\endgroup$ – user36790 Mar 9 '15 at 3:45
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What Bragg meant by now, I cannot know. There is a huge amount of writers who meant all sort of things, and it's impossible to know all these views. The question whether the quantum system (quantum particle) is a wave or is a particle, preoccupies the physicists even today, 91 years after de Broglie formulated his $\lambda = h/p$ formula.

You see, both concepts, particle and wave, are classical. And the quantum mechanics loughs at us in our face of our classical concepts. So, I'll tell you what is believed today, a few approaches:

A) (Standard Quantum Mechanics) The quantum systems are wave-like, i.e. pass simultaneous through two slits, produce interference. However, in the macroscopic measurement apparatuses, they undergo decoherence, then collapse, and on a photographic plate the wave delivers all its energy to a single molecule.

In short, we know nothing more than the wave-function tells us, we don't know of the existence of a particle. The particle is some classical idea of us, because we are eluded by the discrete reaction of the measurement apparatus (the collapse) - the single point on the photographic plate.

B) (Bohm's interpretation) The quantum particle is almost a classical particle, but it floats in a quantum potential produced by the wave-function, and this potential guides the particle about where it is allowed to be and where not.

But this interpretation has problems with the relativity, in short, one has to assume that for the quantum system there exists a preferred frame of coordinates - idea refuted by the relativism.

C) (Asher Peres) We have to change our conceptions of space-time, so as to be able to understand entanglements and the quantum systems in general.

But Peres didn't have time to say something more clear, he passed away.

D) GRW (Ghirardi-Rimini and Weber) interpretation, that says that we have to add to the Schrodinger equation a stochastic term and a nonlocal potential, and that modification will produce for each trial in an experiment, a well-defined result. Though, this interpretation has also some flaws.

E) We have a classical mind and therefore, no chance to understand the quantum behavior. Therefore, we'd better take the wave-function and shut-up and calculate probabilities.

Needless to say, I don't subscribe to this, I agree with Peres.

Next, you ask : "Does the matter wave carry energy & mass? Previously I thought they are just probability waves. But a statement from Resnick & Halliday : " We should expect wavefunction to be more complicated than the corresponding quantity for a light wave as a matter wave in addition to energy & momentum, transports mass & (often) electric charge" . So, is it true?"

As I said above, there are so many views! In the Standard QM there is no particle, we have only the sort of wave, and at each point and point inside the wave there appear all the point-like properties, mass, charge. About energy, if the wave-function is a superposition of energy eigenstates, then the energy and momentum are undefined, so it's a bit difficult to answer Reasnik & Halliday exactly. What yes is defined is their average. But indeed the matter-wave carries energy and momentum.

By Bohm's interpretation, the particle has no other properties than impress a detector. (How so, without properties, it's not clear.) All the properties belong to the quantum potential.

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