There’s a nice little physicsworld article dating back to 2002. It was written by then-editor Peter Rodgers, and it started by asking *“What is the most beautiful experiment in physics?”* The answer was, of course, the double slit experiment, which was first performed by Thomas Young in 1801:

*Double slit experiment image from the **curiosity makes you smarter article** by Ashley Hamer*

People refer to the double slit experiment as an example of the weirdness of quantum physics. Or to promote weird ideas such as the multiverse. See for example Tim Radford’s 2010 Guardian article on the fabric of reality by David Deutsch. That’s where Deutsch referred to the interference pattern from a single photon and inferred the existence of a *“prodigiously complicated, hidden world of shadow photons”*. He also inferred *“a huge number of parallel universes, each similar in composition to the tangible one”. *This is David Deutsch the quantum computing pioneer who also believes in the many-worlds interpretation of quantum mechanics. There is a mention of that in the Wikipedia article on the double slit experiment. However it’s fairly curt, and says *“some scientists are skeptical of this claim”*. You don’t say.

*Particles are waves*

The Wikipedia article also says the double slit experiment belongs to a general class of double-path experiments, in which *“a wave is split into two separate waves that later combine into a single wave. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern”*. I think this is good, because I know the photon has an E=hf wave nature. What’s not so good is that the Wikipedia article says the double-slit experiment is *“a demonstration that light and matter can display characteristics of both classically defined waves and particles”*. I say that because I’ve read Pascual Jordan’s resolution of the conundrum of the wave-particle duality of light by Anthony Duncan and Michel Janssen. Pascual Jordan solved the mystery of wave-particle duality in 1925. Particles are waves, even matter particles like the electron. Hence the Aharonov-Bohm effect, which was first predicted by Ehrenberg and Siday in their 1949 paper on the refractive index in electron optics and the principles of dynamics.

*The facts of the matter*

Something else I don’t like in the Wikipedia article is this: *“moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena”*. Photons and electrons don’t have a fundamentally probabilistic nature. They have a fundamentally *wave* nature. That’s why it’s the wave nature of matter rather than the probabilistic nature of matter. That’s why we can diffract electrons, as per the Davisson-Germer experiment:

*Image from Rod Nave’s **hyperphysics*

This is only to be expected since we make electrons (and positrons) out of light in pair production. Knowing all this, let’s look further at the Wikipedia article: *“The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles”*. No problem with that. Like I said, photons have an E=hf wave nature. What’s next? This: *“However, the light is always found to be absorbed at the screen at discrete points, as individual particles (not waves), the interference pattern appearing via the varying density of these particle hits on the screen”*. There’s a non-sequitur there, and it’s a big one. Why should a dot on the screen change your view about the photon’s wave nature? Didn’t you ever fry ants with a magnifying glass when you were a kid? Next comes this: *“Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave)”*. So what? As above. Next: *“However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through”*. Ditto. And finally there’s this: *“These results demonstrate the principle of wave–particle duality”*. No they don’t. Let me reiterate: particles *are* waves. We’ve known that for the thick end of a hundred years. And we have had timely reminders more recently.

*The secret lives of photons revealed*

Take a look at Physics World reveals its top 10 breakthroughs for 2011. It said this: *“after much debate among the Physics World editorial team, this year’s honour goes to Aephraim Steinberg and colleagues from the University of Toronto in Canada for their experimental work on the fundamentals of quantum mechanics”*. It also said this: “*Using an emerging technique called ‘weak measurement’, the team is the first to track the average paths of single photons passing through a Young’s double-slit experiment – something that Steinberg says physicists had been ‘brainwashed’ into thinking is impossible”*. I was pleased about that, because I’d read the relevant article earlier that year. It was the secret lives of photons revealed:

*3D plot of a single photon showing wavelike behaviour, image from **physicsworld*

It said Steinberg and his team were inspired by work in 2007 by Howard Wiseman of Griffith University in Australia. It also said weak measurement was *“first proposed in 1988 and developed by physicist Yakir Aharonov and his group at Tel Aviv University”*. You can read more about it in the paper on observing the average trajectories of single photons in a two-Slit Interferometer, and in the article furtive approach rolls back the limits of quantum uncertainty.

*Rewriting the textbooks*

The latter says researchers have used weak measurement to resolve apparent paradoxes posed by quantum mechanics. That’s good. It also says they’ve used weak measurement *“to probe things previously thought impossible to probe directly, such as the quantum wave, or ‘wave function’, that describes a particle”*. That’s good too. What’s not so good is that the article talks about an atom spinning in two opposite directions at once, and about negative probabilities and waves going back in time. Hence I would recommend that you focus on the *rewriting the textbook*s section, which talks about the two slit experiment. There’s nothing wrong with this: *“light shines through two parallel vertical slits in a thin plate and onto a distant screen (see figure, below). The waves emerging from the slits overlap on the screen to create bright stripes where the waves reinforce each other and dark stripes where they cancel each other”*:

*Double-slit image from **furtive approach rolls back the limits of quantum uncertainty in ScienceMag*

The article also says the *“interference pattern appears even if the photons pass through the slits one by one. So each particle literally must go through both slits at once and interfere with itself”*. There’s nothing wrong with that either. Or this: *“The experiment, reported recently in **Science **(3 June, p. 1170), doesn’t violate quantum mechanics, Steinberg says; each individual photon still goes through both slits”*. See Steinberg’s uToronto web page for more.

*Catching sight of the elusive wavefunction*

The article tells how in the same month, Jeff Lundeen and colleagues reported that they’d *“used weak measurement to measure directly the wave function of photons emerging from an optical fiber”*. And that this was something that generations of physicists have learned cannot be done*.* Jeff Lundeen’s group were runners-up in the Physics World top 10 breakthroughs for 2011. See the relevant article from earlier in the year. It’s called catching sight of the elusive wavefunction and it refers to their Nature paper on the direct measurement of the quantum wavefunction.

*Artists impression of wavefunction from **catching sight of the elusive wavefunction*

The article says the team *“used weak measurement to map out the wavefunction of an ensemble of identical photons without actually destroying any of them. Quantum tomography, in contrast, maps out the wavefunction at the expense of destroying the state”. *It’s good stuff. So is the uOttawa Lundeen lab website. See the past research page, and then take a look at the semi-technical explanation. It says Niels Bohr’s view was that the wavefunction was merely a mathematical tool, and that this the Copenhagen Interpretation ended up being accepted by most physicists. It also says this: *“with weak measurements, it’s possible to learn something about the wavefunction without completely destroying it”.* And this: *“We hope that the scientific community can now improve upon the Copenhagen Interpretation, and redefine the wavefunction so that it is no longer just a mathematical tool, but rather something that can be directly measured in the laboratory”*. What they’re saying is wavefunction is real.

*Coconuts and corks*

See the non-technical explanation for more: *“The wavefunction embodies the idea that every particle is also a wave. This wave is much like the set of ripples travelling out from a pebble dropped in a pool. And the shape of this set of ripples is what is analogous to the wavefunction. A feature of quantum mechanics is that, unlike a water wave, the very act of observing the wavefunction changes it, making it a slippery object to measure”*. It goes on to say ordinary measurement *is “like placing a coconut at a particular position in the pool to see if the ripples would cause it to bob. As well as bobbing, the coconut would have the unwanted side effect of reflecting the incoming ripples and sending them in every which direction”*. It then talks about weak measurement thus: *“The obvious solution to this problem, to use a lighter float such as a wine cork”. *And that* “one does not get much information about the particle’s position”.* Hence “*The trick is to repeat the gentle position measurement followed by the normal velocity measurement over and over again on many identical wavefunctions until one has enough information to say what the average result of the position measurement is. This average is equal to the wavefunction itself”. *You plot out the wavefunction with weak measurement.

*Wavefunction is real*

So, the takeaway from all this is that wavefunction is real. The current Wikipedia wavefunction article will tell you that wavefunction *“i**s a mathematical description of the quantum state of an isolated quantum system”*. It isn’t. It’s a real thing. It isn’t some *“complex-valued probability amplitude”*. It’s the thing that goes through the double slit. Think of it as something like the pilot wave, but with an important difference: it isn’t piloting anything. The photon isn’t some billiard-ball thing that makes a wave as it bullets through space. It’s a wave in space, and an extended entity like a seismic wave is an extended entity. That’s why like Steinberg said, each individual photon goes through both slits. The mistake is to think a photon is some billiard-ball thing, and then think it’s a miracle that it can go through both slits at once. It isn’t a miracle. There is no magic. The same applies for the electron. It isn’t some billiard-ball thing that has a field, it *is* field, with no outer edge. It’s an extended entity too. Because it’s a self-trapped 511keV photon in a spin ½ configuration that looks like a standing wave. Hence similar rules apply. That’s why you can refract it and diffract it.

*We choose to examine a phenomenon which is impossible, absolutely impossible*

So, what happens at the screen? This: *“the light is always found to be absorbed at the screen at discrete points”. *The same applies for an electron. Look again at the 2002 physicsworld article on the double slit experiment. It says the most beautiful experiment in physics is Young’s double-slit experiment applied to the interference of single electrons going through the slit one at a time. It also says the first double-slit experiment with single electrons was performed by Pier Giorgio Merli, GianFranco Missiroli, and Giulio Pozzi in Bologna in 1974. Their paper was on the statistical aspect of electron interference phenomena. This was some 15 years before the better-known work by Akira Tonomura and colleagues at Hitachi. Their paper was the demonstration of single‐electron buildup of an interference pattern:

*CCASA image** **uploaded by Belsazar with permission of Dr. Tonomura, rearranged by me*

The physicsworld article says most discussions of double-slit experiments with particles refer to what Feynman said: *“We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery”. *But there is no mystery. Instead there’s kids with magnifying glasses, and there’s a trick of the light.

*That’s the trick*

We know light has a wave nature, and we know matter has a wave nature too. Photons have a wave nature, and we make electrons out of photons in gamma-gamma pair production. So we can be confident that both photons and electrons go through both slits. And yet when we detect them on the screen, we see dots. Why?

*Image from The Fourier Transform at Work: Young’s Experiment by P J Bevel *

Have you ever read anything about the optical Fourier transform? Steven Lehar wrote an article about it called an intuitive explanation of Fourier theory. He said a simple lens can perform a Fourier transform in real time. He also said this: *“place an image, for example a slide transparency, at the focal length of the lens, and illuminate that slide with coherent light, like a collimated laser beam. At the other focus of the lens place a frosted glass screen. That’s it!”* The input image is converted into something pointlike:

*Image from Steven Lehar’s **intuitive explanation of Fourier theory*

When you detect an electron on the screen, what you see is a dot. Even though it went through both slits and interfered with itself. Why do you see a dot? Read the Hitachi paper by Tonomura et al. On journal page 119 you can read that the distance from the source to the screen is 1.5m. You can also read that the length of the electron wave packet is as short as ~1μm, so *“there is very little chance for two electrons to be present simultaneously between the source and the detector”*. Note the reference to the electron wavepacket. When an electron interacts with the detector, a fluorescent screen emits circa 500 photons. These excite a photo cathode which emits photo-electrons. These are accelerated to 3kV through the electrostatic lens, and then *“the point image of electrons is formed at the upper surface of the multichannel plate”*. That dot on the screen is not an image of the electron, any more than the eye of the storm is an image of the hurricane. What’s really happening is that an extended entity called an electron is interacting with other extended entities in the fluorescent screen. Just as an extended- entity input image interacts with an extended entity called a lens. What you see is a dot. Now, you might talk of wavefunction interacting with wavefunction and wavefunction collapse and wavefunction squared, written as |ψ|². But I think it’s better to keep it simple and say detection involves something akin to an optical Fourier transform. That’s why you see a dot on the screen. I think it really is that simple. I think that’s the trick.

*No many-worlds multiverse is required *

I went to a wedding a while back. At the reception, my wife and I were sitting at one of the big round tables drinking and chatting and laughing with other guests. Then a magician appeared. He performed a variety of party tricks with cards and coins and other things. He was good. However for one trick, he bent a spoon. I just happened to see the way he held it in both hands as he waved it up then down and quickly snapped his hands to do the deed. He did it fast, almost too fast for the human eye, but not too fast for *my* human eye. The other eleven people on my table were wowed and amazed, but I sat there with my mouth open and my brow raised. After the magician moved on to the next table, I spoke to the guy sitting next to me: *“Didn’t you see that? He bent that spoon right in front of your nose”.* He hadn’t seen it, and nor had anybody else. I was amazed that I was the only one who spotted the trick. It feels similar for the double slit experiment. When you detect the electron at the screen, you perform something akin to an optical Fourier transform on it, so you convert it into something pointlike. Then when you detect the electron at one of the slits, *you perform something akin to an optical Fourier transform on it, so you convert it into something pointlike*. So it goes through that slit only. So the interference patterns disappears. That’s the trick There is no magic. It’s that simple. It isn’t some phenomenon which is *impossible, absolutely impossible*. It is mundane, and no many-worlds multiverse is required.

**Note** 3rd Aug 2019: Art Hobson gave a similar explanation of the double slit experiment in his 2013 paper There are no particles, there are only fields. I’m surprised I haven’t heard about it before.

Congratulations Duff – you’ve moved yourself squarely back into the 19th century! What you’ve written here isn’t far from the “state of affairs” just prior to Einstein’s 1905 paper on the photoelectric effect. Not “far from”, yet still a bit less accurate than what was known then. In just one article you’ve turned back physics at least 114 years prior to what even the average high school student knows in 2019. Awesome!!

“That dot on the screen is not an image of the electron, any more than the eye of the storm is an image of the hurricane. What’s really happening is that an extended entity called an electron is interacting with other extended entities in the fluorescent screen. Just as an extended- entity input image interacts with an extended entity called a lens. What you see is a dot. Now, you might talk of wavefunction interacting with wavefunction and wavefunction collapse and wavefunction squared, written as |ψ|². But I think it’s better to keep it simple and say detection involves something akin to an optical Fourier transform. That’s why you see a dot on the screen. I think it really is that simple.”

Again .. AWESOME!! This kind of “extended” interaction is precisely what Einstein and Planck DIS-proved! It’s THE ENTIRE POINT driving new physics: what you wrote was (and still is) SO provably wrong that an entire new branch of physics needed to be created to account for it. And not just provably so, but wrong AT FIRST GLANCE. Meaning … according to first principles. According to LOGIC alone this idea of “extended” interaction just AINT happnin!! That’s because, you guessed it …

ENERGY EXCHANGES ARE QUANTIZED!!

BAM!!! WELCOME TO WHAT WE CALL “PHYSICS”!

FWIW, there is an entire website and group of physicists that discuss this line of thinking every day. At the most advanced levels. It’s called “Not Even Wrong”, and for a very good reason: it’s not so much that the conclusions are difficult to understand, but rather that the very foundations upon which those conclusions are based is not even nonsense. It’s beyond nonsense, because it’s impossible to know exactly what those foundations ARE! Case in point, any foundations that are intended to help explain natural phenomena should at *least* have their roots in experimental results. I’m not saying you’ll find a home there, but rather that you’ll find a LOT of folks knowing something about the place from whence you come.

Nice Job John!

Not to say your “article” wasn’t entertaining. For me the best part was this idea you (and EXTREMELY FEW OTHERS) have that an electron IS a wave. That’s like telling all those brilliant guys during the entire 20th century that they got it all wrong. They kept using this word “duality”, but here you are clearing it all up to explain that no! After all that experimentation and Harvard/Princeton/Caltech theorizing that .. NO!, the truth is it’s a MONality and no DUality about it.

This idea of MONality absolutely CRUSHES the possibility of E = hc/wavelength. CRUSHES it, because your DUFF MECHANICS requires that whatever “fractional” amount of energy passes through a slit must somehow miraculously “generate” the exact same wavelength as that of the ENTIRE ENERGY!

I’m not sure DUFF MECHANICS is even the right moniker. How about something more like … MAGIC!

I’m glad you found it entertaining John. Yes, the electron

isa wave. It’s a spin ½ standing wave. Only it’s also a “dynamical spinor”. That’s why it goes round in circles in a uniform magnetic field. I recommend you start from the beginning and read through the articles in sequence. I didn’t clear up wave/particle duality. Pascual Jordan did that in 1925. Then in 1926 Erwin Schrödinger talked about a wave group in a small closed path. But rivals including Heisenberg and Pauli promoted Frenkel’s point-particle electron instead. If you don’t have time for the history, read the four articles starting with The photon. Then if you’d like to amend your comments do please let me know. There is no magic.And there it is: complete disregard for experiment, logic and math. I *just* explained not 2 days ago exactly how an electron cannot “be” a wave and your response is to completely ignore the experienced quantum physicist and the logic and the math. Your response is to not think for yourself but to do what weak-minds do: scour the world for opinions that seem to be similar to your own, and then HOLD ON TIGHT AT ALL COSTS!

There are many ways to describe that thought process John. “Scientific” isn’t one of them. “Self Serving” is close however. Whatever makes YOU feel good about yourself … that’s the point, right John?

Your “explanation” was merely an assertion. I would urge you to try to understand the electron. And the photon of course, and how pair production works. Until you do, I’m afraid you’re clinging to ignorance, then trying to justify it with phrases like “the experienced quantum physicist”. I’m sorry, but it isn’t me who’s holding on tight at all costs. It’s you. I recommend you read this too: the hole in the heart of quantum electrodynamics. If you don’t want to read further, just do me one favour. Cut a strip of paper like the sinusoidal shape below, and make a Mobius strip out of it.

.

.

Did this. OK, now … what now?

You need to talk physics instead of being abusive. Your very long comment on Quora is indeed abusive, and you even get Compton scattering wrong. I would urge you to read the articles on this blog and ask questions as relevant. As I said, please don’t hesitate to let me know if, upon reflection, you’d like to withdraw any of your previous comments.

A QUANTA CANNOT BE A WAVE. THE ENTIRE FOUNDATION OF REALITY MUST ADHERE TO THIS FACT. NOT A THEORY BUT A FACT JOHN!

Pick up any undergraduate physics text and by the time you’re half way through it will be clear: NOT A WAVE! This is with minimal exposure to mathematics and experimental results.

Again, this is High School senior level physics at the AVERAGE level.

Please just put your time in like the rest of us have. Please just acknowledge that to be good at something or good at understanding something, or … more to the point in this case: to be good at understanding something …

you MUST actually DO that thing you want to understand. Guessing, or reading up on, or vicariously living “it” …

none of it helps. you need to actually *do* it or you have zero foundation from which to judge anything about it. i.e. John ..

otherwise you are GUESSING.

Hi John (Ahearn),

“A Quanta cannot be a wave” you say???

It is incorrect to assert that a quantum cannot be constructed from wave energy. There is no conflict between these two ideas, between saying that energy comes in waves (which propagate at c), and that the system resolves itself into quanta. There are two main cases where we find quanta. Light and matter.

As for light, the fact is that we do NOT have a discrete set of solutions at all, we have a continuum of solutions, all of which share the same angular momentum. So, the solutions are not quantised only the angular momentum.

This quantisation of angular momentum just means that the product p x r (where r is a characteristic dimension of the system, see below) is an invariant. In particular, and to explain this the most quickly, it is a Lorentz Invariant: Different observers see different momenta for the same photon but they also see different wavelengths. Momentum is inversely proportional to wavelength, so the product momentum times wavelength is invariant. Meanwhile, the r in p x r above scales with the wavelength. In this post, that’s an asseveration, but it’s easily shown. So much for light quanta.

As for matter, indeed we do find a discrete set of solutions. In this case, given that wave energy moves along closed paths in 3 Dimensions, the wavesystem is subject to an additional constraint in the form of a resonance condition or conditions (depending on the kind of matter particle) . Only those solutions where internal interactions provide just the right curvature to bend wave trajectories into repeating paths on the surface of a sphere can exist. (Another asseveration that is easily shown), and it is self evident that the wave propagation must then also satisfy a resonance condition, leading to a discrete spectrum of solutions, which is just what we find.

However, the same scaling of the system applies: characteristic dimensions / wavelengths etc are inverse to the energy-momentum / frequency, with the result that electrons and protons again share the same (half) quantum of the angular momentum.

In short, far from being in conflict, it is the wave nature of energy that explains quantisation.

Cheers….

Andrew

Hey Mr Ahearn, Can you support your assertion that a quanta cannot be a wave? You didn’t make a single coherent argument beyond appeals to authority.

Also, John, thanks for the fascinating blog, it’s certainly thought provoking.

Thanks Eric.

Great, check this article on how to study maths

sigh. oh boy. ughhh … please take some time out to review the following …

1.) eigensolutions of Q.M. energy equations accurately representing REAL WORLD systems – given enough time this will lead you to at least SOME small bit of understanding of what Jordan was trying to explain. to wit … solutions to can be described/represented in terms of series/super-positions of the eigensolutions.

ALL THAT MEANS IS THAT ANY ENTITY AND/OR SYSTEM WITH ENERGY CAN BE REPRESENTED BY WAVEFUNCTIONS. Fine. Whatever. No one else has stated anything differently except you who wants to believe that quanta ARE waves. This is a mathematically and logically incorrect statement.

2.) semantics: how to be accurate with meanings rather than obfuscate simply to “get your way”. I can call anything a wave but prefer not to because it lacks accuracy (and therefore meaning) as per #1 above. You can call anything a wave and do the opposite: you choose to do so BECAUSE obfuscation confuses and appears to support you point hence “getting your way” even though it lacks meaning.

Please! There are a great many undergraduate and graduate Q.M. texts that are quite readable but you MUST put in the time! This can’t be about YOU John. Science is never about the observer / interpreter. It must always be about nature and how nature behaves. Please just set the ego aside and try to learn at least the fundamentals that you appear to be so dead set on disbelieving.

Eric – you write “Hey Mr Ahearn, Can you support your assertion that a quanta cannot be a wave? You didn’t make a single coherent argument beyond appeals to authority.”

My 2nd entry is precisely conclusive, logical, consistent, precise and correct. It’s THE argument used against Duff’s fuzzy thinking and has been so since the time just after Bohr. To tell me it’s not “coherent” is to betray you’re lack of understanding of this fundamental and NOT very complicated point. The argument is SOLIDLY coherent. The argument I stated there is THE reason for needing the entire new branch of science called Quantum Mechanics. This was Planck and Einstein’s contribution. Don’t blame me if you happen to find lack of coherency in the foundation of Quantum Mechanics.

again and to wit …

if a quanta IS a wave then it’s “extended and periodic” in the sense that only part of it is “in between a slit or the slits” at some time. let’s call this time “t”.

we know exactly what the wavelength or the “wave related behavior” is by measuring spacing in between interference patterns. i.e. from the result of the experiment we know the “wave behavior”.

However, there is NO way to reconcile that wavelength with any sort of belief that a quanta is a wave. That’s because E=hc/lambda

Case in point … if a quanta is a wave then E in between the slits is only a fraction of E. So … wrong lambda! Your ideas fail miserably and require an entire new branch of science to explain them. And that’s exactly what happened. That’s why you know the name “De Broglie”.

Sorry to be tardy replying, John. I was tied up with something. The photon is the original quantum. As you said, it has an E=hc/λ nature, where λ is wavelength. So it has a wave nature. Planck’s constant of action h signifies its quantum nature. The dimensionality of action h can be expressed as momentum x distance. It’s meaning is hidden in plain sight. Take a look at some pictures of the electromagnetic spectrum. Note how the wave height is always the same regardless of wavelength:

.

.

As for reconciling the wavelength with the spacing of the interference patterns, you might want to take a look at The Fourier Transform at Work: Young’s Experiment by P J Bevel.

.

.

There is no magic. There is no mystery. There is no many-worlds multiverse. Because particles are waves, and waves are subject to Fourier transforms.

Thank you! Finally some agreement on this topic!

You got it , although you may be misunderstanding the word “transform”. Pretty sure you’re simply re-wording what I’ve written wrt series of eigensolutions (i.e. wavefunctions to the Hamiltonian). Fourier is a specific case, but then so are Spherical Harmonics so … pretty much the same thing.

I love it! You came full circle John just like some of my more “oppositional” yet bright students: we started with “you need to do the math but not ONLY the math and certainly don’t shut up after doing it!!”. And now here you are right in step with my hopeful advice: YOU NEED TO DO THE MATH!!

Awesome. 1) wave behavior because everything has that and 2) quanta localized like a particle even when “described” by series of eigenfunctions to the Hamiltonian that describes the system.

So … quanta non-periodic so NOT a wave in any way, but able to be described by the wavefunction solutions.

If I were you I’d grab a copy of Schiff asap. Seems like you just got past the first advanced lesson. You may be able to view most of the online copy here. Nice!!

https://www.scribd.com/doc/242405223/Quantum-Mechanics-L-Schiff-pdf

LOL, John, you are

kiddingyourself! I’m not rewording anything you’ve written. I haven’t come full circle. Now watch my lips: Pascual Jordan solved the “mystery” of wave-particle duality almost a hundred years ago. The photon has an E=hc/λ wave nature. The λ is the wavelength. We make electrons and positrons out of photons in gamma gamma pair production, and we can refract and diffract both electrons and positrons. Fourier optics and spherical harmonics apply because we are dealing withwaves, not point -particles. I recommend you pay close attention to work by Steinberg et al and Lundeen et al. And do note that spherical harmoncs were named by Thomson and Tait in 1867. Their vortex atom was ahead of its time. Because the electron is an optical vortex.?? It’s like an attempt to optimally mix obfuscation & contrarianism with mis-direction!!

How do you come up with this stuff Duff? From where I sit, it’s like you find out how and what the best and brightest think, and then … you go for those things most easily misunderstood by the uneducated populace. And … (assuming I can follow this line of thinking) … THAT becomes the simplest way to deceive people! Or … something like that?

Either way it’s all about you!. In any other form … Not Even Wrong.

Do the frickin work dude. Have some respect for the amazing people that figured out this amazing shit. Otherwise, you’re just what you appear to be: a lazy and disrespectful person unwilling to accept that a great many others are WAY more intelligent, creative, productive and objective about your same set of interests …

JUST DO THE FRICKIN WORK!!!!

Schiff

ALL of the Feynman lectures

Cohen-Tannoudji

Davydov

At the very least, reading these and solving most problems posed should result in your much better understanding of the topic that you’re interested in. If you choose to NOT do all this work?

You’re nothing but a disrespectful and dishonest cheat.

for anyone reading these posts: my comments are now being disallowed. not surprising as this site is about John Duffield and his ideas. I’m a physicist that was contributing, but because I disagree vehemently with Duffield my comments aren’t allowed apparently.

This site is about physics. Your comments aren’t physics. They’re abuse.

Mr Ahearn makes the point that waves are continuous and quanta are discrete but have wave properties. In my opinion, I am happy to call a thing with wave properties a wave. If I was to chain together lots of these quanta with wave properties together I would find the result hard to distinguish from a continuous wave depending on the length of the chain of quanta. If a wave must be continuous and not constrained in length (periodic ad infinitum), then they cannot exist in the ocean because the ocean is of finite extent. Waves in the ocean could be the result energy propagating in quanta big enough to result in a finite length wave chain but it would certain fall short of the continuous and infinite extent requirement for the idealised mathematical wave. I have no problem with idealised mathematical abstractions in there proper place. However, I think that the previous consideration leads me to the conclusions that while I am happy to accept that a quantised view of the world may underpin a continuous approximation of a wave in the real world, and while I accept that the ideal wave is a good approximation to real world behaviour for many purposes, one always needs to remember that mathematical ideals and abstractions are just that. Ideals and abstractions. They are not the reality. They just describe aspects of reality and are useful as far as they remain useful. So Mr Ahearn’s definition of a wave belongs to a concept that cannot be realised. That basically means it is a mathematically entity that must be used with caution when considering descriptions of the real world.

Hi Andy. The quantum nature of light is to do with the action h in E=hf. It’s the same for all photons, which have a frequency f because they’re waves. The dimensionality of action h can be expressed as momentum x distance, and it’s the same for all photons. It’s like all waves in the ocean are the same height regardless of frequency. Take a look at some pictures of the electromagnetic spectrum, and there it is. All the waves are the same height regardless of frequency:

.

As I mentioned previously, and since you are pointing out that the magnitude of the wave for photons is the same independent of frequency, I would note that I was told on my degree course that the magnitude is sqrt(3)/c. That is “c” the constant, limiting, speed of light in vacuum. That is different from the actual speed of light at any given point in space which will vary with local energy density due to the gravitational well or the material a photon is travelling through, or both. I like to think of the speed of light in space as spatially variable and of the density of vacuum as spatially variable depending on how much light is passing through it.Looked at that way it is easier to think of a constant size universe where the observed redshift is due the increase in vacuum density towards a centre point rather than an assumed expansion because it is assumed vacuum is homogenous and isotropic. But the interesting part with the energy frequency relationship is that a minimum magnitude limit is reached and frequency increases with energy following E=hf. I still do not know why there are not more readily available references for the 3^.5/c number for the magnitude though.

That sounds interesting Andy. It sounds like what I was saying about Andrew Worsley in my last post. He’s come up with expressions like dimensionless c

^{½}/ 3π = 1837.127 and c^{⅓}/ π = 213.037. There’s also the Planck length √(ħG/c³). Replace the √(ħG) with 4πn, where n has the correct dimensionality but a value of 1. Then 4πn / c^{1½}= 2.42 × 10^{-12}m..

I concur that vacuum density is spatially variable, but it’s denser at a lower elevation. When you’re at that location your see photons blueshifted, not redshifted. I see space as something like a gin-clear ghostly elastic, but compressed, like a stress-ball in your fist. Open your fist, and it expands.

PS: the superscript doesn’t work on the normal commment editor. It only works when I use the wordpress “behind the scenes” comment editor. Ditto for images.

To John Ahearn: Having scanned your pompous blathering, I can only conclude your primary objective here is the wholly unjustified inflation of your own ego—and being arrogant at the same time. While this is quite a feat, it is not the comportment of a well-reasoned scientist. Your unresolved mommy issues currently obscure anything of value that you may actually have to say. Please save your energy until you reach an emotional age capable of civilized discourse.