Quantum physics just got less complicated

December 19, 2014
Quantum physics says that particles can behave like waves, and vice versa. Researchers have now shown that this 'wave-particle duality' is simply the quantum uncertainty principle in disguise. Credit: Timothy Yeo / CQT, National University of Singapore

Here's a nice surprise: quantum physics is less complicated than we thought. An international team of researchers has proved that two peculiar features of the quantum world previously considered distinct are different manifestations of the same thing. The result is published 19 December in Nature Communications.

Patrick Coles, Jedrzej Kaniewski, and Stephanie Wehner made the breakthrough while at the Centre for Quantum Technologies at the National University of Singapore. They found that 'wave-particle duality' is simply the quantum '' in disguise, reducing two mysteries to one.

"The connection between uncertainty and wave-particle duality comes out very naturally when you consider them as questions about what information you can gain about a system. Our result highlights the power of thinking about physics from the perspective of information," says Wehner, who is now an Associate Professor at QuTech at the Delft University of Technology in the Netherlands.

The discovery deepens our understanding of and could prompt ideas for new applications of wave-particle duality.

Wave-particle duality is the idea that a can behave like a wave, but that the wave behaviour disappears if you try to locate the object. It's most simply seen in a , where single particles, electrons, say, are fired one by one at a screen containing two narrow slits. The particles pile up behind the slits not in two heaps as classical objects would, but in a stripy pattern like you'd expect for waves interfering. At least this is what happens until you sneak a look at which slit a particle goes through - do that and the interference pattern vanishes.

The quantum uncertainty principle is the idea that it's impossible to know certain pairs of things about a at once. For example, the more precisely you know the position of an atom, the less precisely you can know the speed with which it's moving. It's a limit on the fundamental knowability of nature, not a statement on measurement skill. The new work shows that how much you can learn about the wave versus the particle behaviour of a system is constrained in exactly the same way.

Wave-particle duality and uncertainty have been fundamental concepts in quantum physics since the early 1900s. "We were guided by a gut feeling, and only a gut feeling, that there should be a connection," says Coles, who is now a Postdoctoral Fellow at the Institute for Quantum Computing in Waterloo, Canada.

It's possible to write equations that capture how much can be learned about pairs of properties that are affected by the uncertainty principle. Coles, Kaniewski and Wehner are experts in a form of such equations known as 'entropic uncertainty relations', and they discovered that all the maths previously used to describe wave-particle duality could be reformulated in terms of these relations.

"It was like we had discovered the 'Rosetta Stone' that connected two different languages," says Coles. "The literature on wave-particle duality was like hieroglyphics that we could now translate into our native tongue. We had several eureka moments when we finally understood what people had done," he says.

Because the entropic uncertainty relations used in their translation have also been used in proving the security of quantum cryptography - schemes for secure communication using quantum particles - the researchers suggest the work could help inspire new cryptography protocols.

In earlier papers, Wehner and collaborators found connections between the uncertainty principle and other physics, namely quantum 'non-locality' and the second law of thermodynamics. The tantalising next goal for the researchers is to think about how these pieces fit together and what bigger picture that paints of how nature is constructed.

Explore further: Duality principle is 'safe and sound': Researchers clear up apparent violation of wave-particle duality

More information: "Equivalence of wave-particle duality to entropic uncertainty" Nature Communications DOI: 10.1038/ncomms6814 (2014) Preprint available at http://arxiv.org/abs/1403.4687

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someone11235813
4 / 5 (2) Dec 19, 2014
I don't get it, I thought that if you try to pin a particle down, that the fact that it's momentum is lost, was integrally and precisely because of the wave particle duality!?
Selena
Dec 19, 2014
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antialias_physorg
4.9 / 5 (17) Dec 19, 2014
There are several connected variables where more certainty in one will give you less certainty in another (momentum and position, time and energy, angular momentum and angular position , ... ). So the observable total information over the sum of such conjugate variables is always constant.

So it seems to me they are saying that "waveness" and "particleness" are another of these conjugate variables, right? So one should be able to construict experiments where there is not a full-on show wave or particle properties but a mix of both.
Selena
Dec 19, 2014
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Selena
Dec 19, 2014
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someone11235813
3 / 5 (1) Dec 19, 2014
... But IMO the above article is trying to simplify things in an effort to make them more palatable.


@Selena: I know there must be more to it but I can't figure it out. I mean this is not like Newton realising that the Earth orbits the Sun due to the same 'force' that causes a rock to come back down to Earth when you throw it up. But the article seems to imply that indeed what has been discovered is of equal magnitude.
Selena
Dec 19, 2014
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Selena
Dec 19, 2014
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justindadswell
1.3 / 5 (12) Dec 19, 2014
Oct. 10, a post by me on here(you can look through my posts).
"All matter is a topographical defect.
Hence Cosmic strings are everywhere, everything we see is a cosmic string. Each "Cosmic string" is the twister created by this defect attempting to move it's way back to 0 and reconnect with all the missing parts that are that spread across infinite universes (more like Sliders, then Energy Loaf).
These bits of defect constantly swirl down (4D twister, not 3D). As they move, they swirl through every universe. As a defect leaves our universe it leaves a vacancy, where another small defect from our side of zero can move into. The first defect has since moved to another universe. This accounts for why particles in our universe seem to blink in/out of existence and move all around."

The response to my theory was overwhelming negative. Sucks to be right. Now if only people wouldn't be so forceful about telling me I am wrong (especially when it's not me that's wrong).
justindadswell
1.1 / 5 (10) Dec 19, 2014
@selena.
This isn't Aether, it's different. But you have to understand the differences.

If I were to call it something, I'd call it a Matrix SUSY Multi-verse with energy strings. It's similar to a fluid universe, except different.
Selena
Dec 19, 2014
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justindadswell
1.1 / 5 (9) Dec 19, 2014
Calling this AWT to me is the same as calling it M-theory.

I get where your coming from, but I feel as though there are some fundamental differences.
The difference I think, relativity. The infinite universe is collapsing, but our energy waves are getting smaller at an even faster rate. It's almost the opposite as AWT and how it relates to creation of the universe.

Then again there are articles like "Dual view to Universe expansion by AWT" which basically explain that and call it AWT.
"Because the light dispersion increases both toward lower, both higher wavelengths, our Universe would appear smaller when observed with the light of these wavelengths. ...We should realize, we cannot detect the change in light speed directly in local measurements, because we are using the very same wave
bluehigh
2.3 / 5 (8) Dec 19, 2014
And not all things around us swirl or vibrate
-Selena

Yes they do. It's precisely what Instantiates energy as matter.
Selena
Dec 19, 2014
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Selena
Dec 19, 2014
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bluehigh
1 / 5 (7) Dec 19, 2014
.. and without emergence concept ..


Matter emerges as an interaction producing 'observation' and physical reality. All the twists and swirls are matter. The water surface analogy however disparaged here is equally valid. Just its not about the water. It's the shape. The topography. Those twists and swirls. That's what matters!
bluehigh
1 / 5 (6) Dec 19, 2014
What exactly is twisted, swirls or spirals we may never know. What we can know is the effects are/do/make matter!
Selena
Dec 19, 2014
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EyeNStein
3 / 5 (2) Dec 19, 2014
The point of this article is that the wave-function (which is specific, cyclic, root-probability distribution) and the particle uncertainty (which is like an inverse probability) can now be related through information theory. Both are probability functions but were not easily mathematically related.
They don't include any mathematical formulae so its difficult to know how helpful this will be to those seeking a better understanding of wave/particle duality: They haven't derived anything as useful as a common causality of these two sides of the same coin.
.
reset
1 / 5 (1) Dec 19, 2014
Guys, every quantum system is a waveform.

http://phys.org/n...ged.html

There is no particle in these images. There is energy flow through a system. If these images were a "particle" orbiting another particle the same structure would not be repeated in each image with the only change being energy intensity at various points in the structure. If the helium electrons were truly orbitals and the researchers managed to capture these images, they would have been lucky enough to have timed the pulses with the electrons orbital positions so that they got the same orbital position in every frame. These are time variant images of a quantum system in which the same structure is repeated in each image.

TheGhostofOtto1923
3 / 5 (4) Dec 19, 2014
"It's a limit on the fundamental knowability of nature, not a statement on measurement skill."

-at this point in time, according to the best theory we have at the moment, that is. There is nothing about QM which says it is the last theory we will ever need, nor that a future one will eliminate uncertainty and duality.

This is important to remember when philos will try to use QM to justify 200yo notions about the nature of knowledge. There is no such thing as nature of knowledge.
rmsberger
4.8 / 5 (5) Dec 19, 2014
I'm not clear on what the news is here.
Uncertainty has been known to be a theorem of Fourier analysis (the Gabor limit) as applied to wave functions for some 90 years.

It's even in Wikipedia, on the Fourier transform page, sec. Uncertainty principle, and the Uncertainty principle entry, sec. Signal processing.
TimLong2001
2.3 / 5 (3) Dec 19, 2014
The wave-particle duality is actually the wave motion described by a binary photon structure. The eikonal equation determines whether the particle representation dominates or the wave representation. (BTW, the raters on these comments for various articles seem to be restricting discussion that deviates from the standard model.)
901awenger_md
4 / 5 (4) Dec 19, 2014
First, any scientist worth his salt knows that the wave and particle aspects of particles are basically 'modeling' and do not necessarily describe the exact nature of a particle or photon which is likely just something outside of our experience other than a particle or wave. second, this isn't the first time I've heard or read that the duality is due to the Uncertainty Principle. I guess what is new is the claim that it is not 'proved' (or shown) to be due to Uncertainty. I guess I'll have to look elsewhere (perhaps Nature Communications) to see how this was 'proved'.
antialias_physorg
4.7 / 5 (12) Dec 19, 2014
this isn't the first time I've heard or read that the duality is due to the Uncertainty Principle.

The connection isn't new. The treatment via information theory is.
Whydening Gyre
3 / 5 (6) Dec 19, 2014
Google Eric Andrulis' Theory of Gyres.
It appears to spiral inasmuch as it is actually spinning. (in a particular relative ratio)
tiffihaag
not rated yet Dec 19, 2014
Not that I have any equations to back up this thought (hello, I'm not an astrophysicist... I just like this stuff), but here's my theory:

I've understood the wave concept from my ideas for a long time. What I think they are missing is that you have to measure the amplitude of the transverse electromagnetic wave that the particle is following. Second, you need to measure a spot equal in distance from the location of the particle within the wave in both forward space time, and in the reverse (a negative space time) where the wave exists or has degraded in frequency or any known radiation from the particle. With these 2 points along with the location of the particle, I think that it will give a more accurate picture of how fast the particle is moving through space-time.
rlladbury
not rated yet Dec 19, 2014
This is hardly new. Some of Heisenberg's "proofs" of the Uncertainty principle relied on wave-particle duality, and complementarity subsumes both ideas.
sgniewek
1 / 5 (3) Dec 19, 2014
If simply knowing something about a quantum object changes it's behavior, that means consciousness plays an integral part in the existence of the physical world. Sgniewek@yahoo.com
hankaaron
3.9 / 5 (7) Dec 19, 2014
This idea has been around since the mid 1930's. Bohr, Heisenberg, and most importantly Max Born, posited that particles are particles and that the wavy nature arose from probability. The interference pattern in the electron double slit experiment isn't manifested because the electron acts like a wave. The pattern accumulates from probability.
leDendrite
2.3 / 5 (3) Dec 19, 2014
Everything emits electromagnetic radiation in a wave of potential. Any interaction with or measurement of the wave causes it to collapse into a point. This gives way to the arrow of time.
check these videos out. https://www.youtu...7/videos
mbee1
1 / 5 (1) Dec 19, 2014
Sure a lot of people putting their two cents in. All these folks did was come up with a new mathematical way to describe the quantum effects. They actually did no real world research to verify the equations,simply recast the old equations in a new format. You can do that with math since it is a language just like any other language like say english or chinese which can be used to write a book or tell your girl friend to come a 6 pm. You can do the same with math.
ceeslouis
5 / 5 (1) Dec 19, 2014
Sounds like there is some uncertainty about the principle.
rmsberger
not rated yet Dec 19, 2014
But mbee1, even that's not true. They're using the same information theoretic model that is old enough to be in wikipedia. (And that I learned as an undergrad in the mid-80s.)
Martian00
not rated yet Dec 19, 2014
Big deal. They combined Uncertainty with wave-particle duality!!!
I can even go one step farther and explain where 'Uncertainty' comes from.
Or even why QM uses 'Probability' to get a solution.

But since I can't prove it 'in conventional way', I'll keep my mouth shut.
Auntiegrav
2.1 / 5 (7) Dec 19, 2014
@Selena, Agreed.

Rehashed Dense Aether Physics.

Perhaps the universe as we don't know it is a pseudocrystalline structure and everything we know is limited to what can be constructed from the interference patterns within that crystal lattice.

Other than that, it's turtles (grant money) all the way down to the basement of the colliders blowing holes in the structure and watching it heal.
crusher
not rated yet Dec 19, 2014
I don't think what they have formulated is a general theory since they are focusing on a particular phenomenon made visible by a bohm ahranov interferometer.
Benni
1.7 / 5 (6) Dec 19, 2014
Even still, nothing has yet been said until the final word has been posted by........
IamVal
not rated yet Dec 19, 2014
no kidding.
I've been saying this for 2 years.
Grasshopper
1 / 5 (1) Dec 19, 2014
"They found that 'wave-particle duality' is simply the quantum 'uncertainty principle' in disguise, reducing two mysteries to one."

Um, how is that not COMPLETELY OBVIOUS? I've been thinking that since Modern physics 101.
tonybr7772000
5 / 5 (3) Dec 19, 2014
Great article. This quote is very elucidating: "We were guided by a gut feeling, and only a gut feeling, that there should be a connection,"... I personally suck at math and logic but even at my superficial level I have felt that the two concepts are very much related. It is great this can now be proven.

I am eager to see what insights this framework based in information theory will provide.
I for one hope somebody can apply a Cantor / Godel like technique and demonstrate that the universe can't really end.
Hyperfuzzy
not rated yet Dec 19, 2014
Hypothetically, a particle in free space has a radiant field. Motion may be defined for any state of the particle to create radiation from the particle. Of course within this frame, measurements are defined by Maxwell and not actually available in the thought experiment. In other words, a charged particle's motion may be reduced to a relative frame where the particle appears as stationary and a radiant field. No such motion or frame exist for the wave. Therefore, the equality is only our mathematical description of mass and energy. Would be more interesting to define mass as a collective property. E = MC squared reduces to an equivalency for radiation. No such proof exist for an electron or a proton. Therefore, a mathematical entity, not a real entity. Anyway, isn't a photon simply a field event and not particulate.
Bob Osaka
not rated yet Dec 19, 2014
Delta rho delta x is greater than or equal to one half h-bar or delta E delta t is greater than or equal to one half h-bar. Simple, elegant. http://arXiv:1301.1069 reports a conference of Quantum theorists Jan. 13, 2013. It's embarrassing. Working to create a unified interpretation is a nobel quest, wish them luck.
MRBlizzard
1 / 5 (2) Dec 19, 2014
I recall that the Quantum Double Slit experiment can only be run with two slits, and that it doesn't work with three slits. Maybe, the explanation is that the Canonical Conjugate pairs (i.e., position and momentum) are indeed pairs; and that fact directly maps over to the double slit experiment.
imido
Dec 20, 2014
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bruce36b
1 / 5 (2) Dec 20, 2014
Welcome to 1975. Duh.
imido
Dec 20, 2014
This comment has been removed by a moderator.
imido
Dec 20, 2014
This comment has been removed by a moderator.
imido
Dec 20, 2014
This comment has been removed by a moderator.
vuzion
1 / 5 (8) Dec 20, 2014
Everything is energy. In the experiment there are two different energies entangled. These energies are the wave component of the particle and the physical component of the particle. These two different energies are being separated by the act of observation, which is the addition of another component to the system. The wave-particle that is being observed changes it state. The wave component is the energy that is being transferred to the observer, as no energy can be lost. This wave energy is the energy that gives form of the object being observed within the consciousness of the observer. The remainder is the mass of the wave-particle itself, which is the actual observed. The observer influences the environment. It is the creation of consciousness. Consciousness is energy.

For a more detailed explanation go to au.linkedin.com/in/vuzion and look for: what-smart-people-don-t-see
Steve 200mph Cruiz
5 / 5 (7) Dec 20, 2014
Guys chill out, although this is a very important revelation, it's implications are not completely apparent yet, but the grand pattern of physics follows the formula that seemingly different forces or properties are actually different manifestations of the same fundamental process.

For example, when you punch something that's a force, but if everything is made of tiny particles that would explain what heat is. So that was an early step to theorizing about atoms.
An electric field is really just a magnetic field in motion from your perspective.
Chemistry only makes sense if electrons orbit around a nucleus.
The visual difference between a falling rock and a planet orbiting the sun is simply that an orbiting body is moving sideways fast enough that as it falls to its surface it has moved a 90 degree angle from the sun and doesn't hit the sun.

Hence the term "fundamental force", all other forces can be attributed to being a manifestation of only 4 things. That's what's important.
swordsman
1 / 5 (5) Dec 20, 2014
"Wave-Particle Duality" is nonsense. The problem is that the "double-slit experiment" was thoroughly misinterpreted as based on the Heisenberg Principle, among other things. The results of this experiment are easily determined by applying the principles of optics! It is an electromagnetic effect.
Hyperfuzzy
not rated yet Dec 20, 2014
9.1 E-31*3.0E9*3.0E8 is not the maximum energy from an electron, 8.2E-14 Joules, about 1/2 Mev, . Depends strictly upon relative motion. By the way, it may be greater than MC squared, maybe as high as a Gev or higher.

Wave particle duality, only an expression!
kochevnik
1 / 5 (1) Dec 20, 2014
Basic signal analysis with uncertainty principle represented by Fourier uncertainty principle? Did something change in past century?
malapropism
5 / 5 (3) Dec 20, 2014
Even still, nothing has yet been said until the final word has been posted by........

Posted by whom? Some god (or even a God)? Are you one of those idiots who think they aren't allowed to speak, write, etch on stone, whatever, its / her / his name because it's blasphemous? ("I only said, "that was a meal fit for Jehovah." Ouch!")

Well, I'm pretty sure that your god is most welcome to post here. Or in fact any other blogs. I think a lot of people would be really interested in what he / she has to say about all those nasty things that go on in the books they supposedly dictated. Go ahead and issue the invitation...
Hyperfuzzy
not rated yet Dec 20, 2014
maybe something should change in the 21st century, less you prefer to be idle
imido
Dec 20, 2014
This comment has been removed by a moderator.
MandoZink
5 / 5 (2) Dec 20, 2014
I recall that the Quantum Double Slit experiment can only be run with two slits, and that it doesn't work with three slits.


PI and IQC Researchers Perform 'Triple Slit' Test of Quantum Mechanics:
http://www.perime...echanics

Multiple Slit Diffraction descriptions at Hyperphysics (1,2,3 and 5 slits):
http://hyperphysi...lid.html

Some of positional "uncertainty" is apparently removed when a slit is "chosen".
Whydening Gyre
5 / 5 (4) Dec 20, 2014
An electric field is really just a magnetic field in motion from your perspective.

Couldn't have said it better, Steve...
Whydening Gyre
5 / 5 (4) Dec 20, 2014
An electric field is really just a magnetic field in motion from your perspective.

Couldn't have said it better, Steve...

But I'll try...:-)
Magnetic field in motion inside a larger magnetic field. Electric field is the manifestation of such.
Whydening Gyre
5 / 5 (2) Dec 20, 2014
Magnetic field inside larger field - spins. We see(observe) that with a vectorable perspective. Inasmuch as it is never the same exact surface of what we observe at any given time, the assumption can be made that it is quasi-spherical as it spins. Wave is the surface of the sphere.
Einstein wins.
Hyperfuzzy
not rated yet Dec 20, 2014
Neutrons may not be neutral, think of them as protons that have captured electrons, Imido. This allows a window for multiple protons in close proximity. Ever seen multiple protons in a nucleus without any neutrons? Just because this was dismissed does not mean that was the correct action. The standard model; then, is without logic, unnecessary. Most modern nuclear physics understand the actions of the neutron.

What does a neutron become? Don't think this applies to its constituents, the proton and the electron and the change of charge state and particle velocity that generates a wave, these may be irreducible. Data from CERN, inconclusive! Accept only logical truths, not the popular truths. Think for yourself, and if you can't figure it out, study it before accepting anything!

If the speed of the wave front is not constant, which I can prove, then the relative energy possibilities of any charged particle may approach infinity. What does a giga ev electron look ?
MRBlizzard
not rated yet Dec 20, 2014
MandoZink Thank you for the references. Quantum Mechanics makes very slight changes to the results of a classical double slit experiment. One can predictively calculate the result of the classic double slit experiment. And predictively calculate the classical result of the triple slit experiment. The Hyperphysics site does just that; however, the subtle effects due to Quantum Mechanics don't show up in the Triple Slit experiment, which are the results published by the Perimeter Institute.
Again, thank you for the references.
Hyperfuzzy
not rated yet Dec 20, 2014
Slits, give me a break, all charged particles have a field, therefore a wave nature when in motion. For goodness sake, do the slit experiment with minimal velocity then show the results as v goes to zero as different from what is expected from the particle and its field. If you want to prove the physics, then properly define it!
Hyperfuzzy
not rated yet Dec 21, 2014
Yung coined the word synchronicity and how that plays a role within our belief system. Therefore, with any sound proof, one must eliminate synchronicity, i.e. things that obey probability theory but are not causal. QM does not define causal effects, but is the best tool we have, take results with a grain of salt, don't expect absolutes, but it would be nice! Be very careful ... i'm working on being more pleasant, so hate me or not! The last "give me a break" was uncalled for.
MandoZink
not rated yet Dec 21, 2014
... all charged particles have a field, therefore a wave nature when in motion.

So how does a proton (charged particle) express a wave nature?

- There's the motion-energy (kinetic energy) of the quarks, anti-quarks and gluons as they move around.

- Then there's the interaction-energy (binding energy) contained in the strong nuclear forces (gluon fields) that contain the proton.

It is definitely in motion from the energy, but not from the charge. Fields are there (quark, gluon), tumultuous motion occurring, but not a wave.
MandoZink
not rated yet Dec 21, 2014
For a truly solid, comprehensive, no nonsense understanding of particles and fields, check out theoretical physicist Matt Strassler's site "Of Particular Significance" at
http://profmattstrassler.com/

Under the menu, "ARTICLES", is the sub-menu, "Particle Physics Basics". Under that sub-menu are comprehensive explanations of every aspect of particles, fields and interactions. In no way is he ever disappointing. Fascinating and serious stuff.

On a side note, Matt Strassler pretty much told Zephyr, who repeatedly suggested AWT explanations, that the site was no place for well-invalidated pseudoscience.
imido
Dec 21, 2014
This comment has been removed by a moderator.
imido
Dec 21, 2014
This comment has been removed by a moderator.
Torbjorn_Larsson_OM
5 / 5 (2) Dec 21, 2014
I don't see anything new here. This formal equivalence has long been used to handwave 'information' as a basis for quantum physics, say as (failed) attempts to have pure non-stochasticity or pure stochasticity at its basis.

In quantum physics these are different physical phenomena.

Uncertainty comes out of observation on the wavefunction, it is a Fourier decomposition property of finite wavepackets containing conjugate variables. "the uncertainty relation between position and momentum arises because the expressions of the wavefunction in the two corresponding orthonormal bases in Hilbert space are Fourier transforms of one another (i.e., position and momentum are conjugate variables)." [ http://en.wikiped...rinciple ]

[tbctd]
Torbjorn_Larsson_OM
5 / 5 (2) Dec 21, 2014
[ctd]

While quantum field theory show by way of relativity that the quantum field is the solution to the apparent "wave or particle" picture. "A QFT treats particles as excited states of an underlying physical field, so these are called field quanta. ... Quantum field theory thus provides a unified framework for describing "field-like" objects (such as the electromagnetic field, whose excitations are photons) and "particle-like" objects (such as electrons, which are treated as excitations of an underlying electron field), so long as one can treat interactions as "perturbations" of free fields. " [ http://en.wikiped...d_theory ]
Torbjorn_Larsson_OM
5 / 5 (2) Dec 21, 2014
@MandoZink: Moreover, the poor 'aether' trolls are obvious Dunning-Kruger victims. E.g. we can see how they do not recognize that empiricists use the same measure as they do. Pseudoscience are known to be incorrect ideas that can't be put in an empirical fashion of science by their very construction. And we _know_ 'aether' ideas are pseudoscience, since the idea failed a century ago.

Also, their sites or references are always erroneous, and they show that besides the inability to distinguish measures or recognize that science need quantification, they can often not even read for understanding. E.g. the 'rigorous derivation' of the uncertainty principle linked to has nothing to do with "particle-wave duality" but is a textbook derivation based on the quantum physical wavefunction. (And yes, textbooks mention that a wavepacket is a description of a particle (it's location), because we have a localized momentum associated with it. But it isn't a description of any wave properties.)
Hyperfuzzy
not rated yet Dec 21, 2014
Jung coined the word synchronicity and how that plays a role within our belief system. Therefore, with any sound proof, one must eliminate synchronicity, i.e. things that obey probability theory but are not causal. QM does not define causal effects, but is the best tool we have, take results with a grain of salt, don't expect absolutes, but it would be nice! Be very careful ... i'm working on being more pleasant, so hate me or not! The last "give me a break" was uncalled for.

Steve 200mph Cruiz
5 / 5 (2) Dec 21, 2014
Thanks gyre, I knew I didn't have it right.
Hyperfuzzy
not rated yet Dec 21, 2014
If we define mathematical equalities, we also must ensure the same properties, esp. the stationary properties. Mathematical equivalence is not necessarily holistic. The state of equivalence must be properly defined. Proof or disproof of contra? Particles create waves, not so sure about waves creating particles. Would be very enlightening if it were so. Einstein was mislead on so many issues! Popular truths can be so damaging!
dumpsta101
not rated yet Dec 21, 2014
I think it was obvious that there was a connection between the uncertainty principle and wave particle duality, but what it is impressive is how they just defined this connection. hopefully this will lead to many mathematical breakthroughs in the near future. :) As far as everyone in this forum that seems to have a huge problem with quantum mechanics as a whole, id like to see your formulas on how to get around the uncertainty principle without using a probability formula, or instituting pseudoscience.
Hyperfuzzy
not rated yet Dec 21, 2014
QM is a very good tool, the interpretation of results; however, are left to the reader.
Hyperfuzzy
not rated yet Dec 21, 2014
Lets be clear, Planck defined his quantized constant ... today, based upon reflectivity, absorption, and transmissivity is optics using Maxwell and atomic structure. I mean, Planck's physics almost makes sense, but upon fine inspection ... is this some kind of minimal average possible momentum or some et or ?? It sort of leaves me unfulfilled, like bad wine. Just doesn't taste complete. Are we sure action may be quantized? Does half a punt make sense in football. What are the rules? So QM, ok, but think!
imido
Dec 21, 2014
This comment has been removed by a moderator.
Hyperfuzzy
not rated yet Dec 21, 2014
Imido, I like the way you think, but suppose all scientist 100 years ago were stupid. No, no, they were brilliant, but dealing with a totally different set of knowns. So, yea, many ways to see from their eyes, but today we discern truth, not approximate truth, true?

Think Einstein and the elevator, as a matter of scale, not even close. Who's mislead?
imido
Dec 22, 2014
This comment has been removed by a moderator.
crusher
5 / 5 (1) Dec 22, 2014
But the article seems to imply that indeed what has been discovered is of equal magnitude
Welcome into scientific journalism. The laymen need a feeling, they're a witnesses of scientific revolution, the journalists want to sell their stories and the scientists need a publicity for another grants. The consequences are undeniable: because no one of people involved in the informational chain is actually interested about earthbound factual information, no one will get it.


Are you a layperson yourself? I'm a layperson in the quantum mechanics field and i want factual information too. Some of us scientists want to give laypeople more than a feeling.
Whydening Gyre
5 / 5 (2) Dec 22, 2014
Thanks gyre, I knew I didn't have it right.

But then, I probl'y don't have it right, either...:-)
Whydening Gyre
5 / 5 (3) Dec 22, 2014
Lets be clear, Planck defined his quantized constant ... today, based upon reflectivity, absorption, and transmissivity is optics using Maxwell and atomic structure. I mean, Planck's physics almost makes sense, but upon fine inspection ... is this some kind of minimal average possible momentum or some et or ?? It sort of leaves me unfulfilled, like bad wine. Just doesn't taste complete. Are we sure action may be quantized? Does half a punt make sense in football. What are the rules? So QM, ok, but think!

Try whiskey . It's better and better for you. Even Planck's constants have constituent parts(re - "packets") to be quantized...
Hyperfuzzy
not rated yet Dec 22, 2014
My point, we have it right; however, somethings simply screw with truth. We must make sure we weed these out. Truth is very clear, the untruth creates so many puzzles. Problem is, popular opinion among the ones that MUST know is rather bizarre.
imido
Dec 22, 2014
This comment has been removed by a moderator.
Hyperfuzzy
not rated yet Dec 22, 2014
time?
andrey_grehov
not rated yet Dec 23, 2014
Nice! I also liked reading the Quantum Dead End article at Kukuruku Hub
liquidspacetime
1 / 5 (2) Dec 24, 2014
There is evidence of dark matter every time a double slit experiment is performed; it's what waves.

Dark matter has mass. Dark matter physically occupies three dimensional space. Dark matter is physically displaced by the particles of matter which exist in it and move through it.

The Milky Way's halo is not a clump of stuff anchored to the Milky Way. The Milky Way is moving through and displacing the dark matter.

The Milky Way's halo is the state of displacement of the dark matter.

The Milky Way's halo is the deformation of spacetime.

What is referred to geometrically as the deformation of spacetime physically exists in nature as the state of displacement of the dark matter.

A moving particle has an associated dark matter displacement wave. In a double slit experiment the particle travels through a single slit and the associated wave in the dark matter passes through both.
Hyperfuzzy
not rated yet Dec 24, 2014
See something, collect data, inspect what? How was the data collected? How was interpreted? using what as the yardstick? I prefer to stay away from what's only between someone's ears.
crusher
not rated yet Dec 25, 2014
Quantum Slit experiment can only be run with two slits, and that it doesn't work with three slits
Why http://i.ytimg.com/vi/HcE4YeUNphk/hqdefault.jpg?


what happens with three slits?
imido
Dec 25, 2014
This comment has been removed by a moderator.
Captain Stumpy
3.7 / 5 (3) Dec 25, 2014
I'm a layperson in the quantum mechanics field and i want factual information too
@crusher
Selena is also imido, who is actually zephyr, the advocate for the long defunct and falsified aether philosophy

I don't know where your talents lie (esp with regard to math), but here are some good places to start regarding Quantum Mechanics

First off, there is a book out called Quantum Mechanics Demystified ( found on Amazon.com here : https://duckduckg...71765638 )

You can also Google search Quantum mechanics and find someone to help you, but i suggest going here FIRST:
http://ocw.mit.edu/index.htm
You can learn classical AND Quantum all at one place

MIT suggests you go to a site and register for help with the work which might be the best place to start... depending on what you are looking for: http://openstudy.com/study

What better place to learn QM than MIT?
Hyperfuzzy
not rated yet Dec 25, 2014
Captain Stumpy, good info, the ether theory would be ok, supposed we used the rise time of the e field to a new particles relative position, and used this instead of mass, and charge to define everything, i.e. the very definition of space and time. "Point charges? How do we resolve, maybe as an infinite energy source due to x moving backward in time, doesn't matter how far, a self full filling feedback or ...?"
Hyperfuzzy
not rated yet Dec 25, 2014
4 dimensions and rings in time
Whydening Gyre
5 / 5 (3) Dec 26, 2014
4 dimensions and rings in time

loops, not rings...
Hyperfuzzy
not rated yet Dec 26, 2014
Well, the loop sounds sequential, and mathematically it has to be shown that a ring actually could represent our known physics. I like a universal perspective, i.e. the physics of the universe is the same from every point in space and time. Hence a proper representation would show "now" and into infinity and everywhere in both directions in time. Let distance and time be mapped to any constant frequency, and the measure in all four dimensions then may be either time or spatial. Does this suggest the existence of a transformation from space to time. May this be for any direction or time. What is the functional? Could we just define the entire space, each axis, as a functional of the unit of measure. That is, everything known of a system may be plotted for all time, given the time to wait for the rendering. Note that this would defy the uncertainty principle since once a system is in a known state, the position and time may be created from any perspective.
Hyperfuzzy
not rated yet Dec 26, 2014
Hence, the uncertainty principle, however does not limit the ability to select the correct functional for a given system, the simplere the system, say a single charge, or two charges should define the basic functional for all forces upon all surfaces, problem is, do protons and electrons have surfaces, or could the electron be created from the wake of a proton as energy from the future, loop or ring. This says, these particles are fundamental and indestructible because they are an event within the four dimensional space. Easily represented as a four dimensional functional based upon what we know. But what form?
Hyperfuzzy
not rated yet Dec 26, 2014
Basically, QM does the best job and using 3D&t, results should be the same. However, a refinement can be made where we only use the e field and q. A 4D perspective does not require mass, only location, yielding e or E(r).
Hyperfuzzy
not rated yet Dec 26, 2014
With proper dimensioning, I think q may also be eliminated, i.e. the magnitude. However, not sure + and - points are easily definable, so with space and time, infinite in all directions, is there a structure within this field that defines charge? And is one structure dependent upon the creation of another?

If you are reading this, then you are as crazy as I am. be really cool if its correct.
Hyperfuzzy
not rated yet Dec 26, 2014
Like the kids book, " A Wrinkle in Time"
Whydening Gyre
5 / 5 (1) Dec 26, 2014
not sure I quite get you formulas, but a ring represents a closed set universe. something we have not observed yet.
Loops allow for variation/change/motion/etc - something we do see...

BTW - am a bat shit crazy artist, here...
You have some interesting thoughts on the matter..
crusher
5 / 5 (2) Dec 26, 2014
I'm a layperson in the quantum mechanics field and i want factual information too
@crusher
Selena is also imido, who is actually zephyr, the advocate for the long defunct and falsified aether philosophy

I don't know where your talents lie (esp with regard to math), but here are some good places to start regarding Quantum Mechanics

First off, there is a book out called Quantum Mechanics Demystified ( found on Amazon.com here : https://duckduckg...71765638

What better place to learn QM than MIT?


Thanks for the warning and the search tools.
Hyperfuzzy
not rated yet Dec 26, 2014
Thanks for the correction. Consider this. Somebody in the future has a time machine. They send back in time article x. Upon the face of it, article x moves forward in time and is fixed, article x being sent back in time has a few possibilities. 1. It simply is an event where article x appears as supposed 2. Article x,, moves continuously and has no time to materialize before receiving another and another, out of time. Therefore this point in space-time would be an infinite source of energy. Possible? Well if electrons and protons are permanent then ...

My point is Maxwell in 4D is not GR. But a "Functional" using 4D may include both time directions, its simply an axis to represent our conceptual understanding. If GR can change time and space, why can't we do it without reshaping our grid? I see an open universe ..

loops or rings in space-time, go figure ...
Hyperfuzzy
not rated yet Dec 26, 2014
I tried, but I get consumed with the number of particles. Anyway, mass may be replaced with particle counts, particles replaced by a space-time functional, elements built from allowed geometry on arrangement of particles. Hence,this is where I was going with this. Leave everything and nothing on the table, i.e. just space and time. The idea of mass gives me the creeps, so ... I can be as wrong as the next guy, the way I figure ...

I don't particularly like time-travel but it could be in the functional, no reason to not allow ... Still QM is valid, but the standard model falls, GR falls, BB falls, ... jus say'n.
Hyperfuzzy
not rated yet Dec 26, 2014
Of course, there are multiple subspaces and axis interpretations, I would choose a "Functional" that would be a sort of mean, however, 4D, 3D, 2D, 1D are real or may be real representations and have properties of a time measurement or a spatial measurement. Suggest, simply make each axis dimensionless, all we want is the "subjects" radius vector relative to any point. So the functional may be a sorting algorithm, i.e. each point in space has measure only relative to every other point separated by a distance in space-time. This superposition of every other point may be represented as a state of space relative to any point. Since a particles state may be a relative state, and E(r) defines the entire space.
Mike_Massen
3.7 / 5 (3) Dec 26, 2014
@Benni, here's a simple challenge re your claim

You've so often blurted claim re others NOT able to solve Differential Equation (DE), implying U easily can :-)
Strange Y U provoke & as thermodynamics politely advised U its not as easy as U imagine..!

So Benni, here's a simple challenge for U & Water_Prophet who claimed to graduated as a Physical Chemist (PC) :-)

1. Total Solar Insolation (TSI) has more short wave (SW) energy than long wave (LW) radiance
https://en.wikipe...m_en.svg

2. Earth converts SW to LW (SW emission is negligible)
3. LW to space interfered with by absorption/re-radiation of GHG (esp CO2)
http://www.chem.a.../sim/gh/

Here Benni, re your claim on DEs, offer an estimate of LW radiation resistivity due to CO2 & for Water_Prophet suggest Y it's so much more than the thermal energy contributed by burning fossil fuels ~230,000L petrol/sec (0.1% of TSI) ?

Or google scholar ;-)
Hyperfuzzy
not rated yet Dec 26, 2014
& the increased CO2 in the soil, have we modified our eco system irreversibly?
Whydening Gyre
5 / 5 (3) Dec 26, 2014
& the increased CO2 in the soil, have we modified our eco system irreversibly?

Hunh?!? Wrong thread, I think....
Whydening Gyre
5 / 5 (4) Dec 28, 2014
oops sorry. You were responding to Mikes comment, I guess.

Anybody else notice a prob with this site the last couple o days?
Dang North Koreans, I guess...
Mike_Massen
4.2 / 5 (5) Dec 28, 2014
Whydening Gyre observed
Anybody else notice a prob with this site the last couple o days?
Dang North Koreans, I guess...
Yeah had some odd glitch, someone hacked into site got my private email address & sent me spam with patterns of crafting matching the challenging questions I posed to a few people - someone got snarky.

Not likely Water_Prophet as he's off with bowl that melts ice with a candle & claims its a fact of climate change, surely he would notice melting ice doesn't require HIS model :P

Then there is Benni, who doesnt answer simple questions with Science, instead he makes personal comments designed to insult, pretty impotent though...

Y is it Benni CANNOT answer simple questions that don't even rely on DE's ?

Whereas Water_Prophet cannot even address a simple issue of quantification which should be EASY for a claimed Physical Chemist.

Then there's the backdoor creationist crowd demanding evidence - amazing hypocrisy - LOL !

Or maybe SQL failed :-(
Whydening Gyre
5 / 5 (4) Dec 28, 2014
Just was unable to comment and noticed no one else did, either. Nothing was updating...
Hyperfuzzy
5 / 5 (2) Dec 28, 2014
Think I overloaded the server!
Captain Stumpy
5 / 5 (3) Dec 28, 2014
someone hacked into site got my private email address & sent me spam with patterns of crafting matching the challenging questions I posed to a few people - someone got snarky
@Mike_Massen
Do you have a profile on Sciforums?
i was receiving the same type spam but i tracked it back to http://www.sciforums.com/

ALSO

PO was not letting anyone post, report, rate, ignore, quote or anything for the past couple days... at least, not for the group on Sapo's joint that i contacted and verified with

Thanks for the warning and the search tools.
@Crusher
You are welcome

don't forget to use Google Scholar too
If you ever need help, find me @ http://saposjoint.net/
I am TruckCaptainStumpy there
you can post publicly or private message me

That site is heavily moderated also
you wont see people like zephir there posting insane rants about pseudoscience
also, it is a forum, not a science article site

PEACE

Mike_Massen
3.7 / 5 (3) Dec 29, 2014
Captain Stumpy asked
Do you have a profile on Sciforums?
i was receiving the same type spam but i tracked it back to http://www.sciforums.com/
No, as per my name & not nick its only on one forum here, others have nicks only all with different email address as have a couple of my own domains - case of pre-emptive risk assessment ie. Seen odd things happen for years, so been there now & then so have set up means to track. maybe when phys.org went down it was vulnerable, may not have been the cause though spam was odd, really trying hard to get into my business & personal provocations, classic 1st level targeting it appeared to me, ho hum, over now I expect...

All sorted for now, tah.

Benni & Water_Prophet seemed to have excluded themselves via basic ineptitude since they post on other threads in their commented profile but ignore my Q's pretty definitive that...

Geesh, those guys need a basic education...
liquidspacetime
not rated yet Dec 29, 2014
'EPR program: a local interpretation of QM'
http://arxiv.org/abs/1412.5612

"Wave particle duality is described as the compound system of point particle plus accompanying wave (in the æther)."

There is no such thing as dark matter anchored to matter. Matter moves through and displaces the aether.

In a double slit experiment the particle travels through a single slit and the associated wave in the aether passes through both.
Hyperfuzzy
not rated yet Dec 29, 2014
Show me a timing diagram, e field complexity meeting the particle prior to arrival. Just want to make sure I can translate all this to a frame of a stationary radiant particle, now within a moving frame meeting a discontinuity of the field, reflections or (impedance?) prior to entering the slit. present state of transmitted waves also in the mix, i.e. what are the response of the geometry, particle position relative to the slit, etc., etc.. Anyway, the wave enters the slit first. So, expectations?
Hyperfuzzy
5 / 5 (1) Dec 29, 2014
So the slit experiment cannot resolve the obvious mathematical equality and the physical dissimilarities.
Whydening Gyre
5 / 5 (1) Dec 30, 2014
Anyway, the wave enters the slit first. So, expectations?

Are you saying a preceding "bow shock" of the wave?
McIek
Dec 30, 2014
This comment has been removed by a moderator.
Hyperfuzzy
not rated yet Dec 30, 2014
Depending upon initial conditions and any accompanying control fields, With the tools a four dimensional space may be described as a 4 dimensional invertible matrix, the magnitude is the vector dot product, the vector cross product defines the space-temporal transformation functional->vector, the best view would be from from the center of an electron, surrounded by spatial-time fields are equal radii, when " stationary" relative, other charges, like me, but moving, ... therefore all trajectories within space-time is defined without space-time barricades, i.e. discontinuities within the field ...
Whydening Gyre
5 / 5 (2) Dec 30, 2014
Well, it's not neither bow shock, neither wake wave - but something inbetween. https://www.youtu...A4fgamPE illustrates it well. The pilot wave is formed even around particles at rest and it's stationary. You may think, the particles forming your body are shaking and making the vacuum vibrating around you at proximity. The Cassimir effect is another manifestation of it.

so is body heat and static electricity...
McIek
Dec 30, 2014
This comment has been removed by a moderator.
Hyperfuzzy
not rated yet Dec 30, 2014
can't this be simulated starting with any charged particle? Any other particles field may be generated from a transformation in perspective, time is built into the perspective dimensionally. The summation of the E field is found from superposition. This field is a projection in time and space, just don't know how to express it! A noticeable event, modal response, i,e, a photon is not a particle. But, hey, my system is not yet defined. I don't know that much.
Hyperfuzzy
not rated yet Dec 30, 2014
Must work out the singularity at the center of charge relative to .. somebody has to have an idea!
Hyperfuzzy
not rated yet Dec 30, 2014
Tiny field black hole?
McIek
Dec 30, 2014
This comment has been removed by a moderator.
Whydening Gyre
5 / 5 (2) Dec 31, 2014
Tiny field black hole?


The EXACT center of a dipole magnet?
The EXACT center of an anapole magnet?
Hyperfuzzy
not rated yet Dec 31, 2014
Just an idea, from a geometrical perspective. The neutron may also be a state of a coupled electron and proton. So what are the boundary conditions? Why can't charge explain mass instead vice versa?

In fact fact everything I say is just my idea. Except ..
Hyperfuzzy
not rated yet Dec 31, 2014
Hence, Dec 19th, so what's the question? An understanding of QM or an Understandings of QM's results? That is, make the best selection from all possibilities based upon a few assumptions, the "numbers" and the "actuality" are two different things. Concepts without assumptions have not been proposed. If one sees results of a wave, a wave is present, but I suggest another test for the particle, and another for different types of particles under different conditions, the waves are the physics upon which we see particles. Would like to see an elasticity test for different sets of charges particles. Effect of rebounds, and attractive collisions without assumptions on components or a malleable field based upon mass and nor an assumption on light speed. Think CERN has clear enough data to define the above, empirically?
Hyperfuzzy
not rated yet Dec 31, 2014
And figure out what that "hole" is we call a point charge. It might be an invasion force from another dimension preparing an attack!
McIek
Dec 31, 2014
This comment has been removed by a moderator.
Hyperfuzzy
not rated yet Dec 31, 2014
Using the idea to explain the idea does not produce necessary and sufficient conditions to produce a proof. The argument is self-referent, something like "if God exists then God ..." Simply an interpretation, a mathematical object based upon unproven assumptions, you believe this I have ... I do understand our search for truth overtime; but, I'm not sure we are using our hindsight and knowledge for truth, m=E/c^2 may be a vast mistake if applied too generally. Particles and waves are unique concepts, suggest clear rationale when redefining things. Mass as a function of charge clusters does not imply charge has mass only that mass has charge. Charge as a function of mass clusters, would imply charge has mass but does not imply mass as charge. With this logic, what is our demonstration?. Define yourself.

I'm sticking with the invasion theory until further notice! Reminds me of Carroll's Tweedle Dee and Tweedle Dum. This could go on forever!
OdinsAcolyte
not rated yet Jan 06, 2015
Completely logical when you think it out. The nonsense vanishes. It makes sense.
Whydening Gyre
5 / 5 (2) Jan 06, 2015
Using the idea to explain the idea does not produce necessary and sufficient conditions to produce a proof. The argument is self-referent, something like "if God exists then God ..." Simply an interpretation, a mathematical object based upon unproven assumptions, you believe this I have ... ... m=E/c^2 may be a vast mistake if applied too generally. Particles and waves are unique concepts, suggest clear rationale when redefining things. Mass as a function of charge clusters does not imply charge has mass only that mass has charge. Charge as a function of mass clusters, would imply charge has mass but does not imply mass as charge. With this logic, what is our demonstration?. Define yourself.

I'm sticking with the invasion theory until further notice! Reminds me of Carroll's Tweedle Dee and Tweedle Dum. This could go on forever!

it changes as you add "charge clusters". We make the mistake of changing reference points.
rufusgwarren
not rated yet Jan 07, 2015
I think I'm getting through, mathematics that create a value from some averaged, maxed. or mined distributions and physics, we must be careful what we are actually summing; else I'm just delusional. So the whole idea of space and time being a function of mass, taste sorta, like a Texas steak still roaming the field. Not ready, yet!
Whydening Gyre
5 / 5 (2) Jan 08, 2015
I...we must be careful what we are actually summing;...

Well, rufus - at least you are getting that it is an addition function...

rufusgwarren
not rated yet Jan 08, 2015
basically, summation of E fields, H follows, but what were you thinking?
rufusgwarren
not rated yet Jan 08, 2015
Why do you need anything else if you equate particles to waves? But why define the singularity as a function of mass? That's totally not explained! I don't believe in "quarks." Do you?
Whydening Gyre
5 / 5 (1) Jan 08, 2015
Why do you need anything else if you equate particles to waves? But why define the singularity as a function of mass? That's totally not explained! I don't believe in "quarks." Do you?

Don't know bout quarks, but -
for particles to act as wave, there must be more than one. And there must be a medium 9in motion) to "wave" in.
Space/time.
Whydening Gyre
5 / 5 (2) Jan 08, 2015
So the whole idea of space and time being a function of mass, taste sorta, like a Texas steak still roaming the field. Not ready, yet!

I kinda like the idea of mass/matter being a residual effect of rotating space "dimensions"...
Whydening Gyre
5 / 5 (2) Jan 08, 2015
Why do you need anything else if you equate particles to waves? But why define the singularity as a function of mass? That's totally not explained! I don't believe in "quarks." Do you?

Don't know bout quarks, but -
for particles to act as wave, there must be more than one. And there must be a medium 9in motion) to "wave" in.
Space/time.

Dang... didn't really mean to hit the "submit" button on that little thought experiment...
rufusgwarren
not rated yet Jan 08, 2015
Did we accept the radial, unending, self reproducible, E field relative to any observer, jus 1 particle? Neutrons resolve into a proton and an electron without any assistance, why? Are quarks really fundamentals of a proton? What the "h*ll" is a Gluon? Conceptually, fundamentally necessary? Anyway, quarks? Really?

I'm beginning to repeat myself, forgive me, fundamental radiant field, and how it appears when in motion? Simple. Only thing that I can find that's fundamental, and we don't know what the H**l it is! Let along why there are two flavors we label as + or -. Best I see is Maxwell's report on the state of EM, until I see reasoning as solid as Maxwell's; I say we are trying to define space and time without further empirical truth using a set of questionable assumptions and an unprovable logic with a vector field that is equated to a scalar.

There are better questions than assumptions.
TulsaMikel
1 / 5 (1) Jan 26, 2015
I had to read all the comments to figure out why all of some posters comments were deleted. Apparently some theories should not be discussed? That's a great way to eliminate curiosity. Never go in that room! The things in that room are never to be discussed!! That should keep everyone out.
rufusgwarren
not rated yet Jan 26, 2015
After all the rambling, best I can find is Maxwell. Time, well, temporality and scale!?
Losik
Jan 26, 2015
This comment has been removed by a moderator.
rufusgwarren
not rated yet Jan 26, 2015
@TulsaMikel I'm backing all posts http://www.reddit...cated...


Saw your site. Momentum? The derivative with respect to time of momentum is force. Momentum and waves is only an equality or ...? Puzzling.

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