What exactly is a wave?

I know what wave looks like and the basic idea of a wave but what exactly is a wave in terms of quantum physics?

I am not sure about its conceptual model for quantum physics but any wave is composed of amplitude, distance between crests (wavelength), and frequency. This definition covers ocean waves, light waves and everything in the middle. For light or energy the distance between crests (wavelength) is connected to the frequency; the product equals the speed of light. The amplitude is related to the energy value of the wave.

The energy value of an energy wave is the third dimension of what is normally considered a 2-D wave. For example, if we throw a rock into a pond, it will give off radial wavelength and frequency. If one looks at a glancing angle there will also be height or amplitude in a third dimension.

Although energy travels at C, the wavelength and frequency are finite in our reference. In other words, if a galaxy was hypothetically moving at C, and was giving off energy, the energy would be totally red shifted to infinite wavelength. But energy is different in that even though it travels at C, we do not measure infinite red shifted wavelength, but rather a spectrum of finite wavelength and frequency. The difference between the C reference (infinite) and this finite wave crest-distance/frequency reference is related to its energy value or amplitude. A smaller difference gives the long wavelength energy less energy amplitude and a larger difference gives short wavelength energy higher energy amplitude.

Quantum Physics is a little vague on the whole idea of waves and particles. You really have to abandon any ideas of definite waves and particles. Almost everything can be described as both on a quantum level.

The photoelectric effect assigns particle properties to light, and electron diffraction assigns wave properites to electrons etc. These affects are limited by the size of planck's constant (i.e. very tiny).


This means that effects light quantum tunneling can only happen on a small level (although I do like the idea that if I throw myself into a wall often enough, it's possible I could fly through )

Hi AngeloDS,

Wikipedia on waves

Wikipedia on Wave Particle Duality

Cheers

A Wave is the second Quaternion derivative or the curvature in space-time of a function! Most people never seen the formulation of such a wave because quaternions are not popular in physics.

In 1843 William Rowan Hamilton invented Quaternions, a four dimensional mathematics.
Quaternions consist of a scalar (omnidirectional) and three vectors i,j,k (unidirectional).

Hamilton also invented a vector differential operator DEL = id/dx + jd/dy + kd/dz.

In 1965 I added a scalar differential operator top Hamilton's vector differential operator to create a Quaternion Differential Operator, I call X, for Kephra.

X = d/cdt + id/dx + jd/dy + kd/dz = d/cdt + DEL = R + DEL = Rad + Grad

The scalar differential is d/cdt where c is the speed of light a scalar and t is time. cdt is an omnidirectional spatial differential. R=d/cdt I call "Rad" for radiation.

X consists of a scalar and three vectors and is a quaternion as defined by Hamilton,:
Hamilton's definition is i^2 = j^2 = k^2 = ijk = -1.

X is a quaternion and follows the rules of quaternions and defines waves. The wave is the result of the second quaternion derivative on a quaternion.

X = R + DEL, is the change derivative and X^2 is the wave or curvature derivative:

X^2 = (R + DEL) (R + DEL) = ((d/cdt)^2 - DEL^2) + 2(d/cdt)DEL

The first term in parenthesis is the scalar (Omnidirectional) transport part of the wave, called the D'Alembertian. The second term part is the vector part of the wave operator.

The wave comes from the taking the second quaternion derivative of a quaternion, like E, the electric field. E is a quaternion electric field E = Es + Ev, where Es is the omnidirectional scalar field and Ev is th vector field, Ev=iEx + jEy + kEz.

X^2 E = (d/cdt + DEL)^2 (Es + Ev)

X^2 E= ((d/cdt)^2 - DEL^2)Es - 2(d/cdt)DEL.Ev) + ((d/cdt)^2 - DEL^2)Ev + 2(d/cdt)(DELxEv + DEL Es))

or using R=d/cdt

X^2 E = ((R^2 - DEL^2)Es - 2R DEL.Ev) + ((R^2 - DEL^2)Ev + 2R(DELxEv + DEL Es))

The wave equation is a quaternion eqaution and consists of a scalar omnidirectional (gravitational DEL.Ev) wave and a vector (electromagenetic/transverse DELxEv) wave.

Thus there are are two waves.

The omnidirectional wave is associated with the "Photon like particles" and gravity.

The directional vector wave is transverse like electromagnetic waves.

Quaternions are the substance of the Cosmos. The wave is the result of the quaternion nature of the Cosmos and the quaternion differential change.

This is what a wave looks like in Physics including quantum physics.
Quantum physics comes from the first quaternion derivative equation:

0 =XL The conservation of L. The fundamental variable of the Cosmos I call Life, L.

L = ch where c is the speed of light and h is action like Hamilton's Action h. The unit of L is energy-distance or Joule -Meters.

The first derivative of L, XL = (dLs/cdt - DEL.Lv) + (dLv/cdt + DELxLv + DEL Ls)

is energy. Quantum Theory is the conservation of L, or

0= XL = (dLs/cdt - DEL.Lv) + (dLv/cdt + DELxLv + DEL Ls)

Substituting Ls/c=hs gives Planck's Law:

0 = (dhs/dt - DEL.Lv) + (dhv/dt + DELxLv + DEL Ls)

The scalar part of the quaternion first derivative is Planck's Law:

dhs/dt = Energy or hf = Work-function (DEL.Lv)

Quantum Theory is the realization that the energy of the electromagnetic field is proportional to the frequency, not the amplitude of the wave. That is the quantum difference in physics.

The vector part of XL is the quantum induction similar to electromagnetic induction, 0 = (dBv/dt + DELxEv + DEL Es).

What is a wave?.....Perhaps it's just a recurring instant?

My model of existance has singularities present in all particulate manifestations, maybe these act as an event reversal mechanism, creating the illusion of simple harmonic motion with regards to energy?

Who knows?

Have a browse of my Spacial Vacuoles stuff:Spacial Vacuoles T.O.E

By my Aether Wave Theory the wave is the solution of the wave equation (i.e. the local form of the Newton inertia law) for elastic massive string, the density of which is proportional the energy density of the string waves.



Such recursive solution is astable and leads to the solution of Dirac equation.

hi, answer to nviva@mail.ru for hypercomplex physics please

As quantum physics defines it, the quantum wave represents the probability that a quantum particle will be found. In other words, the crests are high in probability, and the troughs are low probability. It has absolutely no material aspect to it in reality. Hope that helps.

Hi itistoday,

You are right from one point of view but that may not be the entire story. In a mad struggle to grasp the Nobel Prizes and to achieve certain goals, maybe the physicsits have blinded themselves in the quantum interpretation they have achieved. There is a problem when you go a long way down a one way street the wrong way... it is very hard to stop and turn around and go back to the beginning again because there is still progress being made even if the result is a dead end.

Cheers

Righto. You provide no evidence otherwise.

Such irrational stance definitely will not help in understanding, on the contrary.... It simply means: "I'm not able to explain the quantum wave by natural way " - no less, no more...

Fortunately the explanation of quantum wave in term of classical wave mechanic cannot be so difficult at all. By Aether Wave theory the quantum wave arises from the model of elastic massive environment (i.e. the aether), the inertia of it is recursively created by other waves in hidden dimension quite naturally. What I mean by this, exactly?

Try to imagine some dense vibrating foam composed from adjacent bubbles, the mass density of it is proportional the energy density. How? You can simply imagine, if you introduce some additional energy into same place of the foam, the pitch of vibrating (mem)branes increases and the diameter of bubbles will decrease correspondingly to compensate the increased tension. As the result, the mass density of the foam will increase at this place correspondingly to it's energy density. It means, each the additional energy introduced into such environment increases the total energy density of such environment.

How such environment will oscillate, after than?

It's obvious, the vibrations of such matter wouldn't correspond to vibrations of normal homogeneous string, because the mass density of such string will be proportional to it's energy density and it will change in each moment and place. It means, the more energetic are vibrations of such string, the more heavy the string is at such place. Fortunately, such model can be easily solved both analytically, both numerically. How? Well, we can simply solve the wave equation of normal string numerically (...it's trivial task, described at lotta places of Internet...), so we can substitute the string density by the energy density distribution obtained from temporary solution and after than we can repeat the solution in small time step again. The precision of such computation will be the more higher, than smaller time and space step we'll use for such solution...

If you're interested about, you can even play with such concept on line using a simple DHTML applet (sorry, just for MS IE 5+ only). Such applet describes the oscillations of string, the mass density of it (in blue color) is proportional the energy density of the wave alone (in red). The energy of string in each time/space interval is composed from two components: the potential and kinetic energy of string element (E=Ep+Ek). The potential energy of string element is proportional the string amplitude (Ep=mh), whereas the kinetic energy is proportional speed of it squared (Ek=mv2). So we can compute the energy density of string in each moment and place easily and substitute it by mass density of string.



It's obvious, the character of undulations of such string exactly corresponds the character of quantum wave, which can be obtained independently by solving of Schrodinger wave equation. From the analysis of quantum wave follows, it describes the behavior of wave, which is formed by it's own energy density, i.e. the Hamiltonian density. It means, the quantum wave just describes the behavior of such mechanic model of vibrating foam, the density of which is proportional its energy density.



Hope that helps...

I didn't obtained any message yet, sorry.

If you read it well, you can ask easily: "Well, the quantum foam, uhmm - it's nice, but where we can met with such system in the nature, with exception of vacuum? How can I make sure, such foam is real?"

Well, such system can really exist in the nature, but not for light waves, but mechanical ones, the sound waves in particular. At first, it's important to realize, the sound wave should carry a sufficient amount of energy. It requires, such environment has to be both compressible, both inertial (i.e. dense). The water isn't good enough, because it's dense, indeed, but it isn't very compressible. It means, the underwater sound wave cannot carry out a large energy density.

On the other hand, the common gases, like the air, are a quite compressible in general, but they're haven't a sufficiently large density to create inertial waves in bulk. It posses the same problem: the resulting energy wave is just a rather low energy density.

Now we can ask, if some compromise can exists at all. The answer is: Yes! The so called supercritical vapor. What's the stuff?



The series of steps above illustrates the supercritical vapor behavior (you can click to the animation, to see it in original resolution). Simply speaking, its a heavily compressed vapor, which is heated in sufficiently high temperature, so that it cannot condense. After moderate cooling of such system a quite interesting effect appears: the vapor begins condense, but the density of forming liquid is nearly the same, as the density of vapor, because of high pressure and corresponding density of such vapor. As the result, the vapor doesn't creates some droplets, as in common situation. Instead of it will create an intimate mixture of alternating "bubbles" of vapor and liquid similar to the mixture, you can obtain by shaking the same volumes of oil and water with low amount of surfactant (soap), similar to foam.

Under normal conditions, such intimate mixture of foam and vapor isn't very stable due the gravity, which separates both the phases readily. But in microgravity conditions such system is conditionally stable, considering the temperature and pressure remains the very same, so it can serve as the natural model of quantum foam.

Hi All,

My only point of disagreement with this is whether or not such a description is going to help anyone. Clearly there are a fair number of responses from people who are not happy with quantum mechanics and prefer other ideas.

I propose a bit of an experiment to sort the Maxwells from the Heisenbergs. I think most people have accepted the idea of a photon.. though there may be a lot disagreement about what one is and some (like myself) may have to fall back on "don't know".

The experiment is..
1/ We have a source of photons that we imagine will produce 'waves' at ten cycles per second.
2/ We have set up our source so it only produces 20 photons a second.

Describe the associated waveforms (Maxwells) and the associated probabilities (Heisenbergs).

The first objection is that the energy of each photon is going to so low that it will be very difficult to detect. As this is a thought experiment we have the choice of saying we'll be able to detect them or we can change the experiment to run at 5 Teraherz and .. personally I'd rather walk through it at 10 cycles a second if that's ok with everyone else.

Any Heisenbergs that want to be sniffy about measuring 10 photons a second .. I ran the experiment for several hours .. the setup is stable and the average output is 20 photons a second .

The Maxwells have got an average of two photons to make up each of their cycles from .. how will they do it?

Maxwells equations suggest the amplitude will vary with time .. what wll amplitude mean here?

Good luck!

-C2.


http://en.wikipedia.org/wiki/Coherent_state may help to explain some of the confusion.

I'm not really sure I understand what your proposed experiment is and what its purpose is. I was merely answering the OP's question. My answer was correct, as in it has been substantiated by countless scientific experiments (and the words of QM's pioneers).

I've noticed that this forum contains an incredible amount of Einstein wannabes that go around flaunting their "theories", which are not theories at all because nobody has actually tested them (they are at most hypotheses). Quantum Mechanics clashes with their classical mindset and so they just say "NO!" and go on rambling about unsubstantiated crap. To be honest, for a place that's supposed to harbor *scientific* thought, there is very little scientific thought going around at all. All I see is a bunch of unprofessional people going around preaching their untested and unsubstantiated ideas, pretending as if they are fact, and using that to "answer" the OP's question.