April 04 2005

The wave function as a mathematical description of a free particle's possible motion: The 2-slit problem with attempted detection
http://arxiv.org/PS_cache/quant-ph/pdf/0310/0310008.pdf

Pg. 10

"A recent paper by Keller (6) demonstrated rigorously for a propagating particle that its wave function, as an amplitude for location in space, is collapsed by any detection. Using probability theory, he proved that the probability amplitude wave for location of the ongoing quantum particle immediately following the observation becomes limited to the observation area, in other words its effective size is collapsed to that of the observation area."

I know exactly what he is refering to here but let me rephrase it to clear it up. The wavelength amplitude - or total spatical displacement - of the detection "beam" of light defines the maximum wavelength amplitude of the source particle's wavelength when it passes through such detection area. This has relation to Feyman Lectures volume 1 chapter 37 that I previously mentioned, in which the main goal is to figure out which hole the electron went through and the method of detection is key as such ..

"Is there not some way we can see the electrons without disturbing them? We learned in an earlier chapter that the momentum carried by a photon in inversely proportional to its wavelength. Certainly the jolt given to the electron when the photon is scattered towards our eye depends on the momentum that photon carries. Aha! If we want to disturb the electrons only slightly we should not have lowered the intensity of the light, we should have lowered its frequency (the same as increasing its wavelength). Let us use a light of redder color. We could use infrared light, or radiowave (like radar), and see where the electron went with help of some equipment that can see light of these longer wavelengths. If we use "gentler" light perhaps we can avoid disturbing the electrons so much. We shall keep repeating our experiment, each time with a light of longer wavelength.... there is a limitation on how close two spots can be and still be seen as two separate spots. So now, when we make the wavelength longer than the distance between our holes, we see a big fuzzy flash when the light is scattered by the electron. We can no longer tell which hole the electron went through! And it is just with light of this color that we find that the jolts given to the electron are small enough so that P12 - that we begin to get some interference effect."

In that he goes on to note that it is impossible to arrange the light in such a way that one can tell which hole the electron went through, and at the same time not disturb the pattern.

Now to get to my point. If the width of the detection area is >= (greater than equal) the width of the 2-slits then and only then will interference occur because a second path - no matter how much is used - is allowable and used, whereas in the case of <= the path is limited to only 1 slit. But you would think this is the case of a detection that occurs Before or between the source and the 2-slits, what about in the case of a detection occuring after the 2-slits as the experiment shows? That is the paradox, the electrons current wave function (before it reaches the 2-slits) should not be influenced by any future detection if it exsists. Yet somehow it appears that the electron knows that it is going to come accross and pass through a detection beam and its wavelength is altered according to that information. Nonsense? Thats what I say, but the evidence suggests that the very presence of a future detection can explain whether or not interference shows up, whether or not it takes both paths or 1 path depends entirely on the presence of that detection beam and the width of it. Sooo, can we assume that what really is the case is that the detection area covers much more area than we know of? That including the area between the source and the 2-slits? Aha! If the detection area were not truely only behind the 2-slit but in front of it as well, that would explain it! That is, one convienent explaination, whether or not that is the case remains to be seen. Let me remind you this theory applies to a specific method of detection, whether or not it is applicable to other 2-slit experiments is another question.

Let me say for the record in the absense of a detection the electron/photon Will assumingly take both paths, Assuming a reduceable structure to explain interference. And as I have just stated, if a detection beam is present and its width is <= the width of the 2-slits the particle will take only 1 path. The electron or photon is not a truely solid/geometrically fixed entity, it has an uncertainty, a probability of location - to us, only limited by our technology - according to wave function amplitude and its path likewise.

(The following is if you believe the electron splits!)
It can be said that both are more like a reduceable ball of energy which in turn is corupsule like or quanta like in nature. Analagous to a slinky, whereby in wave motion it is stretched out and has a space-time trajectory or path associated with it, yet can also "collapse" to a particle state when not in wave motion. (Note that as we have just learned that "collapsed" does not necessarily assume a lack of wave function, just a reduction) To take both paths or a second path around an obstacle it will indeed split at and according to the width of the obstruction, then reassume shape. During its reformation with itself are the dynamics associated with interference. The cross section of it that hits the obstruction will spring forward through either path with an increase in momentum equal to an inverse loss in momentum as a result of collision. It follows if you will, the momentum of the sections that passes through as if connected to it. Then as if somehow energetically attracted to, the 2 large sections will reform behind the slits and again the dynamics of that reformation will explain interference patterns as it begins to regain its original wave form.


Here is your 2-slits

|

|

|

Or to simplify lets just use a single obstruction, which equally yeilds two paths.

|

Here is the side view of an electron in motion over space-time where A is the head and B is the tail.

.
.B . .A
. .C
.

Here is a front view of the electron in motion, supposedly "beeline" or spiral path.

.B
. .A.
. .
.C.

For simplicity lets say the middle part C will be the section that collides with the obstruction.
It is at C where the particle wave splits all together, it breaks in two then follows the momentum and path of whatever section it is connected to. Section A may go through either or slit but not both, likewise for section B and C1 and C2 ( C split).


Now... To figure out exactly why the electron or photon's wave function amplitude is limited to the detection area amplitude! Maybe I should read Keller's paper. (found it, AJP 1990 Joseph B. Keller "Collapse of wavefunctions and probability densities" , but I cant access it)


April 07 2005

Quantum Mechanics Interactive Simulations

Found these web based experiments which include the 2-slit diffraction.
http://phys.educ.ksu.edu/vqm/index.html

If you mess around with the slit separation, firing an electron, you will see that the greater the separation and energy level the more bands.

If this experiment is accurate to a real world one, One thing is immediately obvious is the need to explain why the electron takes a random path. Sometimes it hits at +5 sometimes at 0 and sometimes at -5 and every marked coordinates inbetween. I think it is safe to assume that this is because of the HUP. What I mean by that is if you were to create electrons that are exactly similar in physical properties and exactly similar in position and momentum along its wavelength then they all should take the same path and hit at the same spot. But that is not the case, the device that is creating and firing electrons is doing so without precision and letting the HUP become realized. So for example if you were to fine tune this device to create like electrons including position and momentum then fire them when the electron oscillates to that defined wavelength position, what will happen is you get no interference pattern.

There seems to be an error with the slit separation meter because using electrons you get a choice between .05nm and 25nm, and using photons you get a choice between 200nm and 10000nm, yet the distances seen are similar in width separation. So I cant comment on the pattern differences between the electron and photon, because as you will notice they are very different which comes as a surprise to me. For example, I get almost no pattern for almost any setting using photons, and I dont get multiple bands like I do with the electrons. Additionally using electrons gives you an energy level in eV slider and photons you get a wavelength slider in nm, so youd have to convert eV into wavelength dimensions to be able to compare the 2 particles.


The HUP is only a technological limitation. True or False?

http://www.physicsforums.com/showthread.php?t=70721

What I really should have said in retrospect is this; Quantum randomness is a technological limitation.

I will go ahead and quote my replies found in the above thread (see link) because I think they are possibly the most important words I have said yet regarding the 2-slit experiment, interference and observed quantum randomness.


"HUP is a technological limitation. True or False?

In quantum physics, the HUP expresses a limitation on accuracy of simultaneous measurement of observables such as the position and the momentum of a particle and is sometimes explained by claiming that the measurement of position necessarily disturbs a particle's momentum. In other words what this is saying is that our method of gathering information (eg. bouncing a photon(s) off of it) will disturb the wavefunction of the particle we are detecting, we alter its position and momentum - think classical mechanics of colliding objects if you want, in a QM sense it could be charge or whatever based but the effect is comparable. We cannot yet achieve a "look but dont touch" method of gathering information. If we could, then that solves alot of questions/problems. So to answer my own question, I would say Yes the HUP is a technological limitation, that eventually I believe we will get around. It should be as simple as substracting the jolt given to the particle upon detection to get the state of the particle had we not influenced it (anyone know what I'm saying?) but that in itself is not so simple.

On the idea regarding a myrid of possibilities converging to a single outcome, a single result. Well what are you saying? That another answer at another location does not exsist? You have to consider that this comes about as a function of time(s) and the exact relationship between time(s) and your angle or method of detection - this is not something unique to the QM world. A particles position and momentum are ever changing and perhaps even repeating so if we have our focus on an area that we know it has or will pass through, any information we gather regards it as what was the system (part of the system) like at t time at l location and if possible can we then go on to predict the future or past - but again our measurement affects the future hence quite an uncertainty in QM arises.

QM collisions are different than classical mechanics macro objects collisions where we have a good idea of all the meaningful varibles involved (including gravity which QM doesn't) and not disturb the system because any disturbance of observation (force of photons, or whatever particles coming into contact) is neglegible.

I wanted to comment on diffraction patterns from a slit also. It is my belief that this pattern (multiple bands/patterns actually) comes about due to the device that creates and emits electrons rather than anything else. Think about it this way, if all electrons that were emited were 'exactly similar' and exactly similar in position and momentum along its wavelength, then wouldnt it be reasonable to assume that they would all take the same path given no extra dynamic varibles to source? In a vacuum for example, the environmental influences- if any- are fairly constant so the paths taken should be identical if identical (in all aspects) electrons are emited. But thats not the case is it? The device that emits electrons will emit unlike electrons therefore the paths taken by them are different and effectively random, therefore an definitive aspect of the HUP becomes realized and observed.
(The above assuming a non random operation of an electron in motion - eg. a predictable period and frequency according to given energy.)
(Also what pattern would you get if they all took the same path? A dot, thats it, no verticle or horizontal displacement, just a dot.)"

and part of a later reply

"What I am describing is the UP of Interpretation within the context of the Copenhagen Intepretation and it's underling relation to the uncontrol of randomness- a technological limitation. The HUP was never defined or stated with regards to any specific experiment or measurement technique so I can, if I want, use the underling principle however I wish and according to a specific experiment, such as the 2-slit, Feyman himself did this.

"Within the widely but not universally accepted Copenhagen interpretation quantum mechanics, the uncertainty principle is taken to mean that on an elementary level, the physical universe does not exist in a deterministic form—but rather as a collection of probabilities, or potentials. For example, the pattern (probability distribution) produced by millions of photons passing through a diffraction slit can be calculated using quantum mechanics, but the exact path of each photon cannot be predicted by any known method. The Copenhagen interpretation holds that it cannot be predicted by any method."

< I am saying that it can eventually given technological advances, be predicted, and that the reason that the path is not currently predictable is because none thought of perhaps that it is actually the device that we need to focus on because as it stands, generates effectively random path electrons."

and part of another reply

"every possible route according to what? I know what your saying I've heard it before. Superposition of paths. Thank you for your insite. Superposition of paths is in actuality the wave function displacement, whether this involves 1 particle or more than one- entanglement. It does not travel a path that its wave function does not displace."

and

"Only because a pattern, no matter what it may be, comes about as the result of uncommon electrons being fired - and subsequently interacting with the obstruction so that over time a pattern results DUE to the different paths taken. I cant make this anymore clear."

and lastly

"I want to make it clear the distinction between a 1 electron fired at a time vrs multiple electrons fired at the same time- which are also spatially independent- accumulated interference pattern.

Given a non reduceable structure of the electron, it cannot interfere with itself as a means to explain interference patterns - this may be contrary to popular opinon and exactly opposite the photon. to quote Dirac's famous dictum

"...each photon interacts with only itself. Interference between different photons never occurs."

We know this must be true given the fact that light 'reflects' off all surfaces in all directions, its impossible to say that given the shear amount of photons in any luminous environment that they would not interfere with each other, effectively altering each others paths. If interference and collision between photons were allowable then the world we see would be a big blur. Fact. The very nature of the photon forbids it, it has no mass nor charge, therefore a collision cannot take place. Photons can only be guided by such things as an indirect effect of gravity. Photons actually do not reflect (suggesting a collision) off a surface, they are absorbed and re-emited - this explains how new information about what it 'reflected' off of gets transmited. < information that would be impossible to explain otherwise according to a direct physical reflection. Now let me also make a clarification, interference and collision are conceptually and interpretivealy two different things. Light rays can certainly interfere with themselves in one sense of interpretation, but in an alternate sense more akin to a physical disturbance (altering its path) it cannot.

His statement also tells us why the pattern produced by photons is different than electrons, it is not just because of different energy levels. Photons are a reduceable structure, they are "packets of light" and will split at a single or 2-slit obstruction and take both paths given the wavefunction displacement is >= the area containing the 2 paths. A beam splitter is a good example of this, a single photon undergoing parametric down conversion will split and become known as an entangled pair of photons each of them having half the energy of the total system.

An electron on the other hand will not split, it will take either or paths but not both. Same thing with protons and neutrons. Dont ask me what happens when an electron hits the obstruction, because I dont know; I do with 'photons', they split at and according to the geometry of the obstruction with relation to thier current position along thier wavelength. Electrons can interfere with other electrons, they have a mass and a charge. They can collide as a condition of having mass or they can repeal and attract according to charge.

Even so, if the electron did interfere with itself my statement regarding the pattern generated over time as a condition of random paths holds theoretically true to the position and momentum along thier wavelength from which they originated. What it not true, is that the electron has a random operation, if that were the case then we could attribute the random path taken to that. But since that is not the case, we need to explain why the apparent random path. Surely none would suggest that the random path is due to a random operation of the electron? No of course not. So explain to me in other words, why the random path taken given a predictable operation of the electron. A predictable operation will enduce a predictable path - if identical in all aspects electrons are created the path will be identical, no interference pattern; even if they interfere with themselves along the way, if they all do interfere with themselves along the way that as well will be predictable and still the identical path is maintained. The only argument you could ever make is random self interference which will subsequently enduce a random path - then you would need to explain the logic and mechanics of random interference among itself. < Conceptually possible yet entirely difficult and chaotic. OR
possibly there are dynamic "unknown" forces (dont want to say hidden varibles) associated with the environment in which the electron travels through causing a random path. < That I will buy but an example is necessary. Explain random path.

And by relative path I meant several things, one of which includes the path of electron A being relative to a subsequent electron B and so forth, and in the case of multiple electrons being present at the same time they have an additional temporal and spatial relative path to each other - such as coherency phase and polarization. Not sure what point I want to make here, your wearing me out ;)

What I'm saying is something new (right or wrong) so I understand questions. But I really think I have said what I wanted to and then some. If I say anymore, mine as well move it to personal theory forum where I can explain it in full."

April 08 2005

Wow this is amazing. A "cosmic smoke ring"
http://www.newscientist.com/channel/space/mg18624945.400

"The cosmic smoke ring is a bizarre galaxy called Hoag's Object (www.arxiv.org/ps/hep-th/0503167) first seen in 1950. Like a giant wheel without spokes, it consists of a bright ring of hot blue stars surrounding a nucleus of yellow stars."


April 11 2005

Ive already discussed at length my thoughts on Einstiens model of gravity but something new came to mind. Lets again pretend for a moment that Einstiens theory of gravity is correct. They say when a supermassive star implodes on itself, its mass condenses and to point where all its mass it focused eg. not spread out. By condensing its mass/geometry it warps space so severly that a blackhole forms. Ok thats one thing, now what about the explosion itself? What about explosions in general, are they able to warp the 'fabric of space'? Its funny I have never thought about it! A supernova is quite an explosion, to what degree, if any, does IT warp the fabric of space? Keeping with this logic, what if perhaps the blackhole is really do to the explosion and it is the blackhole shortly thereafter that condenses the matter of the star? (However, rarely does a white dwarf nova burst create a blackhole... So you would have to say if the above senerio is true, that a specific amount of energy, similar to a specific amount of mass, is required to create enough force to cause a blackhole- Which makes sense.)

I will go ahead an assume that a shockwave would warp the fabric of space. Keep in mind though, that the shockwave is global; however a blackhole according to GR is not global. The shockwave that equals the sound wave is not the same thing here.

Seems like I found yet another loophole in GR (more specifically the physical interpretation or model of gravity that GR leads to eg. a fabric of space). Explosions could and would warp the 'fabric of space'. Another hint here, conceptualize the shift in position and momentum given to the star as a result of the push against the fabric of space when it explodes - using simple thermodynamics logic.

I have a made a simple image to help describe it
local link is http://www.oocities.org/tdunc01/supernovadisplacement.gif

So again the question is does such a verticle displacement of local astronomical bodies exsist during a supernova? I say no but according to GR there should be, but I dont think the question has been asked before.

April 13 2005

How lightning works
http://science.howstuffworks.com/lightning.htm

April 16 2005

/In search of source that specifically details the theory and mathematics, the explaination of how a dark matter halo theoretically [1.] Keeps the galaxy from flying apart [2.] Explains the flat rotation curvature. Because logic tells me that the opposite should be true, a large halo mass around a galaxy would actually couteract the gravitational pull of the central SM Blackhole on stars and help to throw the galaxy apart. Also I just cant get my mind around why such a halo would speed up the stars at the edge - The Halo is an idle non rotating mass. Maybe there is an analagous experiment involving magnetics.


April 20 2005

http://en.wikipedia.org/wiki/Photons
http://en.wikipedia.org/wiki/Polarization

http://dept.physics.upenn.edu/courses/gladney/phys151/lectures/lecture_apr_07_2003.shtml

http://www.lifesci.sussex.ac.uk/home/John_Gribbin/quantum.htm

http://www.eclipse.net/~cmmiller/DM/

http://arxiv.org/PS_cache/hep-th/pdf/0210/0210162.pdf

http://www.telp.com/qw1.htm


April 22 2005

A "Photon" is Not EMR. A Photon is a mediator particle (gauge boson) of the EM field so that other particles (electrons) can interact with each other. EMR consists of no less than two separate parts, one force along an x axis and one force along a y axis. These 2 parts are the electro and magnetic fields, combined they are known as EMR. Polarized light is such a case of 2 vector parts, Unpolarized light can consists of many electro and magnetic fields inbewteen the x and y axis but they always pair up with each other. eg. an electro field always has an magnetic field component in the orthogonal (perpendicular) plane.

http://www.phys.unsw.edu.au/COURSES/FIRST_YEAR/pdf%20files/Waves%20II.pdf (pg. 18)

In many instances polarized light is unpolarized light (many pairs of E and B fields) that now share the same plane. In other words the E field in polarized light is a superposition of individual E fields and when combind they constructively interfere, likewise for the B fields.

A Photon traveling in a wavelike motion, IS the electro field. A Second Photon traveling in a wavelike motion, IS the magnetic field LINES. Typically the E and B fields are a continuous stream of Photons, so that essentially Many Photons are the E field and Many Photons are the B field. However the Electrons themselves are the major componet of the E and B Field. Photons are used to transfer information to other electrons and tell them what to do, how to line up, what spin ect in relation to other electrons. Photons are not the physical phenomenon or force associated with the E and B Fields, only Electrons are because they are the particles with a charge and mass that can excert an attraction or repulsion force on other particles with a charge or mass. Yes it is true that the photons add an energy varible to the field as a whole but keep in mind any physical phenomenon associated with magnetism lies in forces of attraction and repulsion, so the difference is clear.

If we visualize an E wave section that contains say 3 peaks, and 3 troughs, how many Photons do we have?
I believe the answer is minimum of 3 photons, however that is just a guess, it may be there are 6 photons and it may be that it is many more. In all my reading I've never come across the answer simply because I've never heard the question asked. So that is one thing I will be asking anyone who cares to answer it.

More questions that I keep asking myself.

Why or how do particles travel in a wavelike motion?
Why or how does an individual EM wave (a single E particle wave + a single B particle wave) spread out over distance? eg. Increase its amplitude and reduce its energy according to an inverse square law. To answer this question logically requires we answer the first question.

These are not general questions rather I'm looking for a specific explaination or quantum mechanical model.

For aid of visualization, suppose that many many photons are present in the above example, not just 3 or 6. The greater the distance, the greater the amplitude thus the less photons per arbritrary unit of space. What that is saying is that instead of that area absorbing x amount of photons it absorbs y amount of photons where y is significantly less than x. In other words, the wavelength has to displace more space with the same amount of photons thus any defined area will absorb less photons. Sounds like a winner to me, however we didnt answer my questions.

Here are two images to go along with this

http://www.oocities.org/tdunc01/EBField.gif
http://www.oocities.org/tdunc01/EBField2.gif


April 23 2005

Considering the possibility that light actually goes through the material that makes up a diffraction exp obstruction. I should have known this all along. Any light incident on the material increases its wavelength to the left of the spectrum closer radio and infrared. It also suffers a spatial and temporal difference from any light that passes through freely so that the waveform as a whole is now curved. This is demonstrated figuratively in the following diagram

http://www.phys.unsw.edu.au/COURSES/FIRST_YEAR/pdf%20files/Waves%20II.pdf (pg.15)

Light is basically defined by its wavelength. It has a well defined energy level and wavelength when it is emmited from an electron yet will readily increase or decrease both according to what it runs into. With regards to a ray of light, any shift or change of one part does not necessarily change any other part. Obviously, they are many and separate photons in a ray of light. So the waveform front of a ray of light can literally take on any shape according to what it passes through.

It has always occured to me that light was absorbed outright (stopped in its path) if the material was not at least semitransparent. But I realize that is wrong to assume. Light may pass through but its spectrum has shifted so that it is no longer Visible light. However, the important thing to note here is that its doesnt matter what spectrum the light is, interference still occurs, wave function collapse still occurs, superposition still occurs ect. Nothing really changes. Except!... Well lets just keep this in mind, It will hit me sooner or later what this all means. obviously the speed of light/EMR, is not "constant" if any part of the waveform can be curved as demonstrated, but I already knew that.

April 24 2005

I'm wondering whether the fine structure constant or the coupling constant can be used to factor how many photons are present per wavelength in E and B Fields. And whether wavelength or amplitude is an arbitrary artifact in such factorization - this relates to the previous text in where I explain radiation exposure differences according to distance/wavelength. But unfortunatly I cannot read through the mumbo jumbo. (mumbo jumbo includes math!)

http://en.wikipedia.org/wiki/Fine-structure_constant
http://en.wikipedia.org/wiki/Coupling_constant