Problem with the two slit experiment, Observing later

I've been working on the interactions of laser light with molecular dipole antennas.
This might lead to some real breakthroughs. Visa Vis the frequency combs; they are very real devices that synthesize waveforms from much shorter discrete wave pulses on the femtosecond time scale.

Neil,

Are there any giblets you can share? Or is it still in the "but then I'd have to kill you" phase????

NF, et al,

In the early 1990s, a big step in terahertz technology was made by the advent of reliable femtosecond lasers for the generation and detection of terahertz pulses.

The oldest and probably most popular scheme involves photoconductive dipole antennas that are gated by the femtosecond pulses. These antennas consist of a semiconducting substrate onto which a metallic antenna structure is deposited by photolithography techniques.

An external bias is applied to the antenna structure, which comprises a small gap to prevent a short. Current can only flow under the action of a laser pulse that optically excites the semiconducting antenna substrate in the gap.

The generated electron-hole pairs are accelerated in the bias field and cause a short current pulse with a subpicosecond rise time. According to Maxwell’s law, this is the source for a short, and hence, broadband terahertz pulse.

If an unamplified Ti:sapphire laser is used for excitation, the continuous-wave (CW) power level is in the microwatt range.

This is not what your working on by chance, NF?

caio_
yquantum

You mean minds are actually catching up to themselves....

[removed]

Obviously that last post was by someone whose mind is unable of reaching these speeds like the rest of the world....Only because he is too lazy to put forth the effort.

Hi Confused2, TRoc, Laserlight, "THEY", "THEY2" janrinze, Jal, Montec, yquantum, StevenA, "Why Not?", Siau, Neil Farbstein, Terry Giblin, et al,

I disagree entirely. It is a useful transform but unlike the Fourier Transform (FT) it does not have an inverse. In fact the FT is not only time symmetric and conservative in that it can be performed any number of times without losses. This can't be done with the Wavelet Transform (WT). The FT has been used in physics simply because it is so useful. Because it is "harmonic" it is essential to Quantum Theory. It treats time and other dimensions with an even hand and converts from the time domain to the frequency domain as well as from space to reciprocal space. Being causal beings we have a natural affinity for the time domain but the other complementary description is equally valid. Because these descriptions are "Complex" each description contains all the information from either domain so the statement above is very wrong and at the same time this argument is critical to Robi's point of view. You can indeed swap domains and recover the spatial and temporal information as needed performing the Inverse FT on the data.

This all works provided that we retain the Complex Plane Information intact. Projecting the data into a plane of Reals reduces the information content "significantly". This is precisely why particle theory is missing essential complex data and why it sometimes appears "meaningless" or even "magical". The FT is the transform of choice in physics and is useful in any number of dimensions. IMHO it overcomes certain problems related to tensor treatment of curved manifolds and curved manifolds is what electromagnetism is all about... the only problem has been the use of tensors fails once you reach a certain level of deformation where the linear approximation no longer holds while the FT works all the way to a reciprocal description and back again. Being harmonic it is also a "natural description" of waves. The integration limits for the FT usually range over the surface of a "sphere" as in the case of solutions in Quantum Theory of atoms.

It is a full and complete description of the components (any components) and it indicates the context in full unlike the Wavelet Transform.

For the time being I prefer to stay with the FT for very good sound reasons.

Cheers

Hi Good Elf,

I can't find a good reference to explain spatial fourier transforms. Since I am short of time I fall for the temptation to thrust the burden onto you.

Starting with a single slit opening .. what is contributing to the spatial fourier transform. What exactly are we integrating?

Best wishes - C2.

( Excuse for absence .. I've bought a new business )

Theory of relations
From Wikipedia, the free encyclopedia

Hi GE,

Fourier transform is a transformation into a reciprocal space.
This does not mean that wavelet transforms are useless or even non-invertible.
actually the wavelets are just a specific form of Fourier..
They are much more suitable for wave packets.

there is a big misunderstanding about frequency and time.. apparently people tend to believe that one frequency means implicitly that it extends into infinity. (inverse FT will imply such a thing..)

But if a frequency changes over time starts/stops or is only briefly there then the Fourier transform of the signal over infinite space will yield an almost 0 value for that frequency.. (which is correct from the point of view in average energy..)

So, while in mathematics FT is a very useful tool the use of FT in physics largely stretches up until the sample window has been filled by measurement apparatus. The measurement window is then being used as a repeated frame in the discrete Fourier transforms.

So in a way in Physics we 'bend' rules in respect to real infinities. this seems correct if we look at the results..

Jan Rinze.

Hi Janrinze,Good Elf and all,

My motive for going into detail about the FT is that the results of the single photon DSE suggest (to me) that the single photon really does 'extend into infinity' .. I (alone?) see the correspondence between the FT predicted result and the experimental result as a sort of 'proof' of this extension into infinity. It remains to be shown whether the e^(ikx) is bent to give the right answer or whether e^(ikx) is actually the right answer.

Best wishes - C2.

The ? after 'alone' was edited in .. maybe I am not alone..

This post has been edited by Confused2 on Sep 23 2007, 09:53 PM

Hi all,



I agree with JR. I am not asking for a "vote" against Fourier; just that we "update" the historic method, with new computing techniques. If for no other reason, just so that the measurement is "not on a single frame", axis of reference. Not to mention the thought of breaking the Uncertainty Principle, in measuring from a "fixed" angular momentum perspective. If we do that, the result is is "smearing" of accuracy in the other axis, or conjugate variable.


http://users.rowan.edu/~polikar/WAVELETS/WTpart1.html

http://users.rowan.edu/~polikar/WAVELETS/WTpart2.html

It would seem appropriate, to designate both "Wheeler-Feynman" & Cramer Transactional" and any symmetrical separation in Huygens~Doppler sources (2 slit , or multiple grating) wave modeling, as "Non Stationary".


To only look at it from the perspective of the "infinite time line", where "no time" is experienced by the exchange, misses out of the real time that is measured in the experiment, and the constant velocity that the "free space dynamics" produce.


C2 didn't want to get into answering "how much energy is in the curve", perhaps because he knew that the better his answer was, the more uncertain we would be as to "angular frequency" (momentum), thus proving my point of this having a frequency shift.


The window function can NOT be "certain", without a loss of resolution elsewhere. In this case, a dynamical change in frequency, happening " in between" the lines of the "integer harmonics".


The wavelet transform uses a changing window, so that it measures "intervals". These are scalable. The "infinite curve" of the log spiral provides the changing scale, that never converges.


RT gives a similar method; 12 equidistant intervals that nest perfectly in the "near field" (from 1 unit distance, to 2). After this first order, this symmetry is broken, due to the "third harmonic". This is concealed by the standard Fourier transform; it treats it as "equal" to the integer series of mathematical "harmonics", rather than by the principle of the octave, which gives more of a Power relationship, 2_. The "3rd harmonic" should be seen as equvalent to the creation of a new "node" (phase singularity), caused by the "first order, 2:1" resonance, a symmetrical angular momentum exchange that creates the spin induced vortex at this "center" (equidistant) space.



regards,

T.Roc



This post has been edited by TRoc on Sep 23 2007, 10:36 PM

Hi janrinze, Confused2, TRoc, Laserlight, "THEY", "THEY2" janrinze, Jal, Montec, yquantum, StevenA, "Why Not?", Siau, Neil Farbstein, Terry Giblin, et al,

I never said it was useless ... in fact I said that it was useful (check it out), but I find it less useful regarding these Physics matters "so far". I have an open mind but I do not have an argument to convince me to use it. I realize that is what you say that this is a useful technique but think that to be able to justify that statement you need to have a few concrete examples that show where FT's are not suitable and Wavelet Transforms are. The invertibility of FT is known to me the invertibility of WT is not and was not presented in those references by TRoc to Robi Polikar. I am not going to be the interpreter for others.
http://forum.physorg.com/index.php?showtop...ndpost&p=264513
I am not comfortable with wavelet Theory and that is the bottom line. There may be a better presentation of these matters but I do not know of it. I recall something about their use in Wireless World about 20 years ago but I have long since disposed of those back issues.

For me at least the Fourier Transform speaks about basic underlying principles and it is not just a convenient mathematical technique. Particle and wave descriptions are both described by the Fourier paradigm and represents the conjugate nature of the Heisenberg Uncertainty Relationship in the best way we know how.

TRoc... I would prefer that you give more interpretation for your heavy quoting from that source. Quotes are only useful if they support some argument you are presenting. I see no convincing argument so far. It is definitely not "Resonance Theory".... Rectangular waves are not a resonance... This amplitude treatment is not relevant since it requires a phase treatment.

So what I really do not care about the "intensity"... The phase is the more important aspect . I see that an insistence on knowing every bit of information at the same time would be a foolish pursuit. This information is constrained by the HUP or by the nature of conjugate variables as discussed previously. If you have a point state it rather than quoting at length.

Cheers

Hi All,

Sorry I'm not keeping up .. doing my best ..

For the origin of the FT wiki is a bit helpful

http://en.wikipedia.org/wiki/Fraunhofer_diffraction

also (better)

http://en.wikipedia.org/wiki/Huygens-Fresnel_principle

I can't claim to grok it yet but the seeds are there.

Still in http://en.wikipedia.org/wiki/Huygens-Fresnel_principle

psi( r )= e^(ikr) / 4pi r <<<-- this has the look of a psi that extends 'everywhere' rather than just on a 'front' (until detection?) .. personally I think this is what we are seeing in the DSE. Need more maths (and more time)

Best wishes -C2.

This post has been edited by Confused2 on Sep 24 2007, 09:15 AM

Hi all,



GE-

I gave the examples in the "lengthy posts", ( here , or here ). I thought that tying the reason for needing "more" than what Fourier offers, with the explanation of why
Fourier doesn't "cover everything" was clear enough.


It would seem that the recent personal experience, of having the Talbot effect "sneak under your radar", would demonstrate this quite directly. You can not even begin to see what is "between the integers" of the FT. There are fractional, and fractal revivals going on "collectively" in the spherical expansion. (not just "longitudinal", nor symmetrical "x and y axis)


If you do not understand the need for WT, then I think you have a misconception about FT, somewhere, but I do not know. It shouldn't need more explaining, when considering these waves in the context of a ">1" RI; the "degree of quasi-monochromaticity" will force the independent parts of this envelope to travel at different velocities. Their relationship is no longer "stationary", it is "non-stationary". FT can not give us a 3D "map" of the "in between" portion of the DSE (slit wall to screen distance), the phase space tomography & geometry, the Talbot carpet.


In the end, if you want to know more about WT, then you can read the 4 parts that I linked, or any other source you choose. The time is required, regardless of the method. You have seen that it is reversable, and that was part of the last lengthy post, as well.


The interval is the best "window" to look through. This method captures the inherent limitations of HUP, in an area large enough to contain the variance; a happy medium or equilibrium in accuracy, in measuring the conjugate variables involved. (regardless of method / parameters) This gets you through "WT 101".


Resonance Theory uses a discreet interval that allows simultaneous production of a "harmonic series" (integer fractions), and the inverse, "equispaced frequencies" set, giving the capability of an exponential (Dirac) frequency comb. In effect, giving the "apparent location", in complex phase space, of "Maximum Uncertainty", or equivalently, the phase singularity, or "node" between the "Inverse, Maximum Known, with Certainty", anti-nodes.


ciao,

T.Roc



This post has been edited by TRoc on Sep 24 2007, 09:55 PM