# Talk:Planck constant/Archive 4

## Recent Changes

It is really confusing to add new material at the top of talk pages.

It looks like an old battle (the details of which have been removed from the top of this discussion page) has been reignited. What is the point of mention of the Hayward work unless it can be shown to relate to how Planck arrived at his constant? If there is a point, then it should be stated. The reader who does not have a very firm footing in this area will be completely thrown off by this pointless mention. "What am I missing?" will be his or her question.

The series of postings that occurred last year were the only mention I have ever seen that hinted at the idea that Planck took over somebody's work from 40 years before, made some kind of empirical determination of it, and got the Nobel Prize. P0M (talk) 02:29, 9 March 2012 (UTC)

All the groundless assertions now have been transplanted to Specific relative angular momentum. I think an administrator will probably have to give some people time out unless there is a good explanation for what is being done.P0M (talk) 02:36, 9 March 2012 (UTC)

One of the contributors to that page has already been blocked. P0M (talk) 02:40, 9 March 2012 (UTC)

## Six identical references for the value of h

In the first table, at right, the reference [1] is repeated six times, which is useless (and confusing for the measurement units). Perhaps it is sufficient to give the reference just once, in the heading: "Values of h[1]".
Can someone make this edit for me (the page is protected)?--79.19.234.209 (talk) 14:42, 13 March 2012 (UTC)

## Edit request on 15 March 2012

Template:Edit semi-protected See last talk above (Six identical references for the value of h) 87.10.226.136 (talk) 18:07, 15 March 2012 (UTC)

It is quite usual in tables for the reference to be given on every line, even if it is the same reference. This makes it easy to update if just one value is being updated from another source. Also if a new line is added, it is clear that it is unsourced or has a different source. But I won't close the request as I am the admin who protected the page. I will leave it someone else to decide. SpinningSpark 23:20, 15 March 2012 (UTC)

I do not see any problem with the table as it stands. The reader may have ignored the power-of-ten indications. P0M (talk) 23:29, 15 March 2012 (UTC)
Yes, references may be given on every line, but in this table we have just one physical constant (two, if you include the joule-equivalent of 1 eV) expressed in various units, so six references to the same source appear to be redundant.--79.19.234.110 (talk) 17:21, 16 March 2012 (UTC)
P.S. I have not understood the point of "the power-of-ten indications".--79.19.234.110 (talk) 17:21, 16 March 2012 (UTC)
It makes no difference that it is the same constant in different units; they are still different numbers on different lines of the table. I really do not understand your concern, it does not detract from the layout or readability and it is simply clearer that all the numbers have a verification if each line is cited. I don't understand POM's point either. SpinningSpark 17:48, 16 March 2012 (UTC)
I don't think we can implement SPERs where there isn't a clear consensus. FWIW, I don't think it is likely for the individual rows to have different sources and I would put the cite once after the column header, Values of h[1], to avoid anyone confusing the cite for some kind of exponent of the last unit, e.g. acceleration in m/s[2]. Regards, Celestra (talk) 01:07, 17 March 2012 (UTC)

A possible compromise to avoid this confusion could be to add a separate column for the refs: | Values of h | units | ref. |.--87.17.219.56 (talk) 10:30, 17 March 2012 (UTC)

Ok, I have unlocked the page to allow you to do that. Please do not take too long, this page gets attacked quite frequently and it may well get protected again in the future. SpinningSpark 10:58, 17 March 2012 (UTC)
Done, thanks.--87.17.219.56 (talk) 11:19, 17 March 2012 (UTC) - I also made some aesthetic alignments --87.17.219.56 (talk) 11:53, 17 March 2012 (UTC)

## Correction needed by someone with permission to edit

Sentence "One example is time vs. frequency." is incorrect. It should read:"One example is time vs. energy." Page is semi-locked, so someone with appropriate permissions please make a correction. Thanks. — Preceding unsigned comment added by 76.122.89.118 (talk) 23:57, 15 March 2012 (UTC)

Done SpinningSpark 00:42, 16 March 2012 (UTC)
I'm confused. Time vs frequency makes sense when discussing a Fourier analysis. You either know the value at a specific time, or you compute a frequency spectrum - the power contained in each frequency. Why does "energy" make sense in that sentence? Q Science (talk) 05:17, 17 March 2012 (UTC)
Not really my subject, I just mechanically did what the IP asked. However, I do have Paul Davies Quantum Mechanics (ISBN 0710099622) which has at equation [8.12]
${\displaystyle \Delta E\Delta t\sim \hbar }$
"which is known as the energy-time uncertainty relation and should be compared with the momentum-position uncertainty relation." From which I assumed the IP was correct. SpinningSpark 12:29, 17 March 2012 (UTC)

## The Entire Discussion under "Uncertainty Principle...

...is nonideal and perhaps incomplete or erroneous in some respects. (Revised: I deleted these explanations on refactoring.)
I propose to replace this section text and examples with the following here (I am 99.999% done at this point.):

{{#invoke:main|main}}

Heisenberg's Uncertainty Principle is another core concept of Quantum Mechanics where Planck's constant plays a key role. Perhaps Fourier Analysis[3] best demonstrates the idea of an indeterminacy, i.e., something inherently indeterminable for a reason other than apparatus error or the Observer effect. In Fourier Analysis, as in Quantum Mechanics, these indeterminacies are associated with observing wave phenomena, although Heisenberg himself may not have initially understood this.[4]

Fourier Analysis involves transform / inverse transform pairs between the time and frequency domains, between time and energy, between position and momentum, and between other examples of what physicists call canonical conjugates. One may calculate a set of transformed frequency data from a set of measured time data and view either on a 2D plot – but not both at once; it takes all the time data to calculate the transform for each frequency. However, plotting a 3D surface of frequency data (a spectrum) vs time (in frames ${\displaystyle \scriptstyle \Delta t_{F}}$ long) seems to reveal all of it: signal power vs frequency and at each frame time. This 3D plot, sometimes called a waterfall or a spectrogram, is commonly found in Speech, Music, Communications, and Geology; and it is how voiceprints[5] are made. The Spectrogram is a rich example of uncertainty and waves.

The Fourier Transform is defined with integrals from ${\displaystyle \scriptstyle -\infty }$ to ${\displaystyle \scriptstyle +\infty }$; however, in real measurements, the apparatus goes on at ${\displaystyle \scriptstyle t=0}$ and measures samples at intervals of ${\displaystyle \scriptstyle \Delta t_{S}}$ until ${\displaystyle \scriptstyle N}$ samples are collected. Data are analyzed by the Discrete Fourier Transform[6] (DFT), typically with an FFT algorithm. Since the ${\displaystyle \scriptstyle t}$ domain was sampled, the ${\displaystyle \scriptstyle f}$ domain also becomes discrete, having increments of ${\displaystyle \scriptstyle \Delta f\,=\,1/\Delta t_{F}\,=\,1/(N\Delta t_{S})}$; and values of ${\displaystyle \scriptstyle f(k)=k\Delta f}$ for ${\displaystyle \scriptstyle k=0\,to\,(N-1)}$. However, these measurement parameters result in aliasing in the frequency domain that compells one to drop the terms for ${\displaystyle \scriptstyle k=0}$ because time-framing under-samples frequencies ${\displaystyle \scriptstyle f\,<\,1/\Delta t_{F}}$, and to drop the ${\displaystyle \scriptstyle k>(N/2)-1}$ terms because the time data are real and ${\displaystyle \scriptstyle f_{H}\,\,\thickapprox \,1/(2\Delta t_{S})\,=\,f_{S}/2}$ is the Nyquist frequency. Thus, there are uncertainties limiting both ends of the calculated spectrum as well as the resolution: ${\displaystyle \scriptstyle f_{L}\,=\,\Delta f\,=\,1/\Delta t_{F}}$ and ${\displaystyle \scriptstyle f_{H}\,\,\thickapprox \,1/(2\Delta t_{S})}$.

A voiceprint with 10ms frames and a 20kSa/s sampling rate will produce a series of spectra each of which goes from 100Hz to 10kHz in 100Hz increments. Put another way, regardless of how accurately you measure; you cannot detect 100Hz (or a difference of 100Hz) in less than ~10ms because it takes that long for 100Hz to happen. Thus, the indeterminacy of frequency in time means two things:

1. Within a given time frame ${\displaystyle \scriptstyle \Delta t_{i}}$, if an event were detected, there can be no more precise knowledge of when it happened than to observe it was during that particular time frame ${\displaystyle \scriptstyle \Delta t_{i}}$, and
2. Within any time frame ${\displaystyle \scriptstyle \Delta t}$, the actual frequency can be no more precisely known than to observe it is within a range ${\displaystyle \scriptstyle \Delta f\,\,\gtrsim \,\,1/\Delta t}$, while frequencies ${\displaystyle \scriptstyle f\,\,<\,\,1/\Delta t}$ are indeterminable.

In actual lab practice, scientists often use window functions, overlapping data, and other advanced processing to overcome some indeterminacy limitations. Technical choices of windows and strategies affect the ${\displaystyle \scriptstyle \Delta t}$ and the ${\displaystyle \scriptstyle \Delta f}$ in various ways to balance requirements for signal levels, noise levels, spectral leakage, etc. For more details and examples see the Short-time Fourier transform (STFT), the Discrete Fourier transform (DFT), the Discrete-time Fourier transform (DTFT), and the Fast Fourier Transform (FFT).

By introducing Planck's constant, one may obtain Heisenberg's Energy vs Time and Momentum vs Position Uncertainty Relations in one step:

The Fourier Analysis indeterminacies for temporal frequency ${\displaystyle \scriptstyle f}$ and spatial frequency ${\displaystyle \scriptstyle \xi }$:
${\displaystyle \scriptstyle f_{o}\,\,=\,\,1/T_{o}}$    ${\displaystyle \scriptstyle \to }$    ${\displaystyle \scriptstyle \Delta f\Delta t\,\,\gtrsim \,\,1}$      and      ${\displaystyle \scriptstyle \xi _{o}\,\,=\,\,1/\lambda _{o}}$   ${\displaystyle \scriptstyle \to }$   ${\displaystyle \scriptstyle \Delta \xi \Delta x\,\,\gtrsim \,\,1}$
The de Broglie Relations[7] introduce Plancks constant:
${\displaystyle \scriptstyle f\,\,=\,\,E/h}$     and     ${\displaystyle \scriptstyle \lambda \,\,=\,\,h/p}$    (or ${\displaystyle \scriptstyle \xi \,\,=\,\,p/h}$  where ${\displaystyle \scriptstyle \lambda \,\,=\,\,1/\xi }$ )
Substitution reveals the familiar inequalities:
${\displaystyle \scriptstyle \Delta E\Delta t\,\,\gtrsim \,\,h}$      and      ${\displaystyle \scriptstyle \Delta p\Delta x\,\,\gtrsim \,\,h}$

Comparing these results with ${\displaystyle \scriptstyle \Delta f\Delta t\,\,\gtrsim \,\,1}$, one would expect the following also to hold in Quantum Mechanics due to indeterminacies associated with observing wave phenomena characterized by Planck's constant:

${\displaystyle \Delta E\Delta t\,\,\gtrsim \,\,h}$
(the indeterminacy of energy in time)
${\displaystyle \Delta p\Delta x\,\,\gtrsim \,\,h}$
(the indeterminacy of momentum in space)
1. If energy were detected during time frame ${\displaystyle \scriptstyle \Delta t_{i}}$, there can be no more precise knowledge of when it happened than to observe it was during that particular time frame ${\displaystyle \scriptstyle \Delta t_{i}}$.
1. If momentum were detected within the segment of space ${\displaystyle \scriptstyle \Delta x_{i}}$, there can be no more precise knowledge of where it happened than to observe it was inside that particular spatial segment ${\displaystyle \scriptstyle \Delta x_{i}}$.
2. Within any time frame ${\displaystyle \scriptstyle \Delta t}$, the actual energy can be no more precisely known than to observe it is within a range ${\displaystyle \scriptstyle \Delta E\,\,\gtrsim \,\,h/\Delta t}$, while energies ${\displaystyle \scriptstyle E\,\,<\,\,h/\Delta t}$ are indeterminable.
2. Within any spatial segment ${\displaystyle \scriptstyle \Delta x}$, the actual momentum can be no more precisely known than to observe it is within a range ${\displaystyle \scriptstyle \Delta p\,\,\gtrsim \,\,h/\Delta x}$, while momenta ${\displaystyle \scriptstyle p\,\,<\,\,h/\Delta x}$ are indeterminable.

There are other ways like this one that show how Plancks constant relates the Heisenberg Uncertainty Principal inequalities to the Fourier transforms familiar to a broader technical audience. Nevertheless, Heisenberg's first derivation of ${\displaystyle \scriptstyle \Delta p\Delta x\,\,\gtrsim \,\,h}$ in 1927[8] was complex, utilizing the Matrix Mechanics published in 1925-26 by him, Max Born, and Pascual Jordan.[9] Matrix Mechanics is regarded as the first conceptually autonomous and logically consistent formulation of quantum mechanics, comparable to the Wave Mechanics formulation based on the Schrödinger wave equation, published in 1927.[10] The form σpσxħ/2, where the σp and σx are standard deviations and ħ is the reduced Planck constant, is often called the exact solution of the Uncertainty Principle, and it has been shown valid for all wave functions – not just Gaussian waves as Heisenberg later had shown. In the modern mathematical formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits; for example, ${\displaystyle \scriptstyle [{\hat {p}}_{i},{\hat {x}}_{j}]=-i\hbar \delta _{ij}}$ where ${\displaystyle \scriptstyle {\hat {p}}}$ is the momentum operator, ${\displaystyle \scriptstyle {\hat {x}}}$ is the position operator, and δij is the Kronecker delta.

The Uncertainty Principle enables an alternate way of looking at certain classical wave problems, for example, diffraction. Assume the width of the central bright spot is determined by uncertainties in the momentum wave in space introduced by a single slit. The slit, with width = a, causes position uncertainty Δy = a in both the positive and negative y-directions, which in turn causes momentum uncertainty Δpy = h / Δy in each y-direction. The momentum in the x-direction towards the screen is given by px = h / λ (de Broglie). If θ is the angle from the center of the central bright spot to the first minimum on one side, then θ = arctan(Δpy / px) = arctan( λ / a ). When the screen is very far from the slit and θ is small (Fraunhofer diffraction), then θ ≈ sin θ ≈ tan θ, and this reduces to θ = λ / a. This is the same result obtained from classical methods for diffraction (e.g., Huygens' principle) for the minima of single slit diffraction, a sin θ = nλ, when n=1 and θ is small, and for the envelope of the interference pattern in the multi-slit case where each width = a. The uncertainty approach, however, is applicable to matter waves and not only to light. Interestingly, diffraction and interference patterns are the Fourier transforms of the slit patterns that produce them.

### References

1. x
2. x
3. {{#invoke:citation/CS1|citation |CitationClass=book }}
4. {{#invoke:citation/CS1|citation |CitationClass=book }}.
5. {{#invoke:citation/CS1|citation |CitationClass=book }}
6. {{#invoke:citation/CS1|citation |CitationClass=book }}
7. L. de Broglie, Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis (Paris), 1924; L. de Broglie, Ann. Phys. (Paris) 3, 22 (1925).
8. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
9. M. Born, W. Heisenberg, and P. Jordan, Zur Quantenmechanik II, Zeitschrift für Physik, 35, 557–615 (1925). The paper was received on 16 November 1925. [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1]
10. {{#invoke:Citation/CS1|citation |CitationClass=journal }}

ItsTheEquations (talk) 08:43, 6 May 2012 (UTC)
Revised — ItsTheEquations (talk) 01:58, 15 May 2012 (UTC), Revised — ItsTheEquations (talk) 04:29, 15 May 2012 (UTC), Revised — ItsTheEquations (talk) 01:51, 17 May 2012 (UTC), Revised — ItsTheEquations (talk) 20:45, 17 May 2012 (UTC), Revised — ItsTheEquations (talk) 21:59, 17 May 2012 (UTC), Revised — ItsTheEquations (talk) 08:39, 18 May 2012 (UTC), Revised — ItsTheEquations (talk) 11:01, 19 May 2012 (UTC), Revised — ItsTheEquations (talk) 15:31, 19 May 2012 (UTC), Revised — ItsTheEquations (talk) 18:33, 22 May 2012 (UTC), Revised — ItsTheEquations (talk) 19:53, 24 May 2012 (UTC), Revised — ItsTheEquations (talk) 06:55, 25 May 2012 (UTC), Revised — ItsTheEquations (talk) 23:02, 26 May 2012 (UTC), Revised — ItsTheEquations (talk) 22:08, 27 May 2012 (UTC)
ItsTheEquations (talk) 03:23, 29 May 2012 (UTC)

I have not read all your post WP:TLDR, but to answer your final point, the article already gives a link to where this is more fully discussed at Uncertainty principle. You are welcome to improve this, or any other, article. Please take a look at our verifiability policy before you do so. SpinningSpark 12:58, 6 May 2012 (UTC)
Verifiability per Wiki is a great way to do a pedia. Looking toward providing something really useful and clear. Will address Verifiability as I correct the errors in my talk/discussion above. Many folks infer many additional meanings to the Heisenberg Uncertainty statement. Thus, a concise approach may seem unbelievable, so very good citations are needed here. But if the task is to make especially clear why Planck's constant is in there, then it is a worthwhile task. Having this insight goes to the heart of "waves vs particles." — ItsTheEquations (talk) 16:24, 10 May 2012 (UTC)
I am developing a proposal to replace this section. As I have refactored, I replaced my original Talk material with the proposal above for a new section. I will not alter Spinningspark or other editors remarks. Thx for your patience. Feedback is desirable at this point. — ItsTheEquations (talk) 01:58, 15 May 2012 (UTC)
Revised: ItsTheEquations (talk) 18:33, 22 May 2012 (UTC)
Revised ItsTheEquations (talk) 01:51, 17 May 2012 (UTC)

It does look well written, and a good effort, though you should:

• change the statement of "seeing 100Hz" to "measuring 100Hz",
• where you have linked "conjugate variables (explained)" that should be a proper wiki-link, not an external link, like this (and preferably with a simpler and more direct title):
"These are examples of what physicists call conjugate variables
that is;
These are examples of what physicists call [[conjugate variables]].
You can link articles using two square brackets, in the following general way:
[[article#section|paragraph text]]
• Furthermore don't use so much bold, the article will not have a uniform appearance if there is a lot of bold in one section - its only for real emphasis. In the above case you can just use italics for the key words/phrases but not for full sentences, see Wikipedia:Manual of Style.

(Presumably you were going to fix these anyway? Just making sure)... =) 16:34, 17 May 2012 (UTC)

The use of quotation marks should indicate quotations exclusively. Perhaps some of your words in quotes should be set in italics instead, per MOS:WORDSASWORDS. --TSchwenn (talk) 18:30, 17 May 2012 (UTC)

Newcomer is deeply grateful for the gentle advice. Please look for points needing my attention based on new draft that overwrote the old one above. Revised: ItsTheEquations (talk) 18:33, 22 May 2012 (UTC)
ItsTheEquations (talk) 20:45, 17 May 2012 (UTC)

I should have mentioned that you should create a sandbox: User:ItsTheEquations/sandbox (just start typing in it and the page will be created). You can edit this as many times as you like, rather than here on the talk page. About feedback -
• don't get bogged down into calculations,
• just keep it all simple and use summary style: search out the relevant articles and link to them in the text,
• if there is no room for what you have to say, just write see also...[[page]] (or words to effect), never begin and continue from there to emphasize inessential detials when it is covered elsewhere (for example you mentioned slit calculations - there is the article Diffraction formalism you could link to)
• Its good to have some analagous applications/occurances, but use your judgement to decide the scope: usually a sentence or few are eneogh (any more easily becomes paragraphs). I think what you have written is generally fine, but again get rid of the extra bolding, for the above example:
inherently indeterminable
indeterminacy of frequency in time
indeterminacies are associated with measuring wave phenomena
do not need to be bolded or italixed. 16:15, 18 May 2012 (UTC)
You may also have some use for Help:Displaying a formula SpinningSpark 18:35, 18 May 2012 (UTC)
Thanks. I defer to the ones who comment: I will remove bold in paragraphs. (It seems to be allowed in actual practice, and the results look okay to me.) MOS is a lot of disorganized reading, but I will consume it. I write for readers, but I publish for editors; I understand that: somebody will just change it. I converted some of the bold to italics, the rest to plain, and it looks okay.
Objectives – The purpose of the article section is two-fold: (1) to provide a quick low-math way to see Heisenberg using Planck's constant (which requires mentioning canonical conjugate variables and Fourier Analysis for technical legitimacy), and (2) to provide a candidate for others' link-to or perhaps even template-from (since the Planck emphasis is not too obvious). Revised: Only at the end is there mention of the advanced methods used by H and others, and of the supposedly exact form of the HUP: σpσx ≥ ħ/2. This is by design; it is an historical note. Readers who come to Planck|Uncertainty need not to be pushed aside by mumbo jumbo (like Matrix Mechanics) if a simple explanation (like this comparison to Fourier) also is appropriate. Because we are in the Planck article, we have an obligation to do the nutshell section treatment on Heisenberg – and to show it really doesn't happen without Planck (via deBroglie) to get the frequency and wavelength for phenomena in Quantum Mechanics. The whole Uncertainty issue is explained through the more familiar ${\displaystyle \scriptstyle \Delta f\Delta t\,\,\gtrsim \,\,1}$ uncertainty, which is clearly about waves. Then Planck's constant converts this one into the two HUP's in one step.
ItsTheEquations (talk) 11:01, 19 May 2012 (UTC)
Revised: — ItsTheEquations (talk) 18:33, 22 May 2012 (UTC)
Revised: – ItsTheEquations (talk) 06:42, 24 May 2012 (UTC)
It seems to be allowed in actual practice... The quality of Wikipedia articles varies enormously, almost anything will survive, at least for a while. If you want to see what is considered good, look at the articles listed at WP:FA. These have all been very thouroughly reviewed (or an earlier version of them was) and are considered the very best Wikipedia has to offer. Bolding in formulae is reserved for sets, matrices, vectors etc. It is almost certain someone will remove the bolding eventually if you put it in the article like that. MOS:MATH has some good advice on formatting formulae. A small font that approximately matches the inline text size can be forced with the TeX command \scriptstyle but it is not very popular because it can be a nightmare to align properly and is also not genuinely text and will not be searchable. You may prefer to use the {{math}} template. SpinningSpark 11:32, 19 May 2012 (UTC)
I get it. No bold ever, anywhere, period. Someday they may elucidate good rules for this; they even use it on their own pages about best articles. But how to explain it to all editors... I appreciate your warning; I removed it; and results looks fine to me. I appreciate your encouragement and advice, Sparks. ItsTheEquations (talk) 15:31, 19 May 2012 (UTC)
Revised: ItsTheEquations (talk) 06:42, 24 May 2012 (UTC)

I have converted every equation and every variable mentioned in the proposed section to TEX with \scriptstyle as mentioned by SpinningSpark. Looks pretty good. Thanks for the tip. The in-line alignment issue is visible and serious, but it is a tracked bug. All these things notwithstanding, I believe the exclusive availability of the "${\displaystyle \scriptstyle \gtrsim }$" symbol is an overriding consideration in this case. Hopefully, as it is conforming, it also will not be bait for font pedants or rules robots. I realize these formatting conventions are well-known basics, but I am a Newbie; so, thanks for your help.

This edit includes other minor changes and corrections. I removed the popular and intuitive word slice and replaced it with the also popular but less intuitive word chunk, which is used in Wiki the links I included. I am using S as the subscript for sampling, which is rather universal. I use the subscript C for chunk because it seems reasonable. I added a thin summary history of HUP calculations to explain the other HUP with sigmas rather than deltas. Finally, I refactored my remarks here on the talk page to help the reduce the sprawl I cause.

Re: Single Slit – Revised: A new paragraph for this was added at the end.

— ItsTheEquations (talk) 18:33, 22 May 2012 (UTC)
— Revised: ItsTheEquations (talk) 06:42, 24 May 2012 (UTC)
— Revised: ItsTheEquations (talk) 19:53, 24 May 2012 (UTC)
— Revised: ItsTheEquations (talk) 06:55, 25 May 2012 (UTC)


Fixed the slit example, finally. And I made various minor edits.

ItsTheEquations (talk) 23:02, 26 May 2012 (UTC)

• This should have been entirely hashed out on the uncertainty principle page before being brought here. While I agree that the HUP uncertainty principle is just the Fourier uncertainty with h serving to translate frequency into energy, at the same time it's not at all clear why if f*t < 1, why E*t < h, not h/4pi. In any case, when you do get that little matter worked out, it's only going to be a small part of this article (in the little subsection on HUP) and need not be discussed on this article's talk page. Do it on the HUP talk page. SBHarris 23:18, 26 May 2012 (UTC)
Thank you for your feedback. I feel this subarticle may be pushing the size limit for subarticles, but keep in mind the encyclopedia user is starting at Planck constant and THEN stepping into HUP. In a somewhat tutorial style, this article explains HUP from the Planck perspective. I wrote this simply as a response to the frustration I felt as I was trying to better understand the origins and meaning of the HUP. THE ONLY PLACE THIS WAS CLEAR WAS THE MAIN ARTICLE. But it was not very readable, and it did not meet my needs. The Planck/HUP subarticle has ineffective examples (which explain nothing); it has an incorrect equation at the top; and the correct equation at the bottom that only grad students of physics or Math would recognize. Most other HUP subarticles are extremely specific to the article... or they are wrong. THERE IS A NEED TO POINT OUT AUTHORITATIVELY that HUP does NOT mean anything but what it means: it is about observing waves. Period. Many technical users "get" Fourier, and they might be surprised that HUP has more to do with Fourier (1822) than Heisenberg (~1924). For the many people with skills and knowledge of Fourier Analysis, an understanding of HUP is just a Planck's constant away — which is why this subarticle is in this article. This was my thinking.
Keep in mind, that for a long time, even Heisenberg himself thought HUP was about apparatus error (1930). This is why there is an historical paragraph at the end. While it was only vandalism, last night somebody tried to add something about Depak Chopra saying HUP means "anything can happen." It is THIS misconception about HUP I hoped to extinguish within this "easier" context.
Finally, I believe the ΔE*Δt>h form you referred to is correct, because ΔE is not the same as σE. When one uses σE and σt, the right side becomes h/4π = ħ/2 where ħ = h/2π. If I had found a simple reference for how the 1/4π comes out of the variance calculation, I would have included it, too. However, since this subarticle pushes the size envelope, I am glad I did not find it.
ItsTheEquations (talk) 18:13, 27 May 2012 (UTC)

Minor edits for clarity, sentence integrity, etc.
ItsTheEquations (talk) 22:08, 27 May 2012 (UTC)

Changed chunk to frame and the variable ΔtC to ΔtF. Significantly improved misc words, sentences, WikiLinks, and equation formats.
ItsTheEquations (talk) 03:23, 29 May 2012 (UTC)

I have to agree with SBHarris that this material really belongs in uncertainty principle, and should be merely summarised here: a couple of descriptive sentences and the results is all that is needed. "Tutorial style" is the wrong approach for an encyclopedia article, we are not trying to teach the subject. The Planck constant article should be focused on the constant itelf (discovery, history, measurement, brief uses etc).
By the way, it is considered confusing to change previously made talk page posts as you have been doing to the introduction to this section. If you wish to withdraw a comment, the convention is to WP:strikethrough and, if necessary, add a new comment at the end of the thread. The reason for this is that it remains clear what comments from other editors are referring to; it is even possible the meaning of later comments could become changed by amending the initial post. I realise you need to edit the proposed new material, but, due to its length, a better way would have been to create it in your userspace and just link to it here. SpinningSpark 10:05, 29 May 2012 (UTC)
I was working on the subarticle in my user space, but I had started a suggested replacement here so I updated the Talk page. I am sorry I do not get how you do things here. However, it does explain why the quality of this material is so poor. I get too many comments too late. I get no valid technical comments; which is strange considering it is a topic in Physics and Math. I propose to replace a horrible subsection, and you guys resist it. IT IS AN EXPLANATION, NOT A TUTORIAL. THERE IS NOTHING TUTORIAL ABOUT IT — no matter how well explained I made it for the readers. I've written many things; I hoped you could tell. This is not a tutorial like ones I write. I used the word "tutorial" to contrast with the "disjointed lists, incomplete information, and wrong facts" like the predecessor subarticle and many others I read in producing this one. I am sorry I added to the collective vocabulary for dissing people's hard work.
I am willing also to discuss why this article belongs here. Still, I am not willing to address the reason "because, thats why." So far, that's all I have. And does anyone want to present a cogent theory why the CURRENT article is acceptable? You say "a couple of descriptive sentences and the results is all that is needed." Needed by whom? NOBODY needs only that except for authors who do not know the material and cannot produce. This is an affront to encyclopedia everywhere. Here in Planck, you have the opposite problem of the Diffraction authors: they have the same stuff, 30% incomplete, in about ten places. Looks there was a range war over authorship.
Verifiability of content should not be all there is is: how about Existence of content. Quality of content.
The formatting info at first was critically important because I was new. I hope I fixed everything to everyones liking. I think everynbody should take note that Planck constant is a "C" article. Look at the criteria for a "B" article. That looks a lot more like what I wrote for you. By the way, the criteria explicitly state that conformance to MOS style is NOT a requirement to be a "B" article. Seems like folks around here are just rearranging the chairs on the deck of the Titanic. What are readers getting now? Middle school book reports?
I would like to point out what I accomplished in terms of explanation of HUP and Planck: there are no integrals, only High School Algebra II. Moreover, a vast number of technical people will find this subarticle a rich refresher summary of "Fourier meets Planck" and a good takeoff point with WikiLinks.
I may be done here. You have about a page: seven paragraphs, one table, and a few lines of equations. If you want to talk about reducing size, I can do it with minor impact; however, it will lower the quality. If this is the case, then lets keep talking here. Otherwise, I am gone from this area. You could at least fix the bad subarticle you have now. I am totally disgusted.
Please respond soon. Sorry for my rough attitude, but I worked hard on this and got good results. Your initial offer to write just seems insincere at this point. I think you should be welcoming good authors, not chasing them from your pond. ItsTheEquations (talk) 18:11, 29 May 2012 (UTC)

## 1901 experiment

As an undergraduate, I was taught that a 1901 experiment by Planck lead to the quantum theory. This experiment was a crt with a photo-cathode and a grid with a voltage applied just sufficient to stop all emissions. Plotting V against 1/λ is a straight line with a slope proportional to h. This seems to be missing from the article, and to my simplistic engineering mind is an interesting and understandable (not to say important) experiment. SpinningSpark 08:39, 17 May 2012 (UTC)

A link would be useful. Since a crt produces a stream of electrons, I don't know where the λ comes from. Q Science (talk) 13:25, 17 May 2012 (UTC)
Sorry, lecture notes were not put online in my day, we had to write it all down. I will e-mail you a scan if you like (presuming I can still find them). The λ is the wavelength of the incident light on the photo-cathode, so the max energy that an emitted electron can possible have is V=hf and this is the voltage required on the grid to exactly stop emissions reaching the screen. So h is the slope, and the intersection with the vertical axis is the work function of the material (ignoring unit issues). SpinningSpark 14:56, 17 May 2012 (UTC)
Are you referring to something like slide 14 which describes the photoelectric effect? On slide 17, it shows how the data is used to compute h. I was confused because, in a crt, heat causes electrons to leave the cathode and photons are generated when the electrons hit a target. However, in this device, a photon knocks an electron off the emitter and the kinetic energy of the electron is related to the wavelength. Q Science (talk) 15:41, 17 May 2012 (UTC)
Yes, that's the experiment (although the link has just gone dead) except that the diagram does not show the grid. But the description in the slides talks about a "retarding potential" being applied which would require a grid to be in place. I have now dug out my notes (amazing the junk one keeps) which say the experiment is actually due to Millikan, not Planck as I first thought. There was also nothing about the 1901 date, so I might be conflating that with something else, but the date stuck in my mind because it was said that the quantum theory began on the first day of the 20th century (counting 1900 as the last year of the 19th). That might possibly have come from a Paul Davies book, but I couldn't see it on a quick flip through. Probably best to put it all down to a senior moment and I should go book myself into a home. SpinningSpark 17:00, 17 May 2012 (UTC)

## Uncertainty principle examples

In the section "Uncertainty principle" we have: "A practical example is computational neurology trying to both measure the time effect and frequency of a neuron burst. fMRI (functional MRI), whose signal processing is based on Fourier transforms, can resolve frequency, but not time (a limit of Fourier analysis due to uncertainty). An EEG (a time series analysis measurement tool) can resolve time, but not frequency. Due to uncertainty, these are not problems with the design of the measuring instruments, but problems with the nature of quantum measurement and particle realities themselves."

Unless I am completely misunderstanding the author's point, this entire section seems based on misunderstandings of fMRI and EEG. Rather than pick it apart in detail, could I first ask for a citation that either of these have anything to do with "quantum measurement"? Since they are both measurements of bulk phenomena, the "quantum" aspect seems very suspect to me. Gwideman (talk) 13:59, 23 August 2012 (UTC)

I removed the section on MRI and EEG. I agree, it sounds suspicious. If its in fact a quantum effect, let the original editor restore it with citations. To anyone with any experience editing this particular page, the idea that there is a "private club" with anybody "beloved" is hilarious. PAR (talk) 07:23, 25 August 2012 (UTC)
Thank you for correcting my misimpression about the "private club." I am not likely ever to get the way people work here. It is not content-oriented, and there is no authority except for removing material. I don't know how you can succeed like that. How I feel about anything is irrelevant, and should not be expressed here. I am sorry. ItsTheEquations (talk) 01:29, 26 August 2012 (UTC)
Thanks for the responses. I think the removal of the fMRI and EEG "examples" is an improvement. That said, I see, again in the "Uncertainty principle" section, this sentence: "The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis." The quanta => either-or point sounds plausible. But then Fourier analysis is given as an example of an "either-or" choice, and contrasted to time series analysis -- this seems bogus. In signal analysis, one can choose from a continuum of precision (variance) in either the time domain or frequency domain... yes it's a tradeoff, but it's not a binary choice, as seems to be implied here. Gwideman (talk) 08:04, 25 August 2012 (UTC)
Note to ItsTheEquations: I've read your attempt above to provide more of a tutorial background relating to the Uncertainty principle in the context of Planck's constant, and very much applaud your effort and initiative. Inevitably it's difficult to illuminate the points you feel are problems for readers AND get expert contributors to concur that these are points that need elaborating... that's sort of the nature of the endeavor. I guess I'm urging to take this in stride rather than feel frustrated. For my part, I found your tutorial approach helpful, but I thought that discussing the sampling aspect of practical Fourier processing is a bit of a red herring. I'm pretty sure that in principle, the same Fourier processing could be carried out in the analog domain (or continuous math), demonstrating the same tradeoffs between time-domain and frequency domain precision, and one need not deal with aliasing, Nyquist and so on. Perhaps I missed something though. Gwideman (talk) 08:22, 25 August 2012 (UTC)
I believe you will find there is NO continuous (or "analog") use of the Fourier Transform. In practice, one must always sample, and this sampling is therefore a fundamental part of the problem. The sense of a red herring I believe is the confusion that results from "the fourier uncertainties" in sampling itself. You cannot get rid of it. It actually was a surprise to me that I used this thing for so many years and never realized this. My original purpose was to leverage the universal understanding of what a audio spectrum analyzer is. In Quantum Mechanics, it is there in a natural way, but not without plenty of confusion, misunderstanding. Like "is delta T the time the camera lens was open?" Going down the easy road first was intended to explain what it means to say "it takes delta t of time to encompasses the whole wave of frequency f in order to measure the value of f." It is easy to understand f=1/delta_t. That is the Fourier anyone should get. The jump from here to canonical conjugates, even from here, is barely tolerable. Perhaps I failed completely. I would like to discuss this content this way, if you have the time. ItsTheEquations (talk) 01:29, 26 August 2012 (UTC)
The QM (quantum mechanical) wave function and the QM measurement problem is fundamentally different from the measurement of, say, a classical (i.e. non-QM) sound wave or a light wave. In the classical case, you have a wave that is presumably not affected by measurement. In QM, you have a wave that is totally altered by measurement. Therefore, there is no such thing as "sampling" or "measuring" a QM wave function. The QM wave function is an expression of what you know about the position of a particle as the result of a measurement, and its Fourier transform is an expression of what you know about the momentum of that particle as the result of that measurement. The wave function is used to predict the probabilities of future measurements, and the Schroedinger equation tells you how the wave function (and therefore your predictions) will change as time goes by. Every time you make a measurement, the wave function "collapses" and becomes a representation of your new knowledge as the result of that measurement. PAR (talk) 16:41, 26 August 2012 (UTC)
The reason the full, continuous Fourier transfer never is calculated is because it goes from minus infinity to infinity. In theoretical work, you can do that. However, to say the "wave function collapses" is an opinion, one of the several views of Quantum Mechanics. I believe it is obviously wrong, and it is irrelevant anyway to this topic: Uncertainty. It is now a well-understood fact that Uncertainty has nothing to do with the Observer Effect. Simply, it is about how if you would attempt to measure Energy (because of Planck, this is a wave of some frequency in time) or momentum (which via Planck is a wave of some frquency in space), then you must SAMPLE enough of the time (or space, respectively) or else your measurement become a random number... undersampled and indeterminate. The Planck Constant extends the Classical understanding between time and frequency directly into the Quantum Mechanical realm. The talk of wave function collapse and multiple universes and all that is simply off-topic to Heisenberg's Uncertainty principle. The formulae say you must include AT LEAST delta t to measure E or delta E; and you must include AT LEAST delta x to measure p or delta p. In these cases delta x and delta t are given by the famous equation with Plancks Constant. These facts about Uncertainty (and what it is not) can be found elsewhere in Wikipedia. Heisenberg Uncertainty is a self-contained mathematical fact. Wave function collapse is a broader and far more controversial theory of Physics. You could mention it here, but I discovered it is quite difficult to write the "Uncertainty" subchapter for Planck without staying close to the road, as it were. I am so happy to have someone to talk to about this. Please let us continue. ItsTheEquations (talk) 19:39, 27 August 2012 (UTC)
What exactly do you mean by "sample"? I have been assuming it was making successive measurements in time of a wave amplitude, for example.PAR (talk) 21:59, 27 August 2012 (UTC)
Yes. Sampling implies taking successive snapshots of a target spreadout in time or space. But samples need not be successive or sequential or even multiple. One sample, one picture, invokes uncertainty everytime if it involves canonical conjugates. The well-understood freq vs. time (or freq vs. space) is to me the prototype of all conjugates. Taking groups of sequential samples in time creates a large multidimensional fourier problem like the spectrum anaylzer. My having mentioned spectrograms was evidently problematic. Since p=mv, I always was suspicious of HUP because I know I can derive continuous smooth function of velocity whenever I have a continuous smooth function of the position. However, MASS IS THE WAVE, not velocity. You must include enough SPACE to include one cycle of the matter wave (according to the Planck spatial frequency) in order to catch the momentum in your measurement. In this sense, all measurement are samples. The term is at once helpful and confusing. Like referring to a point mass – which cannot exist. Making this clear should have been easier being in a Planck subchapter. But it requires revealing the HUP formula was (really) a hundred years old already – it is Fourier's accomplishment. Heisenberg's genius (and several others) was they did not use Fourier at all. They did not see the obvious. They plowed into a new math called Quantum Mechanics. Along with that brings the difficulty of bulk phenomena and real physical systems. By the time QM matured (30's? 50's?), the Fourier aspect became canonical conjugates. Fourier transforms of transforms that are physical observables. WHAT WAS I TRYING TO DO? "The HUP is simply Fourier with Planck." Which it is. But how to say it without seeming to go way off topic; that is the trick. And then one good example: derive the single slit formula in one step, applicable to both photons AND matter waves. The Classical Optics (i.e., geometrical) approach does not apply to quanta let alone to matter waves. ItsTheEquations (talk) 23:32, 27 August 2012 (UTC)
ItsTheEquations: Again I applaud your passion for communicating this subject. I have to admit that I'm not a heavy thinker on this subject. That said, I continue to feel that sampling, and even Fourier, are a little peripheral to the issue central to H's Uncertainty, which is that we have two phenomena which are conjugates, and whose precision is mutually exclusive. That is to say, more precision in one variable requires more "extent" in the space of the other. In the audio, radio etc, precision in the characterization of frequency (ie: lower variance in stating the frequency) requires more time, and vice versa. Similarly in position vs momentum etc.
Fourier analysis inevitably incorporates this physical reality, and is very familiar to engineers and scientists, but is not the underlying reality itself. So I feel that Fourier perhaps doesn't have to make an appearance at the core of the explanation, and the sampling aspect of actual Fourier-employing instruments is even more of a distraction for readers not already familiar. To put it another way, I think the Uncertainty arises not particularly in the measuring of the phenomena (time-freq, or position-momentum) it's in simply making a statement about them. Gwideman (talk) 01:07, 28 August 2012 (UTC)

"Since p=mv, I always was suspicious of HUP because I know I can derive continuous smooth function of velocity whenever I have a continuous smooth function of the position." - No, not in QM. Assuming you know what particle you are looking at, you know its mass, so measuring velocity is equivalent to measuring momentum. In QM, you cannot have a continuous smooth function of position, because that would imply multiple measurements of exact position, with momentum being little affected. That denies HUP. If you make an exact position measurement, the momentum is completely unknown after that measurement, and upon the next measurement, the particle can be anywhere in the universe (no relativity here). Measure its position exactly again, and again the momentum is completely indeterminate, the next position measurement can be anywhere. If you relax your constraints on position, measure to within delta x, then the uncertainty in momentum will decrease to delta p, but always in accordance with HUP. If you finally go to exact measurement of momentum, then you could predict where it would be next, but you now have no idea where it is to begin with. Again, you cannot assign a clear trajectory to any particle. Its always going to a fuzzy kind of trajectory, constrained by HUP.

Also, the HUP is only equivalent to the continuous Fourier uncertainty when the variables are continuous (e.g. position and momentum, or time and energy). There are other conjugate variables that are not continuous (e.g. angular momentum and angular position). Continuous Fourier uncertainty is an example of HUP, but not the whole story.

When you make a measurement of position, you are not sampling (or measuring) the wave function. For a pure state, you know the wave function to begin with and it tells you the probability of getting a particular result when you measure the position of a particle. Suppose that measurement was "exact". You now have a wave function whose absolute value squared is a Dirac delta function, reflecting the fact that the position has no uncertainty. The momentum wave function's absolute value is completely spread out over momentum space, since the momentum wave function is the Fourier transform of the position wave function and reflects the fact that after your measurement, the momentum of the particle is totally arbitrary. The wave function tells you what you already know and predicts the probabilities of what you will measure, given that knowledge. Measurement (or "preparation") yields the wave function. The fact that this knowledge must be expressed in terms of position and momentum wave functions, and the fact that the position and the momentum wave functions are Fourier transforms automatically constrains your knowledge such that it cannot violate HUP.

Please note I am not being very mathematically rigorous talking about this limiting case of "exact" position and "totally arbitrary" momentum. The entire discussion can be redone replacing "exact" with "very small variance" and "totally arbitrary" with "very large variance". PAR (talk) 03:28, 28 August 2012 (UTC)

Wow, you guys. I'm real tired, so let me touch only a couple of points now; then I will sleep. Okay. PAR said "you know its mass, so measuring velocity is equivalent to measuring momentum." We are there: the mass is distributed in a matter wave. THERE IS NO PARTICLE. Everything is a wave now. The extent one needs to embrace space to measure the momentum of a "particle" is the extent to which the matter wave is spread out in space. That's all. I heard that superconducting electrons can be thirty feet long. (no ref) In theory, probably all particles are infinite in size; you easily get that impression by looking at the sinc function or other self transforms: they go on forever in small amounts. Now from this point of view, one could say the delta_x _was a precision tradeoff of some sort. But not knowing that particular type of wave, consider a wave where a particle is well-contained in space. In this case HUP is NOT a precision tradeoff. Rather, it simply says you must include the whole "wave" or you will get a random number. Maybe you can average it to the right answer; maybe not. Depends on how short you are from the whole thing. However, the important thing is the error BEGINS at the HUP ">" point. Why? Because it is a fourier transform. Do not think of fourier as an advanced topic here. It is as fundamental as adding and multiplying. If you want to know "f" you must measure the whole wave, sin(2pft). Wanting to know p(x) or E(t) is tantamount to knowing "f" of the "quantum wave." Substituting the deBroglie relations for "f" introduces Planck's Constant, and THOSE _are the HUP equations. The derivation of the "exact" HUP (which H never accomplished) involves the acknowledgement of bulk phenomena, changing the deltas to sigmas. I would not try to go THERE in a subchapter under Planck. Besides, the delta form of HUP is the one intro physics texts usually quote and use for simple HUP examples. ItsTheEquations (talk) 05:07, 28 August 2012 (UTC)
No, you are still talking about measuring the quantum wave, which is wrong. A superconducting electron is not thirty feet long. The standard deviation of the square of the absolute value of the positional wave function is thirty feet, and that is not the same thing. It tells you that if you do measure the position of a superconducting electron described by such a wave to within delta x much smaller than thirty feet, you will not be able to predict that position (before the measurement) to within better than about thirty feet. After you make the measurement, the wave function will be different, it will represent your new knowledge of the electron, it will be described by a wave function whose standard deviation of its absolute value squared is delta x. Also, matter is not distributed on the wave. If it were, you could measure a density for a single particle, and you cannot do that with a single measurement. PAR (talk) 09:49, 28 August 2012 (UTC)
You should read Wikipedia. http://en.wikipedia.org/wiki/Observer_effect_(physics)#Quantum_mechanics (Even _that sounds like you wrote it: Many Worlds, etc.) You are wrong going and coming. There is no point in my wasting my time with your being so certain of your wrong "facts." I knew I should not have come back here. And YOU are the editor, eh? Good grief! I am done. This is all yours again. Enjoy looking at it. 71.22.238.46 (talk) 01:56, 29 August 2012 (UTC)
A few points:
• I just entered this conversation a few days ago, and I find no entry by you (71.22.238.46) on this entire page, so perhaps you are addressing someone else? Or perhaps you forgot to log in?
• I am a minor contributor to this article. The last technical contribution I made to this article, other than the one a few days ago, was four years ago. I have never even touched the Quantum mechanics article. You have me confused with someone else.