h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Heisenberg Uncertainty - A826355
Author: Russell - U190219

HEISENBERG UNCERTAINTY

To observe a particle, light must be shined on the particle.
Photons of light are the finest measuring tools a researcher has.

To find both position and momentum of an electron, at least one photon must be utilized.

Observe an electron that has momentum mv, i.e. mass time velocity.

Make the measurement with photons of light that have a wavelength "lambda".

Since the wavelength of a particle is described by the DeBroglie formula as (lambda) = (Planck's constant)/(momentum), the photons wavelength is (lambda) = h/mc. mc = h/(lambda) is the photons momentum. h is Planck's constant and c is tha speed of light in vacuum.

When one of these photons bounces off the electron, the electron's original momentum will be changed.

The amount of change in the electron's momentum is an uncertainty (delta-mv), and will be of the same order and magnitude as the photon's momentum

(delta-mv) is approximately equal to (h/lambda)

(delta-mv) ~= (h/lambda)

The larger the wavelength of the observing photon, the smaller the uncertainty in momentum.

Because of wav-particle duality, the photon of light cannot measure the electron's position (x) with perfect accuracy.

The smaller the wavelength of light, the higher the frequency, higher the energy, and greater the accuracy in measuring the position of the electron. A reasonable estimate is one photon wavelength.

So uncertainty in position (delta-x) is greater than or equal to one photon wavelength.

(delta-x) >= (h/lambda)

The smaller the wavelength, the greater the accuracy in the measurement of the position, but as the wavelength of the photon decreases, its frequency increases according to the equation E = hf, and its energy and momentum increases, and the electron's momentum is changed to a greater degree, i.e. the momentum of the electron has greater uncertainty.

By using photons of short wavelength and higher energy, the greater the accuracy in measurement of the position, but a greater uncertainty in the momentum of the electron.

By using photons of longer wavelength and lower energy, the greater the accuracy in measurement of the momentum, but a greater uncertainty in the position of the electron.

Since (delta-mv) ~= (h/lambda)

and

(delta-x) >= (lambda)

combine the two.

(delta-x)*(delta-mv) >= h

The physics books explain it as...

(delta-x)*(delta-mv) >= h/(2pi)

Position is a particle property and momentum is a wave property.

Russell E. Rierson

Hi Russel, welcome to peer review,

First things first - there's no need to copy your entry into the opening thread when submitting to forums on h2g2. Reviewers will simply click on the automatic link in post 1.

About your entry, it looks like it probably works quite well as something for a pysics text-book, but as a guide entry you could consider making it a bit more user-friendly. In particular, a nice friendly intro explaining what you are going to talk about (in lay terms that even a science-o-phobe like me can understand or at least recognise) and similarly, a nice round conclusion to finish off (conclusions are just the thing for finishing off, bizarrely enough! )

I can't comment on the content, coz of the aforementioned scientifically-challenged nature of my brain. I'm sure someone else will have something more positive (ho-ho) to say on all that.

All the best with this and future writings
spiff

Russel, as Spaceman said this really does need a laymans explanation of what you are explaining - the math and physics is fine but if you know nothing/little of either then this is al just so much gobble-de-gook.

You might mention for instance the cat in the box mind experiment etc.

That seems informative! Keep it up !

Hello,

The author seems to be new here. There are a few things that I would like to point out:

First: There is already a small Edited Entry on that subject: A408638
(related to that an Entry on the Wave-Particle duality):A156449

Second: Edited Guide Entries are generally aimed at an interested lay reader. This entry as it stands requires a *lot* of background knowledge - Maybe you would like to expand your thoughts a bit, to increase readability. Edited Guide Entries are not there to certify that the author knows his stuff - they're there to relay information.

Third: Your formula notation is confusing.

Let me stop my criticism here, and just note the following:

This Entry - in its present form - is IMHO not suitable for the Edited Guide. Yet. The existing Entry on the Uncertainty Principle is a bit thin, so I think it is very desirable to have a new one with more substance. This Entry has more potential, but it's not finished yet. To me it looks like a sketch. I would suggest the author to remove this thread from PR, beef this Entry up, and resubmit it when it is ready.

HELL

PS: There's a lot of quantum mechanical stuff in the Edited Guide already, you might want to have a look at those, to see the common approach. (Try searching h2g2)

PPS: As you are new here, let me remind you that this all is merely MY HUMBLE oppinion, as someone who has been around for a longer while.

Hello again

I have updated the guide entry for Heisenberg Uncertainty and will try to elaborate and clarify further, if you require it.

Just tell me the specific parts that need clarification.

Thanks.

Russ

Hmmm... somehow the new version looks like the old version. A bit thin, and complicated for the layperson.

Checkout the 'Quantum Mechanics' A781823 Entry to see what I mean.

The biggest problem however, is IMO, the existence of another Entry on the same topic... That will be a bit harder to solve.

Cheers,

HELL

PS: Did you update THIS entry? Or have you written another one? You can Edit entries by clicking on the Edit Entry link.

Yep, looks basically the same to me.

How about a first para in plain English along the lines of:

The H Uncertainty is theory in physics, published in 1642 by Erhardt H while he was Professor Regius of Quantum Biomechanics at the University of Middlesex. It explains how mars bars can be used to restore thinning pates by bombarding them with sub-nuclear chocatrons and is the basis of all modern chocological research."

Have I understood right?

A suggestion for the author - take it or leave it as you wish...

Stick in some headers.

Start with "history". Who was Heisenberg? No need for an entire biography - something along the lines of "The Uncertainty Principle is named after its discoverer, Werner Heisenberg (1901-1976), one of the twentieth century's greatest physicists and one of the foremost researchers during World War II in the programme to develop nuclear weapons - for Germany. He first presented the theory in February 1927 in a letter to Wolfgang Pauli (of exclusion principle fame), and published it later that same year."

This gives the reader a little historical context.

Then you can do an introductory bit under a header a bit like "The basics", under which you can cover the whole "you can only measure the variables of motion/position of subatomic particles by means which, in themselves, irrevocably change those variables." It might also be worth mentioning why the theory was necessary.

Then you can do another section - "The Details", say - and mark this "for physicists only". You might even tag it "here comes the science part." That would be more or less the entry as it stands currently.

You could finish up with a section headed "The Consequences", and talk broadly about the upshot of all this. And you simply must include a note saying that this is one of the physical principles which makes teleportation by means of a transporter, as seen in Star Trek, impossible.

We could do with a good entry on this, but it does need to be a bit friendlier to the reader who *hasn't* done any physics since they were 12. Assume the reader is clever, and interested, but not informed.

Hope this helps...

H.

You could also add abrief sentence, or section, explaining, that this all (ie Heisenberg's Stuff) is mere theory (some say it's blank speculation), but that until now, no-one has found convincing experimental evidence contradicting Heisenberg - That does not mean, however, that people are not trying. Heisenberg's principle remains a principle and is not to be confused with the ultimate truth.

Take quantum entanglement, EPR-Stuff, and Bell's theorem (not to mention gravity, but that's just a detail)... They're at the edge of Quantum Mechanics - that's where the laws get blurry flaky and full with loopholes (eg. non-locality). And there are some serious propositions for serious experiments that would contradict Heisenberg. (For example the down-conversion of one photon generating two photons, one might know at the same time the exact momentum of the first and the exact location of the second one. And since they are stemming from the very same original photon, all variables are known simultaneously - of course this takes energy conservation as a premise... *sigh* ...OK, what I am saying is that - you might not want to go into full details, but - you might add a little something explaining that there are limits to that theory, and that people are seriously working on it, either to prove Heisy right or wrong.

HELL

This might interest you: EPR-Stuff - A569126

Good night

HELL

This has definate potential. With the suggestions already made I can see it being a useful addition the the edited guide. You might want to check if there's any info in the currect edited entry that you haven't included. There are also a few typos, but we can deal with them later.

Good luck!

Tango

Hello again, I updated the entry at A826355 and will update further, if you require it. I am not sure if I should remove the equations though. The math is pretty simple, but it can possibly be simplified further, if you wish.

Russ

Hey Russ, I think that except for the bits you added in the intro nothing much changed to improve readability.

Perhaps you should try a different forum to put this entry forward. It has good potential, but you will have to change that stuff a bit faster, and add more substance as suggested above. PR is not intended for Entries that are 'Work in Progress'. (I am not talking about minor changes, or changes that are easy to implement, like inserting a paragraph or even a chapter) In your case it looks as if you had a pretty good sketch - a skeleton - of an Entry. But you will have to add some flesh and hairs to that.

BTW: Some of the new text you added contains first person bits - this is one of the usual no-no's for Edited Guide Entries.


Just my 2p.

HELL

Hi Russell,

Definitely an improvement with the intro.

I agree with Hell, though, that you might be better off in the Writing Workshop - Writing-Workshop

That is a place where you can keep working on an unfinished entry, getting some feedback from other researchers and get your piece 'PR-ready'

Don't Panic! This is not outright rejection. You have done some good work on this and listened and reacted to comments in this thread. That is a great start on the road to getting your first entry into the edited guide. You'll get there.

just a couple of things on the text:

"shined" - at best you need 'shone' as the past part. of 'shine'; but I feel a different (more technical) word may be in order here. You're the expert, of course.

Also, is 'invented' really the right term for what Heisenberg did here? The word you use just above, 'formulate' would seem more accurate. You could change the first bit to something like:

"... a German physicist who was among those who pioneered Quantum physics in the early 20th C. One of his most important contributions was the formulation of the Uncertainty Principle, subsequently named after him."

I'm not suggesting you take my words directly. This is just intended as an indicator.

Just as an aside, I think you have chosen quite a difficult subject for a first guide entry. Laudable, but you have made things difficult for yourself. Just imagine if you had written a little entry on your favourite band or film, or perhaps your home town; how different the reactions would be, and how different the writing experience would be.

all the best with this, however you choose to go with it.
spiff

Thanks for the encouragement and advice, Hell and Spiff. I shall contemplate these things. I will admit, and readily so, that I do not have the gift for gab. Really, the understanding of nature is more important to me. The uncertainty principle is fascinating in and of itself, and the question "why uncertainty?" is a difficult one, to be sure. That's why I wrote it.

Russ

There are some standard explanations in physics that I've never understood ... the ship that edges out an amount of water that has the same weight the ship has ... the rubber sheet that is bent by iron balls illustrating the curved spacetime ... and the photon kicking away an electon making the momentum determination difficult.

To be honest, I don't think that the last two images are really valid, and good textbooks avoid them. Unfortunately proper explanations of the uncertainty principle (UP) are more complicated, and I can't really rule out that this one works.

Russell, I think the best thing is to stick to what the UP *means*, and to mention only marginally a possible 'explanation'. After all, the UP is not just 'yet another effect', but a very instrinsic part of QM, revealing its utter nature. This aspect may be interesting even for the layman and thus is the way to go.

(In this context you could mention the nice sentence from Pauli in answer to the letter from Heisenberg about the UP: 'Finally there is light in quantum mechanics!'.)

So: A little bit context and trivia, the time of discovery, the people involved, as mentioned before in this thread; then what the UP says, with equation (please nicely printed, and it should remain the only formula); then -- shortly -- the thing with photon-hits-electron; then its meaning for quantum mechanics; then some further remarks like 'UP does also exist for other quantity pairs like energy and time'; then a remark why we don't see the UP in our human world.

You have chosen a demanding topic with many facets; it'll be difficult to do justice to it and to be simple and concise. But I think you can do it, since you've proven that you know the subject.

I would like to suggest some modifications. That are my personal views, of course yours can be very different.
You said the uncertainty for macrsocopic objects is smaller than the uncertainty for subatomic particles. You certainly is meaning the relative uncertainty, not the absolute one.
There is a non sequitur when you say "but as the wavelength of the photon decreases, its frequency increases according to the equation E = hf"
You takes the speed of light as 10^8 m/s, probably intending to make just an order of magnitude estimate, but a lay reader will not understand. The full value should be used.
Marcelo Allen

As frequency increases the wavelength gets "shorter", there is no non-sequitur

For a photon the equation would be

c = (frequency)*(wavelength)

Where "c" is the velocity of the photon, i.e. the speed of light in vacuum.

As the frequency of light increases the energy also increases and of course that is why x-rays and gamma rays are considered dangerous.

Hawking told me so

Hey, I removed the "first person" references and changed a couple of sentences at A826355.

If this brief synopsis is deemed unpublishable by h2g2, I might replace my Heisenberg webpage with this new updated "intelligent lay-person" version

Thanks for the help.