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> Problem with the two slit experiment, Observing later
Confused2
Posted: Jun 20 2007, 11:39 PM


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In my last but one post I gave some physical justification for the HUP. It looked like it should appear random. BUT. to keep the total uncertainty the same within a gnats cock is as precise as dealing with a certainty.
If we have a large lens that increases the probability of an interaction at one point then clearly it must decrease the probability of interaction occurring at some other point (to keep the total probability at <= 100%) ..
The addition (superposition whatever) cannot add up to giving the source of the photon anything other than an unknown momentum. With (say) two paths between source and destination we have to introduce a further level of uncertainty which satisfies the
"We need an uncertainty about the momentum impulse given to the source and destination"
"The actual (uncertain) impulse must always be of the same value"

Hot?

Comments welcome.

Best wishes - C2
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Laserlight
Posted: Jun 20 2007, 11:41 PM


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Hi C2,

QUOTE
When A emitted the photon it lost energy and gained an uncertainty about the momentum 'recoil' from the photon.
We could suggest that A and the photon remain entangled and the final momentum of A will only be resolved when the photon is detected.. but we agree (I think) that this could take a thousand years. OR we could give the universe another option .. we formalize the uncertainty of the outcome and say "we'll take the total uncertainty as the actual result". When the photon is emitted from A the energy of A is reduced and A becomes less localized. The photon carries a precise amount of energy and momentum but cannot deliver that momentum in a particular direction without (potentially) messing up conservation of momentum with respect to its source (A). When detected by B the photon gives an increase in energy to B and makes the momentum of B more 'certain' (it becomes more localized). The consequence of the whole (or any part) of the photon moving from A to B is that the knowable momentum of the system is conserved but the actual value of that momentum remains equally uncertain at all times.


IMO, you need to rethink this line of logic....

1. There is no recoil when an atom emits a photon.
2. Atom A drops back to its "ground" state when a photon is emitted.
3. "Localization" represents a changing energy state at a point in space and time
relative to its surroundings. It could represent a coherent wave of multiple
simultaneous photons, emitted at the same time, in the same wave, or a
drop to the ground level. The key is changing energy state.
4. Lasers deliver photon coherent energy (and momentum) in a particular
direction all the time.
5. Energy, transmitted or received is measured in joules, and can be predicted
and measured.

Comments?
LL

This post has been edited by Laserlight on Jun 20 2007, 11:42 PM
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Laserlight
Posted: Jun 21 2007, 12:01 AM


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C2,

Where are you going with this? The HUP is a statistical analysis of all possible
events that could occur within a closed set of variables. The accuracy of the
statistical predictability narrows/improves when controlled circumstances are
introduced that influence the likely outcome. The more variables in the
set, the wider the bell curve "bandwidth" and the lower the chance of an exact
solution being predicted.

Narrow the set of possible variables, and the odds improve of determining a
likely solution. With two slits, and with fixed experimental geometry, the DSE will
yield the same statistical set of results every time.

Ask me....I play the lottery! Geese, I just wish that I only had to pick from two
numbers to win. laugh.gif

LL

This post has been edited by Laserlight on Jun 21 2007, 12:03 AM
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Confused2
Posted: Jun 21 2007, 12:30 AM


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Hi Laserlight,

Thank you for your response.

1. There is no recoil when an atom emits a photon.See http://en.wikipedia.org/wiki/Radiation_pressure .. every action has an equal and opposite reaction. If you had (say) a lightbulb radiating then there would be no net total momentum. If you reflect the photons from the lightbulb in a particular direction then you can generate a net 'thrust'.

2. Atom A drops back to its "ground" state when a photon is emitted. Yes. .Lower energy .. bigger de Broglie wavelength .. less localised.

3. The key is changing energy state. Energy/momentum/localisation .. that's what I'm trying to make sense of.
4. Lasers deliver photon coherent energy (and momentum) in a particular
direction all the time.

I don't claim to have covered all possible effects .. only to have (maybe) isolated one of significance to the DSE. As in response to 1. there are mirrors involved which can turn 'any direction' into a single direction.. this is the game I'm addressing.
5. Energy, transmitted or received is measured in joules, and can be predicted
and measured.

Precisely so.
Comments?
Best wishes -C2.
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Confused2
Posted: Jun 21 2007, 12:36 AM


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Hi LL,

The HUP is a statistical analysis of all possible
events that could occur within a closed set of variables. The accuracy of the
statistical predictability narrows/improves when controlled circumstances are
introduced that influence the likely outcome.


I am taking precisely that and trying to give a physical justification for it. In particular a local 'result undetermined' is enough to work with (locally) AND satisfy the requrements of a larger system. For 'statistical' substitute 'unknown and unknowable' then take the analysis forward with that*.

Best wishes - C2.

* Edit ..we don't know the direction of recoil .. it's all of them .. the source loses 'locality'.

This post has been edited by Confused2 on Jun 21 2007, 12:40 AM
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Good Elf
Posted: Jun 21 2007, 02:10 AM


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Hi jal,

QUOTE (Jal)
QUOTE (Good Elf)
I usually always support the arguments with experiment while the gravitational scheme has no supporting experimental evidence and according to many pundits is beyond the level and scale to ever be proven (... proof lies below the Planck Length).


Pot calling the kettle black.
I think everyone would agree that more than 3 dimensions is beyond experimental evidence.
"...everyone would agree?..."If everyone on earth took a vote on the Laws of the Universe it seems you think this makes it all true. I am just pointing out the fallacy of such statements. You have been listening to committees far too long. That was very bad editing of my statement... I do not support that any proof that lies beyond smaller dimensions below the Planck Length... I insist that proof for my theory is quite the opposite (being the reciprocal). All my proofs for higher dimensions are at our larger dimensions and the reason why we do not notice this is because of the preconceptions of how additional dimensions add to our Universe. I have proposed a mechanism and I have supported this with current experiment.

When I get deliberately misquoted in edits I am very disappointed that my position has been corrupted and it does not represent my true position. I am hoping this is just a misunderstanding on your part. If you have a point in science put it up to public scrutiny like I have done so many times, state what it is that I am saying that is actually wrong and show why it is wrong don't just cry about it. I am a reasonable person and I welcome real tough questions but I expect your mind to be engaged too before you respond. This is not too much to request.

I can only disagree with you unsupported position Jal, but it was ever the case that I am a loner on this point, a position that none of you have provided any contrary evidence other than the "ad hominem" approach that you are showing here. If you have something, anything at all, stand up and place it on the table and then point to the issue in question. . I have pointed to many features of Quantum Physics that have only one clear explanation if all taken together. Find the fault if you can and point it out with supporting evidence from experiment. I refuse to repeat myself ad nausium since a lot has been said already (209 pages on this single topic alone...) much of it dwells on the very topics you are complaining about but you never once brought any scientific argument to this Forum till now. I welcome science but I do not welcome a smokescreen. i know you have your own ideas about these issues and I am sure they answer single points but will it answer 'all" points? If something still remains to be said or questions needed to be asked then ask now but I refuse to repel an "ad hominem" attack.

What people prefer to accept as Quantum Postulates are unjustified with no basis in Physics. The argument that quantum mechanics is the simplest explanation relies on acceptance of all the underlying postulates first. It is clear that in the race to achieve short term gains in quantum theory a number of shortcuts were taken along the way... One of them was accepting a large number of outright unjustified postulates and ignoring any opinions to the contrary even if they were provided by some of the great lights of Physics history. I fully understand that many or most (maybe all) those people following this thread have lost sight of the various arguments proposed by me. There are many reasons for this such as individual prejudices and full acceptance of the current line of thinking based on pure authority ... but that is all it is. I have often been challenged but not on physics grounds and I am the only one providing any proofs to the contrary.

The natural direction when confronted with one of the essential conflicts in the existing theory is to refer to the texts where it says that there are certain things we cannot know. That is BS and we know that those who say that are protecting their vested position. These are the Dragons and Sea Serpents on old maps warning not to proceed beyond the Pillars of Hercules (otherwise you will just possibly fall off the edge). Experiments to find additional dimensions have been "misdirected" and funding for questions that may result in basic additional science is just not being done by those with the purse strings. I really do not care for this "shut up and calculate" approach to all the real problems. As I have often said... the day of the human calculator is over... you need to think about what is being done in calculations to earn a living not just be cleaver with a pencil. As I have said before... If I want a calculator I will go out and buy one, this could mean getting on the internet or having someone do a calculation for me. But I would not spend more than $30 a pop since this "mechanical" aptitude is not worth my spending much money on... that includes people that have dedicated their lives to being nothing but a mindless calculator. Maybe I would spent a couple of times that if I was able to purchase a piece of specialized software that solved a large number of my particular problems. Since I am a qualified programmer maybe I would design my own software. What is the point... everything I want to say mathematically has already been said. Conceptually there is no development or leadership so that is what I am offering.

If people have the answers then let them speak but when they do speak they must give their references and their reasons. I have consistently done this... Most others do not have anything to offer when they simply say that I am wrong... I say put up or shut up. I insist that people verify their sticking points and they support even the most commonly accepted claims because these are the ones that I find are the most in error ad irksome (...I think everyone would agree... etc). If people want maths then they can copy from references as well as I can and add the line or two necessary to extend the functions from other peoples hard work. I am not too proud to accept that others have already done all the ground work... what they have lacked is the foresight and the intestinal fortitude to take the next step... so it is left to "elves" to say if for them.

Regarding Planck Length... With a reciprocal space theory there is no problem with proving the veracity of my claims since the scale of these quantum phenomena are the size of photons which can be the size of a house or bigger or smaller than the smallest atomic particle but I know of nothing for certain at the Planck Length... and neither does anyone else. Please prove me wrong with a verified experiment that actually tests this scale. I have taken the top down approach which is the way that history has chosen in the past to verify the nature of phenomenon. I am not worried by the Planck Length since there is very little extra to be learned down there other than dredging even lower levels out of the holographic domain. So "Alice" number 3 starts to drag "Alice" number 4 out from her mirror domain... big deal.

So less of the "Public Service" voting on the Laws of Physics with a show of hands and more about asking the Universe (through experiment) what it is really on about. To get a really good answer you must pose a very penetrating question. This is what this thread is about and why it is apparently popular. I am sure that if I simply fell into line with accepting the line handed out at "Church" to just believe what I have been told... none of you would be back to this thread again since "we all know the answer!"... Right?

Cheers

This post has been edited by Good Elf on Jun 21 2007, 02:11 AM


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Laserlight
Posted: Jun 21 2007, 02:25 AM


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Hi C2,

QUOTE
Laserlight said: 1. There is no recoil when an atom emits a photon.

C2 said:
See http://en.wikipedia.org/wiki/Radiation_pressure .. every action has an equal and opposite reaction. If you had (say) a lightbulb radiating then there would be no net total momentum. If you reflect the photons from the lightbulb in a particular direction then you can generate a net 'thrust'.


Hmmm, I'm still researching this...I read not long ago that there is no recoil
when a photon is emitted, which amazed me because it seemed contradictory,
I read it a couple of times just to make sure that I read it correctly.
I'll try to find the source where I read this.

In the meantime....this seems to indicate that indeed there is recoil when a photon
is emitted. It is confusing when you read conflicting data.

http://www.tau.ac.il/~lab3/MOSSBAUER/Recoil.html

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

LL
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Montec
Posted: Jun 21 2007, 02:30 AM


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Hello Confused2, et al.

If a dipole is used to model a photon emission then the emission momentum would appear to be spread out over an approximate 360 deg. solid angle. The momentum would actually compress the dipole emitter. What happens within a laser via stimulated emission is not a dipole model of emission. We cannot mix the two models (IMO).

The laser model adds energy (photon) to the current EM wave structure within the laser cavity. The dipole model starts a new EM wave.

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Laserlight
Posted: Jun 21 2007, 03:41 AM


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Hi All,

Some interesting papers on various topics.

http://www.newtonphysics.on.ca/

Video of the nature of a photon.

http://www.newtonphysics.on.ca/Animation/Fund-nature.html

LL

This post has been edited by Laserlight on Jun 21 2007, 03:54 AM
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Good Elf
Posted: Jun 21 2007, 03:55 AM


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Hi Laserlight, confused2,

QUOTE (Confused2)
1. There is no recoil when an atom emits a photon.See http://en.wikipedia.org/wiki/Radiation_pressure .. every action has an equal and opposite reaction. If you had (say) a lightbulb radiating then there would be no net total momentum. If you reflect the photons from the lightbulb in a particular direction then you can generate a net 'thrust'.
In the context of the HUP there is "more". Momentum is not like energy since conservation of momentum (in a certain direction) does not mean that because a zero momentum was there formerly it will necessarily remain zero. In the case of slits we have momentum appearing in the transverse direction. Only the sum of the momenta need be zero. This is not due, as you might naively think, to the photons "bouncing off the edge of the slits", it is the result of Fourier Theory. Mechanical scattering of photons on the slit edges(which is absorption and re-emission) loses the qubit and that re-emitted photon cannot take part in any further diffraction pattern on the back screen (any argument about this??). Any secondary photons will be a different frequency, emitted in some other random direction, and will only add noise to the pattern.
Optical Analog of Uncertainty Principle: Harvard
From the real analysis of this problem through the conjugate variables it becomes an interesting exercise. The question seems to be how this function plays a role in individual photons. It is not a statistical unction though with large ensembles of statistically variant particles it will result in the correct result. What it does not do is link a single pair of measurements to a single photon.

The issues regarding HUP I have dealt with in this recent post...
Good Elf : Problem with two slit experiment
HEP are conjugate variables and are a required part of basic Fourier Theory. I will repeat for clarity...
user posted image
QUOTE (Wikipedia: Conjugate Variables)
A pair of variables mathematically defined in such a way that they become Fourier transform duals of one-another, or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty (Heisenberg uncertainty principle) relation between them. A more precise mathematical definition, in the context of Hamiltonian mechanics, is given in the article canonical coordinates. Examples of canonically conjugate variables include the following:[...]
    * Time and energy - as energy and frequency in Quantum Mechanics are directly proportional to each other.
    * Position and momentum: precise definition of position lead to ambiguity of momentum, and vice versa.
http://en.wikipedia.org/wiki/Canonical_conjugate
I will spell this out ... they are NOT in general statistical functions and for single photons are related to each other directly. The fact that we cannot predict (ahead of time) what the function may be in a particular instance does not remove the fact that this is the relationship between the duals and it is "exact" given a numerically calculated energy and a numerically calculated time or a numerically calculated position and a numerically calculated momentum for a single event. The very act of the physical measurement is what disturbs the relationship between the duals. I suggest you determine for yourselves what the word "dual" in this context really means... to me it is an expression of a reciprocal relationship between exact "reciprocal equivalents". In the quantum context it is speaking about the gross relationships between the two measurable taken over "ensembles". For instance the function as shown in the above relationship of ∆E.∆T is an 'area" under a curve of E vs T and these can be expressed as a relationship of all points on the curve E = K/T where K is a constant of proportionality. a quick look at protective measurements in quantum theory quickly sets us all in reality about what a strong and a weak measurement will do for a particular quanta.
http://www.citebase.org/abstract?id=oai%3A...ep-th%2F9408153
http://tabish.freeshell.org/physics/pm/
User posted image
...Click to enlarge...
Best to look at the original image with the black background in the link above the image here.
user posted image
But you can clearly see that the strength of the measurement results in some limited information regarding the 'duals".

This is exemplified in the correlation between "Doppler" and "range" (as noted in the Wikipedia example above)... Doppler is frequency variation and range is distance measured in time units of the beam. The Doppler gives us a relative velocity and range is a distance. We know this to be a function that is related to Special Relativity. The blue shift and the red shift of objects due to "Doppler" leads to a direct measure of imprecision and in Special Relativity the "error" can lead to differences of estimates of speed being several times the speed of light. A case in question is the Jet from galaxy M87 where the speed of the galaxy 'appears" to be 6 times the speed of light..
http://www.stsci.edu/ftp/science/m87/m87.html
It is clear that without a relativistic correction for the proper motion of the object this position and momentum is wrong. Yet this is just such a pair of variables.... distance and velocity. Leave out the 'exact" correction for relativity and you have a wrong answer.

Cheers

This post has been edited by Good Elf on Jun 21 2007, 03:59 AM


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Why Not?
Posted: Jun 21 2007, 04:45 AM


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Hey C2, LL and all,

C2, Excellent! I am still re-reading, making sure I understand what you are getting at, but so far so good. One question so far... HUP does not say that momentum is uncertain, just that knowledge of momentum and position simultaneously is subject to uncertainty. As the photon arrives at B, as well as when in it departs A, the momentum can be known with 100% certainty, if we disregard position. So are you suggesting that A (somewhat local) emits a photon with some momentum and becomes somewhat less localized because if transfers uncertainty as a quantity? Not “uncertainty in ‘x’” but some quantity of uncertainty (1/2h-bar per set of conjugate variables)?


LL,
QUOTE (Laserlight)
I read not long ago that there is no recoil when a photon is emitted
I think you may have mis-read one of the links to W-F Absorber Theory.

QUOTE (from the link below)
The emission of these time-symmetric electromagnetic waves therefore raises some immediate problems in its correspondence with observation, for the emitter experiences neither recoil (i.e., momentum transfer) nor energy loss in the act of emission. However, if absorption of the emitted retarded wave occurs sometime later, the correspondence with observation is restored. The observed recoils during emission and absorption occur because the respective electrons move in the electromagnetic fields of the waves, advanced and retarded, respectively, sent to them by the other electron, as demonstrated by Wheeler and Feynman[1].
from http://www.npl.washington.edu/npl/int_rep/dtime/node2.html.
"...for the emitter experiences neither recoil (i.e., momentum transfer) nor energy loss in the act of emission." which "raises some immediate problems in its correspondence with observation..."

This post has been edited by Why Not? on Jun 21 2007, 05:32 AM


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Laserlight
Posted: Jun 21 2007, 07:23 AM


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Hi Why Not,

Yep, that was where I read it. The way it is stated seems "misleading".....
it appears that I interpreted that wrong. Does the atom move via recoil,
or does the dipole electron position respond to the changing EM fields?

It is still not real clear what constitutes "recoil", since the electron is changing
energy shells as it accelerates back to the ground level. Then, there is the
issue of emitting atoms locked in the atomic structure of a fixed matrix....

Thanks for posting the link!
LL
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Good Elf
Posted: Jun 21 2007, 07:59 AM


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Hi Why Not?, Laserlight, confused2,

Very accurate comments by "Why Not?". I see that "the message" is getting through about HUP. In the case of Quantum Theory ... as he has said and I have also previously noted... Quantum Field Theory is 100% time symmetric. This is telling us about the nature of those "standing waves" if you consider it for a moment. Photon events "know" beforehand where they are going to end the moment they are initiated. This "sounds" crazy but it is true, in order to have 100% time reversibility this must indeed be the case. To our world and the events in it we are unable to perceive this time symmetry but nevertheless it truly exists. The lack of appreciation of these fundamentals lead to very dumb conclusions by quite knowledgeable people. The preferred reference frame of the Universe is the photon and the photon has no experience of time or space except that small ∆E.∆T that has been expressed as uncertainty but this uncertainty is "everything". It is an expression of the finite size of sources and finite times for interaction that most of the theory makes no recognition of.

If we have chosen to ignore aspects of our universe that define the essence of an event then you can quite easily ignore the underlying truth about the force carriers of our Universe... the transit of photons between source and sinks is entirely "fixed" in the sense that this "event" cannot be changed since its emission and absorption are effectively "predestined" and "reversible". The big "happening" with the photon occurs "before the photon leaves the evanescent region of the source and after arriving at the evanescent region of the sink. Nothing happens to the photon in between (for most operations)... this is because the photon is in a "stationary state" where there is no actual change in energy because there is no change in time for an energy process to actually occur.

If you do not experience time you cannot experience any "process" in our Universe, the Lagrangian cannot work beyond that boundary. Yet there are some wave processes ... the photon's "de Broglie Wave" that can gather information through it's interferences. This has no effect on the actual photon but it is carrying additional information about the rest of the Universe through "seeking all paths". This is why photons that travel directly to a photographic plate have phase information about the rest of a "dark universe". It is all there in the standing waves found frozen inside the plate... holographically recorded. Why standing waves? ... because standing waves are time symmetric, because of curvature progressive waves are not time symmetric. The conclusion is that those standing waves are there "instantly" it is written into quantum physics... not my idea... it has always been there.

To say that these traveling photons are all there is to our universe is also a grave error... the sources and the sinks are time symmetric regarding these single photon events... What is "in between" is what really matters... inside the evanescent zone of the particles the photons still have a life separate from the one it experiences here inside of our space. These are the "identifiable" higher dimensions... The stationary states hide an inner life of their own... the quantum is hidden from our universe and even its energy is hidden from our universe. If the photon experiences no time and no distance due to the most extreme form of space and time dilation then from its point of view these two endpoints occupy that small ∆E.∆T the surface of some small sphere of existence in which the event is unfolding... you decide what the geometry of that surface is yourselves. wink.gif

Here is a clue...
User posted image
... Click to enlarge...
Of course it needs more generalization in those higher dimensions. This is the way the quantum "moves" and "propagates".

Naturally this is not the "entire" story but it is a good start. From this you can easily arrive at orbitals and waves propagating between atoms etc. They are simply a series of interconnected cavities. Our entire Universe is an "interconnected cavity"... That photon propagating through "space" is simply a transition of a photon between two connected cavity states. Our experience of reality becomes very "complicated".

Cheers


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Confused2
Posted: Jun 21 2007, 10:15 AM


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Since I've been less than enthusiastic about everyone else's ideas I thought I ought to put in some ideas for everyone to be less than enthusiastic about.

I'm mostly making this next bit up for dramatic effect.

--------------------- start of dramatic bit ----------------
Let us imagine the 7th duc de Broglie flounces into Dirac's office and says
"BTW I've worked out this incredibly clever thing and if you were half as smart as me you'd have been able to see it too"
Dirac, being a man of science and integrity, naturally tells de Broglie he's talking nonsense. At this point we must assume Dirac leaves de Broglie in his office to mess about with his pencils while he goes off to work out just how stupid and stupendously wrong de Broglie actually is. As a man of some integrity myself I can imagine just how pleased he was when he realized de Broglie might actually be on to something. When he has recovered a bit he goes back to his office, tells de Broglie to put the pencils back in the drawer and says:-
"right answer .. but not for the right reason".
We might guess that Dirac, being a man of science and integrity, never told de Broglie (or anyone else) what the real reason is. So then and now de Broglie remains a man with a hypothesis because he wasn't smart enough to work out what Dirac meant when he said '.. but not for the right reason'.
------------------ end of dramatic bit--------------

So de Broglie claims it all works perfectly if you put the right momentum in. My guess is that Dirac failed to point out that it also works perfectly if you put the wrong (any vector) momentum in.
Comments? Therapy?
Best wishes - C2.

Edit.. Why Not? seems to have seen precisely what I'm on about.

This post has been edited by Confused2 on Jun 21 2007, 10:28 AM
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Good Elf
Posted: Jun 21 2007, 12:08 PM


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Hi Confused2 and Why Not?,

QUOTE (Confused2)
So de Broglie claims it all works perfectly if you put the right momentum in. My guess is that Dirac failed to point out that it also works perfectly if you put the wrong (any vector) momentum in.
Not true (I think!)... what does "it" mean?? We elves are "all ears" but you must tell us a true story. I am not Dirac or "Why Not?"... elves are soulless morons... you explain just what question you actually want to ask and let that be the measure of any answers. It has always been my experience that if anyone can frame their question with some precision they will receive a very precise answer.

You might (or might not) find this interesting from Maths Pages... though it may be best to read it all from the reference below..
QUOTE
Fourier_Transforms_and_Uncertainty.

In other words, the probability amplitude distributions of two conjugate variables are simply the (suitably scaled) Fourier transforms of each other. We saw previously that the dispersions (variances) of two density distributions that comprise a Fourier transform pair satisfy the inequality (2), so the variances of the probability amplitude distributions of conjugate observables in quantum mechanics satisfy such an inequality. Thus Heisenberg's uncertainty principle for conjugate pairs of observables follows directly from the fact that those observables are essentially the Fourier transforms of each other.

Of course, this attribute of Fourier transform pairs is purely mathematical, and has no a priori applicability to pairs of observables such as position and momentum, or time and energy. The physical content of quantum mechanics is based on the two relations
  E =h-bar * w p = h-bar K
where E is energy, p is momentum (in one dimension), h-bar is Planck's (reduced) constant, w is the frequency with units second^-1, and k is the wave number with units meter^-1. These relations were introduced in the early 1900's by Planck, Einstein, and deBroglie to account for non-classical phenomena such as cavity radiation and the photo-electric effect, both of which depend on the particle-like behavior of entities that had previously been modeled as waves, as well as phenomena involving wave-like behavior of material particles. These are the relations that associate the familiar observables of energy, momentum, space, and time, with the frequency domain. Indeed in terms of the characteristic time t = 1/w and distance D = 1/k the above relations can be written as
  tE = Dp = h-bar
which already clearly reveals the conjugacy of time and energy, and of distance and momentum. In view of this, it isn't surprising to find that the product of the dispersions of two conjugate observables (such as position and momentum) cannot be less than one quanta of action, represented by h-bar .

In a sense, there is also a conjugacy between space and time - two observable that had been regarded as disjoint and independent prior to the early 1900s. In special relativity the inertial space and time intervals dx and dt between two events are components of a single invariant spacetime interval ds between those events. These intervals are related according to the Minkowski metric, which can be written in the form
{dx/dt + ds/dt}{dx/dt -ds/dt} = 1/c^2

This can be regarded as an "uncertainty relation" for space and time. In general, physics was based, prior to 1900, on the premise that h-bar and 1/c^2 were both zero. With the advent of quantum mechanics and special relativity, it was realized that they both have non-zero values, although they are extremely small in terms of ordinary units.

http://www.mathpages.com/home/kmath488/kmath488.htm


As you already know I think that the de Broglie Relationship is the "low velocity end" of Special Relativity... as V -> 0 ...
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Cheers

This post has been edited by Good Elf on Jun 21 2007, 12:16 PM


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"Aa' menle nauva calen ar' ta hwesta e' ale'quenle"
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