Patent Application
20110235044
The present invention relates to how physical system-specific characteristics might challenge the absolute nature attributed to the uncertainty principal, thereby making uncertainty a system-specific concept, and more particularly applies chaos concepts to the situation at the slits of a double slit system with the proposal that a photon or particle that contributes to a positive slope region in an interference pattern formed by a double slit system is more likely to have passed through the left slit of the double slit system, (as viewed from the source), and a particle or photon which contributes to a negative slope region of the interference pattern is more likely to have passed through the right slit thereof. An experiment is proposed that would allow verification thereof, and which would allow near-simultaneous measurement of particle position and momentum.
It is generally considered that the Heisenberg Uncertainty (ISSN 1798-2448).
Said articles provide good insight to the progression in thought that has led to the present invention, and are incorporated herein by reference.
A reference that explains how the uncertainty principle applies to a double slit system, is Chapter 37 of the “Lectures On Physics”, Addison Wesley, 1963, Feynman describes an experiment proposed by Heisenberg, with an eye to overcoming the Uncertainty Principle. The idea involves placing a plate containing double slits on rollers so that if a particle passes through one slit thereof, it will transfer momentum to the plate in one direction, and if it passes through the other slit momentum will be transferred to the plate in the opposite direction. It is proposed that this momentum transfer could be monitored to determine, through which slit the particle passed. The problem that presents, however, is that the slit location then becomes uncertain. Again, the proposed approach does nothing to challenge the Uncertainty Principle. Feynman concludes Chapter 37 by saying that no one has been able to measure both position and momentum of anything with any greater accuracy than that governed by the Uncertainty Principle, but in a recorded lecture added that someone, sometime might figure it out, (which served as my encouragement to try, leading to the disclosure herein).
Batelaan, in Chp. 2 of Wave-Particle Duality with Electrons, the Perimeter Inst. (2011) states that to date no-one knows what a particle does in a double slit system.
An article by Mittelstaedt et al. titled Unsharp Particle-Wave Duality in a Photon Split-Beam Experiment, of Quantum Mechanics, is an absolute. This is based in Fourier Transform-type mathematics, and to the authors knowledge is never modified by known characteristics of a physical system to which it is applied. It is argued herein that characteristics of a physical system to which the uncertainty principal is applied can serve to render the uncertainty principal less than absolute.
Continuing, the Heisenberg Uncertainty Principle holds that uncertainty in a measurement of a photon or particle's position times the uncertainty of a measurement of its momentum must always exceed a quantity closely related to Planks constant. Further, it is generally considered that the Heisenberg Uncertainty Principle governs formation of an interference pattern when photons or particles are directed toward a double slit system, such that at least some of them pass through a slit and impinge on a screen. In particular, as the momentum of a photon or particle directed toward the slits can be set with arbitrary accuracy, based on the uncertainty principle it is generally believed that it is impossible to know anything about through which slit it passes. Further, as it is possible to measure where on a screen a photon or particle impinges with arbitrary accuracy, it is generally accepted that it is impossible to know anything about its lateral momentum, hence through which slit passed.
Two very relevant articles are titled:
Another reference, Optics, Hecht, Addison-Wesley, 1987 is also disclosed as in Chapter 10 thereto, it provides an excellent mathematical description of the Double Slit experiment.
Other known references include:
The present invention is a method of determining through which slit of a double slit system a particle passes, or at least is more likely to have passed, in formation of an interference pattern comprising the steps of:
Said screen further has means for allowing lateral motion in response to momentum transfer from an impinging particle.
The method continues with:
Another present invention method comprising the steps of:
Said screen further has means for allowing motion perpendicular to a lateral locus of said screen in response to momentum transfer from an impinging particle.
Said method further comprises:
The present invention will be better understood by reference to the Detailed Description Section of the Specification, in combination with the Drawings.
a and 2b show the condition where one of a Fourier Transform pair is an infinite peak, and the other a distribution with an infinite uncertainty.
a and 5b show important slopes in the application of the Welch Certainty Principle.
a, 8b and 8c show that a likely consequence of this is that a photon or particle exiting the left slit (SLL) will contribute to a positive slope region in an interference pattern and that a photon or particle exiting the right slit (SLR) will contribute to a negative slope region in an interference pattern as was determined with respect to the after the fact scenario wherein a reference interference pattern on a reference screen (SC) was applied to determine the same conclusion.
To begin, it is of benefit to consider that if one measures the exact position of an object at an exact instant in time, it is literally impossible to know how fast the object might be moving because at an exact instant in time no time passes. At the exact instant of measurement the object could be standing still, moving at near the speed of light, or moving at any velocity in between, because at the precise instant of measurement, there is no information available to allow determination of its velocity, (ie. some time must pass for a velocity to be measured). Likewise, if an object is moving it is present at a continuum of locations when that velocity is measured, hence there is no way to define exactly where it is located while measuring velocity. As the velocity scenario might be a bit more difficult to grasp, it is further noted that to measure how fast an object is moving, you necessarily have to measure the location of that object at, at least, two instants of time and you need to know how much time elapsed between the two location measurements. However, while having such information lets you calculate the ---average--- velocity at which the object was moving between said two measured locations, such information does not tell you what its exact velocity was at a particular point between the measurement locations, or anywhere else for that matter. This is because the object could have been slowing down or speeding up, (or a combination thereof), between the two precise measurements of the locations and the same average velocity would be arrived at in many different cases. Therefore it remains unknown what the precise velocity was at any precise position. The only apparent approach to minimizing this problem is to make the two precise measurements of the object position very close to one another, thereby minimizing the effect of change in velocity therebetween very small. However, as long as some distance exists between the measurement locations this approach cannot guarantee that the velocity was not changing between said precise location measurements. And in the limit, where the distance between location measurements becomes dx=0.0 so that no velocity change occurs, we again arrive back at the problem that a precisely measured position provides no information as to velocity, as described the start of this paragraph. (Note, that the objects velocity can be multiplied by its mass, and the term velocity replaced by momentum in the foregoing). In view of the foregoing, even on a macroscopic object level, the seeds of an uncertainty as regards the ability to simultaneously measure both the precise location and the precise velocity of a moving object, can be appreciated. While the foregoing scenario is, as a practical matter, not particularly troublesome to people in their every day lives where knowing an average velocity is normally more than sufficient, it does becomes a major source of indeterminacy when very small objects are involved. In fact, it is generally accepted in Quantum Mechanics that it makes no sense to even ask what the position ---and--- the momentum of a particle are simultaneously. That is, a particle can be observed to have one or the other, but not both a position and-- a momentum simultaneously. In fact, it is generally accepted that if one measures the position of a particle exactly, then the uncertainty as to what its momentum is at that time, is infinite. And likewise, if one measures the exact momentum, then the uncertainty in the position thereof is infinite.
When one surveys mathematical functions that provide an amplitude, and another parameter that assumes a larger value when a related parameter assumes a smaller value, Fourier Transforms should come to mind. This is because when the width (standard deviation) of one member of a Fourier Transform pair of functions becomes narrower, the standard deviation of the other member increases in width, and vice versa. For instance, Fourier Transformation:
f(t)=e−at2
F(ω)=(π/a)1/2e−ω2/2a
can be applied to a Normal Distribution, (which is characterized by a peak amplitude (A) in a bell shaped plot, and by a Standard Deviation that indicates its width (W)) and the result is another Normal Distribution that has a standard deviation of (1/W).
a and 2b below demonstrate the sort of results that one obtains when applying mathematical approach just disclosed.
Continuing, while Fourier Transform mathematics is just that, mathematics, the approach demonstrated thereby has been adopted in Quantum Mechanics to characterize Conjugate Variables, (eg. position (X) and Momentum (P), or Energy (E) and Time (T), or Spatial Field Strength (FS) and Rate of Change of thereof (d(FS)/dt). As applied in quantum mechanics,
In the foregoing it was shown how uncertainty concepts can be understood based in macroscopic examples. Table 1 presents another relevant macroscopic example involving the results obtained by the throwing of two dice, which can result in a sum of 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 or 12. It is further known that there are probabilities associated with obtaining said results:
Now, if one measures only the sum total of the results of throwing two dice, it becomes readily apparent that, other than for the values of 2 and 12, one can not be absolutely certain what each of the dice contribute. That is, the measurement per se. does not disclose how the measured result was arrived at. However, by analyzing the system that produced the measured result, one can know that a certain result, (eg. 7), was arrived at by a selection from a known group of six definite possibilities, (a chance for each of (⅙)). Notice also, that if a 3, 4 or 5 was measured it is known with certainty, by analysis of the system involved, that neither die showed a 4, 5 or 6, respectively. Further, if a 3 or 11 results, note that one can not determine which dice has the 2 or 5 and which has the 1 or 6, from the sum total. One can, however, tell a lot about what information is imparted by a measurement provided by a system, by analyzing the physical system involved to determine how it could produce various measured results, and a probability can be assigned to specific results in view thereof.
The dice example described in the Disclosure Section shows that knowledge of a system can provide inferred knowledge about it, which is not subject of direct measurement. In that light, it is noted that in an article titled The Welch Uncertainty Principal, ISAST Vol. 1, No. 3, 2011, Welch proposes that the physical characteristics of a Double Slit system allow inferring that it is more likely that a photon or particle which impinges on a screen thereof can be determined to more likely have passed through one of the slits than the other. As described in the cited articles, the described result can be understood by considering that a reference interference pattern can formed on a reference screen (SC) by firing a large number of photons or particles thereat through, respectively, left and right double slits (SLL) and (SLR), and the resulting interference pattern can be fixed in place as a reference. This is followed by placing a test screen (SC) just in front of said reference screen (SC), and firing a single photon or particle thereat, and noting where thereupon it impinges. Next, lines are projected from each slit (SLL) and (SLR) through said location at which the single photon or particle impinged upon the test screen (SC). When this is done it will be found that one of said projected lines intercepts the reference interference pattern on the reference screen (SC) at a higher probability location, and that indicates which slit (SLL) (SLR) it is more likely that the single photon or particle passed. When this approach is repeated with many photons or particles, it is found that it is always more likely that a photon or particle which contributes to a positive slope region of the test screen is always more likely to have passed through the left slit, (as viewed from a source of photons or particles), and that a photon or particle that contributes to a positive slope region of an interference pattern is more likely to have passed through the right slit, (again as viewed from a source of photons or particles), if it impinges contributes to a negative slope region of an interference pattern. And, as the distance between the reference (SC) and test (SC) screens can be reduced to zero (0.0),
Continuing, in a letter published in the ISAST Transactions on Computers and Intelligent Systems, No. 2, Vol. 2, 2010 (ISSN 1798-2448) Welch disclosed an approach to improving the probability of knowing which slit, in a double slit system, a photon or particle passed in formation of an interference pattern. Briefly, a reference interference pattern is formed on a reference screen (SC), (see
In a paper published in the ISAST Transactions on Computers and Intelligent Systems, No. 1, Vol. 3, 2011 (ISSN 1798-2448), titled The Welch Certainty Principle Welch demonstrated that practice of his method which utilizes a reference pattern as disclosed in The Uncertainty of Uncertainty article, leads to the conclusion that it is always more likely that a photon or particle which proceeds through a left slit, (as viewed from the source thereof), in a double slit system is more likely to contribute to a positive slope region of an interference pattern, and that it is always more likely that a photon or particle which proceeds through a right slit, (as viewed from the source thereof), in a double slit system is more likely to contribute to a negative slope region of an interference pattern. This result, it is emphasized, was based on use of a reference pattern to which a photon or particle which impinges on a test screen is compared. (The reference pattern was described as having been formed on a reference screen before the single photon or particle is caused to impinge on the test screen, which reference screen is positioned behind the test screen). The basis for this proposal is that projections from both slits through the position on the test screen at which the single photon or particle impinged, provides insight that one of the projection lines was progressing along a trajectory that would lead it to intersect the reference pattern at a higher probability location thereof.
With the foregoing review in mind, attention is now turned to a before the fact, of a photon or particle impinging on a screen (SC) (SC), approach to arriving at the same result as described in the foregoing after the fact approach. This results from focusing on application of Chaos properties to photons or particles that pass through a slit of a double slit system. That is, the foregoing after the fact approach utilizes a reference pattern and looks at the situation after the fact of a photon or particle impinging onto a test screen, while the following looks at situation before a photon or particle impinges on a screen in formation of an interference, in light of Chaos effects at a slit. Turning now to
However, this is simply a limits of experimental equipment objection. With a sufficient vacuum present in the experimental system, and with the Test Screen (SC′) placed at the smallest possible distance from the Slits (SLL) (SLR) which is consistent with formation of an interference pattern, this objection is not considered to be fatal to the proposal herein.
Finally, as Science always seeks experimental verification of any theoretical proposal, it is suggested that a verifying experiment could be performed with a double slit system comprising a test screen (SC), (not the slits as proposed and rejected in Feynman, mounted so that it can, in a monitorable manner, move to both the left and right, and return to a central location between tests. If a test particle impinges upon such a screen it will impart its lateral momentum thereto and the screen will move. Further,
It is also proposed that a particle impacting a screen (SC′) which can move along a trajectory perpendicular thereto might also provide an approach to measuring position and momentum substantially simultaneously. The position will be indicated by the point of initial impact, and momentum by screen (SC′) movement. If a screen (SC′) could be constructed to allow combined lateral and perpendicular motion, that would also provide a valuable experimental tool.
Two approaches point to the conclusion that it is possible to know which slit of a double slit system it is more likely that a photon or particle (having known, with certainty, momentum as it approaches the slits), passed in the formation of an interference pattern. One approach is termed after the fact and the other before the fact, (of a photon or particle impinging on a test screen). The after the fact approach involves application of a reference interference pattern, at least in derivation of the approach, and is based on observing where, in an emerging interference pattern, a photon or particle contributes thereto, (ie. where a photon or particle impinges on a test screen). The before the fact approach looks to chaos effects, based on where a photon or particle is within the width of a slit it passes through, and how a photon or particle passing through a slit is encouraged by interfering wavelets from the two slits to proceed toward one or another of the peak regions in an interference pattern. Both approaches lead to the same conclusion that it is more likely a photon or particle passes through the left slit (as viewed from the source thereof), of a double slit system, if it contributes to a positive slope region of a formed or forming interference pattern, and it is more likely that the photon or particle passes through the right slit if it contributes to a negative slope region thereof. An experiment, which could allow simultaneous measurement of particle position and momentum to test the proposal, is also suggested. Further, the Heisenberg Uncertainty Principle as conventionally presented, is an Absolute. That is, if one knows, for instance, the position/momentum of a photon or particle exactly, then the uncertainty in the knowledge of its momentum/position is infinite. It is suggested that this is not valid and that consideration of system-specific characteristics in a double slit setting can allow one to know more about the location and momentum of a photon or particle which contributes to formation of an interference pattern therein, than is allowed by the Heisenberg formulation. This is in the form of an improved knowledge of which slit (SLL) (SLR) it is ---more likely--- that a photon or particle passed when it contributed to formation of an interference pattern. It is suggested that a physical system-specific approach to reformulating the uncertainty principle should be considered in other physical systems as well. An experiment, which, if physically possible, could overturn uncertainty is also disclosed.
Finally, even Einstein rejected Quantum Mechanics, believing it was incomplete. Perhaps the foregoing points a pathway to “completing” the topic by adding system-specific particle considerations, to the wave considerations which so very accurately predict an interference pattern, but say nothing as to what a panicle is doing.
Having hereby disclosed the subject matter of the present invention, it should be obvious that many modifications, substitutions, and variations of the present invention are possible in view of the teachings. It is therefore to be understood that the invention may be practiced other than as specifically described, and should be limited in its breath and scope only by the Claims.
This application is a CIP of Ser. No. 12/806,521 Filed Aug. 16, 2010; and of Pending application Ser. No. 12/387,450 Filed May 4, 2009, and there via Claims Benefit of 61/211,514 Filed Mar. 31, 2009. This application also directly Claims benefit of 61/397,156 Filed Jun. 9, 2010 and directly Claims benefit of 61/399,165 Filed Jul. 8, 2010 and of 61/458,596 Filed Nov. 29, 2010, 61/464,123 Filed Feb. 28, 2011 and of 61/465,856 Filed Mar. 26, 2011.
| Number | Date | Country | |
|---|---|---|---|
| 61397156 | Jun 2010 | US | |
| 61399165 | Jul 2010 | US | |
| 61458596 | Nov 2010 | US | |
| 61464123 | Feb 2011 | US | |
| 61465856 | Mar 2011 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 12806521 | Aug 2010 | US |
| Child | 13066755 | US | |
| Parent | 12387450 | May 2009 | US |
| Child | 12806521 | US |
