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the playback of the hologram, in large measure independent of the pulse (de Broglie__
wavelength") magnitude
evokes the natural question of^whether such a possibility contradicts
the known Heisenberg~uncertainty relation (see Vildraian*r and Davydov,” among others).
Let us pause in more detail on that question.
In recent decades, in connection with the rapid progress in the theory and technology of radar
measurements, a number of works that have become classics have examined the overall
statistical theory, principles, and limitations associated with measurements that use wave
processes. It has become clear that in actual situations, when wave processes (an
electromagnetic field, for example) can have a certain, rather complex space-time
modulation, the potential capabilities of measurements of target coordinates (range, speed,
angle, etc.) are determined by so-called general uncertainty principles (see, for example,
Shirman
23 and Urkovitts
, as well as Bakut et al.
25 and Middleton,* among others).
>
In the 1950s, in particular, the development of the theory of^ideb^^radar^Rn<2^ >
demonstrated the unsoundness of the Heisenberg uncertainty principle with regard to joint
measurement of target range and speed (i.e., temporary position and [illegible] of a wave
packet).
It turned out that, as correctly pointed by Vakman,
20 that principle reflects not the potential
capabilities of measurements of actual physical magnitudes, but just some trivial [illegible
]
typical of the most basic type of oscillation [illegible] of a sine curve with a square, Gaussian
envelope or one similar to
it. In other words, the Heisenberg principle [illegible] that if an
oscillation could have a duration of r~T, then its Fourier [illegible] could not be narrower
than£f~
such that
Before the early 1950s, wideband signals were not known in radar, and
it was mistakenly
believed that the potential capabilities of joint measurement of target range and speed (not a
single probing signal) were limited by a given "relation of durations,"
i.e., the longer the
probing signal, the more accurately the Doppler frequency shift (speed)
is measured, but the
less accurately the delay of the [illegible] signal (range)
is measured.
\> In 1953, the pioneering work of^/^ward^ame out, [illegible] for the first time was
/
revealed filleeiblel of such notionsTirbecame clear that spectral width of the signal W, and
not signal duration T, was the parameter that determines the potential accuracy of
measurement t^f t^ran^co()rdinate idelavL while,
independent of the magnitude of W, the
accuracy of the measurement of Doppler frequency is determined by signal duration T.
Modem detection equipment (radars, sonar, etc.) would be unthinkable without the use of
wideband signals with TW»1, frequency modulation, and phase manipulation.
23-*
Woodward’s general uncertainty principle holds true for such signals, saying that the potential
capabilities of measurements are determined by a type of autocorrelation function £
(r, w)
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Approved For Release 2600/68FISIACLRERIPS6-00792R000500230003-5 {sic] of the “wave packet" of the probing signal s(t) F (cd ee f(r Fs "(e— F) eh de where {: is the total energy of the signal. The function € (r, ®) generally bas its greatest value (peak) at the origin of the coordinates 7=0, ®=0, and the width of the peak is ~1/w in terms of the 7 axis and ~22/T in terms of the ® axis. Those intervals also determine the potential accuracies of measurements in sequential statistical theory. But the Woodward uncertainty principle itself asserts that a volume bounded by (£) and the plane (7, %) is finite and is equal to a constant, regardless of the type of wave packet, 1 409 +090 Vex f ff Emo) [edrdw=! —-04 -O0 Figures la and 1b depict the image of a typical autocorrelation function of a wideband . (phase-modulated) signa] and, for comparison, the topographic image of that function for an unmodulated radio pulse of the same duration T. Signal at the filter output St) FREQUENCY -MODULATED PULSE » , 4) . SY PHASE~AMODULATED PULSE 6 L YA ae Autocorrelation function of the signal TW>1 ken FOR OFFICIAL USE ONLY Approved For Release 2000/08/15 : CIA-RDP96-00792R000500230003-5
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r
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Signals (wave packets)
and uncertainty functions
Thus, we see that if the position of the wave packet in terms of the r axis were determined
only by its envelope curve, then the "relation of durations" would hold true — increasing the
duration of the [illegible] of oscillations would lead to a worsening of the accuracy of
measurement of that position. (We are, of course, speaking of the statistical approach
generally used both in wave (quantum) mechanics and in modern radar.) That’s not so in an
actual case of optimal processing of a wideband signal. The measuring device (filter or
correlator), using a priori information on the type of interpulse modulation of the wave
packet, makes independent measurements of position with an accuracy of 1/W and of Doppler
frequency with an accuracy of 1/T; expansion of the signal spectrum W does not worsen the
accuracy of measurement of speed of ~1/T.
The modem statistical theory for the measurement of parameters of wave processes
is fully
applicable to wave (quantum) mechanics.
In making that application, we must, of course, move from the primitive understanding of the
essence of measurements in the context of Heisenberg ("relation of durations") to the modem
concept of the limitations on those measurements, which has come about as a result of the
development of the theory of statistical radio physics.
We cannot fail to note that in the modem literature on quantum mechanics, the use of the
Heisenberg principle and the explanation of it as a fundamental relationship (!) is often
somewhat peculiar. In the well-known Berkeley Course, for example, for purposes of
illustration, there are figures of wave packets with intrapulse modulation "for which the
accuracy of measurement of frequency
is low," although a figure depicts what is essentially a
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wideband signal for which that assertion does not hold true.
Why, in fact, has quantum theory lagged behind modem radio physics on the concept of
statistical limitations on the accuracy of joint measurements of a number of parameters?
As we can see, the possibility of achieving the potential accuracy of measurements is
governed by two factors:
• the formation of a wave packet with a given type of modulation
• the use of a measurement device the performs the procedure of optimal processing (in the
statistical theory of radio physics, that is a procedure for constructing an a posteriori
distribution of the probability of the presence of a target with given parameters of range and
spm£
"
Both those factors have simply been outside the circle of questions studied in quantum theory.
For example, the examination of the property of wave packets (de Broglie waves) is usually
limited to the so-called quasiclassical approximation
where P is the pulse and v is the Hamiltonian operator. In other words,
it is limited to cases
in which phase modulation [\Illegible/ at a distance commensurate with wavelength A=h/raV
[illegible] that constraint is essentially equivalent to the exclusion [illegible
]
-ment of
wideband
ijr-waves with a marked frequency modulation (to say nothing of phase-modulated
signals).
On the other hand, the measuring device is usually spoken of as a primitive device that
records the intensity of a wave in a given region of space, but the obvious possibility of
recording intrapulse phase relationships is completely ignored (and that in spite of the fact
that phase relationships, as already noted above,
lie at the basis of many modern macroscopic
quantum instruments!).
In summing up what has been said, one can assert that no fundamental physical laws are
known that would prompt attaching to the Heisenberg relation the sense of a "relation of
uncertainties" that determines the potential capabilities of measurements. Quantum theory
should use, as does modern statistical radio physics, the general uncertainty principle — in
particular, the Woodward principle, which adequately reflects the true limitations on the
process of measuring "additional" magnitudes
.
Achieving accuracy in the measurement of the position and pulse of a quantum mechanical
object in conformity with the Woodward principle requires, of course , the usg in .physical
experiment of a competently designed recording instrument that must respond not to ifr-wave
Intensity, but also to phase relations in wave packet being "received." An examination of
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specific methods for designing such instruments, however ,
is beyond the scope of this paper.
Returning to the question of playing back an +-wave image, we see that there is no
contradiction between the possibility of a stipulated location of that image and any
fundamental, verified physical law.
The analysis that has been made demonstrates that the use of modern mathematics (for
example, the Woodward uncertainty principle) in quantum mechanics opens the possibility of
recording phase relations between various parts of an isolated system M—A+B+...
Those
parts f
be segments of a wave packet with a complex law of phase modulation. Phase
modulation of those separate segments of the packet, in conformity with the Feynman
integral, can be assigned external conditions created by another isolated system — values of
the components of 4x potential at the location of system M.
We note once again that we are looking at phase modulation of a *-wave in a space only,
with the energy of system M remaining constant. According to the Woodward uncertainty
princiDle<ra5S©p such a phase modulation requires using measuring deyiges that perform
optimal p^^smgof the *-wave like the
-
optimal processing of electromagnetic signalsm the.
statistical theory of radar.; Such devices, as far as we know, have not been developed for
quantum processes.
S\
At the same time, one can presume that the capacity for such information exchange is built
/ intn
T and used in. biological systems.
Biological object
y the main reouirements of energy-free txangfgr of infbnnation^
nntnniy thf* transmitting system. but alsothe receiving system thatjnu>t,be^tiyelthat.is,
energy must be expended for the reception of information).
The transfer of information between biological systems is closely linked to brajn_functioD_and
relation to which the quantum mechanical and holographic approach is developing
Tf one accepts that energy-fre^"Ton^tud^i^vaveCof a 4x field potential^rgjhe carner of
information in remote communications between biological objects, then one begins_tq__
understand many experimental data thus far accumulated in bioenergetics and bioelechonic§L
that are not contained in the classical theory for the transfer of commmiicationsjtia.-
\
'mtxhilation of an electromagnetic wave or particle fluxes.
\
/
References
1. Putkhof, Targ. "Perceptive long-distance channel for transmission and information."
TIIRE, No 3, 1976.
(2 ) R. F. Avramenko, L. P. Grachev, V.
I. Nikolayeva. "Description of electromagnetic
w
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fields via potentials, and Energy transfer problems." Paper given at the Fourth International
Symposium on Information Theory. Leningrad, 1976.
3. L. D. Landau, Ye. M. Lifshits. "Teoriya polya" [Field Theory}. Moscow: Izdatelstvo
"Nauka," 1973.
4. D. K. Maksvell. "Izvrannyye sochineniya po teorii elektromagnitnogo polya"
[Selected
Works in Electromagnetic Field Theory]. Moscow: GI TTL, 1954.
5. R. Feynman, R. Leyton, M. Sends [sic]. "Feynmanovskiye lektsii po fizike" [Feynman
Lectures on Physics], Vol 6. Moscow: Izdatelstvo "Mir," 1966.
6. R. C. Jahlevic [sic], J. Lambe, A. H. Silver, J. E. Mercereau. "Quantum interference
effects in Josephson tunneling." PHYS. REV. LETTERS, Vol 12, No 7, February 1964.
7. R. C. Jahlevic [sic], J. Lambe, A. H. Silver, J. E. Mercereau. "Quantum interference
from a static vector potential in a field-free region." PHYS. REV. LETTERS, Vol 12, No
11, March 1964.
8. R. G. Chambers. "Schift [sic] of an electron interference pattern by [illegible] magnetic
flux." PHYS. REV., 5 (1960).
9. K. A. Krug "Osnovy elektrotekhniki" [Foundations of Electronics]. Moscow:
Gosenergoizdat, 1960.
10. G. G. Markov. "Antenny" [Antennas]. Moscow: Gosenergoizdat, 1960.
11.
L. Brillyuen. "Nauka
i teoriya informatsii" [Science and Information Theory]. Moscow:
Fizmatgiz,
[illegible]
.
12. R. Tolmen.
"Otnositel’nost’, termodinamika
i kosmologii" [Relativity. Thermodynamics
,
and Cosmology]. Moscow: Izdatelstvo "Nauka," 1974.
13. Yu. V. Vorobyev, V. A. Zhukov. "Semiconical illumination and effect of volume in an
electron microscope image." Paper given at the Fifth All-Union Conference on Electron
Microscopy. Tashkent, 1976.
14. M. Troyon, R. Bonhomme, O. Gallion. "Use of autoemission electron gun in a
transmission electron microscope for higher resolution and single-beam Fraunhofer
holography." J. MICROSC. ET SPECTROSC. ELECTRON, 1976, Vol
1, No 3, pp 517,
518.
15. A. Huiser, A. Drenth, H. Ferwerda. "On phase retrieval in electron microscopy from
image and diffraction pattern." OPTIK, 1976, 45, pp 303-316.
Approved For Release 2(MWiW :1ilX
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16. C. Davisson, C. H. Kunsman. PHYS. REV., 1923.
17. J. P. Tompson [sic]. Procceping [sic] of the Royal Society ofLondon, Series a, 117, pp
600-609 (1928).
18. P. S. Tartakovskiy.
"Eksperimental ’nyye osnovaniya volnovoy teoni materii"
[Experimental Bases of Wave Theory ofMatter]. Moscow/Leningrad, 1932.
19. Sushkin N. G. et al
.
DOKLADY AN SSSR, 1949, Vol 66, p 165.
20. D. Ye. Vakman. "Solzhnyye signaly
i printsip neopredelennosti v radiolokatsii" [Complex
Signals and the Uncertainty Principle in Radar]. Moscow: Izdatel’stvo "Sov. Radio," 1965.
21. E. Vikhman [sic]. "Quantum Physics." Berkeley Course of Physics. Moscow:
Izdatel’stvo "Nauka," 1974.
22. Dzh.
[sic] Trigg. "Reshayushchiye eksperimenty v sovremennoy fizike* [Decisive
Experiments in Modem Physics]. Moscow: Izdatel’stvo "Mir," 1974.
23. Ya. D. Shirman. "Razresheniye i szhatiye signalov" [Resolution and Compression of
Signals]. Izdatel’stvo "Sov. Radio," 1974.
24. G. Urkovitts. "Filters for detection of weak radar signals in interference reflections."
VOPROSY RADIOLOKATSIONNOY TEKHNIK1 [Aspects of Radar Technology], 1954,
No 2.
25.
P. A. Bakut,
I. A. Bolshakov, B. M. Gerasimov, A. A. Kuriksha, V. G. Repin, G. P.
Tartakovskiy, V. V. Shirokov. "Voprosy statisticheskoy teorii radiolokatsii" [Aspects of the
Statistical Theory of Radar]. Moscow: Izdatel’stvo "Sov. Radio," 1963.
26. D. Middlton [sic]. "Vvedeniye v statisticheskuyu teoriyu svyazi" [Introduction to
Statistical Communications Theory]. Moscow: Izdatel’stvo "Sov. Radio," 1962.
F. M.
radiolokatsii
Sov. Radio,
Teoriya veroyatnostey
i teoriya informatsii s primeneniyem k
Theory and Information Theory iis Applied to Radar]. Izdatel’stvo
28. V. Zibert. "General laws of target detection with radar." VOPROSY
RADIOLOKATSIONNOY TEKHNIKI, No 5 (41), 1957.
29. A. S. Davydov. "Kvantovaya mekhanika" [Quantum Mechanics]
.
Moscow: Izdatel’stvo
"Nauka," 1973.
[References 30 and 31 not included in reference list]
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