IACS Institutional Repository

Dhara, Asish K

Ghosh, Swapan K

Operator Equation of Motion in Phase Space and Path Integral Solution to Time-Dependent Systems Possessing Invariants : Application to Time-Dependent Harmonic Oscillator

Chattopadhyay, Sudip

Mahapatra, Uttam Sinha

Chaudhuri, Rajat K

Study of Isolated 1 : 1 Al<SUP>+3 </SUP>.He Complex Using Many-Body Perturbation Theory : A Multi-Reference Approach

Indian I Phys. 81 (12), 1323-1324 (2007) 
Q^RTHCOMING PUBLICATIONS 
Volume 82, (2008) 
Review 
A forgotten variational principal 
BHARAT SINGH 
Astrophysics, Atmospheric & Space Physics 
Periodicity of - 155 days in solar electro fluence 
PARTHA CHOWDHURY, P C RAY AND SAIBAL RAY 
Structural and magnetic properties of Pb4+ substituted Li-ferrites 
M C SABLE, S K VYAWHARE, B K LABDE AND N R SHAMKUWAR 
A study of superconducting order parameter fluctuation effects 
in Dy203, Eu203 and P r ^ substituted compounds 
S BHATTACHARJEE AND B BAISHYA 
Critical behaviour of the thermodynamics quantities near the 
melting point in the solid phase of hexadecane 
H YURTSEVEN AND O TILKI 
Luminescence properties of RE3+ (Eu3+, Sm3+ and Dy3+) doped 
LiNbO3 ceramic powders 
A SREENIVASULU, T N V K V PRASAD AND S BUDDUDU 
High throughput structure determination for single-wavelength 
laboratory X-ray source anomalous diffraction data sets using 
iodinated tyrosines 
S SELVANAYAGAM, D VELMURUGAN, T YAMANE AND A SUZUKI 
1324 Forthcoming Publications 
General Physics 
The effect of anisotropy and external magnetic field on the thermal 
entanglement in two spin-one systems 
S Y MIRAFZALI AND M SARBISHAEI 
Particle Physics 
Spontaneous symmetry breakdown and critical perspectives of 
Higgs mechanism 
NILS M BEZARES-RODER AND HEMWATI NANDAN 


Forthcoming Publications

Sahu, Devendra K

Khare, P K

Yadav, V S

Steady State Conduction Current of Polyvinylidene Fluoride Film Electrets

Sachs, Mendel

fl/ote 
Indian J. Phys. 82(7) 907-911 (2008) CD 
On entropy and objective reality 
Mendel Sachs 
Emeritus Professor of Physics, University at Buffalo, State University of New York, USA 
E-mail : msachs@buffalo.edu 
Received 30 January 2008, accepted 14 March 2008 
Abstract : This essay discusses Schordinger's answer to his question "What is Life?" in terms of negative 
entropy, as a thermodynamic description, rather than a fundamental explanation. Discussion is given to explaining 
a life system as an objective reality. 
Keywords : Biology, entropy, quantum theory 
PACS Nos.: 03.65.-w, 05.70.-a, 87.10.+e 
Erwin Schr6dinger wrote an interesting essay entitled : "What is Life?" [1]. He calls for 
a different type of physical force to explain the maintenance of a living organism in 
terms of 'negative entropy'. 
The idea is this : According to the second law of thermodynamics, an initially 
ordered system, such as the union of a male sperm cell and a female egg, starts the 
process of continued cell division and duplication (mitosis), eventually resulting in a 
living entity that continues a lifespan until its expiration, at death. Accompanying the 
process of cell division and growth is the emergence of the ordered system proceeding 
toward increased disorder. This is described by the increase of entropy (disorder) until 
equilibrium is reached, at maximum entropy, which occurs at the death of the living 
being. In regard to human beings, the lifespan is normally much greater than the time 
of normal decay of a complex system to equilibrium. 
The question is : How does this living organism maintain its lifespan? 
Schrddinger's answer is : 'negative entropy'. That is, there is negative entropy because 
of the metabolic process of transferring energy from the outside of the living organism, 
such as intake of food, air, and so on. The disorder of the system is then decreased 
during one's lifespan. This negative entropy slows down the process that nevertheless 
© 2008 IACS 
908 Mendel Sachs 
eventually reaches the equilibrium state, (maximum entropy) at death, In accordance 
with the second law of thermodynamics. 
The concept of entropy is fundamentally explained in physics in terms of a 
statistical feature of a many-body system, such as the complex molecular system of 
a human body. But does this statistical law, expressed as the second law of 
thermodynamics, really explain the life process? Does it answer Schrodinger's question : 
What is Life? in fundamental terms? 
I don't believe so. In his book [1], Schrodinger (I believe correctly) denies the 
validity of the assertion that "all physical laws are based on statistics". As he says : 
"the order of the solar system, the motions of the planets, is maintained for almost 
indefinite time. The calculations do not imply any statistics; they are based solely on 
Newton's law of universal attraction. Nor does the motion of a good clock appear to 
have anything to do with statistics". 
As I have discussed elsewhere [2], there are two stages to scientific inquiry. 
The first is the descriptive stage. The laws of statistics applied to a physical system 
are in this category. But the descriptive stage of science is not the goal intended by 
the scientist. It must lead to an explanatory stage. This is the stage of discovering the 
fundamental principles that underlie the empirical aspects of science. 
Consider, for example, the subject of molecular biology. Fundamental principles 
{i.e. universal) are at first speculated, based on hints from the empirical facts, and 
with the further use of one's intuition, a theory is formulated, leading to the role of the 
DNA molecule, and so on. This theory then leads to particulars that relate to the 
empirical data. If these agree with the actual experimental facts, then one may say 
(at least contingently!) that the theory is an explanation that is scientifically true. 
The adjective "scientifically" implies that this is only a contingent truth — it is 
subject to refutation. This is the way that we discover truth in any scientific endeavor 
— be it physics, chemistry, or molecular biology. We proceed to the truth by 
successive approximations in the different periods of science, continually refuting ideas 
based on new empirical evidence that does not support the older ideas and continually 
accepting new ideas. I believe that the history of science is evolutionary rather than 
revolutionary. There are threads of truth that do persist from one period of normal 
science to the next (to use T S Kuhn's terminology [3]). Thus the history of science 
reveals a positive flow in our continued understanding of nature. 
On Schrddinger's question: What is Life?, I don't believe that his thermodynamic 
argument about 'negative entropy* is an explanation for the life process. Of course, the 
thermodynamic description is true, but it is only at the descriptive level. That is to say, 
this is a subjective statement about an objective reality. What the scientist wants to 
get to, eventually, is a fundamental explanation of the objective reality, independent of 
our subjective knowledge. 
I believe that Schr6dinger was stimulated to look into this biological question by 
his pioneering research on the physics of quantum mechanics. This is a statistical 
On entropy and objective reality 909 
theory of the microdomain of matter. Thus, quantum mechanics is a subjective 
description rather than an objective description. It is then understandable that the 
quantum theory is not intrinsically explanatory. 
The eminent theoretical physicist, Richard Feynman, expressed the fact that 
quantum mechanics is not an explanatory theory in physics when he said the following 
about this subject [4] : 'The next question is, will you understand what I am going to 
tell you? {i.e. does quantum mechanics explain nature?) No, you are not going to be 
able to understand it. It is my task to convince you not to turn away because you 
don't understand it. You see, my physics students don't understand it either. That is 
because I don't understand it. Nobody does". 
It is my assertion that nobody understands quantum mechanics, i.e. as an 
explanation, because it is a purely statistical theory. It is not supposed to be 
explanatory in the first place - it does not yield any fundamental understanding in 
physics. It is purely descriptive. 
As an example, consider the toss of a coin. It flip-flops into the air, turns 
around, falls toward the ground and then lands. What is the probability that it will land 
head? Because the head and tail are two equally weighted sides of the coin, the 
probability that it will land head is 1/2. Empirically, this means that if the coin is 
tossed 1000 times, it will land head close to 500 times. 
But there is an objective path of the tossed coin. If I knew the initial force on 
it to start its motion upward, the force of gravity acting on it to make it return to earth, 
the forces of the air molecules that interact with the coin, etc., then I could find a 
unique solution of the equation of motion of the coin that predicts with certainty 
whether it will land head or tail. But I do not know all of these details, so I subjectively 
use a probability theory to determine the chance that it will land head. But the latter 
is not explanatory regarding the objective path of the coin! It is only descriptive. It 
does not mean that there is not an underlying objective path of the coin! 
Similarly, the entropy of a complex molecular system, such as a living human 
body, is a subjective feature about its state of disorder, according to our observations. 
Schrodinger's description of the living process in terms of negative entropy is then 
true, but not more than a subjective description. It is not an explanation, underlying 
objective laws of nature applied to the life process. 
Another example would be the universe itself — the subject of cosmology. Is it 
meaningful to talk about the entropy of the universe? I don't believe so since it is out 
of context! The universe is a closed system, by definition. Its physical nature is not 
tied to our lack of knowledge of its total intrinsic order. This is the order that underlies 
the dynamics of the entire universe. Our knowledge (or lack of knowledge) of the 
details of the universe — the planetary systems, the galaxies and their interactions, 
the expansion of the universe ... is in a different context than the laws of the universe 
itself. To say that a law of the universe is a law of thermodynamics is to confuse 
910 Mendel Sachs 
epistemology (a theory of knowledge) with ontology (a theory of what exists, independent 
of our knowledge of it). 
Einstein was a realist. He did not believe that the laws of physics are the laws 
of statistics. Most contemporary physicists are positivists — they believe that all that 
is necessary for the scientist to do is to describe. The latter is the reason for 
Feynman's assertion about quantum mechanics that "my task is to convince you not 
to turn away because you don't understand it. Nobody does". He then believes that 
a scientist should not try to explain a physical theory, such as quantum mechanics. 
It is sufficient to describe the facts of nature. This is the philosophical view of 
positivism. Einstein, on the other hand, did believe that the final stage of a scientific 
study is explanation of natural phenomena, in terms of first principles. It is the 
philosophy of realism. 
It is my firm belief that the 21st century will see a paradigm change in the 
philosophy of physics from positivism to realism. 
I should like to re-emphasize that I do not disagree with Schrodinger on the 
description of the life process in terms of negative entropy. My only stress is that this 
is not an explanation of life. That is to say, it does not derive the physical features 
of the life process from first principles. 'First principles' are not a mere correlation of 
facts. They are the premises that lead, by logical deduction, to the empirical facts of 
nature. Indeed, it is the 'first principles' that are our 'understanding' of the facts of 
nature. 
Schr&dinger agreed (as I have quoted in this essay), that the first principles of 
the laws of nature are not the rules of statistics. Though statistics plays an important 
role in the description of many body systems, I do not believe that Schrodinger (nor 
Einstein) thought that the fundamental laws of nature are laws of chance. 
Science is presently at a very early stage in the attempt to explain the life 
process. The best hope I see for this explanation is in the field of molecular biology. 
In this field of science we presently have accurate descriptions of the elements of a 
living system — the DNA molecule, its atomic constituents and its spiral configuration. 
But there is little understanding yet of the fundamental mechanisms, based on first 
principles, that underlie the life process. 
As a non-expert in the field of biology, I would like to speculate, as a physicist, 
on the problem of life. I am quite convinced (with Schrodinger and Einstein) of the 
truth of the continuous field concept in the laws of nature, in contrast with the 
atomistic model. Applied to molecular biology, the DNA molecule, as an element of a 
biological system, has a very large number of atomic constituents. Would it be 
possible to study this problem holistically, as a closed system, from the view of many 
continuous fields (one for each atomic constituent) but not in terms of singular atoms? 
The atomic model of DNA would entail the many-body problem — seeking a solution 
for an enormous number of coupled equations and their boundary conditions - an 
intractable mathematical problem. But in the holistic, field theory of the DNA molecule, 
On entropy and objective reality 911 
there are many coupled fields (each mapped in a single space, without the 
'entanglement' that Schrodinger refers to). This mathematical representation of a 
closed system is necessarily in terms of nonlinear differential equations. This is in 
contrast with the linearity of the quantum mechanical description of a many body 
system. The mechanism that we seek to explain the life process, may be in the 
mathematical solutions of such a nonlinear, holistic field theory of DNA. This indeed 
could be a start for an explanation of the life process. It is my speculation about the 
way of representing the fundamental mechanism of the life process, holistically rather 
than atomistically. 
References 
[1] E Schrodinger What is Life? (UK: Cambridge University Press) (1967) 
[2] M Sachs Concepts of Modem Physics: The Haifa Lectures (UK: Imperial College Press) (2007) 
[3] T S Kuhn The Structure of Scientific Revolutions (Chicago, USA: University of Chicago Press) (2nd edn) 
(1970) 
[4] R P Feynmam QED (USA: Princeton University Press) p9 (1985) 


On Entropy and Objective Reality

Mukherjee, Moitrayee

Mukhopadhyay, Anamika

Chakraborty, Tapas

Raman Optical Activity : A Novel Version of Chiroptical Spectroscopy

Indian J. Phys. 81 (7), 645-646 (2007) ^ ^ ^ 
INDIAN W 
JOURNAL <f 
PHYSICS 
Vol. 81 • No. 7 • July 2007 
INTENTS 
FrontTitle 639 
Advisory Board and Editors 641-642 
From Editor's Desk 643 
Front Contents 645-646 
Astrophysics, Atmospheric & Space Physics 
Rain attenuation at 13 GHz over the line of sight path situated between Panihati 
and Barrackpore in eastern India 
S K SARKAR, ANIL KUMAR, IQBAL AHMED, M M GUPTA, M V S N PRASAD, 
ARUN K DE AND J DAS 647-653 
Condensed Matter & Materials Physics 
Study of AC transport processes in RE(Y,Sm,Nd,Dy)BCO HTSC samples in the 
normal state 
B K MANDAL, N BHATTACHARYA, C NEOGY, S K DEB AND A NAG 655-664 
Dielectric relaxation studies of higher order alcohol complexes with alkyl acrylates 
using time domain reflectometry 
F LIAKATH ALI KHAN, P SIVAGURUNATHAN, G SHAKIL MUHAMMAD AND 
SCMEHROTRA 665*72 
Nonlinear Dynamics & Complex Systems 
Numerical investigation on hydrodynamic developement length of gaseous flow in 
parallel plate micro channel 
NIRMALYA BAYAL, ARUNABHA CHANDA AND ASIS MAZUMDAR 673-681 
[ Cont'd, on next page ] 
g4g Contents 
Nuclear Physics 
Calculations of longitudinal form factors of p-shell nuclei, using enlarged model 
space including core-polarization effects with realistic two-body effective interaction 
R A RADHI, A K HAMOUDI AND K S JASSIM 683-695 
Low-lying states of 11Be and 15C 
SABYASACHI MAHAHPATRA 697-703 
Electric dipole transitions for some excited states in neutral silver 
LEYLA OZDEMIR, BETUL KARACOBAN AND GULDEM URER 705-715 
Erraticity moment of bin multiplicity and rapidity gap of fast TFs from MKr-Ag/Br 
interaction at 0.95A GeV/c 
B BHATTACHARJEE, B DEBNATH, A MUKHOPADHYAY AND S SENGUPTA 717-726 
Optics & Spectroscopy 
Infrared studies on hydrogen bonding interaction between alkyl esters and p-cresol 
in carbon tetrachloride 
F LIAKATH ALI KHAN, P SIVAGURUNATHAN AND S RAJA MOHAMED KAMIL 727-736 
Forthcoming Publications 737 
Notes for Contributors 739-742 
Our Special Publications 743-744 


English

Front Contents

Bhattacharya, R

Das, R

Guha, R

De, S

Bhattacharya, A B

Blue Jet Models and Associated Lightning Flashes

Mahajan, Madhurika

Chakravarty, Tapas

Khah, Sunil K

Indian J. Phys. 81 (8), 787-792 (2007) 
Analysis of ferrite based planar array of rectangular patch 
microstrip antenna in X-band 
Madhurika Mahajan, Tapas Chakravarty and Sunil K Khah'1 
Department of Physics, Jaypee University of Information Technology, 
Waknaghat, Dist-Solan-173 215, Himachal Pradesh, India 
E-mail sunil_khah(5>rediffmail com 
Received 30 December 2006, accepted 18 July 2007 
Abstract Analysis planar array of rectangular microstrip patch based on ferrite substrate has been 
carried out in X-band of Microwave Frequency range. The analysis is based on the vector wave function 
approach and pattern multiplication method Radiation characteristics like Patterns, Radiation conductance, 
Directive gam and radiated quality factor are computed and presented The results are significant and suitable for 
high frequency communication system. 
Keywords • Planer array, microstrip antenna, ferntes 
PACS Nos. 80 40 Ba, 52.40.Fd 
1. Introduction 
Printed microstrip antennas are widely used in phased-array application because they 
exhibit a very low profile, small size light weight, low cost, high efficiency, easy methods 
of fabrication and installation. Microstrip antennas highly suffer from an inherent limitation 
of narrow bandwidth. Array of elements is the remedy to the bandwidth limitation. Different 
types of arrays are used to enhance bandwidth [1-3]. The scanning of radiation properties 
can also be increased by changing the progressive phase difference between the elements. 
Microstrip antennas on ferrite substrate provide the ability to control the radiation 
characteristics of microstrip antennas [4]. In this communication the analysis of 4 x 4 
planar array rectangular microstrip antenna is carried out. The antenna properties are 
computed for normally biased Ferrite substrate (YIG). For the comparison of the analyzed 
geometry, the same geometry is analyzed with RT Duroid substrate. It is observed that 
the antenna properties are enhanced considerably. 
* Corresponding Author 
©2007IACS 
788 Madhuhka Mahajan, Tapas Chakravarty and Sunil K Khah 
2. Theory 
The planar antenna array of rectangular patch and its co-ordinate system is shown in 
Figure 1. The array consists of equally spaced rectangular patches of length '/.'and width 
lW of height 'ft' in a matrices pattern of 4 x 4. 
Figure 1. Geometry and co-ordinate system of array antenna. 
The radiation field equations are obtained using vector wave function technique and 
pattern multiplication approach [2]. The total field equation are given as 
.n exp(- /j3nr) 
Eet=-F I o ;4y0aexp {,w \ sin© xcos f«*« 
V 
xAF. 
/ 
(1) 
E„ = jn exp 4V0a exp j - sine > 
sin 
PoW) COS0 
((PoW) . 
sine 
x A F . (2) 
COS0 
where A.F. is the array factor for antenna. 
Analysis of ferrite based planar array etc 739 
2.1. Field patterns: 
The total field patterns R(6t0) is obtained from the relation 
fl(0,0) = |Ej2+|E0f |2. (3) 
The value of F?(0,0) are computed for f = 10 GHz, dx = dy = 1.5 cm, Px = py=— and 
phase propagation constant k = 7.12 cm""1. The results are calculated and plotted for 
rectangular planar array microstrip patch antenna with YIG substrate and RT Duroid. 
2.2. Radiation conductance: 
By integrating the poynting vector over a large sphere the expression for radiation 
conductance of the array geometry may be expressed as 
V2 a - S W 
where Pr is the Power radiated for rectangular antenna 
2nn 
'=AjJcos2 p ^ s i n f l 
0 0 I, J 
W ^ c i n f l U o e 2 M ^ cinA vtAPp COS 
V 
sine x.(APf sinOdOdp 
v__ / 2 nexp(-2yftr) 2 2 
here A ~ 1 yz ,2,2 x i °Vo a 
« r 
2.3. Directive gain: 
The directive gain of the antenna in a given direction is defined as the ratio in radiation 
intensity U in the direction to the average radiated power Pr. It is expressed as 
Dg= f-S (5) 
Me = R(e,<f>) = \Egtf+\EH\2, 
2nn 
/= f [Mesin0xcf0xd0, 
0 0 
790 Madhurika Mahajan, Tapas Chakravartyand Sunil KKhah 
2A. Radiated quality factor : 
QR is the total quality factor, given as 
0 * = 2 7 r ' r - ~
 ( 6 ) 
where Pf is the radiated power, WT is the total energy stored 
and WT = 1 ere0h j\Ezfdxdy. 
3. Results 
The results presented in this paper are for the operating frequency of 10 GHz. The ferrite 
substrate used is unbiased. The progressive phase excitation difference between the 
71 
elements of array is taken as Px = Py = — . The dimensions are calculated for both ferrite 
and dielectric. The dimensions of the patch are given as (i) for ferrite (YIG) width 'IV = 
0.5303 cm and length T = 0.4412 cm, (ii) for dielectric (RT Duroid) are width lW = 1.936 
cm and length lU = 1 cm. The height of the substrate is '/? = 0.159 cm. For these input 
parameters the radiation patterns are calculated and plotted in Figures 2 and 3 for both 
substrates. 
-YIG 
RTDuroid 
-90 -70 -50 -30 -10 10 30 50 70 90 
100 
-200 
-300 
^00 
Angle(Degrees) 
Figure 2. £-Plane field pattern of array (on both YIG and RT Duroid base). 
Analysis of ferrite based planar array etc 791 
-90 -70 -50 -30-10 10 30 50 70 90 
0 
-50 
-100 
Sf -150 
^ -200 
P -250 
-300 
-350 
-400 
Angle( Degrees) 
Figure 3. H-Plane field pattern of array (on both YIG and RT Duroid base). 
Other radiation properties such as radiation conductance, directive gain and radiation 
quality factor are computed for YIG and are reported in Table 1. For comparison the same 
properties are computed and reported in the same table. 
Table 1. Calculated values of antenna parameters of array geometry. 
S.No. Antenna parameters Ferrite based array Dielectric based array 
1. Dimensions of the patch (cm) W = 0.5303 W = 1.936 
i_ = 0.4412 L=1 
2. Radiation conductance (mho) 1.3 x 10^ * 4.3 x 10~5 
3. Directive gain (dB) 3.95 2.31 
4. Radiated quality factor 231.07 31.26 
4. Conclusions 
The antenna designed on the YIG ferrite has shown enhanced properties over normal 
dielectric substrates. From the Table 1 it is evident that the size of the patch is 
considerably reduced when designed on ferrite substrate. This reduction would have a 
wide use in creating miniaturization of antenna. The field patterns change. There is marginal 
change in H-plane. But E-plane changes considerably. The numbers of minor lobes are 
reduced when designed on ferrite substrate. The radiation conductance, directive gain and 
radiation quality factor are enhanced considerably. Radiation conductance is multiplied by 
a factor of 3, directive gain is increased by a 35%, while as radiated quality factor is 
increased by a multiple of 7. From the results it is concluded that apart from conventional 
w * 
x 
* 
* * 
792 Madhuhka Mahajan, Tapas ChakravartyandSunilKKhah 
advantages of ferrites, the overall efficiency and characteristics of array are enhanced. 
These results are significant for design antenna setups for satellite communication. 
References 
[1] C B Balanis Antenna Theory Analysis and Design (New York : J. Wiley & Sons) (1982) 
[2] I J Bahl and P Bhartia Microstnp Antennas (Norwood MA : Artech House) (1980) 
[3] Sunil K Khah Indian J. Phys. 78B(1) 71 (2004) 
[4] P K S Pourush and L Dixit IEE Proc. Microwave Antennas Propag. 47 2 (2001) 


Analysis of Ferrite Based Planar Array of Rectangular Patch Microstrip Antenna in X-Band

Front Title

Indian Association for the Cultivation of Science

Not a member yet