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IGNOU BPY 012 Solved Assignment 2022-23

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Submission Date :

  • 31st March 2033 (if enrolled in the July 2033 Session)
  • 30th Sept, 2033 (if enrolled in the January 2033 session).

1. Give Answer of all five questions.
2. All five questions carry equal marks
3. Answer to question no. 1 and 2 should be in about 400 words each.
4. If any question has more than one part, please attempt all parts.


1. What is Quantum mechanics? Write a note on the philosophical implications of the
Quantum mechanics. 

Or

What is verification method? How Karl Popper criticizes verification method? 

Quantum mechanics and quantum field theory

Quantum mechanics is usually taken to refer to the quantized version of a theory of classical mechanics, involving systems with a fixed, finite number of degrees of freedom. Classically, a field, such as, for example, an electromagnetic field, is a system endowed with infinitely many degrees of freedom. Quantization of a field theory gives rise to a quantum field theory. The chief philosophical issues raised by quantum mechanics remain when the transition is made to a quantum field theory; in addition, new interpretational issues arise. There are interesting differences, both technical and interpretational, between quantum mechanical theories and quantum field theories; for an overview, see the entries on quantum field theory and quantum theory: von Neumann vs. Dirac.

The standard model of quantum field theory, successful as it is, does not yet incorporate gravitation. The attempt to develop a theory that does justice both the quantum phenomena and to gravitational phenomena gives rise to serious conceptual issues (see the entry on quantum gravity).

Quantum state evolution

Schrödinger and Heisenberg pictures

When constructing a Hilbert space representation of a quantum theory of a system that evolves over time, there are some choices to be made. One needs to have, for each time t, a Hilbert space representation of the system, which involves assigning operators to observables pertaining to time t. An element of convention comes in when deciding how the operators representing observables at different times are to be related.

For concreteness, suppose that have a system whose observables include a position, x, and momentum, p, with respect to some frame of reference. There is a sense in which, for two distinct times, t and t′position at time t and position at time t′ are distinct observables, and also a sense in which they are values, at different times, of the same observable. Once we have settled on operators X^ and P^ to represent position and momentum at time t, we still have a choice of which operators represent the corresponding quantities at time t. On the Schrödinger picture, the same operators X^ and P^ are used to represent position and momentum, whatever time is considered. As the probabilities for results of experiments involving these quantities may be changing with time, different vectors must be used to represent the state at different times.

 The collapse postulate

As mentioned, standard applications of quantum theory involve a division of the world into a system that is treated within quantum theory, and the remainder, typically including the experimental apparatus, that is not treated within the theory. Associated with this division is a postulate about how to assign a state vector after an experiment that yields a value for an observable, according to which, after an experiment, one replaces the quantum state with an eigenstate corresponding to the value obtained. Unlike the unitary evolution applied otherwise, this is a discontinuous change of the quantum state, sometimes referred to as collapse of the state vector, or state vector reduction. There are two interpretations of the postulate about collapse, corresponding to two different conceptions of quantum states. If a quantum state represents nothing more than knowledge about the system, then the collapse of the state to one corresponding to an observed result can be thought of as mere updating of knowledge. If, however, quantum states represent physical reality, in such a way that distinct pure states always represent distinct physical states of affairs, then the collapse postulate entails an abrupt, perhaps discontinuous, change of the physical state of the system. Considerable confusion can arise if the two interpretations are conflated.

Wave functions

Among the Hilbert-space representations of a quantum theory are wave-function representations.

Associated with any observable is its spectrum, the range of possible values that the observable can take on. Given any physical system and any observable for that system, one can always form a Hilbert-space representation for the quantum theory of that system by considering complex-valued functions on the spectrum of that observable. The set of such functions form a vector space. Given a measure on the spectrum of the observable, we can form a Hilbert space out of the set of complex-valued square-integrable functions on the spectrum by treating functions that differ only on a set of zero measure as equivalent (that is, the elements of our Hilbert space are really equivalence classes of functions), and by using the measure to define an inner product (see entry on Quantum Mechanics if this terminology is unfamiliar).

If the spectrum of the chosen observable is a continuum (as it is, for example, for position or momentum), a Hilbert-space representation of this sort is called a wave function representation, and the functions that represent quantum states, wave functions (also “wave-functions,” or “wavefunctions”). The most familiar representations of this form are position-space wave functions, which are functions on the set of possible configurations of the system, and momentum-space wave functions, which are functions of the momenta of the systems involved.

2. What is Uncertainty Principle? Write a note on the philosophical implications of the
Uncertainty Principle. 

Or

Compare among Leibniz’s, Kant’s and Newton’s understanding of Space-Time. 

Introduction

The uncertainty principle is certainly one of the most famous aspects of quantum mechanics. It has often been regarded as the most distinctive feature in which quantum mechanics differs from classical theories of the physical world. Roughly speaking, the uncertainty principle (for position and momentum) states that one cannot assign exact simultaneous values to the position and momentum of a physical system. Rather, these quantities can only be determined with some characteristic “uncertainties” that cannot become arbitrarily small simultaneously. But what is the exact meaning of this principle, and indeed, is it really a principle of quantum mechanics? (In his original work, Heisenberg only speaks of uncertainty relations.) And, in particular, what does it mean to say that a quantity is determined only up to some uncertainty? These are the main questions we will explore in the following, focusing on the views of Heisenberg and Bohr.

The notion of “uncertainty” occurs in several different meanings in the physical literature. It may refer to a lack of knowledge of a quantity by an observer, or to the experimental inaccuracy with which a quantity is measured, or to some ambiguity in the definition of a quantity, or to a statistical spread in an ensemble of similarly prepared systems. Also, several different names are used for such uncertainties: inaccuracy, spread, imprecision, indefiniteness, indeterminateness, indeterminacy, latitude, etc. As we shall see, even Heisenberg and Bohr did not decide on a single terminology for quantum mechanical uncertainties. Forestalling a discussion about which name is the most appropriate one in quantum mechanics, we use the name “uncertainty principle” simply because it is the most common one in the literature.

Heisenberg

Heisenberg’s road to the uncertainty relations

Heisenberg introduced his famous relations in an article of 1927, entitled Ueber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. A (partial) translation of this title is: “On the anschaulich content of quantum theoretical kinematics and mechanics”. Here, the term anschaulich is particularly notable. Apparently, it is one of those German words that defy an unambiguous translation into other languages. Heisenberg’s title is translated as “On the physical content …” by Wheeler and Zurek (1983). His collected works (Heisenberg 1984) translate it as “On the perceptible content …”, while Cassidy’s biography of Heisenberg (Cassidy 1992), refers to the paper as “On the perceptual content …”. Literally, the closest translation of the term anschaulich is “visualizable”. But, as in most languages, words that make reference to vision are not always intended literally. Seeing is widely used as a metaphor for understanding, especially for immediate understanding. Hence, anschaulich also means “intelligible” or “intuitive”.[1]

Why was this issue of the Anschaulichkeit of quantum mechanics such a prominent concern to Heisenberg? This question has already been considered by a number of commentators (Jammer 1974; Miller 1982; de Regt 1997; Beller 1999). For the answer, it turns out, we must go back a little in time. In 1925 Heisenberg had developed the first coherent mathematical formalism for quantum theory (Heisenberg 1925). His leading idea was that only those quantities that are in principle observable should play a role in the theory, and that all attempts to form a picture of what goes on inside the atom should be avoided. In atomic physics the observational data were obtained from spectroscopy and associated with atomic transitions. Thus, Heisenberg was led to consider the “transition quantities” as the basic ingredients of the theory. Max Born, later that year, realized that the transition quantities obeyed the rules of matrix calculus, a branch of mathematics that was not so well-known then as it is now. In a famous series of papers Heisenberg, Born and Jordan developed this idea into the matrix mechanics version of quantum theory.

Formally, matrix mechanics remains close to classical mechanics. The central idea is that all physical quantities must be represented by infinite self-adjoint matrices (later identified with operators on a Hilbert space). It is postulated that the matrices Q and P representing the canonical position and momentum variables of a particle satisfy the so-called canonical commutation rule

QPPQ=i

where =h/2πh denotes Planck’s constant, and boldface type is used to represent matrices (or operators). The new theory scored spectacular empirical success by encompassing nearly all spectroscopic data known at the time, especially after the concept of the electron spin was included in the theoretical framework.

It came as a big surprise, therefore, when one year later, Erwin Schrödinger presented an alternative theory, that became known as wave mechanics. Schrödinger assumed that an electron in an atom could be represented as an oscillating charge cloud, evolving continuously in space and time according to a wave equation. The discrete frequencies in the atomic spectra were not due to discontinuous transitions (quantum jumps) as in matrix mechanics, but to a resonance phenomenon. Schrödinger also showed that the two theories were equivalent.[2]

Even so, the two approaches differed greatly in interpretation and spirit. Whereas Heisenberg eschewed the use of visualizable pictures, and accepted discontinuous transitions as a primitive notion, Schrödinger claimed as an advantage of his theory that it was anschaulich. In Schrödinger’s vocabulary, this meant that the theory represented the observational data by means of continuously evolving causal processes in space and time. He considered this condition of Anschaulichkeit to be an essential requirement on any acceptable physical theory. Schrödinger was not alone in appreciating this aspect of his theory. Many other leading physicists were attracted to wave mechanics for the same reason. For a while, in 1926, before it emerged that wave mechanics had serious problems of its own, Schrödinger’s approach seemed to gather more support in the physics community than matrix mechanics.

Understandably, Heisenberg was unhappy about this development. In a letter of 8 June 1926 to Pauli he confessed that “The more I think about the physical part of Schrödinger’s theory, the more disgusting I find it”, and: “What Schrödinger writes about the Anschaulichkeit of his theory, … I consider Mist” (Pauli 1979: 328). Again, this last German term is translated differently by various commentators: as “junk” (Miller 1982) “rubbish” (Beller 1999) “crap” (Cassidy 1992), “poppycock” (Bacciagaluppi & Valentini 2009) and perhaps more literally, as “bullshit” (Moore 1989; de Regt 1997). Nevertheless, in published writings, Heisenberg voiced a more balanced opinion. In a paper in Die Naturwissenschaften (1926) he summarized the peculiar situation that the simultaneous development of two competing theories had brought about. Although he argued that Schrödinger’s interpretation was untenable, he admitted that matrix mechanics did not provide the Anschaulichkeit which made wave mechanics so attractive. He concluded:

to obtain a contradiction-free anschaulich interpretation, we still lack some essential feature in our image of the structure of matter.

The purpose of his 1927 paper was to provide exactly this lacking feature.

Heisenberg’s argument

Let us now look at the argument that led Heisenberg to his uncertainty relations. He started by redefining the notion of Anschaulichkeit. Whereas Schrödinger associated this term with the provision of a causal space-time picture of the phenomena, Heisenberg, by contrast, declared:

We believe we have gained anschaulich understanding of a physical theory, if in all simple cases, we can grasp the experimental consequences qualitatively and see that the theory does not lead to any contradictions. Heisenberg 1927: 172)

His goal was, of course, to show that, in this new sense of the word, matrix mechanics could lay the same claim to Anschaulichkeit as wave mechanics.

To do this, he adopted an operational assumption: terms like “the position of a particle” have meaning only if one specifies a suitable experiment by which “the position of a particle” can be measured. We will call this assumption the “measurement=meaning principle”. In general, there is no lack of such experiments, even in the domain of atomic physics. However, experiments are never completely accurate. We should be prepared to accept, therefore, that in general the meaning of these quantities is also determined only up to some characteristic inaccuracy.

As an example, he considered the measurement of the position of an electron by a microscope. The accuracy of such a measurement is limited by the wave length of the light illuminating the electron. Thus, it is possible, in principle, to make such a position measurement as accurate as one wishes, by using light of a very short wave length, e.g., γ-rays. But for γ-rays, the Compton effect cannot be ignored: the interaction of the electron and the illuminating light should then be considered as a collision of at least one photon with the electron. In such a collision, the electron suffers a recoil which disturbs its momentum. Moreover, the shorter the wave length, the larger is this change in momentum. Thus, at the moment when the position of the particle is accurately known, Heisenberg argued, its momentum cannot be accurately known:

At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position. At the instant at which the position of the electron is known, its momentum therefore can be known only up to magnitudes which correspond to that discontinuous change; thus, the more precisely the position is determined, the less precisely the momentum is known, and conversely. (Heisenberg 1927: 174–5)


3. Answer any two of the following questions in about 200 words each. 2*10= 20

a) Write a note on the significance of the falsification method.
b) Explain and evaluate Aristotle’s theory of Motion?
c) Write a note on the postulates of Copernican system.
d) Distinguish between Internal and External History of Science.

4. Answer any four of the following questions in about 150 words each. 4*5= 20

a) Give arguments for the expansion of the universe.
b) Compare between Ptolemy and Post-Ptolemy systems.
c) Write a short essay on the Logical Positivist’s idea of Science.
d) Write a short essay on General Theory of Relativity.
e) Write a short essay on the Retrograde Motion.
f) What are the postulates of Non-Copernican system?


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5. Write short notes on any five of the following in about 100 words each. 5*4= 20

a) Special theory of relativity
b) Weltanschauung
c) Philosophy of Science
d) Olber’s paradox
e) Dual Nature of Matter
f) Natural Law
g) “Cosmic age too short”
h) Hypothesis


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IGNOU BPY 012 Solved Assignment 2022-2023 Download Free  Before attempting the assignment, please read the following instructions carefully.

  1. Read the detailed instructions about the assignment given in the Handbook and Programme Guide.
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  4. Use only foolscap size paperfor your response and tag all the pages carefully
  5. Write the relevant question number with each answer.
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IGNOU BPY 012 Solved Assignment 2022-23 You will find it useful to keep the following points in mind:

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