Atomic Physics And Human Knowledge

by Niels Bohr

کتاب حاضر که دنبالۀ دو مجموعۀ آثار منتشرشدۀ پیشین است، سلسله‌ای از رساله‌هایی است، که نیلس بور در پنج سال آخر زندگی خود، یعنی از ۱۹۵۸تا ۱۹۶۲نوشته است. انتشار این مجموعه را پدرم طی سالیان پیش همواره در نظر داشت، امّا گمان می‌کرد که تا آماده‌کردن نوشتۀ “نور و حیات-یک‌بار دیگر” بازهم صبر کند. امّا اکنون این مجلّد، که دست‌نویس ناتمام آن را دربر دارد، منتشر می‌شود.

Genres: Science, Philosophy, Physics, Nonfiction, Essays, Metaphysics, Mathematics

112 pages, Paperback

First published January 1, 1958

About the author

Niels Henrik David Bohr (Danish pronunciation: [ni:ls ˈboɐ̯ˀ]) was a physicist who made foundational contributions to understanding atomic structure and quantum mechanic. Bohr mentored and collaborated with many of the top physicists of the century at his institute in Copenhagen. He was part of a team of physicists working on the Manhattan Project. Bohr has been described as one of the most influential scientists of the 20th century.

In 1922 Niels Bohr was awarded the Nobel prize in physics "for his services in the investigation of the structure of atoms and of the radiation emanating from them".

Bohr married Margrethe Nørlund in 1912, and one of their sons, Aage Bohr, grew up to be an important physicist who in 1975 also received the Nobel Prize.

Reviews

[Kin · Rating 4 out of 5]

I wouldn't say that i understand every chapter, but i consider it a good read though you're not familiar with physics since the book also deals with philosophical and cultural issues.

[Marily_p88 · Rating 4 out of 5]

Il faut s'accrocher à la lecture surtout au milieu mais c'est un plaisir finalement de lire les mots directs de celui qui a tenu tête à Einstein. L'édition fournit énormément d'information sur l'histoire de la physique quantique et les différents courants de la discipline.

[Bint E]

nothing

[J.D. Steens · Rating 1 out of 5]

I've seen references to this book regarding Bohr's thinking about the distinction between life and non-life, and I looked at his book from that perspective. Bohr states that physics has moved beyond the mechancal determinism that for so long defined post-Newtonian thought. There's no such determinism in quantum theory. Bohr does discuss the "finality" of life and its open-system nature that make life distinct from non-life matter and energy, but how (whether?) he sees key connections between life and quantum theory, I can't tell. Bohr is a turgid writer - not pompous, but stuffy and overly formal.

[Kyle · Rating 4 out of 5]

Glad I got to know more about the man who went toe-to-toe with Einstein in developing quantum theory that works, at least for the Copenhagenists. He has a lot of respect for the many different branches of science, but keeps the more mystical element at arms reach. Whatever can't be quantified isn't as important as the long history of disproving Aristotle's idea of perfection and purpose while transmuting ancient atomism into atomic physics.

[Nouru-éddine · Rating 3 out of 5]

::انطباع عام::
========

ربما كان ليس على نيلز بور أن يكتب: للأسف طريقة كتابته جافة جدًا وغير مريحة. عندما أقارن ما قرأته مع ستيفن هوكينج أو ميتشيو كاكو أو طبعًا كارل ساغان - أرى الفرق الشاسع في قدرة المذكورين على نقل العلوم المعقدة بطريقة إنسانية وأخاذة جدًا. في حين أرى أن نيلز بور لم تكن لديه تلك المهارة للأسف؛ حتى محاضراته المترجمة كانت رتيبة جدًا ولم تنقل إلى الكثير من المعلومات.
المفيد في الكتاب هو نقل الصورة التي تطورت بها ميكانيكا الكم والظروف التي نشأ فيها هذا العلم الذي لم يطرأ عليه أي تغيير من ساعتئذ.
أما عن جزء مناقشة الحياة البيولوجية وربطها بالفيزياء الحديثة فأرى أن كتاب ما الحياة؟ الجانب الفيزيائي للخلية الحية كان أكثر متعةً بكثير، وأسلوب شرودنجر في العرض كان أكثر بهجة من نيلز بور.
جاءت الترجمة من المهندس مصطفى العدوي فوق الممتازة كما عودنا في كل ترجماته العلمية.
***
::في سطور::
=========
هي مجموعة مقالات نُشرت عام ١٩٥٨ للفيزيائي نيلز بور، والتي تستكشف الآثار المعرفية لميكانيكا الكم والفيزياء الذرية على فهم المعرفة في مختلف المجالات. يجادل بور بأن المفاهيم التي كشفت عنها الفيزياء الذرية، مثل المكاملة، تتحدى المفاهيم التقليدية للسببية، ولها صلة واسعة بالثقافة الإنسانية، والفلسفة الطبيعية، والمشكلات الأساسية للحياة والمعرفة.

المكاملة: يطور بور مفهومه للمكاملة، الذي يشير إلى أن بعض الظواهر الفيزيائية لا يمكن فهمها إلا من خلال أوصاف متبادلة الاستبعاد ولكنها متساوية في صحتها، وهو مبدأ يوسع نطاقه ليشمل المجالات غير الفيزيائية.
حدود السببية: كشفت الفيزياء الذرية أن مبدأ السببية، الذي اعتُبر لفترة طويلة أساسًا لتفسير الظواهر الطبيعية، أضيق من أن يشمل الانتظامات الغريبة التي تحكم العمليات الذرية الفردية.
***
::وحدة المعرفة::
==========
المفكرين الهنود القدماء بالفعل فهموا الصعوبات لمنطقية في إعطاء تعبير شامل لمثل هذا الكمال، لقد وجدوا مهربًا من التنافُر الظاهر في الحياة من خلال التأكيد على عدم جدوى المطالبة بإجابة السؤال عن معنى الوجود، مدركين أنَّ أيَّ استخدامٍ لكلمة معنى" يعنى المقارنة، لكن مع أي شيء يمكننا أن نقارن الوجود كله؟ الهدف من حجتِنا هو تأكيد أنَّ جميعَ التجارِب، سواء في العلم والفلسفة أو الفن، التي قد تكون مفيدة للبشرية، يجب أن تكون قادرة على التواصُل بوسائل التعبير البشرية، وعلى هذا الأساس سوف نتناول مسالة وحدة المعرفة.
***
::الراصد والكون::
==========
"أجهزة القياس أصبحت جزءًا من التجربة، وليست عنصرًا مستقلاً بذاته."
"كل ما نطلق عليه حقيقيًا مكون من أشياء لا يمكن اعتبارها حقيقية."
"على مسرح الوجود العظيم نحن أنفسنا ممثلون ومتفرجون."
*.*.*.*.*

[Aaron Wenger · Rating 3 out of 5]

Hardly penetrable without a solid understanding of particle physics and the history of the science.

[Shubhang Goswami · Rating 4 out of 5]

A small book that can be read over a long flight.

Sit back, relax and let old uncle neil tell you stories about rutherford, the solvay conferences, and the very beginning of quantum. It sheds light on the famous personalities and the wonderul scientists involved in science in the early 20th Century.

The first essay is very tough to understand, he does not write so well I think, its just so difficult. Though it might be the translation from german. But its very informative!

(Neils Bohr loves using ‘as regards’ a lot, always threw me off reading this book!)

[William Bies · Rating 3 out of 5]

The collected philosophical writings of the great Danish quantum physicist Niels Bohr, aside from addresses to the contemporary physics community for which he is famous (vols. i and iv, reviewed here and here), contain two volumes on atomic physics and human knowledge: vol. ii (1933-1957) and vol. iii (1958-1962). These reproduce lectures for the general public which are of less intrinsic scientific interest than those found in vols. i, iv. Nevertheless it can be good at least to scan them in order to get an overview of Bohr’s mature views of topics of general philosophical interest. At just 101 resp. 100 pp. anyway, they won’t detain the reader for very long in any event. Back in the day scientists were not just experts in their field but also cultured men who would have thought about the implications of their work for society at large and have been in a position to have something worthwhile to say about it (Bohr’s is probably the last generation in which a statement such as this would hold true for the great majority of practicing scientists).

Let us jump around to consider what Bohr has to say in a more logical order and start with a lecture from 1954 on the unity of knowledge (pp. 67-82). In the first several pages, Bohr recounts how, in order to devise a physical theory applicable to the atomic domain, it proved necessary to relinquish the naïve perspective of classical determinism – familiar material to any student of physics, but then presses home his central point in this lecture:

As we shall now proceed to show, the epistemological lesson contained in the development of atomic physics reminds us of similar situations with respect to the description and comprehension of experience far beyond the borders of physical science, and allows us to trace common features promoting the search for unity of knowledge. (p. 74)

He turns first to biology, then to psychiatry. The key point to realize is summed up in the following two passages:

From a biological point of view, we can only interpret the characteristics of psychical phenomena by concluding that every conscious experience corresponds to a residual impression in the organism, amounting to an irreversible recording in the nervous system of the outcome of processes which are not open to introspection and hardly adapted to exhaustive definition by mechanistic approach. (p. 77)

Such considerations point to the epistemological implications of the lesson regarding our observational position, which the development of physical science has impressed on us. In return for the renunciation of accustomed demands on explanation, it offers a logical means of comprehending wider fields of experience, necessitating proper attention to the placing of the object-subject separation. Since, in philosophical literature, reference is sometimes made to different levels of objectivity or subjectivity or even of reality, it may be stressed that the notion of an ultimate subject as well as conceptions like realism and idealism find no place in objective description as we have defined it; but this circumstance of course does not imply any limitation of the scope of enquiry with which we are concerned. (pp. 78-79)

The reductionist’s dream, therefore, in which practically speaking every contemporary analytic philosopher is temperamentally invested, reveals itself to be only a mirage from the sober physicist’s perspective. So far, good – a telling point, but the continuation becomes less persuasive when Bohr essays a comparison of science and art. Here is his resolution:

Above all, the recognition of inherent limitations in the notion of causality has offered a frame in which the idea of universal predestination is replaced by the concept of natural evolution. (p. 81)

Yet it scarcely seems plausible that the elementary quantum of action, being so tiny as it is, could figure in any important manner in phenomena in the domain of lived experience: isn’t Bohr contradicting here his own basic philosophical stance, to the effect that there has to be a macroscopic domain in which the concepts of classical physics prevail?

Next, is the relation between different cultures complementary? Naturally, our author understands this could not be true in a strict sense but rather as a potentially instructive metaphor. For Heisenberg’s uncertainty principle along with Bohr’s signature idea of complementarity are not of course directly applicable to the world of human experience but still invite reflection along the lines of Thomas Kuhn’s thesis of an inevitable incommensurability between differing paradigms. A good example would be the contrast between Aristotelian physics versus seventeenth-century classical mechanics. The Aristotelian presumption that any motion of a body depends on a driving force and lasts only as long as such a force continues to be applied seems impossible, on the face of it, to reconcile with the modern concept of inertial motion (first-order versus second-order differential equation of motion). Popular stereotypes about the scholastics are overblown, of course. The medievals were engaged in critical reception of Aristotle, influenced by the commentaries of Avicenna and Averroes. Indeed by the 14th century they had, with the novel theory of impetus, departed from Aristotelian premises in the first stage of a drawn-out revolution that would eventually issue in the modern concept of inertial motion and impressed force. So: the opposition may not necessarily be as drastic as it might initially seem – could this be true in every case? Bohr at any rate is not equipped enough as a historian of science to pursue questions such as these at any length or in depth.

A major extract giving Bohr’s contribution to the 1949 entry in the Library of Living Philosophers devoted to Einstein (pp. 32-66) goes over limitations of human knowledge once again and includes a conversation with Einstein on epistemological issues. Starts out with a reprise (pp. 39-40) of the celebrated Como lecture of 1927 on complementarity and gets down to his epic confrontation with Einstein on pp. 42ff. Basically just a layman’s account of his debates with Einstein at the 1927 and 1930 Solvay conferences as well as a response to the EPR paper; better to read the original literature, doesn’t add anything of value.

Two lectures in vol. ii (pp. 3-22, 94-100) concern the problem of whether it will ever be possible to arrive at a scientific understanding of the phenomena of life. Bohr declares himself against vitalism (p. 9) but considers it impossible to study an animal at the atomic level empirically – he does not explain why not in theory, though, since he concedes ‘we should not expect to find any features foreign to inorganic matter’; cf. the following passage:

In every experiment on living organisms there must remain some uncertainty as regards the physical conditions to which they are subjected, and the idea suggests itself that the minimal freedom we must allow the organism will be just large enough to permit it, so to say, to hide its ultimate secrets from us. On this view, the very existence of life must in biology be considered as an elementary fact, just as in atomic physics the existence of the quantum of action has to be taken as a basic fact that cannot be derived from ordinary mechanical physics. Indeed, the essential non-analyzability of atomic stability in mechanical terms presents a close analogy to the impossibility of a physical or chemical explanation of the peculiar functions characteristic of life. (p. 9)

So there is some tension here but Bohr is working towards the view that organisms have holistic properties (we might say, non-perturbative) for which entirely new physical principles will be called for if there is to be any scientific understanding of their behavior – isn’t this then just tantamount to vitalism à part le nom?

Chapter two (pp. 13-22), from 1937, outlines the early Bohr’s take on the relation between biology and atomic physics. His main initial point is that the elementary quantum of action accounts for stability of atomic and molecular systems which is inexplicable in old-fashioned mechanical terms. He denies that quantum mechanics has anything to do with the traditional philosophical problem of free will. He suggests that complementarity (in a rather loose sense) will be relevant to biological description, but this claim is problematic (see below; most processes even at the subcellular level involve many times the elementary quantum of action). Bohr fails to see that Schrödinger’s equation should allow for derivation of higher-level processes in biology from elementary constituents in principle just as it does for those in atoms and molecules; hence we would term it a mechanistic explanation even though not mechanical in the sense of being reducible to a single definite trajectory in configuration space (the only sense in which Bohr means by mechanical).

In a final article completed in 1957 based on his Steno lecture of 1949 (pp. 94-100) on the physical sciences and the problem of life, Bohr brings out a favorite quotation from his father (a medical doctor), from which stance he never departed:

As far as psychology can be characterized as a special branch of natural sciences, its specific task is to investigate the phenomena peculiar to the organism as a given empirical object in order to obtain an understanding of the various parts in the self-regulation and how they are balanced against each other and brought into harmony with variations in external influences and inner processes. It is thus in the very nature of this task to refer the word purpose to the maintenance of the organism and consider as purposive the regulation mechanisms which serve this maintenance. Just in this sense we shall in the following use the notion ‘purposiveness’ about organic functions. In order that the application of this concept in each single case should not be empty or even misleading it must, however, be demanded that it be always preceded by an investigation of the organic phenomenon under consideration, sufficiently thorough to illuminate step by step the special way in which it contributes to the maintenance of the organism. Although this demand, which requires no more than the scientific demonstration that the notion of purposiveness in the given case is used in accordance with its definition, might appear self-evident, it may nevertheless not be unnecessary to stress it. Indeed, physiological investigations have brought to light regulations of utmost fineness in a multitude so great that it is a temptation to designate every observed manifestation of life as purposive without attempting an experimental investigation of its detailed functioning. By means of analogies which so easily present themselves among the variety of organic functions, it is merely the next step to interpret this functioning from a subjective judgment about the special character of purposiveness in the given case. It is evident, however, how often, with our so narrowly limited knowledge about the organism, such a personal judgment may be erroneous, as is illustrated by many examples. In such cases, it is the lacking experimental illumination of the details of the process which is the cause of the erroneous results of the procedure. The a prior assumption of the purposiveness of the organic process is, however, in itself quite natural as a heuristic principle and can, due to the extreme complication and difficult comprehension of the conditions in the organism, prove not only useful, but even indispensable for the formulation of the special problem for the investigation and the search of ways for its solution. But one thing is what may be conveniently used by the preliminary investigation, another what justifiably can be considered an actually achieved result. As regards the problem of the purposiveness of a given function for the maintenance of the whole organism, such a result can, as stressed above, be secured only by a demonstration in detail of the ways in which the purpose is achieved. (p. 96)

Bohr goes on to mention once more (p. 98) the limit posed by Planck’s constant but doesn’t deal with the fact that most metabolic not to mention organismic processes still take place at the classical level – so while inarguably true from an abstract point of view, it is hard to see what relevance it has to biology, which when treating the living organism is constrained to follow an indirect methodology and thus resembles observational astronomy more than experimental physics. Again Bohr suggests (p. 99) the principle of complementarity might be relevant to thinking about biology but doesn’t say why since he goes on right away to speak about molecular biology and the double helix structure of DNA – discoveries which don’t seem to have been all that troubled by any experimental limitation posed by complementarity. Bohr points out that concepts of teleology, while foreign to mechanistic physics, seem to be ineradicable in biology yet there is no real contradiction between the two. So his position comes down to the statement that the functioning of biological processes is best to be thought of as analogous to structure in molecular physics as determined holistically by quantum mechanics (a stationary state somehow knows about and reflects conditions all across the system) hence there can be no fine-grained mechanical spatio-temporal description of them as we can have for instance in celestial mechanics. Hardly controversial – the point was novel in his lifetime; Bohr lived through it himself – but from our perspective doesn’t seem very deep and fails to answer the question whether, say, quantum computational chemistry can aspire to a complete understanding of enzymatic catalysis, photosynthesis, chemiosmotic transduction etc. (perhaps assisted by simulations run on a quantum computer!).

Bohr does craft his sentences with care to say exactly what he means to say, often putting them through protracted revisions. A mildly stimulating, none too taxing read: everyone should go through these lectures once to fix his bearings on the debates of Bohr’s era. While the Copenhagen interpretation seems since to have fallen into disfavor – notwithstanding its acceptance at the time by the majority of the contributors to the discovery of the quantum mechanics themselves – it does have the merit, in Bohr’s hands, of keeping always in mind the experimental setting; that is to say, Bohr himself does not think about quantum physics primarily in terms of Dirac or von Neumann’s formal axiomatics, as everyone nowadays does, but more intuitively. That is why the present generation of physicists ought to find it valuable to be reminded of his older viewpoint.

[William Bies · Rating 3 out of 5]

Vol. iii in the collection of Niels Bohr’s philosophical writings offers his mature views on complementarity and limitations of human knowledge – the question around which our review will circle is this: can we detect any advance over vol. ii?

The first lecture in this volume from 1958 promises to elucidate the connection between quantum mechanics and philosophy, with particular focus on the issues of causality and complementarity. Bohr’s main point: quantum mechanics defeats classical determinism but remains scientific i.e. retains an objective not subjective basis of explanation, see the following key passages:

It is against this background that quantum mechanics may be seen to fulfill all demands on rational explanation with respect to consistency and completeness. Thus, the emphasis on permanent recordings under well-defined experimental conditions as the basis for a consistent interpretation of the quantal formalism corresponds to the presupposition, implicit in the classical physical account, that every step of the causal sequence of events in principle allows of verification. Moreover, a completeness of description like that aimed at in classical physics is provided by the possibility of taking every conceivable experimental arrangement into account. (p. 6)

The very fact that quantum regularities exclude analysis on classical lines necessitates, as we have seen, in the account of experiences a logical distinction between measuring instruments and atomic objects, which in principle prevents comprehensive deterministic description. Summarizing, it may be stressed that, far from involving any arbitrary renunciation of the ideal of causality, the wider frame of complementarity directly expresses our position as regards the account of fundamental properties of matter presupposed in classical physical description, but outside its scope. (p. 6)

Two lectures from 1960 (pp. 8-16, 17-22) recur to the theme of the unity of knowledge and the connection between the sciences. Bohr explains what was for him the most striking novelty to emerge from the discovery of quantum mechanics, in simple terms for the layman:

Faced with the question of how under such circumstances we can achieve an objective description, it is decisive to realize that however far the phenomena transcend the range of ordinary experience, the description of the experimental arrangement and the recording of observations must be based on common language. In actual experimentation this demand is amply satisfied with the specification of the experimental conditions through the use of heavy bodies such as diaphragms and photographic plates, the manipulation of which is accounted for in terms of classical physics. Just this circumstance, however, excludes any separate account of the interaction between the measuring instruments and the atomic objects under investigation. Especially this situation prevents the unlimited combination of space-time coordination and the conservation laws of momentum and energy on which the causal pictorial description of classical physics rests. Thus, an experimental arrangement aiming at ascertaining where an atomic particle, whose position at a given time has been controlled, will be located at a later moment implies a transfer, uncontrollable in principle, of momentum and energy to the fixed scales and regulated clocks necessary for the definition of the reference frame. Conversely, the use of any arrangement suited to study momentum and energy balance – decisive for the account of essential properties of atomic systems – implies a renunciation of detailed space-time coordination of their constituent particles. (p. 11)

Next, Bohr applies his principle of complementarity to psychology, where he calls attention to the problem of the subject-object separation peculiar to the field and illustrates it with an amusing literary anecdote. On ethics: Bohr seems to say (p. 15) that complementarity implies cultural relativism (without being upfront about it). The second lecture takes on the question of the logical relation between quantum mechanics and chemistry, on the one hand, and molecular biology, on the other; see esp. p. 21. The final paragraph (p. 22) contains a paean favorable to harmony in nature (Ørsted), appreciation of which is vital to maintain balance in the face of the detrimental tendencies encouraged by the technologistic attitude towards existence.

The same thing goes for the unfinished manuscript about biology from 1962, found among Bohr’s papers after his death (pp. 23-29). Reflecting on the tremendous advances in the nascent field of molecular biology the previous decade had witnessed, Bohr sums up his position:

Notwithstanding such general considerations, it appeared for a long time that the regulatory functions in living organisms, disclosed especially by studies of cell physiology and embryology, exhibited a fineness so unfamiliar to ordinary physical and chemical experience as to point to the existence of fundamental biological laws without counterpart in the properties of inanimate matter studied under simple reproducible experimental conditions. Stressing the difficulties of keeping the organisms alive under conditions which aim at a full atomic account I therefore suggested that the very existence of life might be taken as a basic fact in biology in the same sense as the quantum of action has to be regarded in atomic physics as a fundamental element irreducible to classical physical concepts. (p. 26)

Nothing else new or of note here.

The last three chapters (pp. 30-100) sketch for the layman the historical development of quantum mechanics from point of view of a participant. Can we learn anything not otherwise accessible? Just a little: read them for personal reminiscences including passages from letters to Bohr from Rutherford, not for any logical reconstruction of the thought processes behind rise of quantum mechanics itself [for which see Max Jammer’s classic, The conceptual development of quantum mechanics]. To be viewed as source material for the historian of science seeking to put together the personal relationships among the players in the quantum revolution, not as documents with much of any intellectual content of their own.

Conclusion: was Bohr any good as a philosopher of science as opposed to a pioneer of quantum mechanics? Compare quickly with his contemporaries Planck, Poincaré and Heisenberg. Bohr isn’t quite at Planck’s level, makes no attempt at a systematic philosophy of science proper such as we get with Poincaré and is by no means as discerning with respect to general philosophical and theological issues as was Heisenberg. Considering the amount of attention he has received, Bohr appears to be overrated in this department, in that his actual published lectures as reflected in the volume presently under review and the immediately preceding one come across as repetitive and somewhat meager in content; while one often speaks of the late Bohr versus the early Bohr, the advance in insight one can trace over the thirty-year period covered here looks pretty minuscule to this reviewer. All around, he was probably better informed than the typical scientist of today but this is not attributable to his science per se as much as to the fact that he enjoyed an old-fashioned humanistic education of the type progressives began to dismantle during his lifetime.

[Emma · Rating 4 out of 5]

"This discovery revealed in atomic processes a feature of wholeness quite foreign to the mechanical conception of nature, and made it evident that the classical physical theories are idealizations valid only in the description of phenomena in the analysis of which all actions are sufficiently large to permit the neglect of the quantum."

[Scott Andrew · Rating 4 out of 5]

Good specialized knowledge

This book is not appropriate for the casual reader. However, the book is indispensable for anyone seeking an introduction to the epistemological challenges created by quantum mechanics for classical, mechanistic understanding of physics.

[Joseph Patterson · Rating 4 out of 5]

Niels Bohr is a hilariously confusing writer to digest.

[Kristian Francisco Milla Nielsen · Rating 3 out of 5]

Meget uforståelig og sær men sådan er genier

[Chant · Rating 3 out of 5]

Publishers love using the most flattering photo.

[Joaquin Andres · Rating 2 out of 5]

Disappointing. Repetitive. If you're interested in qm history you'll do better reading schrödinger or heisenberg

[Abdullah Alhomoud · Rating 3 out of 5]

في الصفحه ٦٠ حاليا.... جميع اللي قرأته كان عن الافكار القديمة المتادوله في الخطابات والمحاضرات...
ماني مستعد حاليا اكمل القراءه... سوف أتوقف الآن قراءة هذا الكتاب وسأعاود قرائته مره اخرى في وقت لاحق