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Articles: Devotion | In quest of infinity - 9
- Prof. venkata ramanamurty mallajosyula
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Even in a small lump of iron, we would have about 1023 atoms of iron, and in such a case, it is difficult to say by looking at a pattern like (a-ii) whether a rotation has been performed or not, and if so, by what angle. In such a situation, we say there is perfect rotational symmetry, that is the BEFORE and AFTER situations are indistinguishable. This is the concept of symmetry – invariance to a physical operation performed on the system. Turn now the pair in (b). Here, the BEFORE and AFTER situations, illustrated in (b-i) and (b-ii) respectively are clearly distinguishable; we describe this by saying that in this case, magnetic rotational symmetry is broken.
Notice that when there is symmetry, there is no order and vice versa. The message we get is: When there is symmetry there is no order; therefore, order parameter is zero. When symmetry is broken, there is order and consequently, order parameter has a value different from zero. Symmetry-breaking is a powerful concept in physics, particularly elementary particle physics.
Suppose you take a good look at (a-i). I now ask you to close your eyes, and when your eyes are closed, I rotate the pattern so that it becomes as in (a-ii). Now if we are dealing with trillions of arrows, then it is really not possible to distinguish between (a-i) and (a-ii). One can rotate the first figure by 1 degree, by 42 degrees, 88.4 degrees, or whatever. It makes no difference; one cannot distinguish the unrotated pattern from the rotated one. In such a case, one says there is symmetry, in this case, rotational symmetry. Now look at (b-i) and (b-ii); in this case, it is quite easy to say that the second pattern is definitely rotated compared to the first one. We are able make this distinction because the arrows are all pointing in one direction.
So we get a basic rule [simplified of course]. When there is no order, there is greater symmetry, but when symmetry is lost or broken as physicists say, then there is order. Thus, the symmetry-breaking and the appearance of order go hand in hand. This happens all the time in many physical systems, and thus the study of phase transitions is actively pursued by many. The idea of symmetry breaking [originally applied heavily in the study of solids and liquids] was borrowed by particle physicists to explain some fundamental aspects of microscopic physics. And that part is important for us. How? That is what I shall consider now. Remember the question posed earlier? Let us go back to that.
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