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Monday, May 5, 2008

[mukto-mona] Both Jiten Roy and Subimal Chakrabarty are Correct (Re: Aparthib's Quantum Analogy)

I am responding to the latest post on the thread by Mr. Subimal Chakrabarty.  First, I must say that I was deeply pained by the acrimony that developed over this argument between two otherwise decent and knowledgeable individuals.  Second, upon reviewing all the exchanges between Mr. Subimal Chakrabarty and Dr. Jiten Roy and doing a litle thinking, I find that both were correct.  This second statement may come as a shocker (and a pleasant one) but it is true.  Let me explain.

 

I will start my explanation by saying that what we are discussing here is high school level or at most college freshman level physics.  Therefore, I would ask my fellow physicists not to get annoyed at my discussion of such rudimentary material with so much seriousness.  This is being done for the benefit of non-physicists on the forum who may have some interest on this topic.  I myself would like to be similarly entertained with rudimentary material from chemistry, biology or say, music.  I would request my fellow physicists to either bear with me or not read this post at all if they do not want to.

 

In classical physics, events can be viewed in an inertial reference frame or a non-inertial reference frame.  An inertial frame is what we normally use to describe physical events such the ordinary Cartesian (x, y and z) or polar co-ordinate (r, theta and phi) system.  Such a reference frame is either stationary or moving with unifrom speed.  An example of a non-inertial reference frame is a rotational frame in which the radial axis is rotating around a central point.  A physical event, when it is viewed in a non-inertial frame, can have quite different characteristics than how it appears in an inertial frame.  The difference, for example, might include, existence of forces in one reference frame that does not exist in the other.

 

If we observe the electron moving around the nucleus in an inertial frame, the only force acting on the electron is the centripetal force, in the form of Coulomb attraction of the proton in the nucleus.  At every instant, the electron experiences acceleration in the inward radial direction. The resultant is such that the electron bends slightly from the tangential direction to keep it on a circular orbit. 

 

Now, let us view the same event in a rotational reference frame.  Assume that the reference frame is rotating at the same speed (i.e. angular speed) as the electron.  Relative to this frame, the electron experiences no motion.  In particular, there is no motion along the radial direction.  However, we still have the electrostatic Coulomb force toward the center.  We, therefore, need another force to balance the electrostatic force and to explain the absence of motion in the radial direction.  Therefore, we invoke a balancing "pseudo force" in the form of a centrifugal force *on the electron* that is pushing it outward in the radial direction. 

 

The physical implication of viewing the same event in two different reference frames is that while in an inertial frame, there is only the centripetal force, in the rotational frame, there is also a balancing "pseudo force" on the electron. The pseudo force is not really fictitious either.  The rotating object does actually experience an outward "tug" but an observer in an inertial frame will not observe it.

 

To discuss the matter of stationary states of an electron, we have to bring in quantum physics.  What we have discussed so far is classical physics.  According to classical physics, an accelerated charge, such as a rotating electron, would radiate energy.  Therefore, the electron would gradually lose energy, slow down and drop into successively smaller orbits, and eventually collapse into the nucleus.  This obviously does not happen and a new explanation was needed. Niels Bohr proposed an atomic model, based on quantum physics,  that posits that the electron can be in discrete stationery states, which are, in simple lay man's terms, orbits of certain radii.  Whenever it is in one of such states, there is no change in energy.  It can, however, absorb energy and move to the next higher stationary state or lose energy and drop to the next lower stationary state.  

 

Therefore, both Dr. Jiten Roy and Mr. Subimal Chakrobarty were right.  Dr. Roy correctly explained the physical event in a rotational frame and Mr. Subimal Chakrabarty (and myself) correctly explained the event in an inertial frame.  All the acrimonious argumentation could have been avoided if we all remembered our lesson on reference frames from Physics 101 (or its Dhaka University equivalent).  Then, we would have stated at the beginning of each of our discussions what reference frame we were assuming in our analysis.

 

I must add that it is not that unusual to forget elementary material that we learned a long time ago as one moves to more advanced studies.  Nor is it rare for experts in a field to have very poor aptitude for rudimentary parts of the same field.  Albert Einstein was notorious for making silly mistakes while doing simple arithmetic.  He was probably trying to use tensors and Riemannian geometry to figure out something like 2.3 x 4.5! 

 

Now turning to personal comments made by Mr. Subimal Chakrabarty, I am pleased to learn that he is a former classmate of my younger brother.  You probably know, Mr. Chakrabarty, that Khaleq tragically died of a sudden heart attack in September, 2001.  I am deeply moved every time I come across a person who knew him closely.  I am flattered by your comment about my alleged brilliance but I have to say that I do not deserve any such accolade.

 

I want Dr. Roy to confirm that he is indeed my former classmate.  He is if he graduated with an M.Sc. at the beginning of 1975, and our other classmates included Haider, Kamal, Sanjoy, Lutful Bari, Joyonta, Hassan, Pran, Shafique, etc.  This would be a pleasant surprise.  Please confirm this and I will have the pleasure of addressing you as Jiten as opposed to Dr. Roy.

 

Finally, I want to apologize for a few typos in my last post, including misspelling "Schrodinger" as "Schrodinder."

 

Best wishes,

 

M. Harun uz Zaman

 



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