ট্যাগ আর্কাইভ: কোয়ান্টাম বলবিজ্ঞান

Quantum Mechanics – Interpretations

Whenever we talk about Quantum Mechanics, one of the first questions would be, “What about the cat?” This question, সত্যিই, is about the interpretations of Quantum Mechanics. The standard interpretation, the so-called Copenhagen interpretation, leads to the famous Schrodinger’s cat.
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Quantum Field Theory

In this post on Quantum Mechanics (QM), we will go a bit beyond it and touch upon Quantum Field Theory – the way it is used in particle physics. In the last couple of posts, I outlined a philosophical introduction to QM, as well as its historical origin – how it came about as an ad-hoc explanation of the blackbody radiation, and a brilliant description of the photoelectric effect.
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Historical Origin of Quantum Mechanics

এই অংশে, we will try to look at the historical origin of Quantum Mechanics, which is usually presented succinctly using scary looking mathematical formulas. The role of mathematics in physics, as Richard Feynman explains (in his lectures on QED given in Auckland, New Zealand in 1979, available on YouTube, but as poor quality recordings) is purely utilitarian.
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কোয়ান্টাম মেকানিক্স

কোয়ান্টাম মেকানিক্স (QM) is the physics of small things. How do they behave and how do they interact with each other? Conspicuously absent from this framework of QM is why. Why small things do what they do is a question QM leaves alone. এবং, if you are to make any headway into this subject, your best bet is to curb your urge to ask why. Nature is what she is. Our job is to understand the rules by which she plays the game of reality, and do our best to make use of those rules to our advantage in experiments and technologies. Ours is not to reason why. সত্যিই.

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Uncertainly Principle

The uncertainty principle is the second thing in physics that has captured the public imagination. (The first one is E=mc^2.) It says something seemingly straightforward — you can measure two complimentary properties of a system only to a certain precision. উদাহরণস্বরূপ, if you try to figure out where an electron is (measure its position, যে) more and more precisely, its speed becomes progressively more uncertain (বা, the momentum measurement becomes imprecise).

Where does this principle come from? Before we can ask that question, we have to examine what the principle really says. Here are a few possible interpretations:

  1. Position and momentum of a particle are intrinsically interconnected. As we measure the momentum more accurately, the particle kind of “spreads out,” as George Gamow’s character, জনাব. Tompkins, puts it. অর্থাৎ, it is just one of those things; the way the world works.
  2. When we measure the position, we disturb the momentum. Our measurement probes are “too fat,” বলিতে কি. As we increase the position accuracy (by shining light of shorter wavelengths, উদাহরণস্বরূপ), we disturb the momentum more and more (because shorter wavelength light has higher energy/momentum).
  3. Closely related to this interpretation is a view that the uncertainty principle is a perceptual limit.
  4. We can also think of the uncertainly principle as a cognitive limit if we consider that a future theory might surpass such limits.

ঠিক আছে, the last two interpretations are my own, so we won’t discuss them in detail here.

The first view is currently popular and is related to the so-called Copenhagen interpretation of quantum mechanics. It is kind of like the closed statements of Hinduism — “Such is the nature of the Absolute,” উদাহরণস্বরূপ. Accurate, হতে পারে. But of little practical use. Let’s ignore it for it is not too open to discussions.

The second interpretation is generally understood as an experimental difficulty. But if the notion of the experimental setup is expanded to include the inevitable human observer, we arrive at the third view of perceptual limitation. এই দেখুন, it is actually possible to “derive” the uncertainty principle.

Let’s assume that we are using a beam of light of wavelength \lambda to observe the particle. The precision in the position we can hope to achieve is of the order of \lambda. অর্থাৎ, \Delta x \approx \lambda. In quantum mechanics, the momentum of each photon in the light beam is inversely proportional to the wavelength. At least one photon is reflected by the particle so that we can see it. সুতরাং, by the classical conservation law, the momentum of the particle has to change by at least \Delta p \approx constant\lambda from what it was before the measurement. সুতরাং, through perceptual arguments, we get something similar to the Heisenberg uncertainty principle \Delta x \Delta p = constant.

We can make this argument more rigorous, and get an estimate of the value of the constant. The resolution of a microscope is given by the empirical formula 0.61\lambda/NA, যেখানে NA is the numerical aperture, which has a maximum value of one. সুতরাং, the best spatial resolution is 0.61\lambda. Each photon in the light beam has a momentum 2\pi\hbar/\lambda, which is the uncertainty in the particle momentum. So we get \Delta x \Delta p = (0.61\lambda)(2\pi\hbar) \approx 4\hbar, approximately an order of magnitude bigger than the quantum mechanical limit. Through more rigorous statistical arguments, related to the spatial resolution and the expected momentum transferred, it may possible to derive the Heisenberg uncertainty principle through this line of reasoning.

If we consider the philosophical view that our reality is a cognitive model of our perceptual stimuli (which is the only view that makes sense to me), my fourth interpretation of the uncertainty principle being a cognitive limitation also holds a bit of water.

Reference

The latter part of this post is an excerpt from my book, অবাস্তব ইউনিভার্স.

লিঙ্গ এবং পদার্থবিদ্যা — নিউটন, Feynman অনুযায়ী

পদার্থবিদ্যা একবার একটি সময় প্রসন্নতা একটি বয়স মাধ্যমে যায়. প্রসন্নতা সম্পূর্ণতার একটা ধারনা থেকে উত্পন্ন হয়, আমরা সবকিছু আবিষ্কার করেছেন যে একটা অনুভূতি জানা আছে, পথ পরিষ্কার এবং পদ্ধতি ভাল বোঝা.

ঐতিহাসিকভাবে, প্রসন্নতা এই বাড়াতেও উপায় পদার্থবিদ্যা সম্পন্ন করা হয় বৈপ্লবিক যে দ্রুত উন্নয়ন দ্বারা অনুসরণ করা হয়, আমাদের দেখাচ্ছে আমরা কতটা ভুল. ইতিহাসের এই নিচু পাঠ বলে নিউটন, Feynman অনুরোধ জানানো কি সম্ভবত:

প্রসন্নতা যেমন একটি বয়স 19 শ শতাব্দীর পালা এ অস্তিত্ব. কেলভিনের মত বিখ্যাত ব্যক্তি কি বাকি ছিল যে সব আরো সুনির্দিষ্ট পরিমাপ করা ছিল যে মন্তব্য. হয় Michelson, যারা অনুসরণ বিপ্লব একটি অত্যন্ত গুরুত্বপূর্ণ ভূমিকা পালন করে, একটি প্রবেশ করতে না পরামর্শ দেওয়া হয় “মৃত” পদার্থবিদ্যা মত ক্ষেত্র.

20 শতকের মধ্যে কম এক দশকের মধ্যে যে চিন্তা করে, আমরা স্থান এবং সময় মনে পরিবর্তন সম্পন্ন হবে? তাদের অধিকার মনে কে আমরা আবার স্থান ও সময় আমাদের ধারণার পরিবর্তন করতে হবে যে এখন বলতে হবে? আমি কি. তারপর আবার, কেউ কি কখনও একটি অধিকার মন আমাকে অভিযুক্ত করেছে!

আরেকটি বিপ্লব গত শতাব্দীর অবশ্যই সময় স্থান গ্রহণ — কোয়ান্টাম মেকানিক্স, নিয়তিবাদ আমাদের ধারণা সঙ্গে দূরে করেনি এবং পদার্থবিদ্যা সিস্টেম পর্যবেক্ষক দৃষ্টান্ত একটি গুরুতর ঘা মোকাবিলা. একই বিপ্লব আবার ঘটবে. এর অপরিবর্তনীয় হিসাবে আমাদের ধারণা রাখা না; তারা নয়. এর অব্যর্থ হিসাবে আমাদের পুরানো কর্তা মনে করি না যাক, তারা না. নিউটন, Feynman হিসাবে নিজেকে বাতলান হবে, পদার্থবিদ্যা একা তার পুরানো কর্তা ভ্রান্তি আরো উদাহরণ কথা. এবং আমি চিন্তা একটি সম্পূর্ণ বিপ্লব এখন বাকি বলে মনে করেন.

আপনি এই সব লিঙ্গের সাথে কি আছে ভাবছি কি হতে পারে. ভাল, আমি শুধু সেক্স ভাল বিক্রি হবে. আমি ডান, আমি ছিল না? আমি বলতে চাচ্ছি, আপনি এখনও এখানে!

নিউটন, Feynman বলেন,

দ্বারা ফোটো "গুহামানব মুর্গীর" Coker cc

Einstein on God and Dice

Although Einstein is best known for his theories of relativity, he was also the main driving force behind the advent of quantum mechanics (QM). His early work in photo-voltaic effect paved way for future developments in QM. And he won the Nobel prize, not for the theories of relativity, but for this early work.

It then should come as a surprise to us that Einstein didn’t quite believe in QM. He spent the latter part of his career trying to device thought experiments that would prove that QM is inconsistent with what he believed to be the laws of nature. Why is it that Einstein could not accept QM? We will never know for sure, and my guess is probably as good as anybody else’s.

Einstein’s trouble with QM is summarized in this famous quote.

It is indeed difficult to reconcile the notions (or at least some interpretations) of QM with a word view in which a God has control over everything. In QM, observations are probabilistic in nature. বলতে হয়, if we somehow manage to send two electrons (in the same state) down the same beam and observe them after a while, we may get two different observed properties.

We can interpret this imperfection in observation as our inability to set up identical initial states, or the lack of precision in our measurements. This interpretation gives rise to the so-called hidden variable theories — considered invalid for a variety of reasons. The interpretation currently popular is that uncertainty is an inherent property of nature — the so-called Copenhagen interpretation.

In the Copenhagen picture, particles have positions only when observed. At other times, they should be thought of as kind of spread out in space. In a double-slit interference experiment using electrons, উদাহরণস্বরূপ, we should not ask whether a particular electron takes on slit or the other. As long as there is interference, it kind of takes both.

The troubling thing for Einstein in this interpretation would be that even God would not be able to make the electron take one slit or the other (without disturbing the interference pattern, যে). And if God cannot place one tiny electron where He wants, how is he going to control the whole universe?