Tag Archives: kwantum meganika

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.
Lees verder

Historical Origin of Quantum Mechanics

In hierdie afdeling, 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.
Lees verder

Kwantummeganika

Kwantummeganika (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. En, 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. Regtig.

Lees verder

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. Byvoorbeeld, if you try to figure out where an electron is (measure its position, dit is) more and more precisely, its speed becomes progressively more uncertain (of, 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, Mnr. Tompkins, puts it. Met ander woorde, 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,” soos dit was. As we increase the position accuracy (by shining light of shorter wavelengths, byvoorbeeld), 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.

Alle regte, 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,” byvoorbeeld. Accurate, mag wees. 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. In hierdie siening, 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. Met ander woorde, \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. So, 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. So, 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, waar NA is the numerical aperture, which has a maximum value of one. So, 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, Die onwerklik Heelal.

Seks en fisika — Volgens Feynman

Fisika gaan deur 'n tyd van die geveg een keer in 'n rukkie. Geveg is afkomstig van 'n gevoel van volledigheid, 'n gevoel dat ons ontdek alles wat daar is om te weet, die pad is duidelik en die metodes goed verstaan.

Histories, hierdie aanvalle van die geveg is gevolg deur vinnige ontwikkelinge wat 'n rewolusie die manier fisika gedoen, wys ons hoe verkeerd het ons. Hierdie vernederende les van die geskiedenis is waarskynlik wat Feynman gevra om te sê:

So 'n ouderdom van die geveg teen die draai van die 19de eeu. Famous personas soos Kelvin het opgemerk dat al wat oorgebly het om te doen was meer akkurate metings te maak. Michelson, wat 'n deurslaggewende rol in die rewolusie gespeel te volg, is aangeraai om nie 'n te betree “dood” gebied soos fisika.

Wie sou kon dink dat in minder as 'n dekade in die 20ste eeu, ons sal voltooi verander die manier waarop ons dink van ruimte en tyd? Wie in hulle verstand sal nou sê dat ons weer ons begrippe van ruimte en tyd sal verander? Ek doen. Dan weer, niemand het my ooit daarvan beskuldig van 'n verstand!

Nog 'n rewolusie plaasgevind het gedurende die loop van die vorige eeu — Kwantummeganika, wat weggedoen het met ons idee van determinisme en hanteer 'n ernstige terugslag vir die stelsel-waarnemer paradigma van fisika. Soortgelyke omwentelings sal weer gebeur. Laat ons nie hou op om ons konsepte as onveranderlike; hulle is nie. Laat ons nie dink ons ​​ou meesters as onfeilbare, want hulle is nie. As Feynman homself sou uitwys, fisika alleen het meer voorbeelde van die feilbaarheid van die ou meesters. En ek voel dat 'n volledige omwenteling in gedagte agterstallig is nou.

Jy mag dalk wonder wat al hierdie het te doen met seks. Wel, Ek het net gedink seks sou beter verkoop. Ek was reg, was ek nie? Ek bedoel, jy is nog hier!

Feynman het ook gesê,

Foto deur "Grotman Chuck" Coker cc

Einstein op God en Dice

Hoewel Einstein is die beste bekend vir sy teorieë van relatiwiteit, Hy was ook die hoof dryfkrag agter die koms van kwantummeganika (QM). Sy vroeë werk in foto-voltaïese effek geplaveide pad vir toekomstige ontwikkelings in QM. En hy het die Nobelprys, nie vir die teorieë van relatiwiteit, maar vir hierdie vroeë werk.

Dit moet dan kom as 'n verrassing vir ons dat Einstein het nie heeltemal glo in QM. Hy het die laaste deel van sy loopbaan probeer toestel gedagte eksperimente wat sou bewys dat QM is strydig met wat hy geglo word die wette van die natuur. Hoekom is dit dat Einstein nie QM kon aanvaar? Ons sal nooit weet vir seker, en my raaiskoot is waarskynlik so goed soos enigiemand anders se.

Einstein se probleme met QM word opgesom in hierdie beroemde aanhaling.

Dit is inderdaad moeilik om die begrippe te versoen (of ten minste 'n paar interpretasies) van QM met 'n woord siening waarin 'n God het beheer oor alles. In QM, waarnemings is probabilistiese in die natuur. Dit is om te sê, as ons een of ander manier te bestuur twee elektrone te stuur (in dieselfde toestand) down dieselfde balk en neem hulle na 'n rukkie, kan ons twee verskillende waargenome eienskappe kry.

Ons kan hierdie onvolmaaktheid in waarneming as ons onvermoë om 'n identiese aanvanklike state te interpreteer, of die gebrek aan akkuraatheid in ons metings. Hierdie interpretasie gee aanleiding tot die sogenaamde verborge veranderlike teorieë — beskou ongeldig vir 'n verskeidenheid van redes. Die interpretasie tans gewild is dat onsekerheid is 'n inherente eienskap van die natuur — die sogenaamde Kopenhagen interpretasie.

In die Kopenhagen prentjie, deeltjies posisies net waargeneem. Op ander tye, hulle moet beskou word as 'n soort van versprei in die ruimte. In 'n dubbel-interferensie eksperiment met elektrone, byvoorbeeld, moet ons nie vra of 'n bepaalde elektron neem op spleet of die ander. Solank as wat daar is inmenging, dit soort van vat beide.

Die ontstellende ding vir Einstein in hierdie interpretasie sou wees dat selfs God nie in staat sou wees om die elektron neem een ​​gleuf of die ander (sonder om die interferensiepatroon, dit is). En as God kan nie een klein elektron plek waar hy wil, hoe gaan hy die hele heelal te beheer?