"Determinism" - This word means a lot to every Classical Physicist who ever lived or any other human living with a sound brain. Determinism is something which we humans are equipped with almost every time. A person driving a car immediately determines an impact if something suddenly appears in front of the car and reflexively applies brakes, a juggler can exactly determine where each ball will land due to the force with which he threw it upwards and hence positions his hands at that place before the ball comes down, etc. In Classical Physics, "Determinism" states that an experimenter is able to predict the exact results he/she would achieve in an experiment by knowing the present condition of his/her apparatus and using the Laws of Classical Physics to determine how it would evolve with time. These "laws" are basically "Newton's Three Laws of Motion" which almost everyone is familiar with. They predict how the "state" of a "system" would change with time. But, what does a "state" and a "system" mean firsthand? A system can be regarded as any object or a collection of objects which is under study and isolated from the experimenter. It can be a football lying on the ground, or a collection of billiard balls, or a gas in a container. The "state" of a system is then its initial set of conditions. For example, if you are a system then your state would be specified by your identity, physical traits, job, etc. In Classical Physics the state of a system is mostly defined by the "positions" and "momenta"(mass multiplied by velocity) of all the objects in that system. If these two quantities are known then one can easily calculate other quantities like Energy from these two. Newton's Laws of Motions can then be applied on this state to predict the future state with certainty. However in the 20th century, Physicist's started experimenting with small scale objects and phenomena, and realized that they behaved too strangely. Not only did the concept of "Determinism" broke down at those small scales but also some strange observations were made which defied our intuitions. These observations just not fitted in the scope of Classical Physics and demanded a separate branch - "Quantum Physics". In part 1 of this blog article, I shall discuss what truly defines the foundations of Quantum Physics with a little bit of historical background.
First, let us see some history behind the birth of Quantum Physics. It is not born from a single experiment but is a result of accumulated observations from experiments performed to study small scale objects such as atoms, molecules, electrons as well as by studying the nature of electromagnetic radiations or light. I am not going into the detail of each experiment, but we would discuss the results of each one and how they connected in the end to form a Quantum Theory. In 1900, a German physicist Max Planck was studying the radiations absorbed by a black body. When he proceeded to formulate a mathematical theory for his observations, he encountered severe problems. His mathematical results gave infinities. Whenever an infinity pops up into Physics, its not good for the theory. Planck found only one way around the problem using a mathematical trick. The trick was to assume that radiant energy can only be absorbed and emitted in "chunks" or "packets" and not continuously. One such chunk of energy is called a "Quanta". Hence, the name - Quantum Physics. For example, if you have a garden in the quantum world where "water" has a quanta. Then you can only water your plants with packets of water and not continuously using a water pipe. Planck then proceeded to show that a single quanta of energy is directly proportional to the frequency of that radiation. He expressed it as -
E=hv
where v is the frequency of radiation and h is a constant called as the Planck's constant. Thus, one chunk of energy is equal to hv and any body can only absorb energy in whole number multiples of this "chunk" like 2hv, 5hv, etc. but not 0.5hv. Max Planck initially thought these results to be ridiculous and abandoned his theory. It took Albert Einstein, to experimentally prove that Planck was right by his Photoelectric Experiment for which Einstein was awarded the Nobel Prize. He demonstrated how light can only be absorbed in discrete chunks called as "photons" (the particle of light). A revolution was sparked and was about to shatter all physicists living in the comfort and warmth of Classical Physics. Soon after Einstein proved Max Planck's Theory the haze of confusion started spreading. The reason being everyone was aware of the fact that Light or Electromagnetic Radiations behave as waves. Maxwell's Equations and many other experiments such as Thomas Young's Double Slit Experiment proved that light propagated in the form of waves in the electric and magnetic field. Just like ripples on the surface of a pond. But then Einstein demonstrated it behaved as a particle too in the Photoelectric effect. The results were paradoxical. As we know, a wave does not have a definite position. It is spread out in space. It makes no sense to ask at what point a wave is located? - It is everywhere at once. However a particle has a definite position in space. How can then something behave both as a particle and as a wave at the same time? This gave rise to the Wave-Particle Duality in Quantum Physics. It was stated that light behaves both as a particle and as a wave depending on the circumstances. In Thomas Young's Double Slit Experiment, light behaves as waves and shows interference. Whereas, in Einstein's Photoelectric Experiment it behaves as particles. Problem solved? - Not yet. In 1924, Louis De-Broglie published his PhD thesis in which he reasoned that since light was initially thought to be waves but then turned out to also be like particles. Matter - which is thought to be like particles might also be waves in some circumstances. He called them - "Matter Waves". Mathematically, he postulated that the wavelength of these "Matter Waves" is inversely proportional to the momentum of body. Higher the momentum, lesser the wavelength and lesser is the wave behavior. Soon, experiments confirmed that matter indeed behaved like a wave sometimes. However, this wave effect is seen on extremely small scales. Particles like electrons show wave like behavior in certain circumstances. They diffract and show interference just like waves. Why large scale objects don't show wave behavior? - Because they carry large momentum, owing to their high mass. Since, De-Broglie's law stated that more the momentum, lesser the wavelength and lesser is the wave behavior. We don't see everyday objects acting like waves.
This discovery came as something unexpected. The story didn't end here. We are yet to come to Heisenberg, Bohr and Schrodinger. The pioneers of early Quantum Physics. Soon, the results of Quantum Theory were used to explain stability of atoms. Neils Bohr put forth his atomic model which perfectly explained why electrons are able to revolve around the nucleus of atom in fixed energy levels without collapsing onto it. In 1925, a young physicist- Werner Heisenberg published a paper which carried the famous "Uncertainty Principle". Heisenberg discovered something in the strange quantum experiments which were coming up. With De-Broglie's idea of "Matter Waves", Heisenberg deduced that the idea imposes a limitation on how much we can know about the "state" of a "system" (more precisely a "quantum" system). Earlier, I explained the meaning of "state" and "system" in Physics. The "positions" and "momenta" of all objects in the system are known specify its "state". But, the limitation imposed by Heisenberg's Uncertainty Principle was rather a severe one. It stated that - "It is impossible to simultaneously have exact knowledge of the position and momentum of a quantum object." No matter how hard you try, you cannot know the position and momentum of a particle at the same time with certainty. If you know one then the other would be uncertain. The original way in which Heisenberg reached this conclusion was different than today's interpretation for the principle. Today's explanation for the reason behind this principle is linked with the "wave behavior" of matter predicted by De-Broglie. As stated before, the wavelength of the matter wave of an object depends on its momentum. When any object is carrying a lesser momentum it has a longer wavelength. This means that it shows more wave-like behavior and as I said before - a wave is not localized in space. It is spread out and does not have a well defined position. On the other hand, if a particle carries more momentum, it has a shorter wavelength and lesser wave behavior. It is then said to be localized in space at a point. Thus, it is easy to understand where the Uncertainty Principle came from. A quantum particle whose momentum is well known, possess a defined wavelength and shows wave behavior. Its position then becomes uncertain. Whereas, a particle whose momentum is not known, does not have a wavelength defined, and is localized at a position like a particle.
The Uncertainty Principle now forms the heart of Quantum Physics. If it is disproved then the entirety of this subject would fall apart. But no one has ever been able to do so. There is just no way around it. Uncertainty Principle is a fundamental limitation in the Quantum World. It is responsible for majority of the chaos associated in Quantum Physics. This principle then implied that it is impossible to have complete knowledge of the "state" of a "quantum system". As we saw before, that position and momentum are needed to completely specify the state of a system. But the Uncertainty Principle forbids simultaneous knowledge of these two variables. Thus, one can never specify the state of "quantum system". This is where the entire notion of "Determinism" collapses. If one is not able to specify the present state of a system without ambiguity, then it would not be possible to determine its future state with certainty. Here, the final piece of our Quantum Puzzle fits in - "Probability". The world on its tiniest scale is totally random and in-deterministic. In 1926, a physicist named - Max Born formulated the Statistical Interpretation of Quantum Mechanics. I am going to discuss this interpretation precisely in part 2 of this article. But for now, it introduced "Probability" in Quantum Mechanics. When we are unaware of certain events we assign a probability or "chance" or "odds" to it. Similarly, in Quantum Physics since it is impossible to predict the future state of a system with certainty, we can find out the probability of a system to end up in a specific state. Einstein was most against this view of Quantum Physics and stated - "God does not play dice".
Summing it all up, Quantum Mechanics is chunky, random and unpredictable. Things in the quantum realm like Energy or Electric Charge do not have continuous values but only come in indivisible chunks of definite value. Also they act both as waves and as particles depending on the circumstance. In the quantum world, you cant predict the exact position and momentum of the particle at the same time. If you know one precisely, there is an ambiguity in the other. This means that you cant determine the outcome of an experiment with hundred percent certainty. Rather, you can say the probability that an outcome has in a given experiment. So this is it? - No. I would call this the story before interval. We are yet to see what happens when these observations of Quantum Mechanics contradicts our intuitions and are faced by many other explanations to make sense of it. All this along with "the climax" would be discussed in part 2 of this article.
- Thank You!
First, let us see some history behind the birth of Quantum Physics. It is not born from a single experiment but is a result of accumulated observations from experiments performed to study small scale objects such as atoms, molecules, electrons as well as by studying the nature of electromagnetic radiations or light. I am not going into the detail of each experiment, but we would discuss the results of each one and how they connected in the end to form a Quantum Theory. In 1900, a German physicist Max Planck was studying the radiations absorbed by a black body. When he proceeded to formulate a mathematical theory for his observations, he encountered severe problems. His mathematical results gave infinities. Whenever an infinity pops up into Physics, its not good for the theory. Planck found only one way around the problem using a mathematical trick. The trick was to assume that radiant energy can only be absorbed and emitted in "chunks" or "packets" and not continuously. One such chunk of energy is called a "Quanta". Hence, the name - Quantum Physics. For example, if you have a garden in the quantum world where "water" has a quanta. Then you can only water your plants with packets of water and not continuously using a water pipe. Planck then proceeded to show that a single quanta of energy is directly proportional to the frequency of that radiation. He expressed it as -
E=hv
where v is the frequency of radiation and h is a constant called as the Planck's constant. Thus, one chunk of energy is equal to hv and any body can only absorb energy in whole number multiples of this "chunk" like 2hv, 5hv, etc. but not 0.5hv. Max Planck initially thought these results to be ridiculous and abandoned his theory. It took Albert Einstein, to experimentally prove that Planck was right by his Photoelectric Experiment for which Einstein was awarded the Nobel Prize. He demonstrated how light can only be absorbed in discrete chunks called as "photons" (the particle of light). A revolution was sparked and was about to shatter all physicists living in the comfort and warmth of Classical Physics. Soon after Einstein proved Max Planck's Theory the haze of confusion started spreading. The reason being everyone was aware of the fact that Light or Electromagnetic Radiations behave as waves. Maxwell's Equations and many other experiments such as Thomas Young's Double Slit Experiment proved that light propagated in the form of waves in the electric and magnetic field. Just like ripples on the surface of a pond. But then Einstein demonstrated it behaved as a particle too in the Photoelectric effect. The results were paradoxical. As we know, a wave does not have a definite position. It is spread out in space. It makes no sense to ask at what point a wave is located? - It is everywhere at once. However a particle has a definite position in space. How can then something behave both as a particle and as a wave at the same time? This gave rise to the Wave-Particle Duality in Quantum Physics. It was stated that light behaves both as a particle and as a wave depending on the circumstances. In Thomas Young's Double Slit Experiment, light behaves as waves and shows interference. Whereas, in Einstein's Photoelectric Experiment it behaves as particles. Problem solved? - Not yet. In 1924, Louis De-Broglie published his PhD thesis in which he reasoned that since light was initially thought to be waves but then turned out to also be like particles. Matter - which is thought to be like particles might also be waves in some circumstances. He called them - "Matter Waves". Mathematically, he postulated that the wavelength of these "Matter Waves" is inversely proportional to the momentum of body. Higher the momentum, lesser the wavelength and lesser is the wave behavior. Soon, experiments confirmed that matter indeed behaved like a wave sometimes. However, this wave effect is seen on extremely small scales. Particles like electrons show wave like behavior in certain circumstances. They diffract and show interference just like waves. Why large scale objects don't show wave behavior? - Because they carry large momentum, owing to their high mass. Since, De-Broglie's law stated that more the momentum, lesser the wavelength and lesser is the wave behavior. We don't see everyday objects acting like waves.
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| Interference Pattern of Light in Double Slit Experiment |
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| Interference Pattern showed by accumulated electrons passing through Double Slit. |
This discovery came as something unexpected. The story didn't end here. We are yet to come to Heisenberg, Bohr and Schrodinger. The pioneers of early Quantum Physics. Soon, the results of Quantum Theory were used to explain stability of atoms. Neils Bohr put forth his atomic model which perfectly explained why electrons are able to revolve around the nucleus of atom in fixed energy levels without collapsing onto it. In 1925, a young physicist- Werner Heisenberg published a paper which carried the famous "Uncertainty Principle". Heisenberg discovered something in the strange quantum experiments which were coming up. With De-Broglie's idea of "Matter Waves", Heisenberg deduced that the idea imposes a limitation on how much we can know about the "state" of a "system" (more precisely a "quantum" system). Earlier, I explained the meaning of "state" and "system" in Physics. The "positions" and "momenta" of all objects in the system are known specify its "state". But, the limitation imposed by Heisenberg's Uncertainty Principle was rather a severe one. It stated that - "It is impossible to simultaneously have exact knowledge of the position and momentum of a quantum object." No matter how hard you try, you cannot know the position and momentum of a particle at the same time with certainty. If you know one then the other would be uncertain. The original way in which Heisenberg reached this conclusion was different than today's interpretation for the principle. Today's explanation for the reason behind this principle is linked with the "wave behavior" of matter predicted by De-Broglie. As stated before, the wavelength of the matter wave of an object depends on its momentum. When any object is carrying a lesser momentum it has a longer wavelength. This means that it shows more wave-like behavior and as I said before - a wave is not localized in space. It is spread out and does not have a well defined position. On the other hand, if a particle carries more momentum, it has a shorter wavelength and lesser wave behavior. It is then said to be localized in space at a point. Thus, it is easy to understand where the Uncertainty Principle came from. A quantum particle whose momentum is well known, possess a defined wavelength and shows wave behavior. Its position then becomes uncertain. Whereas, a particle whose momentum is not known, does not have a wavelength defined, and is localized at a position like a particle.
The Uncertainty Principle now forms the heart of Quantum Physics. If it is disproved then the entirety of this subject would fall apart. But no one has ever been able to do so. There is just no way around it. Uncertainty Principle is a fundamental limitation in the Quantum World. It is responsible for majority of the chaos associated in Quantum Physics. This principle then implied that it is impossible to have complete knowledge of the "state" of a "quantum system". As we saw before, that position and momentum are needed to completely specify the state of a system. But the Uncertainty Principle forbids simultaneous knowledge of these two variables. Thus, one can never specify the state of "quantum system". This is where the entire notion of "Determinism" collapses. If one is not able to specify the present state of a system without ambiguity, then it would not be possible to determine its future state with certainty. Here, the final piece of our Quantum Puzzle fits in - "Probability". The world on its tiniest scale is totally random and in-deterministic. In 1926, a physicist named - Max Born formulated the Statistical Interpretation of Quantum Mechanics. I am going to discuss this interpretation precisely in part 2 of this article. But for now, it introduced "Probability" in Quantum Mechanics. When we are unaware of certain events we assign a probability or "chance" or "odds" to it. Similarly, in Quantum Physics since it is impossible to predict the future state of a system with certainty, we can find out the probability of a system to end up in a specific state. Einstein was most against this view of Quantum Physics and stated - "God does not play dice".
Summing it all up, Quantum Mechanics is chunky, random and unpredictable. Things in the quantum realm like Energy or Electric Charge do not have continuous values but only come in indivisible chunks of definite value. Also they act both as waves and as particles depending on the circumstance. In the quantum world, you cant predict the exact position and momentum of the particle at the same time. If you know one precisely, there is an ambiguity in the other. This means that you cant determine the outcome of an experiment with hundred percent certainty. Rather, you can say the probability that an outcome has in a given experiment. So this is it? - No. I would call this the story before interval. We are yet to see what happens when these observations of Quantum Mechanics contradicts our intuitions and are faced by many other explanations to make sense of it. All this along with "the climax" would be discussed in part 2 of this article.
- Thank You!
So picture abhi Baki hai... Seems interesting!! Waiting for second part.
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