Table of Contents<\/h2>- Werner Heisenberg’s Uncertainty Principle Explained<\/a>
- The Origins of Quantum Mechanics<\/a><\/li>
- Quantum Uncertainty<\/a><\/li>
- What Does Uncertainty Even Mean?<\/a><\/li><\/ul><\/li>
- Learn More About Quantum Uncertainty<\/a><\/li><\/ul><\/div>\n\n\n\n
Werner Heisenberg’s Uncertainty Principle Explained<\/h2>\n\n\n\n
In his book A Brief History of Time<\/a><\/em>, Hawking explains that Heisenberg’s uncertainty principle states there is always at least a certain amount of uncertainty in your measurement of the position and velocity of a particle. <\/strong>This is important because, to predict where a particle will go (or is most likely to go) in the future, you need to know where it was and which way it was going at some point in the past or present. Uncertainty about the present creates greater uncertainty about the future.<\/p>\n\n\n\n(Shortform note: Hawking explains how uncertainty can limit the accuracy of your predictions in physics, but this general concept is applicable to other areas as well, especially in fields like the social sciences where outcomes are harder to measure or quantify. In his book Superforecasting<\/em><\/a>, <\/em>Philip Tetlock discusses the importance of measurement<\/a> in predicting the future. In particular, he points out that many political and economic forecasters\u2019 predictions are never actually checked against measurements after the fact. This makes it difficult to assess the credibility of the forecaster or the accuracy of their methods.)<\/p>\n\n\n\nTo understand how the uncertainty principle works, it’s important to know a few things about quantum mechanics. For one thing, as Hawking notes, a basic premise of quantum mechanics is that certain quantities like energy and frequency have to be incremented by at least a certain minimum value. (Shortform note: This minimum unit is called a \u201cquantum\u201d of energy, which is where \u201cquantum mechanics\u201d gets its name.)<\/p>\n\n\n\n
To explain this phenomenon, it\u2019s helpful to consider how quantum mechanics was discovered, so let’s discuss its origins. Then, we\u2019ll show how quantum mechanics gives rise to the uncertainty principle.<\/p>\n\n\n\n
The Origins of Quantum Mechanics<\/h3>\n\n\n\n
Hawking recounts that, circa 1900, scientists realized that their theories of radiant heat transfer predicted that any hot object should radiate an infinite amount of energy, which was obviously not the case. The reason was that in these theories, radiation could have any frequency, and objects were thought to give off radiation uniformly over a range of frequencies.<\/p>\n\n\n\n
For example, a hot object might give off radiation at 10 Mhz, 10.1 MHz, 10.01 Mhz, and so on. Mathematically, there are an infinite number of frequencies between 10 and 11 MHz (or any two frequencies), so if the object radiates energy at every possible frequency, then it will give off an infinite amount of energy. <\/p>\n\n\n\n
Hawking explains how, to resolve this problem, Max Planck hypothesized that physical quantities like the frequency of radiation are \u201cquantized,\u201d meaning they can only have certain distinct values. If frequency could only be incremented by a finite value, then an object would only give off a finite amount of radiation because there would only be a finite number of frequencies at which it could give off radiation. This solved the problem and led to the development of the theory of quantum mechanics.<\/p>\n\n\n\n
Shortform Note: Standing Waves and Quantization<\/h4>\n\n\n\n
As Hawking recounts, Planck was the first to recognize that electromagnetic energy was quantized, and Planck may have coined the term \u201cquantum.\u201d However, in Planck\u2019s day, it was already common knowledge that certain physical quantities were \u201cquantized,\u201d in the sense that they could only have certain values.<\/p>\n\n\n\n
In particular, the harmonics of standing waves<\/a> are quantized, as Pythagoras described around 500 BC. If you pluck a guitar string (or any string stretched between two fixed points) it will only vibrate at certain frequencies, called harmonics. This is because the fixed ends of the string constrain it, such that it can only support waves if the length of the string is equal to half the wavelength of the wave, or a whole-number multiple of this length. So, if your guitar string is 24 inches long, it will only vibrate at frequencies that correspond to waves with a wavelength of 48 inches, 24 inches, 16 inches, 12 inches, 9.6 inches, and so on.<\/p>\n\n\n\n![\"\"](\"https:\/\/lh3.googleusercontent.com\/3eA_QWB78UMH5BAdtbclyrdIM8iyk7Rcz0WulaEucjmFY_YeVu9tfk13okIPxZVYUcct_nXF9MaQbS7IJh7i6W51bj9ezEKtjuwDR4Mqc4xuxCtKgL5r9DOOP4ZITlL1KHJoEV0\")
<\/figure>\n\n\n\nToday, physicists often describe an electron\u2019s orbit around an atom\u2019s nucleus as a type of standing wave<\/a> and use this to explain the quantization of electromagnetic energy.<\/p>\n\n\n\nQuantum Uncertainty<\/h3>\n\n\n\n
But how does the fact that frequency is quantized give rise to the uncertainty principle? It has to do with the way <\/strong>light disturbs particles.<\/p>\n\n\n\nAs Hawking explains, you can see something only<\/strong><\/strong> if it is reflecting (or otherwise emitting) light<\/strong>. If there\u2019s no light, you won\u2019t be able to see it. The same principle applies to measuring subatomic particles: The instruments that measure their position and velocity can only \u201csee\u201d them by bouncing light (or other particles, like electrons) off of them. <\/p>\n\n\n\nHowever, according to Hawking, this imposes fundamental limitations on the accuracy of the measurement, because bouncing photons or electrons off of a subatomic particle will change its velocity.<\/strong> The higher the frequency of the light bouncing off a subatomic particle, the more energy its photons have, and the more it will change the velocity of the particle you\u2019re trying to measure. The frequency is also inversely proportional to the wavelength, and the light that bounces off the particle will only indicate its position to the nearest wavelength. <\/p>\n\n\n\nThus, if you use very high-frequency light, you can measure the particle\u2019s position very accurately, but you\u2019ll disrupt its velocity so much that you get no useful information about its velocity. If you use very low-frequency light, you can measure its velocity accurately, but not its position. If you use an intermediate frequency, you can measure both position and velocity with an intermediate amount of uncertainty, but your <\/strong>total<\/em><\/strong> uncertainty will always be at least a certain value.<\/strong><\/p>\n\n\n\n
- The Origins of Quantum Mechanics<\/a><\/li>
- Quantum Uncertainty<\/a><\/li>
- What Does Uncertainty Even Mean?<\/a><\/li><\/ul><\/li>
- Learn More About Quantum Uncertainty<\/a><\/li><\/ul><\/div>\n\n\n\n
Werner Heisenberg’s Uncertainty Principle Explained<\/h2>\n\n\n\n
In his book A Brief History of Time<\/a><\/em>, Hawking explains that Heisenberg’s uncertainty principle states there is always at least a certain amount of uncertainty in your measurement of the position and velocity of a particle. <\/strong>This is important because, to predict where a particle will go (or is most likely to go) in the future, you need to know where it was and which way it was going at some point in the past or present. Uncertainty about the present creates greater uncertainty about the future.<\/p>\n\n\n\n
(Shortform note: Hawking explains how uncertainty can limit the accuracy of your predictions in physics, but this general concept is applicable to other areas as well, especially in fields like the social sciences where outcomes are harder to measure or quantify. In his book Superforecasting<\/em><\/a>, <\/em>Philip Tetlock discusses the importance of measurement<\/a> in predicting the future. In particular, he points out that many political and economic forecasters\u2019 predictions are never actually checked against measurements after the fact. This makes it difficult to assess the credibility of the forecaster or the accuracy of their methods.)<\/p>\n\n\n\n
To understand how the uncertainty principle works, it’s important to know a few things about quantum mechanics. For one thing, as Hawking notes, a basic premise of quantum mechanics is that certain quantities like energy and frequency have to be incremented by at least a certain minimum value. (Shortform note: This minimum unit is called a \u201cquantum\u201d of energy, which is where \u201cquantum mechanics\u201d gets its name.)<\/p>\n\n\n\n
To explain this phenomenon, it\u2019s helpful to consider how quantum mechanics was discovered, so let’s discuss its origins. Then, we\u2019ll show how quantum mechanics gives rise to the uncertainty principle.<\/p>\n\n\n\n
The Origins of Quantum Mechanics<\/h3>\n\n\n\n
Hawking recounts that, circa 1900, scientists realized that their theories of radiant heat transfer predicted that any hot object should radiate an infinite amount of energy, which was obviously not the case. The reason was that in these theories, radiation could have any frequency, and objects were thought to give off radiation uniformly over a range of frequencies.<\/p>\n\n\n\n
For example, a hot object might give off radiation at 10 Mhz, 10.1 MHz, 10.01 Mhz, and so on. Mathematically, there are an infinite number of frequencies between 10 and 11 MHz (or any two frequencies), so if the object radiates energy at every possible frequency, then it will give off an infinite amount of energy. <\/p>\n\n\n\n
Hawking explains how, to resolve this problem, Max Planck hypothesized that physical quantities like the frequency of radiation are \u201cquantized,\u201d meaning they can only have certain distinct values. If frequency could only be incremented by a finite value, then an object would only give off a finite amount of radiation because there would only be a finite number of frequencies at which it could give off radiation. This solved the problem and led to the development of the theory of quantum mechanics.<\/p>\n\n\n\n
Shortform Note: Standing Waves and Quantization<\/h4>\n\n\n\n
As Hawking recounts, Planck was the first to recognize that electromagnetic energy was quantized, and Planck may have coined the term \u201cquantum.\u201d However, in Planck\u2019s day, it was already common knowledge that certain physical quantities were \u201cquantized,\u201d in the sense that they could only have certain values.<\/p>\n\n\n\n
In particular, the harmonics of standing waves<\/a> are quantized, as Pythagoras described around 500 BC. If you pluck a guitar string (or any string stretched between two fixed points) it will only vibrate at certain frequencies, called harmonics. This is because the fixed ends of the string constrain it, such that it can only support waves if the length of the string is equal to half the wavelength of the wave, or a whole-number multiple of this length. So, if your guitar string is 24 inches long, it will only vibrate at frequencies that correspond to waves with a wavelength of 48 inches, 24 inches, 16 inches, 12 inches, 9.6 inches, and so on.<\/p>\n\n\n\n
Today, physicists often describe an electron\u2019s orbit around an atom\u2019s nucleus as a type of standing wave<\/a> and use this to explain the quantization of electromagnetic energy.<\/p>\n\n\n\n
Quantum Uncertainty<\/h3>\n\n\n\n
But how does the fact that frequency is quantized give rise to the uncertainty principle? It has to do with the way <\/strong>light disturbs particles.<\/p>\n\n\n\n
As Hawking explains, you can see something only<\/strong><\/strong> if it is reflecting (or otherwise emitting) light<\/strong>. If there\u2019s no light, you won\u2019t be able to see it. The same principle applies to measuring subatomic particles: The instruments that measure their position and velocity can only \u201csee\u201d them by bouncing light (or other particles, like electrons) off of them. <\/p>\n\n\n\n
However, according to Hawking, this imposes fundamental limitations on the accuracy of the measurement, because bouncing photons or electrons off of a subatomic particle will change its velocity.<\/strong> The higher the frequency of the light bouncing off a subatomic particle, the more energy its photons have, and the more it will change the velocity of the particle you\u2019re trying to measure. The frequency is also inversely proportional to the wavelength, and the light that bounces off the particle will only indicate its position to the nearest wavelength. <\/p>\n\n\n\n
Thus, if you use very high-frequency light, you can measure the particle\u2019s position very accurately, but you\u2019ll disrupt its velocity so much that you get no useful information about its velocity. If you use very low-frequency light, you can measure its velocity accurately, but not its position. If you use an intermediate frequency, you can measure both position and velocity with an intermediate amount of uncertainty, but your <\/strong>total<\/em><\/strong> uncertainty will always be at least a certain value.<\/strong><\/p>\n\n\n\n
- Quantum Uncertainty<\/a><\/li>