Uncertainty principle

Uncertainty principle （ The principle of uncertainty ）

• Heisenberg's principle is based on 1927 year 3 month 23 in 《 Journal of Physics 》 Published on , It's called Uncertainty Principle.
• 1925 year , Heisenberg gave the matrix form of quantum mechanics , And find its multiplication rule ：p×q≠q×p.
• How to understand p×q≠q×p Well ？p It's momentum ,q Is the position , This is not to say ,, First observe the momentum p, Re observation position q, This is the same as observing first q Observe again p, Is the result different ？
• Suppose we have a small ball moving forward , So at every moment , Its momentum and position are two definite variables ？ Why is it just a difference in the order of observation , The result will be different ？ Unless you measure momentum p The action itself , It's affecting q The numerical . In turn, , measurement q The action of also affects p Value . however , If I measure at the same time p and q Well ？
• p×q≠q×p, Does it mean , Simultaneously measure p and q Is it impossible ？
• The key ： measurement ！ The length and width of a giant are fixed , While measuring its length , Its width will never change , vice versa . For a classic ball , How to measure its position ？ You must see it , Or use some instrument to detect it , No matter what , Need to touch it in some way , How else do you know its location ？ With “ notice ” For example , How can “ notice ” The position of a small ball ？ You need a photon to start from the light source , Hit the ball , And reflect it into your eyes . For a classic ball , Photons hitting it is like ants hitting elephants , The impact on it is negligible , It will never affect its speed . therefore , After its position can be measured , And then measure its speed , The error is negligible .
• But for an electron , Electrons are so small and light , So that the impact of photons on it can never be ignored . If we measure the position of electrons , Let a photon perform this task （ Hit this electron ）, The electron was hit hard and I don't know where it flew , And the current speed is unknown . so , In order to measure the position of electrons , We dramatically changed the speed of the electrons , That's momentum . therefore , It is impossible to know exactly the position of an electron at the same time , At the same time, we can accurately understand its momentum （ That is, the uncertainty principle ）.
• The formula $△p\times △q>\frac{h}{4\pi }$
  • $△p$ and $△q$ They are measurement p And measure q The error of the ,h It's the Planck constant .
  • measurement p And measure q The error of the , Their product must be greater than some constant .
  • If you put p The measurement is very accurate , in other words △p A very small , So correspondingly ,△q It's bound to get very big , That is to say, we are about q Our knowledge will become very vague and uncertain . In turn, , If we put the position q The measurement is very accurate ,p It becomes unstable , The error increases sharply .
  • If you put p Measured 100% accuracy , in other words △p=0, that △q It will become infinite .
• If we know the momentum of an electron p Full information , Then we lose its position at the same time q All the information about , We have no idea , Where is it , No matter how we arrange the experiment, we can't do it better .
• A typical fish and bear's paw cannot have both .p and q Like a pair of enemies , Life does not meet , With me without it , This peculiar quantity is called “ Conjugate quantity ”.
• There is also a set of conjugate quantities ： energy E And time t. Just energy E The more accurate the measurement is , moment t The more blurred ; In turn, , Time t The more accurate the measurement is , energy E Began to fluctuate on a large scale . and , The relationship between them follows similar uncertainty rules ：$△E\times △t>h$.
• t The more accurate the measurement is ,E The more uncertain . So in a very, very short moment , That is to say t A very definite moment , Even in a vacuum, there are huge fluctuations in energy . This kind of energy comes out of thin air completely depending on uncertainty , It does violate the law of conservation of energy ！ But this moment is very short , People haven't found out yet , It disappeared mysteriously , So that the law of conservation of energy can be maintained as a whole . The shorter the interval ,t The more certain ,E The more uncertain , The more energy that can appear out of thin air . therefore , The vacuum is boiling all the time , Mysterious energy is generated and disappeared everywhere . This energy is before we catch it , It disappeared . And the vacuum itself , Is the best medium to provide this fluctuation .