What exactly is the Heisenberg Uncertainty Principle?

Natural science, does not simply describe and explain nature, it is part of the interplay between nature and us – Werner Heisenberg

Some of you readers might have read about the Heisenberg Uncertainty Principle in high school or maybe even in college if you’ve attended courses on Quantum mechanics and Atomic Chemistry. But here we’re going to touch this topic both on an intuitive and mathematical level. Life has many trade-offs, the way my professor explained this to me is a very intuitive way of understanding this topic.

Let’s say you’re observing the routine of your mom and after a week, you realized that she’s gone to the Church on Saturday. Now, based on just this information, can we predict that your mom goes to the Church every Saturday? Of course not, we need further time for observation. Let’s say you then observe her for a month and notice that she goes to the church every Saturday. Based on this we might be able to make a statistical prediction, that your mom goes to the Church every Saturday. But still, we can’t be a 100% sure. Now let’s say you observe her for a year and see that she goes to the Church every Saturday.

Based on these observations, we can say that there’s a high probability that your mom goes to the Church every Saturday, but we still cannot be a 100% sure as it’s entirely possible that your mom decides to go the school next Saturday. Hence, we see that we would require an infinite amount of time to perfectly predict whether your mom goes to the Church every Saturday. Thus, there is a trade-off between the frequency of her visits and time.

This is an intuitive example of a real-world situation, like what our beloved Heisenberg Uncertainty Principle says. Introduced in 1927 by the German physicist Werner Heisenberg, the principle states that the more precisely the position of a particle is determined, the less precisely it’s momentum can be predicted from initial conditions and vice versa. This can majorly only be applied in the quantum realm and cannot be applied to everyday macroscopic objects like you and me.

 So, basically what the Heisenberg Uncertainty Principle wants to tell us is that let’s say there’s an electron revolving around its orbit and if we accurately measure it’s velocity with 100% precision, we have absolutely no idea where the exact position the electron is located ! How cool is that! in such a case where we know a particle’s velocity, it’s position can be graphed as a probability function. Hence the exact location of the electron is not certain but is rather expressed as a probability. 

Mathematically we can say that the probability of finding an electron at a point within an atom is directly proportional to |Ψ2| at that point. |Ψ2| is known as probability density and is always positive. |Ψ2| can also be interpreted as the probability of finding an electron in a unit volume. Hence, the probability of finding the electron in an infinitesimally small volume dV = |Ψ2|dV. Ψ (pronounced as psi) is also called the amplitude function and has a few interesting properties that can be mathematically proven. It in continuous, single valued and finite. Also, since the probability of finding the electron in the entire volume that we’ve assumed is 1, we can also write the integral equation ʃ|Ψ2|dV=1 with limits from -∞ to ∞.

Ψ is basically the mathematical representation of waves in quantum mechanics and is called wave function, its value depends on the coordinates of the electron in the atom and doesn’t have any physical meaning. It is found in many other equations too including the Schrodinger’s Equation (that deserves a separate article on it altogether), radial probability density, radial probability distribution etc.

For some of you math freaks, here’s an interesting triple integral. Considering the position of the electron in three dimensions, we can also state that the probability of finding it in that three-dimensional space is 1. Hence, we have the triple integral, ʃʃʃ|Ψ2|dx dy dz =1 with limits from -∞ to +∞ in each integral. If a wave satisfies that triple integral, it is said to be a normalized wave function.

The concept of treating the electron both as a particle and a wave is called wave particle duality (this too deserves an independent article). Coming back to the Heisenberg Uncertainty Principle, we can mathematically represent it as Δx Δp ≥ h/4∏. Here Δx represents uncertainty in position and Δp represents uncertainty in momentum, h is called the Planck’s constant and its value is 6.62 X 10-34 Joule second.


Therefore, this equation says that the product of uncertainty in position and uncertainty in momentum must always be greater than or equal to h/4∏. This essentially means that if uncertainty in position is very less i.e., we exactly know where the particle is located with a high degree of precision, then uncertainty in momentum must be very high to satisfy the equation i.e. we know very little about its momentum. And since momentum and velocity are closely related (p=mv), we don’t know its exact velocity in this case.

In the realm of quantum mechanics, we call variables such as position and momentum as conjugate or complementary variables. This in mathematics means that these variables such as position and momentum become Fourier transform duals. Other examples of conjugate variables would be time and frequency, Doppler and range etc. The important thing to be remembered is that the Heisenberg Uncertainty Principle can only be applied in the Quantum World on microscopic bodies showing wave particle duality. It cannot be applied on everyday macroscopic objects like you and me because macroscopic objects tend to have a high degree of particulate nature with an infinitely small wavelength.

Heisenberg formulated the Uncertainty Principle at Niels Bohr Institute in Copenhagen. According to Albert Einstein, randomness is a reflection of our ignorance and inability to comprehend a fundamental physical reality. On the other hand, Niels Bohr debated that probability distributions are irreducible and fundamental. Einstein and Bohr deliberated over the Heisenberg uncertainty principle for many years.

Heisenberg came to a very beautiful conclusion that formed as a base for further studies in the field of Quantum Mechanics. He theorized that absolute determinism was impossible as it required both position and momentum of the particle. This paved the way for the use of probabilistic determination of a particle due to the relation between position and momentum. This concept forms the base for the Copenhagen Interpretation of Quantum Mechanics.

A particularly interesting way to interpret the uncertainty principle is an illustration of how we see everyday objects. You can view and read this article due to photons of light which strike the surface and then bounce away. These photons inevitably transfer some energy to the surface it has bounced from. This energy will change the momentum of the electron on the surface. This way, we will be able to determine its momentum but not position. On the other hand,since quantum particles move at high speeds, it may no longer be in the same place. In either case, the uncertainly principle works and we cannot exactly determine the position and momentum of the electron.  

The uncertainty principle explains many phenomenons that cannot be explained using classical physics. For example, in atoms, negatively charged electrons orbit the positively charged nucleus. According to the theory of classical electrodynamics, the two opposite charges should attract each other eventually making the electron fall out of orbit and collapse in a spiral way. In such cases, the uncertainty principle makes things a lot simpler. If the electron gets too close to the nucleus, then its position can be precisely determined. But since its position can be accurately defined, its momentum would have a large error in measurement. Phew! Heisenberg saved us there. 

The uncertainty principle can also explain alpha decay. Alpha particle is a helium nucleus having two protons and two neutrons emitted by a heavy nuclei such as Uranium-238. These alpha particles are usually present inside the nucleus and require a very high amount of energy to break out. But since an alpha particle inside the nucleus has a well defined position, it doesn’t have a well defined velocity. This means that there is a very small chance that it might escape from the nucleus. This result sin alpha decay and radioactivity is observed. This process is known as Quantum Tunneling.  

One of the most intriguing results of the uncertainty principle is about vacuums. Vacuum in general sense means the absence of matter. However, in the quantum realm, things are not that straight-forward. Here, Heisenberg’s uncertainty principle is expressed in the form of energy and time. Thus, we can only accurately measure either the energy or time but not both. In this case, energy and time are conjugate variables. 

Uncertainty, which although seems very complex and some mystical theory, is fairly easy to understand and we probably wouldn’t be here if this principle wouldn’t exist. Werner Heisenberg received the Noble Prize for Physics in 1932 for his work in Quantum Mechanics. Another interesting thought example given by Albert Einstein disproves the Heisenberg Uncertainty Principle. Let’s say we have two balls, stick them together. Now spring them out so that both go in mutually opposite directions. Now, we can find the position of the first ball and not the momentum. Similarly, we can find the momentum of the second ball but not its position. But since the momentum of the second ball is mathematically related to the first ball, we can find the momentum of the first ball too! And voila, we hence can know both the exact position and momentum of both objects. I’ll leave this thought experiment open to interpretation to our readers. 

What exactly is the Heisenberg Uncertainty Principle?8 min read

640 thoughts on “What exactly is the Heisenberg Uncertainty Principle?8 min read

  1. Pranav it is a very difficult topic. We did it in final year of BSc and not many were clear with it . You have very lucidly simplified the complex topic of quantum mechanics which is mechanics of subatomic particles and is much different from classical mechanics where you can see and measure in real time every entity. Whereas in subatomic space what you have is probable momentum and probability position in real time . You are still in 10th class . It is laudable. Congratulations Pranav . Grandpa

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    Moderate Benefits Reported
    Manufacturers may succumb to the need to make untrue claims about their products’ abilities when promoting their goods. Even though we know that not all detox solutions are created equal, any top-quality THC detox product must meet a certain standard of efficacy. To do this, we looked for trustworthy companies with ethical and credible advertising.
    Use of Natural Ingredients Backed by Science
    It is not enough for a THC product to have substances that have scientific support; it also needs to have all-natural ingredients without any chemical additives. The best outcome is most likely to be achieved by products that have both of these.
    There is currently little scientific evidence to support using herbal treatments to remove THC from the body. However, we selected companies whose THC detox products are made with scientifically studied substances, including vitamins, antioxidants, and fruit juices, such as cranberry juice, lemon juice, apple cider vinegar, etc.
    Money-back And Satisfaction Guarantee
    All THC detox businesses assert that their solutions eliminate THC from your body. However, only the top THC detox firms offer a money-back guarantee to support those assertions. The greatest producers will give you peace of mind with a money-back guarantee since they are confident that their goods perform when you follow the directions. A THC detox company may not be assured of the efficacy of its medicine if they don’t provide this guarantee.
    Comfort and Flexibility
    Some people use futile strategies, such as drinking a lot of water, to remove THC from their bodies. Although this might be useful, it is unreliable because different body types and types of makeup exist. To do this, we selected companies that produce user-friendly THC detox solutions for all body types.
    Is it simple to use the THC detox product? Do you have to adhere to detailed instructions for days on end? Is there a temperature that the synthetic urine must reach in the microwave? Or does the business make any efforts to make its products as user-friendly as possible? The top THC detox pills offer tested cleansing power and simplicity of use.
    Brand Reputation and Reliability
    Since 2000, the top-ranked THC detox companies on our list have been producing effective goods. They have more than 22 years of expertise using tested items to assist customers in passing exams. These producers are transparent about their ingredients’ sources and manufacturing facilities. Some have registered dietitians on staff, a medical advisory board, and other health professionals to help them develop their recipes.
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    Organic, FDA-approved Components
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    Customer Reviews & Actual Success Rate
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    Since there’s a good chance you’ll need your detox product quickly, brands need a dependable shipping system that is quick, safe, and reasonably priced. We chose companies with low-cost delivery choices that are also quick enough to assist consumers in getting ready for urgent drug testing. The companies on our list provide free shipping in addition to other benefits.
    Fair and Competitive Pricing
    THC detox products are not inexpensive. Companies are aware that you’ll spend more to pass an exam. For many, it is the difference between losing their job and maintaining it—or facing other grave repercussions. However, we continued to favor THC detox solutions that offered fair, competitive pricing. It’s acceptable to charge more, but we avoided sellers who used price-gouging strategies or did so significantly.
    How Do THC Detox Products Work?
    THC metabolites are naturally removed from your system by THC detox products, which aid in your ability to pass THC drug tests. When you take THC, your body metabolizes it, resulting in the formation of THC. THC metabolites may linger in your body after THC and its effects have subsided.
    THC drug testing checks for THC metabolites in your blood, urine, saliva, or hair. The likelihood of failing a drug test increases with the number of metabolites in your system.
    THC can stay in your system for 36 hours to 90 days, depending on your degree of THC use, body weight, frequency of use, test type, and other factors. THC typically lasts 36 hours in your blood, 48 hours in your saliva, 3 to 30 days in your urine, 7 to 14 days in your sweat, and 90 days in your hair.
    Blood or saliva test is the most frequently used drug test. Using the THC detox kits listed above, you could pass a blood or saliva test after a few hours or a few days of preparation.
    THC and other toxins can dissolve in fat. This means that your body stores these pollutants as fat. Your body can accumulate an excessive amount of these toxins over time with heavy use. You can test positive for THC if you don’t utilize a decent THC detox product because your fat contains cannabinoids.
    THC is a fat-soluble toxin; thus, heavier individuals with increased body fat percentages may require more potent THC detox products than leaner or more muscular ones.
    The most common THC metabolite that is detected in drug testing is THC-cooh. Your body produces this THC-cooh as it breaks down THC. A THC drug test may be able to find levels of this metabolite even weeks after your last THC consumption, depending on the testing procedure.
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    Several THC detox products include natural, plant-based ingredients such as cranberry, aloe vera, etc., which have been scientifically proven to help cleanse THC out of the body. Below we have discussed some of these ingredients commonly found in THC detox cleanses and how they are backed by science:
    Apple Cider Vinegar
    Apple cider vinegar is a natural detoxifier, but it can also help you get rid of the toxins stored in your body from marijuana use. Apple cider vinegar has been used for centuries as a natural remedy for many health conditions. It helps to cleanse the liver, kidneys, and colon and helps to flush out heavy metals like mercury and lead.
    It’s also an effective way to detoxify the body after smoking or ingesting cannabis. The acetic acid in apple cider vinegar breaks down the tetrahydrocannabinol (THC) in weed into harmless byproducts, making it easier to pass through the digestive system.
    A study published in the Journal of Ethnopharmacology found that people who drank ACV before eating had lower levels of THC metabolites in their urine than those who didn’t drink ACV beforehand.
    The researchers concluded that “ACV may be useful in reducing the adverse effects associated with THC consumption.”
    Cranberry juice contains high amounts of vitamin C, which helps to boost your immune system and fight off infection. Cranberries have long been known to help prevent urinary tract infections, making them a great addition to any cannabis detox plan.
    Cranberries contain more antioxidants than blueberries, blackberries, strawberries, raspberries, and even red wine! They also contain flavonoids called proanthocyanidins, which act as powerful anti-inflammatory agents.
    When you consume marijuana, some of its active ingredients will remain in your bloodstream for several hours. If you smoke or vape during the day, you could still test positive for THC when you go to bed at night.
    Cranberries can remove these THC molecules from your bloodstream because they contain large amounts of tannin, which binds to the cannabinoids and carries them out of your body.
    This process takes time, so you should start drinking cranberry juice about two weeks before you stop using marijuana. You can continue drinking cranberry juice daily until you feel completely clear of THC.
    Lemon Juice
    Lemons contain vitamin C, potassium, magnesium, calcium, iron, and fiber. These nutrients stabilize blood pressure, improve heart function, and strengthen bones.
    Lemons contain citric acid, which works as an antiseptic agent. When you eat lemons, this citric acid travels through your stomach and intestines, dissolving the fats and proteins in food.
    Because of this, lemon juice can help to break down THC molecules in your body. One study found that consuming lemon juice and THC helped reduce the number of THC metabolites in your urine.
    A double-blind, randomized controlled trial conducted at the University of California San Diego School of Medicine found that participants who consumed lemon juice before smoking pot were less likely to test positive for THC in their urine.
    The researchers concluded: “Our findings suggest that lemon juice ingestion reduces the likelihood of cannabinoid detection in urine samples collected up to 24 h post-smoking.”
    Aloe Vera
    Aloe vera is often used to treat sunburns and other skin conditions. It has many healing properties, including vitamins and minerals like Vitamin B12, zinc, copper, manganese, and iron.
    It’s also loaded with polysaccharides, complex sugars that give aloe plants their thick, succulent leaves. Aloe vera contains aloin, which acts as a natural diuretic.
    Aloe vera contains enzymes called lipases, which break down fat cells in your body. Because THC is stored inside fat cells, aloe vera can help to dissolve these fat stores and flush them out of your system.
    In addition, aloe vera contains mucilage, which helps to bind water into gel form. It is similar to gelatin but doesn’t need heat to set. Instead, it forms naturally when plant sap comes into contact with air.
    Mucilage is also known to help remove toxins from the body, as it was recently discovered that it might help treat people suffering from liver disease.
    Zinc is essential for maintaining healthy immune systems and keeping your hair, nails, teeth, and muscles strong. Zinc deficiency can lead to poor memory, depression, and even seizures.
    When you consume marijuana, THC molecules attach to zinc atoms in your brain and nervous system. As a result, THC can interfere with how your brain processes information.
    If you have low levels of zinc in your body, you may experience cognitive impairment after smoking weed. A recent study published in the journal Psychopharmacology found that zinc supplementation reduced the number of THC metabolites in the urine of cannabis users.
    According to the authors, “These results indicate that zinc supplementation may be effective in reducing the risk of developing adverse effects associated with chronic use of cannabis.”
    THC Detox FAQs
    Q: Can THC Drug Tests be Defeated?
    A: Yes, even if you’ve recently used THC, you can still pass a drug test. While heavy users can employ THC detox kits to pass a drug test, a light THC user can eliminate all traces of THC from their system in as little as 2 to 4 days. So, passing a drug test is pretty straightforward if you use a few THC detox products.
    Q: How do THC Drug Tests Happen?
    A: A drug test looks for THC metabolites in your blood, sweat, saliva, hair, or urine, including THC-cooh, the most predominant metabolite.
    Q: Which Natural Ingredients are Part of The Best THC Detox Kit?
    A: Although it might not seem like it, apple cider vinegar, lemon juice, and cranberry juice work well in detoxing THC. People can use all these ingredients to pass a drug test successfully.
    Q: How Does Apple Cider Vinegar Help in THC Detox?
    A: Due to its antibacterial qualities, apple cider vinegar eliminates any hazardous germs, including THC, from your body. Many people have used ACV to pass drug tests because it removes THC buildup from hair follicles, a fantastic property of the vinegar that it doesn’t just affect the blood or urine drug tests. Therefore, apple cider vinegar is an excellent choice for people who don’t want to add to the confusion by taking medications and drinks.
    Q: Can ACV Help Detox THC?
    A: ACV is a natural detoxifier that can help you get rid of toxins in your body, including those from marijuana use. It’s also an antioxidant and anti-inflammatory agent.
    If you’re thinking about quitting smoking or using cannabis for the first time, it might be worth trying to detoxify with ACV before doing so. There are many reasons why this may work:
    ACV has been shown to reduce cravings for nicotine (and other substances): Apple cider vinegar is one of the most effective ways to quit smoking.
    ACV helps break down nicotine into water and carbon dioxide: When you inhale, you don’t absorb any nicotine into your bloodstream.
    ACV helps flush out toxins: When you drink apple cider vinegar, it breaks down some heavy metals and other toxins in your system.
    ACV boosts your immune system: Apple cider vinegar contains acetic acid, an antibacterial and antiviral agent.
    ACV reduces inflammation: The acetic acid in apple cider vinegar works as an anti-inflammatory agent. If you have arthritis, gout, fibromyalgia, or another inflammatory condition, drinking ACV could help relieve symptoms.
    Q: How Does Marijuana Affect Your Body?
    A: Marijuana contains hundreds of different chemicals called cannabinoids. Cannabinoids interact with specific proteins in our bodies called cannabinoid receptors. These receptors help control various processes in the body, such as inflammation, pain, hunger, and memory.
    When you smoke or eat marijuana, cannabinoids bind to your brain and body receptors. This interaction triggers changes in your brain chemistry and produces the feeling of being high.
    Q: What are the Effects of THC on The Brain?
    A: THC can affect many parts of the brain, including the hippocampus, which controls learning and memory. It also affects the amygdala, a structure involved in emotions and stress responses. This can cause anxiety and paranoia.
    Q: How Does Marijuana Affect the Heart?
    A: The heart rate increases when people use marijuana because it stimulates the sympathetic nervous system. This causes blood pressure to rise and makes the heart beat faster.
    In addition, THC may cause an irregular heartbeat by interfering with the electrical activity of the heart muscle cells.
    Q: How Does Marijuana Impact the Lungs?
    A: Smoking marijuana can damage lung tissue. People who smoke marijuana regularly have more respiratory problems than those who don’t smoke at all.
    Inhaling marijuana smoke irritates the lungs and damages the air sacs in the lungs. As a result, breathing becomes more challenging and takes longer. A study published in the Journal of Clinical Pharmacology found that smoking marijuana reduces the amount of oxygen in the bloodstream.
    Q: How Does Marijuana Change Mood?
    A: Marijuana alters mood by changing neurotransmitters like dopamine and serotonin levels. Dopamine helps regulate movement and motivation, while serotonin regulates sleep and appetite.
    People who use marijuana tend to feel happier, calmer, and less anxious. They also report having fewer negative thoughts. However, some studies suggest long-term marijuana use may be associated with depression and anxiety disorders.
    Q: What Is Fake Urine Made Of?
    A: Synthetic urine combines corn syrup, sugar, sodium bicarbonate, and citric acid. These chemicals react together to create a chemical reaction that mimics human urine.
    When you add these chemicals to your urine sample, it will look like real urine.
    Q: Why Do People Use Synthetic Urine?
    A: People who use synthetic urine often do so for two reasons:
    To avoid getting caught while using drugs: This is especially true if you’re going through rehab or jail. A person who uses synthetic urine can pass a urine test without going to the bathroom.
    To hide their drug use: Some people use synthetic urine to conceal their drug use. They’ll mix the urine with alcohol or coffee to make it appear more diluted.
    Q: Can A Hair Follicle Test Detect Marijuana?
    A: A hair follicle test detects THC; however, several factors affect how accurate this test is. For example, the time between when you smoked weed and when you had your hair tested affects whether the results show up.
    Also, the type of marijuana used matters. Some strains of marijuana contain higher amounts of THC than others. Finally, the method of ingestion—smoking versus eating—also affects the accuracy of the test.
    Q: Which Is More Harmful – Smoking THC or Ingesting It?
    A: Smoking THC is much worse for your body than ingesting it. When ingested, THC enters your bloodstream quickly. It doesn’t stay in your system long enough to cause harm.
    However, when you smoke weed, THC stays in your lungs longer. This allows it to enter your bloodstream and circulate throughout your entire body.
    In addition, inhaling THC causes your brain to release dopamine. Dopamine is a neurotransmitter that makes you feel happy. So, when you smoke weed regularly, you may experience feelings of happiness.
    Final Verdict on The Best THC Detox Products of 2022
    Whether you keep or lose your work may depend on passing a drug test. It might also play a role when looking for your ideal employment. Therefore, if you use marijuana frequently, getting one of the top THC detox pills we evaluated above would be beneficial.
    Depending on the exam you’re getting ready for, you can get rid of THC from your body within a few hours or days with the correct product and pass a drug test. You can also find other strategies that complement each other and help you pass the drug test.
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    The links contained in this product review may result in a small commission if you opt to purchase the product recommended at no additional cost to you. This goes towards supporting our research and editorial team. Please know we only recommend high-quality products.
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