what is quantum entanglement and what is the force or phenomenon responsible for it.
The history of quantum entanglement can be traced back to the early days of quantum mechanics in the 1920s and 1930s.
In 1927, the German physicists Werner Heisenberg and Wolfgang Pauli proposed the concept of "entanglement" or "Verschränkung" in German, to describe a peculiar property of quantum mechanics. They realized that when two quantum systems interacted and became "entangled", their individual properties became indeterminate and instead became correlated with each other.
The concept of entanglement gained further attention in 1935 when Albert Einstein, Boris Podolsky, and Nathan Rosen published a paper that became known as the EPR paper. They argued that the entanglement of two particles violated the principles of local realism, which stated that physical properties should exist independently of observation and that distant events should not be able to instantaneously influence each other. They proposed a thought experiment to show that entangled particles must have a more complete description than was currently allowed by quantum mechanics.
In 1964, the Irish physicist John Stewart Bell proposed a way to test the EPR paradox experimentally using a set of inequalities that became known as "Bell's inequalities". He showed that if the predictions of quantum mechanics were correct, certain correlations between entangled particles could violate these inequalities and thus demonstrate the nonlocality of entanglement.
Experiments testing Bell's inequalities were conducted in the 1970s and 1980s, and they consistently showed violations of the inequalities that were not possible under the assumptions of local realism. These results provided strong evidence for the reality of entanglement and the nonlocality of quantum mechanics.
Since then, entanglement has become a key concept in quantum mechanics, with applications in fields such as quantum cryptography, quantum computing, and quantum teleportation. The study of entanglement continues to be an active area of research in both theoretical and experimental physics.
The following are the various developments since the phenomenon of quantum entanglement was discovered.
Since the inception of quantum entanglement in the 1920s and 1930s, there have been many developments in the study of entangled quantum systems. Here are some of the key developments:
Bell's inequalities and experimental tests: In 1964, John Stewart Bell proposed a set of inequalities that could be used to test for the nonlocality of entangled quantum systems. These inequalities were violated by the predictions of quantum mechanics, leading to a series of experimental tests that confirmed the reality of entanglement and the nonlocality of quantum mechanics.
Applications in quantum cryptography: The correlations between entangled particles can be used to generate secure keys for quantum cryptography, which is a method for secure communication that is based on the principles of quantum mechanics. Entanglement-based quantum key distribution (QKD) protocols have been implemented in the lab and have shown promise for secure communication.
Applications in quantum computing: Entangled states can be used to perform quantum operations that are faster than classical operations, leading to the development of quantum algorithms and quantum computers. Entanglement is a key resource for quantum computing and quantum error correction.
Applications in quantum teleportation: The properties of an entangled state can be used to transfer the quantum state of one particle to another particle in a process called quantum teleportation. This has potential applications for secure communication and quantum computing.
Developments in theory: The study of entanglement has led to new theoretical insights into the foundations of quantum mechanics, including the role of entanglement in the measurement problem, the nature of quantum correlations, and the relationship between quantum mechanics and classical physics.
Quantum entanglement is a phenomenon that occurs in the field of quantum mechanics, which is the branch of physics that describes the behavior of particles at the smallest scales. In quantum entanglement, two or more particles become linked in such a way that their quantum states become correlated, meaning that the properties of one particle are dependent on the properties of the other particle.
When two particles are entangled, any measurement made on one particle will instantaneously affect the state of the other particle, regardless of the distance between them. This property of entanglement has been referred to as "spooky action at a distance" and has been verified through numerous experiments.
Entanglement plays a critical role in the development of quantum technologies such as quantum computing and quantum cryptography. It also has implications for our understanding of the nature of reality and the fundamental principles of physics.
A mathematical description of quantum entanglement is typically given in terms of a state vector, which is a mathematical object used to describe the state of a quantum system.
Suppose we have two particles, A and B, that are in an entangled state. We can describe this state using the following equation:
|Ψ⟩ = a|0⟩A |1⟩B + b|1⟩A |0⟩B
In this equation, |0⟩A and |1⟩A represent two possible states of particle A, and |0⟩B and |1⟩B represent two possible states of particle B. The coefficients a and b represent the probability amplitudes for the particles to be in each of the possible states.
The entangled state described by this equation means that if we measure particle A and find it to be in state |0⟩A, then particle B will be in state |1⟩B with probability |a|^2 and in state |0⟩B with probability |b|^2. Similarly, if we measure particle A and find it to be in state |1⟩A, then particle B will be in state |0⟩B with probability |a|^2 and in state |1⟩B with probability |b|^2.
This equation demonstrates the correlation between the states of the two particles, which is the hallmark of quantum entanglement.
A photon is a fundamental particle of light and electromagnetic radiation. It is the smallest possible unit of light, and it has no mass or electric charge.
In physics, light is understood as a wave-like phenomenon, but it can also be described as a stream of particles called photons. Photons are quantized packets of energy that are emitted or absorbed when charged particles, such as electrons, change their energy levels or when charged particles accelerate.
Photons exhibit properties of both particles and waves, and their behavior is described by the principles of quantum mechanics. For example, photons can interfere with one another like waves, and they can also be localized and detected like particles.
Photons play a critical role in a wide range of phenomena, from the transmission of information in optical fibers to the generation of electricity in solar cells. They also have many applications in fields such as medical imaging, telecommunications, and quantum computing.Photons are elementary particles, which means they are not composed of smaller sub-particles. Therefore, they do not have a size in the traditional sense.
However, the wavelength and frequency of a photon are related to its energy and momentum, and these quantities can be used to describe certain aspects of the photon's behavior. The wavelength of a photon can range from picometers to meters, depending on its frequency and energy. In general, photons with higher energy (e.g., gamma rays) have shorter wavelengths, while photons with lower energy (e.g., radio waves) have longer wavelengths.
Despite not having a size, the effects of photons can be observed through their interactions with matter. For example, when a photon is absorbed by an atom, it can cause an electron to move to a higher energy level. This process is the basis for many phenomena in optics and quantum mechanics. photons can have wavelengths that are incredibly long. The wavelength of a photon is inversely proportional to its frequency, and since frequency is related to energy, photons with very low energy can have very long wavelengths.
For example, radio waves are a type of electromagnetic radiation that have very long wavelengths, ranging from centimeters to kilometers. These radio waves are still composed of individual photons, but the photons have very low energy and very long wavelengths.Despite their large wavelength, radio photons still travel at the speed of light and exhibit wave-like properties such as interference and diffraction. However, their low energy and long wavelength make them less useful for many applications that require higher energy photons such as visible light, X-rays, or gamma rays.
Here's an equation that describes two subatomic particles, A and B, that are entangled by a single photon of long wavelength:
|Ψ⟩ = 1/√2(|0⟩A |1⟩B - |1⟩A |0⟩B)
In this equation, |0⟩A and |1⟩A represent the two possible states of particle A, and |0⟩B and |1⟩B represent the two possible states of particle B. The coefficients before each state represent the probability amplitudes for the particles to be in each of the possible states.
The entangled state described by this equation means that if we measure particle A and find it to be in state |0⟩A, then particle B will be in state |1⟩B with a probability of 1/2 and in state |0⟩B with a probability of 1/2. Similarly, if we measure particle A and find it to be in state |1⟩A, then particle B will be in state |0⟩B with a probability of 1/2 and in state |1⟩B with a probability of 1/2.
The long-wavelength photon that entangles the two particles is not explicitly included in the equation, but it is implied as the mediator of the entanglement. This type of entanglement, where two particles are entangled through the exchange of a single photon without continous interaction, is known as "quantum teleportation" and has been demonstrated experimentally.
However is the photon is continously having an interaction or maintaining a stable state it can be just quantuam entanglement,where a change in one body will instaneously have an effect of another body.
An equation that describes the entangled state of two particles, A and B, that are entangled by a photon with a wavelength of 200,000 meters:
|Ψ⟩ = 1/√2(|0⟩A |1⟩B - e^(iλ/2π) |1⟩A |0⟩B |1⟩photon - e^(-iλ/2π) |1⟩A |0⟩B |0⟩photon)
In this equation, λ represents the wavelength of the photon, which is 200,000 meters in this case. |0⟩A and |1⟩A represent the two possible states of particle A, and |0⟩B and |1⟩B represent the two possible states of particle B. |0⟩photon and |1⟩photon represent the two possible states of the photon.
The coefficients before each state represent the probability amplitudes for the particles and photon to be in each of the possible states. The first term in the equation represents the state where particle A is in state |0⟩A and particle B is in state |1⟩B, while the second term represents the state where particle A is in state |1⟩A and particle B is in state |0⟩B, with the photon in state |1⟩photon.
The last two terms represent the state where particle A is in state |1⟩A and particle B is in state |0⟩B, with the photon in either state |0⟩photon or |1⟩photon, respectively. The coefficients in these terms involve the phase factor e^(iλ/2π) and its complex conjugate e^(-iλ/2π), which are related to the wavelength of the photon and the distance between the particles.
Note that this equation assumes that the two particles and the photon are in a pure state, and it describes their entangled state at a specific moment in time. The state of the particles and the photon can change over time due to their interactions with their environment, and this may affect their entanglement.
it is possible to describe the mathematical state of entanglement of two particles A and B that are maintained in a steady state by a photon with a wavelength of 200,000 meters.
In general, the entangled state of two particles A and B can be described using a wave function or state vector, which is a mathematical representation of the probabilities of the different possible outcomes of measurements on the particles. The wave function typically involves complex numbers, and its evolution over time is governed by the Schrödinger equation.
For two particles A and B that are entangled by a photon, the state of the system can be described using a tensor product of the individual states of each particle and the photon. In the case of a photon with a wavelength of 200,000 meters, the state of the photon can be approximated as a plane wave with a well-defined momentum and energy, while the states of the particles can be represented as spin states, energy levels, or other relevant properties depending on the system.
The entangled state of the two particles and the photon can then be described using a combined wave function or state vector, which takes into account the correlations between the particles and the photon due to their entanglement. The exact form of this wave function depends on the specific details of the system and the measurement basis chosen for the particles.
In summary, the mathematical description of the state of entanglement of two particles A and B maintained in a steady state by a photon of wavelength 200,000 meters would involve a wave function or state vector that represents the correlations between the particles and the photon due to their entanglement. This wave function can be determined using the principles of quantum mechanics and the specific details of the system.
