The present paper is concerned with the derivation of the Einstein's formula of equivalence of mass and energy, E = mc^2 , from the universal uncertainty relations. These relations are a generalization of the original uncertainty relations developed by Werner Heisenberg in 1927. Thus, this approach unifies two of the most important laws of physics as provides the proof of a) the quantum mechanical nature of the above formula, and, b) the correctness of the universal uncertainty relations that I found in 2012.
The present paper is concerned with the derivation of the Einstein's formula of equivalence of mass and energy, E = mc^2 , from the universal uncertainty relations. These relations are a generalization of the original uncertainty relations developed by Werner Heisenberg in 1927. Thus, this approach unifies two of the most important laws of physics as provides the proof of a) the quantum mechanical nature of the above formula, and, b) the correctness of the universal uncertainty relations that I found in 2012.
The Heisenberg equation may not be as well-known as Einstein’s e=mc^2. But the Heisenberg equation’s implications that there is an irreducible uncertainty with regard to the position of an object are no less intriguing than the implications of Einstein’s relativity equation that time slows to a stop when the relative velocity of an object approaches the speed of light. Using elementary mathematics and science, this paper begins by examining the physics of motion of an everyday object such as a tennis ball. The paper shows that the same physics that applies to everyday objects in fact also applies when it comes to subatomic particles, such as an electron in motion. And by taking gradual incremental steps in developing the mathematics of the underlying physics, the paper leads to the conclusion that the universe is inherently uncertain, that it is impossible to know the exact position of any object.
The Heisenberg equation may not be as well-known as Einstein’s e=mc^2. But the Heisenberg equation’s implications that there is an irreducible uncertainty with regard to the position of an object are no less intriguing than the implications of Einstein’s relativity equation that time slows to a stop when the relative velocity of an object approaches the speed of light. Using elementary mathematics and science, this paper begins by examining the physics of motion of an everyday object such as a tennis ball. The paper shows that the same physics that applies to everyday objects in fact also applies when it comes to subatomic particles, such as an electron in motion. And by taking gradual incremental steps in developing the mathematics of the underlying physics, the paper leads to the conclusion that the universe is inherently uncertain, that it is impossible to know the exact position of any object.
This paper is a small discussion about the uncertainty principle. With the great discoveries and researches made by predecessors, I try to answer some questions within the uncertainty principle. Using the definition of momentum, the momentum in de Broglie wave, the property of cosine function, the Euler’s formula, the basic property of plane wave, the law of derivative, the energy of quantum discovered by Max Planck, the photon energy discovered by Albert Einstein, the energy equation of a system and the Hamiltonian operator, I figure out the Schrodinger equation successfully. With the help of Schrodinger equation, the possibility density of a wave function, the concept of normalization, the average value of position and momentum, the Fourier transform, the integration by parts and the limit of normalized wave functions, I find the position operator and the momentum operator. Then using some knowledge of the standard deviation and the variance, the concept of inner product of vectors, some property of Dirac symbol, the law of calculation of complex number and the law of operator calculation, I obtain the general uncertainty relationship of abstract mathematical quantities. According to the general relationship, I get the inequality of uncertainty principle, and discuss the specific relationship between the position and the momentum. After getting the inequality, I use Heisenberg’s experiment of measuring an electron by using the γ ray to hit the electron to explain why we cannot measure the position and the momentum simultaneously. Based on Heisenberg’s experiment, I give my own explanation by discussing the earth and a spacecraft. Transforming the perspective, we can easily see how the accuracies of position and momentum change. In addition, I attempt to figure out why the uncertainty exists. However, I can only explain it by discussing the time and frequency in mathematical method and have no idea to work it out in a pure physics approach.
This paper proposes that quantum uncertainty arises from stochastic mass-energy interconversion at the subatomic level. Integrating Einstein's mass-energy equivalence and quantum mechanics, the hypothesis introduces fluctuating mass terms into mathematical frameworks like the Schrödinger equation, yielding novel implications for the Heisenberg Uncertainty Principle. The theory extends to quantum field theory, string theory, and cosmology, suggesting a dynamic mechanism for phenomena ranging from particle decay rates to black hole evaporation. By bridging quantum mechanics and general relativity through stochastic fluctuations, this framework offers testable predictions for high-energy physics, gravitational wave analysis, and cosmological observations, advancing the search for a unified Theory of Everything.
In this paper, we will revisit the derivation of Heisenberg's uncertainty principle. We will see how the Heisenberg principle collapses at the Planck scale by introducing a minor modification. The beauty of our suggested modification is that it does not change the main equations in quantum mechanics; it only gives them a Planck scale limit where uncertainty collapses. We suspect that Einstein could have been right after all, when he stated, ``God does not throw dice." His now-famous saying was an expression of his skepticism towards the concept that quantum randomness could be the ruling force, even at the deepest levels of reality. Here we will explore the quantum realm with a fresh perspective, by re-deriving the Heisenberg principle in relation to the Planck scale. We will show how this idea also leads to an upper boundary on uncertainty, in addition to the lower boundary. These upper and lower boundaries are identical for the Planck mass particle; in fact, they are zero, and this highlights the truly unique nature of the Planck mass particle. Further, there may be a close connection between light and the Planck mass particle: In our model, the standard relativistic energy momentum relation also seems to apply to light, while in modern physics light generally stands outside the standard relativistic momentum energy relation. We will also suggest a new way to look at elementary particles, where mass and time are closely related, consistent with some of the recent work in experimental physics. Our model leads to a new time operator that does not appear to be in conflict with the Pauli objection. This indicates that both mass and momentum come in quanta, which are perfectly correlated to an internal Compton `clock' frequency in elementary particles.