Mass and velocity
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Mass-Velocity Relationship in Physics
Classical and Relativistic Mass-Velocity Equations
The relationship between mass and velocity has been a central topic in physics, especially since the development of special relativity. In classical Newtonian mechanics, mass is considered independent of velocity, meaning an object's mass does not change as its speed increases 49. However, in the early 20th century, Lorentz introduced a formula suggesting that mass increases with velocity, specifically ( m = m_0 / \sqrt{1 - v^2/c^2} ), where ( m_0 ) is the rest mass, ( v ) is velocity, and ( c ) is the speed of light 14. This formula has been experimentally confirmed for certain particles, like electrons, up to about 0.75 times the speed of light .
Alternative Theories and Critiques
Several researchers have questioned the theoretical foundations and experimental evidence for the mass-velocity relationship in special relativity. Some argue that the derivations of the mass-velocity formula based on Lorentz transformations are flawed or cannot be fully justified, suggesting the formula is more empirical than theoretical . Others propose that the apparent increase in mass with speed is a result of how momentum is measured, not a true change in the substance of the object 69. New equations, such as exponential forms, have been proposed to address mathematical issues in the traditional formulas and to allow for the possibility of superluminal (faster-than-light) velocities, which the Lorentz equation forbids 16.
Mass, Velocity, and Energy Conversion
Some studies suggest that as an object's velocity approaches the speed of light, its mass may actually decrease due to conversion into energy, challenging the traditional view that mass increases indefinitely . The relationship between mass, velocity, and energy is complex, with some findings indicating that the energy equivalent of a given mass may be less than what Einstein's famous equation predicts . Additionally, the transformation of mass into energy or even "anti-mass" at extreme velocities has been discussed, though these ideas remain speculative .
Mass-Velocity Relations in Astrophysics
In astrophysics, the mass-velocity relationship is observed on much larger scales, such as in galaxies and galaxy clusters. Empirical relations, like the mass–velocity dispersion relation (MVDR), show a tight correlation between the baryonic mass of galaxies and their velocity dispersion 510. These scaling relations are important for understanding the dynamics of galaxies and clusters and are used to test models of dark matter and modified gravity 510. Notably, some recent studies find that these relations do not always fit predictions from standard dark matter models, suggesting the need for alternative explanations 510.
Derivations Without Light or Lorentz Transformations
Some researchers have shown that the mass-velocity and mass-energy relations can be derived without relying on the invariance of the speed of light or Lorentz transformations. By focusing on the linear transformation of momentum and energy between reference frames, these derivations suggest that the relationships have a broader validity than previously thought .
Conclusion
The relationship between mass and velocity is a nuanced topic with ongoing debate. While the Lorentz mass-velocity formula is widely used and experimentally supported in some cases, alternative theories and critiques highlight unresolved issues and the need for further experimental verification, especially at extreme velocities. In astrophysics, empirical mass-velocity relations provide valuable insights into the structure and dynamics of galaxies and clusters, sometimes challenging standard models. Overall, the mass-velocity relationship remains a rich field for both theoretical exploration and experimental investigation 13456789+1 MORE.
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