質量のない粒子

Massless particle — Grokipedia Fact-checked by Grok 3 months ago Massless particle Ara Eve Leo Sal 1x A massless particle , also known as a luxon, is an elementary particle in physics whose invariant mass (rest mass) is exactly zero, meaning it possesses no intrinsic mass when at rest and must always propagate at the speed of light in vacuum . [1] [2] This property arises from the principles of special relativity , where the energy-momentum relation E 2 = ( p c ) 2 + ( m 0 c 2 ) 2 E^2 = (pc)^2 + (m_0 c^2)^2 E 2 = ( p c ) 2 + ( m 0 ​ c 2 ) 2 simplifies to E = p c E = pc E = p c for zero rest mass m 0 m_0 m 0 ​ , ensuring that such particles cannot be slowed down or accelerated without violating causality or becoming undetectable. [2] In the Standard Model of particle physics, the confirmed massless particles are the photon , which mediates the electromagnetic force, and the gluon , which carries the strong nuclear force between quarks. [1] [3] These particles are gauge bosons, fundamental force carriers that do not interact with the Higgs field, thereby remaining massless unlike fermions such as quarks and leptons, which acquire mass through the Higgs mechanism . [4] Gluons, however, are never observed in isolation due to color confinement in quantum chromodynamics , while photons are ubiquitous as quanta of light . [1] Theoretically, the graviton is proposed as another massless spin-2 particle responsible for gravity in quantum gravity theories, though it remains undetected and unconfirmed. [5] Massless particles exhibit unique quantum properties, such as helicity (a projection of spin along the direction of motion) that is fixed—right-handed or left-handed—due to their inability to change velocity direction without mass. [6] Their relativistic invariance makes them crucial for understanding fundamental interactions, from electromagnetic radiation to the binding forces in atomic nuclei. [7] Theoretical Foundations Definition and Invariant Mass In special relativity , a massless particle is defined as one possessing zero invariant mass , denoted as $ m = 0 $, which serves as the rest mass in the particle's hypothetical rest frame . [8] This contrasts with massive particles, for which the invariant mass remains a fixed, observer-independent scalar quantity that characterizes the particle's intrinsic inertia even when at rest. [9] The invariant mass arises from the spacetime structure of special relativity , ensuring that it is Lorentz invariant under transformations between inertial frames. [10] The concept of invariant mass is formalized using the four-momentum vector $ p^\mu = (E/c, \mathbf{p}) $, where $ E $ is the energy and $ \mathbf{p} $ is the three-momentum. In the mostly-minus metric signature ($ \eta_{\mu\nu} = \operatorname{diag}(+1, -1, -1, -1) $), the invariant mass squared is given by the contraction p μ p μ = E 2 c 2 − p 2 = m 2 c 2 , p^\mu p_\mu = \frac{E^2}{c^2} - \mathbf{p}^2 = m^2 c^2, p μ p μ ​ = c 2 E 2 ​ − p 2 = m 2 c 2 , which holds for all observers. For a massless particle, $ m = 0 $ implies $ p^\mu p_\mu = 0 $, meaning the four-momentum is null (light-like) for real particles with positive energy. In natural units where $ c = 1 $ and $ \hbar = 1 $, this simplifies to $ p^2 = m^2 = 0 . [ ] ( h t t p s : / / w w w . d a m t p . c a m . a c . u k / u s e r / t o n g / e m / e l 4. p d f ) T h i s n u l l c o n d i t i o n d i s t i n g u i s h e s m a s s l e s s p a r t i c l e s f r o m t i m e − l i k e ( .[](https://www.damtp.cam.ac.uk/user/tong/em/el4.pdf) This null condition distinguishes massless particles from time-like ( . [ ] ( h ttp s : // www . d am tp . c am . a c . u k / u ser / t o n g / e m / e l 4. p df ) T hi s n u ll co n d i t i o n d i s t in gu i s h es ma ss l ess p a r t i c l es f ro m t im e − l ik e ( m > 0 $) or space-like trajectories in Minkowski spacetime. The foundational framework for massless particles emerged in Albert Einstein's 1905 paper on special relativity , which established the invariance of the speed of light $ c $ in vacuum and the relativity of simultaneity , laying the groundwork for treating light propagation without a rest frame . [11] Early recognition of zero rest mass applied to electromagnetic waves, as their propagation at exactly $ c $ implied no inertial rest frame , consistent with the absence of invariant mass in the relativistic energy-momentum formalism. [12] A key implication of zero invariant mass is that massless particles must travel at the speed of light $ c $ in vacuum in all inertial frames, precluding the existence of a rest frame where their three-velocity would be zero. [9] Without a rest frame , concepts like proper time along the particle's worldline become degenerate, and their dynamics are governed solely by the light-like constraint $ E = |\mathbf{p}| c $. This classification underpins the distinction between massive and massless particles in relativistic physics. [8] Energy-Momentum Relation In relativistic mechanics, the total energy E E E of a particle is related to its three-momentum p ⃗ \vec{p} p ​ and rest mass m m m by the dispersion relation E = ( p c ) 2 + ( m c 2 ) 2 , E = \sqrt{(pc)^2 + (mc^2)^2}, E = ( p c ) 2 + ( m c 2 ) 2 ​ , where p = ∣ p ⃗ ∣ p = |\vec{p}| p = ∣ p ​ ∣ is the magnitude of the momentum and c c c is the speed of light in vacuum. [13] This equation arises from the Lorentz invariance of the spacetime interval and the conservation of four-momentum in special relativity. [13] For massless particles, where the invariant mass is zero, the rest mass term vanishes ( m = 0 m = 0 m = 0 ), simplifying the relation to E = p c . E = pc. E = p c . This holds exactly, as the energy-momentum four-vector satisfies the null condition. [14] Step-by-step, the derivation begins with the general form, which combines the classical kinetic energy in the non-relativistic limit ( E ≈ m c 2 + p 2 2 m E \approx mc^2 + \frac{p^2}{2m} E ≈ m c 2 + 2 m p 2 ​ ) and extends to high speeds via the Lorentz factor γ = 1 / 1 − v 2 / c 2 \gamma = 1/\sqrt{1 - v^2/c^2} γ = 1/ 1 − v 2 / c 2 ​ . [13] As m → 0 m \to 0 m → 0 , the rest energy m c 2 mc^2 m c 2 approaches zero, leaving only the relativistic kinetic contribution, which is linear in momentum: the particle's energy is entirely kinetic and proportional to p p p , with the constant of proportionality c c c . [15] This linear dispersion distinguishes massless particles from massive ones, where E > p c E > pc E > p c even at high energies. The four-momentum of a massless particle is the contravariant vector p μ = ( E / c , p ⃗ ) p^\mu = (E/c, \vec{p}) p μ = ( E / c , p ​ ) in Minkowski space with metric signature ( + , − , − , − ) (+,-,-,-) ( + , − , − , − ) . [14] The invariant mass squared is given by the contraction p μ p μ = ( E / c ) 2 − p 2 = 0 p^\mu p_\mu = (E/c)^2 - p^2 = 0 p μ p μ ​ = ( E / c ) 2 − p 2 = 0 , confirming E = p c E = pc E = p c and implying that the particle's worldline is light-like (null geodesic in spacetime ). [14] Such particles trace paths at the invariant speed c c c , with their trajectories confined to the light cone . In particle detectors at scattering experiments, the relation E = p c E = pc E = p c is applied to reconstruct the four-momentum of candidate massless particles, such as photons, from calorimeter energy deposits and shower positions that provide directional information for p ⃗ \vec{p} p ​ . [16] This assumption allows computation of invariant mass es for decay products; for instance, pairs of reconstructed photons yielding near-zero invariant mass confirm their massless nature, distinguishing them from massive particle pairs (like π 0 \pi^0 π 0 mesons) where E > p c E > pc E > p c leads to non-zero reconstructed masses. [16] Such analyses in collider events, like those at the LHC, enable precise kinematic fits and signal-background separation. [16] Physical Properties Speed and Dispersion In special relativity , massless particles are required to propagate at the speed of light c c c in vacuum, as their invariant mass is zero, precluding any rest frame and thus forbidding subluminal or superluminal velocities for real particles. [17] [2] This universal speed arises directly from the energy-momentum relation E = p c E = pc E = p c , where the absence of a mass term mandates v = c v = c v = c . [18] The dispersion relation for massless particles is linear, given by ω = c k \omega = c k ω = c k , where ω \omega ω is the angular frequency and k k k is the wave number. This linearity implies that the phase velocity ω / k = c \omega / k = c ω / k = c equals the group velocity d ω / d k = c d\omega / dk = c d ω / d k = c , resulting in non-dispersive propagation where wave packets do not spread over distance . The invariance of c c c was indirectly supported by the Michelson-Morley experiment of 1887 , which detected no variation in light speed due to Earth's motion through a presumed luminiferous aether , consistent with relativistic predictions. [19] Subsequent direct measurements of photon speeds in vacuum have confirmed this invariance to high precision, aligning with the theoretically mandated value of c = 299 , 792 , 458 c = 299{,}792{,}458 c = 299 , 792 , 458 m/s. [20] In material media, massless particles exhibit an effective phase velocity reduced by the refractive index n > 1 n > 1 n > 1 , such that v = c / n v = c / n v = c / n , due to interactions with the medium; however, their intrinsic propagation speed in vacuum remains c c c , preserving masslessness. [21] Helicity and Polarization In quantum field theory, helicity is defined as the projection of a particle's intrinsic spin angular momentum onto the direction of its linear momentum. For massless particles, which travel exclusively at the speed of light and possess no rest frame, helicity emerges as a Lorentz-invariant quantum number that characterizes their one-particle states. This invariance arises because boosts along the momentum direction leave the helicity unc