Koncept mase u specijalnoj teoriji relativnosti

master's thesis

• Title (english): The concept of mass in special relativity
• Author: Karmen Kapustić
• Mentor: Davor Horvatić (mentor)
• Committee member: Davor Horvatić (predsjednik povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Committee member: Maja Planinić (član povjerenstva)
• Committee member: Mihael Makek (član povjerenstva)
• Committee member: Katarina Jeličić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-02-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Specijalnu teoriju relativnosti je 1905. godine predstavio Albert Einstein. Važan doprinos teoriji dali su Max Planck koji je predstavio relativističku količinu gibanja i Hermann Minkowski koji je doprinio njenoj geometrijskoj formulaciji. U ovome radu je pokazano da je masa jednaka u svim referentnim sustavima i da ne ovisi o brzini opažača. Koncept relativističke mase koji se odnosi na masu koja se mijenja s brzinom je u neskladu s današnjom formulacijom specijalne teorije relativnosti koja je temeljena na geometrijskim svojstvima četverodimenzionalnog prostorvremena. Međutim, koncept relativističke mase još uvijek se koristi pri poučavanju specijalne teorije relativnosti u sklopu formalnog obrazovanja i u popularizaciji znanosti. Einstein nikada nije upotrebljavao relativističku masu iako se upravo njemu najčešće pripisuje. Einstein je u početku predstavio izraze za longitudinalnu i transverzalnu masu koji se mogu smatrati pretečama relativističke mase. Međutim, nakon što je Planck predstavio relativističku količinu gibanja, Einstein je u svim člancima i predavanjima o specijalnoj teoriji relativnosti naglasak stavljao na relativističke izraze za energiju i količinu gibanja. Iz izraza za relativističku količinu gibanja i ukupnu energiju, uz Lorentzove transformacije koje slijede iz geometrije prostorvremena proizlazi da je masa invarijantna veličina.

Abstract (english)

In 1905 Albert Einstein introduced special relativity. Valuable contributions to the theory came from Max Planck who introduced the relativistic momentum. Hermann Minkowski introduced four-dimensional space-time, which is a key to the geometric formulation of special relativity. This thesis outlines the idea that mass is the same for all observers and independent of reference frame. The concept of relativistic mass refers to the mass of the object in motion that depends on its velocity. Today it is known that relativistic mass is at odds with the accepted kinematics that stems from the geometric formulation of special relativity. However, relativistic mass is still used, and many believe that consequently no harm is made. Widespread use of relativistic mass is found in education, both in schools and universities. Additionally, is used to a great extent for the popularization of science. The concept of relativistic mass is repeatedly ascribed to Einstein although he never established it. Initially, he did propose transverse and longitudinal mass which can be taken as the forerunners of relativistic mass. However, after Planck derived the expression for relativistic momentum, Einstein has forsaken those notions. In all of his future articles and lectures, Einstein put to the fore the relativistic expression for energy and momentum. Based on the relativistic expression for energy and momentum with the geometry of special relativity, mass is found to be Lorentz invariant i.e. the same in all reference frames for all observers.

• Keywords: specijalna teorija relativnosti; geometrijska formulacija specijalne teorije relativnosti; masa; relativistička masa; odnos mase i energije; energija mirovanja; inercija
• Keywords (english): special relativity; geometric formulation of special relativity; mass; relativistic mass; mass-energy relation; rest energy; inertia
• Language: croatian
• URN:NBN: urn:nbn:hr:217:879310
• Study programme: Title: Physics; specializations in: Education; Course: Education; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra edukacije fizike (magistar/magistra edukacije fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-03-21 10:18:30