Den storste oppdagelsen i solsystemet som ble gjort i 2014, var at vi na kan vaere sikre pa at de... more Den storste oppdagelsen i solsystemet som ble gjort i 2014, var at vi na kan vaere sikre pa at det er organiske stoffer pa Mars. De kjemiske byggesteinene som er nodvendige for at det skal oppsta liv, har trolig eksistert i flere milliarder ar pa Mars, men liv pa Mars eller noe annet sted i solsystemet utenom pa jorda er det forelopig ikke funnet tegn til. Det oppdages stadig flere planeter utenfor solsystemet, men man trenger bedre observasjonsutstyr enn vi forelopig disponerer over, for a kunne utfore detaljerte studier av de kjemiske egenskapene til eksoplanetenes atmosfaerer, pa jakt etter spor av liv utenfor solsystemet. I mars var det store overskrifter om en dramatisk ny oppdagelse. Et forskerteam kalt BICEP2 med observasjonsutstyr pa Sydpolen mente a ha sett spor av gravitasjonsbolger fra Big Bang – opprinnelsen til vart univers – i polarisasjonsmonsteret i den kosmiske bakgrunnsstralingen. Dette ville ha vaert en oppdagelse av Nobelpris kaliber. Da ville man ha apnet vinduet tilbake til en brokdel av et sekund etter universets begynnelse. Og man ville ha oppnadd en ny bekreftelse av en av den generelle relativitetsteoriens forutsigelser: eksistensen av gravitasjonsbolger. Dessverre er det oppstatt usikkerhet om BICEP2 teamet har tolket sine observasjonsdata korrekt. Det ser ved overgangen til 2015 ut til at det de har observert, er et polarisasjonsmonster forarsaket av intergalaktisk stov i Melkeveien. Det kommer nye rapporter om dette i 2015. Utgivelsesdata Tittel:Nyhetsbrev om stjerner og universet 2013Forfatter(e):Oyvind GronSerie:HiOA rapportIssn:1892-9648Nr:2014 nr 2Utgiver:HiOAAvdeling/fakultet:Fakultet for teknSider:234Pris:400,– ISBN-print:978-82-93208-55-6
Det er nå bekreftet at de dypeste kratrene ved polene på solsystemets innerste planet, Merkur, in... more Det er nå bekreftet at de dypeste kratrene ved polene på solsystemets innerste planet, Merkur, inneholder betydelige mengder med vannis. Sporene etter store forekomster av overflatevann på Mars i tidligere tider, blir stadig tydeligere. Vann er et vanlig stoff i solsystemet. Trolig er det vann i ekstrasolare planetsystemer også. Nå vet vi også at det er millioner av planeter i den beboelige sonen til moderstjernene i Melkeveien. Så det skulle være rart om det ikke er liv der ute, kanskje til og med i planetsystemet som nå er oppdaget rundt en av Solas nærmeste nabostjerner, Alfa Centauri B. Årets største fysikknyhet er at Higgspartikkelen trolig er funnet. Kanskje har dette også kosmisk betydning, for dermed er også eksistensen av Higgsfeltet bekreftet, og det kan være den viktigste ingrediensen i universets mystiske mørke energi. Men mysteriet med den ukjente mørke materien er like stort. For Higgspartikkelen er ekstremt kortlivet, så den må dannes hele tiden, og mer der det er galakser enn andre steder, hvis den mørke materien skulle bestå av Higgspartikler. Både fysikere og kosmologer anser dette som uforenlig med universets egenskaper. Fortsatt vet vi ikke hva den mørke materien består av. Utgivelsesdata Tittel:Nyhetsbrev om stjerner og universet 2012Forfatter(e):Øyvind GrønSerie:HiOA rapportIssn:1892-9648Nr:2013 nr 1Utgiver:HiOAAvdeling/fakultet:Fakultet for tekn.Sider:150Pris:400,– ISBN-print:978-82-93208-28-
Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwar... more Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a nonvanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell.
The main points in the history of the cosmological constant are briefly discussed. As a conceptua... more The main points in the history of the cosmological constant are briefly discussed. As a conceptual background, useful for teaching of physics at an elementary college and university level, Newton's theory formulated locally in terms of the Poisson equation is presented, and it is shown how it is modified by the introduction of the cosmological constant. The different physical interpretations of the cosmological constant, as introduced by Einstein in 1917 and interpreted by Lemaitre in 1934, are presented. Energy conservation in an expanding universe dominated by vacuum energy is discussed. The connection between the cosmological constant and the quantum mechanical vacuum energy is mentioned, together with the problem that a quantum mechanical calculation of the density of the vacuum energy gives a vastly too large value of the cosmological constant. The article is concluded by reviewing a solution of this problem that was presented on May 11, 2017.
A new apparent relativistic paradox is presented involving only one space-time event. This is dif... more A new apparent relativistic paradox is presented involving only one space-time event. This is different from earlier 'relativistic paradoxes' involving extended bodies or events at different positions. A collision between a rod and a ring impacting at an oblique angle to each other is considered in the context of the special theory relativity. A question arises as to where along the length of the rod the point of impact will be according to two observers following the rod and the ring, respectively. The observers argue from a purely kinematical point of view in favor of two different points of impact along the rod. However there can only exist one point of impact. In order to solve this apparent paradox we use the asynchronous formulation of relativistic kinematics in which the consequences of the relativity of simultaneity are built into the formalism. We show that this reconciles the descriptions from the two frames of reference, and hence that the new 'paradox' leads to a strong argument for the relevance of the asynchronous formulation of relativistic kinematics.
In this chapter we shall first find a general expression of the acceleration of gravity due to a ... more In this chapter we shall first find a general expression of the acceleration of gravity due to a mass distribution. Then we shall deduce the solution of Einstein’s field equations inside an incompressible star—the internal Schwarzschild solution. Furthermore we shall present Israel’s formalism for describing singular mass shells in the general theory of relativity, and apply this first to a shell consisting of dust particles, and then to find a source of the conformally flat, spherically symmetric Levi-Civita—Bertotti—Robinson metric, and finally to the Kerr spacetime. Lastly we shall introduce a river model of space.
The relativistic equation of motion of a radiating charge is discussed with special emphasis upon... more The relativistic equation of motion of a radiating charge is discussed with special emphasis upon a clarification of the significance of the Schott energy for the energy-momentum conservation of the charge and the field it produces. In particular hyperbolic motion is studied. The case that a charge with constant velocity enters and leaves a region with hyperbolic motion is analysed. We find that the Schott energy is increased as the particle enters the region and that the energy it radiates while the charge moves hyperbolically comes from the Schott energy. A result of our analysis is that this energy is localized in the field close to the charge.
We show that there are distinct periods when three ocean variability series in the Atlantic and t... more We show that there are distinct periods when three ocean variability series in the Atlantic and the Pacific Oceans persistently lead or lag each other, as well as distinct periods when ocean variability series lead the rate of changes in global temperature anomaly (∆GTA) and in atmospheric CO2 concentration (1880–2019). The superimposed lead-lag (LL) relations that can be formed from the five climate series (three ocean series, GTA and CO2), ΣLL(10), change directions or weaken synchronously at 6 years: 1900, 1926, 1965, 1977, 1997, and 2013. During the same years, the Pacific decadal oscillation (PDO) changes between positive ( +) and negative (-) phases, but with an additional phase shift in 1947/48. We find bi-decadal oscillations in the rate of change in global temperature, ∆GTA, during the same years. Since the hiatus periods are closely related to the cold phase (-) in PDO, the hiatus periods may also be related to global changes in ocean interactions.
In the standard formulation of the twin paradox an "accelerated" twin considers himself as at res... more In the standard formulation of the twin paradox an "accelerated" twin considers himself as at rest and his brother as moving. Hence, when formulating the twin paradox, one uses the general principle of relativity, i.e. that accelerated and rotational motion is relative. The significance of perfect inertial dragging for the validity of the principle of relativity is made clear. Three new results are reviewed in the discussion: 1. A cosmic time effect which cannot be reduced to the gravitational or the kinematical time dilation; 2. Perfect dragging in an exact solution of Einstein's field equations describing flat spacetime inside a shell with Kerr spacetime outside it; 3. An extended model of Minkowski spacetime in order to avoid introducing absolute acceleration and rotation through the asymptotic emptiness of the Kerr spacetime.
Den største oppdagelsen i solsystemet som ble gjort i 2014, var at vi nå kan være sikre på at det... more Den største oppdagelsen i solsystemet som ble gjort i 2014, var at vi nå kan være sikre på at det er organiske stoffer på Mars. De kjemiske byggesteinene som er nødvendige for at det skal oppstå liv, har trolig eksistert i flere milliarder år på Mars, men liv på Mars eller noe annet sted i solsystemet utenom på jorda er det foreløpig ikke funnet tegn til. Det oppdages stadig flere planeter utenfor solsystemet, men man trenger bedre observasjonsutstyr enn vi foreløpig disponerer over, for å kunne utføre detaljerte studier av de kjemiske egenskapene til eksoplanetenes atmosfærer, på jakt etter spor av liv utenfor solsystemet. I mars var det store overskrifter om en dramatisk ny oppdagelse. Et forskerteam kalt BICEP2 med observasjonsutstyr på Sydpolen mente å ha sett spor av gravitasjonsbølger fra Big Bang – opprinnelsen til vårt univers – i polarisasjonsmønsteret i den kosmiske bakgrunnsstrålingen. Dette ville ha vært en oppdagelse av Nobelpris kaliber. Da ville man ha åpnet vinduet tilbake til en brøkdel av et sekund etter universets begynnelse. Og man ville ha oppnådd en ny bekreftelse av en av den generelle relativitetsteoriens forutsigelser: eksistensen av gravitasjonsbølger. Dessverre er det oppstått usikkerhet om BICEP2 teamet har tolket sine observasjonsdata korrekt. Det ser ved overgangen til 2015 ut til at det de har observert, er et polarisasjonsmønster forårsaket av intergalaktisk støv i Melkeveien. Det kommer nye rapporter om dette i 2015. Utgivelsesdata Tittel:Nyhetsbrev om stjerner og universet 2014Forfatter(e):Øyvind GrønSerie:HiOA rapportIssn:1892-9648Nr:2015 nr 1Utgiver:HiOAAvdeling/fakultet:TKDSider:266Pris:400,– ISBN-print:978-82-93208-82-
Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwar... more Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a nonvanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell.
The electromagnetic field of a charged particle with hyperbolic motion is described. The field of... more The electromagnetic field of a charged particle with hyperbolic motion is described. The field of a particle with eternal hyperbolic motion is found by taking the limit of a situation with limited hyperbolic motion. The flow of energy in the electromagnetic field is discussed. The question whether the charged particle emits radiation is briefly touched upon in this first article in a series on the electrodynamics of radiating particles and their fields.
Den storste oppdagelsen i solsystemet som ble gjort i 2014, var at vi na kan vaere sikre pa at de... more Den storste oppdagelsen i solsystemet som ble gjort i 2014, var at vi na kan vaere sikre pa at det er organiske stoffer pa Mars. De kjemiske byggesteinene som er nodvendige for at det skal oppsta liv, har trolig eksistert i flere milliarder ar pa Mars, men liv pa Mars eller noe annet sted i solsystemet utenom pa jorda er det forelopig ikke funnet tegn til. Det oppdages stadig flere planeter utenfor solsystemet, men man trenger bedre observasjonsutstyr enn vi forelopig disponerer over, for a kunne utfore detaljerte studier av de kjemiske egenskapene til eksoplanetenes atmosfaerer, pa jakt etter spor av liv utenfor solsystemet. I mars var det store overskrifter om en dramatisk ny oppdagelse. Et forskerteam kalt BICEP2 med observasjonsutstyr pa Sydpolen mente a ha sett spor av gravitasjonsbolger fra Big Bang – opprinnelsen til vart univers – i polarisasjonsmonsteret i den kosmiske bakgrunnsstralingen. Dette ville ha vaert en oppdagelse av Nobelpris kaliber. Da ville man ha apnet vinduet tilbake til en brokdel av et sekund etter universets begynnelse. Og man ville ha oppnadd en ny bekreftelse av en av den generelle relativitetsteoriens forutsigelser: eksistensen av gravitasjonsbolger. Dessverre er det oppstatt usikkerhet om BICEP2 teamet har tolket sine observasjonsdata korrekt. Det ser ved overgangen til 2015 ut til at det de har observert, er et polarisasjonsmonster forarsaket av intergalaktisk stov i Melkeveien. Det kommer nye rapporter om dette i 2015. Utgivelsesdata Tittel:Nyhetsbrev om stjerner og universet 2013Forfatter(e):Oyvind GronSerie:HiOA rapportIssn:1892-9648Nr:2014 nr 2Utgiver:HiOAAvdeling/fakultet:Fakultet for teknSider:234Pris:400,– ISBN-print:978-82-93208-55-6
Det er nå bekreftet at de dypeste kratrene ved polene på solsystemets innerste planet, Merkur, in... more Det er nå bekreftet at de dypeste kratrene ved polene på solsystemets innerste planet, Merkur, inneholder betydelige mengder med vannis. Sporene etter store forekomster av overflatevann på Mars i tidligere tider, blir stadig tydeligere. Vann er et vanlig stoff i solsystemet. Trolig er det vann i ekstrasolare planetsystemer også. Nå vet vi også at det er millioner av planeter i den beboelige sonen til moderstjernene i Melkeveien. Så det skulle være rart om det ikke er liv der ute, kanskje til og med i planetsystemet som nå er oppdaget rundt en av Solas nærmeste nabostjerner, Alfa Centauri B. Årets største fysikknyhet er at Higgspartikkelen trolig er funnet. Kanskje har dette også kosmisk betydning, for dermed er også eksistensen av Higgsfeltet bekreftet, og det kan være den viktigste ingrediensen i universets mystiske mørke energi. Men mysteriet med den ukjente mørke materien er like stort. For Higgspartikkelen er ekstremt kortlivet, så den må dannes hele tiden, og mer der det er galakser enn andre steder, hvis den mørke materien skulle bestå av Higgspartikler. Både fysikere og kosmologer anser dette som uforenlig med universets egenskaper. Fortsatt vet vi ikke hva den mørke materien består av. Utgivelsesdata Tittel:Nyhetsbrev om stjerner og universet 2012Forfatter(e):Øyvind GrønSerie:HiOA rapportIssn:1892-9648Nr:2013 nr 1Utgiver:HiOAAvdeling/fakultet:Fakultet for tekn.Sider:150Pris:400,– ISBN-print:978-82-93208-28-
Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwar... more Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a nonvanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell.
The main points in the history of the cosmological constant are briefly discussed. As a conceptua... more The main points in the history of the cosmological constant are briefly discussed. As a conceptual background, useful for teaching of physics at an elementary college and university level, Newton's theory formulated locally in terms of the Poisson equation is presented, and it is shown how it is modified by the introduction of the cosmological constant. The different physical interpretations of the cosmological constant, as introduced by Einstein in 1917 and interpreted by Lemaitre in 1934, are presented. Energy conservation in an expanding universe dominated by vacuum energy is discussed. The connection between the cosmological constant and the quantum mechanical vacuum energy is mentioned, together with the problem that a quantum mechanical calculation of the density of the vacuum energy gives a vastly too large value of the cosmological constant. The article is concluded by reviewing a solution of this problem that was presented on May 11, 2017.
A new apparent relativistic paradox is presented involving only one space-time event. This is dif... more A new apparent relativistic paradox is presented involving only one space-time event. This is different from earlier 'relativistic paradoxes' involving extended bodies or events at different positions. A collision between a rod and a ring impacting at an oblique angle to each other is considered in the context of the special theory relativity. A question arises as to where along the length of the rod the point of impact will be according to two observers following the rod and the ring, respectively. The observers argue from a purely kinematical point of view in favor of two different points of impact along the rod. However there can only exist one point of impact. In order to solve this apparent paradox we use the asynchronous formulation of relativistic kinematics in which the consequences of the relativity of simultaneity are built into the formalism. We show that this reconciles the descriptions from the two frames of reference, and hence that the new 'paradox' leads to a strong argument for the relevance of the asynchronous formulation of relativistic kinematics.
In this chapter we shall first find a general expression of the acceleration of gravity due to a ... more In this chapter we shall first find a general expression of the acceleration of gravity due to a mass distribution. Then we shall deduce the solution of Einstein’s field equations inside an incompressible star—the internal Schwarzschild solution. Furthermore we shall present Israel’s formalism for describing singular mass shells in the general theory of relativity, and apply this first to a shell consisting of dust particles, and then to find a source of the conformally flat, spherically symmetric Levi-Civita—Bertotti—Robinson metric, and finally to the Kerr spacetime. Lastly we shall introduce a river model of space.
The relativistic equation of motion of a radiating charge is discussed with special emphasis upon... more The relativistic equation of motion of a radiating charge is discussed with special emphasis upon a clarification of the significance of the Schott energy for the energy-momentum conservation of the charge and the field it produces. In particular hyperbolic motion is studied. The case that a charge with constant velocity enters and leaves a region with hyperbolic motion is analysed. We find that the Schott energy is increased as the particle enters the region and that the energy it radiates while the charge moves hyperbolically comes from the Schott energy. A result of our analysis is that this energy is localized in the field close to the charge.
We show that there are distinct periods when three ocean variability series in the Atlantic and t... more We show that there are distinct periods when three ocean variability series in the Atlantic and the Pacific Oceans persistently lead or lag each other, as well as distinct periods when ocean variability series lead the rate of changes in global temperature anomaly (∆GTA) and in atmospheric CO2 concentration (1880–2019). The superimposed lead-lag (LL) relations that can be formed from the five climate series (three ocean series, GTA and CO2), ΣLL(10), change directions or weaken synchronously at 6 years: 1900, 1926, 1965, 1977, 1997, and 2013. During the same years, the Pacific decadal oscillation (PDO) changes between positive ( +) and negative (-) phases, but with an additional phase shift in 1947/48. We find bi-decadal oscillations in the rate of change in global temperature, ∆GTA, during the same years. Since the hiatus periods are closely related to the cold phase (-) in PDO, the hiatus periods may also be related to global changes in ocean interactions.
In the standard formulation of the twin paradox an "accelerated" twin considers himself as at res... more In the standard formulation of the twin paradox an "accelerated" twin considers himself as at rest and his brother as moving. Hence, when formulating the twin paradox, one uses the general principle of relativity, i.e. that accelerated and rotational motion is relative. The significance of perfect inertial dragging for the validity of the principle of relativity is made clear. Three new results are reviewed in the discussion: 1. A cosmic time effect which cannot be reduced to the gravitational or the kinematical time dilation; 2. Perfect dragging in an exact solution of Einstein's field equations describing flat spacetime inside a shell with Kerr spacetime outside it; 3. An extended model of Minkowski spacetime in order to avoid introducing absolute acceleration and rotation through the asymptotic emptiness of the Kerr spacetime.
Den største oppdagelsen i solsystemet som ble gjort i 2014, var at vi nå kan være sikre på at det... more Den største oppdagelsen i solsystemet som ble gjort i 2014, var at vi nå kan være sikre på at det er organiske stoffer på Mars. De kjemiske byggesteinene som er nødvendige for at det skal oppstå liv, har trolig eksistert i flere milliarder år på Mars, men liv på Mars eller noe annet sted i solsystemet utenom på jorda er det foreløpig ikke funnet tegn til. Det oppdages stadig flere planeter utenfor solsystemet, men man trenger bedre observasjonsutstyr enn vi foreløpig disponerer over, for å kunne utføre detaljerte studier av de kjemiske egenskapene til eksoplanetenes atmosfærer, på jakt etter spor av liv utenfor solsystemet. I mars var det store overskrifter om en dramatisk ny oppdagelse. Et forskerteam kalt BICEP2 med observasjonsutstyr på Sydpolen mente å ha sett spor av gravitasjonsbølger fra Big Bang – opprinnelsen til vårt univers – i polarisasjonsmønsteret i den kosmiske bakgrunnsstrålingen. Dette ville ha vært en oppdagelse av Nobelpris kaliber. Da ville man ha åpnet vinduet tilbake til en brøkdel av et sekund etter universets begynnelse. Og man ville ha oppnådd en ny bekreftelse av en av den generelle relativitetsteoriens forutsigelser: eksistensen av gravitasjonsbølger. Dessverre er det oppstått usikkerhet om BICEP2 teamet har tolket sine observasjonsdata korrekt. Det ser ved overgangen til 2015 ut til at det de har observert, er et polarisasjonsmønster forårsaket av intergalaktisk støv i Melkeveien. Det kommer nye rapporter om dette i 2015. Utgivelsesdata Tittel:Nyhetsbrev om stjerner og universet 2014Forfatter(e):Øyvind GrønSerie:HiOA rapportIssn:1892-9648Nr:2015 nr 1Utgiver:HiOAAvdeling/fakultet:TKDSider:266Pris:400,– ISBN-print:978-82-93208-82-
Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwar... more Recently Abramowicz and Bajtlik [ArXiv: 0905.2428 (2009)] have studied the twin paradox in Schwarzschild spacetime. Considering circular motion they showed that the twin with a nonvanishing 4-acceleration is older than his brother at the reunion and argued that in spaces that are asymptotically Minkowskian there exists an absolute standard of rest determining which twin is oldest at the reunion. Here we show that with vertical motion in Schwarzschild spacetime the result is opposite: The twin with a non-vanishing 4-acceleration is younger. We also deduce the existence of a new relativistic time effect, that there is either a time dilation or an increased rate of time associated with a clock moving in a rotating frame. This is in fact a first order effect in the velocity of the clock, and must be taken into account if the situation presented by Abramowicz and Bajtlik is described from the rotating rest frame of one of the twins. Our analysis shows that this effect has a Machian character since the rotating state of a frame depends upon the motion of the cosmic matter due to the inertial dragging it causes. We argue that a consistent formulation and resolution of the twin paradox makes use of the general principle of relativity and requires the introduction of an extended model of the Minkowski spacetime. In the extended model Minkowski spacetime is supplied with a cosmic shell of matter with radius equal to its own Schwarzschild radius, so that there is perfect inertial dragging inside the shell.
The electromagnetic field of a charged particle with hyperbolic motion is described. The field of... more The electromagnetic field of a charged particle with hyperbolic motion is described. The field of a particle with eternal hyperbolic motion is found by taking the limit of a situation with limited hyperbolic motion. The flow of energy in the electromagnetic field is discussed. The question whether the charged particle emits radiation is briefly touched upon in this first article in a series on the electrodynamics of radiating particles and their fields.
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