Tuomo Suntola Physics Foundations Society

Esitys aiheesta: "Tuomo Suntola Physics Foundations Society"— Esityksen transkriptio:

1 Tuomo Suntola Physics Foundations Society
Luonnonfilosofian seura The Finnish Society for Natural Philosophy 1988 – 2013 Kvantin luonteesta Tuomo Suntola Physics Foundations Society Luonnonfilosofian seura

2 Kineettisen kaasuteorian tausta ja kehitys
Joseph Gay-Lussac ( ) Isaac Newton (1643–1727) Rudolf Clausius (1822–1888) Francis Bacon (1561–1626) ”Kerrassaan mitään ei voida tietää ” Daniel Bernoulli (1700–1782)  Ludwig Boltzmann ( ) Robert Boyle ( ) ”Ei voi olla vähempiä periaatteita kuin mekaanisen filosofian kaksi suurta, aine ja liike.” P ~ 1/V  James Maxwell (1822–1888) Michael Faraday (1791–1867) Antoine Lavoisier (1743–1794) Valistusfilosofeja: Thomas Hobbes ( ), Leviathan, 1651 (ontologinen materialismi) De Corpore (Concerning Body, 1655), conatus (vis mortua) John Locke ( ), Francis Bacon (1561–1626), one of the pioneers of the empirical scientific method. Novum Organum Scientiarum – True directions Concerning the Interpretation of Nature, ”absolutely nothing can be known”. Robert Boyle ( ): Boyle’s law P ~ 1/V ( at constant T ). There can’t be fewer principles than the two grand ones of mechanical philosophy, matter and motion. Corpuscular principles are enormously comprehensive. If one part of matter x collides strongly enough with another y, the necessary effect of this is either to break or divide y up into particles that have determinate motions, shapes, sizes, postures, orders and textures. Daniel Bernoulli (1700–1782) showed that the pressure will be proportional to the kinetic energy of the particles (= 1/2 mv^2). Hydrodynamique resembles Joseph Louis Lagrange's Mécanique Analytique in being arranged so that all the results are consequences of a single principle, namely, conservation of energy. Antoine Lavoisier (1743–1794), total mass is conserved in chemical reactions – burning means reaction with oxygen. Joseph Gay-Lussac ( ) and others showed that pressure increases in proportion to temperature if the volume is held constant, or volume increases in proportion to temperature if pressure is held constant; these relations can be summarized in the equation PV = NR (t + 273) , where N is proportional to the total mass of gas present, t is the temperature in degrees Celsius (centigrade) and R is a universal constant. But it was not yet known whether the equation would be valid down to temperatures so low that (t + 273) is zero, or whether all gases would condense before that point of "absolute cold" is reached so the equation would no longer apply. In 1857 Rudolf Clausius, according to his own words independently of Krönig, developed a similar, but much more sophisticated version of the theory which included translational and contrary to Krönig also rotational and vibrational molecular motions. In this same work he introduced the concept of mean free path of a particle. In 1859, after reading a paper by Clausius, James Clerk Maxwell formulated the Maxwell distribution of molecular velocities, which gave the proportion of molecules having a certain velocity in a specific range. In 1871, Ludwig Boltzmann generalized Maxwell's achievement and formulated the Maxwell–Boltzmann distribution. Also the logarithmic connection between entropy and probability was first stated by him. Amedeo Avogadro (1776–1856) René Descartes (1596–1650) ”Kausaalinen päättely” Gottfried Leibniz (1646–1716) ”Energiaa yhtä paljon syyssä ja seurauksessa” John Dalton (1766–1844)

3 Jatkuvasta aineesta atomeihin ja kvantteihin
1901 J.J. Thomson elektronit atomin osana Daniel Bernoulli (1700–1782) Hydrodynamics 1865 J. J. Loschmidt Avogadron vakion numeroarvo Paine verrannollinen kaasumole-kyylien kineettiseen energiaan 1913 Niels Bohr Atomi-malli Wien’s and Rayleigh’s säteilylait 1900 Max Planck’s Säteily-laki 1924 Louis de Broglie dB-aallon-pituus “from mole to atom” RT  kT Max Born Werner Heisenberg Erwin Schrödinger Paul Dirac 1811 Amedeo Avogadro: Molekyylien määrä moolissa. 1834 Michael Faraday Varaus/mooli vakio elektrolyysissä Ludwig Bolzmann: Ekvipartitio-periaate Säteilykvantti E = hf 1874 George Stoney 1-ioni kantaa yksikkövarauksen 1923 Arthur Compton Compton-aallonpituus Robert Boyle ( ) Boylen laki: kaasun tilavuus ja paine kääntäen verrannolliset Gas laws: In 1738 Daniel Bernoulli (Bur’noo-lee) published Hydrodynamica, which laid the basis for the kinetic theory of gases. In this work, Bernoulli posited the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel, and that what we experience as heat is simply the kinetic energy of their motion. In 1856 August Krönig (probably after reading a paper of Waterston) created a simple gas-kinetic model, which only considered the translational motion of the particles.[10] In 1857 Rudolf Clausius, according to his own words independently of Krönig, developed a similar, but much more sophisticated version of the theory which included translational and contrary to Krönig also rotational and vibrational molecular motions. In this same work he introduced the concept of mean free path of a particle. In 1859, after reading a paper by Clausius, James Clerk Maxwell formulated the Maxwell distribution of molecular velocities, which gave the proportion of molecules having a certain velocity in a specific range. In his 1873 thirteen page article 'Molecules', Maxwell states: “we are told that an 'atom' is a material point, invested and surrounded by 'potential forces' and that when 'flying molecules' strike against a solid body in constant succession it causes what is called pressure of air and other gases.” In 1871, Ludwig Boltzmann generalized Maxwell's achievement and formulated the Maxwell–Boltzmann distribution. Also the logarithmic connection between entropy and probability was first stated by him. 1805 John Dalton presented the first table of relative atomic mass (atomic weight) and (Gay-Lussac) 1811 Amedeo Avogadro proposed that the volume of a gas (at a given pressure and temperature) is proportional to the number of atoms or molecules regardless of the nature of the gas Avogadro constant (symbols: L, NA): the number of constituent particles in one mole of a given substance. 1865 Johann Josef Loschmidt estimated the numerical value of the Avogadro based on the kinetic gas theory n=pN/RT 1874: George Stoney estimated the unit charge: Faradayn varaus / Avogadron vakio 10–20 Coulombia (1,6·10–19 C). In 1856 with Rudolf Kohlrausch (1809–1858) he demonstrated that the ratio of electrostatic to electromagnetic units produced a number that matched the value of the then known speed of light. Philip Lenard, made precise measurements on the photoelectric effect, Einstein’s first wife, Mileva Maric worked as Lenard’s assistant American physicist Robert Millikan measured the charge on an electron in 1910. 1856 Wilhelm Weber Valon nopeus sähkövakioista 1805 John Dalton: Atomipainot 1905 Albert Einstein Valosähköisen ilmiön kvanttitulkinta Heinrich Hertz, Philip Lenard, Valosähköinen ilmiö James Maxwell Maxwellin yhtälöt Maxwellin jakautuma Satyendra Nath Bose 1926 Bose-Einstein jakautuma

4 Mustan kappaleen säteily
Kaikki kappaleet lähettävät sähkömagneettista säteilyä aallonpituuksilla, jotka ovat tunnusomaisia kappaleen lämpötilalle. Kvantti-käsitteen varhainen muotoutuminen liittyi läheisesti mustan kappaleen säteilyn aallonpituusjakautumaan. The early development of the concept of a quantum is closely related to the observations of the wavelength distribution of heat radiation. LFS 25th Anniversary Symposium

5 Atomeista ja ideaalikaasusta mustan kappaleen säteilyyn
f [Hz] 104 106 108 1010 10 12 Tehotiheys [ W/Hz/m2 ] Havaittu säteily Max Planck (1901) Wilhelm Wien (1896): Säteilyn taajuus suljetussa tilassa on verrannollinen seinämien emittoivien atomien kineettiseen energiaan, The emission spectrum of heat radiation was observed to be essentially independent of the emitting material. The spectrum had very specific form with the power maximum a function of the temperature. The first theoretical solution to the blackbody spectrum was given by Wilhelm Wien in 1896: … he concluded that the emission frequency is proportional to the thermal velocity (energy) of the emitting molecule … so, due to the Maxwell-Boltzmann distribution of the emitters, the number of emitters for high frequencies is reduced … Wien’s radiation law fitted very well to the observed spectrum at the high frequency end … but not very well at low frequencies … … shortly after Wien’s radiation law – Lord Rayleigh introduced a different radiation law … he applied the equipartition principle and the average thermal energy of a molecule to the standing waves of harmonic frequencies in a black body cavity – accordingly, the energy density increases linearly with the increasing frequency … Rayleigh’s radiation law worked very well at the low frequency part of the spectrum … but led to an ultraviolet catastrophe at high frequencies … In 1901 Max Planck combined the two approaches with an experimental equation … he justified the solution with the famous hypothesis of energy packages, quanta, which allowed radiation to be studied as particle-like energy objects with a specific distribution function … A proposal for the theoretical basis of Max Planck’s distribution function was presented by Bose 25 years later – complemented by Einstein, the distribution is known as the Bose-Einstein distribution. - NEXT SLIDE In the late 19th century, the challenge in the theory of blackbody radiation was in combining findings related to ideal gases, thermodynamics, atomic theory, electromagnetism and electromagnetic radiation. The gas constant R related temperature to energy at the molar scale. The Boltzmann constant k did the same for a molecule. For ideal gases the average thermal energy/molecule is 3/2 kT, equal to ½kT´per degree of freedom. The classical ideal gas theory comprises the findings of Robert Boyle, Daniel Bernoulli, Joseph Louis Gay-Lussac (French: [ʒɔzɛf lwi ɡɛlysak] 1802) , Bernoulli The early development of atomic theory is generally credited to John Dalton in his search for “the rules of greatest simplicity” Avogadro’s constant linked mole to a molecule The equipartition of kinetic energy was proposed initially in 1843, and more correctly in 1845, by the Scottish physicist John James Waterston. Michael Faraday’s experiments with electrolysis linked the unit charge to a molecule. Bose-Einstein jakautuma (1926) Lord Rayleigh (1900): Jokainen seisovan aallon jakso sisältää energian kT LFS 25th Anniversary Symposium

6 Kaksi lähestymistapaa mustan kappaleen säteilyyn
Max Planck (1901) Wilhelm Wien: Ekvipartitioperiaatetta sovelletaan emittoivien molekyylien energiajakautumaan  Maxwell-Boltzmann jakautuma Säteilyspektri määräytyy emittereistä Max Planck: Säteily emittoituu aaltopaketteina, joiden energia on verrannollinen taajuuteen yhtälön E = hf mukaisesti - tiheysjakautumaa sovelletaan aaltopaketteihin  Kvantti on säteilyn ominaisuus Lord Rayleigh: Ekvipartitioperiaatetta sovelletaan harmoonisten taajuuksien seisoviin aaltoihin mustan kappaleen (jokainen aalto sisältää keskimäärin energian kT )  Säteilyspektri on säteilyn ominaoisuus Wilhelm Wien’s solution was based on the Maxwell-Boltzmann distribution of the emitters, which means that the spectrum is a property of the emitters Lord Rayleigh’s solution applied the equipartition principle to the standing waves of harmonic frequencies in the blackbody cavity, which made the spectrum a property of radiation To unite the two approaches, Max Planck postulated that radiation is emitted as localized radiation quanta with the energy proportional to the frequency … which made the quantum an inherent property of radiation. LFS 25th Anniversary Symposium

7 Mikä on minimiannos säteilyä?
Wilhelm Wien, Nobel luento 1911, loppuyhteenveto: … Planckin teoriaa ei vielä ole saatettu täsmälliseen muotoon. Tieteessä, pelastava idea tulee usein täysin toisenlaisesta suunnasta, tutkimukset avian toisenlaisella alalla tuovat usein odottamatonta valoa ratkaisemattomien ongelmien pimeisiin kohtiin … “Radioinsinööri voi tuskin ajatella pienempää annosta sähkömagneettista säteilyä kuin säteilyannos, jonka tuottaa yhden elektronin yksi värähdysjakso dipolissa.“ Maxwellin yhtälöt: Dipolin säteilemä tehotiheys: B q r E j z0 So, let’s go back to the basis … is a quantum a property of radiation or the emission process ? In the final comments of his Nobel lecture in 1911 Wilhelm Wien stated … … the Planck theory has not yet been brought into a definite form. In science, the redeeming idea often comes from an entirely different direction, … investigations in an entirely different field often throw unexpected light on the dark aspects of unresolved problems. … so, let’s study a radio engineer’s approach to the emission of electromagnetic radiation … He bases his view on Maxwell’s equations and the standard solution for the average power of radiation from a dipole … which is given in every physics textbook … We start elaborating the formula by replacing the angular frequency with frequency f … … … relate the dipole length z0 to the emission wavelength … NEXT LFS 25th Anniversary Symposium

8 Mikä on minimiannos säteilyä?
“Radioinsinööri voi tuskin ajatella pienempää annosta sähkömagneettista säteilyä kuin säteilyannos, jonka tuottaa yhden elektronin yksi värähdysjakso dipolissa.“ B q r E j z0 … and the electrical constant epsilon(0) into the magnetic constant my(0) we need some more space … LFS 25th Anniversary Symposium

9 Mikä on minimiannos säteilyä?
“Radioinsinööri voi tuskin ajatella pienempää annosta sähkömagneettista säteilyä kuin säteilyannos, jonka tuottaa yhden elektronin yksi värähdysjakso dipolissa.“ B q r E j per unit charge Energy/cycle z0 Geometriatekijä Vakio … next, we solve the energy emitted into one cycle of radiation by dividing the power by the frequency … we set N equal to 1 for a single electron and set the length of the dipole equal to the wavelength … as shown by the next equation … … we now have the product of a geometrical factor 2/3 characteristic to a Hertzian dipole, a constant with the dimension of the Planck constant [kg m^2 / s] and the frequency … in essence, we have entered into the formulation of the Planck equation … …. By setting the geometrical factor of our dipole to we enter into the Planck constant h, which is now linked to the velocity of light and the basic electrical constants, a unit charge and the vacuum permeability NEXT h LFS 25th Anniversary Symposium

10 Mikä on minimiannos säteilyä?
Miten pistelähde voi toimia yhden aallonpituuden dipolina ? “Radioinsinööri voi tuskin ajatella pienempää annosta sähkömagneettista säteilyä kuin säteilyannos, jonka tuottaa yhden elektronin yksi värähdysjakso dipolissa.“ Geometriatekijä Vakio Energia/jakso Yksi alkeis-varaus B q r E j z0 Pistelähde etenee yhden jakson aikana yhden aallonpituuden neljännessä ulottuvuudessa … we obtained the Planck equation for the energy emitted by a one-wavelength dipole with the geometrical factor about one … 1. so, … how can atomic point sources, like the emitters at a black body surface, serve as one-wavelength dipoles ? We choose the direction of the dipole as the imaginary dimension, the fourth dimension perpendicular to the three space directions … In one cycle, which we are studying, time interval delta T is equal to the cycle time, which means that the line element c * delta T in the fourth dimension, and, accordingly, the “effective length of our point source dipole” is equal to the wavelength ! … remembering that the 4th dimension is perpendicular to any space direction, we may expect a geometrical factor close to one for our dipole NEXT The line element in the fourth dimension is ds = c*dt. For dt=1/f, ds = lambda. Dipoli 4. ulottuvuudessa on kohtisuorassa kaikkiin avaruussuuntiin nähden h LFS 25th Anniversary Symposium

11 Pelkistetty Planckin vakio
Massaobjektin aallonpituusekvivalentti = Compton-aallonpituus, Säteilyjakson aallonpituus-ekvivalentti “Pelkistetty” Planckin vakio Hienorakannevakio osoittautuu puhtaaksi numero- tai geometriatekijäksi ilman yhteyttä muihin luonnonvakioihin Now we have the Planck constant linked to the basic electrical constants. We notice that the velocity of light appears as a factor in the Planck constant We define the “Intrinsic Planck constant” excluding the velocity of light … the new constant has now dimensions of [kg*m] Applying the Intrinsic Planck constant … we get a new formulation of the energy of a quantum ... … we convert frequency into wavelength and enter into the formulation … h(0)/lambda * c2 where h(0)/lambda has the dimension of mass * c2 … so, the energy of our quantum, which we found as a property of the emission process, can be expressed as the rest energy of mass m(lambda), to be called the mass equivalence of a unit cycle of electromagnetic radiation … the linkage of the Planck constant to basic electrical constants makes the fine structure constant independent of any physical constants, so it appears just as a geometrical or numerical factor … we defined the mass equivalence of radiation …. correspondingly, we can define the wavelength equivalence of mass… … which is the Compton wavelength NEXT …. we raise the question of the essence of a quantum h LFS 25th Anniversary Symposium

12 Massan aaltoluonne Sähkömagneettinen säteily
Säteilyjakson massaekvivalentti Massaobjekti levossa Massaobjektin aallonpituus-ekvivalentti (=Compton-aallonpituus) Im Re Massa-objektin kuvaaminen resonaattorina Nikolai Tesla (1856–1943) : “Jos haluat löytää universumin salaisuudet, ajattele kaikkea energiana, taajuutena ja värähtelynä”. “If you like to found the secrets of the universe, think everything as energy, frequency and oscillation”.

13 Kvantin olemus Radioinsinöörin kvantti on johdettu
Max Planckin kvantti pääteltiin postuloituna suureena mustan kappaleen säteilystä. Max Planckin kvantti on lokalisoitunut ja säteilyn itseisominaisuus. Radioinsinöörin kvantti on johdettu Maxwellin yhtälöistä: kvantti on yhden alkeis-varauksen yhteen säteilyjaksoon emittoima energia. Radioinsinöörin kvantti on lokalisoitunut, jos se on emittoitu suuntaavasta lähteestä – ja ei-lokalisoitunut aaltorintama, kun se on emittoitu ei-suuntaavasta lähteestä. Selittääkö antennitarkastelu mustan kappaleen säteilyn aallonpituusjakautuman? Max Planckin kvanttia kuvaa “vaikutuskvantti” h Radioinsinöörin kvanttia kuvaa “intrinsiikkinen Planckin vakio” h0, joka aallonpituuden kanssa määrittelee säteilyjakson massaekvivalentin So, let’s summarize 1. Max Planck’s quantum was deduced from blackbody radiation as a postulated quantity. Max Planck’s quantum is localized and an intrinsic property of radiation. Radio-engineer’s quantum is derived from Maxwell’s equations as a single radiation cycle emitted by a unit charge transition in an emitter. Radio-engineer’s quantum is localized when emitted by a directional emitter – and a non-localized wave front when emitted by a non-directional emitter. 2. Max Planck’s quantum is characterized by the Planck constant h defining a “quantum of action” Radio-engineer’s quantum is characterized by the “intrinsic Planck constant” h0 defining the mass equivalence of an elementary cycle of radiation 3. Next we ask whether the antenna approach can explain the energy/wavelength spectrum of blackbody radiation LFS 25th Anniversary Symposium

14 Emissio mustan kappaleen pinnasta
Kyllä, antennitarkastelu selittää mustan kappaleen säteilyn energia/aallonpituusspektrin - erittäin havainnollisella tavalla. Antennin säteilypinta-ala “potentiaalinen” emissiviteetti puoliavaruuteen Antenni-tiheys Yksikköenergia /antenni Aktivaatio-jakautuma Wien: Rayleigh-Jeans: The active area of an antenna is A = lambda2/4pi, which means that the potential emissivity to half-space is 2pi/lambda2 …. Which is identical with the intensity term Rayleigh-Jeans radiation law When all antennas on the surface are energized at least with hf , which happens when kt > hf , we get exactly the Rayleigh-Jeans radiation law When hf gets close to kT, some of the antennas are not energized (due to the Maxwell-Boltzmann distribution of the energies of the emitting molecules) At increasing frequencies only a diminishing share of the antennas are energized, and the emission power follows the Wien distribution … the two limiting mechanisms are combined in the Planck equation So, … the answer is: Yes, the antenna approach explains the energy/wavelength spectrum of blackbody radiation in a very illustrative way. NEXT Lähde on “pinta-alarajoittunut” Lähde on “aktivaation rajoittama” LFS 25th Anniversary Symposium

15 LFS 25th Anniversary Symposium
Kvantin vastaanotto Säteilykvantti absorboituu, jos säteilyn energia/jakso antennin sieppauspinnalla on hf tai suurempi. Let’s look at the receiver: How is a quantum received … when a wide wave front approaches an antenna, a quantum is detected if the energy/cycle within the antenna active area is hf or higher. A single localized quantum from a laser is detected …. …. if the whole localized quantum hits the antenna active area If a localized quantum is defocused and diluted outside the antenna active area …. no detection occurs Importantly, an antenna is wavelength selective with an energy threshold NEXT Antenni on aallonpituusselektiivinen ja edellyttää kynnysenergian ylitystä. LFS 25th Anniversary Symposium

16 Kvantti emissio/absorption –prosessin ominaisuutena
Kvantti emissio/absorption –prosessin ominaisuutena selittää - yhtä hyvin kuin lokalisoitunut kvantti - kokeet, kuten valosähköinen ilmiö ja Compton-sironta, Joita on käytetty todisteena lokalisoituneelle kvantille. Quantum as a property of the emission/absorption process explains - just as well as the localized radiation quantum - experiments like the photoelectric effect, and Compton scattering used as experimental evidence for the localized radiation quantum. NEXT LFS 25th Anniversary Symposium

17 Kvantin olemuksesta, eräitä seurauksia
1. Kvantti säteilyn ominaisuutena 2. Kvantti emissio/absorption-prosessin ominaisuutena Planckin vakio h [ kg m2/s] on postuloitu vaikutuskvantti h0 [kg m] säteilyjakson massaekvivalentin – se on johdettu Maxwellin yhtälöistä Aineen/säteilyn energia Säteilyn energia E=hf Aineen lepoenergia E=mc 2 Yhteinen, Massan olemus - Partikkelin ominaisuus - Energian ilmenemismuoto Energian ilmentämisen substanssi de Broglie -aalto Koska c on piilotekijänä h:ssa de Broglie -aalto lukittuu valon nopeuteen Kuljettaa liikemäärää objektin nopeudella (de Broglien intuitiivinen ajatus) Atomin elektronien energiatilat Diskreettejä kvanttitiloja Jatkuvaluonteisia tiloja Avaruuden laajenemisen vaikutus Laajenevassa avaruudessa etenevä säteily menettää energiaansa (= yksi pimeän energian tarpeeseen vaikuttava tekijä) Säteilyjakso säilyttää energiansa; energiatiheys pienenee aallonpituuden kasvaessa. Meaning of a quantum: Quantum of action - mass equivalence of radiation De Broglie wave: Once the velocity of light is a hidden factor in the Planck constant, also the de Broglie wave is fixed to the velocity of light in the case of the intrinsic Planck constant the de Broglie wave carries the momentum at the velocity of the moving particle - which, in fact, corresponds to the original intuitive idea of de Broglie The essence and definition of the concept of mass is fundamental, traditionally it was liked to the inertial property …. Later on, mass was seen as a manifestation of energy - the intrinsic Planck constant and the concept of mass equivalence shows mass as the substance for the expression of energy – both for particles and radiation – as well as to gravitational energy. Importantly, the redefinition of mass and the expression of energy and momentum as complex quantities allows a unified expression of energy, which applies both for particles and radiation The Planck equation as an inherent property of radiation has a dramatic cosmological consequence: in expanding space radiation loses energy, which, in fact, is one of the factors creating the need for “dark energy” in standard cosmology – in the case of the quantum linked to the emission process, the energy is conserved but the energy density is reduced with the increasing volume LFS 25th Anniversary Symposium

18 Pelkistetty Planckin vakio ja energian yhtenäinen ilmasu
Säteilyn yksikköjakso Im Re … neljännen ulottuvuuden dynaaminen tulkinta … Aineen lepoenergia Im Re Compton-aallonpituus Im Aineen kokonaisenergia Re In the antenna solution of the quantum, we applied a dynamic interpretation of the 4D line element … … which allows the interpretation of the rest energy as the product of velocity and momentum in the 4th dimension … the total energy of mass now becomes a complex quantity comprising momentums in space and in the fourth dimension … 4. Also the Coulomb energy can be expressed in terms of mass equivalence and the velocity of light 5. We may observe, that acceleration of a charges mass object in Coulomb field releases mass equivalence m(c) … looks like giving the relativistic mass increase to the object accelerated … … this may need some further study Kiihdytys Coulombin kentässä siirtää massan Im Im Re Coulombin energia LFS 25th Anniversary Symposium

19 Liikemäärän ja energia käsittely kompleksisuureina
“Relativistinen” massan kasvu ei ole seuraus nopeudesta vaan lisämassa, joka on tarvittu liikkeen aikaansaamiseen. Karakteristiset taajuudet: Im Re Liikkeessä oleva atomikello käy hitaammin ! Im Re Aineen kokonaisenergia The total momentum, now, consists of mv originating from the tiled rest momentum, and delta(m)*c from the Coulomb energy The real component of the momentum (= the momentum in space) gets mv from the tilted rest momentum and delta(m)*c from the Coulomb energy We can conclude, that the “relativistic mass increase” is not a consequence of the velocity but the mass contribution needed to obtain the velocity The price paid for the share mv in the real component is that the imaginary component, the rest energy of the moving object, is reduced This is very interesting, because the characteristic frequencies of atomic oscillators, like atomic clocks, are proportional to the rest momentum Which means reduction of the frequency with the velocity Clocks in motion run slower because part of their energy is used for the motion in space. Kiihdytys Coulombin kentässä siirtää massan Im Im Re Coulombin energia LFS 25th Anniversary Symposium

20 Liikemäärä ja energia kompleksisuureina
Pelkistetyn Planckin vakion käyttö sekä liikemäärän ja energian ilmaisu kompleksifunktioina ilmaisee suhteellisuuden seurauksena energiatilasta eikä muuntuneesta ajasta ja etäisyydestä …. Suhteellisuus kuvaa kokonaisenergian säilymistä avaruudesta … The use of the intrinsic Planck constant and the complex function presentation of momentum and energy shows relativity in terms of “the energy state” instead of “the proper time and the proper distance” …. just by taking care of the energy bookkeeping in creating motion in space … LFS 25th Anniversary Symposium

21 Kvantin olemuksesta, eräitä seurauksia
1. Kvantti säteilyn ominaisuutena 2. Kvantti emissio/absorption-prosessin ominaisuutena Planckin vakio h [ kg m2/s] on postuloitu vaikutuskvantti h0 [kg m] säteilyjakson massaekvivalentin – se on johdettu Maxwellin yhtälöistä Aineen/säteilyn energia Säteilyn energia E=hf Aineen lepoenergia E=mc 2 Yhteinen, Massan olemus - Partikkelin ominaisuus - Energian ilmenemismuoto Energian ilmentämisen substanssi de Broglie -aalto Koska c on piilotekijänä h:ssa de Broglie -aalto lukittuu valon nopeuteen Kuljettaa liikemäärää objektin nopeudella (de Broglien intuitiivinen ajatus) Atomin elektronien energiatilat Diskreettejä kvanttitiloja Jatkuvaluonteisia tiloja Avaruuden laajenemisen vaikutus Laajenevassa avaruudessa etenevä säteily menettää energiaansa (= yksi pimeän energian tarpeeseen vaikuttava tekijä) Säteilyjakso säilyttää energiansa; energiatiheys pienenee aallonpituuden kasvaessa. Meaning of a quantum: Quantum of action - mass equivalence of radiation De Broglie wave: Once the velocity of light is a hidden factor in the Planck constant, also the de Broglie wave is fixed to the velocity of light in the case of the intrinsic Planck constant the de Broglie wave carries the momentum at the velocity of the moving particle - which, in fact, corresponds to the original intuitive idea of de Broglie The essence and definition of the concept of mass is fundamental, traditionally it was liked to the inertial property …. Later on, mass was seen as a manifestation of energy - the intrinsic Planck constant and the concept of mass equivalence shows mass as the substance for the expression of energy – both for particles and radiation – as well as to gravitational energy. Importantly, the redefinition of mass and the expression of energy and momentum as complex quantities allows a unified expression of energy, which applies both for particles and radiation The Planck equation as an inherent property of radiation has a dramatic cosmological consequence: in expanding space radiation loses energy, which, in fact, is one of the factors creating the need for “dark energy” in standard cosmology – in the case of the quantum linked to the emission process, the energy is conserved but the energy density is reduced with the increasing volume LFS 25th Anniversary Symposium

22 Compton-aallonpituudesta de Broglie-aallonpituuteen
Im Havainnon synnyttää objektin luovuttama kineettinen energia! Re Compton “resonaattori” Etuaallon liikemäärä kasvaa Havainnot lepokehyksessä Taka-aallon liikemäärä pienenee Doppler-ilmiö: Nettoaalto/liikemäärä havaitaan lepokehyksessä We describe a mass object with a Compton resonator. In the state of rest the momentum in space is zero due to the equal opposite momentums of the opposite waves. When the resonator is put into motion – for observers at rest … the frequency of the front wave is increased … and frequency of the front wave is increased due to the Doppler effect … the resulting sum wave carries the momentum of the object …. When expressed in terms of the de Broglie wave the velocity is fixed to the velocity of light … but applying the intrinsic Planck constant the sum wave follows the moving object … A momentum-wave propagating at the velocity of the mass object was something de Broglie was looking for … such a solution gives a natural explanation to the double-slit interference (the Thomas Yang double slit experiment) Compare to Aristotle’s movent and John Philoponus’s and Jean Buridan’s impetus ! LFS 25th Anniversary Symposium

23 Pelkistetty Planckin vakio ja energia ilmaiseminen
Kun valon nopeus irroittetaan Planckin vakiosta, voidaan de Broglie –liikemäärä ilmaista maassa-aaltona, joka liikkuu liikkuvan objektin nopeudella … “netto Doppler-aaltona”, joka syntyy liikkuvasta Compton-resonaattorista. As a consequence of the removal of the velocity of light from the Planck constant … the de Broglie momentum can be described as a mass wave propagating at the velocity of the moving object … simply, as the “net Doppler” wave of the moving Compton wave resonator. LFS 25th Anniversary Symposium

24 Kvantin olemuksesta, eräitä seurauksia
1. Kvantti säteilyn ominaisuutena 2. Kvantti emissio/absorption-prosessin ominaisuutena Planckin vakio h [ kg m2/s] on postuloitu vaikutuskvantti h0 [kg m] säteilyjakson massaekvivalentin – se on johdettu Maxwellin yhtälöistä Aineen/säteilyn energia Säteilyn energia E=hf Aineen lepoenergia E=mc 2 Yhteinen, Massan olemus - Partikkelin ominaisuus - Energian ilmenemismuoto Energian ilmentämisen substanssi de Broglie -aalto Koska c on piilotekijänä h:ssa de Broglie -aalto lukittuu valon nopeuteen Kuljettaa liikemäärää objektin nopeudella (de Broglien intuitiivinen ajatus) Atomin elektronien energiatilat Diskreettejä kvanttitiloja Jatkuvaluonteisia tiloja (joiden minimikohta vastaa kvanttitilaa) Avaruuden laajenemisen vaikutus Laajenevassa avaruudessa etenevä säteily menettää energiaansa (= yksi pimeän energian tarpeeseen vaikuttava tekijä) Säteilyjakso säilyttää energiansa; energiatiheys pienenee aallonpituuden kasvaessa. Meaning of a quantum: Quantum of action - mass equivalence of radiation De Broglie wave: Once the velocity of light is a hidden factor in the Planck constant, also the de Broglie wave is fixed to the velocity of light in the case of the intrinsic Planck constant the de Broglie wave carries the momentum at the velocity of the moving particle - which, in fact, corresponds to the original intuitive idea of de Broglie The essence and definition of the concept of mass is fundamental, traditionally it was liked to the inertial property …. Later on, mass was seen as a manifestation of energy - the intrinsic Planck constant and the concept of mass equivalence shows mass as the substance for the expression of energy – both for particles and radiation – as well as to gravitational energy. Importantly, the redefinition of mass and the expression of energy and momentum as complex quantities allows a unified expression of energy, which applies both for particles and radiation The Planck equation as an inherent property of radiation has a dramatic cosmological consequence: in expanding space radiation loses energy, which, in fact, is one of the factors creating the need for “dark energy” in standard cosmology – in the case of the quantum linked to the emission process, the energy is conserved but the energy density is reduced with the increasing volume LFS 25th Anniversary Symposium

25 Elektronin resonanssitilat vetyatomissa
2 4 6 8 10 12 14 16 r/r0 EZ,n [eV] 13.6 [eV] n=1 n=2 n=3 Im φ Re Vetyatomin pääkvanttilukuun liittyvät energiatilat ilmenevät jatkuvaluonteisten energiatilojen minimeinä - eivät diskreetteinä kvanttitiloina Energy at minima Radius at minima LFS 25th Anniversary Symposium

26 Kvantin olemuksesta, eräitä seurauksia
1. Kvantti säteilyn ominaisuutena 2. Kvantti emissio/absorption-prosessin ominaisuutena Planckin vakio h [ kg m2/s] on postuloitu vaikutuskvantti h0 [kg m] säteilyjakson massaekvivalentin – se on johdettu Maxwellin yhtälöistä Aineen/säteilyn energia Säteilyn energia E=hf Aineen lepoenergia E=mc 2 Yhteinen, Massan olemus - Partikkelin ominaisuus - Energian ilmenemismuoto Energian ilmentämisen substanssi de Broglie -aalto Koska c on piilotekijänä h:ssa de Broglie -aalto lukittuu valon nopeuteen Kuljettaa liikemäärää objektin nopeudella (de Broglien intuitiivinen ajatus) Atomin elektronien energiatilat Diskreettejä kvanttitiloja Jatkuvaluonteisia tiloja Avaruuden laajenemisen vaikutus Laajenevassa avaruudessa etenevä säteily menettää energiaansa (= yksi pimeän energian tarpeeseen vaikuttava tekijä) Säteilyjakso säilyttää energiansa; energiatiheys pienenee aallonpituuden kasvaessa. Meaning of a quantum: Quantum of action - mass equivalence of radiation De Broglie wave: Once the velocity of light is a hidden factor in the Planck constant, also the de Broglie wave is fixed to the velocity of light in the case of the intrinsic Planck constant the de Broglie wave carries the momentum at the velocity of the moving particle - which, in fact, corresponds to the original intuitive idea of de Broglie The essence and definition of the concept of mass is fundamental, traditionally it was liked to the inertial property …. Later on, mass was seen as a manifestation of energy - the intrinsic Planck constant and the concept of mass equivalence shows mass as the substance for the expression of energy – both for particles and radiation – as well as to gravitational energy. Importantly, the redefinition of mass and the expression of energy and momentum as complex quantities allows a unified expression of energy, which applies both for particles and radiation The Planck equation as an inherent property of radiation has a dramatic cosmological consequence: in expanding space radiation loses energy, which, in fact, is one of the factors creating the need for “dark energy” in standard cosmology – in the case of the quantum linked to the emission process, the energy is conserved but the energy density is reduced with the increasing volume LFS 25th Anniversary Symposium

27 Säteilykvantti laajenevassa avaruudessa
Planckin vakio säteilyn itseisominaisuutena Planckin vakio emission ominaisuutena Energiatiheys pienenee kuten Doppler ilmiössä mutta jakson kantaman energia säilyy (suhteessa avaruuden kokonaisenergiaan). Energiatiheys pienenee kuten Doppler ilmiössä ja kvantin energia pienenee (Tolmannin “intensiteettitekijä”). Säteily säilyttää energian avaruuden laajetessa – energiatiheys pienenee ! Säteily hukkaa energiaa avaruuden laajetessa ! LFS 25th Anniversary Symposium

28 Luminosity and power dilution due to redshift, Tolman 1930
Planck equation PNAS 1930;16; Doppler effect Planck & Doppler comoving distance

29 Kvantin ja pimeän energia tulkinta vaikutus Ia supernovahavaintojen tulkintaan standardikosmologiassa comoving distance Standard model (FLRW) Wm = 0.3, WL=0.7 Dark energy z m Standard model (FLRW) Wm = 1, WL=0 Planckin yhtälön tulkinta säteilyn itseisominaisuudeksi on yksi tekijöistä, jotka johtavat pimeän energian tarpeeseen ! Planckin yhtälö kuvaa emissio/absorptio prosessia. With the Planck equation as a property of the emission/absorption process - combined with “zero-energy space” with the energies of motion and gravitation in a balance, a beautiful fit to the supernova observations is obtained with a simple equation without “dark energy” or any other experimental parameters. Optinen etäisyys pallosymmetrisesti suljetussa nollaenergia-avaruudessa

30 FLRW kosmologia, etäisyysmääritelmät
DC Mukana liikkuva etäisyys = etäisyys pisteestä B’ pisteeseen A’ valon saapumishetkellä DC Tolman 1930, Hubble & Tolman 1935 Friedmann 1922 B’ A’ DL kirkkausetäisyys, Tolman 1930 DLT DA B A Doppler ”laimennus” Planck ”laimennus” A” Havaittu kirkkaus

31 Etäisyydet FLRW-avaruudessa ja Dynaamisessa Universumissa
B’ B A A’ B’ A’ ... and the optical distance D. B A

32 Kiitos tarkkaivaisuudestanne!
Luonnonfilosofian seura The Finnish Society for Natural Philosophy 1988 – 2013 Kiitos tarkkaivaisuudestanne! We do not put reality at risk by looking at it from a new perspective ! LFS 25th Anniversary Symposium