Physics; Watching the Game From the Outside

Transcription

1 Physis; Wathing the Game From the Outside Roald C. Maximo Feb It is a good thing to have two ways of looking at a subjet, and also admit that there are two ways of looking at it. James Clerk Maxwell, on addressing the question of two versions of eletromagneti theory, one due to Mihael Faraday and the other to Wilhelm Weber Abstrat: When the omplete answer is not known, In a sense everyone is a rakpot Halton Arp It is a known fat that, often, the perfet idiot who wathes the game from the outside is the one who diserns the best move! I'm an assumed rank As an engineer I an perhaps be aquitted, however there are numerous examples of renowned physiists that, oasionally, slide to a striking eentriity. It's not unommon for them to seek a omplex explanation where a simple one is at hand. The daring intention behind this paper is to throw a fierer light into three disreetly shadowed points whih, in my opinion, appear hazy or misoneived. To start with, I take it that zero and infinity are logial limits. Anything in between has to be a irumstantial limit. Light veloity is a irumstantial limit sine it is determined by the permeability m and permittivity e whih are irumstantial properties of the e/m propagation medium, perhaps related, in some way, to the zero point energy; no one knows for sure yet and, paraphrasing Halton Arp, in that ase everyone is a rakpot! In ases where suh a limit is at stake, it seems best to make it expliit and used it as a starting point given that the underlying irumstanes are not known. Otherwise we risk our reasoning to go astray and beome unbound. [] Time and kineti energy Unless otherwise speified, all alulations further on will use SI system of units. Take one seond as a referene time and, from that, it follows: t s = <= referene time E max = J () <= absolute upper energy limit μ ε Eq.() is telling you that E max = M! or E = p (momentum) x

2 E kmax μ ε = () <= kineti energy limit or simply E kmax = (3) Taking (3) as the referene energy and starting point and v as the speed of a moving body E k = v = v (4) <= left over energy apable of aelerating that body t μ ε = t (5) <= distane in meters traveled by light in one seond From Eq.(4) the impliit speed v i must be v i = v (6) t t = <= time fration relative to t where t v i = m substituting (6) above for v i t = t v whih may be written as t t = (7) length of time at speed v as related to referene time t = seond v

3 [] Mass inrease or lak of thrust power? Confronted with Newtons Law of fore f = m or f s v s = that is: fore equals mass versus aeleration and trying to aelerate a given mass, you have two independent variables and hoies: postulate a mass inrease with speed or a progressive lak of thrust energy. Ask an aeronautial engineer whih one he will hose. He will say a jet engine is only useful as long as the exhaust gases speed u from the engine are grater then the vehile veloity v, as the net engine thrust is the same as if the gas were emitted with veloity (u - v). He will laugh in your fae if you say that the airraft mass inreases with speed. The law of onservation of energy and momentum preludes a jet airraft of flying faster than the speed of the engine's exhaust gases and, for exatly the same reason, it preludes anything subjet to eletromagneti propulsion of attaining a speed grater than the veloity light. And, please, do not try to attribute mystial properties to light! Remember that eletromagneti radiation also has momentum. It is amazing that so few people have questioned suh an outlandish idea. In this respet I must, with justie, ite an artile by Musa Abdullahi* whih makes a terse objetion to the onept of mass inrement. Consonant with what was hitherto established t = s and kineti energy is given by t J k = (8) t t m = m ===> J k = t applying the just newly derived (7) Lorentz transformation for t in Eq. (8) J k t = redues to t v v J k = (4 bis) As you an see, we are obviously bak to equation (4) when applying the gamma fator to (8). The ubiquitous gamma fator lurks in several alulations involving (^ - v^)! The graph below shows how the thrust fore dereases as the speed approahes the veloity of light. 3

4 f = (9) <= remaining thrust fore still available at speed v v m relative fore x relative speed.8 f( v) f( ) v a = v m () <= maximum possible aeleration at speed v [3] The muh disputed transverse Doppler effet = light veloity vetor v s = light soure speed vetor = reeiver or observer speed vetor The terms reeiver and observer will be, here, used interhangeably representing the same entity. The omplete Doppler equation for wavelength is + v s os( θ) v s + v s λ = () λ = () + os( θ) + 4

5 Inluding the newly derived γ fator (7) for soure and reeiver γ s = γ r = v s () beomes γ s os( θ) v s + v s λ = (3) γ r os( θ) + or λ r γ r = (4) for soure at rest os( θ) + and λ s γ s os( θ) v s + v s = (5) for observer at rest Plotting (4) and (5) above as a funtion of theta for = one meter and speed v s = = half the veloity of light: [The graphs are plotted against the simpler, and usual, in line Doppler formula (6)] v s = v r = v s = m 5

6 v s os( θ) λ sl ( θ) = (6) + v s os( θ) <=== in line Doppler λ s ( θ) = γ s os( θ) v s + v s Graph (soure) transverse Doppler = λ sl ( θ) λ ( θ) s 8.5 λ s =.9 m 33 λ sl = m θ λ rl ( θ) m = λ λ sl ( θ) r ( θ) = γ r os( θ) + 6

7 Graph (reeiver) transverse Doppler = λ ( θ) rl λ ( θ) r 8.5 λ r =.5m 33 λ rl = m θ The equations baround olors refer to the respetive traes in the graphs. If you solve Eq.(4) or Eq.(5) for θ making λ = you get the omplement of the light aberration angle Eq.(7) for a star in the zenith. The solution is the same for both equations, indiating that only relative speed is at stake, independently of whether soure or observer are onsidered moving. This only enfores the fat that there an be no light aberration for o-moving soure and observer. For the data in the improbable example above, θ would be 6 degrees and φ = 3 degrees. Putting "down to Earth" figures in it: = 9.78 km <== Earth mean orbital speed s 7

8 + γ r θ = aos (7) <= omplementary angle for starlight aberration when a star is on the zenith θ = deg φ = θ (8) <== Angle of aberration φ = arse omparing with the simple geometri alulation: Maximum starlight aberration angle ==> atan γ r = arse (9) both equations (8) and (9) expand in series equally to Did you notie that only Newtonian physis have been used throughout? * Musa D. Abdullahi Explanations of the Results of Roger's and Bertozzi's Experiments Without Reourse to Speial Relativity The General Siene Journal 8