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mahesh khati

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  1. sorry please check your mathematics again. Sorry but in physics, even in relativity in any mathematical equation which we form. If we put units of all quantity in right side & left side both must be equal for example in E = m c2 sum of right side units & left side unit gives same result for example in E = m c2 N. m = kg. m2/s2 kg , m/s2 . m = kg . m2/s2 kg. m2/s2 =kg . m2/s2 L.H.S = R.H.S equation may be any, like famous mass equation of relativity then also this thing is true but in your expression of work this fails to do that put the units of work, C, u du you find that kg. m2/s2 =kg . m4/s4 means, L.H.S. is not equal to right hand side Same problem remain in your concluding expression also. 2nd point :- If your concluding expression is applied to problem of old man pulling cart in direction perpendicular to motion of train Consider man pulled cart 1 m then work done will be different If man pulled cart 10 m then work done will be more Means work is depend on displacement but your final expression do not address the displacement. It only depend on V & ux Please chech all math again. Sorry Relativities famous equation E = m c2 is proved by Einstein starting from expression, Work = F . dr where dr is displacement in that frame (I can give page no of that text book also) then to say using Work done = force in that frame x displacement in that frame by me is wrong. This is not correct. Mathematical proof & experimental findings are mutually related. Many times some thing is proved by mathematics & we find that it is experimently perfect after many years. So, if you want to prove me wrong mathematically then that is correct way to oppose me mathematically.
  2. I heard but here space contraction due to relative velocity is applicable. For example intermolecular distance in velocity direction of thread will decrease or length of thread or side will only reduce.
  3. Means your calculation gives the same thing i.e. as V increases Work done or consumption of energy decreases as I say. Thanks. Using formula as I use Work done in that frame= Force in that frame X displacement in that frame is also not wrong in relativity for example Work W = F X dr .....where dr is displacement is used by Einstein to prove his famous equation E = mc2 If you prove oppsite that work done do not decreases by increasing velovity V of train then I will be wrong. Thanks Complete theory of relativity started by considering the velocity of light in any reference frame is constant. All theory is so much interdependent on one another that this theory becomes palace of cards. Even Einstein know that very well. So, he says that several proof is not sufficient to prove me correct but one single proof is sufficient to prove me wrong. So, even if we take out one card from that palace then whole palace of card will get collapsed. So to say Einstein may be wrong in this contrain & may be true in other constrain is wrong. Relativity may be wrong or correct. Both things correct at one time is not possible. 1991, When I was in Engineer College one of my professor of physics challenge me to prove Einstein is wrong logically. I just go to black board & draw rectangle ABCD. I say consider, I have pulleys A, B, C, D at four corner of rectangle which is mounted by one string. Now, consider string has started revolving around four pulleys then what will happen by relativity. 1) As pulleys are at rest with relative to me their position can not be changed by relativity. But 2) String is moving with velocity V. So, molecular distance in string has to decrease or length of string (sides of rectangle) at any moment has to decrease with relative to me. Now, logically without changing location of pulley how can you change length of string? This is completely wrong. This is something like corner of rectangle remain as it is & length of side of rectangle decreases. I can create many such situations where we can prove that relativity is logically wrong but now we can prove it wrong mathematically.. (At the place of string you may consider flow of electrons & at the place of pulleys you may consider magnetic deflector. ) Thanks
  4. Force, energy, momentum, work are not frame invarient means Force, energy, momentum, work are frame varient both has same meaing & I proved that using mathematics of standard test book also refer math 3 & 4 of chapter 1 .Only problem is that force decreases with increasing velocity. To understand it is also simple refer the unit of force i.e. N or kg.m/s2.. This clearly indicate that relative change in mass can not get balanced due to the relative change is time. This is not my mathematics but mathematics given in standard text book it also gives the same result.
  5. Consider, observer is in rest train on the platform & on the platform one old man is pulling cart in perpendicular direction to length of train then in that frame of reference the work done by old man = force x displacement of cart on platform in that rest frame I think above mathematics is simple & clear. Second condition:- Now, Consider train is moving with constant velocity V then for observer in train watching the same event then due to relativity. Force (force perpendicular to train motion) decreases & displacement remain same as contraction of space is not happening in that direction. So, product of force & displacement due to force applied by old man in that frame decrease. So, for observer in train work done by old man decreases .
  6. Many friends has same thoughts as you have. So, I actually taken into account the time dilution in all 4 mathematics posted in first chapter of paper but I was surprise to find that perpendicular force atually decrases as velocity increases. This force may be gravity or may be force applied by old man on cart moving perpendicular to the motion of train (observer). Change in the force create problem because due to it, there is action, work & consumption of energy happens etc.
  7. Please refer first paper on web site www.maheshkhati.com which proves that Einstein theory of relativity is wrong. First chapter proves that force perpendicular to motion decreases with increasing velocity. Means, work done decreases as velocity increases. Means, consumption of energy decreases as velocity increases but as per strong equivalence principle of mass & energy of relativity, consumption of energy should be increases, not decreases as velocity increases. This makes Einstein relativity wrong. Before year in discussion of this forum some says that you’re using mathematics of school. So, I refer standard text book of relativity of Msc in math 3 & 4, I proves that mathematics of standard test book of relativity also gives same result. In second chapter, I proved that relative velocity can be more than light velocity. Some says that the frame in which velocity is more than light is non-inertial frame. So, in chapter 3, I proved that we can not differentiate between inertial & non-inertial frame of references. Inertial frame is completely relativistic concept & happens due to local relative effect. In chapter 4, I proved that all relative inertial frames are not same but some of it is more special. In chapter 5, I prove that photon can not be a bundle of energy. Until now it is accepted that photon has dual nature without any explanation. How single photon moves from both slits in interference experiment and form a interference pattern can not be explain by any logic in science but excepted as fact.. It is explain in this chapter. ( In future same logic can used to explain instantanious quantum entangle which is also problem in physics) This paper gives solution to problem of dark matter which is impossible to explain until now. I know in future experimentally we will prove the Einstein is wrong. Experiment of quantum entangle is one of them.
  8. For pri-monsoon inspection of major bridges, I was completely busy for month. Sorry In relativity at the place of mass, generally momentum phrase is used. It indicate substance basic characteristic to oppose the change of state of motion in that frame when force is applied on it. If relativity says mass is frame variant then it comes from momentum which is frame variant means rate of change of momentum is frame variant. It is simple. So, force is frame variant. I can give example for that. In accelerator, for same acceleration of electron more force is required when velocity of electron increases because rate of change of momentum increases as velocity of electron increases. OR force also depends on velocity of electron with related to observer. Imp point:-a) Total mass of electron can be divided in to relative mass & rest mass. Rest mass can also be divided into mass due to gravity (negligible), mass due to electromagnetic field {3/5 e2/(c2.r)} & intrinsic mass of electron. b)Mass of composite system like gas balloon is summation of above mass plus contribution of kinetic energy of indivisible molecule for example one mole of ideal gas has average kinetic energy =3/2. K. T where K is Boltzmann’s constant & T is absolute temperature. This energy also contributes to mass of gas. c) This clearly proves that rest mass cannot be called as purely intrinsic mass. This mass may contain contribution by gravity, electromagnetic & kinetic energy of constituents. We can not omit kinetic energy constituent of mass at micro level or at macro level, Many say that then what is alternative to this concept of relativity. I say that alternative is very simple localized the relativity completely. Consider only electrons in any substance, that will create very very high –ve field around any substance. This effect is nullify by +ve field of protons. Around every substance very high balanced flux of +ve & -ve electromagnetic field is present. (Even charge less photon split up in to electron & positron. I consider substance as accumulation of fields). Elementary particle expresses their kinetic energy with relative to substance present very near to it because it expresses its kinetic energy with relative to that near electromagnetic flux acting on it. By This reason, photon express it velocity with relative to glass when it is moving in side glass. It express it velocity with relative to train cabin when it is in the train cabin, it express its velocity with relative to measuring instrument when it is near to it. Even small pin in space will create its reference frame due to electromagnetic flux present near to it. This is not true for photon but for all elementary particles. This is reason for getting same velocity of light or neutrinos for measuring instrument in all directions on earth. Electron also expresses its velocity with relative to electromagnetic flux of nucleus in atom. As this flux field create reference frame may have effect on all properties of frame like inertial mass, time etc. Photon may slow down inside glass due to slow down of time due to very very high electromagnetic flux present in that substance, time near to earth surface may slow down due to more electromagnetic flux present near to surface. This whole earth system is get tide by very strong fields & act as one substance. This is dance of fields around sun. That is reason for photon to communicate through long distance instantly. For us they are different but they are part of one system.
  9. PART I :- Please answer where I am wrong in above calculation for this paradox, Calculation1:- Weight of ball =d/dt (Moment in y direction) -------(Step as per relativity) =d/dt {(M rel) . (Vy)} -------(Step as per relativity) =d/dt {(γ. Mo) .(dSy/dt)} -------(Step as per relativity) Here, γ =1/(1-V2/C2)0.5 & Mo is rest mass. As V, C & Mo is constants. Weight of ball =d/dt {(γ. Mo). .(dSy/dt)}----------- (1) -------(Step as per relativity) FOR TRAIN RIDER :- equation (1) changes to Weight of ball =d/dt {Mo .(dSy/dt)}----------- (2) -------(Step as per relativity) As γ = 1 FOR PADRE ON PLATFORM:- equation(1) changes to Time = γ t as t is time for train rider & Padre on platform see clock in train is moving slow. Weight of ball =d/d(γ.t) {γ. Mo .dSy/d(γt )} =1/γ .d/dt . {(γ. Mo). .(dSy/γdt)} (As, event happen perpendicular to train motion. Distance travel remains unaffected by length contraction.) -------(Step as per relativity) =1/ γ . d/dt {Mo .(dSy/dt) -------(Step as per relativity) As γ is constant Equation changes to Weight of ball = 1/ γ . d/dt {Mo .(dSy/dt)} ----------- (3) -------(Step as per relativity) From (2) & (3) Weight of ball for Padre on platform = 1/ γ . Weight of ball for train Rider This calculation & other real life calculation in other my post which gives same result, clearly indicate that when force is perpendicular to motion of observer & event is just to begin at that time. Force for observer in motion = 1/ γ . force for observer at rest -------(Step as per relativity) (Mr Joseph o was right. As mass, time & space is frame variant, Force is also frame variant in S.R.) Such calculation is also not require just see unit of force i.e. Newton or kg. m/s2 i.e. mass in kg increases by γ multiple & time in second decreases by γ2 multiple then resultant will be force decreases by γ multiple. Part II :- Just consider that I am true. Force is frame variant & Force for observer in motion = 1/ γ . force for observer at rest Then if force is not balanced by opposite force then there is displacement in the direction of force & work is done in that reference frame in that direction. Consider that dSy is very small displacement in the direction of force (this remain same as this distance or event is unaffected by space contraction) then Force for observer in motion x dSy= 1/ γ . force for observer at rest x dSy Work done by force for observer motion = 1/ γ . Work done for observer at rest For this work done some energy from some system will get consumed then Energy consumed for observer in motion = 1/ γ . Energy consumed for observer at rest. i.e. E r = 1/ γ . Eo ----------(1) by strong principle of equivalence energy & mass are the same and get related by equation E = m c2 Means, energy must get related with each other by same principle as mass i.e. Mr = γ Mo i.e. E r = γ Eo but equation (1) gives completely different result. Such things create inconsistency in relativity. (I have tried to explain lot of thing in very short way. You may refer my paper for detail.) Part III :- (This is loosely related to this thread but important.) Why I am so much against relativity? I don’t except anything until my hart accept it. My great teachers & Professors are all relativity lover but they can’t convince me to except relativity. When I was in school. Teacher said that photon is the bundle of energy. I asked question to teacher that definition of energy is it is capacity to do work. Can anybody make a bundle of any capacity? Total energy of photon is kinetic energy can you make bundle of that kinetic energy. Photon is not the bundle of energy but some thing else. May be bundle of granules of vibrating fields as I consider. I was in engineering college. Professor was teaching relativity. He said that velocity of light is constant with relative to any observer I asked question why only photon gets such special power. If I fixed frame of reference on earth then all photons in the universe will have velocity C with relative to this frame of reference of observer. Then I calculate linear velocity of nearest star i.e. 4 light years away with related to frame fixed on revolving earth & find very interesting thing that all stars on equator are revolving around us with linear velocity more than C. As V= R.W, R= radius & W = angular velocity I asked question to professor that if velocity of stars will be more than light then velocity of light coming from that stars in opposite direction must be much more than C. He answers me that this frame is not an inertial frame of reference. This frame has angular acceleration. I asked him to give example of any one frame or substance which is not accelerating. Every one is accelerating. One day we may find that this world may be accelerating with related to some other world. Stable ness or inertial filling is very local phenomena. For example observer in falling closed lift may consider he is inertial observer as filling of force is absent there. So, to differentiate frames as inertial & non inertial is wrong. Every one is accelerating in world. This is the only tool by which substances avoid collision and world remain alive. in1991, when I was Engineering College. I mate Dr Ram Mohan Rao. In discussion with them he said that distinct galaxies are accelerating away from us with velocity more than light. I said that this is against theory of relativity. He said,” World is expanding & as space is expanding any two points in that space moves away from one another. This is not forced acceleration.” I said,” In big bang world started from point. Some substance moves so much distance away from one another due to expansion & some substance like distance between atoms remain at same distance. In any matter distance between two elementary particles remain at same distance. Now, we are on conveyor belt moving away from one another and to remain at same distance every particle has do work against this motion continuously. If force of attraction between particles is responsible for this same distance then that force will have to do work against this motion continuously & as this time, length of this world is relatively infinite, whole energy of every elementary particle in universe has get exhausted by doing work against expansion of world until now & to keep some near matter together.” He just stop & ask me to meet next day when I mate him he said, “There is dark energy that pool this galaxies away from one another.” I said,” then this is force acceleration. If dark energy exert forces on galaxies & pooling it away from another with velocity more than light then that is against relativity. & now only galaxial distance will increase which is the fact.” He was relativity lover & get angry. I have seen same anger some time from relativity lover. These are some points to explain my position.
  10. point 1:- Mathematics 1 of post 5:- Let, X- axis is in direction of motion of train with velocity V & Y-axis is in vertical direction. Due to velocity of train, contraction of space happens in X direction only & as event happen perpendicular to V. Event is not affected by space contraction. Weight of ball = d/dt (Moment in y direction) =d/dt {(M rel) . (Vy)} =d/dt {(γ. Mo) .(Vy)} ----------- (1) Here, γ = 1/(1-V2/C2)0.5 FOR TRAIN RIDER :- equation (1) changes to Weight of ball =d/dt {Mo .Vy}= d/dt {Mo.(dSy/dt)}----------- (2) As ball in same frame, γ =1 & Sy is vertical displacement FOR PADRE ON PLATFORM:- equation (1) changes to Time = γ t as t is time for train rider & Padre on platform see clock in train is moving slow. Weight of ball =d/d(γ.t) {γ. Mo .dSy/d(γt )} As γ is constant for constant V Equation changes to Weight of ball = 1/ γ . d/dt {Mo.(dSy/dt)} ----------- (3) From (2) & (3) Weight of ball for Padre on platform = 1/ γ . Weight of ball for train Rider Means as train velocity increases weight of ball also increases by relativity. This is basic calculation given by me in post 5 by using relativity. I have utilized all relativistic calculation perfectly here & which will give same result. Point 2:- classical mechanics has some basic formulae like distance = velocity x time , force = rate of change of momentum (or mass in that frame x acceleration in that inertial frame), acceleration = (final velocity - initial velocity)/ time. This formulae are not wrong in relativity also & if proper relative tranformation is applied with proper calculation. Point 3:-If you solve relativity matrix in Y direction then force Fy = m. γ. ay here m is rest mass, m γ is relative mass & ay is acceleration in Y direction. a)relative mass changes with observer frame & b)acceleration is also, time function & as time changes it also changes with observer frame of reference as ay = d/dt(dSy/dt) or event of acceleration slow down as relative velocity with observer increases. Here, mass increases by γ multipul & acceleration decreases by by 1/γ2 multipule so, net effect will be force changes by 1/γ multipul.
  11. 1)I am completely agree with you that the laws of physics are the same, everywhere, all the time, on every scale, and don't change based on wishful thinking of an observer. & If it changes due to Einstein relativity calculation then that is wrong. 2)As relative calculation given in post 26 is true then force will change as per the observer frame & any irreversible event may happen in one frame due to additional force in that frame which is not present in other inertial frame. This is unnatural. 3)This will create more problem because any additional force done the additional work by consuming additional energy this additional energy can not be explain by any relative calculation. 4)Calculation suggest that as velocity increases we require less force to done same event this is also unnatural.
  12. Point 1:-I have one quection for juanrga. If I am in one inertial frame frame of reference like Padre on platform & Padre is observing event in rail cabin then mass of ball & time of event will not be different for both observers i.e. Padre & train rider?. If relative mass & time are different. Then, calculation given in post 22 is also different for both observers. Means, weight will be different for both observers. Point 2:-In all post, I am talking about rate of change of moment is force. Equaction E^2 =m^2 c^4 +P^2 C^2 also indicate that when energy E increases moment increases. If we solve same equation, we get relative mass equation of Einstein. If you solve the matrix given in post 11, you will get mass in Y direction as I have taken. As fx = m .γ^3 . ax , fy = m. γ. ay & fz = m . γ. az . Here, m.γ is the relative mass of object. Point 3:- Even you consider mass is same for both observers (for just consideration) then also this Paradox will not get solve because time is relative.It changes with observer, so velocity, so moment & then force changes. Point 4:-At the place of gravity, any other force is applied which will done same acceleration then also same complecated results will be obtained. FOR EXAMPLE :- PARADOX IS SAME ONLY LANGUAGE & EVENT IS CHANGED & GRAVITY IS OMITTED Consider luggage cart with frictionless bearing is pulled in perpendicular direction to coming train on the platform with force 20 N & for 1 second. One Padre is on platform observing event & other observer is in the train. Then For Padre on platform:- Let, mass of cart m = 10 kg , Then acceleration a =Force/m = 20/10 = 2m/s2 After 1 second, distance travel by cart will be at Distance S=0.5 a t2 S= 0.5 x 2 x 12 S=1m For Observer in train :-For observer in train event happen slowly, So, 1 one second changes to γ seconds & mass m changes to m γ . (As, event happen perpendicular to train motion. Distance travel remain unaffected by length contraction.) Distance S=0.5 a t2 Acceleration a=1/(0.5 x γ 2) .a = 2/ γ 2 Force F = mass X acceleartion = Y m . 2/ γ 2 Force F = 2. m/ γ =2 x 10 / γ =20/ γ Newton Means, now we require only 20/ γ force to performed same event. Comment: - Only by changing observer, force require for same event to perform can be adjusted or changed.
  13. Point1 :- I am completely agreed with you. That is the one of the reason for which I am completely against relativity. In relativity, Einstein gives much important to observer. So, some time relative math will give some amazing results. Here, observer turned in to creator of event. Point 2:- In any frame upward force is not balanced by downward force then relative motion will happen or braking will happen. Point 3:- If I add the weight of string also then braking will takes placed at the top of the string but braking will not stop. Point 4:- If any additional force or weight is created only by changing observer then that will create chain of other problems like unequal work done etc. You may refer attached file to my first post.
  14. Now I convert expression of variable in to real event consider 1 kg ball falls from height 19.62 m in rail cabin then what will happen is given below In any inertial frame of reference, if we saw some thing is accelerating then force which causes this acceleration is equal to the rate of change of moment in that frame. Einstein in accelerating ship will also accept this fact. Now,same mathematics is applied here In rail cabin:-Consider 1 kg of ball is falling from height 19.62 m in rail cabin. Let, falling event will happen in time T then Height = 0.5 g T2 T2=2(19.62/9.81) T2=4 T=2 sec Acceleration g = (V-U)/T Here, U=0 So, g = V/T &, V =9.81 x 2 = 19.62 m/s Hence, force causing this acceleration or weight = rate of change of momentum =(M .V-M U)/T Here, M = mass Weight or force = (1x19.62 - 1 x 0)/2 =9.81 N --------------(1) For Padre on Platform: - Mass changes from 1 kg to γ kg, clock in rail slows down for person on platforms. So, event of ball falling happens slowly. & time 2 second changes to 2 γ second. To find acceleration, height = 0.5 a T2 Acceleration a=2(19.62)/(2 γ) 2 . a = 9.81/ γ 2 Final velocity V = Time x acceleration =2 γ x (9.81/ γ 2) =19.62/γ Force causing this acceleration or weight =rate of change of momentum Force or Weight = (M. V – M U)/T =(M V)/T as U =0 Put, Mass = γ, V= 19.62/γ , time = 2 γ weight = (γ ) (19.62/ γ) / (2 γ) =9.81/γ --------------- (2) N (1) & (2) is not equal. Hence weight is different for different reference frames. If anybody has problem, to call this force which creat acceleration as weight ,may call it as simply force causing acceleration but problem remain same.
  15. According to me, Straight line or linearity is very local phenomena for example, I have drawn straight line on black board. Here, my pen motion with relative to observer in class room is in straight line but for observer in space this motion is not linear but curve as my pen moves in curve path with revolving earth. In world nothing is moving in exact straight line or with constant velocity these are very local relative terms. Everything is falling towards something. There is nothing like 100 % inertial or stable or linear in the world. I may say that perfect inertial frame is not present in this universe. This may be only my view. thanks
  16. Even If we consider gravity acts on only rest mass & not on inertial mass then also this paradox is not get solve. This is because time in both frames are different, so acceleration event happen in train cabin is slower for Padre on platform, as time slows down. Means, if any ball falls in train cabin that event when observe by Padre on platform he will see that that event happen to slowly. When this acceleration is resisted (as in accelerated ship) filling of weight is different in both frame of references. Acceleration dVy/dt or d/dt(dSy/dt) are the time functions & g is not fix.
  17. 1)Energetic photon whose total energy is kinetic energy and no rest mass can be converted in to electron & positron pairs which has rest mass & vice versa. So, as electron & positron distorted the space, similarly photon can also distorted the space with his kinetic energy. or kinetic energy can not distort the space is wrong. 2)In my paradox lenght contraction is taken place in direction of motion i.e. in X-direction but as event happen in Y direction that event is remain uneffected by lenght contraction. Time dilution is already consider in the event.
  18. 1)even photons (light quanta whose total energy is kinetic energy), if trapped in a container space (as a photon gas or thermal radiation), would contribute a mass associated with their kinetic energy to the container's rest mass. So, rest mass is associated with total energy of constituents. Kinetic energy is also the part of it. This clearly indicate that other energy (rest mass) & kinetic energy (or inertial mass) distorted space in same way. 2)When sun emits photon radiation (total energy of photon is kinetic energy), Rest mass of sun will not remain same but will decreases due to emission of photon (or kinetic energy). This clearly indiacate that in relativity their is equivalence of mass & energy. That energy may be kinetic energy or any other energy. 3)In relativity total energy , rest mass & momentum is co-releted with each other by realtivistic energy-momentum relation. If momentum increases, total energy also increases.
  19. If we take out all types of motion from the any substance that substance becomes less massive this is because kinetic energy of constituents, contributes some part of its total mass or energy. So, rest mass of substance is contributed by kinetic energy of constituents. We can not differentiate between mass & energy in relativity. They are same thing. Kinetic energy can also distorted the space according to that frame of reference. If you solve the above matrix in Y- direction, you get same mass as I predicted. If anybody asked I will say " I am completely against theory of relativity. I think that relativity is wrong. Some thing is their in physics which we do not know".
  20. Gravitation is the reality which I fill every day, so to deny it is wrong. Einstein may equate that force with equivalent acceleration of spaceship. I have done the same thing at the place of space ship acceleration, I used the the term dvy/dt on earth, Not use mass x g formulae in calculation directly given by newton where g is fixed. dvy/dt changes according to relativity in my calculation.
  21. Point1:-The Weak equivalence principle is postulated: the gravitational and the inertial mass of every object are the same. The mass-energy equivalence, combined with the Weak Equivalence Principle, results in the prediction that all forms of energy contribute to the gravitational field generated by an object. This observation is one of the pillars of the general theory of relativity. That energy may be kinetic energy. For example, I have 1kg of metal ball; its equivalent weight is 9.81 N. In that 1kg of mass of metal ball, some mass is rest mass of particles of in that metal ball & some is inertial mass of the particles in the metal ball. Means, some weight or gravitational field is generated by rest mass & some due to inertial mass of the particles of metal ball. So to say that inertial mass or kinetic energy (same things) will not contribute to formation of gravitational field or weight is wrong. Point2:- I have not mixed Newtonian physics & special relativity, If you read attached paper it becomes very clear. I have given two sets of mathematics & they are based on relativity completely Mathematics 1:- Let, X- axis is in direction of motion of train with velocity V & Y-axis is in vertical direction i.e. in direction of g. Due to velocity of train, contraction of space happens in X direction only & as event happen perpendicular to V. Event is not affected by space contraction. Weight of ball = d/dt (Moment in y direction) =d/dt {(M rel) . (Vy)} =d/dt {(γ. Mo) .(Vy)} ----------- (1) Here, γ = 1/(1-V2/C2)0.5 FOR TRAIN RIDER :- equation (1) changes to Weight of ball =d/dt {Mo .Vy}= d/dt {Mo.(dSy/dt)}----------- (2) As ball in same frame, γ =1 & Sy is vertical displacement FOR PADRE ON PLATFORM:- equation (1) changes to Time = γ t as t is time for train rider & Padre on platform see clock in train is moving slow. Weight of ball =d/d(γ.t) {γ. Mo .dSy/d(γt )} As γ is constant for constant V Equation changes to Weight of ball = 1/ γ . d/dt {Mo.(dSy/dt)} ----------- (3) From (2) & (3) Weight of ball for Padre on platform = 1/ γ . Weight of ball for train Rider Means as train velocity increases weight of ball also increases by relativity. This can also be proved by second set of mathematics Mathematics 2:- Let, X- axis is in direction of motion of train with velocity V & Y-axis is in vertical direction i.e. in direction of g. Due to velocity of train contraction of space happens in X direction only & as event happen perpendicular to V. Event is not affected by space contraction. Weight of ball = d/dt (Moment in y direction) =d/dt {(M rel) . (Vy)} =d/dt {(γ. Mo) .(Vy)} Here, γ =1/(1-V2/C2)0.5 & Mo is rest mass. As V, C & Mo is constants. Weight of ball = (γ. Mo). dVy/dt dVy/dt = acceleration due to gravity in that frame of reference =g Weight of ball = (γ. Mo). g ----------- (1) To find out g for train rider & Padre on platform, consider one more event in train cabin. Let, consider ball of any mass falling from height h in cabin this event is observer by both observer then FOR TRAIN RIDER :- Height h = 0.5 . g . t2 g = 2. h/ t2 Equation (1) changes to Weight of ball = 2 (γ. Mo). h/ t2 Here, γ = 1/(1-V2/C2)0.5 = 1 , as V = 0 So, Weight of ball = 2 . Mo . h / t2 ----------- (2) FOR PADRE ON PLATFORM:- Time = γ t Height h = 0.5 . g . (γ . t)2 ( h remain same as it is perpendicular to V) g = 2. h/ (γ .t)2 Equation (1) changes to Weight of ball = 2 (γ. Mo). h/ (γ.t)2 = (2/ γ) . Mo. h/ t2 ----------- (3) From (2) & (3) Weight of ball for Padre on platform = 1/ γ . Weight of ball for train Rider Means as train velocity increases weight of ball also increases.
  22. Paradox:- One man is in the train moving from one station to another. He has hanged ball with mass m from his hand with threads which is just sufficient to resist m.g force i.e. gravitational attraction on ball. This train’s cabin has big window. One Cockroach is sitting on that ball from lower side. One Padre is waiting at next station & observing this approaching train with binocular & also see through big window of train. He is observing the man having ball in his hand from that window. Then what will happen by relativity. 1) For man in train’s cabin:-Nothing is happen. As ball are stable with relative to observer. Mass of ball will remain m & weight will be m.g. As string is sufficient to resist force m.g, ball will not fall & Cockroach will be live. 2) For Padre on next station:- He observed that due to velocity, mass of ball increases from m to m+dm & weight of ball increases from mg to (m+dm)g due to relativity. String is just sufficient to take force mg, so as force in string increases from mg to (m+dm)g for this frame. String will break & ball will fall on the floor of cabin & Cockroach will get killed due to collision. Padre shouted “Oh, that man has killed that innocent Cockroach”. Now, train reaches to next station after slowing down. Padre rushed into train cabin & shouted to man “You have killed that Cockroach. I have observed it & blood is there on that ball” Man innocently said,” Cockroach is not killed in collision. I, ball & Cockroach all are at same rest position. Cockroach is live.” Now both Padre & man are at same frame of reference means only one is true. Who is true? Cockroach is killed in collision or Cockroach is not dead & still sitting on ball. Please answer this problem. For detail visit topic "Inconsistency in special theory of relativity" in paper "What is the world made up of?" on my web site www.maheshkhati.com. RELATIVITY_dec12_.pdf
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