paradox in relativity

[mahesh khati]

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.

Edited March 27, 2013 by mahesh khati

[fertilizerspike]

Like all these "paradoxes" of "relativity" this one is resolved by arriving at the conclusion 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. Despite what Terrance Mckenna rambles about in a drug-addled haze. Wait, is the roach smoking DMT?

[mahesh khati]

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.

[swansont]

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.

 

As has been pointed out repeatedly, you can't take classical formulations of equations and patch in relativistic terms. If your calculation concludes that whatever effect you are looking at occurs in one frame but not in another, then this means you have done the calculation wrong. (i.e. an invalid formulation, not just a calculator error)

[mahesh khati]

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.

Edited April 5, 2013 by mahesh khati

[Markus Hanke]

Let me attempt to show that within the axioms of SR it is actually impossible to arrive at any paradoxes; SR is an internally self-consistent system, rendering any alleged "paradoxes" physically meaningless.


Fundamental Postulates of Special Relativity

(1) The substance existing at any world point can always be conceived to be at rest, if time and space are interpreted suitably. In other words - locally, all events can be considered to be in an inertial frame
(2) Between all inertial frames the same laws of physics apply, regardless of their states of relative motion
(3) Space-time can be considered isotropic and homogenous
(4) Rulers and clocks function independently of their past history


Self-Consistency Condition

(5) In order for (1)-(4) to hold, the line element measuring the distance between two events in space-time must be the same for all observers, i.e. must not vary if going from one frame to another, regardless of their states of relative motion. Going from one frame to another, and then back to original frame, will yield the same event in space-time.


Mathematical Proof

The distance between two events in space-time can be defined as a line element of the form

[latex]\displaystyle{ds^2=d\mathbf{R}\cdot d\mathbf{R}=g_{\mu \nu }dx^{\mu }dx^{\nu }}[/latex]

wherein [latex]g_{\mu \nu }[/latex] shall be called the metric tensor, and can be thought of as a 4x4 matrix which transforms according to certain rules.
The mathematical description of going from one inertial frame into another is realised by introducing a linear transformation between two vectors x' and x of the form

[latex]\displaystyle{{x}'^{\mu }=L{^{\mu }}_{\nu }x^{\nu }+a^{\mu }}[/latex]

wherein L is a general transformation matrix which represents an as-per-yet unspecified boost and rotation in arbitrary directions, and the 4-vector a represents a shift of origin. We now demand the following restriction to hold :

[latex]\displaystyle{L^{T}gL=g}[/latex]

which corresponds to the simple observation that, when performing a rotation and its inverse, you always arrive at the original vector, i.e. a rotation and its inverse chained together will yield the unity matrix. In tensor language this corresponds to

[latex]\displaystyle{g_{\mu \nu }L{^{\mu }}_{\rho }L{^{\nu }}_{\sigma }=g_{\rho \sigma }}[/latex]

In order to prove (5) one now only needs to show that such a transformation L leaves the space-time line element ds invariant, meaning that the distance between two events in space-time is the same for all inertial observers :

[latex]\displaystyle{g_{\mu \nu }d{x}'^{\mu }d{x}'^{\nu }=g_{\mu \nu }L{^{\mu }}_{\rho }L{^{\nu }}_{\sigma }dx^{\rho }dx^{\sigma }=g_{\mu \nu }dx^{\mu }dx^{\nu }}[/latex]

Quod erad demonstrandum. What this means is that, because above line element is invariant under said transformation, all inertial observers experience the same laws of physics.

References

Minkowski, Hermann (1908/9). "Raum und Zeit". Jahresberichte der Deutschen Mathematiker-Vereinigung: 75–88.

• English translation: Space and Time. In: The Principle of Relativity (1920), Calcutta: University Press, 70-88

That is the one of the reason for which I am completely against relativity.

 

Address the above, then.

Edited April 30, 2013 by Markus Hanke

[elfmotat]

Let me attempt to show that within the axioms of SR it is actually impossible to arrive at any paradoxes; SR is an internally self-consistent system, rendering any alleged "paradoxes" physically meaningless.

 

 

Fundamental Postulates of Special Relativity

 

(1) The substance existing at any world point can always be conceived to be at rest, if time and space are interpreted suitably. In other words - locally, all events can be considered to be in an inertial frame

(2) Between all inertial frames the same laws of physics apply, regardless of their states of relative motion

(3) Space-time can be considered isotropic and homogenous

(4) Rulers and clocks function independently of their past history

 

 

Self-Consistency Condition

 

(5) In order for (1)-(4) to hold, the line element measuring the distance between two events in space-time must be the same for all observers, i.e. must not vary if going from one frame to another, regardless of their states of relative motion. Going from one frame to another, and then back to original frame, will yield the same event in space-time.

 

 

Mathematical Proof

 

The distance between two events in space-time can be defined as a line element of the form

 

[latex]\displaystyle{ds^2=d\mathbf{R}\cdot d\mathbf{R}=g_{\mu \nu }dx^{\mu }dx^{\nu }}[/latex]

 

wherein [latex]g_{\mu \nu }[/latex] shall be called the metric tensor, and can be thought of as a 4x4 matrix which transforms according to certain rules.

The mathematical description of going from one inertial frame into another is realised by introducing a linear transformation between two vectors x' and x of the form

 

[latex]\displaystyle{{x}'^{\mu }=L{^{\mu }}_{\nu }x^{\nu }+a^{\mu }}[/latex]

 

wherein L is a general transformation matrix which represents an as-per-yet unspecified boost and rotation in arbitrary directions, and the 4-vector a represents a shift of origin. We now demand the following restriction to hold :

 

[latex]\displaystyle{L^{T}gL=g}[/latex]

 

which corresponds to the simple observation that, when performing a rotation and its inverse, you always arrive at the original vector, i.e. a rotation and its inverse chained together will yield the unity matrix. In tensor language this corresponds to

 

[latex]\displaystyle{g_{\mu \nu }L{^{\mu }}_{\rho }L{^{\nu }}_{\sigma }=g_{\rho \sigma }}[/latex]

 

In order to prove (5) one now only needs to show that such a transformation L leaves the space-time line element ds invariant, meaning that the distance between two events in space-time is the same for all inertial observers :

 

[latex]\displaystyle{g_{\mu \nu }d{x}'^{\mu }d{x}'^{\nu }=g_{\mu \nu }L{^{\mu }}_{\rho }L{^{\nu }}_{\sigma }dx^{\rho }dx^{\sigma }=g_{\mu \nu }dx^{\mu }dx^{\nu }}[/latex]

 

Quod erad demonstrandum. What this means is that, because above line element is invariant under said transformation, all inertial observers experience the same laws of physics.

 

 

References

 

Minkowski, Hermann (1908/9). "Raum und Zeit". Jahresberichte der Deutschen Mathematiker-Vereinigung: 75–88.

• English translation: Space and Time. In: The Principle of Relativity (1920), Calcutta: University Press, 70-88

 

 

Address the above, then.

 

As good as this is, crackpots don't tend to be very familiar with mathematical rigor. So while a consistency check is good for those of us who are familiar with relativity and the Poincare group, I doubt it will be very convincing to people who are "completely against relativity."

 

I do appreciate input from competent people, so thank you.

[Markus Hanke]

As good as this is, crackpots don't tend to be very familiar with mathematical rigor. So while a consistency check is good for those of us who are familiar with relativity and the Poincare group, I doubt it will be very convincing to people who are "completely against relativity."

 

I do appreciate input from competent people, so thank you.

 

No problem, glad to be able to make a contribution.

[michel123456]

Let me attempt to show that within the axioms of SR it is actually impossible to arrive at any paradoxes; SR is an internally self-consistent system, rendering any alleged "paradoxes" physically meaningless.

 

 

Fundamental Postulates of Special Relativity

(...)

S.R. or G.R.?

Where there is acceleration, mass, gravitation, what do you use?

[Markus Hanke]

S.R. or G.R.?

Where there is acceleration, mass, gravitation, what do you use?

 

It's SR, for Special Relativity. In that framework you don't have acceleration and gravity.

I doubt very much that our friend Mahesh would be able to tackle General Relativity...but if he does I'll be there

[joseph o]

In SR, time varies with frame, mass varies with frame & lenght varies with frame then can force remain same in all frames? No,. Force will have to change with frame of reference. There is some substance in mahesh argument. .

[elfmotat]

In SR, time varies with frame, mass varies with frame & lenght varies with frame then can force remain same in all frames? No,. Force will have to change with frame of reference. There is some substance in mahesh argument. .

 

The usual definition of mass does not vary in different reference frame, and force is a covariant four-vector whose magnitude is the same in all frames.

[xyzt]

You seem to be the standard antirelativistic crank: the type with a website.

 

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.

Edited May 4, 2013 by xyzt

[Markus Hanke]

You seem to be the standard antirelativistic crank: the type with a website.

 

Indeed. Repeatedly asserting "inconsistencies" in SR even though it has been mathematically proven that there cannot be any such inconsistencies paints a pretty bad picture.

[xyzt]

"But I havea website, therefore Einstein MUST be wrong. It is proven on my website!"

[hypervalent_iodine]

!

Moderator Note

xyzt,

 

We have clear rules on what is and is not acceptable when interacting with others here. Insulting people and making personal comments about them is very much in the not acceptable basket. This is not the first post from you of this sort that staff have identified, hence the red note. It stops here.

[mahesh khati]

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.

1. 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.
2. 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.
3. 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.
4. 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.

[Markus Hanke]

It always amazes me how people go on and on, even though they have already been shown wrong. I will never understand this...

[mahesh khati]

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.

1. 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.

1. As this flux field create reference frame may have effect on all properties of frame like inertial mass, time etc.
2. 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.
3. 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.

[Markus Hanke]

I think even a thread in "Speculations" ought to have at least some connection to real physics.

This one clearly does not.