paradox in relativity

[mahesh khati]

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

[ACG52]

 

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.

 

Relativistic mass is pretty much an obsolete concept, leading to confusion as we can see from the above. The mass does not increase, the relative kinetic energy does, and has no effect on weight.

[ldarko218]

You cannot just combine formulas from newtonian physics and (special) relativity.

[elfmotat]

As the others have mentioned, plugging relativistic mass into the Newtonian gravity equation is meaningless.

[mahesh khati]

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.

[ACG52]

'Relativistic mass' (which is misleading term) does not interact with gravity. There is no change in gravitational attraction due to 'relativistic mass'.

[Przemyslaw.Gruchala]

What you obviously missed is fact that either string, ball and Cockroach should also receive kinetic energy, and their relativistic mass should be also accordingly adjusted to velocity of train using m=m0/sqrt(1-v^2/c^2)

 

You're calculating strength of string using it's rest mass.

[elfmotat]

What you obviously missed is fact that either string, ball and Cockroach should also receive kinetic energy, and their relativistic mass should be also accordingly adjusted to velocity of train using m=m0/sqrt(1-v^2/c^2)

 

You're calculating strength of string using it's rest mass.

 

No, what he missed was that F=mg is not a valid equation in relativity, as has been pointed out multiple times not. The strength of a string has nothing to do with its relativistic mass, similar to how in Newtonian physics the strength of a string has nothing to do with its kinetic energy.

[Przemyslaw.Gruchala]

For somebody who is inside of train F=mg is still valid. From this person point of view, string, cockroach and ball are at rest.

Edited February 19, 2013 by Przemyslaw.Gruchala

[swansont]

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.

 

A1 kg ball is not made up of part rest mass and part inertial mass. That's abusing (or not understanding) the terminology. The inertial mass (F=ma) and gravitational mass (GMm/r^2, non-relativistically) are the same thing.

[elfmotat]

For somebody who is inside of train F=mg is still valid. From this person point of view, string, cockroach and ball are at rest.

 

No it's not. In relativity there's no such thing as a gravitational force. Special Relativity does not cover gravitation, and applying Newtonian formulas will only lead to confusion. In General Relativity, gravity is a consequence of geometry.

 

 

The inertial mass (F=ma) and gravitational mass (GMm/r^2, non-relativistically) are the same thing.

 

If by "inertial mass" we're talking about the coefficient relating three-force to three-acceleration, then that's not true. By this definition "inertial mass" is actually a matrix. If an object with rest mass m is moving along the x-direction, then:

 

[math]f^i=M^i_{~j} a^j[/math]

 

where:

 

[math]M^i_{~j}=\begin{bmatrix} \gamma^3 m & 0 & 0\\ 0 & \gamma m & 0\\ 0 & 0 & \gamma m \end{bmatrix}[/math]

Edited February 19, 2013 by elfmotat

[mahesh khati]

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.

[SamBridge]

Relativistic mass is pretty much an obsolete concept, leading to confusion as we can see from the above. The mass does not increase, the relative kinetic energy does, and has no effect on weight.

In a way relativistic mass doesn't make sense, the number of atoms aren't changing, but energy still distorts the fabric of space, so if something has a greater relative energy it will cause a greater distortion in space according to that frame of reference. There's probably some simpler way to break it down in terms of time dilation and length dilation.

Edited February 21, 2013 by SamBridge

[mahesh khati]

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".

[ACG52]

Kinetic energy can also distorted the space according to that frame of reference

In that frame of reference it has no kinetic energy. Kinetic energy is relative.

Edited February 25, 2013 by ACG52

[mahesh khati]

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.

[mahesh khati]

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.

[mahesh khati]

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.

Edited March 3, 2013 by mahesh khati

[ydoaPs]

!

Moderator Note

Off-topic speculative post moved to Speculations

[Didymus]

Change the. Cockroach's name to schrodinger and you've got a deal.

[ravi1]

I have not seen anything wrong in mathematics given in post 5 by mahesh. he has taken care off mass & time changes as per relativity. If this calculation is true, as mass & time changes with observer, weight will also change as per the observer.

[mahesh khati]

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.

[ccwebb]

What you obviously missed is fact that either string, ball and Cockroach should also receive kinetic energy, and their relativistic mass should be also accordingly adjusted to velocity of train using m=m0/sqrt(1-v^2/c^2)

 

You're calculating strength of string using it's rest mass.

 

Agreed. Though the entire math may be correct, there is something being missed here. The string won’t break simply because someone else is viewing the train moving faster, thus more kinetic energy.

 

[mahesh khati]

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.

[juanrga]

Gravitation is the reality which I fill every day, so to deny it is wrong.

 

Who said or insinuated such thing? Precisely on the leading textbooks on general relativity (that by Misner, Thorne, and Wheeler) is titled Gravitation.

 

We can not differentiate between mass & energy in relativity.

 

Untrue, we can differentiate both and denote mass by "m" and energy by "E" as in the expression

 

[math]E = \sqrt{m^2 c^4 + p^2c^2}[/math]

 

I have not seen anything wrong in mathematics given in post 5 by mahesh. he has taken care off mass & time changes as per relativity. If this calculation is true, as mass & time changes with observer, weight will also change as per the observer.

 

No, mass is an relativistic invariant. E.g. the mass of an electron [math]m_e[/math] which you can find in a table of scientific constants is the same for any observer.

 

You and him seem confused by the outdated concept of relativistic mass (which varied with the observer), but precisely due to this variation with the system of reference it could not be considered a property of the object under study: i.e. was not the mass of the object.