__Force without acceleration in S.R. __

__& acceleration without force in S.R. __

__& applied force is less than acting force in S.R.__

__STEP 1:-__**This problem can easily be understood by following paradox.**

**{Before starting this paradox, I want to put some relativity formulae’s**

**In any frame for force in X-direction**

Fx = d/dt( y. mo. ux) where y=(1-u^{2}/c^{2})^{-0.5 (formula given in all standard book on S.R.) }

After differentiation, we get

So, Fx=y. mo. ax+y^{3} mo. (ux/c^{2}} (ux ax+uy ay+uz az) ------(1)}

**Now, Paradox**:-

On frictionless platform, object is moving with constant velocity ux in X-direction & only magnetic force is acting in Y-direction & there is **acceleration in Y-direction only with velocity uy** & Fz=0

If we apply eq(1) to this case then result will be

Fx= y^{3} mo. (ux/c^{2}} uy ay

Or Fx=Fay as this force is form due to ‘ay’ only

Mean’s even there is **no magnetic force** acting on object from outside in x-direction & no ‘ax’ then also **above force will act on object in +ve direction of x-axis due to ‘ay’ **

**Important point (1):-**

**Mean’s **__applied magnetic force__ on object in X-direction is 0 & __acting force__ in X-direction is

Fx= y^{3} mo. (ux/c^{2}} uy ay+0 or Fay+0=Fay

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**STEP 2:-Now, Force acting in X-direction is ** Fx= y^{3} mo. (ux/c^{2}} uy ay or Fay

**Now, after this happen, very small magnetic force of same intensity -fx = -**y^{3} mo. (ux/c^{2}} uy ay or -Fay start **acting on object in direction opposite to above force (but velocity is still positive ux) & cancel that above force. **

**Mean’s equation (1) becomes**

0=y. mo. ax+y^{3} mo. (ux/c^{2}} (ux ax+uy ay)

Or 0 =y. mo ax. (1+ y^{2} {ux^{2}/c^{2}} ) +Fay

(Here as Fay= y^{3} mo. (ux/c^{2}} uy ay)

Mean’s Fay = y. mo. -ax. (1+ y^{2}. {ux^{2}/c^{2}} )

**Mean’s there must be acceleration in –ve X-direction to fulfil above equation of S.R.**

**Now, see above equation carefully, it is of nature**

** 0= -fx + Fay **

**Important point (2):- Mean’s **__applied magnetic force__ on object in X-direction is -fx & __acting force__ in X-direction is -fx + Fay = 0 ## or 0.

**Here, resultant force in X-direction is zero but there is acceleration.**

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**STEP3:- same things happen for +ve force in X-direction (for less than Fay or more)**

Now, I am generalising above result.

Step 1&2 clearly shows that when we apply any magnetic force (Fmx) in X-direction on the object, actual force acting on object is more & that quantity is (Fmx+Fay)

Similarly,

If we apply any magnetic force (Fmy) in Y-direction on the object then actual force acting on object is more & that quantity is (Fmy+Fax)

This is completely complicated results, which says that applied force & acting forces on objects are different & more in S.R.

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**STEP4:- Force does work, consume energy, gain energy & we must know that energy cannot be created. It can be transferred only:-**

From above setup it must be clear that energy get transfer from magnet to object but if applied force is less than acting force then energy gain by object will be more than energy loose by the magnet. Means due to more work done by more force for same displacement, more energy get generated.

HERE, more energy (& force) is the problem.

**Where this additional energy (& force) does comes from?**

**No answer in S.R.**

**(You will be surprise that I am against S.R. but not totally against G.R. )**

**Edited by maheshkhati, 03 March 2016 - 02:53 AM.**