Relativity Prob:-can u get me a proof for mass velocity relation!!?

Question

1)By famous einstein's relativistic mass equation ,
M=Mo/(1-v^2/c^2)^1/2.....
consider v tends c.... v^2/c^2 is near to 1......
so in equation denominator is small quantity and 1/small quantity is very big .....
when velocity is increased relativistic mass increases .....here mass depends directly on velocity.
and relativistic mass becomes much significant when v approaches to c............

2)Now consider de-broglie equation lamda=h/mv....
by analysis mass is function of velocity and mass inversely proportional to velocity when lamda is constant .....but lamda isn't constant when velocity approaches to c ....then how they are related ?
can anyone show mass velocity direct proportionality in de broglie equation?
also in E=mc^2.....show their relation ...where E is not a constant (kinectic energy is prominent)

by first disscussion they are directly proportional ........is it an ambuiguity in relativity or ????

plz give a solution to this ....

Answer 1

From relativity we know that,

m=mo/sqrt(1-v^2/c^2)

m is the relativistic mass

mo is the rest mass

v is the velocity of the object of rest mass mo

c is the speed of light.



Leave de-Broglie's eqn aside for some time. Now when the object tries to approach c the Lorentz factor sqrt(1-v^2/c^2) approaches zero and the m approaches inf. So increase in v increases the relativistic mass. So mass can be considered to be varying directly with velocity.



now consider the wave eqn, lambda=h/mv becomes

lambda=h/[(mo v/sqrt(1-v^2/c^2))]

lambda=h x root(1-v^2/c^2) / (v x mo)

when v increases considerably, numerator decreases and denominator increases, total change will be the lambda decreases. So as velocity increases lambda decreases.

We can say that lambda is varying inversely with velocity, at h/mo as constant.



but we also know that lambda=h/p, p=mv=mov/root(1-v^2/c^2)

As lambda is decreasing, momentum should increase.

So, as velocity increases, lambda decreases so momentum increases.

But momentum is the product of mass and velocity.

So as momentum increases m should also increase. Which implies that as velocity increases relativistic mass also increases. So just by seeing the eqn you are contradicting with relativity. But when you analyse like this you would say relativistic mass increases with increase in velocity.



If anything is wrong in my analysis please let me know.

Answer 2

I'm having a little trouble with your terminology. "Directly proportional" means a straight-line graph. When one doubles, the other doubles. You say "by first discussion THEY are directly proportional". I assume you mean m and v. But they are not directly proportional. If you graph relativistic mass against velocity, you do not get a straight line.

The de Broglie equation gives us the wavelength of a "particle" at a given velocity. The "m" would be the relativistic mass, so h/mc is the simplified version (i.e. for small velocity, lambda is inversely proportional to mass). We don't say that mass and velocity are inversely proportional because 1. lambda is not a constant (as you correctly said) and 2. mass depends on velocity.

If you juggle de Broglie around, you get m = h/lambda-v. An inverse proportion between m and v would be m=k/v where k is a constant, which doesn't apply in this case.

-Rob

Answer 3

SPIRITUAL ET COSMIC MATHEMATICS => E = mc2

E = mc2

Let’s substitute…

E = Soul’s energy or Shakti of a Soul;

m = mass of the body ;

c = speed of light;



Before we can explain this Einstein’s theory of relativity in spiritual language, we must clearly understand the difference between the MIND and SOUL.

MIND - has several attributes like

i. Conscience

ii. Thought

iii. Creativity

iv. Intelligence

v. Perception

vi. Comprehension

vii. Memory

viii. Maturity

ix. Emotional status

x. Sensory function and

xi. Motor function

Conscience has several planes. These planes roughly (limited to human/my level of understanding) but not exactly corresponds to the functional efficacy and limitations of various CHAKRAS. Conscience limited to Mooladhara keeps the host (body) limited to primitive totally carnal, mundane and easily accessible pleasures. The highest plane is when the host (body)volunteers to lose even the life for eternal and spiritual causes.



Thought is thinking, speaking, writing and communicating to others.



Creativity is thinking in a novel way like composing poetry, music, painting, dancing and like in a unique and totally individualized mode.



Intelligence is the ability interpret an old information in a new way



Perception is to understand an object fully based o the sensory perception like touching a coin and recognizing its value.



Memory is the entire information in the mind that can be recalled at will (information not recalled at will but receiving in a haphazard and fragmented way is called a DREAM)



Maturity is the capacity and willingness to adapt to changing times and changing circumstances



Emotional status is enjoying, suffering and tolerating with varied external behavioral expression.



Sensory function is touching, seeing, smelling, tasting and hearing



Motor function is moving, resting gesturing etc.



Mind of each human being is highly individualized. One may think well, be intelligent, but not creative, another may be creative but blind or deaf, yet another may be intelligent, creative, mature but be primitive in conscience.



Imagine a theoretical human being who is at the highest level of conscience (like Yudhistira), think effectively (like Vikramadithya) be very creative (like Thyagaraja), extremely intelligent (like Bruhaspati), perceive the world perfectly(like an Avadhani), comprehend mundane and spiritual matters well (like a Yogi), has an extraordinary memory (like Srinivasa Ramanujam), very mature, emotionally stable i.e. accepting pleasure and pain with similar smiling face (like Yudhistira), perfect in all senses and motor functions of a yogi (like Pathanjali). Such a human does not exist.

But that theoretical human mind is otherwise known as SOUL.



SOUL is perfect but mind is not.

The SPIRITUAL energy of a single human SOUL is nearly limitless.

What happens if all humans become perfect by SADHANA and all such SOULS seek THE LORD?

A single SOUL MULTIPLIPIES BY ITSELF? Yes, PERFECTION CAN BE IMPROVED ONLY BY MULTIPLYING ITS "PERFECTON".

HUMAN BODY MULTIPLIED BY SOUL ENERGY, MULTIPLIED BY SOUL ENERGY, BECOMES COSMIC SOUL ENERGY (PARAMATMA).



This concept is difficult to understand but not impossible.