# Mass Variation

## Main Question or Discussion Point

hi there i was wondering that why does not an electron or any other subatomic particle gains mass even when they are moving quite close to the speed of light like when beta particle is accelarated from a radioactive source it,s mass does not change why????

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Pythagorean
Gold Member
What makes you think it should?

i think it is quite simple you travel close to the speed of light you mass varies it is proven by theory of relativity it does not matter what the object is it has to gain mass as it gains higher speeds in fact the reason why something cannot approach the speed of light is that at the speed of light the mass becomes infinite and and an infinite force is needed to accelarate it which is not available

I don't know the speed of beta particles, but many particles relativistic increase in energy and even lifespan with high velocity have been experimentally observed....We can pretty well guarantee an increase in relativistic mass of anything that is "moving" but for everyday day stuff ...relatively low speeds....it's so small as to be almost undetectable...

but an beta particle at the speed of 10 to power 7 seven must show some detectble changes in its mass

but an beta particle at the speed of 10 to power 7 seven must show some detectble changes in its mass
The term "relativistic mass" is just a short-hand way of saying total energy, which is the sum of a particle's true rest mass plus kinetic energy. The particle's mass does not increase at relativistic velocities; only its kinetic energy does.

Bob S

jtbell
Mentor
you travel close to the speed of light you mass varies it is proven by theory of relativity
It depends on which definition of "mass" you use. In classical physics, there is only one "mass" which is used in several ways. In relativity, this isn't true. People have developed different concepts of "mass" in relativity, and their popularity has changed with time. The "relativistic mass" that varies with speed, is an early concept. Nowadays, most physicists prefer to think in terms of "invariant mass" which is also known as "rest mass," and you find "relativistic mass" mostly in popular treatments of relativity, and in some introductory textbooks.

When different people say simply "mass", some (mostly non-physicists) mean "relativistic mass" and others (including most physicists) mean "invariant mass." That's why we get conflicting statements in this forum and elsewhere about whether mass increases with speed.

If you prefer to think in terms of "relativistic mass," keep in mind that it's not a drop-in repacement for the classical mass. In general, you can't convert classical equations to relativistic ones simply by substituting "relativistic mass" for the classical mass.

The term "relativistic mass" is just a short-hand way of saying total energy, which is the sum of a particle's true rest mass plus kinetic energy. The particle's mass does not increase at relativistic velocities; only its kinetic energy does.

Bob S
so traveling close to the speed of light does not make anything HEAVIER but is that so then y it is said that you cannot approach the speed of light because at the speed of light the MASS becomes infinite and if the body is not becoming heavier (only gaining energy) so why cant any thing just travel faster than light ?????????

so traveling close to the speed of light does not make anything HEAVIER but is that so then y it is said that you cannot approach the speed of light because at the speed of light the MASS becomes infinite and if the body is not becoming heavier (only gaining energy) so why cant any thing just travel faster than light ?????????
The relativistic mass is just a theoretical impression that most physicists prefer to not use it due to being completely unphysical! The answer to your question can be given through the use of length contraction (LC). Suppose that two stationary observers A and B are put away from each other at a distance of L (as measured by them) and let a particle C be moving between A and B with the velocity $$v$$ according to the observers. Look at the formula of LC,

$$L'=L\gamma^{-1},$$

where L' denotes the distance between observers as measured by C. If we intended to plug in the speed of light c for v, then one would get $$L'=0$$ which means A and B are coincident in C's perspective. But no dice to make A and B closer than no distance away.

This whole scenario says that the speed of objects traveling through space can't exceed the speed of light, c!

AB

DrGreg
Gold Member
so traveling close to the speed of light does not make anything HEAVIER but is that so then y it is said that you cannot approach the speed of light because at the speed of light the MASS becomes infinite and if the body is not becoming heavier (only gaining energy) so why cant any thing just travel faster than light ?????????
The simplest reason is that the second postulate doesn't allow it! The second postulate asserts that all inertial observers measure the same speed of light, so even if you are travelling at 99.99999% of light relative to some external observer, from your own point of view you are still going 299,792,458 m/s too slow, and you are no nearer your target than when you started.

Another way of looking at it is in terms of energy E and momentum p. The relativistic equations for these are

$$\begin{array}{rcl} E & = & \frac{mc^2}{\sqrt{1 - v^2 / c^c}} \\ p & = & \frac{mv}{\sqrt{1 - v^2 / c^c}} \end{array}$$​

where m is rest mass, and these both increase without limit as v approaches c. So there isn't enough energy in the Universe to get you to the speed of light.

The relativistic mass is just a theoretical impression that most physicists prefer to not use it due to being completely unphysical! The answer to your question can be given through the use of length contraction (LC). Suppose that two stationary observers A and B are put away from each other at a distance of L (as measured by them) and let a particle C be moving between A and B with the velocity $$v$$ according to the observers. Look at the formula of LC,

$$L'=L\gamma^{-1},$$

I READ A BOOK WHICH TELLS THAT IF ANYTHING CANT APPRACH THE SPEED OF LIGHT IS BESAUCE AT THAT SPEED ITS MASS BECOMES INFINITE SO WUOLD THAT REASON BE CALLED WRONG?????????
AND IS THERE ANY EXPLANATION FOR THE BAZAAR CONCEQUENCES OF TRAVELLING AT THE SPEED OF LIGHT ????????/LIKE MASS VARIATION LENGTH CONTRACTION AND TIME DILATILATION[/SIZ

I READ A BOOK WHICH TELLS THAT IF ANYTHING CANT APPRACH THE SPEED OF LIGHT IS BESAUCE AT THAT SPEED ITS MASS BECOMES INFINITE SO WUOLD THAT REASON BE CALLED WRONG?????????
AND IS THERE ANY EXPLANATION FOR THE BAZAAR CONCEQUENCES OF TRAVELLING AT THE SPEED OF LIGHT ????????/LIKE MASS VARIATION LENGTH CONTRACTION AND TIME DILATILATION[/SIZ

I can barely understand your sentences because of the capital letters you use to write make my eyes crazy!

But no such thing as "relativistic mass" or "variational mass" in some sense exists in reality and all that depends on the frame so if I'm seeing someone in a spaceship travelling at the speed of .8c with a heavier mass won't make the 'guy' really obese in his own frame so talking about the relativistic mass as a reason for why we can't increase our velocity up to c is somewhat misleading though it can be seen for instance by the LC that the impossiblity of getting c is just describable via our own measurements relative to an observer being at rest.

Let me shed some light on this. The relativistic version of the second law of Newton reads

$$F=m \frac{ d(\gamma v)}{dt}=m\frac{d}{dt}(\frac{v}{\sqrt{1-v^2/c^2}}),$$

where $$a$$ is the acceleration that an object gains by a uniform force $$F$$ acting on it and $$v$$ represents the velocity of the object in motion and $$m$$ being the object's rest mass. Now from the above definition you can observe the fact that if $$v=c$$, then the force F becomes infinite and thus the force needed to apply to a particle with the rest mass $$m$$ to start moving at velocity c with a finite acceleration is infinite. No thrust can be applied to particles in order to make them move the same way as photons do. Remember that relating this behavior to the $$\gamma m$$ tending to infinity is meaningless as long as the limit of velocities is $$c$$, as SR claims! A better reason is to say the acceleration gets infinite as long as $$v=c$$ and no force in ordinary scales would ever make something like this happen!

AB

I can barely understand your sentences because of the capital letters you use to write make my eyes crazy!

But no such thing as "relativistic mass" or "variational mass" in some sense exists in reality and all that depends on the frame so if I'm seeing someone in a spaceship travelling at the speed of .8c with a heavier mass won't make the 'guy' really obese in his own frame so talking about the relativistic mass as a reason for why we can't increase our velocity up to c is somewhat misleading though it can be seen for instance by the LC that the impossiblity of getting c is just describable via our own measurements relative to an observer being at rest.

Let me shed some light on this. The relativistic version of the second law of Newton reads

$$F=m \frac{ d(\gamma v)}{dt}=m\frac{d}{dt}(\frac{v}{\sqrt{1-v^2/c^2}}),$$

where $$a$$ is the acceleration that an object gains by a uniform force $$F$$ acting on it and $$v$$ represents the velocity of the object in motion and $$m$$ being the object's rest mass. Now from the above definition you can observe the fact that if $$v=c$$, then the force F becomes infinite and thus the force needed to apply to a particle with the rest mass $$m$$ to start moving at velocity c with a finite acceleration is infinite. No thrust can be applied to particles in order to make them move the same way as photons do. Remember that relating this behavior to the $$\gamma m$$ tending to infinity is meaningless as long as the limit of velocities is $$c$$, as SR claims! A better reason is to say the acceleration gets infinite as long as $$v=c$$ and no force in ordinary scales would ever make something like this happen!

AB
man you explained it so well sorry for the wierd text though :redface
but i also asked if there is any explanation of the effects of travelling at the speed of light or close to it what about that?????????? :

man you explained it so well sorry for the wierd text though :redface
but i also asked if there is any explanation of the effects of travelling at the speed of light or close to it what about that?????????? :
All effects of motions at the speeds close to the speed of light will be seen in special relativity (SR) and general relativity (GR) and they generally obey or are described by the whole set of laws governing SR and GR. But as long as we are travelling at the speed of light, we are massless and our equation of motion will be described by electromagnetism (EM) and thus all effects obey or are described by the laws governing EM.

AB

so if travelling close to the speed of light does not make you heavier then what does the mass variation equation stand for i mean you are not getting any heavier you are just aquiring more energy ??????

so if travelling close to the speed of light does not make you heavier then what does the mass variation equation stand for i mean you are not getting any heavier you are just aquiring more energy ??????
The change in energy is due to the increase in velocity and thus it has no relevance with mass! The mass variation equation does only stand for a meditatively theoretical formula that can be useful when trying to find the relativistic effects! For instance, in the relativistic energy formula we absorb the Lorentz factor into the mass and the result is called collectively as the "relativistic mass"!

AB

Oh, and FizixFreak? Don't feel weird or silly, because this is one of those concepts that is a BEAR to teach to yourself. The language is used in so many ways, and has become "popular". Remember that many books speak in terms of common language and are not intented as true "introductions to physics". Take a deep breath and get ready to discard or adjust some of the concepts and models you used to get this far, because now they change or go away. Good forum to do it on too...

Oh, and FizixFreak? Don't feel weird or silly, because this is one of those concepts that is a BEAR to teach to yourself. The language is used in so many ways, and has become "popular". Remember that many books speak in terms of common language and are not intented as true "introductions to physics". Take a deep breath and get ready to discard or adjust some of the concepts and models you used to get this far, because now they change or go away. Good forum to do it on too...
thanx man i appreciate that (though i did kinda felt stupid ) and can you recommend a site which will help me out on this (i mean which tells about the REAL concept)