Velocity of an Electron from Momentum

[dbmorpher]

Homework Statement

If I know the momentum and mass of a particle how do I determine/differentiate the Lorentz Factor and velocity?

Electron rest mass: 9.10938215e-31kg
c=299792458m/s
y=Lorentz Factor
m=mass
p=momentum
e=energy
Calculated momentum: 2.019006271e+14kg m/s

Homework Equations

E^2=(mc^2)^2+p^2c^2
p=ymv
y=1/((1-v^2/c^2)^0.5)

The Attempt at a Solution

2.216403086e+44 = yv

I tried multiple times to isolate v by using the equation for the Lorentz function but alas was not able to do it. If anyone could help that would be greatly appreciated.

Thank you,
dbmorpher

 

[Simon Bridge]

Why not express the lorentz factor in terms of v in $p=\gamma mv$ then just solve for v?

 

[dbmorpher]

That is what I tried to do however I received some very unusual answers such as an almost zero number. i. e. I need some help with isolating velocity because I can't seem to be able to myself.

 

[Orodruin]

What do you get if you insert your expression for p in your expression for E^2?

On another note: 2e+14 kg m/s is a humongous momentum. A space shuttle with that momentum would be traveling at relativistic velocities ... I think you should have a minus in the exponent ;)

 

[Simon Bridge]

That is what I tried to do however I received some very unusual answers such as an almost zero number. i. e. I need some help with isolating velocity because I can't seem to be able to myself.

Please show your working.

 

[dbmorpher]

Well I had a lot of working but I deleted it because it didn't work. However I found a similar thread that solved my problem. Thank you for your interest. If you were wondering the reason the acceleration is so high is because I am trying to create a black hole by accelerating an electron to a high enough energy that the mass creates a black hole with the same radius and charge of an electron. But as I'm typing this I realize that I may be an order of magnitude too high because the radius I used was multiplied by ten. So thank you for your help I think I can get it myself now.

 

[Orodruin]

You cannot do that. You can always make a Lorentz transformation to the electron rest frame and whatever happens in that frame must happen in all frames. Black holes are the domain of general relativity and you will never be able to argue for creating one using SR.

 

[dbmorpher]

If a particle gains energy when it gains mommetum then by extension it gains mass. My idea if you get an electron traveling fast enough the energy will increase enough to turn it into a black hole with the same radius as the electron and can therefore be fed with the electron.

 

[Orodruin]

This is not true and depends on what you mean by mass. The invariant mass of the electron is always ca 511 keV/c^2. The bottom line is that current physical theories do not allow what you are trying to accomplish - it is an unfortunate conclusion that I suspect many laymen draw from the concept of relativistic mass.

 

[Simon Bridge]

It's a very common mistake... comes from mixing special relativity with Newtonian gravitation.
The correct way to mix gravity with relativity is in General Relativty - which paints a different, somewhat more tricky, picture.
See also: https://www.physicsforums.com/threads/does-relativistic-mass-create-gravity.68454/

 

[dbmorpher]

So basically no matter how fast an electron goes its mass never increases because relativistic mass does not correlate to the actual mass of the particle?

 

[Simon Bridge]

The word "mass" refers to the invarient mass, and this is considered the "actual" mass of the particle.
(note: the word "actual" is problematic in relativity, avoid it.)

What has historically been considered the mass-increase for "relativistic mass" is understood in terms of kinetic energy.

You cannot just blindly convert energy into matter for use in Newtons equation of gravity - to handle gravity in a relativity framework you have to use the Einstein field equations instead. These equations supplant Newtonian gravity, which has a more narrow application so cannot be expected to give good results in extreme situations such as you are contemplating.

The calculation you have contemplated would be a nice setup for an experiment proving that Newtonian gravity cannot be used in this way.