@Relativisticcucumber jigglypuff~

@Relativisticcucumber oh nose! kitty was also really sick, but not due to covid

Trying to get an overall vibe of the popular perception of relativity through time

It is a bit tough

Having to wade through random newspapers and books

Basically nothing before 1919 when Einstein got his big break with the eclipse result

a lot of the sources offered b y google ngram are just not available at all

Although the results can be delightful

"His new equations are based on the assumption that gravitation an electricity are the same thing."

books.google.fr/…

A lot of people were rejecting relativity in the early days, so Tesla's reaction was probably just normal for the time

Gotta figure out if I can legally use some of those pictures by figuring out when the guys died

If a particle is moving with a relativistic velocity, but I know it's momentum, would it be correct to calculate the velocity as v=p/m ?

By "velocity" do you mean the measured velocity ie distance travelled per time, or do you mean the 4-velocity

And ditto with momentum, is it a vector or a 4-vector

the momentum is the 3D momentum

then no, the relation has the Lorentz gamma factor in it

So my situation is the following, I am having a Z boson from which 2 \tau leptons emergy. Now, the momentum of the leptons have some value a. I am given as info that in the rest frame of the lepton it has a mean liftime \tau. So I did the following. I considered the rest frame of Z and that of the lepton, and I came across

$\Delta t=\gamma \Delta '$, where

$\Delta t$ is the mean lifetime of the lepton as seen from the reference frame of the boson

@imbAF IMHO, it's a bit confusing because you have a tau lepton with a mean lifetime of tau, since tau is also commonly used for proper time. And of course, the mean lifetime in the rest frame of the particle is a proper time. ;)

@imbAF As Slereah said, you need the relativistic equation for momentum, which is $p=mv\gamma$. There are nice trigonometric relationships between $v, \gamma, v\gamma$.

@PM2Ring yes the meanlifetime is in the leptons frame. But I want to find it as seen from the Z boson

The only problem I am facing with is, calculating \gamma

Let $\beta=v/c$. Then $\beta^2+1/\gamma^2=1$. So if you write $\beta=\sin\theta$ then $\gamma=\sec\theta$ and $\beta\gamma=\tan\theta$

I see

But in the solution it has $\gamma=\frac{E_\tau}{m_\tau c^2}$ which I don't see how it's derived

from

the general

$\gamma=\frac{1}{\sqrt{1- \frac {v^2}{c^2}}}$

But it is more common to use hyperbolic functions. $\beta=\tanh\phi$, where $\phi$ is called the rapidity. Then $\gamma=\cosh\phi$ and $\beta\gamma=\sinh\phi$.

Are you familiar with this equation for kinetic energy, $E_K = (\gamma-1)mc^2$?

no

But I believe I need to describe my problem a little bit better

Give me a moment

The mean lifetime of resting τ -leptons is 2.956 · 10−13s. How far do the τ -leptons get on average?

So I am operating from the POV of the bozon

as such I find $c\Delta t==\gammac\Delta t'$

And I am thinking of using the fact that

v=p/m, plug it in and find what I need

But I am not sure

@imbAF No, v=p/m won't work.

Yes it won't

just to make sure tho

for my understanding

Give me a minute. I'm a bit slow typing Latex on my phone...

ah

Do you know the total energy equation, $E^2=(pc)^2 + (mc^2)^2$ ?

I used that

to find the energies of the leptons

since they have same mass and same momenta (absloute value)

therefore their energy is half of the energy that the boson represents

Great. Back in a minute.

More than the answer I'd like to derive it myself with your help

Well I have a few questions

why is p=mv\gamma

because you are using relativistic mass?

@PM2Ring

m is the rest mass, $m\gamma$ is the relativistic mass. But we prefer to avoid that these days. ;) It's better to think in terms of the total energy, which we just showed is $E=mc^2\gamma$

isn't mass though

$E=\sqrt{(pc)^2 + (mc^2)^2}$ ?

What? $m$ in that equation is the mass.

the rest mass?

or the relativistic mass?

Rest mass

So , one can go from $E=\sqrt{(pc)^2 + (mc^2)^2}$ to $E=mc^2\gamma$?

where in the first you have the rest mass

and in the 2nd the relativistic mass?

As I said, $m$ is the rest mass. $m\gamma$ is the relativistic mass. But we prefer to avoid relativistic mass these days because it tends to create confusion.

Ok

But how does one derive that?

I had no idea of this expression

so there must be a way to derive it, from the energy momentum relation, I would assume?

If we subtract the rest energy $mc^2$ from the total energy, we get the equation for kinetic energy that I gave in chat.stackexchange.com/transcript/message/64281752#64281752

@imbAF Derive what?

I am a bit confused

This is the kinetic energy $E=mc^2\gamma$?

@imbAF No, that's the total energy= kinetic energy + rest energy. Kinetic energy is $E=mc^2(\gamma-1)$

ok

can you see the tachyons?

If you're wondering where $p=mv\gamma$ comes from, it can be derived using the Lorentz transform. See en.wikipedia.org/wiki/Four-momentum

I am a little concerned about my model given that it seems a bit too symmetrical

@PM2Ring In what you linked it is using the lagrangian

I think I got the answer from Brill and Goodman (1967)...

No...sorry I didn't get it...what they did was consider the Coulomb potential and calculated the electric field and showed it to be causal (and equivalent to that calculated with the Lorenz gauge).

I am looking for getting the retarded scalar potential itself...and now I am wondering what will I get if get retarded scalar potential and also retarded vector potential (with transverse source) if the solution with the ordinary Coulomb potential and retarded vector potential gave the retarded solution itself!

Hello Everyone..

what book would yall recommend learning stat mech out of

@SillyGoose from which level of understanding to which level of understanding?

hm i suppose introductory undergraduate, but more precise and rigorous than the level of schroeder

And maybe a book that is undergrad/grad level for looking into specific topics in more detail

Have you understood why we care about entropy up to the level of Feynman Lectures?

If you do, then I would suggest Ian Ford

Schroeder is just so unreadable

I do not (i haven’t done any stat mech)

Then you should read Feynman lectures on the energy and heat parts

all in vol 1

then Ian Ford

After you do Ian Ford, you should read Callen, and Kittel & Kroemer

Okie i shall try these out

in vol 1 are you suggesting 39-45?

also, do treatments of statt mech that assume (undergrad level) knoweldge of probability theory and quantum mechanics exists/are better than usual treatments of thet subject?

@SillyGoose yes. Also read the front bits on energy

@SillyGoose I think so? if you dont know some prob and stats, and quantum, stat therm will be unreadable

for introductory, the text will have to contrast classical thinking with quantum, so not knowing the full quantum business will be part of the journey

hm but is a classical discussion not a waste of time if the audience is expected to know quantum>

?

For grad level stuff, that will be the case.

But this is introductory, and we kinda want to contrast what classical expectations v.s. quantum statistics say things should be, and thereby show that a classical description of our universe is kinda impossible to defend

When an equation is said to be lorentz covariant, does it mean it doesn't change as we change reference frame?

@naturallyInconsistent makes me wanna kms

@Relativisticcucumber YONK

That's a yo honk FYI