What equations are affected by Lorentz Transformations

[dimension10]

Many equations are affected by Lorentz transformations. Time, mass, volume of a moving object, momentum, force etc. I want to know if the following equations are affected by Lorentz transformations:

1. Distance=velocity*time (r=vt)
2. E=hv
3. j*=ot
4. F=G*m1*m2/r^2

Also, is the Newton's Theory of Universal gravitation affected by General Relativity?

 

[Pengwuino]

I'm not sure what your third equation is but the first one is obviously changed as the time is modified. The second one, I assume you mean $E = \hbar \omega$ which is also modified because the angular frequency is modified. This causes red/blue-shifts. Newton's law of gravitation is modified as well because of the length contraction.

However, Lorentz transformations are a feature of special relativity. General relativity is not so simple.

 

[jtbell]

Also, is the Newton's Theory of Universal gravitation affected by General Relativity?

General Relativity replaces Newton's theory of gravitation.

 

[bcrowell]

I think Pengwuino's analysis is correct as far as chages in the values of the variables. But if the OP intended to ask about changes in the forms of the equations, then the form of 1 and 2 is frame-invariant.

 

[dimension10]

I'm not sure what your third equation is...

Oops. I meant it to be j*=ot^4 where j* is the power radiated and o is sigma, the stefan's constant.

However, Lorentz transformations are a feature of special relativity. General relativity is not so simple.

So $$F=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}$$ is changed in General Relativty also?

...the first one is obviously changed as the time is modified. The second one, I assume you mean $E = \hbar \omega$ which is also modified because the angular frequency is modified. This causes red/blue-shifts. Newton's law of gravitation is modified as well because of the length contraction.

Thanks.

General Relativity replaces Newton's theory of gravitation.

So, $$F=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}$$ is changed in General Relativty?

 

[Pengwuino]

So, $$F=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}$$ is changed in General Relativty?

Yes, it no longer makes sense to speak of forces in GR.

 

[dimension10]

Yes, it no longer makes sense to speak of forces in GR.

But in modern physics, string theory does talk about gravity as a force, right? And in string theory,

$$F=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}$$

is still correct right?

 

[Pengwuino]

But in modern physics, string theory does talk about gravity as a force, right? And in string theory,

$$F=G\frac{{m}_{1}{m}_{2}}{{r}^{2}}$$

is still correct right?

No it isn't.

 

[bcrowell]

Dimension10, relativity isn't just a matter of putting fudge factors in equations. If you want to learn some relativity, some good books are (from easiest to hardest):

Takeuchi, An Illustrated Guide to Relativity
Mermin, It's About Time: Understanding Einstein's Relativity
Taylor and Wheeler, Spacetime Physics

 

[dimension10]

Dimension10, relativity isn't just a matter of putting fudge factors in equations. If you want to learn some relativity, some good books are (from easiest to hardest):

Takeuchi, An Illustrated Guide to Relativity
Mermin, It's About Time: Understanding Einstein's Relativity
Taylor and Wheeler, Spacetime Physics

Thanks. I have also read the paper itself but I can't really find his equation for the Gravitational force...

 

[bcrowell]

Thanks. I have also read the paper itself but I can't really find his equation for the Gravitational force...

What paper are you referring to? There is no relativistic equation for gravitational force, because gravity isn't described as a force in relativity.

 

[WannabeNewton]

Thanks. I have also read the paper itself but I can't really find his equation for the Gravitational force...

Are you maybe talking about an equation describing tidal gravitational forces?