Shortest Paths

[□h=-16πT]

cool... this is very cool

 

right or wrong it's still cool' date=' I am going to learn this very fast.

 

I will pay close attention.

 

 

In the trace above, what are the four terms called from left to right?[/quote']

 

Yeah, I love relativity. The first is the mass-energy distribution, which could be a constant or could be a function of radius etc. The other three are the pressures in the x, y, z directions respectively, which could again be functions.

[Johnny5]

Yeah, I love relativity. The first is the mass-energy distribution, which could be a constant or could be a function of radius etc. The other three are the pressures in the x, y, z directions respectively, which could again be functions.

 

[math]

(p+\rho)U^{\alpha}U^{\alpha}+g^{\alpha\beta}p

[/math]

 

 

[math]

 

\rho+p_x+p_y+p_z

 

[/math]

 

 

 

You can hook this up to quantum mechanics if the inertia waves.

 

 

Rho is the "mass-energy" distribution. Units?

 

Other three are pressures. Pressure how, where?

[□h=-16πT]

Here it is.

 

what are the terms called from left to right?

 

 

i recognize

 

[math]g^{\alpha\beta}[/math]

as the metric tensor.

 

I am interested in the momentum flux you just mentioned.

 

Is there a momentum wave?

 

And if so' date=' what is the speed?[/quote']

 

Momentum flux: The momentum that flows over a surface of unit area in an amount of unit time.

 

No such thing as a momentum wave, or at least I think so.

 

The metric with the raised indices are the inverse components, remember this. The other components are (from left to right) pressure, mass-energy distribution, four-velocity, inverse metric and pressure again.

[Johnny5]

Momentum flux: The amount of flux flowing over a surface of unit area in an amount of unit time.

 

No such thing as a momentum wave' date=' or at least I think so. Momentum is a vector, the wave equation solves to a sinusoidal function (a scalar).

 

The metric with the raised indices are the inverse components, remember this. The other components are (from left to right) pressure, mass-energy distribution, four-velocity, inverse metric and pressure again.[/quote']

 

What waves in GR???????????????????????

[Johnny5]

Momentum flux: The momentum that flows over a surface of unit area in an amount of unit time.

 

No such thing as a momentum wave' date=' or at least I think so. Momentum is a vector, the wave equation solves to a sinusoidal function (a scalar).

 

The metric with the raised indices are the inverse components, remember this. The other components are (from left to right) pressure, mass-energy distribution, four-velocity, inverse metric and pressure again.[/quote']

 

Momentum is inertial mass times velocity yes?

 

Give me a formula for momentum flux.

 

[math] \Phi_p = \oint \frac{d\vec P}{dt} \bullet d\vec a [/math]

 

?

 

I guess it's gravitational mass right? Principle of equivalence?

 

I need to know about the mass.

 

Do photons mediate the gravitational force?

[□h=-16πT]

[math]

(p+\rho)U^{\alpha}U^{\alpha}+g^{\alpha\beta}p

[/math]

 

 

[math]

 

\rho+p_x+p_y+p_z

 

[/math]

 

 

 

You can hook this up to quantum mechanics if the inertia waves.

 

 

Rho is the "mass-energy" distribution. Units?

 

Other three are pressures. Pressure how' date=' where?[/quote']

 

Units of mass-energy density: mass per unit volume (energy having the same units of mass in SR). In SI it would be Kg/m³. Volume is also a frame dependant quantity, as lengths contract. I don't know any QM beyond A-level, really.

[Johnny5]

Do photons mediate the gravitational force?

[Johnny5]

Units of mass-energy density: mass per unit volume (energy having the same units of mass in SR). In SI it would be Kg/m³. Volume is also a frame dependant quantity, as lengths contract. I don't know any QM beyond A-level, really.

 

 

slowly, because i know things...

 

Listen to me...

 

 

Forget about volume being a frame dependent quantity.

 

Focus on the mass. That which has units of kilograms.

 

Why is it called "mass-energy" density, why not just density, or mass density, energy has units of time, we don't want that.

 

Time makes everything complicated.

 

 

And here is an important question...

 

You said that volume is a frame dependent quantity, is that because of SR?

[□h=-16πT]

What waves in GR???????????????????????

 

It is space-time that waves. Ever heard of gravitational waves? My name is the field equation in weak form. The square is the d'Alembertian, or wave operator, and the h is part of the following expression for the metric of a slightly curved space time

 

[math]g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}[/math]

 

Where eta is the Lorentz metric of SR and h is a number that maybe dependant upon position, time etc. The idea of this equation is to demonstrate the small "deviation" from a flat space time (described by the Lorentz metric) by an amount h. So, by the equation I have as my name, the h is a wave and so space-time waves. I tried to get that down ASAP and so the discussion has suffered for brevity. The result is similar for strong fields, but I haven't educated myself in this yet.

 

Remember E=mc²? It is called mass-energy density because the two are equivalent and in SR the units of energy are the same as those of mass because (in normalised units) 1 second=c metres. Before you ask, natural units are those used in SR, where c=1, whereas geometrized units are for GR because in this theory G is going to come up (kg=G/c² metres).

 

Photons don't warp ST as they have no SE tensor (no mass, not a fluid etc.). And of course they don't carry the gravitational force, unless they're the same thing as a graviton...?

 

Yes, volume being frame dependant is a result of SR. In the inertial frame of a fluid element moving in the x direction the volume is [math]\Delta x\Delta y\Delta z[/math]. In the frame of another observer O the length in which the fluid element moves, the x direction, is contracted and so (by the length contraction formula) the volume element of the moving fluid in O's frame is

 

[math]\Delta x\Delta y\Delta z\sqrt ( 1-v^2)[/math]

 

You're really going to have to get used to natural and geometrized units.

[Johnny5]

Space-time waves. Ever heard of gravitational waves? My name is the field equations in weak form. The square in the d'Alembertian' date=' or wave operator and the h is part of the following expression for the metric of a slightly curved space time

 

[math']g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}[/math]

 

Where we eta is the Lorentz metric of SR and h is a number that maybe dependant upon position, time etc. The idea of this equation is to demonstrate the small "deviation" from a flat space time (described by the Lorentz metric) by an amount h. So, by the equation I have as my name, the h is a wave and so space-time waves. I tried to get that down ASAP and so the definition has suffered for brevity. The result is similar for strong fields, but I haven't educated myself in this yet.

 

I have to go, unfortunately.

 

Yes, I have heard of gravitational waves.

 

Do photons mediate the gravitational force?

 

I will pick this up tomorrow.

[revprez]

Do photons mediate the gravitational force?

 

Photons mediate the electromagnetic force.

[revprez]

Could you not take the SE tensor in invariant matrix form' date=' diagonalise it and then see what you get?

 

The components in any frame being:

 

[math'](p+\rho)U^{\alpha}U^{\alpha}+g^{\alpha\beta}p[/math]

 

I can't remember the diagonalisation procedure right now. I'll grab my book, flick through the chapter on matrices and give it a go a bit later.

 

Wait, let me try this out. I'll get back to you.

[Johnny5]

Photons mediate the electromagnetic force.

 

I think they do both, what do you think?

[□h=-16πT]

I think they do both, what do you think?

 

Maybe, would proove useful in a unified field theory. I don't think we have any mathematical or experimental evidence at this moment to be able to show this though. Although gravitational waves being the wave part of the duality of light smacks of ether to me. How's it going with your self education by the way?

[□h=-16πT]

Wait, let me try this out. I'll get back to you.

 

Righto.

 

Also, Johnny5, the components of the SE tensor in the MCRF as previously given are only for those systems in a Minkowski space-time (the flat space of SR). The components of the inverse metric differ for a general space-time. For example the line element in the Schwarzshild metric is (I use this metric again because it's easy to remember)

 

[math]

ds^2=-\left( 1-\frac{2M}{r}\right) dt^2+\left( 1-\frac{2M}{r}\right)^{-1}dr^2+r^2d\theta ^2+r^2\sin ^2\theta d\phi ^2

[/math]

 

One usually factors out the r² in the last two terms (as they don't depend on the nature of the space) and calls the remainder [math]d\Omega ^2[/math], i.e. [math]d\Omega ^2=d\theta ^2+\sin ^2\theta d\phi ^2[/math]. The terms before each infinitesimal change on the right hand side are the components of the metric, I couldn't be doing with the hassel of putting them into a matrix.

 

[math]

ds^2=-\left( 1-\frac{2M}{r}\right) dt^2+\left( 1-\frac{2M}{r}\right)^{-1}dr^2+r^2d\Omega ^2

[/math]

 

Just thought I'd give you an example of one solution to the field equations. As an aside, the metric above is the only asymptotically flat solution to E's equations (i.e. is flat at r=infinity). If you want to know why, search for Buchdal's theorem as I don't know the proof myself, just the theorem.

[fuhrerkeebs]

 

I think they do both, what do you think?

 

The particle that mediates the gravitational force (if there is one) has a spin 2, whereas the photon is spin 0.

[Johnny5]

Maybe, would proove useful in a unified field theory. I don't think we have any mathematical or experimental evidence at this moment to be able to show this though. Although gravitational waves being the wave part of the duality of light smacks of ether to me. How's it going with your self education by the way?

 

I will have total recall of linear algebra in less than 30 days. It's going well.

[Johnny5]

The particle that mediates the gravitational force (if there is one) has a spin 2, whereas the photon is spin 0.

 

How did you reach the conclusion that the particle which mediates the "gravitational force" has spin 2?

[revprez]

Righto.

 

Also' date=' Johnny5, the components of the SE tensor in the MCRF as previously given are only for those systems in a Minkowski space-time (the flat space of SR). The components of the inverse metric differ for a general space-time. For example the line element in the Schwarzshild metric is (I use this metric again because it's easy to remember)

 

[math']

ds^2=-\left( 1-\frac{2M}{r}\right) dt^2+\left( 1-\frac{2M}{r}\right)^{-1}dr^2+r^2d\theta ^2+r^2\sin ^2\theta d\phi ^2

[/math]

 

And just for clarity's sake, the [math]\left(\frac{2M}{r}\right)[/math] term is chosen with units such that G and c = 1.

[□h=-16πT]

Wait, let me try this out. I'll get back to you.

 

And...?

[revprez]

And...?

 

I have to agree with you. I think that's the way to go about it.

[□h=-16πT]

I have to agree with you. I think that's the way to go about it.

 

*two thumbs up*

 

Aww...this thread has kinda dried up; I was enjoying this discussion. Want to know anything at all or require any help, Johnny?

[Johnny5]

*two thumbs up*

 

Aww...this thread has kinda dried up; I was enjoying this discussion. Want to know anything at all or require any help' date=' Johnny?[/quote']

 

Yes, I have a million questions for you, but I am trying to restore all of my knowledge of linear algebra.

 

How about just tell me very simple things at first.

 

Explain to me why space expands according to GR.

 

 

Does the Euclidean metric describe reality?

[Johnny5]

Yes. Just remember that SR uses greek indices that take the values 0, 1, 2, 3 (time, x, y, z respectively).

 

 

Is this right?

 

 

Let V denote a vector in SR. We write:

 

[math] \vec V = V^\alpha \hat e_\alpha [/math]

 

?

[revprez]

*two thumbs up*

 

Aww...this thread has kinda dried up; I was enjoying this discussion. Want to know anything at all or require any help' date=' Johnny?[/quote']

 

Yeah, I got kinda caught up with work. Gotta love this shit, though.