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I heard dTau measures time for the person traveling on a worldline. If the person traveling on that world line chalked marks on the world line every 1 minute, would those intervals be the same distance from each other?

so if I added the c^2 terms back into the final equations from peterdonis at post #10 I would get "ticks" per second? and then if I wanted to calculate time at r for the clock, standing on earth, I would take the doppler blueshift off, and just calculate the gravitational shift at r?

Wouldn't the clock tick slower as it gets closer to the person standing on Earth though? https://en.wikipedia.org/wiki/Gravity_Probe_A

I was wondering what someone standing far away from a planet with mass would see if he drops a clock towards the mass. And then vice versa if I was standing on the planet, what would I see. would I see the clock tick fast and then slow as it approaches? Thanks!

If I had a chart of Cartesian coordinates and it had four axis's, t, x, y and z, how would I induce motion of a test particle by curving those axis's ? If the test particle was standing still and only moving in the t axis, how do i get it to move in the other axis's, x, y, z. I can understand a...

Hi, What would happen if I set L in this equation to zero? I can have an L that is zero right?

Where can I find numerical relativity source code?

How does general relativity shows the conservation of energy. Because I was reading and listening to something today that touched on this subject. It almost seems as though if you scale GR to larger sizes it stops working and turns into an incomplete law of nature like Newton's laws of gravitation.

PeterDonis many experiments found that GR is incorrect. This is just another one that was published on BBC.

Hello can someone help me understand the difference between Spacelike timelines and the two others found in Carroll page 71?

well i feel like in SR we can talk about length contraction okay but in GR it seems like taboo or something. Idk much about the difference between timelike worldlines or spacelike worldlines. But I mean eitherway it sounds like equivalent. But okay I need to go to bed to go to work tomorrow.

I don't see how this is any harder than it should be, if the clock comes back and is off, that distance changed. Because certainly if I traveled with that clock the whole round trip, inside it, the speed of light would have not changed. If I made the clock big enough. I didn't say global...

Well okay, let us do like the twins, two clocks; one goes around a very massive object, and comes back to me, I'm very very far away with the other clock. I picked one. Now we know that in all frames c is the speed of light. Now if that clock is off by one millisecond, something happened.

Well does it make any difference which way I pick. What I want to know is does the clock slow down as it gets closer to a mass?

But you can imagine me making two clocks right, same height, and I throw one into a black hole and one stops ticking. Then I will know.

Well if we look at MTW Gravitation, on page 1054, they talk about experiments with elementary particles. So there is certainly an experimental basis on which I can assume time dilation in a curved spacetime. But as to how I would measure the up and down motion between the two mirrors that is...

hutchphd I want to measure the length between the two mirrors. A light clock is kind of easier to understand since light will travel between those two mirrors at c always. I'm imagining standing an infinite distance away from a mass, and then letting the clock go and free fall into the curved...

I would measure the initial distance between the two mirrors in my frame, and afterwards I would use time to figure the other distances in other frames, I guess. We can talk about time-dilation in general relativity right?

Hi, can i use a light clock made out of mirrors a distance appart to measure whether there is length contraction in different regions of spacetime? If the clock speeds up then the distance between the mirrors decreased. If the clock slows down the distance between mirrors increased.

Btw, I figured this problem by doing a simple 2D version, instead of a box a square. So in the above case I would figure the distances from the corners of the XY plane to the point I'm interested in on the XY plane. and then I add up these distances. after that I add...

Suppose I have a R^3 manifold that goes into R^3 charts, if that is possible. The manifold has curvature and is Riemannian and has a metric. I want to eliminate all curvature in R^3 charts, so I want to add another dimension to the manifold, I would extract all the curvature information from the...

ok thx

Okay thanks ibix. Is lambda in those equations wavelength, or some other parameter?

So if that is true, the equation b = L/E can only be calculated at r=infinity and no where else? if I want to know the orbit of the photon at any other r from the mass, I would have to find another equation.

ok heh

You meant E measured locally, or E measured as though you are traveling with the photon?

Depending on the r distance from the mass the photon's E would change right? does the L change too, so it keeps the same b along the trajectory?

Well I did read past equation 25.61. But because it was a ratio now that says that you can have a photon with a lot of energy and a photon with lower energy have same trajectory along the geodesic given you adjust their L accordingly, they can have same b. I will read the chapter on Redshift...

I am reading MWT gravitation and on page 676, they are talking about orbits of photon, and I don't understand it very well. Energy and angular momentum of the photon are important as a ratio when calculating the orbit. But not energy alone or angular momentum alone. Why is that, and the energy...

Is there a spherically symmetric metric that doesn't have a singularity in the middle of it(like the schwartzchild metric). Something like our planet.

Fair enough... Well I'm going to add, even though I know it is wrong, that a region of space has to have a set energy because energy is quantized.

Why can't you measure mass/energy in a certain region of space in GR? I thought because the manifold is Riemann and has a metric on it, I can take measurements. I can cut the manifold in cubes and measure the cubes and these measurements would be independent of coordinate system. I can know how...

Thanks Paul. I think it is a matrix/tensor yes. 3x3. so at P_j i would get a temperature W_j? Which is a scalar. Is it possible to get a direction of the flow of the heat at point P_j? (sorry idk how to use latex)

Well Ibix I was trying to understand the internal structure of a star or planet when you change gravity. A fun one was trying to imagine what would happen to the Earth if all gravity disappeared. I was thinking that the sun is affected to some degree by the gravity of the other planets...

So I have a cube in 3d space and this cube is made out of 8 coordinate points at each corner. Now I have a temperature reading at each point of these corner points. Inside the box I have another point, I want to be able to use the information from the 8 points surrounding the the one middle...

watts/m^2 at some distance r.

If I take away the planets in the solar system and leave the sun alone, would the sun have less energy than before?

is that what changing the angular momentum means in this instance? picking a different coordinate system?

Well bare with me for a minute, I know that there is a kinetic term and also a "potential term" that is the slope of the curved line I posted up and the total energy should be fixed. I'm just trying to understand if increasing the total energy of the system, right, does anything to the...

That is what setting phi = pi/2 means right?

But we got this from the metric of the spacetime. And this chart with the energy level would allow you to draw an orbit around the center mass.

I was looking at this chart and I didn't understand how increased angular momentum of the test particle curves the spacetime around the center mass. If that is how it's interpreted. Now the way it looks like is that the curvature is dependent on the angular momentum of the test particle.

alright fine gravity is the curvature in spacetime.

well since I've been asked to try again, I'll try again. People in this thread have been saying that as soon as you have curvature in the spacetime you will see these test masses start free falling along these geodesics. Gravitational waves, are curves in spacetime. So I would assume that as...

Well I believe that because of gravitational waves, GR strips away the meaning of force. Newtonian gravity has 0 notions that waves exist. By saying there is a dynamic fabric that constantly interacts with mass and also with itself, (probably), GR is saying spacetime curvature is not a artifact...

GR predicts WAVES which were observed by LIGO. WAVES traveling in spacetime, probably interacting with each other, in physical world. Which to me at least says that GR's spacetime curvature has real physical meaning in real life. Not that I ever thought other wise...

well then the good thing about GR is that it means General Theory of Relativity and not General Theory of Gravity.

Ibix are you saying there may still be a particle that might be mediating the force of gravity? That the curvature of spacetime is an artifact of this mediating force field ?

If gravity is just curvature in spacetime, why does mass curve spacetime in the first place though.

How can someone tell the difference between a super massive galaxy's redshift and a galaxy that is accelerating away?