Jorrie, interesting post, but what do you mean by Schwarzschild coordinates? Further, you wrote about 'time-time coefficient', etc. What are these?

Quoting Guest: "Jorrie, interesting post, but what do you mean by Schwarzschild coordinates? Further, you wrote about 'time-time coefficient', etc. What are these?"

There is a fairly technical article on Wikipedia on Schwarzschild coordinates, but very loosely and briefly: it is used to represent the space-time outside a static, non-rotating, spherical black hole carrying no electrical charge. The metric has the form:

ds² = -g_tt c²dt² + g_rr dr² + r² (dز + sin²Θ dز)

where s represents space-time interval, t is time and r, Ø and Θ are polar coordinate variables. The time-time coefficient g_tt refers to the way mass warps time and the radial-radial coefficient g_rr refers to the way mass warps space. Taken together, it is the warping of space-time into a manifold.

This is all very nice, Jorrie, but please tell me where the "4 Engineers" part leaves off and the purely theoretical science begins. Please don't get me wrong, and please do not take my comments here as being critical of your work - which looks quite good, in fact - but I can't help but wonder, after reading your work, how an engineer might apply his new knowledge in a practical way. In its most general sense engineering is, after all, the application of science to the solution of practical, everyday problems. Some problems may require some rudimentary knowledge of Special Relativity. As an electrical engineer, for example, I might need to know how to design an RF quadrapole in an optimum way that accounts for the relativistic effects of 10 MeV ions in my company's new implanter. Or I might be designing a new, high-resolution CRT and would need know how to best design its electron optics so that relativistic effects don't take me by surprise. I'm considerably less sure, however, why I might be called upon to calculate the spacetime metric in the vicinity of a non-rotating black hole having no electrical charge. The last time I checked, W. W. Grainger was fresh out of black holes and didn't expect deliveries any time soon. You seem to have done some quality work here. It's quite good, actually, but my question for you is how your chosen audience might make the most effective use of your labors? --Europium

Thanks Europium, good questions. I guess the answer lurks 99.99% in my signature (curiosity) and the rest in some practical applications.

Apart from the ones you mentioned, there are possibly: Doppler effects in space observations, particle accelerator design and of course the GPS. Whether it makes up 0.01%, I doubt! It appears to me as if about 0.2% of engineers are interested enough in relativity and cosmology to read up on it.

Most of those engineers have probably never needed and will never use relativity in their careers. Nevertheless, I offer them a somewhat more engineering-like spin than what the physics and math guys offer us. To me, it's just a hobby.

Jorrie

Hi Jorrie

Suddenly I have discovered that you have been writing a series of papers on relativity and gravity. So thanks to the well ordered series with links to previous chapters, I have collected all links to them in a special favourite's folder to try reading them all as soon as possible. I hope your articles will be saved for ever at CR4, because I have not read them yet.

I am not at all an expert in physics, so my questions are very elementary:

Suppose "thin" disk with a mass M and a radius R, rotating at "relativistic" angular speed, the questions are:

1) What would be the interaction between the gravitation of Earth and that of the rotating disk?

2) If one "0 ppm" atomic clock is attached to the center of the disk, and other "0 ppm" clock rotates attached to the edge of the disk, does a time difference accumulates between the two clocks?

On rotating a disk up to relativistic angular speeds, some time/space distortion should appear around the disk and inside the materials of the disk, even more, to prove this it should not be necessary to rotate the disk at relativistic angular speed, just to do it at high speed should be enough, because as it can be seen by inspection, relativistic equations depart being true from low speeds.

I would love to do this experiment, but in a safe desert, far from populated areas, may be in the north of Chile, as you know many telescopes are being installed there precisely for the high mountain plain deserts available there.

Ok, I should read all your articles first

Thank you very much for what you are writing at CR4.

Jaime Soto Figueroa

Santiago, Chile

http://www.matharts.cl/ http://www.artefractal.cl/

Hi Jaime, I think my OP in this thread answers some of it, but my take on your questions, by number:

1) "What would be the interaction between the gravitation of Earth and that of the rotating disk?"

Apart from the centrifugal forces that will try to destroy your disk, Earth's gravity will 'suck' it more firmly in the direction of Earth's center of mass. The edge can experience up to 3 times normal "g", as I stated in the OP above.

2) If one "0 ppm" atomic clock is attached to the center of the disk, and other "0 ppm" clock rotates attached to the edge of the disk, does a time difference accumulates between the two clocks?

I'm not sure what a "0 ppm" clock is, but what I'm sure off is that the edge clock will lose time on the center clock, purely due to velocity time dilation of the edge clock that is going at relativistic speeds relative to the center clock. The centrifugal/centripetal forces make no difference, as long as the clocks stay operational!

Before we discuss it further, first contemplate the above and let me know what you think.

Regards, Jorrie

Hi Jorrie

0 ppm means "zero parts per million" error. Of course no clock has that precision, for example crystal oscillator integrated circuits with automatic temperature control reach some 0.2 ppm at most. Are you sure that "Earth's gravity will 'suck' it more firmly in the direction of Earth's center of mass". This is discouraging; it means that gravitational levitation is impossible. I wish that Earth rejects the rotating disk instead. Any hope?

Jaime

Jaime, thanks for the clarification.

I am afraid that, unless Einstein was wrong (and I doubt that), the more energy an object has, the 'heavier' it will be in Earth's gravitational field. Now don't you think a very fast spinning disk has more energy than a non-rotating disk? Discouraging it is!

My recommendation: until you understand standard gravitation theory to a reasonable extent, don't waste your time with anti-gravity schemes!

Hi Jorrie

Ok, but imagine two identical counter rotating disks within a vacuum chamber, but imagine them so thin and so close that in the limit they seem just like a single disk with two sides, where every infinitesimal element rotating at one side has its exact counterpart rotating at the same angular speed in opposite direction in the opposite side.

On viewing this disk pair from far away it can be stated that there is no rotation because all movements are exactly cancelled. ¿Is the direction of angular rotation totally indifferent?

Jaime

Hi Jaime, you said: "...imagine two identical counter rotating disks within a vacuum chamber..."

You can say the average angular velocity is zero, but NOT that the total angular energy is zero! Energy is a scalar with no direction - as you know you use v² for kinetic energy, so the sign is lost.

In Newtonian mechanics, your two counter rotating disks have twice the kinetic energy of a single disk (more than twice in relativistic mechanics). This extra energy makes your disks heavier than non-rotating disks!

Jorrie,

You Wrote:

"This will apply to an electron accelerated to near the speed of light in a horizontal direction on Earth"

Do they have to compensate for this in particle accelerators? would the particle would feel more than the normal 1 g of gravity?

Its hard to get my head around, but thats because I have a lot to learn.

When there's no gravitational field, that's special relativity and space is flat? So when you add a gravitational field your basically curving space? And the metrics are matrices that alter the velocity vectors in this gravitational field? Basically applying the principles of special relativity on a curved space instead of flat space. Am I getting this right, or am I off?

Roger, you wrote: "Do they have to compensate for this in particle accelerators? would the particle would feel more than the normal 1 g of gravity?"

Yes, they surely do - it has to do with the increased energy (a.k.a. 'relativistic mass') of the electron. Since the radius of space-time curvature on Earth is large (about a light-year long), the gravity effect is tiny - the problem accelerating and turning an electron or other particle is much more severe!

More about your other question later - I've got to rush off to work (I'm at central European time)

Quoting Jorrie: "More about your other question later - I've got to rush off to work (I'm at central European time)"

Hi Roger, I successfully fended off the traffic and the worst project problems at work, so here's an attempt at your other questions.

Q2:"So when you add a gravitational field your basically curving space?" Yep, although it is more correct to say that you're curving space-time - although space alone is also curved.

Q3:"And the metrics are matrices that alter the velocity vectors in this gravitational field?" Not quite. The metric matrix coefficients alter the geometry of space-time, which alters the paths of geodesics, which may or may not alter velocity vectors in 3-space. My chapter "What is Relativity?" makes this idea fairly clear. (BTW, tx for buying the eBook!)

Q4:"Basically applying the principles of special relativity on a curved space instead of flat space. Am I getting this right, or am I off?" You're pretty close to the truth! The only provisos are that you apply it over an infinitesimally small piece of curved space-time and that you are in free-fall (a true inertial observer).

One can normally (not always) stretch the 'infinitesimally small' proviso a bit when the field is weak and velocity not to high.

Jorrie,

You Wrote: (BTW, tx for buying the eBook!)

Thanks for writing it. I've wanted to study relativity for a very long time now but things always seemed to conspire against me. The texts are often too "thick" to understand without taking a course to compliment them. Your book fills the gap nicely, with the added bonus that I can ask you questions ;)

I'm actually going through it when I have time. I already rereading sections to get a better understanding and those questions I asked were "feelers" to see if I'm thinking about things correctly. I think I'm getting there. Slowly.

Thanks for your responses to my questions, I should have more very soon.

Roger

ps- I think the book is very well done, so give yourself a pat on the back from me.