The Missing Chapter Of General Relativity?

[sol invictus]

This looks pretty good:

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravField.htm

I recommend you read the section on superposition and just below. For instance:

"Note that the force is exactly zero at the origin, and everywhere else it points towards the origin."

Even better:

"Field Inside a Spherical Shell

This turns out to be surprisingly simple! We imagine the shell to be very thin, with a mass density kg per square meter of surface. Begin by drawing a two-way cone radiating out from the point P, so that it includes two small areas of the shell on opposite sides: these two areas will exert gravitational attraction on a mass at P in opposite directions. It turns out that they exactly cancel. "

 

[DeathDart]

This looks pretty good:

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/GravField.htm

I recommend you read the section on superposition and just below. For instance:

"Note that the force is exactly zero at the origin, and everywhere else it points towards the origin."

Even better:

"Field Inside a Spherical Shell

This turns out to be surprisingly simple! We imagine the shell to be very thin, with a mass density kg per square meter of surface. Begin by drawing a two-way cone radiating out from the point P, so that it includes two small areas of the shell on opposite sides: these two areas will exert gravitational attraction on a mass at P in opposite directions. It turns out that they exactly cancel. "

That is a Newtonian Definition. In relativity the field never cancels out. The center of the mass has the highest field. The force is zero.

 

[DeathDart]

Now when my momentum changes, my clock changes. My clock would run the slowest it can run in this hole in the universal energy field called ‘earth’ if I could place the clock right next to the very center of mass of the earth. That would be the slowest clock running spot on this planet.

http://www.awitness.org/unified/pages/time_dilation.html

 

[sol invictus]

That is a Newtonian Definition. In relativity the field never cancels out. The center of the mass has the highest field. The force is zero.

Wrong again. The field inside a spherical shell of mass is exactly zero in GR too. Why? Because the field cancels.

http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity)

"Another interesting consequence of Birkhoff's theorem is that for a spherically symmetric thin shell, the interior solution must be given by the Minkowski metric; in other words, the gravitational field must vanish inside a spherically symmetric shell. This agrees with what happens in Newtonian gravitation."

 

[Ziggurat]

That is a Newtonian Definition. In relativity the field never cancels out. The center of the mass has the highest field. The force is zero.

You have confused the field with the potential. They are not the same. The field at the center of a spherical mass is zero, and the potential is at its lowest value there, not its highest value. We already told you that you were confused about this, but you would not listen. How many times will it take before you figure this out?

 

[godless dave]

The Time Space where the clock and the atom is 10X. 10X Faster .

The photon that the atom produces has ten times the frequency that it would have in the Time Space we occupy. Because inertia is lower in this time frame the amount of energy is equivalent in our Time Space at 1/10th the frequency.

There is not any way for the photon to enter our space without successively traveling though stronger gravitational fields and slower time.

10X Time Space is always bounded by either 9X Time Space, or 9x and 11X Time Space.

There isn't any way for a photon from a 10X Time Space to directly pass through to 1X space. This would represent an impossible gravity gradient.
When we look at the clock face the information it presents shows a 10X time flow. This information is not affected by the intervening space.

So why did you say it would look different through a telescope than with the naked eye?

 

[RVM45]

Friends, I couldn't follow all the Labyrinthine Logic--Well,I could have, maybe--but it would take much concentrated cogitation.....

However, the OP did ask one rhetorical question that got me to wondering.

The speed of light is the same everywhere, regardless of the observer's frame of reference.

That's mind expanding--but I think I can wrap my mind around that....

But why is C= 186 272 Miles Per Second ?

The question "Why" seems at times, to imply Conscious Intent--and I don't mean to imply that.

Can we rigorously examine what sort of Universe we would be living in--what some of the logical consequences would be, if

C=Infinity?

Or C= 186 272 186 Miles Per Second?

Or C= 383 272 Miles PerSecond?

Or C= 100 000 Miles Per Second ?

Or C= 186 272 Miles Per Hour?

Or C= 186 Miles Per Hour?

Or C= 5 Miles Per Hour.

Presumably, the universe as we know it, could not exist if C were much different from what it is now (but why?)

But how much could it be off, and still allow our universe?

.....RVM45

 

[DeathDart]

No. You're completely wrong. You're so wrong that the only explanation is that you have some totally different idea about what a field is than the actual accepted definition of a field.

Go get yourself an introductory physics textbook. You are so badly mistaken about so many basic things that there's really no chance that this is going to be a productive discussion.

You have given yourself away. Did your adviser step out of the room and you though you could answer the question?

The field doubles, it is the answer.

 

[jsfisher]

You have given yourself away. Did your adviser step out of the room and you though you could answer the question?

The field doubles, it is the answer.

You, of course, can back up this incredible claim with supporting evidence beyond the waving of hands, no?

 

[sol invictus]

You have given yourself away. Did your adviser step out of the room and you though you could answer the question?

The field doubles, it is the answer.

Are you serious?

When you've found the mistake in Birkhoff's theorem (which appears in every textbook on GR, and which I've derived independently myself several times in various different forms), please let me know what it is.

 

[sol invictus]

Can we rigorously examine what sort of Universe we would be living in--what some of the logical consequences would be, if

C=Infinity?

Or C= 186 272 186 Miles Per Second?

Or C= 383 272 Miles PerSecond?

Or C= 100 000 Miles Per Second ?

Or C= 186 272 Miles Per Hour?

Or C= 186 Miles Per Hour?

Or C= 5 Miles Per Hour.

Presumably, the universe as we know it, could not exist if C were much different from what it is now (but why?)

But how much could it be off, and still allow our universe?

It's a good question, but it's better when re-phrased in slightly different terms. The trouble is, c is a quantity with dimensions (meters/second, say) - and so when you ask about it changing, you have to include in your question with respect to what? In other words, you need to say what you're keeping fixed as you change the value of c.

For instance, c->infinity can be interpreted as simply a non-relativistic limit. It's the limit in which all velocities relevant to the problem or experiment you're interested in are much less than c. And as such, the answer to your question is very easy - of c=infinity, the world is pretty much as Newton and Galileo conceived of it. There are no relativistic effects like time dilation and Lorentz contraction, and there's a fixed, absolute time that's truly separate from space.

The opposite limit, where c is small, is like asking about a situation where all relevant velocities are relativistic (close to c, since nothing can exceed c). That kind of world would be very bizarre - time dilation would be an important effect in everyday life, so a twin taken on a car trip might still be a baby while her stay-at-home sister is dying of old age, and people living in the mountains would age much faster than those by the sea.

 

[Ziggurat]

You have given yourself away. Did your adviser step out of the room and you though you could answer the question?

The field doubles, it is the answer.

No, it does not. You are apparently unable to distinguish between a field and a potential. I suggest you consult an introductory physics textbook, because you're clueless.

There's nothing wrong with being clueless about physics, but when you become arrogant about your cluelessness, that's when you truly make a fool out of yourself. And you have done so repeatedly now, without ever learning from your mistakes.

 

[DeathDart]

No, it does not. You are apparently unable to distinguish between a field and a potential. I suggest you consult an introductory physics textbook, because you're clueless.

There's nothing wrong with being clueless about physics, but when you become arrogant about your cluelessness, that's when you truly make a fool out of yourself. And you have done so repeatedly now, without ever learning from your mistakes.

An introductory physics text book covers the fine points of G.R.?

Your argument works to describe forces, and how to integrate masses so you can calculate the forces they might generate. It does not describe G.R.

http://physics.stackexchange.com/qu...point-where-two-gravitational-fields-cancel-e

gravitational potential not gravitational forces. Since potentials add, instead of cancelling like the forces, we get twice the time dilation with two planets than we get with one, as @Jim Graber said.

 

[Vorpal]

An introductory physics text book covers the fine points of G.R.?

Your argument works to describe forces, and how to integrate masses so you can calculate the forces they might generate. It does not describe G.R.

Yeah, it does.
Inside an empty spherical shell, spacetime is completely flat. It looks just like Minkowski spacetime, and there is no gravitational time dilation between test clocks anywhere in the shell, despite space being empty, and in contradiction to your claims.
Relative to a stationary observer at infinity, the clocks of an inhabitant of that hollow shell run slower. This is the effect of the curvature of spacetime outside the shell caused by its mass. The amount of time dilation is not infinite: it's a factor of (1-2M/R)^1/2 for a thin shell of radius R and mass M.

http://physics.stackexchange.com/qu...point-where-two-gravitational-fields-cancel-e

You realize that only proves Ziggurat's point that you're conflating field and potential?

 

[sol invictus]

An introductory physics text book covers the fine points of G.R.?

Your argument works to describe forces, and how to integrate masses so you can calculate the forces they might generate. It does not describe G.R.

Why do you keep ignoring the mathematical theorem that proves that the gravitational field is precisely zero inside a spherically symmetric shell of mass, in general relativity as well as in Newtonian gravity?

Can you answer that, please?

 

[DeathDart]

Ok, first things first.

Big math error on my part.

Time divides directly into MASS, not velocity. This is also true for high velocities mass/time. Time decreases, mass increases.

In 10X faster space velocity increases SQRT(10) = 3.162

 

[DeathDart]

Why do you keep ignoring the mathematical theorem that proves that the gravitational field is precisely zero inside a spherically symmetric shell of mass, in general relativity as well as in Newtonian gravity?

Can you answer that, please?

Because an atomic clock will run slower there. The potential has no vector to cancel out, it adds.

 

[sol invictus]

Because an atomic clock will run slower there. The potential has no vector to cancel out, it adds.

That's true, but that's not what you've been saying. Instead, it's precisely what we've been telling you.

At least have the grace to admit what's obvious to everyone reading the thread: you screwed up, we corrected you, you denied it repeatedly, and now finally you've learned something.

You're talking to people that know far more than you do. Try a little humility.

 

[DeathDart]

Yeah, it does.
Inside an empty spherical shell, spacetime is completely flat. It looks just like Minkowski spacetime, and there is no gravitational time dilation between test clocks anywhere in the shell, despite space being empty, and in contradiction to your claims.
Relative to a stationary observer at infinity, the clocks of an inhabitant of that hollow shell run slower. This is the effect of the curvature of spacetime outside the shell caused by its mass. The amount of time dilation is not infinite: it's a factor of (1-2M/R)^1/2 for a thin shell of radius R and mass M.


You realize that only proves Ziggurat's point that you're conflating field and potential?

What this link is about is that an object between two masses has twice the time dilation of one mass. Force cancels out. Potential adds. The sphere is exactly the same thing. The forces cancel out, the potential adds. Time dilation is higher.

 

[Roboramma]

You have confused the field with the potential. They are not the same. The field at the center of a spherical mass is zero, and the potential is at its lowest value there, not its highest value. We already told you that you were confused about this, but you would not listen. How many times will it take before you figure this out?

http://physics.stackexchange.com/qu...point-where-two-gravitational-fields-cancel-e

gravitational potential not gravitational forces. Since potentials add, instead of cancelling like the forces, we get twice the time dilation with two planets than we get with one, as @Jim Graber said.

Just to be clear, you quoted that the show that you agree that you confused field and potential, correct?