# Bending of space and time, is it true?

PeterDonis
Mentor
2020 Award
In GR the curvature of space-time is not zero inside the shell
No, that's not correct. Spacetime is flat inside the shell. The redshift of light going from inside to outside the shell is due to what happens to it when it passes through the shell (and then through the curved spacetime outside the shell). Light going from one point to another inside the shell has zero redshift, which is one manifestation of the flatness of spacetime inside the shell.

PeterDonis
Mentor
2020 Award
the mass of the particles (reactants) is equal to the mass of the products
If you mean invariant mass, this is not correct; the invariant mass of the products in a nuclear reaction is less than the invariant mass of the reactants (meaning, in each case, the sum of the invariant masses of all the particles). You can check the numbers for typical reactions to confirm this.

If by "mass" you just mean the total energy of the system, yes, this is conserved, but it's just restating what you say in your next sentence.

PeterDonis
Mentor
2020 Award
I find Newton's theory more reasonable

Since Newton's theory is just the low velocity, weak field limit of GR, then if Newton's theory is reasonable, so is GR.

I didn't say rotational speed, I said speed. If the surface of the Earth is moving at Xmph, relative to the moon say, and I throw a ball in the same direction at 10mph then the moon sees the ball moving at X+10mph.

I see.... but I was asking about the "rotational speed", and not by the a perceiver's eye, but say a machine or something which calculates it.

Drakkith
Staff Emeritus
No, that's not correct. Spacetime is flat inside the shell. The redshift of light going from inside to outside the shell is due to what happens to it when it passes through the shell (and then through the curved spacetime outside the shell). Light going from one point to another inside the shell has zero redshift, which is one manifestation of the flatness of spacetime inside the shell.

I realize that no redshift takes place inside the shell, but I was under the impression that spacetime was still curved in some fashion compared to an observer far away from the shell. Would a clock placed inside the shell experience time dilation as viewed from this observer?

Wrong. Size has nothing to do with speed, and you cannot cover less distance with a slower speed.

Let's put it this way. If the object is larger, it cover's more distance in the constant "t" rather than another object lesser in size relative to it. Both of their measurements are relative to Earth.
For ex.
Speed=Distance/time
For the object which is larger in size.
Speed=distance/time,
= d/t
Same for the smaller object
Speed=distance/time
d1/t

Now d> d1 because the "m" of the bigger object is greater than the m1 {The mass of smaller object}
The more mass the more size the more distance travelled in a specified time t , where both the objects compared are relative to any body with mass

Can I conclude that?

PeterDonis
Mentor
2020 Award
Would a clock placed inside the shell experience time dilation as viewed from this observer?

Yes, but that doesn't mean spacetime is curved inside the shell. It only means that spacetime has to be curved somewhere between the clock inside the shell and the observer far away. The curvature of the shell region plus the region outside the shell is sufficient to cause the observed time dilation.

The flatness of spacetime inside the shell is a simple consequence of the shell theorem, which holds in GR just as it does in Newtonian mechanics: a vacuum region of spacetime inside a spherically symmetric matter distribution must be flat.

Drakkith
Staff Emeritus
Let's put it this way. If the object is larger, it cover's more distance in the constant "t" rather than another object lesser in size relative to it. Both of their measurements are relative to Earth.

I'm sorry you've lost me. What type of motion/speed are we talking about here? Rotational speed? Linear speed?

I'm sorry you've lost me. What type of motion/speed are we talking about here? Rotational speed? Linear speed?

Rotational

Drakkith
Staff Emeritus
Yes, but that doesn't mean spacetime is curved inside the shell. It only means that spacetime has to be curved somewhere between the clock inside the shell and the observer far away. The curvature of the shell region plus the region outside the shell is sufficient to cause the observed time dilation.

So if I place a clock inside this shell, wait a period of time, then retrieve this clock, it should read as having less time passed than a clock left behind far away from the shell. Now, what if I wait twice as long, according to the 2nd clock, before retrieving the 1st clock?

phinds
Gold Member
I see.... but I was asking about the "rotational speed", and not by the a perceiver's eye, but say a machine or something which calculates it.
I have no idea what you are talking about

Drakkith
Staff Emeritus
Rotational

Then an object with a larger radius will have a larger rotational speed* for any given angular velocity compared to an object with a smaller radius. Mass has nothing to do with it.

*Note that rotational speed usually means the same thing as angular velocity, which is revolutions per unit of time, typically rotations per second. For this post I mean the speed at which the surface at the equator is moving.

Then an object with a larger radius will have a larger rotational speed* for any given angular velocity compared to an object with a smaller radius. Mass has nothing to do with it.

*Note that rotational speed usually means the same thing as angular velocity, which is revolutions per unit of time, typically rotations per second. For this post I mean the speed at which the surface at the equator is moving.

The more mass the more size the larger radius? . And that note thing you mean theta?

Drakkith
Staff Emeritus
The more mass the more size the larger radius?

Not in general, no. A 1kg ball of lead is much smaller than a 1kg ball of aluminum.

And that note thing you mean theta?

No, I mean exactly what I said.

PeterDonis
Mentor
2020 Award
So if I place a clock inside this shell, wait a period of time, then retrieve this clock, it should read as having less time passed than a clock left behind far away from the shell.

Yes. But the difference will be the same no matter where inside the shell you place the first clock. If spacetime were curved inside the shell, the difference in times would vary with location inside the shell.

what if I wait twice as long, according to the 2nd clock, before retrieving the 1st clock?

Then the difference will be larger; but again, it won't depend on where inside the shell you place the first clock.

Drakkith
Staff Emeritus
Okay, that's just what I thought would happen. Perhaps I worded my earlier post badly. I didn't mean to suggest that the curvature between different points inside the shell is non-zero.

Not in general, no. A 1kg ball of lead is much smaller than a 1kg ball of aluminum.

No, I mean exactly what I said.

*Size? , and Angular Displacement=Theta right?

Drakkith
Staff Emeritus
*Size? , and Angular Displacement=Theta right?

I meant I misplaced size by mass, that's why I put a "*" mark, sorry if you didn't understood. And I see I'm a starter so I will face some problems at first, but I'll try my best. Hope you can bear with my way of posting

phinds
Gold Member
I meant I misplaced size by mass, that's why I put a "*" mark, sorry if you didn't understood. And I see I'm a starter so I will face some problems at first, but I'll try my best. Hope you can bear with my way of posting
Just to be sure you understand, the biggest problems with your way of posting are:

(1) you make categorical statements of things being true when in fact you simply misunderstand reality. It's perfectly fine for beginners to have lots of misunderstandings. We all do that. What's not OK is to state your misunderstandings as though they were fact.
(2) You don't seem to clarify your thoughts before posting and so we have a really hard time following what you are talking about.

Just to be sure you understand, the biggest problems with your way of posting are:

(2) You don't seem to clarify your thoughts before posting and so we have a really hard time following what you are talking about.

Well, I always do that to check any imperfection in my question, but I guess I need to clarify my question to get a better answer. I see thanks