Do gravitational waves transmit energy in all cases?

[rdai]

I was told that there are two kinds gravitational waves. One dies out as 1/r, another one dies out as 1/r^2. The former is what LIGO detected, the latter is not. While I trust the professional qualification of the person very much, as a non-physics professional, I would like to a second person to confirm that. The following is the context of the conversation I had:

Me:

As a non-physics professional, what I am more interested is not GW but what we can learn from GW about the nature of spacetime. Now we have already learned that spacetime can be curved by a mass...we also know that the change of curvature caused by a mass could be propagating at a finite speed of light...

Now if there is a Frequency of a GW and the frequency could be independent of any oscillating source like the characteristic frequency of a matter, then it means that the spacetime also could RESIST the change of its curvature created by mass...but now the following answer from Jorrie asserts that it is NOT the case:

There will be no GWs seen in the math unless some or other deforming mass is present, at least symbolically, e.g. the mass is just seen as M (or as M1 and M2 in the case of binaries).

That is an important assertive information to me :) Thanks a lot.

However, I am still having some concern about the following statement:

The events creating GWs must be oscillating events of a certain type, i.e, in ordinary language it must be changing from "short and fat" to "long and thing" repetitively, at least for some time.

as I understand that the spacetime is curved by the presence of a mass...so when the presence of that mass changes (e.g. increase of value or change of location), the curvature in spacetime created by it would change as well...and this change is NOT instantaneously but propagates out at the finite speed of light...Therefore, it seems to me, even if there is just ONE SHOT of change (hypothetically at least) , the change still should be transmitted out at the speed of light, but without any wavy rippling (unlike in a medium of matter like water)...Please correct me if I am wrong.

---------------------------------------

RESPONSE from JORRIE:

Yes, any change of the mass distribution will cause a change in curvature that will spread out at 'c' in all directions. This is gravity that changes, not GWs. A good example is the tidal pull of the Moon on Earth that has a period of somewhat over 12 hours. So it is a 'wave', but not a gravitational wave, which has a specific mathematical definition in relativity.

In fact, the Earth/Moon system does emit tiny gravitational waves, but only from somewhat outside the orbit of the Moon. An observer there will obviously see the orbiting system as an alternating "thin body" and a "fat body".
These tiny ripples travel outwards at 'c' and the amplitude fall off with inverse if distance (1/r), while the tidal gravity is a shorter range range phenomenon, because its amplitude falls off with the inverse square of distance (1/r2).

Tidal gravity is much larger than GWs at smaller distances, but there is a point outside the Moon's orbit where the amplitude of the tidal gravity will become smaller than the amplitude of the GWs. This is more or less where gravitational waves is said to originate.

--
Regards
Jorrie

 

[bcrowell]

You tagged this "A" (advanced), meaning that you want answers at the level of a graduate course, but your question is written at more of a "B" or "I" level.

These tiny ripples travel outwards at 'c' and the amplitude fall off with inverse if distance (1/r), while the tidal gravity is a shorter range range phenomenon, because its amplitude falls off with the inverse square of distance (1/r2).

As far as I know, the only standard technical definition of tidal versus non-tidal gravity is that non-tidal gravity is what's measured by the Einstein tensor. By this definition, the far field of a gravitational wave is tidal; its Einstein tensor is zero. The far field falls off like $1/r$ simply because of conservation of energy.

Your nonmathematical description of where gravitational waves "originate" doesn't work. It doesn't work for the same reason that it wouldn't work in E&M.

By the way, could you please refrain from using bold face for long blocks of text? It gives the impression that you're shouting. Thanks.

 

[rdai]

You tagged this "A" (advanced), meaning that you want answers at the level of a graduate course, but your question is written at more of a "B" or "I" level.
As far as I know, the only standard technical definition of tidal versus non-tidal gravity is that non-tidal gravity is what's measured by the Einstein tensor. By this definition, the far field of a gravitational wave is tidal; its Einstein tensor is zero. The far field falls off like $1/r$ simply because of conservation of energy.

Your nonmathematical description of where gravitational waves "originate" doesn't work. It doesn't work for the same reason that it wouldn't work in E&M.

By the way, could you please refrain from using bold face for long blocks of text? It gives the impression that you're shouting. Thanks.

Hi bcrowell,

First of all, thanks a lot for your response!

Second of all, I accept your suggestion of "By the way, could you please refrain from using bold face for long blocks of text? It gives the impression that you're shouting."

Third of all, what you quoted in your response was not given by me, but given by another respectful SENIOR member of another forum similar to yours here. I respect his seniority and his knowledge.

Fourth of all, even though you did NOT explicitly say the word, it seems that you DISAGREE with what Jorrie said (as you quoted), which is meaningful to me since I am here seeking either confirmation or disagreement on what I learned from Jorrie from another forum site.

Fifth of all, I agree that mathematical expression is important, but my humble opinion is that if Einstein is alive, he would be VERY GOOD at explaining his ingenious mathematical works in non-mathematical terms, which is important to this world (not sure if you or anyone else would agree with me on this here :) ), and that's why he is NOT ONLY considered as a scientist but also considered as a GREAT PHILOSOPHER.

Thanks again
Ron

 

[bcrowell]

Hi, Ron. I see -- sorry about the confusion as to what you were writing rather than what you were quoting.

Fifth of all, I agree that mathematical expression is important, but my humble opinion is that if Einstein is alive, he would be VERY GOOD at explaining his ingenious mathematical works in non-mathematical terms, which is important to this world (not sure if you or anyone else would agree with me on this here :) ), and that's why he is NOT ONLY considered as a scientist but also considered as a GREAT PHILOSOPHER.

PF welcomes discussion at a nonmathematical level. However, you picked the "A" tag for the level of this thread, which indicates that you wanted answers at the mathematical level of a graduate course. Since that doesn't seem to be what you actually wanted, I'll request that the level of the thread be changed to "I."

 

[rdai]

Hi, Ron. I see -- sorry about the confusion as to what you were writing rather than what you were quoting.
PF welcomes discussion at a nonmathematical level. However, you picked the "A" tag for the level of this thread, which indicates that you wanted answers at the mathematical level of a graduate course. Since that doesn't seem to be what you actually wanted, I'll request that the level of the thread be changed to "I."

Hi Ben,

Thanks again for your response.

First of all, my apology of confusion on how the system works here.

I don't really care which level it is marked...I guess what caused me to mark it as highest was trying to get attention from senior member like you. I guess it worked :). But now I learn how the system works here and next time I would tag the thread correctly.

Thanks
Ron

 

[rdai]

Hi Ben,

I have one more issue about what you said

The far field falls off like 1/r simply because of conservation of energy.

because as I read from online that Gravitational Waves only adds or extracts energy from the system but does NOT carry energy by itself since spacetime does not contain energy itself...

Would you agree with that?

Thanks
Ron

 

[bcrowell]

because as I read from online that Gravitational Waves only adds or extracts energy from the system but does NOT carry energy by itself since spacetime does not contain energy itself...

No, that's not true. It sounds like a misunderstanding or oversimplification of how energy works in GR.

 

[rdai]

Ben:

Thanks so much for your very quick response...However, it is easy for me to accept the other theory but hard to accept that Gravitational Waves could carry energy since space-time does NOT have any MASS, where would it's energy be stored if it does carry energy?

Thanks
Ron

 

[bcrowell]

Thanks so much for your very quick response...However, it is easy for me to accept the other theory but hard to accept that Gravitational Waves could carry energy since space-time does NOT have any MASS, where would it's energy be stored if it does carry energy?

Mass is not required in order to have energy. A laser beam has zero mass, but it has energy.

 

[rdai]

Ben:

Thanks again. Let me do more study. The first impression I got from your answer seems to be that because it has energy so that it has mass. I can accept that as long as it does contain energy like EM does...I believe there must be energy since you said so :)...it is very complicated issue to me even though you think it should be tagged as "I"...:)

Here is a link of chapter in a textbook talking about Gravitational Waves: http://www.lightandmatter.com/html_books/genrel/ch09/ch09.html

It says:

...
Now strictly speaking, we have only shown that gravitational waves can extract or donate mechanical energy, but not that the waves themselves transmit this energy. The distinction isn't one that normally occurs to us, since we are trained to believe that energy is always conserved. But we know that, for fundamental reasons, general relativity doesn't have global conservation laws that apply to all spacetimes (p. 148). Perhaps the energy lost by the Hulse-Taylor system is simply gone, never to reappear, and the energy imparted to the sticky bead is simply generated out of nowhere. On the other hand, general relativity does have global conservation laws for certain specific classes of spacetimes, including, for example, a conserved scalar mass-energy in the case of a stationary spacetime (p. 248). Spacetimes containing gravitational waves are not stationary, but perhaps there is something similar we can do in some appropriate special case.
...
Specifically, when one wants to discuss gravitational waves, it is usually possible to assume an asymptotically flat spacetime. In an asymptotically flat spacetime, there is a scalar mass-energy, called the ADM mass, that is conserved. In this restricted sense, we are assured that the books balance, and that the emission and absorption of gravitational waves really does mean the transmission of a fixed amount of energy.

Thanks again
Ron

 

[bcrowell]

Your quote from #10 is a quote from my own book.

 

[rdai]

Your quote from #10 is a quote from my own book.

really? :-) so this link is your link: http://www.lightandmatter.com/html_books/genrel/ch09/ch09.html ......that's where I found that Gravitational Waves does not follow energy conservation...that Gravitational waves does not transmit energy...

Since that's your book, then I guess that you do mean that...:-)

I need to digest what you said in your book and what you said above...I am a bit confused because they don't sound the same :-)...let me study more...

 

[bcrowell]

really? :-) so this link is your link: http://www.lightandmatter.com/html_books/genrel/ch09/ch09.html ......that's where I found that Gravitational Waves does not follow energy conservation...that Gravitational waves does not transmit energy...

General relativity does not have conservation of energy in all cases. However, in an asymptotically flat spacetime we do have conservation of energy. Real-world detection of gravitational waves can be analyzed in terms of an asymptotically flat spacetime. Gravitational waves do transmit energy.