# B Gravitational waves 50X total stars and not be felt?

1. Sep 19, 2016

### Albertgauss

Hi all,

On the subject of being able to feel gravity waves as a human without machines, I couldn't find a very definitive answer to what I was looking for. First, I reference the video:

at 40 tp 55 seconds.

Its called: LIGO, journey of a G wave.

They say in this clip that when the black holes that merged that were detected by LIGO, more energy was released in the gravity waves of that merger than 50 times all the stars in the universe combined. There was also no other ordinary matter around.

I couldn't figure out if such an event would have the same consequences as something like a quasar, super-super nova, etc. in some local stellar neighborhood. Let's say there is a solar system near the merger LIGO found the G-waves in but not close enough to get swallowed up. I know a quasar release of Electromagnetic energy would vaporize the solar system down to fundamental particles, but what if all that energy is in gravity waves? Is gravity so weak, as some of the other posts suggest, that 50 times E = m[c][/2] all-stars-in-the-universe would not have any effect because the weak effect of gravity negates the tremendous energy release talked about here? Or, is energy conserved, and 50 times E = m[c][/2] all-stars-in-the-universe is still 50 times E = m[c][/2] all stars-in-the-universe, no matter what form, and the gravitational waves from the merger will still vaporize the solar system? I can't figure out if I should imagine the same violent release of energy in such a merger through gravity waves that I imagine with the normal cosmic violent explosions of quasars, super-super nova, etc. or if I should imagine these ultra-energetic but super-weak gravity waves somehow passing through spacetime with hardly any influence on matter they encounter.

2. Sep 20, 2016

### Staff: Mentor

3. Sep 20, 2016

### Ibix

It's also worth noting that the video is talking about peak power output, not energy output. The total energy output is nothing to sneer at (three solar masses), but it is released over a very short time. That makes for awesome power figures, but it's not sustained as stars' output is.

4. Sep 20, 2016

### Albertgauss

Okay. I looked up some of the numbers. I read that other thread but it didn't help much. But I will make a crude calculation so I guess I did get that much out of that other thread.

First, you're right, they're talking about power more than 50 times all the stars in the universe in the video, not energy. Sorry, my mistake.

But here's what I did find (and maybe this will help with some of the numbers on this matter on this website):

From wiki:

https://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)

(Scroll down to 10^47)

and also wiki power order of magnitude

https://en.wikipedia.org/wiki/Orders_of_magnitude_(power)

(scroll down to Greater than one thousand yottawatts)

the energy released by the black hole merger detected by Ligo was 5.4(10^47) Joules. This compares with the most powerful gamma ray burst ever recorded which has 8.8×10^47 J. The power of the black hole merger is 3.6 × 10^49 Watts (yes, I got my power and energy straightened out here), which is above the record breaking luminosity for a gamma ray burst (quoted in power of 10^45 Watts, luminosity itself not mentioned for the GRB on the wiki site above). The duration of the merger pulse energy seems to be about 15 msec, too quick for a human being to perceive ordinarily. A google search of "gamma ray burst duration" immediately suggested 2.0 seconds as the duration of a Gamma Ray Burst. A human being can easily perceive 2 seconds.

For comparison, a solar flare is 10^25 Joules. Let's say the solar flare emitted by the surface of the sun spreads out over the surface of the sun when it begins. The ratio is 10^25 Joules divided by the 6(10^12) kilometers squared (sun surface area)= 1.67(10^12) Joules/km^2. A solar flare within a solar system causes lots of chaos, certainly. What surface area would the expanding gravity wave merger flare have to fill for the same ratio of energy to surface area as a typical solar flare at the sun's surface? I divide the merger energy 5.4(10^47) Joules by the ratio of 1.67(10^12) Joules/km^2 to get a surface area of 3.2(10^35) km^2. If you divide the surface area 3.2(10^35) km^2 by 4*Pi and take the square root you get 1.6(10^17) km for a radius. This is 17,000 light years.

So, the merger wave has to travel 17,000 light years for its passing energy to dilute over a sphere of enough area such that its energy per square meter matches a solar flare.

Within that 17,000 light years, would such an enormous amount of energy be felt? Would it vaporize planets and blow apart suns? Or would it just simply pass through since gravity is so weak? It seems to me that such energy should be perceived easily, as easily as a solar flare or greater is readily perceived electromagnetically. I say energy is energy, and if 10^47 Joules is spreading out within 17,000 years, it should cause the same havoc a GRB should. The electro-magnetic fields of GRB radiation push and destroy everything in their path, charged particles or not, and the E &M fields of such radiation really do carry energy and momentum. A gravity wave with this much energy also has energy and momentum and should also push around or destroy or anything in their path. I feel like the gravity waves inside 17,000 light years will vaporize suns and planets. I think anything with mass will feel all this energy. That's my opinion so far. Can anyone confirm if my opinion is correct or not?

5. Sep 21, 2016

### pervect

Staff Emeritus
The amplitude of a gravitational wave can be described by two components, $h_+$ and $h_x$. The energy flux, "a quantity that measures the rate of transfer of energy per unit area", is proportional to the square of the time derivative (rate of change) $\dot{h_+}^2 + \dot{h_x}^2$, where the "dot" represents taking the time derivative. See for instance http://www.tat.physik.uni-tuebingen.de/~kokkotas/Teaching/NS.BH.GW_files/GW_Physics.pdf, page 12, the section on "energy flux caried by gravitational waves", which unfortunately uses slightly different notation, choosing instead to write it the expression in terms of the amplitude and the frequency omega rather than the time derivative. But $d/dt \sin \omega t = \omega \cos \omega t$, so one can see that the factor of $\omega$ corresponds to taking the time derivative.

Ligo only measures one component of the GW, we'll call that component h. h is proportional to 1/r, and we know that h was $\approx 10^-21$ for Ligo at a distance of 410 Mpc from the Ligo page, https://dcc.ligo.org/LIGO-P150914/public . And we know that 1Mpc is about 3 million light years, see for instance https://www.google.com/search?q=Mpc+in+light+years&ie=utf-8&oe=utf-8. So I make the figure of 170000 light years as about 5000pc, or .005 Mpc.

This leads us to believe that at the distance of 17000 light years specified from the Ligo event, the amplitude h would be roughly on the order of 100,000 times larger That makes $h$ on the order of $10^-16$ rather than $10^-21$.

Now, I'm not absolutely positive what effect this would have on, say, a planet, but if we consider two test particles separated by a distance of the diamter of the Earth, their separation will change by about .001 microns. Which makes it reasonable to assume that not much happens to a planet, I think. Certainly nothing much happens to something smaller, like an astronaut in a spaceship.

The "why" of all this is trickier. An important point is that the energy in a GW is calculated as an average over at least one wavelengths, it's not possible to localize the energy as it is for, say, electromagnetism. This is well known, but hard to explain in popular language. What we can say, though, is that the it seems unlikely the GW's would be very destructive, based on the calculations of what happens in terms of the amplitude h, in spite of the large numbers for the energy of the GW. To go into more detail would require, I think, studying exactly how the energy of a GW is defined and computed - this can be done, but it's a relatively advanced subject.

6. Sep 23, 2016

### A.T.

I don't understand this argument. Like with all waves, it's not about the total energy of the wave, but how much energy is absorbed by the obstacles, which in turn depends on the specifics of the interaction.

Last edited: Sep 23, 2016
7. Sep 23, 2016

### Albertgauss

Hi all, I think this did answer my question. I think part of my confusion (which answers AT) is that I had trouble imagining such a large amount of energy causing so little effect. As I was thinking about gravitational waves, I was reaching too hard by analogy with what I knew about electromagnetic waves. I also battled in my mind that, even though gravitational waves carry so much energy, this form of energy might not cause noticeable effects. When you think about what processes occur as you go down the wiki table on energy orders of magnitude, the greater the energy, the more the catastrophe. I had a hard time accepting that, despite the abundance of energy, the spacetime stretch is very small. This must mean, somehow, that an enormous amount of energy is required to stretch spacetime. The only other analogy I can think of is that of E=m[c][/2]: it takes a lot of energy to make mass. The approximations given in pervects post gives the ballpark numbers I was looking for.

8. Sep 24, 2016

### A.T.

Even with EM waves you cannot directly relate total energy to damage. The absorbed energy usually depends on the wavelength and the properties of the object.

9. Sep 24, 2016

### GeorgeDishman

Yes, the question is how much damage would a very bright flash of light do to something that was almost perfectly transparent.