# B Gravitational Waves @ relativistic speed?

1. Mar 10, 2016

### tionis

What would happen if I were to fly toward a gravitational wave pulse at relativistic speed? Would I be destroyed by the Doppler-shifted pulse? Would the wave become visible?

2. Mar 11, 2016

### rootone

I don't think anyone has done that yet, so nobody knows.

3. Mar 11, 2016

### pervect

Staff Emeritus
The wave would be stronger. I don't see any reason why you'd see it. Being destructive is remotely possible, but would require a very energetic wave and/or an extremely high value of the relativistic velocity / gamma factor.

4. Mar 11, 2016

### tionis

Thx, rootone and pervect. I have so many disjointed thoughts about GWs, that I don't even know where to begin, but I will try.

First, are GWs a distinct form of spacetime, meaning it's a form of spacetime that moves at relativistic speed (curving the geometry of it), whereas normal space (flat) is just sitting there? If so, then, for example, would relativistic bodies such as the protons in the LHC detect in their frame of reference a stronger opposing energy or curvature when encountering a GW that would make them deviate from their trajectory, or perhaps even boost them depending of where the GW pulse came from?

Second, would there be any visible effects that would betray the presence of an approaching GW pulse such as the lensing of background stars or galaxies while approaching the GW pulse at close to c?

5. Mar 11, 2016

### tionis

What I'm asking here is that since the LHC proton beam is already going at close to c, wouldn't a GW pulse boost the proton past c? Since it's space that is moving at c, there wouldn't be any violation if the proton were to ride the wave, no?

6. Mar 11, 2016

### A.T.

The GW approaches you at c, just like the light from the distant Galaxies. So before the GW reaches you, you also won't see any light that met it.

7. Mar 11, 2016

### tionis

I'm sorry, I've forgotten that I couldn't see any stars or light because it would have been Doppler-shifted to the invisible part of the spectrum as I approached c. But since GWs are spacetime in motion, it should generate some sort of radiation i.e, Hawking/Unruh, no?

8. Mar 11, 2016

### A.T.

You can user other detectors than your eyes. And stars emit frequencies below the visible range, which would be shifted into that range.

9. Mar 11, 2016

### tionis

Very true. I should simplify my scenario:

Suppose space was devoid of any luminous object and it was just me in a spaceship traveling at close to c. Ahead of me, a pulse of gravitational waves goes off and now I'm in a collision course with a GW on steroids (because of the Doppler boost). What effects would I experience? Would my spaceship be tear apart by the tremendous energy of the GW? Or maybe even start moving backwards as it is carried by the GW?

I mean there are bodies in space moving at and close to the speed of light. Surely these bodies encounter GWs all the time. And because they are moving at tremendous speeds, the GWs in their frame of reference have more energy, so there must be an energy contribution. How do, for example, protons going at close to c deal with a boosted GW?

10. Mar 11, 2016

### tionis

I have another question: what is the technical name of the spacetime GWs occur in? Do they occur in curved spacetime and continue to exist in curved spacetime, or as soon as they leave the source they become something else like flat spacetime?

IOW, would it be correct to say that the recently detected GWs occurred in Kerr spacetime (curved) and were detected in Minkoswki (flat) space?

11. Mar 11, 2016

### Staff: Mentor

No. There's only one spacetime in the universe; in some regions it is highly curved and in other regions it is less highly curved. Solutions like the Kerr and Minkowski spacetimes may be more or less good approximations to the local curvature in a particular region, but neither comes even remotely close to describing the curvature in the local neighborhood of two colliding black holes.

12. Mar 11, 2016

### tionis

OK, Nugatory: what do we call the spacetime region where gravitational waves exist? Do we just call it ''spacetime?''
But as these waves travel, they depart from a flat spacetime, right? IOW, they carry an intrinsic curvature with them. Why doesn't this particular propagating spacetime metric have an assigned name to it?

13. Mar 11, 2016

### pervect

Staff Emeritus
I was thinking about this question more, fleshed it out a bit more, and realized that I didn't know for sure. First let me describe the detailed version of the revised question.

We have a gravitational wave, characterized by a dimensionless strain function h(t), with the peak of h(t) being $10^{-21}$ and "chirps" from 35 to 250 hz, based on what Ligo measured. What hapens when we do an ultrarelativistic boost?

Well, it's a transverse wave, so h(t) shouldn't change. It should still be $10^{-21}$ after the boost. But the chirp frequency should go up, the wavelength should go down. Suppose we assume that we boost the chrip frequency to, say 3.5 - 25 Thz, which if the pulse were electromagnetic, would put it into the visible range at the low end, and well into the ionizing range at the high end. This should put the wavelength of the gravitational wave at the atomic level, where I'd naievly expect the best coupling to atoms. What happens to, say, a target atom in the wave?

I don't know. The effective energy density goes up like $\dot{h}^2$, so we've increased that by $10^{22}$, the $\gamma^2$ dependence I'd expect. But we still have a very small value of h(t), it just happens faster. Do we have enough energy density to potentially do anything? I can't rule it out - I suppose I could do more calculations but I haven't. Would it couple to matter effectively enough to do anything? I don't see how, but I don't feel confident I understand all the potential mechanisms at this point.

Perhaps more to the point is the question - at what value of h(t) would we start to see observable and/or ionizing effects on an atom? Can we calculate this classically, or do we need a theory of quantum gravity?

14. Mar 11, 2016

### tionis

Good question. I was hoping for a classical explanation. That is why I boosted the GWs in the thought experiment. Let me ask you another question: can I use the reference frame of the GW pulse to see how my spaceship would look, or is this forbidden--meaning just like the photon, GWs don't have one?

15. Mar 11, 2016

### tionis

I'm trying to workout all the consequences that I would encounter if I were to have a head-on collision with a pulse of GWs at relativistic speed... and it just occurred to me that my time, according to a remote observer, would also be affected not only by my relative speed (close to c), but also by my interaction with the GW pulse. What happens to my clock as viewed by a remote observer? Would I notice anything different happening to time in my ship as the GW pulse hits me?

16. Mar 11, 2016

### Staff: Mentor

No, they aren't. Spacetime doesn't move; it just is. GWs are just a spacetime geometry that has ripples in it. Remember that "time" in spacetime is just another dimension; it's part of the geometry, not an external parameter.

It does; it's called a gravitational wave.

17. Mar 11, 2016

### tionis

Hi, Peter. I don't quite understand when you say spacetime doesn't move, but has ripples in it. What is the difference? And these ripples move at c, so it appears that we treat time, when measuring GWs pulses, as an independent parameter, don't we?

Also, would you please address my post #15. I really want to know what happens. Thanks

18. Mar 11, 2016

### tionis

I did a search on Wiki and it appears that the term I'm looking for is 'p-p wave spacetime.' But now I'm not so sure. Is it correct to say that what we detected was a p-p wave spacetime? Is it correct to say that the p-p wave originated in a Kerr spacetime?

Are physicists going to define GWs by the spacetime they originate in? For example: when a GW occurs do to a binary collision of black holes, is the corresponding wave going to be called a Kerr GW? If we detect cosmological GWs, would they be called FLRW GWs?

19. Mar 11, 2016

### Staff: Mentor

Saying that "spacetime is a 4-dimensional geometry" is a simple description. (Not all 4-dimensional geometries have ripples in them; but a spacetime that contains gravitational waves does.) A 4-dimensional geometry is a perfectly well-defined mathematical object. One of the 4 dimensions is "time", so the 4-dimensional geometry of spacetime contains all the information about how things within spacetime "move".

But saying that the 4-dimensional geometry itself "moves" doesn't even make sense. Where would it move to?

20. Mar 11, 2016

### Staff: Mentor

If we consider the "ripples" as things moving within spacetime, yes, they move at c. But there is another way of viewing them: they are just part of the 4-dimensional geometry of spacetime, and the crests and troughs of the ripples lie along particular kinds of curves (null curves) in that 4-dimensional geometry.

No. "Time" is one of the 4 dimensions; when we say something "moves", we are being sloppy. What we should say, to be perfectly precise, is that the something we are interested in is described by a curve, or a family of curves, in the 4-dimensional geometry. "Time" and "space" are just ways of labeling the points on the curves.

No. We didn't detect a "spacetime". We detected a particular piece of the geometry of the spacetime we are already in.

GWs don't "originate in a spacetime". "Spacetime" means the entire 4-dimensional geometry of the universe--not just the universe at a single instant, but the entire history of the universe. There aren't different spacetimes for different parts of the universe; there is just one spacetime, the entire universe.