Mushy questions about gravitational waves

[Danijel Gorupec]

Few questions based on the analogy with light/sound waves. I suppose most cannot be answered strictly, but at least give me your hunches.

 

1. Should I expect that gravitational waves may reflect when they hit some sort 'wall'? Can such wall exist? Can we have phase-change and non-phase-change reflections? Can you suggest a 'wall' (either active or passive) that causes phase-change or non-phase-change reflection of gravitational wave?

 

2. I suppose gravitational waves can interfere? Is this a linear or non-linear process?

 

3. Can we imagine a standing gravitational wave? Can we imagine resonant cavities for gravitational waves (possibly allowing amplification)?

 

4. If we have multiple controlled sources of gravitational waves that act near-coherently, can we employ beam-forming - thus making a directional source of gravitational wave?

 

5. If directional gravitational antennas are possible, will such an antenna experience an impulse to the opposite side of the main gravitational lobe?

[studiot]

1 hour ago, Danijel Gorupec said:

Few questions based on the analogy with light/sound waves. I suppose most cannot be answered strictly, but at least give me your hunches.

 

1. Should I expect that gravitational waves may reflect when they hit some sort 'wall'? Can such wall exist? Can we have phase-change and non-phase-change reflections? Can you suggest a 'wall' (either active or passive) that causes phase-change or non-phase-change reflection of gravitational wave?

 

2. I suppose gravitational waves can interfere? Is this a linear or non-linear process?

 

3. Can we imagine a standing gravitational wave? Can we imagine resonant cavities for gravitational waves (possibly allowing amplification)?

 

4. If we have multiple controlled sources of gravitational waves that act near-coherently, can we employ beam-forming - thus making a directional source of gravitational wave?

 

5. If directional gravitational antennas are possible, will such an antenna experience an impulse to the opposite side of the main gravitational lobe?

Interesting questions.  +1

 

We know that (some) gravitational waves passing through the solar system experience gravitational deflection and redshift in the same way that light does.

So can we cause this ? I think we would need to grow alot to at least planetary size.

Yes they can interfere with each other, but reflection I'm not so sure about since they are not obstructed by matter, unlike light.

There are both linear and non linear models available.

[Markus Hanke]

22 hours ago, Danijel Gorupec said:

Should I expect that gravitational waves may reflect when they hit some sort 'wall'? Can such wall exist?

There is no known physical mechanism that can “shield” gravity in this way, so no reflection - in the sense that term is used for light e.g. - can happen. It is, however, possible to deflect gravitational waves, i.e. change their principle direction of propagation via interaction with background curvature, or other gravitational waves.

22 hours ago, Danijel Gorupec said:

I suppose gravitational waves can interfere? Is this a linear or non-linear process?

Yes they can, and in full theory of GR that is a highly non-linear process (but linear approximations can sometimes be used to describe this).

23 hours ago, Danijel Gorupec said:

Can we imagine a standing gravitational wave? Can we imagine resonant cavities for gravitational waves (possibly allowing amplification)?

Yes, the Einstein equations emit solutions - both in vacuum and in so-called null dusts - which can be physically interpreted as the equivalent of standing waves. I don’t know about the amplification bit, since this is a non-linear situation, so one would have to run the maths on it.

23 hours ago, Danijel Gorupec said:

If we have multiple controlled sources of gravitational waves that act near-coherently, can we employ beam-forming - thus making a directional source of gravitational wave?

This should theoretically be possible I think, though again, one would have to do the maths (which wouldn’t be trivial at all) to be absolutely sure. 

23 hours ago, Danijel Gorupec said:

If directional gravitational antennas are possible, will such an antenna experience an impulse to the opposite side of the main gravitational lobe?

I don’t understand this question…can you explain further?

[Danijel Gorupec]

8 hours ago, Markus Hanke said:

 

I don’t understand this question…can you explain further?

Thanks Markus... Because gravitational waves carry energy, I would suppose that they also carry momentum (Or not? I have a hard time imagining this). If gravitational waves do carry momentum, and if some source is emitting gravitational waves directionally (like a directional antenna), then I suppose the source will be receiving impulse in the direction opposite to the direction of emitted waves (possibly propelling itself through the space).

[Markus Hanke]

10 hours ago, Danijel Gorupec said:

I would suppose that they also carry momentum

Yes, they do “carry” energy-momentum.

10 hours ago, Danijel Gorupec said:

if some source is emitting gravitational waves directionally (like a directional antenna), then I suppose the source will be receiving impulse in the direction opposite to the direction of emitted waves (possibly propelling itself through the space)

That’s an interesting question (I never really considered sources of directional g-radiation), the answer to which I am not sure about. There are two main issues here that make this situation somewhat different from Newtonian mechanics:

1. The energy-momentum in a gravitational wave cannot be localised, and

2. There is no global law of energy-momentum conservation in curved spacetimes of this sort. 

Point (2) is to say that yes, energy-momentum is conserved everywhere locally in small neighbourhoods that can be considered approximately flat; but there is no such conservation law for larger, curved regions. Take careful note here of the difference between a conservation law being violated, and no such law existing in the first place.

In the absence of meaningful energy-momentum conservation (in the Newtonian sense), it is not at all clear to me whether or not a source of directional g-radiation would receive an impulse in the opposite direction. I’d say before even considering this issue one what have to first ascertain whether such a thing as a directional beam of g-radiation can even exist, which is in itself not clear. 

I’m very careful to commit to any definite answer on this, as this is one of those scenarios where ordinary Newtonian intuition can very quickly lead one down the wrong road. The best I can say is that it would be necessary to actually do the maths, which would be highly non-trivial.

[studiot]

Since you chose not to respond to my mushy comments, is there any reason I should add to them ?

[Danijel Gorupec]

25 minutes ago, studiot said:

Since you chose not to respond to my mushy comments, is there any reason I should add to them ?

Thanks for your comments... I didn't expect strict answers in the first place. For me, the most interesting part in your comment was about 'redshift' - are you talking about measured or calculated effect?

[studiot]

1 hour ago, Danijel Gorupec said:

Thanks for your comments... I didn't expect strict answers in the first place. For me, the most interesting part in your comment was about 'redshift' - are you talking about measured or calculated effect?

OK

Both, I believe.

Misner, Thorne and Wheeler include description and references in their chapter on gravity waves.

 

But I would say my most important point concerned was the sheer size of objects involved, seeing as you seem to be interested in what possibilities there are for manipulating gravity.

On 2/16/2023 at 1:58 PM, studiot said:

So can we cause this ? I think we would need to grow alot to at least planetary size.

 

You also need to be careful to distinguish between working in space and time separately  v spacetime.

A wave equation is an eqaution connecting space and time.

The ordinary (linear) wave eqaution allows separation of these two variables, by virtues of the linearity.

Gravity waves occur in spacetime, but as I said before linear ( ie linearised versions), so the model is essentially non linear.

This arises because the solutions to the wave equation, being a partial differential equation, contain arbitrary functions, and it is usual to choose the simplest.

But a gravity wave equation will have additional complicated (even complex) relativistic conditions that must also be met.

 

Considering your antenna:

Antennas are passive devices (and only thre dimensional at that), which means that they do not generate the required wave, that has to be done by somethng else, as does any modulating signal.

So you would still need all the paraphanalia already under discussion.

Also since the waves are actually 4D, what do the 'lobes' of such an antenna look like in 4D ?

Directional antennas are not impossible in theory because there is already a phenomenon called gravitational lensing (which again involves the big guns) under observation.

[Genady]

4 minutes ago, studiot said:

Directional antennas are not impossible in theory because there is already a phenomenon called gravitational lensing

Does gravitational lensing affect gravitational waves similarly to the EM ones? (I doubt, because of the non-linearity.)

[Markus Hanke]

54 minutes ago, Genady said:

Does gravitational lensing affect gravitational waves similarly to the EM ones? (I doubt, because of the non-linearity.)

I think this would depend. In principle both EM radiation and G radiation should propagate along the same geodesics, so for “ordinary” objects like stars etc and “ordinary” G waves the deflection angle should be nearly the same since any non-linear effects are negligible. However, if the wave length of the G radiation becomes very large, and/or the background field is very strong, I would imagine there might be situations were such effects cannot be neglected, and the deflection angles differ. I’m not sure though.

This may be relevant:

https://arxiv.org/abs/2001.01710

[Goldwinpie3]

I wonder if gravitational waves can carry or carry information?

[Genady]

26 minutes ago, Goldwinpie3 said:

I wonder if gravitational waves can carry or carry information?

They can and they do.

[swansont]

26 minutes ago, Goldwinpie3 said:

I wonder if gravitational waves can carry or carry information?

We make EM waves carry information by rapidly modulating them, which would be tough to do with gravitational waves.