Gravitational Wave Creation: Is a Stationary Wave Possible?

[pelinkovac]

TL;DR

A couple of questions regarding Clutton Brock's 1965 paper and the nature of gravitational waves (10.1038/2071079a0).

Hello,

Apart from the graviton postulate, which would permit such a mechanism, my question is: would a similar mechanism be possible with a stationary wave? (the simplest scenario I can immagine is of two opposing waves).

My background is in DSP and Acoustics so I might get things wrong (a reason why I tend to stick to my field), would such a wave have a constant local amplitude?

Another question which relates (and comes also from an experiment on a physical modelling of a vibrating toroidal membrane) is; If the boundary conditions are unbounded i.e. the size of the universe is "infinite", permitting "infinite" wavelengths, in terms of frequency (of the gravitational waves) the possibility is to have components which tend to zero Hertz (a term which in DSP is defined as "DC offset"), would that have any measurable consequences?

Thank You.

https://ui.adsabs.harvard.edu/abs/1965Natur.207.1079B/abstract

 

[PeterDonis]

Summary:: A couple of questions regarding Clutton Brock's 1965 paper and the nature of gravitational waves (10.1038/2071079a0).

Unfortunately the paper appears to be paywalled so I can't read it.

Apart from the graviton postulate, which would permit such a mechanism

What is "the graviton postulate", what is "such a mechanism", and why do you think the graviton postulate would permit such a mechanism?

would a similar mechanism be possible with a stationary wave?

What do you mean by "a stationary wave"? If you mean a gravitational wave that only varies in space, not time, no such thing is possible, for the same reason it isn't possible with EM waves: gravitational waves have to travel at the speed of light.

the possibility is to have components which tend to zero Hertz

This is impossible in vacuum; see above. "DC" EM phenomena take place in a material medium, not vacuum.

 

[pelinkovac]

Unfortunately the paper appears to be paywalled so I can't read it.
What is "the graviton postulate", what is "such a mechanism", and why do you think the graviton postulate would permit such a mechanism?

I'm sorry, it seems the only source left is pay-walled: "The Wheeler-Feynman formulation of electrodynamics postulates a time-symmetric solution, with an advanced field as well as a retarded field [...] Presumably, a similar formulation may be made for the graviton..." and continues "The advanced wave, instead of being converted into radiation reaction, will be propagated to the remotest parts of the universe with negligible attenuation"

What do you mean by "a stationary wave"? If you mean a gravitational wave that only varies in space, not time, no such thing is possible, for the same reason it isn't possible with EM waves: gravitational waves have to travel at the speed of light.

A stationary wave would be the opposite, a wave which oscillates in time but the amplitude profile doesn't vary in space. A simple yet effective definition on https://en.wikipedia.org/wiki/Standing_wave
And I would please like to know the argument on why such thing should be impossible. I'm sorry this being my first post, so I need to pose the questions properly but please motivate your answers, i am here to learn. Thank You.

This is impossible in vacuum; see above. "DC" EM phenomena take place in a material medium, not vacuum.

Thank You for elucidating, I saw nothing above, just another impossible. Maybe I'm wrong at considering space-time a medium?

I have been reading and have been aware of this forum for many years now and have managed to always find answers to my questions. This was my first (and probably last) post about something I truly wanted to learn and go in depth with, I will search for other resources. Thank You "kind" sir for all the knowledge shared.

 

[PeterDonis]

The Wheeler-Feynman formulation of electrodynamics

Which, IIRC, turned out not to work, because there was no way to account for effects like the Lamb shift that required self-interaction.

Also, I don't see what this has to do with "matter creation".

A stationary wave would be the opposite, a wave which oscillates in time but the amplitude profile doesn't vary in space.

This is also not possible for a gravitational wave in vacuum. See below.

I would please like to know the argument on why such thing should be impossible.

Because there is no such solution to the wave equation in vacuum. The wave equation in vacuum, schematically, is (in the simple one-dimensional case, since that's enough for this discussion)

$$
\frac{\partial^2 A}{\partial t^2} = c^2 \frac{\partial^2 A}{\partial x^2}
$$

Where $A$ is the wave amplitude and $c$ is the invariant speed of the wave in vacuum (the speed of light, in our actual universe, but mathematically it can be any invariant speed). Obviously any solution to this equation must vary with both $t$ and $x$.

 

[PeterDonis]

Maybe I'm wrong at considering space-time a medium?

It's not a material medium, which is the kind that is required for "DC" effects.

Some physicists have hypothesized that spacetime could be treated like a "medium" in some respects, but it wouldn't be a material medium and wouldn't share the properties of a material medium.

 

[DrStupid]

Because there is no such solution to the wave equation in vacuum. The wave equation in vacuum, schematically, is (in the simple one-dimensional case, since that's enough for this discussion)

$$
\frac{\partial^2 A}{\partial t^2} = c^2 \frac{\partial^2 A}{\partial x^2}
$$

Where $A$ is the wave amplitude and $c$ is the invariant speed of the wave in vacuum (the speed of light, in our actual universe, but mathematically it can be any invariant speed). Obviously any solution to this equation must vary with both $t$ and $x$.

What's wrong with $A = A_0 \cdot \sin \left( {k \cdot x} \right) \cdot \sin \left( {k \cdot c \cdot t} \right)$?

 

[er404]

Which, IIRC, turned out not to work, because there was no way to account for effects like the Lamb shift that required self-interaction.

This is not correct, although that was Feynman's assumption.

From: https://arxiv.org/abs/1509.06040

"But when Feynman turned his attention to the quantum level, he noted that certain relativistic effects, such as the Lamb shift, required some form of self-action of a charge. Unable to reconcile this with his assumption that self-action cannot be allowed in a direct-action theory, he abandoned it. However, that assumption was apparently not correct. It was based on the idea that all interactions involve energy transfer, which is not the case at the quantum level. In the early 1970’s, Davies plunged onward, and provided a fully developed quantum version of the direct-action theory[4]. This theory incorporates the fact that, at the quantum level, currents are indistinguishable, so there is no way to say whether or not a given current is undergoing self-action. However, this does not result in infinities, since the self-action does not lead to energy transfer from a current to itself. "

 

[PeterDonis]

What's wrong with $A = A_0 \sin (k \cdot x) \sin (k \cdot c \cdot t )$?

It's a function of both $x$ and $t$, so it's consistent with what I said.

 

[DrStupid]

It's a function of both $x$ and $t$, so it's consistent with what I said.

It's a standing wave and your post above sounds like that's not possible.

 

[PeterDonis]

It's a standing wave

No, it's not. It's a function of both $x$ and $t$. A standing wave, in the usual interpretation of that term, would be a function of $x$ only. A "stationary wave", as that term is being used by the OP, would be a function of $t$ only.

 

[DrStupid]

A standing wave, in the usual interpretation of that term, would be a function of $x$ only. A "stationary wave", as that term is being used by the OP, would be a function of $t$ only.

No and no (see the Wikipedia entry pelinkovac already posted above). The standing wave as used by the OP is a function in x and t. It has even been mentioned that such waves can be generated by 2 opposing traveling waves (e.g. ${\textstyle{1 \over 2}}A_0 \cdot \sin \left[ {k \cdot \left( {x + c \cdot t} \right)} \right] + {\textstyle{1 \over 2}}A_0 \cdot \sin \left[ {k \cdot \left( {x - c \cdot t} \right)} \right]$).

Btw: Your equation has solutions that are not functions in both x and t.

 

[PeterDonis]

The standing wave as used by the OP is a function in x and t.

Not according to the OP:

A stationary wave would be the opposite, a wave which oscillates in time but the amplitude profile doesn't vary in space.

"The amplitude profile doesn't vary in space" is the key phrase. By contrast, I was using "standing wave" this way:

a gravitational wave that only varies in space, not time

I see that the Wikipedia page uses "standing wave" to mean neither of those things, but I was not going by what the Wikipedia page says, I was going by what the OP said as quoted above.

All that said, I don't think the OP's underlying question about "matter creation" actually depends on whether the gravitational wave in question varies in both $x$ and $t$ or not.

The equation has solutions that are not functions in both x and t.

Such as?

 

[DrStupid]

"The amplitude profile doesn't vary in space" is the key phrase.

As it is not clear what that actually means I refer to "(the simplest scenario I can immagine is of two opposing waves)" as the key phrase. Maybe we need a clarification from the OP.

Such as?

$A = k \cdot x$