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Let's assume a person is close enough to an object in space time to be able to observe it's gravitational effects and the light coming from it. If that object suddenly pops out of existence (hypothetical situation), what will the person observe first,

  1. The gravitational field's absence
  2. The object disappearing (light stops coming)

P.S.- pardon me for the noobness of this question, physics isn't one of my strongest subjects.

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it's an interesting question. It could ask about any violent transient effect that produces light and gravitational waves, though "popping out of existence" is the ultimate step function.

electromagnetic (EM) radiation is slowed very slightly by the presence of interstellar medium (especially by free electrons) and it's wavelength dependent. The image below from this answer shows the lower frequency radio waves arriving later than the higher frequency ones due to such an effect.

The farther away an object is, the larger the time difference, so this technique can be used to determine a likely distance for a given object.

So if you relax the term "light" to include a wide range of wavelengths which many astronomers now do, you can see a quite a big delay.

Answers to How fast can and do gravitational waves travel? say that gravitational waves generally travel at the speed of light, and answers to Have more recent LIGO/VIRGO gravitational wave measurements narrowed down the speed of gravity further? addresses experimental confirmation. I've never heard of an "index of refraction" for gravity that deviates from unity and could slow it with respect to the speed that an EM wave would travel between the same two points, so I think it's probably safe to assume that it will always come before the EM waves.

enter image description here

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    $\begingroup$ Alright, Thanks for the answer. $\endgroup$ – quantumbiker Dec 26 '19 at 15:12
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    $\begingroup$ @quantumbiker Also, we don't normally answer impossible hypothetical questions on this site. It gets tricky giving scientifically precise answers when the scenario itself contradicts the laws of science. ;) We need to use GR (General Relativity) to precisely answer your question about gravitational waves, but GR says that mass-energy cannot pop into or out existence. $\endgroup$ – PM 2Ring Dec 27 '19 at 13:24
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    $\begingroup$ Yeah, I understand, I was just trying to find a way to create a situation where an event might have an instant effect. I just wanted to get the idea whether gravity is a property of space or time, but then you used the term general relativity and then I realised it's a property of spacetime. Thanks anyways :)( please excuse the terminology if it's not technically correct, I'm just a hobbyist who's trying to grasp these concepts...) $\endgroup$ – quantumbiker Dec 27 '19 at 18:00
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    $\begingroup$ @quantumbiker In addition to Astronomy SE there is Physics SE at one end of the spectrum and Worldbuilding SE at the other end. It's great to be curious about these things; you may find several existing and answered questions here and in those sites that address your interests, and if one leaves something unanswered for you you can always ask a new question and link back to an old answer. $\endgroup$ – uhoh Dec 27 '19 at 23:55
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    $\begingroup$ @quantumbiker Gedankenexperiments are obviously a recognized way to address problems in physics for sure and that's what you were doing here, introducing a step-function and asking about how it might propagate. But in Stack Exchange there is some resistance to hypothetical/impossible scenarios because sometimes people just ask random impossible questions without thinking things through, and it's hard to tell the difference from a two-sentence question that doesn't show evidence any prior reading. $\endgroup$ – uhoh Dec 27 '19 at 23:58

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