I Disappearing Sun: A Thought Experiment on the Effects of Gravity and Light

[Byron Forbes]

TL;DR Summary

Speed of gravity thought experiment

Thought experiment - the sun suddenly disappears.

Light stops after 8 mins and, according to LIGO and Albert, so will gravity.

The light part is easy to understand - the photons are already in flight so they get here 8 mins later.

But what about the gravity? Assuming that the gravity did indeed last for 8 mins then how would it do so? Would it last at the same magnitude for the entire 8 mins and then cease completely or would it drop off gradually?

But most importantly, how would it last at all? If it did, wouldn't it mean there was something between the sun and Earth that was coupling them even before the sun disappeared? Otherwise, how could the gravity possibly be sustained?

 

[PeroK]

The Sun can't suddenly disappear without the conservation laws that govern GR being violated.

 

[Byron Forbes]

The Sun can't suddenly disappear without the conservation laws that govern GR being violated.

Alright.

Let me try again. So another sun enters our solar system and hits our sun, creating one huge mass traveling away from us at a substantial speed.

Let 10 mins or so pass so that the gravity from this new mass is reaching us simultaneously i.e acting like a single mass.

In another 10 mins the g pull will be less than 10 mins prior. At any moment in that time, the g pull will be greater than if the speed of gravity was infinite. So when the new mass is at a distance that would normally create a pull of, say, a little less than G, the Earth will still feel a pull of G.

How? If there is nothing in the space between the suns and Earth providing some sort of coupling (pull) then how could this be so?

 

[PeroK]

How? If there is nothing in the space between the suns and Earth providing some sort of coupling (pull) then how could this be so?

This is how: $$G_{\mu \nu} = 8\pi G T_{\mu \nu}$$

 

[Byron Forbes]

This is how: $$G_{\mu \nu} = 8\pi G T_{\mu \nu}$$

There's 8 pies between us and the sun? :)

 

[Ibix]

Let me try again. So another sun enters our solar system and hits our sun, creating one huge mass traveling away from us at a substantial speed.

...so this second sun has come past us, and changed our local gravitational field.

Let 10 mins or so pass so that the gravity from this new mass is reaching us simultaneously i.e acting like a single mass.

So this is silly - we'd have been affected by the gravity of the second sun for a long time before the collision. There'd be nothing especially notable about the moment of the collision.

In another 10 mins the g pull will be less than 10 mins prior.

Well, gravity isn't a force in general relativity. And it's quite difficult to imagine the Earth remaining peacefully in place as another sun comes tearing past it. So it's a little difficult to work out exactly what you mean here. Are you intending on Earth (or maybe a rocket) doing something like holding its position with respect to distant stars while the combined suns move away? If so, it seems likely that the thrust required to do so would reduce over time after the collision, yes.

At any moment in that time, the g pull will be greater than if the speed of gravity was infinite.

Maybe. What model are you thinking of in which the speed of propagation of gravitational changes is infinite?

How? If there is nothing in the space between the suns and Earth providing some sort of coupling (pull) then how could this be so?

The same way it works every day - curvature of spacetime.

 

[Byron Forbes]

The same way it works every day - curvature of spacetime.

So the GR explanation is that spacetime is yet to be changed?

So in other words, GR has zero physics explanation, just concept and math?

 

[weirdoguy]

So in other words, GR has zero physics explanation

Please define "physics explanation".

 

[Ibix]

So the GR explanation is that spacetime is yet to be changed?

So in other words, GR has zero physics explanation, just concept and math?

I don't understand. You seem not to have any problem with the idea that Earth remains in orbit around the Sun every day because of the curvature of spacetime. Why is spacetime curvature suddenly not a sufficient explanation with a different situation?

 

[PeroK]

So the GR explanation is that spacetime is yet to be changed?

So in other words, GR has zero physics explanation, just concept and math?

The Einstein Field Equation in post #4 is conceptually similar to Maxwell's equations for electromagnetism.

GR: Mass tells space how to curve, space tells mass how to move:

EM: Charges create EM fields, EM fields tell charges how to move.

That's the physics of it. To solve any particular problem, you need to set up the appropriate Einstein or Maxwell equations and, yes, do the math.

 

[Dale]

How? If there is nothing in the space between the suns and Earth providing some sort of coupling (pull) then how could this be so?

Umm, spacetime does provide “some sort of coupling”. The EFE is a non-linear equation. I am not sure how that is relevant, since the issue you describe would happen with any local theory whether it is linear or not. I don’t get your objection here. You describe a situation with a propagation delay but ask about coupling.

 

[sophiecentaur]

Summary:: Speed of gravity thought experiment

Thought experiment - the sun suddenly disappears.

That's been dealt with in the thread.

So another sun enters our solar system and hits our sun, creating one huge mass traveling away from us at a substantial speed.

Another Sun arriving at any speed would affect Earth whilst it was on its way so there wouldn't be any sudden change in the gravitational field acting on us. You don't need any GR theory to predict the sort of thing that would happen. Nothing would involve a step change in our situation. Planetary orbits would be distorted to a greater or lesser extend, depending on whether it was a direct hit, a near miss or a distant miss. I'd suggest that any 'final collision' would actually be spread over a long time as they merged and received radiation increased.

Effects of the approaching star would be visible as stars and planets would appear to be disturbed by the effect on our orbit. A suitable (t = D/c) delay would apply to what we would observe during its approach.But whatever happened, that delay would spread any effect over a long period. The star would not be approaching at significantly 'relativistic speed'. I can say that because the blue shift of any observed star has never been excessive.

 

[Vanadium 50]

o in other words, GR has zero physics explanation, just concept and math?

Please define "physics explanation".

That would be concept plus math.

 

[Dale]

That would be concept plus math.

And experiment, which GR also has

 

[Buzz Bloom]

But what about the gravity? Assuming that the gravity did indeed last for 8 mins then how would it do so? Would it last at the same magnitude for the entire 8 mins and then cease completely or would it drop off gradually?

Hi Byron:

I think I have gotten an understanding of the question you are asking. You want to understand the phenomenon of the delay in the gravitational effect of the sun on the Earth if the sun suddenly does something very odd which causes a large change in the Earth's orbit. If this is what you are seeking, in order to avoid answers that are no help to you, you need an example of the sun-Earth situation that does not violate knows laws of physics. The following is my try to create such an example. The key is to focus only on the gravity effects. I think the answer I am presenting is not exactly correct, but the incorrecteness is rather small and not releveant to the question you are asking as I understand it.

Assume a system with an object S whose mass is (2 x 10³⁰ kg) approximately equal to the sun's mass, and a second object E with a mass (6 x 10²⁴ kg) approximately equal to the Earth's mass. Assume E and S are in circular orbits about the center of gravity of S and E. Assume the distance between S and E is approximately 150,000,000 km. Assume that S contains ejectable material accounting for 99% of S's mass. Assume that S has an engine which ejects material towards E at a velocity 0.9 c relative to S as it moves away from E. The rate of the material ejected per second is a constant. Since the mass of S gets smaller (by the amount of ejected material) at a constant rate, it's acceleration away for E will increase until all of the ejectable material has been ejected. The question is: How long will it take from the time that S begins to ejects material for the motion of the Earth to begin to change from its circular orbit?

The answer is (approximately) 8 minutes.

Otherwise, how could the gravity possibly be sustained?

Answer: Gravity is manifested by the shape of space as it is distorted by mass. It takes 8 minutes for the change in the shape of space due to the movement of S to reach E. The change in space's shape near E will afterwards change gradually.

Regards,
Buzz

 

[A.T.]

GR has zero physics explanation, just concept and math?

You mean just like Newtonian gravitation? Yes.

 

[Richard R Richard]

But what about the gravity? Assuming that the gravity did indeed last for 8 mins then how would it do so? Would it last at the same magnitude for the entire 8 mins and then cease completely or would it drop off gradually?

You have sparked my imagination
In your thought experiment, the mass cannot simply disappear from the region instantly. No object with “non-zero” mass travels at the speed of light.
Suppose the sun explodes, 500 seconds later we would see the explosion, but what about gravity? you wonder ...
Well, any disturbance of space-time also travels as a wave and those waves move at the speed of light, therefore also at 500s you would begin to notice something different in gravity, even so during that period the Earth would rotate, for the same geodesy that he had been doing before the explosion.
Let us now assume that the entire mass of the sun reaches 0.99c of radial velocity, following the rough calculation, the ejected mass would take 505.05s to reach the earth, that is, in 5.05s we would be impacted by the ejected mass, that is, during that In the interval we could think that the mass of the sun is distributed in a concentric spherical cap, increasing in radius and surface, but that it reduces its thickness while conserving the volume, with that distribution of mass as a function of time, a calculation of the gravity, both according to Newton and also according to Einstein with GR, with the first there would be no difference in gravity, during those 5.05s, but if there would be any difference when applying a metric other than Swcharzchild, we would notice that the tidal force would vary, and the geodesic described by the Earth I understand would tend to decrease in radius.
During the 5.05 after seeing the explosion we would see how the sun increase in size until we would suffer a devastating collision ... Well ... but suppose that this collision does not destroy the Earth and we can remain there as simple observers ... after the cap of mass of the sun, there would no longer be mass (or energy density) as a source of curvature at the origin of coordinates, the curvature of spacetime would become zero and the trajectory of the planet would begin to be a straight line
During the brief period in which the solar mass passes through the position, we would notice a change in the gravitational field, or we would notice a gravitational wave (change of gravity with time).
It should be noted that in the interior of a centered hollow sphere of matter, gravity is zero.
What happens after this is simple, since 0.99c is greater than the escape velocity of the sun's gravity, the mass would never collapse back on itself, so the space would ideally remain Minkowski plane.

 

[artis]

Isn't it true that while sun's gravity affects the motion of planets within the solar system including ours the very gravity that we as objects of mass feel here on Earth is almost exclusively due to earth?

Also as to the OP, I think even though changes in EM field travel at the same speed as those in gravity, but unlike EM field gravity cannot be switched off because it's source is mass and one cannot simply get rid of mass like that, we can move mass and do other stuff with it but we cannot switch it off like we can a radio transmitter of EM waves, so this thought experiment is just a sci-fi one.

 

[jbriggs444]

Isn't it true that while sun's gravity affects the motion of planets within the solar system including ours the very gravity that we as objects of mass feel here on Earth is almost exclusively due to earth?

Yes. The force that we "feel" and call gravity here on the surface of the Earth is from the Earth's pull. The sun pulls both the Earth and ourselves nearly equally. The only thing left to feel from the sun is the minor discrepancy that we typically notice only as the difference between spring and neap tides.

Technically, one does not feel uniform gravity at all. It is an inertial force that pulls all parts of one's body equally and leaves nothing to feel. What one actually feels are the strains on the body arising from the floor upon which one is standing or from the chair in which one is sitting.

 

[artis]

What one actually feels are the strains on the body arising from the floor upon which one is standing or from the chair in which one is sitting.

Or strains from pain from the ground unto which one (me) is falling after a miscalculated move (true story).

 

[Halc]

Isn't it true that while sun's gravity affects the motion of planets within the solar system including ours the very gravity that we as objects of mass feel here on Earth is almost exclusively due to earth?

Earth accounts for most of our local coordinate acceleration, yes. One cannot actually 'feel' gravity, as evidenced by the guys in the ISS being in nearly the same gravitational pull as us, but cannot feel it at all.

What we feel is the force of the ground on us from below, and that is of course from Earth since Earth is the thing applying that force.

Another example: You could be on the moon and 'feel' the gravity of the moon as weight force being applied from the moon-ground below you. That moon could be falling into a super-massive black hole with far more gravity than the moon, yet the gravity you 'feel' would still be about moon gravity. You could be on the side facing the black hole, and barring tidal forces (which is why I made our black hole super-massive), you'd not be sucked off the surface of the moon falling. Likewise, the Earth exerts less gravitational force on the moon than does the sun, so the path of the moon is always curved towards the sun even when it is between the two. Nevertheless, the moon is not sucked away from its orbit around the Earth.