Life on a planet near a black hole

[livelar]

Suppose life would evolve on a planet near a black hole, like the water planet on Interstellar. And just like on Earth, they eventually discover a theory of relativity and also how to send a rocket away from planet/black hole and back. Could they take advantage of the huge time dilation between the surface of the planet and the rocket? Like send a computer with a complicated problem that would take years to solve on the surface, but only hours on the rocket? Isn't this "free energy" in a way?

Also, if one would watch the rocket leave the surface, would they see it speed up exponentially much faster than it should, as time dilation gradually kicks in the further it gets from the black hole?

 

[pervect]

Suppose life would evolve on a planet near a black hole, like the water planet on Interstellar. And just like on Earth, they eventually discover a theory of relativity and also how to send a rocket away from planet/black hole and back. Could they take advantage of the huge time dilation between the surface of the planet and the rocket? Like send a computer with a complicated problem that would take years to solve on the surface, but only hours on the rocket? Isn't this "free energy" in a way?

I believe they could. But it'd hardly be "free" energy. You'd need enormous energy to get out of the gravity well. In "Interstellar", Kip Thorne added a gravitational flyby to get the needed energy, but the producers didn't include that in the final script.

Also, if one would watch the rocket leave the surface, would they see it speed up exponentially much faster than it should, as time dilation gradually kicks in the further it gets from the black hole?

That rather depends on what one "expects". Would this intelligent race develop Newton's laws, or would they, as in Greg Egan's "Incandescence", jump right to General Relativity?

 

[nitsuj]

lol what an interesting and funny consequence of differential aging.

 

[livelar]

I believe they could. But it'd hardly be "free" energy. You'd need enormous energy to get out of the gravity well. In "Interstellar", Kip Thorne added a gravitational flyby to get the needed energy, but the producers didn't include that in the final script.

Thats it.. way more struggle to get back would make so much sense, too bad it was omitted... That place is a relativistic mindf*ck, I wish they had explored it more.

That rather depends on what one "expects". Would this intelligent race develop Newton's laws, or would they, as in Greg Egan's "Incandescence", jump right to General Relativity?

How long would it take before life realized time runs slower on top of mountains? I think very plausible they'd jump straight to relativity :) Anyway thanks, finding a lot of "science of interstellar" blogs and articles keeping me busy for a while :)

 

[lekh2003]

I think very plausible they'd jump straight to relativity

In such a world, I can assume that relativity would be deeply embedded in classical physics. Even concepts like forces and kinematics would be discovered after relativistic effects.

 

[newjerseyrunner]

In such a world, I can assume that relativity would be deeply embedded in classical physics. Even concepts like forces and kinematics would be discovered after relativistic effects.

Unlikely, that requires pretty serious maths. Math that has to be built from simpler systems.

I'm not sure how you would come to that conclusion if you did not already understand that light has a constant speed. I would think they would come up with Newtonian physics and explain away things like light bending around the hole as a simple attraction and acceleration on the light.

 

[pervect]

I already mentioned Greg Egan's "Incandescence" once before, but I'll mention it again. Egan has a fictional race living on a small tidelocked object orbiting a black hole. The race doesn't have vision as we know it, and aren't even familiar with light, much less special relativity. Nonetheless, they manage to stumble onto a theory that's equivalent to General Relativity based on observations of "weight", the sort of weight one might measure with a spring-based scale that measures the force required to hold the body in place in the "frame" of the tidelocked body. The weight will be zero at the center of the tidelocked body, and will change as one moves away from the center. It turns out that the weight is proportional to the distance away from the center, the proportionality constant depends on the direction one moves in. (Choices of direction are radial, orbital, and perpendicular to both].

Just calculating these quantities is quite a difficult exercise already knowing General Relativity. I wrote an Insight article on the topic (of the calculation already knowing GR) at https://www.physicsforums.com/insights/a-problem-from-incandescence/

I'll summarize the end results.

The weight can be viewed as the sum of the tidal forces and the centrifugal forces. The tidal forces for a stationary object in geometric units in an orthonormal basis frame would be:

$$\left[ -\frac{2M}{r^3} \quad \frac{M}{r^3} \quad \frac{M}{r^3} \right]$$

The sign convention is that tidal stretching forces have a minus sigh, tidal compressive forces have a plus sign.

For an orbiting body, though, the weights due to the tidal forces are different. A lengthly calculation gives:

$$ \left[ -\frac{2M}{r^3} \left( \frac{1 – \frac{3M}{2r} } {1 – \frac{3M}{r} }\right) \quad \frac{M}{r^3} \left( \frac{1}{1- \frac{3M}{r}} \right) \quad \frac{M}{r^3} \right] $$

And the centrifugal force "weights" add to the above, and are for a tidelocked body

$$ \left[ -\frac{M}{r^3} \quad 0 \quad -\frac{M}{r^3} \right] $$

Summing these, we get the observed weights:

$$\left[ -\frac{3M}{r^3} \left( \frac{1 – \frac{2M}{r} } {1 – \frac{3M}{r} } \right) \quad \frac{M}{r^3} \left( \frac{1}{1- \frac{3M}{r}} \right) \quad 0\right]$$

This does not explain the interesting topic of the principles of the derivation of GR, but it demonstrates that there are non-trivial and measurable GR effects as simple as measuring the "weight" of a body with a spring scale.

The Newtonian results can be derived from the above by taking the limit where r goes to infinity, we see the ratio of the two nonzero components is -3:1:0, the GR calculation gives slightly different results sufficiently close to the black hole.

The fun doesn't stop there though - the black hole in Egan's book rotating, so further refinements need to be (and are) made. It's rather interesting that the alien physicists stumble on the notion of a limiting velocity from these simple measurements, without having directly observed it.

Egan makes the interesting claim that GR is equivalent to the alien physicist's principle called "Zach's principle", which is that the sum of the weights in a non-rotating frame of reference is zero. I'm not aware of the derivation of this purported equivalence. (Note that I'm easy, and I personally trust the author on this point, but since it's a work of fiction that's a dangerous thing to do, and probably not actually a good idea.].

 

[lekh2003]

Unlikely, that requires pretty serious maths. Math that has to be built from simpler systems.

I'm not sure how you would come to that conclusion if you did not already understand that light has a constant speed. I would think they would come up with Newtonian physics and explain away things like light bending around the hole as a simple attraction and acceleration on the light.

I think you should just think about this again.

When we had to discover relativity, we found that light speed is constant, but we had never seen the effects of this conclusion before. Only later did Einstein theorize that all of the effects of relativity we actually happening. Then we could see miniscule effects of the light speed being constant.

On this hypothetical world, the people would have no clue about light being constant. That is agreed. However, they can experimentally derive the equations to explain the odd ways that time and length work on their world. They would probably come up with a "relativity constant". This relativity constant would be related to what we now know as the speed of light.

The only thing is that these hypothetical people have no clue why relativity is happening. But they eventually will figure it out when they work on Newtonian physics.

Just because they don't know the reason, doesn't mean they can't come up with the equations experimentally. The effects would be so evident on this hypothetical Earth that I can easily say it would be simple for genius minds to come up with equations.

 

[newjerseyrunner]

When we had to discover relativity, we found that light speed is constant, but we had never seen the effects of this conclusion before. Only later did Einstein theorize that all of the effects of relativity we actually happening. Then we could see miniscule effects of the light speed being constant.

That's not true. Maxwell had discovered mathematically that light had a constant velocity. This violated Galilean Relativity. This was the problem than Einstein was trying to solve with Special Relativity.

 

[Ibix]

That's not true. Maxwell had discovered mathematically that light had a constant velocity. This violated Galilean Relativity. This was the problem than Einstein was trying to solve with Special Relativity.

In fact, we'd seen lots of effects following from the constancy of light speed - like Michelson-Morley and Fizeau's experiments. We just hadn't recognised the theoretical underpinning until Einstein took Maxwell's apparently daft prediction of a constant speed of light at face value.

 

[lekh2003]

That's not true. Maxwell had discovered mathematically that light had a constant velocity. This violated Galilean Relativity. This was the problem than Einstein was trying to solve with Special Relativity.

What I meant is that we found the constancy of light speed before finding relativity. The hypothetical people will find these discoveries the other way around in time.