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hit the earth at 15,000,000,000,000,000 times the speed of light?


Kerbal4
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Let’s say a ball 10 meters in diameter with an indestructible 5 m diameter core, was to hit the earth at 15,000,000,000,000,000 times the speed of light, somehow, right on the empire state building. 

I think there would be a very loud bang, a column of smoke, and a very big crater where new york used to be. and a lot of very hot plasma where there used to be breathable air, but i did no research for that answer, I was wondering what you think?

Edited by Kerbal4
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As KSP teaches us, the ball would phase right through the planet without even touching it, as the physics cant keep up when you are in 15,000,000,000,000,000x time warp.

Furthermore, Einstein wants to have a word with you, he thinks you've been watching too much TV.

Edited by Dafni
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Trying to figure out what happens at faster than light speed in real universe is inherently futile, since speed greater than c in meaningless.

We could talk about what happens as the speed approaches c, but once at c, any mass has infinite kinetic energy, and our math falls apart (just like anything that happens to be in the path of that object).

Edited by Shpaget
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2 hours ago, Kerbal4 said:

Let’s say a ball 10 meters in diameter with an indestructible 5 m diameter core, was to hit the earth at 15,000,000,000,000,000 times the speed of light, somehow, right on the empire state building.

I.e. "Let's assume that known natural laws do not exist. What natural laws predict if...". So, do not expect meaningful answers if your question contains superluminal speeds or indestructible matters.

Practically kinetic energy determines what happens if macroscopic piece of matter hits to Earth at relativistic velocities. Structural strength or other properties of matter are negligible in such conditions. Even very small objects can have very high energy and my guess is that effects are quite similar than nuclear explosion.

 

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At that speed there wouldn't be any Earth to hit at all. Go faster than light and physics break down. 

Heck, with that number of zeroes there would barely have been time for physics to happen even in the frame of physics as we know them. It may be that a ball of such "super-matter" capable of moving at such high speeds wouldn't have time to even interact with physical matter because it would instantly travel the width of the universe, passing through all of it without leaving a mark. Time itself is a very iffy concept when high relativistic velocities are involved. From the ball's perspective, the universe would go straight from the Big Bang to heat death the instant the ball appeared in it. From the universe's perspective, the ball wouldn't exist for long enough for its existence to even be registered.

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1 hour ago, Shpaget said:

Trying to figure out what happens at faster than light speed in real universe is inherently futile, since speed greater than c in meaningless.

Well, mostly meaningless. Speed of light is a local limit, not a global one. Space-time curvature can allow for an object to travel much faster than speed of light relative to anything that's not in its immediate neighborhood. That's why our universe is allowed to be less than 14 bilion years old and over 90 billion light years wide. While energies required would be entirely absurd and non-physical, purely from perspective of mathematics of General Relativity, one can construct such space-time curvature as to allow an object to approach Earth at many times the speed of light, and also to have transition be sharp enough that the object has no chance of slowing down despite immense gravitational gradients this is sure to result in. That will result in the incoming projectile creating a shockwave in space-time itself, frame-dragging a region of space-time that allows it to continue at FTL speeds relative to whatever's in front of the shockwave. Anything the shockwave encounters will be turned into gamma radiation, because any mass the matter has is absolutely meaningless compared to the energies involved. Naturally, no two particles collide at FTL speeds in this scenario, because that would actually violate locality and causality, but the boundary across the shockwave can be pretty thin, so you can think of it as something punching a hole through Earth at FTL speeds. In terms of an outcome, the difference between this and simply encountering a sub-light object with similar kinetic energy is entirely academic. In both cases, Earth gets blasted into rapidly expanding hyper-relativistic particle soup which will probably produce many new galaxies as it cools down.

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According to Atomic Rockets, you need 2.9*10^32 J of energy to completely destroy Earth: specifically to reduce it to bits of gravel and move the pieces to infinity.

I'll assume a density of 2500 kg/m^3. With a 5m radius, this means a mass of 1,308,997 kg.

Using non-relativistic kinetic energy equations (KE = 1/2 * m*v^2), it would need to be traveling at 2.1*10^13 m/s, or about 70,000c. Substantially less than what the OP posted.

I'm substantially less familiar with relativistic physics, so I may have done the math incorrectly, but I think the required velocity using relativistic kinetic energy equations is c*(1 - 4.1*10^-10), or about 0.9999999996c.

All of this, of course, implies perfect conversion of the impactor's kinetic energy to overcoming Earth's binding energy, but even given some inefficiencies, I suspect New York City is toast.

 

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5 hours ago, MinimumSky5 said:

More like the sudden collapse of the baseball itself into a black hole just from it's kinetic energy alone, long before it hits the Earth

Common misconception -- relativistic energy alone cannot create a black hole.

6 hours ago, Kerbal4 said:

Let’s say a ball 10 meters in diameter with an indestructible 5 m diameter core, was to hit the earth at 15,000,000,000,000,000 times the speed of light, somehow, right on the empire state building.

Obligatory "nothing can go faster than light", etc etc.

However, you can represent speeds greater than by measuring celerity (w) rather than velocity (v). Velocity is the distance per unit time as measured by an observer, while celerity is distance as measured by an observer per unit of time as measured by the object. There is no upper limit to celerity. "15 quadrillion times the speed of light makes no sense" (it is like saying "a vacuum with 15 times more suction than empty space") but 15 quadrillion does make sense as a measure of celerity.

For celerity many times greater than c, the Lorentz factor γ is approximately equal to the celerity given in multiples of c. So an object with 15 quadrillion w/c has a Lorentz factor of 15 quadrillion, which means its relativistic mass is 15 quadrillion times greater than it would otherwise be. However, it impacts other things as well. That 10 meter ball will undergo length contraction by a factor of 15 quadrillion, making it approximately the thickness of a single proton as viewed by an Earth observer. From the perspective of the ball, Earth will have shrunk to a disc only 0.8 nanometers thick, slightly smaller than a strand of DNA.

The ball would pass through Earth without interacting.

 

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7 hours ago, Kerbal4 said:

15,000,000,000,000,000 times the speed of light,

In our universe, this actually does not have a meaning.

It is broadly equivalent to asking "What happens when you purple a zebra?"

It sounds strange that Xm/s would make sense and ManyXm/s would not, but the universe is under no obligation to make sense.

***

One school of thought would say that your relativistic mass would become a very large infinity, traveelling backwards through time fast enough to leave the big bang far behind you. And "being" may not have existed before that soooooo....

Every other school of thought says you cant do it.

And all of them agree none of it makes sense.

***

Im not mocking you, you're just asking questions so far beyond known physics, or potentially possible physics, that the answers are absurd.

It really is like the purple zebra thing.

 

 

****

7 hours ago, Kerbal4 said:

I think there would be a very loud bang, a column of smoke, and a very big crater where new york used to be. and a lot of very hot plasma where there used to be breathable air, but i did no research for that answer, I was wondering what you think?

If we are going to make up a classical answer, you are really thinking many, many orders of magnitude too small.

Your hypothetical situation not only has enough energy to vaporise NewYork, but also Earth, Jupiter, the Sun, the Mily Way and possibly most of the universe too, and probably some esoteric things like "time" or "happiness", just from the kinetic energy (note - an object that has mass and is travelling at 1c, has *infinite* kinetic energy)

Luckily, the wave of destruction would be confined to a single c, so people living in the universe could live happily their entire exiestances, because your folly is confined by time (and the  LAWS OF PHYSICS THANK YOU VERY MUCH) to the other side of the universe. We on Earth might not thank you though)

Also I think the word "hot" might just lose all of its meaning.

 

This is a situation SO extreme, that it would have metaphysical effects such as alterations to grammar and morality (Im only half joking, physics does in fact approach philosophy when you start really tearing at the walls of reality)

Edited by p1t1o
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1 hour ago, p1t1o said:

If we are going to make up a classical answer, you are really thinking many, many orders of magnitude too small.

Your hypothetical situation not only has enough energy to vaporise NewYork, but also Earth, Jupiter, the Sun, the Mily Way and possibly most of the universe too, and probably some esoteric things like "time" or "happiness", just from the kinetic energy (note - an object that has mass and is travelling at 1c, has *infinite* kinetic energy)

Luckily, the wave of destruction would be confined to a single c, so people living in the universe could live happily their entire exiestances, because your folly is confined by time (and the  LAWS OF PHYSICS THANK YOU VERY MUCH) to the other side of the universe. We on Earth might not thank you though)

Also I think the word "hot" might just lose all of its meaning.

This is a situation SO extreme, that it would have metaphysical effects such as alterations to grammar and morality (Im only half joking, physics does in fact approach philosophy when you start really tearing at the walls of reality)

If we use "15 quadrillion times the speed of light" as a measure of celerity rather than speed, we can do a little more work. As I explained above, length contraction would shrink the Earth to the thickness of a strand of DNA, making interaction unlikely. However, let's handwave that part.

The original post doesn't specify mass for the object, but in any question of penetration, the most "indestructible" object will always be the object with the greatest density. Osmium is the densest naturally-occurring mineral, so I'll go with that. A five meter sphere of osmium would mass 11.83 metric tonnes.

A Lorentz factor of ~15e16 can be used with the standard equations to determine the relativistic kinetic energy K of the impactor: K = (γ - 1)*m*c2. The kinetic energy of our impactor is going to be a nice charming 1.595e37 Joules. To put it in perspective, as much energy as the sun produces in 10,667 years. It is enough energy to obliterate 100,000 Earths.

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5 hours ago, sevenperforce said:

If we use "15 quadrillion times the speed of light" as a measure of celerity rather than speed, we can do a little more work. As I explained above, length contraction would shrink the Earth to the thickness of a strand of DNA, making interaction unlikely. However, let's handwave that part.

The original post doesn't specify mass for the object, but in any question of penetration, the most "indestructible" object will always be the object with the greatest density. Osmium is the densest naturally-occurring mineral, so I'll go with that. A five meter sphere of osmium would mass 11.83 metric tonnes.

A Lorentz factor of ~15e16 can be used with the standard equations to determine the relativistic kinetic energy K of the impactor: K = (γ - 1)*m*c2. The kinetic energy of our impactor is going to be a nice charming 1.595e37 Joules. To put it in perspective, as much energy as the sun produces in 10,667 years. It is enough energy to obliterate 100,000 Earths.

By "interaction unlikely"... how unlikely? A 10 meter sphere contains an awful lot of protons, electrons, and neutrons, so even if the probability of one particle interacting with the Earth is low, there's an awful lot of particles to be doing the interacting.

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6 hours ago, cubinator said:

Earth would be instantaneously destroyed, the fallout from the explosion would do the same to the moon one second later.

Okay, important safety tip. Thanks, Egon.

 

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15 hours ago, sevenperforce said:

A five meter sphere of osmium would mass 11.83 metric tonnes.

Uhh... this doesn't quite make sense to me. Its density is 22.59 g/cm3, or 22 590 kg/m3. A five meter sphere of osmium would have a volume of 65.4 m3 and weigh almost 1500 tons. Assuming you input that wrong number in your calculations, your already pretty spectacular estimates are too low by a factor of almost 150.

Edited by Codraroll
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