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

[Shpaget]

21 hours ago, K^2 said:

snip

You are, of course, right. In my defense, I did sneak that "real" qualifier.

TLDR, big boom, a really big boom.

[sevenperforce]

3 hours ago, Codraroll said:

19 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.

Yikes...looking back, I actually messed it up in two places. I initially overestimated because when I asked Wolfram to give me the volume of a 5-meter-diameter sphere it dropped "diameter" which gave me 524 cubic meters. 524 cubic meters of osmium would mass 11,830 tonnes, not 11.83 tonnes, so I messed up again.

But yes, the correct value is going to be 1,479 metric tonnes. 

Plugging in the numbers from before, that gives a relativistic kinetic energy of 1.994e39 Joules. The relativistic mass of the object would be roughly the same as the mass of the large asteroid Juno. If all its energy was deposited into the Earth at impact, it would not only obliterate the Earth, but accelerate every particle of Earth in every direction at 8.6% of the speed of light. The explosion of Earth would be so energetic that the expanding cloud of relativistic plasma would be energetic enough to obliterate the moon, Mars, and Venus. At the distance of Jupiter, the shockwave would hit the gas giant with a total flux of 4.9e32 Joules...not enough to blow it up, but enough to rip away the majority of its volume (though only a small fraction of its total mass). 

14 hours ago, Starman4308 said:

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.

I was going back of the envelope, so YMMV, but I am fairly sure that the interaction cross-section simply will not be great enough if you have that much length contraction. See the ladder paradox for more info.

[magnemoe]

On 2/18/2020 at 10:40 AM, Dafni said:

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.

This, in KSP you are likely to clip trough the planet. I managed to do that once, had an probe on an impact trajectory with Eve. Wanted to wait until inside SOI before modify it to an aerobrake a bit before coming there I managed to ramp up to maximum time acceleration and then I slowed down I had past Eve. I was going so fast that I also skipped the slow down zones around planets, on Eve that is 600.000 km for 100.000 x acceleration. 
I was moving at around 9 km/s so with the acceleration it would been 900.000 km/s or 3 times the speed of light relative to Eve.

 

[kerbiloid]

When the contact duration / impactor length have been shortened below the Planck, won't this cause some additional funny effects to be put on youtube?

[p1t1o]

On 2/18/2020 at 6:30 PM, sevenperforce said:

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.

I must be missing something because that doesnt make sense, how can a massive object at 15e16c have a finite kinetic energy?

How can it have such a stunningly low kinetic energy?

This implies that if I have such a number of joules available, I can accelerate an object to 15e16c. And as far as I know, it is still impossible even to reach 1.00000c, let alone 15e16...

Do the Lorentz terms apply above 1c?

 

[sevenperforce]

22 hours ago, p1t1o said:

I must be missing something because that doesnt make sense, how can a massive object at 15e16c have a finite kinetic energy?

How can it have such a stunningly low kinetic energy?

This implies that if I have such a number of joules available, I can accelerate an object to 15e16c. And as far as I know, it is still impossible even to reach 1.00000c, let alone 15e16...

Do the Lorentz terms apply above 1c?

 

Speeds in excess of c have no physical meaning, but celerity in excess of c is meaningful. So I calculated based on celerity.

Celerity is speed as the distance in the rest frame divided by the time elapsed in the moving frame.

Edited February 21, 2020 by sevenperforce

[K^2]

5 hours ago, sevenperforce said:

Speeds in excess of c have no physical meaning, but celerity ib excess of c is meaningful. So I calculated based on celerity.

Celerity is speed as the distance in the rest frame divided by the time elapsed in the moving frame.

Well played, sir. Well played.

[Kerbal4]

why don’t we magically have it’s temperature at 0.0000000000000000001 kelvin? what would happen then??? 

[kerbiloid]

Then the magic gets proven.

[Starman4308]

15 hours ago, Kerbal4 said:

why don’t we magically have it’s temperature at 0.0000000000000000001 kelvin? what would happen then??? 

It would warm up, the magnitude of which depends on what it interacts with. If nothing else, the cosmic microwave background radiation should warm it up to ~2 Kelvins.

It would not in any noticeable way affect any results of impacting Earth (assuming it even manages to interact).

[wumpus]

On 2/20/2020 at 12:10 PM, p1t1o said:

I must be missing something because that doesnt make sense, how can a massive object at 15e16c have a finite kinetic energy?

How can it have such a stunningly low kinetic energy?

This implies that if I have such a number of joules available, I can accelerate an object to 15e16c. And as far as I know, it is still impossible even to reach 1.00000c, let alone 15e16...

Do the Lorentz terms apply above 1c?

 

Lorentz terms presumably divide by zero above c.  And regardless of kinetic energy, anything with [rest*] mass should have infinite momentum at c, and greater than infinite** momentum.  Kinetic energy should be even worse, but doesn't have any obvious proofs (unless there are real ways to convert momentum into kinetic energy).

* "rest mass" is a bad term.  Newton's laws work fine if you change F=ma to F=dp/dt.  Then you don't have to worry about "relativistic mass" and don't fall into the fallacy of "how fast does something go to have enough relativistic mass to create a black hole?".

** see Cantor's diagonal argument for proof the existence of values for "greater than infinity".  Although even 10¹⁵ times infinity will hardly rate an "alph 1" on the Cantor scale (assuming the momentum of an object at c is alph 0).

[YNM]

On 2/18/2020 at 8:18 PM, K^2 said:

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.

But does the universe's space-time fabric have enough resolution to consider the object hitting the Earth ? XD

[K^2]

8 hours ago, YNM said:

But does the universe's space-time fabric have enough resolution to consider the object hitting the Earth ? XD

In pure GR, yes. In Quantum Gravity, I'm not sure. I don't think there's a problem, because neither time nor space are actually quantized in Standard Model. There's Planck length, which is the shortest wavelength you can have, but that merely sets the limit on how thin the shockwave can be, not how rapidly it can travel, or how fine of time resolution you have on interaction. Things don't actually jump from state to state in quantum physics, despite what poorly-written chemistry text books might be trying to convince you of. All of the physics we know are some flavor of field theory, and time and space is continuous in these models. So while I'm by no means an expert in Quantum Gravity, and given that no solutions to equations of Quantum Gravity are known, so I have nothing concrete to reference, I don't think that will be a problem. Of course, if laws of physics we know are merely approximations and fall apart at relevant energy scales, *giant shrug*.

[sevenperforce]

13 hours ago, wumpus said:

Lorentz terms presumably divide by zero above c.  And regardless of kinetic energy, anything with [rest*] mass should have infinite momentum at c, and greater than infinite** momentum.  Kinetic energy should be even worse, but doesn't have any obvious proofs (unless there are real ways to convert momentum into kinetic energy).

As I explained, you can use celerity (proper velocity) rather than standard velocity to get meaningful Lorentz terms for multiples of c.

[YNM]

On 2/24/2020 at 4:57 PM, K^2 said:

Of course, if laws of physics we know are merely approximations and fall apart at relevant energy scales, *giant shrug*.

Sadly the things that keeps us awake at night... 

[magnemoe]

On 2/24/2020 at 12:59 AM, Starman4308 said:

It would warm up, the magnitude of which depends on what it interacts with. If nothing else, the cosmic microwave background radiation should warm it up to ~2 Kelvins.

It would not in any noticeable way affect any results of impacting Earth (assuming it even manages to interact).

This, even at orbital speeds say 20 km/s object temperature can be ignored unless its an nuclear fireball. You can also ignore the chemical energy. 

[Kerbal4]

what effect would this have on the other planets in the solar system?

[Codraroll]

5 minutes ago, Kerbal4 said:

what effect would this have on the other planets in the solar system?

Read the replies by Sevenperforce. Either none at all, or it would rip apart Jupiter.

[kerbiloid]

If it hits a single dusticle...

[KerikBalm]

On 2/18/2020 at 4:32 PM, sevenperforce said:

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.

Isn't the lenght contraction only along the axis of motion? So you'd have a 5m diameter very flat disk (very flat = proton thickness)... and likewise the Earth would appear to still be the sam idameter, but 0.8 nm thick, no? 

That should still register as a collision, I would think

[sevenperforce]

6 hours ago, KerikBalm said:

Isn't the lenght contraction only along the axis of motion? So you'd have a 5m diameter very flat disk (very flat = proton thickness)... and likewise the Earth would appear to still be the sam idameter, but 0.8 nm thick, no? 

That should still register as a collision, I would think

BOTE says no, but YMMV. See the Ladder Paradox.

[KerikBalm]

BOTE?

The ladder paradox isn't really relevant here.

In the ladder paradox, the only relevant length contraction is along the direction of motion, so if that was the case, we'd still have a very very thin, but 5m wide disk hitting the earth... or a 0.2nm thick disk-Earth hitting the sphere

[kerbiloid]

Spoiler

So, finally... The flat Earth...

Great...

 

[sevenperforce]

3 hours ago, KerikBalm said:

BOTE?

The ladder paradox isn't really relevant here.

In the ladder paradox, the only relevant length contraction is along the direction of motion, so if that was the case, we'd still have a very very thin, but 5m wide disk hitting the earth... or a 0.2nm thick disk-Earth hitting the sphere

The issue is the solution to the ladder paradox: simultaneity. If you are hitting a thin-disk earth at nearly the speed of light, you will not necessarily have time for simultaneous force interactions. Back of the envelope estimate says you'll have frame-dragging effects (which might actually be rather extreme) but nothing else. 

[KerikBalm]

Well, we have plenty of relativisitic collisions from subatomic particles that have no problem interacting... I don't see how some events not being simultaneous from certain reference frames would allow it to pass through.

https://en.wikipedia.org/wiki/Oh-My-God_particle