What-If 0109: "Into the Blue"

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nowhereman
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What-If 0109: "Into the Blue"

Postby nowhereman » Thu Aug 21, 2014 4:29 am UTC

http://what-if.xkcd.com/109/

Image

This is probably the funniest way I can imagine ending this debate.

That said, I wonder how this would scale. Lasers do not have a perfect focus. As such, I would expect that at very large distances, the radius of destruction (I love this measure. I vote we give more funding to any field that uses this phrase) should get extremely large. If the laser spread at .5 degrees (.00873 radians), at a distance of 10 000ly, the RoD would be 87.3ly. I think if this was aimed at the galactic core, it would hit it. After all, there is a lot of energy in this beam of death. I think the odds of hitting any object would be higher than currently described.
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Re: What-If 0109: "Into the Blue"

Postby dylanarena » Thu Aug 21, 2014 4:45 am UTC

I don't know whether this is the right place, but I thought I'd give it a shot:

"Neptune would be the [hardest] to hit, followed by Uranus and Mercury. Pluto would be the hardest, but it might be worth it."

I think this first "hardest" should be "easiest" instead. I'm just pointing it out in case it is a typo, in which case Randall can fix it and make the Internet safe again! (Cf. strip 386.)

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Re: What-If 0109: "Into the Blue"

Postby Sir Lunch-a-lot » Thu Aug 21, 2014 5:53 am UTC

nowhereman wrote:http://what-if.xkcd.com/109/

Image

This is probably the funniest way I can imagine ending this debate.


:shock: But what planet DID she hit??!!

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Re: What-If 0109: "Into the Blue"

Postby rhomboidal » Thu Aug 21, 2014 6:10 am UTC

Hmm, I'm starting to suspect that by "a random point," Garrett D actually means "Alderaan." And the "D" stands for "Darth."

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Re: What-If 0109: "Into the Blue"

Postby herbys » Thu Aug 21, 2014 6:11 am UTC

That is no moon. It is a space station. And it has a powerful laser aiming at us.

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Re: What-If 0109: "Into the Blue"

Postby waveney » Thu Aug 21, 2014 8:04 am UTC

Sir Lunch-a-lot wrote:
nowhereman wrote:http://what-if.xkcd.com/109/

Image

This is probably the funniest way I can imagine ending this debate.


:shock: But what planet DID she hit??!!

If she pointed it in a random direction almost 50% would hit a planet, and in most cases it would end the argument.

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Re: What-If 0109: "Into the Blue"

Postby keithl » Thu Aug 21, 2014 8:53 am UTC

End of paragraph 10 sez ( at this time):
4 times pi times 57.3 = 41,253 square degrees.

Uh, no. 4 times pi times 57.32, squared. And since 57.3 is an approximation for 360 / 2 pi, the calculation simplifies to 3602/ pi = 41252.96... square degrees. So where can I buy a "squaretractor", which measures solid angle the way a protractor measures planar angle?

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Re: What-If 0109: "Into the Blue"

Postby keithl » Thu Aug 21, 2014 9:08 am UTC

The Moon and the Sun each take up about 0.2 square degrees, and so the chance of hitting either one of them is about 1 in 180,000. Those aren't great odds, but they're better than the odds of hitting anything else.
Your chance of hitting a cloud is higher.

I wonder what your chance of hitting an airplane is? People tend to cluster near cities with airports, so there are probably more airplanes in your sky than at a random place on earth. Hit a plane with enough laser energy, and you are now pointing at a cloud.

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Re: What-If 0109: "Into the Blue"

Postby Neil_Boekend » Thu Aug 21, 2014 10:44 am UTC

keithl wrote:
The Moon and the Sun each take up about 0.2 square degrees, and so the chance of hitting either one of them is about 1 in 180,000. Those aren't great odds, but they're better than the odds of hitting anything else.
Your chance of hitting a cloud is higher.

I wonder what your chance of hitting an airplane is? People tend to cluster near cities with airports, so there are probably more airplanes in your sky than at a random place on earth. Hit a plane with enough laser energy, and you are now pointing at a cloud.

Hit a plane with enough laser energy and you are now pointing at a planetary drive. And you're screwed.
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Re: What-If 0109: "Into the Blue"

Postby Eternal Density » Thu Aug 21, 2014 11:07 am UTC

I really enjoyed reading this one :D
Neil_Boekend wrote:
keithl wrote:
The Moon and the Sun each take up about 0.2 square degrees, and so the chance of hitting either one of them is about 1 in 180,000. Those aren't great odds, but they're better than the odds of hitting anything else.
Your chance of hitting a cloud is higher.

I wonder what your chance of hitting an airplane is? People tend to cluster near cities with airports, so there are probably more airplanes in your sky than at a random place on earth. Hit a plane with enough laser energy, and you are now pointing at a cloud.

Hit a plane with enough laser energy and you are now pointing at a planetary drive. And you're screwed.
Unless you're a pope.
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Re: What-If 0109: "Into the Blue"

Postby cellocgw » Thu Aug 21, 2014 11:21 am UTC

Eternal Density wrote:I really enjoyed reading this one :D
Neil_Boekend wrote:
keithl wrote:
The Moon and the Sun each take up about 0.2 square degrees, and so the chance of hitting either one of them is about 1 in 180,000. Those aren't great odds, but they're better than the odds of hitting anything else.
Your chance of hitting a cloud is higher.

I wonder what your chance of hitting an airplane is? People tend to cluster near cities with airports, so there are probably more airplanes in your sky than at a random place on earth. Hit a plane with enough laser energy, and you are now pointing at a cloud.

Hit a plane with enough laser energy and you are now pointing at a planetary drive. And you're screwed.
Unless you're a pope.


Is that a regular Vatican pope or a PagePope? (careful, you will get tossed into the abyss instead of crossing the bridge if you answer wrong).

But my actual reason for posting was to reference https://xkcd.com/1276/ which is sort of the reverse of the calculation here. Oh, and to point out that any laser (or light) beam will spread due to those dang self-diffraction laws. A couple million miles away, the Airy Disk is gonna be fricken huge! Maybe if we attached the laser to the head of a whale...
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Re: What-If 0109: "Into the Blue"

Postby cellocgw » Thu Aug 21, 2014 11:22 am UTC

waveney wrote:
Sir Lunch-a-lot wrote:
nowhereman wrote:http://what-if.xkcd.com/109/

Image

This is probably the funniest way I can imagine ending this debate.


:shock: But what planet DID she hit??!!

If she pointed it in a random direction almost 50% would hit a planet, and in most cases it would end the argument.


Except if she hit Pluto, in which case they would be agreeing on eight. And presumably she didn't hit Terra, since they're still alive.
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Re: What-If 0109: "Into the Blue"

Postby FOARP » Thu Aug 21, 2014 11:51 am UTC

An infinitely strong laser pointer would deliver an infinite amount of energy to the air in its path, which would in turn radiate an infinite amount of energy in all directions, which would destroy everything.


Hmmm . isn't there actually a theoretical upper-limit on how much energy air molecules can absorb from a laser, and then re-emit randomly? And wouldn't the laser actually reduce the matter to something tha might not be absorbed anywhere, rendering the path of the beam a vacuum?

Evidence: our universe is filed with high-energy events, and no super-powerful gamma-rays have destroyed the Earth yet.

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Re: What-If 0109: "Into the Blue"

Postby rmsgrey » Thu Aug 21, 2014 12:04 pm UTC

FOARP wrote:
An infinitely strong laser pointer would deliver an infinite amount of energy to the air in its path, which would in turn radiate an infinite amount of energy in all directions, which would destroy everything.


Hmmm . isn't there actually a theoretical upper-limit on how much energy air molecules can absorb from a laser, and then re-emit randomly? And wouldn't the laser actually reduce the matter to something tha might not be absorbed anywhere, rendering the path of the beam a vacuum?

Evidence: our universe is filed with high-energy events, and no super-powerful gamma-rays have destroyed the Earth yet.


Counterpoint: all those events are (almost) nothing compared to infinite power.

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Re: What-If 0109: "Into the Blue"

Postby mojacardave » Thu Aug 21, 2014 12:11 pm UTC

dylanarena wrote:I don't know whether this is the right place, but I thought I'd give it a shot:

"Neptune would be the [hardest] to hit, followed by Uranus and Mercury. Pluto would be the hardest, but it might be worth it."

I think this first "hardest" should be "easiest" instead. I'm just pointing it out in case it is a typo, in which case Randall can fix it and make the Internet safe again! (Cf. strip 386.)


Nope, definitely still hardest - Neptune is small and is the furthest [proper] planet from Earth. It's a slightly misleading paragraph, because it then states that Pluto would be the hardest to hit, without mentioning that the scope of the calculation has been changed.

cellocgw wrote:..my actual reason for posting was to reference https://xkcd.com/1276/ which is sort of the reverse of the calculation here...


Randall actually references that comic himself - follow the 'angular size' link just under the image of the girl with the vendetta against the moon!

I'm kind of surprised that Randall picked this question to answer - I'm assuming that he has to weed out a lot of nonsense questions that make no sense when he's hunting for 'What If' ideas, I'd have grouped this one under 'meaningless questions', especially since it's so similar to something he's already answered.

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Re: What-If 0109: "Into the Blue"

Postby Zassounotsukushi » Thu Aug 21, 2014 12:26 pm UTC

FOARP wrote:
An infinitely strong laser pointer would deliver an infinite amount of energy to the air in its path, which would in turn radiate an infinite amount of energy in all directions, which would destroy everything.


Hmmm . isn't there actually a theoretical upper-limit on how much energy air molecules can absorb from a laser, and then re-emit randomly? And wouldn't the laser actually reduce the matter to something tha might not be absorbed anywhere, rendering the path of the beam a vacuum?

Evidence: our universe is filed with high-energy events, and no super-powerful gamma-rays have destroyed the Earth yet.


This is totally what I thought this what-if would be about. He began talking about how the physics equations don't work when you plug infinity in. I imagine this has to do with cross sections for light interactions with gas molecules.

An important point remains to be resolved. What is the wavelength of this beam? There are physical limits to the density of a beam of light (holography mostly), but that's sort of irrelevant of the wavelength if I understand correctly. The wavelength is what will determine how strongly it interacts. If it's in the visible spectrum, then there are still plenty of possible interactions.

In my mental image, it wouldn't just be the beam of light that creates a vacuum, but secondary interactions would also blow the air out into space. That means that you'll have sort of a cone volume that's a hard vacuum. Actually, the "infinite" part of this is very tricky. It shouldn't take much time for it to destroy Earth's entire atmosphere. One single stray particle from the center of the beam might potentially be able to blow away tons of our atmosphere.

But maybe the infinities aren't quite so insanely difficult to manage, if the photon energy is finite. Consider that the molecules would experience a "normal" interaction with light, it just happens to interact at an infinite rate. I imagine that it's possible that rayleigh scattering actually saturates, and the molecule won't increase in speed any more. That's probably not likely, since photons are massless.

But consider that proposition again... the air in the beam's path might accelerate to the speed of light, but what is the angle it travels at? It seems plausible that it must be perfectly in the direction of the beam. This isn't good, but Earth might be able to survive that. There would, thus, be no conical effects from secondary interactions with the rest of the atmosphere, because getting in the path of the beam removes the air effectively instantly. This also means that it would take a long time to deplete Earth's atmosphere, although the person holding the beam would find themselves cold and gasping.

Also, the accelerated air would become a black hole. Thankfully that's not a problem for us, since it's traveling far away. Earth becomes a micro black hole factory. We're saved from the Hawking Radiation due to the nearly infinite redshift.

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Re: What-If 0109: "Into the Blue"

Postby Whizbang » Thu Aug 21, 2014 12:52 pm UTC

But what happens when an Infinite Laser hits an Infinite "Energy" Shield?

And what happens if it hits a black hole?

And wouldn't every point in this laser become a black hole?

And wouldn't "every point" really just be one, since as soon as it is turned on, a BH forms and sucks in everything around it, including the infinite battery.

And if the BH is infinite, wouldn't it eventually just become the universe?

Maybe this has already happened.

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Re: What-If 0109: "Into the Blue"

Postby cellocgw » Thu Aug 21, 2014 1:21 pm UTC

Whizbang wrote:But what happens when an Infinite Laser hits an Infinite "Energy" Shield?


Well, having recently read Iain Banks' "Walking on Glass," I can tell you that

Spoiler:
The infinite force is stopped, and
The immovable object moves .



:twisted:
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Re: What-If 0109: "Into the Blue"

Postby Burton » Thu Aug 21, 2014 1:48 pm UTC

From the List of Sexually Active Popes:

"When the blessed Peter saw his own wife led out to die, he rejoiced ..." - Clement of Alexandria

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Re: What-If 0109: "Into the Blue"

Postby esbboston » Thu Aug 21, 2014 1:54 pm UTC

At the end the number of planets was reduced by one after the blasting. But I think it should be increased by one, with the new planets named Nep and Tune. :shock: :D

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Re: What-If 0109: "Into the Blue"

Postby Trickster » Thu Aug 21, 2014 2:32 pm UTC

dylanarena wrote:"Neptune would be the [hardest] to hit, followed by Uranus and Mercury. Pluto would be the hardest, but it might be worth it."

Precede the word "Pluto" by "If Pluto were a planet, then ". Or, alternately, change the second "hardest" to "even harder" (and yes that is still correct English for some reason).

Also: I feel math stupid which I often do for fun, but this time it is not intentional. Can someone please explain to me how the sky is 57 degrees? Because I kinda see 180 degrees when I'm on a flat plane. I am very, very confused.

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Re: What-If 0109: "Into the Blue"

Postby stib » Thu Aug 21, 2014 2:40 pm UTC

I'm no physicist, but wouldn't space's curvature mean that if you pointed it forward, eventually the laser beam would hit you in the back of the head? Assuming you stood there for the billions of years it took for that to happen.

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Re: What-If 0109: "Into the Blue"

Postby schapel » Thu Aug 21, 2014 3:22 pm UTC

Trickster wrote:Also: I feel math stupid which I often do for fun, but this time it is not intentional. Can someone please explain to me how the sky is 57 degrees? Because I kinda see 180 degrees when I'm on a flat plane. I am very, very confused.

If the circumference of a circle is 2 pi r, and a circle has a circumference of 2 pi radians, then we can think of the radius of a circle as "1 radian", which is about 57 degrees. Plug the radius of 57 degrees into the formula for surface area of a sphere, 4 pi r^2, and you get a bit over 40000 square degrees in a sphere.

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Re: What-If 0109: "Into the Blue"

Postby mojacardave » Thu Aug 21, 2014 3:23 pm UTC

stib wrote:I'm no physicist, but wouldn't space's curvature mean that if you pointed it forward, eventually the laser beam would hit you in the back of the head? Assuming you stood there for the billions of years it took for that to happen.


I don't think anybody knows enough about the universe to say what would happen to the route of the infinitely powerful beam, on the universal scale.

Trickster wrote:Also: I feel math stupid which I often do for fun, but this time it is not intentional. Can someone please explain to me how the sky is 57 degrees? Because I kinda see 180 degrees when I'm on a flat plane. I am very, very confused.


The sky is 57 degrees away.

Mathematically, if you imagine a spherical shell around you, then the distance to the sphere will be the same distance as a line along the surface of the sphere that covers an angle of 57.3 degrees from the centre. It's using 'degrees' as a measurement of straight line distance which is very difficult to get your head round, but it means that you can use the same units as you make the sphere bigger, until it's the same size as the universe. That means you can easily compare the 'relative size to us' of the sun and the moon and Jupiter and Alpha Centurai even though they're all different distances away.

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Re: What-If 0109: "Into the Blue"

Postby Dan H » Thu Aug 21, 2014 3:55 pm UTC

stib wrote:I'm no physicist, but wouldn't space's curvature mean that if you pointed it forward, eventually the laser beam would hit you in the back of the head? Assuming you stood there for the billions of years it took for that to happen.

No. Curved space isn't the same as closed space. Think of a sheet of paper that you can make as big as you want. You can bend it any which way, but if you draw an "infinitely" long line on it and bend the paper, the line only forms a closed loop if you bend it in certain ways.

Randall never mentioned the fact that photons carry momentum. If you pointed an infinitely powerful laser upward and switched it on, conservation of momentum dictates that the Earth would be launched with infinite velocity in the opposite direction. The sudden acceleration would rip everything to pieces. A quick calculation using Newton's Laws and the energy-momentum relationships for photons yields the equation (laser power) = (Earth mass) x (Earth recoil acceleration) x (speed of light). A very powerful handheld laser is 2 Watts, which would cause the Earth to recoil at 10^-33 m/s^2. I think the world record for most powerful laser pulse in a lab is about 10^15 W, which if you pointed it straight up would cause the Earth to recoil at 5 x 10^-19 m/s^2. But if you had a laser a couple quintillion times as powerful as that lab record (2 x 10^34 W), you could fire it upward and cause the entire Earth to recoil at about 10 m/s^2. On your side of the Earth, you would suddenly feel weightless. On the opposite side of the Earth, people would feel twice as heavy. And you'd noticeably affect the Earth's orbit. But a laser that powerful would use up the entire current yearly energy production of the Earth in a few femtoseconds, which might create difficulties in the design process.

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Re: What-If 0109: "Into the Blue"

Postby speising » Thu Aug 21, 2014 4:14 pm UTC

not the earth, but the laser would recoil. which just means it wil smash into the earth at c (since it had infinite acceleration) and hilarity ensues.

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Re: What-If 0109: "Into the Blue"

Postby Zassounotsukushi » Thu Aug 21, 2014 5:26 pm UTC

Whizbang wrote:And wouldn't every point in this laser become a black hole?


Maybe, kind of. Any air particles in the path of the laser would become a black hole to us, unless the frequency produces a speed limit. More than likely, the frequency does pose a speed limit. At some point, the light is so heavily redshifted to the gas molecule that the wavelength is too large to hit it. But it's still an infinite intensity. I don't know. I can go either way with this assumption right now.

Anyway, all the gas molecules are being accelerated to the speed of light. That gives the molecules infinite mass, making them a black hole to us. However, that's only because of reference frames. In the reference frame of the gas molecules, they don't necessarily have to become a black hole. They would need to hit each other for this to happen, and hit at tremendous energies. Tremendous energies we have, but since the flux is uniform (it's infinite, after all), it's difficult to see any molecule being accelerated at a different rate than another. But then again, literally ANY speed difference is sufficient since the flux is infinite. These are the logic circles we work ourselves in with the absurd premise.

However, this is more complicated than necessary. Best if we just assume that collisions between accelerated air molecules do not create black holes as long as they're in the same cohort. On the other hand, some molecules enter the stream at a different relative velocity, because gas molecules move. That will hit one of the already-accelerated molecules and create a black hole no matter what reference frame you use.

In other words, black holes are created on the edge of the beam cylinder, not inside it.

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Re: What-If 0109: "Into the Blue"

Postby Moose Anus » Thu Aug 21, 2014 5:30 pm UTC

speising wrote:not the earth, but the laser would recoil. which just means it wil smash into the earth at c (since it had infinite acceleration) and hilarity ensues.
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Re: What-If 0109: "Into the Blue"

Postby Trickster » Thu Aug 21, 2014 5:33 pm UTC

If the circumference of a circle is 2 pi r, and a circle has a circumference of 2 pi radians, then we can think of the radius of a circle as "1 radian", which is about 57 degrees. Plug the radius of 57 degrees into the formula for surface area of a sphere, 4 pi r^2, and you get a bit over 40000 square degrees in a sphere.

Thank you! (Though it turns out I did figure that out shortly after I asked the question.) :P

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Re: What-If 0109: "Into the Blue"

Postby schapel » Thu Aug 21, 2014 5:34 pm UTC

Zassounotsukushi wrote:
Whizbang wrote:And wouldn't every point in this laser become a black hole?

Maybe, kind of.

I think it would be a Kugelblitz, light so intense it forms a black hole. But of course, even before the energy source was transformed into light, it would still have infinite mass, so a black hole would form just from the energy source being gathered and prepared for the blast of light. On the other hand, it would take an infinite amount of time to gather the energy, even assuming that an infinite amount of energy exists that we could gather into one place, so the whole question of an infinitely powerful laser is just nonsense. It's as nonsense as asking what happens if you keep counting until you reach infinity -- you never will!

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Re: What-If 0109: "Into the Blue"

Postby Trickster » Thu Aug 21, 2014 5:43 pm UTC

stib wrote:I'm no physicist, but wouldn't space's curvature mean that if you pointed it forward, eventually the laser beam would hit you in the back of the head? Assuming you stood there for the billions of years it took for that to happen.

This is a great question! Given that all evidence suggests the universe is infinite in all directions, the answer is no.

If the universe were finite but unbounded as was previously believed (by cosmologists anyway; astronomers were less biased and turned out to be correct), then it would be possible, but you'd be assuming that the universe were completely uniform and its curvature unaffected by mass, neither of which is the case.

Some wacky things like space expanding can affect this kind of thing too. The cosmic background radiation isn't bright because it is stretched out into radio frequency from the universe expanding. We don't see an infinity of stars in part because there was a period when the universe expanded faster than light can move, and partly because everything prior to the CBR was obscured by high-energy physics.

Whizbang wrote:But what happens when an Infinite Laser hits an Infinite "Energy" Shield?

This makes as much sense as saying "We can't divide by zero, but what if we did?" It's not a well-formed question. Neither of those things can exist because each by itself is self-contradictory, so the question is nonsensical.

Whizbang wrote:And wouldn't "every point" really just be one, since as soon as it is turned on, a BH forms and sucks in everything around it, including the infinite battery.

And if the BH is infinite, wouldn't it eventually just become the universe?

Maybe this has already happened.

Sort of: see "holographic principle".

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Re: What-If 0109: "Into the Blue"

Postby nowhereman » Thu Aug 21, 2014 6:00 pm UTC

Zassounotsukushi wrote:
Whizbang wrote:And wouldn't every point in this laser become a black hole?


Maybe, kind of. Any air particles in the path of the laser would become a black hole to us, unless the frequency produces a speed limit. More than likely, the frequency does pose a speed limit. At some point, the light is so heavily redshifted to the gas molecule that the wavelength is too large to hit it. But it's still an infinite intensity. I don't know. I can go either way with this assumption right now.

Anyway, all the gas molecules are being accelerated to the speed of light. That gives the molecules infinite mass, making them a black hole to us. However, that's only because of reference frames. In the reference frame of the gas molecules, they don't necessarily have to become a black hole. They would need to hit each other for this to happen, and hit at tremendous energies. Tremendous energies we have, but since the flux is uniform (it's infinite, after all), it's difficult to see any molecule being accelerated at a different rate than another. But then again, literally ANY speed difference is sufficient since the flux is infinite. These are the logic circles we work ourselves in with the absurd premise.

However, this is more complicated than necessary. Best if we just assume that collisions between accelerated air molecules do not create black holes as long as they're in the same cohort. On the other hand, some molecules enter the stream at a different relative velocity, because gas molecules move. That will hit one of the already-accelerated molecules and create a black hole no matter what reference frame you use.

In other words, black holes are created on the edge of the beam cylinder, not inside it.


I don't think you answered his question. I think he was referring to the energy density of a photon beam that was infinitely large. Photons, even in a vacuum have a gravitational attractive force.

Using e=mc^2, we can solve for mass giving m = e/c^2. Using the Schwarzschild radius of these photons (Rs = 2Gm/c^2, which becomes Rs = 2Ge/c^4 when you substitute the previous equation in), we can determine the amount of energy that must be in a particular width of the laser beam to cause a sufficient amount of curvature to create a black hole (e = Rsc^4/2G). Suppose we measure the beam intensity at a distance of 1m where the radius of the beam would be 8.73mm (at .5 degrees). The amount of energy we would need to pump into this beam to cause a black hole to emerge would be approximately 5.294×10^41 joules, which Wolfram alpha cheerily told me was .99 the energy equivalent of the Earth.
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Klear
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Re: What-If 0109: "Into the Blue"

Postby Klear » Thu Aug 21, 2014 6:21 pm UTC

Garrett D. wrote:If I shot an infinitely strong laser beam into the sky at a random point, how much damage would it do?


First of all, if you aimed in a truly random direction, you would have an almost 50% chance of hitting the Earth.


I was kinda disappointed by this. Usually Randall takes the exact working of the question into account.

Also, "List of Sexually Active Popes"? GOOMHR!

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Re: What-If 0109: "Into the Blue"

Postby speising » Thu Aug 21, 2014 6:59 pm UTC

btw, a beam of sufficient energy density wouldn't disperse due to diffraction, thanks to the self pinching effect.

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Re: What-If 0109: "Into the Blue"

Postby Quizatzhaderac » Thu Aug 21, 2014 7:13 pm UTC

The list of sexually active popes seems more like an argument that the world is that bad.

Three things Randal didn't explore:

If you fired a laser upward on a clear day/night, what proportion would escape into space?

With planet destroying energy in a laser pointer volume, would photon-photon (other photons being ambient) annihilation be significant?

With that much energy, moving that fast, what frame dragging effects could we expect around the laser?
The thing about recursion problems is that they tend to contain other recursion problems.

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Re: What-If 0109: "Into the Blue"

Postby nwimpney » Thu Aug 21, 2014 8:10 pm UTC

I think the whole what-if is under the false assumption that perfectly columnated lasers exist.

I buy all of my nearly infinitely powerful laser pointers from the dollar store, and their beams are usually quite divergent. I haven't done the math properly, but it seems to me that my odds of hitting any planet will be quite similar, since they'll rely more on my distorted cone of laser light, rather than the angle of sky covered by the target.

-Nick

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Re: What-If 0109: "Into the Blue"

Postby seikatsukan » Thu Aug 21, 2014 8:47 pm UTC

I registered only to say that, if that was an attempt at reverse psychology at the end, it was successful. Wikipedia felt it.

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Re: What-If 0109: "Into the Blue"

Postby Dan H » Thu Aug 21, 2014 9:42 pm UTC

speising wrote:not the earth, but the laser would recoil. which just means it wil smash into the earth at c (since it had infinite acceleration) and hilarity ensues.

That's a fair point - I implicitly assumed the laser was securely bolted to the Earth and treated the whole laser+Earth system as a rigid body. In reality a force large enough to accelerate the whole Earth at 10 m/s^2 would be easily large enough to cause material failure of any support structure you might design. But even when the laser smashed backward into the Earth, it would transfer its linear momentum to the Earth, just in a complicated way involving large areas of vaporized matter. So there's still an interesting physical consequence Randall didn't discuss for some reason.

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Re: What-If 0109: "Into the Blue"

Postby Pfhorrest » Thu Aug 21, 2014 10:17 pm UTC

I was figuring that the laser pointer, like most of them, would be held in the unfortunate asker's hand, thus placing them at ground zero of the resultant impact (and given the way laser points are often held, would likely be the first thing impacted, other than the air between the laser pointer and themselves).
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Re: What-If 0109: "Into the Blue"

Postby nwimpney » Thu Aug 21, 2014 11:42 pm UTC

Klear wrote:
Garrett D. wrote:If I shot an infinitely strong laser beam into the sky at a random point, how much damage would it do?


First of all, if you aimed in a truly random direction, you would have an almost 50% chance of hitting the Earth.


I was kinda disappointed by this. Usually Randall takes the exact working of the question into account.


Well, the laser is going into the sky eventually, right?


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