What-If 0014: "Short Answer Section I"

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What-If 0014: "Short Answer Section I"

Postby MarvinM » Tue Oct 02, 2012 8:34 am UTC

http://what-if.xkcd.com/14/

Pretty mixed for me, I wonder if a stream of water, assuming removing the angular momentum wouldn't just boil away in the heat and solar wind. Also I remember the superman thing to happen in 2 stages, a reversing and putting back, so at least in the cut of the film I remember it is as stupid as I thought it was. Also the solution for the portal violates conservation of energy, a consistent solution would include a force needed to cross the boundary equivalent to the kink in space-time and you'd be left with differences in pressure due to weather.
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Re: What-if 0014: Short answer section.

Postby honnza » Tue Oct 02, 2012 8:40 am UTC

This ... isn’t actually a question.

But thank you for sharing!


I think I'll be using it now and then when browsing Yahoo Answers :D

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Re: What-if 0014: Short answer section.

Postby Max™ » Tue Oct 02, 2012 9:15 am UTC

I did the perfect harmonic gas once, leaned up to try to be quiet so I wouldn't wake up the people in the next room to hear a perfect "ooooooooooooooooooooooooooooovrrp!" like running your finger around the rim of a wine glass.

When it started I froze for fear of ending it... it was amazing.
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Re: What-if 0014: Short answer section.

Postby rhomboidal » Tue Oct 02, 2012 9:31 am UTC

I expect Michael Phelps will probably attempt to replicate Superman's feat, except in the world's oceans. 10:1 -- that he'll attempt it.

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Re: What-if 0014: Short answer section.

Postby mojacardave » Tue Oct 02, 2012 9:48 am UTC

I was kind of underwhelmed by the Michael Phelps answer. Only 3 hours to swim to the bottom of the Marianas Trench and back? That seems disappointingly easy. I'm aware that the pressure issues make it impossible, and that humans won't be getting down there any time soon, but I'd always assumed the maximum ocean depth on the planet was one of those inconceivable numbers. Turns out oceans aren't really that deep at all physically, they're only deep in terms of practicality.

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Re: What-if 0014: Short answer section.

Postby ElWanderer » Tue Oct 02, 2012 9:59 am UTC

mojacardave wrote:I was kind of underwhelmed by the Michael Phelps answer. Only 3 hours to swim to the bottom of the Marianas Trench and back? That seems disappointingly easy. I'm aware that the pressure issues make it impossible, and that humans won't be getting down there any time soon, but I'd always assumed the maximum ocean depth on the planet was one of those inconceivable numbers. Turns out oceans aren't really that deep at all physically, they're only deep in terms of practicality.

Yeah. To the bottom of the Challenger Deep and back is about 22km. As a comparison, the English Channel is 34km wide (edit - at its narrowest), and the record for swimming that is about 7 hours.
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Re: What-if 0014: Short answer section.

Postby Vroomfundel » Tue Oct 02, 2012 11:10 am UTC

ElWanderer wrote:Yeah. To the bottom of the Challenger Deep and back is about 22km. As a comparison, the English Channel is 34km wide, and the record for swimming that is about 7 hours.


Still, the calculation is quite oversimplified - although it's correct within orders of magnitude.
Due to positive buoyancy of the human body it's harder to swim downwards than along the surface, and you can't make up for that when coming up as pressure differential is dangerous. And generally we'd be better off to start with an estimate of a real diver's speed, rather than this guy breaking a record in an insane way, although he's pretty cool I must admit
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Re: What-if 0014: Short answer section.

Postby s.wilson » Tue Oct 02, 2012 11:14 am UTC

About Superman time travel, I was sure it was a sort of metaphysical thing about time zones and "travelling to yesterday" (if you pass the International Date line fast enough it don't see you and you are in yesterday :D ), but maybe it's too silly even for comic book science.

ps: to see Phelps swimming make me think about Kraken, so I’m not surprised if he is at home in abyss :lol:

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Re: What-if 0014: Short answer section.

Postby AvatarIII » Tue Oct 02, 2012 11:20 am UTC

Vroomfundel wrote:
ElWanderer wrote:Yeah. To the bottom of the Challenger Deep and back is about 22km. As a comparison, the English Channel is 34km wide, and the record for swimming that is about 7 hours.


Still, the calculation is quite oversimplified - although it's correct within orders of magnitude.
Due to positive buoyancy of the human body it's harder to swim downwards than along the surface, and you can't make up for that when coming up as pressure differential is dangerous. And generally we'd be better off to start with an estimate of a real diver's speed, rather than this guy breaking a record in an insane way, although he's pretty cool I must admit


if we assume Phelps doesn't need to breathe, we can also assume that he doesn't need to have air in his lungs. I know for a fact that I am most definitely NOT positively buoyant unless I have air in my lungs. and iirc, even with full lungs there is a depth at which humans become negatively buoyant anyway, due to compression, at something like 10 - 15 m depth.

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Re: What-if 0014: Short answer section.

Postby Yoduh » Tue Oct 02, 2012 1:22 pm UTC

I'm starting to notice a few of these What If questions have also been answered on the "vsauce" youtube channel. A video on what would happen if everyone on Earth jumped together was actually uploaded 2 days before the same xkcd what-if. They've also discussed the what-if of everyone on the planet being in one spot, and what happens if you tried to douse the sun with water. I'm sure it's just coincidental, but I guess if you like What-Ifs you'd also really like the vsauce youtube channel.

link: http://www.youtube.com/user/Vsauce

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There is one-way glass

Postby cellocgw » Tue Oct 02, 2012 1:30 pm UTC

Randall is correct that no simple pane of glass with overcoatings can be a one-way mirror, but there are ways to do it.
First, there are gadgets in the fiber-optic world which rotate the polarization state twice with an "analyzer" in between whose transmission is polarization-sensitive. Light in one direction goes thru fine, but in the reverse direction the polarization state is perpendicular to the transmission axis, and it's blocked.

These modern days, there's also stuff called "metamaterials." One example is a carefully crafted asymmetric crystalline lattice which causes constructive or destructive interference depending on the direction of entry (of the light waves).
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Re: What-if 0014: Short answer section.

Postby J L » Tue Oct 02, 2012 2:06 pm UTC

I was quite surprised to learn that according to Wikipedia (no source is given) humans can handle up to 534 m of depth: http://en.wikipedia.org/wiki/Saturation ... th_records

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Re: What-if 0014: Short answer section.

Postby ElWanderer » Tue Oct 02, 2012 2:57 pm UTC

J L wrote:I was quite surprised to learn that according to Wikipedia (no source is given) humans can handle up to 534 m of depth: http://en.wikipedia.org/wiki/Saturation ... th_records

That same page quotes a 701m depth equivalent in a test chamber, which is pretty amazing (and there are some reference links, though the first is to New Scientist which'll only let me read four paragraphs).

The free-diving (no breathing equipment) record of 273m (Wikipedia) is also pretty amazing. At that depth your lungs are holding only 1/28th of the volume of air as at the surface. I always thought that meant your lungs would damage themselves, but it seems there's part of the mammalian diving response that shifts blood around to keep the organs from being crushed. I wonder how deep in the water that works. For comparison "World War II German U-boats generally had collapse depths in the range of 200 to 280 meters [citation needed]"...
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Re: What-if 0014: Short answer section.

Postby Hal_10000 » Tue Oct 02, 2012 3:01 pm UTC

One quibble: the Sun will not turn into a black hole unless you add a heck of a lot of mass (like eight solar masses). It's going to end up as a white dwarf.

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Re: What-if 0014: Short answer section.

Postby SecondTalon » Tue Oct 02, 2012 3:04 pm UTC

Hal_10000 wrote:One quibble: the Sun will not turn into a black hole unless you add a heck of a lot of mass (like eight solar masses). It's going to end up as a white dwarf.

.... like eight solar masses of water from a giant hose?
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Re: What-if 0014: Short answer section.

Postby ElWanderer » Tue Oct 02, 2012 3:05 pm UTC

Hal_10000 wrote:One quibble: the Sun will not turn into a black hole unless you add a heck of a lot of mass (like eight solar masses). It's going to end up as a white dwarf.

I thought the Chandrasekhar limit was only 1.4 solar masses...
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Re: What-if 0014: Short answer section.

Postby Hal_10000 » Tue Oct 02, 2012 3:11 pm UTC

ElWanderer wrote:
Hal_10000 wrote:One quibble: the Sun will not turn into a black hole unless you add a heck of a lot of mass (like eight solar masses). It's going to end up as a white dwarf.

I thought the Chandrasekhar limit was only 1.4 solar masses...


That's to convert a white dwarf into a neutron star. And that's for a stellar *remnant*. The original star can be much larger.

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Re: What-if 0014: Short answer section.

Postby rmsgrey » Tue Oct 02, 2012 3:12 pm UTC

ElWanderer wrote:
Hal_10000 wrote:One quibble: the Sun will not turn into a black hole unless you add a heck of a lot of mass (like eight solar masses). It's going to end up as a white dwarf.

I thought the Chandrasekhar limit was only 1.4 solar masses...

Yeah, but the collapse starts with a supernova which sheds a lot of mass

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Re: What-if 0014: Short answer section.

Postby Archgeek » Tue Oct 02, 2012 3:14 pm UTC

Amusingly, plugging in the speed proffered and green in place of red, an actual green light would appear deep violet with a significant UV component, making them rather dim to boot.
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Re: What-if 0014: Short answer section.

Postby Jackpot777 » Tue Oct 02, 2012 3:22 pm UTC

I'm more worried because Lois Lane died because Superman was saving an entire town from drowning in a flood. But he went back in time to alter events so that she was saved instead. Needs of the Lois outweigh the needs of the many, and so on.

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Re: What-if 0014: Short answer section.

Postby ElWanderer » Tue Oct 02, 2012 3:30 pm UTC

Hal_10000 wrote:
ElWanderer wrote:
Hal_10000 wrote:One quibble: the Sun will not turn into a black hole unless you add a heck of a lot of mass (like eight solar masses). It's going to end up as a white dwarf.

I thought the Chandrasekhar limit was only 1.4 solar masses...


That's to convert a white dwarf into a neutron star. And that's for a stellar *remnant*. The original star can be much larger.

Ah right, I sit corrected :)
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Re: What-if 0014: Short answer section.

Postby Vir4030 » Tue Oct 02, 2012 6:33 pm UTC

Here's the original Superman footage. He flies one direction to set the earth going backwards, then time reverses, then he flies the other direction to return the earth's spin to normal.

So, Randall had it right his entire life.

http://www.youtube.com/watch?v=TjgsnWtBQm0

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Re: What-if 0014: Short answer section.

Postby taralluccio » Tue Oct 02, 2012 7:30 pm UTC

Wonderful, as always!

I remember the calculation of the red light/green light doppler effect. It was in a Casey and Andy comic.

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Re: What-if 0014: Short answer section.

Postby Himself » Tue Oct 02, 2012 8:47 pm UTC

"Fast enough to strip pavement from a parking lot." Bit of an understatement.
But this also makes me rethink the ending of Portal 2. Using the equation Randall gives, I get speeds in the range of 640-870 mph for that particular situation, probably closer to the high figure. I expect the size of the portal would reduce this (how much, though?), but even with that I doubt Chell could have held on.
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Re: What-if 0014: Short answer section.

Postby mathmannix » Tue Oct 02, 2012 9:31 pm UTC

Jackpot777 wrote:I'm more worried because Lois Lane died because Superman was saving an entire town from drowning in a flood. But he went back in time to alter events so that she was saved instead. Needs of the Lois outweigh the needs of the many, and so on.


If he went back in time (or temporarily reversed time, same difference) then he was in both places, saving everyone on the dam (including Jimmy Olsen, who obviously made it to the sequels) and Lois by being in two places at the same time.

Still though... all that for Margot Kidder Lois? Erica Durance Lois sure. Terri Hatcher Lois, you betcha...
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Re: There is one-way glass

Postby Pfhorrest » Tue Oct 02, 2012 10:04 pm UTC

cellocgw wrote:Randall is correct that no simple pane of glass with overcoatings can be a one-way mirror, but there are ways to do it.
First, there are gadgets in the fiber-optic world which rotate the polarization state twice with an "analyzer" in between whose transmission is polarization-sensitive. Light in one direction goes thru fine, but in the reverse direction the polarization state is perpendicular to the transmission axis, and it's blocked.

These modern days, there's also stuff called "metamaterials." One example is a carefully crafted asymmetric crystalline lattice which causes constructive or destructive interference depending on the direction of entry (of the light waves).

Wouldn't the second law of thermodynamics take issue with a true one-way mirror, however constructed, as you could use it to take a volume uniformly full of maximally entropic photons bouncing around and turn it into a half-volume with twice the photon density and a half-volume with no photons bouncing around in it?

I suppose you could still do it, but there would be a catch somewhere offsetting the entropy somehow. Same with any apparently unidirectional filter.
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Re: What-if 0014: Short answer section.

Postby mathrec » Tue Oct 02, 2012 10:33 pm UTC

I was surprised to see that Randall got the relativistic doppler effect wrong (?!)

The ratio of the velocity to the speed of light is

v/c = (1-r)/(1+r), where r is the ratio of the frequencies (source/observed). I would choose a ratio of 51/65, but I wouldn't really quibble with Randall's 3/4, so 3/4 it is.

v/c = (1/4)/(7/4) = 1/7.

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Re: What-if 0014: Short answer section.

Postby webgrunt » Tue Oct 02, 2012 10:38 pm UTC

"We were both (luckily) amazed and surprised and I have often wondered what the odds are for something like that happening. "

I think the question he meant to ask is, "What are the odds for something like this happening?"

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Re: There is one-way glass

Postby Himself » Tue Oct 02, 2012 11:33 pm UTC

Pfhorrest wrote:
cellocgw wrote:Randall is correct that no simple pane of glass with overcoatings can be a one-way mirror, but there are ways to do it.
First, there are gadgets in the fiber-optic world which rotate the polarization state twice with an "analyzer" in between whose transmission is polarization-sensitive. Light in one direction goes thru fine, but in the reverse direction the polarization state is perpendicular to the transmission axis, and it's blocked.

These modern days, there's also stuff called "metamaterials." One example is a carefully crafted asymmetric crystalline lattice which causes constructive or destructive interference depending on the direction of entry (of the light waves).

Wouldn't the second law of thermodynamics take issue with a true one-way mirror, however constructed, as you could use it to take a volume uniformly full of maximally entropic photons bouncing around and turn it into a half-volume with twice the photon density and a half-volume with no photons bouncing around in it?

I suppose you could still do it, but there would be a catch somewhere offsetting the entropy somehow. Same with any apparently unidirectional filter.

How about shedding the excess energy from the photons as heat?
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Re: There is one-way glass

Postby Invisiblemoose » Wed Oct 03, 2012 2:18 am UTC

Himself wrote:
Pfhorrest wrote:
cellocgw wrote:Randall is correct that no simple pane of glass with overcoatings can be a one-way mirror, but there are ways to do it.
First, there are gadgets in the fiber-optic world which rotate the polarization state twice with an "analyzer" in between whose transmission is polarization-sensitive. Light in one direction goes thru fine, but in the reverse direction the polarization state is perpendicular to the transmission axis, and it's blocked.

These modern days, there's also stuff called "metamaterials." One example is a carefully crafted asymmetric crystalline lattice which causes constructive or destructive interference depending on the direction of entry (of the light waves).

Wouldn't the second law of thermodynamics take issue with a true one-way mirror, however constructed, as you could use it to take a volume uniformly full of maximally entropic photons bouncing around and turn it into a half-volume with twice the photon density and a half-volume with no photons bouncing around in it?

I suppose you could still do it, but there would be a catch somewhere offsetting the entropy somehow. Same with any apparently unidirectional filter.

How about shedding the excess energy from the photons as heat?

So the light would bounce around forever while generating heat?

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Re: What-if 0014: Short answer section.

Postby ijuin » Wed Oct 03, 2012 3:32 am UTC

taralluccio wrote:Wonderful, as always!

I remember the calculation of the red light/green light doppler effect. It was in a Casey and Andy comic.


Here's the link for that one: http://galactanet.com/comic/view.php?strip=39

They got arrested for driving 400 million miles per hour over the speed limit. :D

Regarding the perfect one-way mirror bit, if you had that, you would essentially have Maxwell's Demon, which is generally believed to violate the Second Law of Thermodynamics. http://en.wikipedia.org/wiki/Maxwell%27s_demon

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Re: There is one-way glass

Postby Himself » Wed Oct 03, 2012 4:01 am UTC

Invisiblemoose wrote:
Himself wrote:
Pfhorrest wrote:
cellocgw wrote:Randall is correct that no simple pane of glass with overcoatings can be a one-way mirror, but there are ways to do it.
First, there are gadgets in the fiber-optic world which rotate the polarization state twice with an "analyzer" in between whose transmission is polarization-sensitive. Light in one direction goes thru fine, but in the reverse direction the polarization state is perpendicular to the transmission axis, and it's blocked.

These modern days, there's also stuff called "metamaterials." One example is a carefully crafted asymmetric crystalline lattice which causes constructive or destructive interference depending on the direction of entry (of the light waves).

Wouldn't the second law of thermodynamics take issue with a true one-way mirror, however constructed, as you could use it to take a volume uniformly full of maximally entropic photons bouncing around and turn it into a half-volume with twice the photon density and a half-volume with no photons bouncing around in it?

I suppose you could still do it, but there would be a catch somewhere offsetting the entropy somehow. Same with any apparently unidirectional filter.

How about shedding the excess energy from the photons as heat?

So the light would bounce around forever while generating heat?

No, the energy of the light would get absorbed by the walls. Or is the assumption that the walls are reflective?
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Re: What-if 0014: Short answer section.

Postby JamesOwen » Wed Oct 03, 2012 4:39 am UTC

mathrec wrote:I was surprised to see that Randall got the relativistic doppler effect wrong (?!)

The ratio of the velocity to the speed of light is

v/c = (1-r)/(1+r), where r is the ratio of the frequencies (source/observed). I would choose a ratio of 51/65, but I wouldn't really quibble with Randall's 3/4, so 3/4 it is.

v/c = (1/4)/(7/4) = 1/7.


I noticed something funny here, too. For speeds at which the lorentz factor is much different from one, shouldn't the speed be given by v/c = (r^2-1)/(r^2+1)? The answer still comes out to right about 1/3c, so it doesn't affect the shift too much.

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Re: There is one-way glass

Postby Pfhorrest » Wed Oct 03, 2012 4:41 am UTC

Himself wrote:
Invisiblemoose wrote:
Himself wrote:
Pfhorrest wrote:
cellocgw wrote:Randall is correct that no simple pane of glass with overcoatings can be a one-way mirror, but there are ways to do it.
First, there are gadgets in the fiber-optic world which rotate the polarization state twice with an "analyzer" in between whose transmission is polarization-sensitive. Light in one direction goes thru fine, but in the reverse direction the polarization state is perpendicular to the transmission axis, and it's blocked.

These modern days, there's also stuff called "metamaterials." One example is a carefully crafted asymmetric crystalline lattice which causes constructive or destructive interference depending on the direction of entry (of the light waves).

Wouldn't the second law of thermodynamics take issue with a true one-way mirror, however constructed, as you could use it to take a volume uniformly full of maximally entropic photons bouncing around and turn it into a half-volume with twice the photon density and a half-volume with no photons bouncing around in it?

I suppose you could still do it, but there would be a catch somewhere offsetting the entropy somehow. Same with any apparently unidirectional filter.

How about shedding the excess energy from the photons as heat?

So the light would bounce around forever while generating heat?

No, the energy of the light would get absorbed by the walls. Or is the assumption that the walls are reflective?

Well if we are assuming as an initial condition, before placing the one-way mirror in there, that there is a volume full of photons bouncing around, then the photons have to be bouncing, i.e. reflecting, off the walls.

Even if you did have the walls absorbing the light and some source of new light emission, you would still get second law violations from the one-way mirror if your only catch is "the walls absorb the light and turn it into heat", because then the walls on one side will absorb more light and thus get hotter than the walls on the other side, and now you have a heat gradient you can use to do useful work, when before you had a system at maximal entropy and thus no such gradients and no ability to do work.

To avoid a second law violation, the one-way mirror would have to somehow generate more entropy than would be reduced by the creation of the energy gradient, whether that energy be in the form of light or heat. (In practice you would probably want to use the light to generate heat to power any actual engine to do useful work, so may as well call it heat in either case). The mirror would have to use energy somehow (from outside the system), and output waste heat, in the process of sorting photons from one side of itself to the other.
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Re: What-if 0014: Short answer section.

Postby Red Hal » Wed Oct 03, 2012 6:12 am UTC

Regarding the singing chair. By definition any wind liberated from the body is discrete, the trick is to be discreet about it.
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Re: What-if 0014: Short answer section.

Postby Neal J. King » Wed Oct 03, 2012 8:46 am UTC


Postby JamesOwen » Wed Oct 03, 2012 4:39 am UTC

mathrec wrote:I was surprised to see that Randall got the relativistic doppler effect wrong (?!)

The ratio of the velocity to the speed of light is

v/c = (1-r)/(1+r), where r is the ratio of the frequencies (source/observed). I would choose a ratio of 51/65, but I wouldn't really quibble with Randall's 3/4, so 3/4 it is.

v/c = (1/4)/(7/4) = 1/7.



I noticed something funny here, too. For speeds at which the lorentz factor is much different from one, shouldn't the speed be given by v/c = (r^2-1)/(r^2+1)? The answer still comes out to right about 1/3c, so it doesn't affect the shift too much.


JamesOwen:

You are correct, the relativistic formula can be easily obtained from:
http://en.wikipedia.org/wiki/Relativist ... ler_effect

Using r = f_green/f_red = 3/2 in accordance with Randall's first answer,
v/c = (9 - 4)/(9 + 4) = 5/13 = 0.38461530

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Re: What-if 0014: Short answer section.

Postby Judah » Wed Oct 03, 2012 11:39 am UTC

Neal J. King wrote:

Postby JamesOwen » Wed Oct 03, 2012 4:39 am UTC

mathrec wrote:I was surprised to see that Randall got the relativistic doppler effect wrong (?!)

The ratio of the velocity to the speed of light is

v/c = (1-r)/(1+r), where r is the ratio of the frequencies (source/observed). I would choose a ratio of 51/65, but I wouldn't really quibble with Randall's 3/4, so 3/4 it is.

v/c = (1/4)/(7/4) = 1/7.



I noticed something funny here, too. For speeds at which the lorentz factor is much different from one, shouldn't the speed be given by v/c = (r^2-1)/(r^2+1)? The answer still comes out to right about 1/3c, so it doesn't affect the shift too much.


JamesOwen:

You are correct, the relativistic formula can be easily obtained from:
http://en.wikipedia.org/wiki/Relativist ... ler_effect

Using r = f_green/f_red = 3/2 in accordance with Randall's first answer,
v/c = (9 - 4)/(9 + 4) = 5/13 = 0.38461530
I'm no physicist, so I'm not even going to try to verify the following, but for what it's worth, Randall's old employer, addressing this same question, specifically notes that in this case the relativistic equation must be used, gives the ratio of the frequencies in question as 65/47, and comes up with .3c as the final answer.

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SerMufasa
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Re: What-if 0014: Short answer section.

Postby SerMufasa » Wed Oct 03, 2012 1:31 pm UTC

Regarding Superman time travel: if he can travel back in time (and yes, despite what is shown in the movie, the intention of the writer was that Superman was traveling back in time via superfast flight), why doesn't he just go back far enough to stop the missiles entirely?

Of course:
http://www.youtube.com/watch?v=yavK0mnE3wI

Regarding the last "question", I'm not sure what the issue is. Air passing through holes can make noise. Just because the fart was silent, there's still an expulsion of gas, and the gas went through the hole at the correct angle to generate a sound.

Regarding the sun becoming a black hole, I believe Randall was indicating that there was enough mass via water added to have it become a black hole rather than a white dwarf... I would've liked to have seen the calculations for that tho!
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Felis cattus diabolicus
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Re: What-if 0014: Short answer section.

Postby Felis cattus diabolicus » Wed Oct 03, 2012 1:44 pm UTC

Randall wrote:Someone recently blew my mind by telling me I’d been misinterpreting that scene all my life. I like their take on it way better:

Superman wasn't exerting a force on the Earth. He was just flying fast enough to go back in time. (Faster than light, I guess? Comic book physics.) The Earth changed direction because we were watching time run backward as he traveled. It didn't actually have anything to do with the direction he was flying.

SerMufasa wrote:Regarding Superman time travel: if he can travel back in time (and yes, despite what is shown in the movie, the intention of the writer was that Superman was traveling back in time via superfast flight), why doesn't he just go back far enough to stop the missiles entirely?

But after he did so, he would have to change his path of flight - otherwise we would crash himself.
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Re: What-if 0014: Short answer section.

Postby JoeZ » Wed Oct 03, 2012 1:55 pm UTC

I also noticed the issue with the doppler shift question, having just done that problem recently.

Solving the relativistic doppler shift equation for u yields;

u = [((w_source)/(w_observed))^2 -1]/[((w_source)/(w_observed))^2 + 1]

The correct velocity should be closer to;

u = c/7

(varying a bit, depending on what wavelengths you choose for red and green.)
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