## What-If 0014: "Short Answer Section I"

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Simon
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### Re: What-if 0014: Short answer section.

From the first question:
During one phase, called a helium flash, the reaction rate is proportional to the 40th power of the temperature—which is probably the largest exponent I’ve ever seen in a physics equation!

I'd be surprised if that were true, since I'm sure Randall's come across the vacuum energy problem (that the measured value is ~10120 smaller than the value QFT predicts (famously called "the worst theoretical prediction in the history of physics").

Though I guess he could argue that the difference between a measured and predicted value isn't technically 'a physics equation'.
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wumpus
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### Re: What-if 0014: Short answer section.

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?

The other catch is that using a 50m time for a three hour swim is like using Usian Bolt's time to extrapolate a marathon. Randal was stuck with that time as "freestyle" does not allow more efficient underwater swimming and thus we lack records of what a world class swimmer can do underwater for longer distances.

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

Himself wrote:"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.

Well if we simplified a bit we could use the ratio of the portal area to the surface of the hemi-sphere of points as far away from the portal as Chell.

Assuming a circular portal (for laziness) the portal has an area of pi r2. A sphere has a surface area of 4 pi r2, so a hemisphere has an area of 2 pi r2. Assuming Chell was 5 portal radii from the portal center that gives us a ratio of (pi r2 )/ (2 pi (5r)2) = 1/50. So 12.8 - 17.4 mph for Chell using your numbers.
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Forsythe
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### Re: There is one-way glass

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.

This is nearly spot on, but isn't quite correct. You can build a one way mirror using optical components, but it's a bit more than having an 'analyser' in the middle. It requires the use of a Faraday material, which is a material with a high Verdet constant. The Verdet constant dictates how much the polarisation of light passing through the material is rotated by an external magnetic field. It turns out that counterpropagating polarised light travelling through a high Verdet material is rotated in opposite directions. Essentially transmission through the material is not the same in both directions, so we can build in a somewhat 'one way mirror'. Unfortunately it will only work at a specific wavelength, so no full colour one way mirrors are possible.

KarenRei
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### Re: What-if 0014: Short answer section.

MarvinM wrote: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.

Portal only breaks conservation of energy if it's a closed system. So long as there's a corresponding energy input, its all okay. Also, information can't be allowed to travel through the portal faster than c.

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

That last one brings a whole new meaning to musical chairs.

Felis cattus diabolicus
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### Re: What-if 0014: Short answer section.

KarenRei wrote:
MarvinM wrote: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.

Portal only breaks conservation of energy if it's a closed system. So long as there's a corresponding energy input, its all okay. Also, information can't be allowed to travel through the portal faster than c.

What with the difference of the potential energy? To be fully energy-conservative the portal would require a huge amount of some-substitute-type-of-energy (kinetic energy?) for each body going up the portal to compensate the extra potential energy gain. Likewise it would produce some of the substitute energy for each body going down.
As a result, I presume, such a wind would never blow.

Also, preforming the infinite fall by portals, you would never accelerate, I think. And if you just started with a free fall, it wouldn't even make a full loop – the kinetic energy would be smaller than the potential gravitational energy needed and the falling would just end on the portal edge.

Edit: Or would the portal suck the kinetic energy of molecules, freezing them up?

What do you think?
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Max™
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### Re: What-if 0014: Short answer section.

Wouldn't there be lateral acceleration towards the ground beyond the portal edge, as well as the influence from the ground through the upper portal, and then there is your own mass through the portal.
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Himself
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### Re: What-if 0014: Short answer section.

Himself wrote:"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.

Well if we simplified a bit we could use the ratio of the portal area to the surface of the hemi-sphere of points as far away from the portal as Chell.

Assuming a circular portal (for laziness) the portal has an area of pi r2. A sphere has a surface area of 4 pi r2, so a hemisphere has an area of 2 pi r2. Assuming Chell was 5 portal radii from the portal center that gives us a ratio of (pi r2 )/ (2 pi (5r)2) = 1/50. So 12.8 - 17.4 mph for Chell using your numbers.

But would the escaping air take the form of an expanding hemisphere or a conical jet?
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ehque
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### Re: What-if 0014: Short answer section.

Himself wrote:But would the escaping air take the form of an expanding hemisphere or a conical jet?

In the near-vacuum of the moon surface, it should be an expanding hemisphere.

It can be modelled as a hole of radius r in a infinite plane separating two volumes, one held at atmospheric pressure, the other at vacuum. Since the plane has negligible thickness, the air should not form a jet.

ijuin
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### Re: What-if 0014: Short answer section.

Simon wrote:From the first question:
During one phase, called a helium flash, the reaction rate is proportional to the 40th power of the temperature—which is probably the largest exponent I’ve ever seen in a physics equation!

I'd be surprised if that were true, since I'm sure Randall's come across the vacuum energy problem (that the measured value is ~10120 smaller than the value QFT predicts (famously called "the worst theoretical prediction in the history of physics").

Just to give a bit of a sense of scale here, Wikipedia puts the estimated mass of the observable universe at approximately 3.35 * 10^54 kg, roughly equal to the mass of 2.02 * 10^81 protons. In other words, the difference between the observed and calculated values of the vacuum energy is about a trillion trillion TRILLION times greater than the difference between a single proton and the entire observable universe!
http://en.wikipedia.org/wiki/Observable_universe

s7vfFNAA
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### Re: What-if 0014: Short answer section.

The doppler equation seems to have been changed.

What is "Car of light?"

What's the difference between "Your speed" and "Car speed"?

nate1481
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### Re: What-if 0014: Short answer section.

If anyone wants to put some numbers on the Red light dopler shift one:

[url]http://www.wolframalpha.com/input/?i=Speed+of+light%C3%97%28Red+light+wavelength^2%E2%88%92Green+light+wavelength^2%29%2F%28Green+light+wavelength^2%2BRed+light+wavelength^2%29[/url]

rmsgrey
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### Re: What-if 0014: Short answer section.

ijuin wrote:
Simon wrote:From the first question:
During one phase, called a helium flash, the reaction rate is proportional to the 40th power of the temperature—which is probably the largest exponent I’ve ever seen in a physics equation!

I'd be surprised if that were true, since I'm sure Randall's come across the vacuum energy problem (that the measured value is ~10120 smaller than the value QFT predicts (famously called "the worst theoretical prediction in the history of physics").

Just to give a bit of a sense of scale here, Wikipedia puts the estimated mass of the observable universe at approximately 3.35 * 10^54 kg, roughly equal to the mass of 2.02 * 10^81 protons. In other words, the difference between the observed and calculated values of the vacuum energy is about a trillion trillion TRILLION times greater than the difference between a single proton and the entire observable universe!
http://en.wikipedia.org/wiki/Observable_universe

I took Randall's comment to refer to exponents of variables (which have real physical meaning) rather than exponents that happen to occur in the notation of a number (which are purely notational).

It's usually a sign that something's gone wrong with your derivation when you get something varying as the 4th or 5th power of a variable, never mind anything higher, while large numbers are usually just a sign that you might want to rethink your units...

JustDoug
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### Re: What-if 0014: Short answer section.

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.

Not instead, but "in addition." That's one of the neat things about Time Travel: while your younger, pre-travel self is busily saving the Day of some town in peril, your older Travelled Self gets to save the love interest.

Time Travellers: (un)Natural Multitasking At Its Finest.

FrankZappa
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### Re: What-if 0014: Short answer section.

I am probably completely wrong about this, but, for the light to be seen as green due to the Doppler Effect wouldn't you have to be traveling away from the light instead of towards it? I would think that traveling at high speed towards a light that was red would cause a shift toward the infrared or low part of the spectrum rather than towards the higher portion. If anything a more appropriate claim would be seeing no light at all.

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

FrankZappa wrote:I am probably completely wrong about this, but, for the light to be seen as green due to the Doppler Effect wouldn't you have to be traveling away from the light instead of towards it? I would think that traveling at high speed towards a light that was red would cause a shift toward the infrared or low part of the spectrum rather than towards the higher portion. If anything a more appropriate claim would be seeing no light at all.

Nope, its the opposite. Red light gets stretched as you pull away from it, making its wavelength longer, shifting it to the infrared. If you move towards it, it becomes blueshifted (i.e. the wavelength shortens to the blue end of the spectrum), hence it would turn green.

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Extragorey
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### Car Speed

Since Randall didn't actually say the speed you'd have to travel at to perceive red as green, I'll finish his calculation here:
Car speed = 300,000,000 m/s * (sqr(0.000000635 m) - sqr(0.000000532 m)) / (sqr(0.000000532 m) + sqr(0.000000635 m))
Car speed = 52,546,961.82 m/s = 189,169,000 km/h
So about 190 giga-metres per hour.
Which is about 15,000 times faster than the current air speed record (set by an SR-71 Blackbird travelling at almost 3,530 km/h).
It would take you just over three-quarters of a second to drive around the Earth (40,075 km). And at that speed, I don't even think you'd need bridges...

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### Re: Car Speed

Extragorey wrote:Since Randall didn't actually say the speed you'd have to travel at to perceive red as green, I'll finish his calculation here:
Car speed = 300,000,000 m/s * (sqr(0.000000635 m) - sqr(0.000000532 m)) / (sqr(0.000000532 m) + sqr(0.000000635 m))
Car speed = 52,546,961.82 m/s = 189,169,000 km/h
So about 190 giga-metres per hour.
Which is about 15,000 times faster than the current air speed record (set by an SR-71 Blackbird travelling at almost 3,530 km/h).
It would take you just over three-quarters of a second to drive around the Earth (40,075 km). And at that speed, I don't even think you'd need bridges...

I guess Randall didn't bother because there's not really a world standard for traffic light colours. The wavelengths you've used appear to be typical laser diode (eg laser pointer) colours. Using the peak wavelength from the spectrum graphs on this University of Wisconsin page for actual LED traffic lights, we get
red = 657 nm, green = 500 nm
speed = 0.266484657c = 79890090 m/s = 287604325 km/h = 178709042 mph
Those speed numbers are overly precise, since we don't have anywhere near that precision in the wavelengths; I just left the extra digits in, in case someone wanted to check my arithmetic.

FWIW, the linked page also has spectra for incandescent traffic lights; the green one is rather messy.

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

Those are ridiculous speeds though, to get going that fast... hell, you'd need Yoda pitching baseballs from the rear of your craft at a high enough velocity to vaporize say, half a mile of water. You'd want to be careful about the pressure waves as well, the shockwaves and pressure differentials might set up partial vacuums as you travel, it would certainly be hard to find an upside to that much broken glass flying around... plus I can't determine where Yoda would get that much power from... perhaps he can rechannel the energy stored in the rotation of the planet... I wonder if that could have a downside if it weren't directed along the rotational axis?

I'm not interested in doing the calculations, but we could always find some way to trick grad students into doing them, or perhaps high school students could get it right eventually... but I'd be worried if they found out what we were doing, though it's not like they'd become self aware and try to kill John Connor.

If they did, then I suppose we could set up like, an online "find your one true match" scam and gather them all together in one place, not sure if it would always be a scam though, I guess some might actually find love... though it would be a pain to count them all, I suppose if we had a large enough pressure plate and had them all jump on it we could determine how many were present at a high and low end estimate... though we'd have to take into account other things, like the amount of bird shit that might strike the plate at the same time, or the amount of people so drunk they passed out instead of jumping... not sure how bird shit hitting them would change the calculations though... but perhaps we could just tell them we were trying to set a record for a radio station, then after we get them all on the plate we could activate a massive laser array beneath it in order to hurl them all into space... but we need to make sure it doesn't fail before they leave the atmosphere... that many burned drunks would smell worse than anything short of say, a massive mountain of rodents.
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### Re: What-if 0014: Short answer section.

s.wilson wrote: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 ), but maybe it's too silly even for comic book science.

I always tought it was "fly faster than light, and you'll move backwards in time". Which is comic-book physics. Of course, with sufficient speed the frame-dragging effects could reverse earth rotation. Not sure it would affect time though.

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

Hafting wrote:
s.wilson wrote: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 ), but maybe it's too silly even for comic book science.

I always tought it was "fly faster than light, and you'll move backwards in time". Which is comic-book physics. Of course, with sufficient speed the frame-dragging effects could reverse earth rotation. Not sure it would affect time though.

Look up a Tipler Cylinder - a massive, rapidly-rotating body can be used as a time machine...

ijuin
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### Re: What-If 0014: "Short Answer Section I"

Well, it WAS established in the pre-Crisis DC universe that Superman could fly through time allegedly by flying faster than light.

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

Hafting wrote:
s.wilson wrote: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 ), but maybe it's too silly even for comic book science.

I always thought it was "fly faster than light, and you'll move backwards in time". Which is comic-book physics. Of course, with sufficient speed the frame-dragging effects could reverse earth rotation. Not sure it would affect time though.

The problem with moving near the speed of light is that, according to relativity, additional energy to make you move faster appears rather as increased mass with a minimal increase of speed. If you had infinite energy to apply, you would merely reach the speed of light (as seen in the rest of the universe) and no more.

Some physicists have speculated that, if there were some "perpendicular" component to velocity that was available, it would be theoretically possible to avoid this trap at light speed. But what that means, or how it could be possible, is beyond my poor understanding of the math.
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### Re: What-If 0014: "Short Answer Section I"

ijuin wrote:Well, it WAS established in the pre-Crisis DC universe that Superman could fly through time allegedly by flying faster than light.

While the Flash changed at some point from time-travel by FTL to time-travel by altering the vibrational speed of his fundamental particles (probably around Crisis on Infinite Earths - I think pre-Crisis the vibration thing let him transfer between parallel universes instead)

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

bmonk wrote:according to relativity, additional energy to make you move faster appears rather as increased mass with a minimal increase of speed.
Thinking in terms of "relativistic mass" generally involves more confusion than clarity.

Better to simply realize that energy in special relativity includes a gamma term, where gamma is 1/sqrt(1-v^2/c^2), which goes to infinity as v goes to c.

In other words, additional energy all goes to increase speed, it's just that a given increase in speed requires asymptotically more energy as your current speed approaches that of light in a vacuum.
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### Re: What-if 0014: Short answer section.

gmalivuk wrote:Better to simply realize that energy in special relativity includes a gamma term, where gamma is 1/sqrt(1-v^2/c^2), which goes to infinity as v goes to c.
"Better to simply": I do not think that means what you think it means.
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### Re: What-If 0014: "Short Answer Section I"

Care to elaborate on anything whatsoever in that post?
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### Re: What-If 0014: "Short Answer Section I"

I got the impression he was snarking that about the applicability of "simply" to the rest of that sentence, at which large and math-challenged portions of the populace would have their eyes glaze over.
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### Re: What-If 0014: "Short Answer Section I"

Well yes, although I'm honestly not 100% sure you believe you statement to be simpler, it which case it would seem you're using "Better to simply"in a way I'm unfamiliar with. Since Poe's law applies, I'll explicitly state that this post isn't sarcastic.
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### Re: What-If 0014: "Short Answer Section I"

I never said "simpler", I said "better". If you don't think it's really simple enough to say "simply", pretend I left that word out. It is still *better* to realize that, because it leads to less confusion and misunderstanding.

Though I also think it is simpler to use the actual equation instead of trying to work with some vague imprecise notion of "fast stuff gets heavier", which will never help you calculating any actual numbers. Furthermore, "fast stuff gets heavier" doesn't illustrate the fact that "fast stuff experiences time more slowly" and "fast stuff gets shorter" by the same factor, whereas realizing where gamma shows up in those equations does illustrate this.
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### Re: What-If 0014: "Short Answer Section I"

Pfhorrest wrote:I got the impression he was snarking that about the applicability of "simply" to the rest of that sentence, at which large and math-challenged portions of the populace would have their eyes glaze over.

Maybe a graph showing the relationship between v and gamma would be helpful for such people. Or even better, a graph of (v/c) and (1/gamma), since that's just a unit (semi)circle.

OTOH, I suspect that people who find the equation that gmal posted too complex are probably not that interested in knowing the details of special relativity.

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### Re: What-If 0014: "Short Answer Section I"

PM 2Ring wrote:OTOH, I suspect that people who find the equation that gmal posted too complex are probably not that interested in knowing the details of special relativity.

Fair enough, but putting it in the same sentence as "simply" is still quite jarring.

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### Re: What-If 0014: "Short Answer Section I"

I really still don't get what is so unsimple about realizing that there's a term in the energy equation that goes to infinity as you get close to the speed of light.
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### Re: What-If 0014: "Short Answer Section I"

gmalivuk wrote:(...) additional energy all goes to increase speed, it's just that a given increase in speed requires asymptotically more energy as your current speed approaches that of light in a vacuum.

Simple.

gmalivuk wrote:(...) energy in special relativity includes a gamma term, where gamma is 1/sqrt(1-v^2/c^2), which goes to infinity as v goes to c.

Not simple.

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### Re: What-If 0014: "Short Answer Section I"

It is simple for anyone who has any business trying to say things about special relativity.
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### Re: What-If 0014: "Short Answer Section I"

gmalivuk wrote:It is simple for anyone who has any business trying to say things about special relativity.

Yes, meaning it is not simple at all, by most standards =P

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### Re: What-If 0014: "Short Answer Section I"

Forgive me for holding relativity discussions on this forum to a higher standard, then.
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### Re: What-If 0014: "Short Answer Section I"

gmalivuk wrote:It is simple for anyone who has any business trying to say things about special relativity.

Something about this statement bothers me, like it's unnecessarily elitist: "If you don't already understand, shut up and go away." Certainly, if someone wants to talk about the effects or uses of special relativity, they should know the basics at the very least. And I don't know you; maybe you were born with an innate understanding of complex physics. For me, though, everything that is simple now was once complex and indecipherable. I didn't stop at "complex and indecipherable," mostly because other, more knowledgeable people didn't tell me to shut up and go away.

But I figure that if you reply to this at all, it will be to say that you said nothing of the sort, which is possibly fair. Just, try not to look down too hard at people for whom this is not all second nature.

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### Re: What-If 0014: "Short Answer Section I"

gmalivuk wrote:I never said "simpler", I said "better".
To me "better to simply Y" when responding to X, strongly implies Y is better than X because it's simpler; as X has been established as context for simplicity. You apparently didn't mean it that way, which is fine as I'm not Lord Policing dictator of the English language.
gmalivuk wrote:It is simple for anyone who has any business trying to say things about special relativity.
Which kind of entirely defeats the point. BMonk's statement was explain an aspect of special relativity, to those without a strong basis. Saying "includes a gamma term" may only be one relationship to you, but to anyone you might actually be explaining it to, "includes the term: 1/sqrt(1-v^2/c^2)" is seven relationships.
gmalivuk wrote:Though I also think it is simpler to use the actual equation instead of trying to work with some vague imprecise notion of "fast stuff gets heavier", which will never help you calculating any actual numbers. Furthermore, "fast stuff gets heavier" doesn't illustrate the fact that "fast stuff experiences time more slowly" and "fast stuff gets shorter" by the same factor, whereas realizing where gamma shows up in those equations does illustrate this.
Okay, so are you saying that it's simpler to apply the actual equation, not that the actual equation contains less information or requires less background knowledge?
Last edited by Quizatzhaderac on Wed Aug 28, 2013 2:37 pm UTC, edited 1 time in total.
The thing about recursion problems is that they tend to contain other recursion problems.