Too many comments to read them all, so someone may have already posted something similar. This doesn't defy any laws of physics because of the key reference to "the medium." Here is an elementary explanation about how the speed that something travels is greatly dependent upon the medium in which it is traveling. By looking at some of the comments, I can tell some people need it. Assume person A is standing in the endzone of a football field and person B is standing in the opposite endzone.Scenario1: Person B yells "Hello!!!" across the football field so the medium is air and the distance is 100 yards. Approximate time until person A hears "Hello" is approximately 1/4 second.Scenario2: Person A and person B each have telephones. Person B says "Hello" into the telephone so the medium here is the telephone circuitry with a distance well over 100 yards. Approximate time until person A hears "Hello" is approximately 0 seconds. Hard core physics people can now start bashing away at why this was a poor example.
Not Possible. Einstein's theories specifically state that light goes at the same speed NO MATTER WHAT. This is what Einstein spent years proving. Not to mention that it would take an infinite amount of energy to just get something to the speed of light because the faster an object goes, its mass increases.@koko775I feel your pain...
@ everyoneFinally this thread is dead! I have won!@ teeceI doubt you'll even read this but, as a sophomore, I no doubt had not the knowledge to understand complex physics, but as a graduating senior 5 years later (see its called the 7 year plan and it involves lots of studying, global travelling and transfering from one school to another) things are a lot different. I've done all that math you suggested, and most of the physics work you have suggested. I swapped majors not because it was *hard* but because I became more interested in programming, game development and creative writing. I dunno, at the time it seemed like there was so much more to life than physics, and I did not want to be trapped in that later in life. So I swapped it out into more of the hobby realm and swapped writing and programming into the career realm. thats how it is and imaginary numbers are fun.
"It's effective speed is below c because the photons keep being absorbed and emitted by the atoms.It's speed in between the intervals that is still c."Eh, I think that's semantics. The light is moving in its direction of travel on the macroscale at a speed well below c. That's what I meant."Because of this absurdity, it's 'obvious' that real numbers are fake: a mere mathematical trick dreamed up to solve a problem. Ditto negative numbers. Ditto zero. Ditto irrational numbers."I would disagree. I haven't worked a *whole* lot with imaginary numbers, but I have used them in math classes and read up about them because they're interesting.The difference for me is that every example I can find of how real numbers are just like imaginary numbers is a bad comparison. I have two points of view on this:The "but to a person counting apples, there's no such thing as 7/5 or -4!" argument. While they may not be actively using fractions or negative numbers, they're easy to explain. Fractions are cutting the apples into pieces, and negative numbers are owing someone that number of apples. You can even relate the two to get the integer/remainder thing - If you sell apples for 3 cents, I have a nickel, and you have no change, I can buy one apple and you will keep a note that next time you will sell me another apple for a penny.The abstract math perspective, which you brought up - "you can't describe 3/2 using integers." But you can *approximate* it, which you did with the "2, remainder 1."Maybe I am missing out on some really good discussion of complex numbers somewhere (in which case I'd really like to read it), but neither of those things are true of them as far as I can tell. Here's the best one I've come across so far:<a class="user" href="http://www.math.toronto.edu/mathnet/answers/imagexist.html">http://www.math.toronto.edu/mathnet/answers/imagexist.html</a>But it still falls apart for me in terms of conveying that imaginary numbers are as "real" as real numbers. The reason is that anything involving real numbers can be related to the real world in some way, as I did above. But (again, unless I am missing something), this is not true for imaginary numbers. I have only ever seen them used as a kind of mathematical hyperspace to get between two points that can't be done using real numbers. You never have have i electrons in your trap, or (as you said) something that has a mass of i. They're used to calculate real things, but the end result is always real. I think they're really interesting and a valuable tool, but I haven't come across anything that makes me think they have an analogue in the real world like real numbers do.
isn't it kind of absurd to start debating whether imaginary numbers or integers or real numbers or infinities exist? Math is a pure science; we map it into reality in ways that are convenient for us, and use it to describe the universe around us. Math is, at it's heart, purely an abstract construction. IF you think "Well, Integers exist, because I can have a single apple, or two apples, or three apples", it's just as abstract as saying that e or pi or i exist... because they can be used to describe something.Remmeber, the fact that you see and feel and taste an apple is also juts an abstraction.. I can point you to lots of zen monks who will quickly point out that you and the apple are, in fact, not separate objects, but one and the same.
shaunsJan 6, 2006
Too many comments to read them all, so someone may have already posted something similar. This doesn't defy any laws of physics because of the key reference to "the medium." Here is an elementary explanation about how the speed that something travels is greatly dependent upon the medium in which it is traveling. By looking at some of the comments, I can tell some people need it. Assume person A is standing in the endzone of a football field and person B is standing in the opposite endzone.Scenario1: Person B yells "Hello!!!" across the football field so the medium is air and the distance is 100 yards. Approximate time until person A hears "Hello" is approximately 1/4 second.Scenario2: Person A and person B each have telephones. Person B says "Hello" into the telephone so the medium here is the telephone circuitry with a distance well over 100 yards. Approximate time until person A hears "Hello" is approximately 0 seconds. Hard core physics people can now start bashing away at why this was a poor example.
ioxerJan 6, 2006
Not Possible. Einstein's theories specifically state that light goes at the same speed NO MATTER WHAT. This is what Einstein spent years proving. Not to mention that it would take an infinite amount of energy to just get something to the speed of light because the faster an object goes, its mass increases.@koko775I feel your pain...
mobbydickJan 6, 2006
the pictures with the blue glow are freaking cool
ammgyrpJan 6, 2006
@ everyoneFinally this thread is dead! I have won!@ teeceI doubt you'll even read this but, as a sophomore, I no doubt had not the knowledge to understand complex physics, but as a graduating senior 5 years later (see its called the 7 year plan and it involves lots of studying, global travelling and transfering from one school to another) things are a lot different. I've done all that math you suggested, and most of the physics work you have suggested. I swapped majors not because it was *hard* but because I became more interested in programming, game development and creative writing. I dunno, at the time it seemed like there was so much more to life than physics, and I did not want to be trapped in that later in life. So I swapped it out into more of the hobby realm and swapped writing and programming into the career realm. thats how it is and imaginary numbers are fun.
blincolnJan 8, 2006
"It's effective speed is below c because the photons keep being absorbed and emitted by the atoms.It's speed in between the intervals that is still c."Eh, I think that's semantics. The light is moving in its direction of travel on the macroscale at a speed well below c. That's what I meant."Because of this absurdity, it's 'obvious' that real numbers are fake: a mere mathematical trick dreamed up to solve a problem. Ditto negative numbers. Ditto zero. Ditto irrational numbers."I would disagree. I haven't worked a *whole* lot with imaginary numbers, but I have used them in math classes and read up about them because they're interesting.The difference for me is that every example I can find of how real numbers are just like imaginary numbers is a bad comparison. I have two points of view on this:The "but to a person counting apples, there's no such thing as 7/5 or -4!" argument. While they may not be actively using fractions or negative numbers, they're easy to explain. Fractions are cutting the apples into pieces, and negative numbers are owing someone that number of apples. You can even relate the two to get the integer/remainder thing - If you sell apples for 3 cents, I have a nickel, and you have no change, I can buy one apple and you will keep a note that next time you will sell me another apple for a penny.The abstract math perspective, which you brought up - "you can't describe 3/2 using integers." But you can *approximate* it, which you did with the "2, remainder 1."Maybe I am missing out on some really good discussion of complex numbers somewhere (in which case I'd really like to read it), but neither of those things are true of them as far as I can tell. Here's the best one I've come across so far:<a class="user" href="http://www.math.toronto.edu/mathnet/answers/imagexist.html">http://www.math.toronto.edu/mathnet/answers/imagexist.html</a>But it still falls apart for me in terms of conveying that imaginary numbers are as "real" as real numbers. The reason is that anything involving real numbers can be related to the real world in some way, as I did above. But (again, unless I am missing something), this is not true for imaginary numbers. I have only ever seen them used as a kind of mathematical hyperspace to get between two points that can't be done using real numbers. You never have have i electrons in your trap, or (as you said) something that has a mass of i. They're used to calculate real things, but the end result is always real. I think they're really interesting and a valuable tool, but I haven't come across anything that makes me think they have an analogue in the real world like real numbers do.
3denJan 8, 2006
isn't it kind of absurd to start debating whether imaginary numbers or integers or real numbers or infinities exist? Math is a pure science; we map it into reality in ways that are convenient for us, and use it to describe the universe around us. Math is, at it's heart, purely an abstract construction. IF you think "Well, Integers exist, because I can have a single apple, or two apples, or three apples", it's just as abstract as saying that e or pi or i exist... because they can be used to describe something.Remmeber, the fact that you see and feel and taste an apple is also juts an abstraction.. I can point you to lots of zen monks who will quickly point out that you and the apple are, in fact, not separate objects, but one and the same.
iworksJan 9, 2006
thus we live in the matrix and I just saw the women in the red dress pass by faster than the speed of light
thelveresJun 24, 2009
You don't turn matter into energy by burning it mate.. you are merely fusing it with oxygen with an exothermic reaction into a lower energy state.