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The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an "effective procedure" (e.g., a computer program, but it could be any sort of algorithm) is capable of proving all truths about the relations of the natural numbers (arithmetic). For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system. The second incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency.
MichiganSwampBuck
Kinetic energy is motion which is equivalent to time.
When people speak of anti-matter, it's important to recognize that anti-matter isn't some sort of 'negative' matter. An anti-particle is just as real as any other particle. If you use Einstein's famous E=mc2 relation you find that an anti-particle has positive energy, since it has a mass which is identical to the mass of its partner 'particle.' The 'anti-' part of the name just signifies the fact that the quantum numbers that the particle has are opposite of those of the corresponding particle.
If there's a mass of 3 kilograms, and if the square of 5 Joua per second is equal to 25 Joua per 1 second, then Energy will be equal to 3*((5^2)/1), or 3*(25). In other words, 75.
In "c^2", only the distance is squared, not the time component. By this I mean that for instance, if "A" would represent "5 meters covered each 1 second", then "A^2" becomes "25 meters covered in 1 second", and not "25 meters covered in 5 seconds".
Now all that's left for us to do is to separate Time from the c component. We know that Time is equal here to 1 second. But 1 cannot give 5 on its own. Which means, 5 must be divided by another 5, which happens to be the value of the distance component:
What is time? We can walk backward in space, but never backward in time. It's the great mystery, which prevents us to reach the past.
Nice try, but you made a mistake. in the equation E=mc², d and t have a fixed ratio, and your equation doesn't represent that fixed ratio. So the exact point of your mistake is this:
swanne
Where d is the distance, equal to 299,792,498 meters.
You can't do that and retain the meaning of the original equation.
Now all that's left for us to do is to separate Time from the c component.
yorkshirelad
So. I'm afraid that unless the higgs field imparts an as yet undiscovered vector component to mass that equation will never result in negative time.
TheRedneck
Incorrect. If c is in the units of m/s, then c² is in the units of m²/s². Somehow you managed to come up with an accurate final equation despite this.
swanne
The "c" component represents a very specific, fixed speed: light speed (299,792,498 meters per second). As you know, speed is, in fact, reducible to two components: distance divided by time.
In "c^2", only the distance is squared, not the time component. By this I mean that for instance, if "A" would represent "5 meters covered each 1 second", then "A^2" becomes "25 meters covered in 1 second", and not "25 meters covered in 5 seconds".
Imaginary time. Interesting. I've been wondering about imaginary numbers representing another dimension in the normal x-y-z graphs.
there has to be an imaginary component (which really means a vector at 90 degrees or 270 degrees).
When people speak of anti-matter, it's important to recognize that anti-matter isn't some sort of 'negative' matter. An anti-particle is just as real as any other particle. If you use Einstein's famous E=mc2 relation you find that an anti-particle has positive energy, since it has a mass which is identical to the mass of its partner 'particle.' The 'anti-' part of the name just signifies the fact that the quantum numbers that the particle has are opposite of those of the corresponding particle.
in the equation E=mc², d and t have a fixed ratio, and your equation doesn't represent that fixed ratio.
(5 meters / 2 seconds) squared becomes (25 meters squared / 4 seconds squared)
Also note that 25 meters squared is a measurement of area (two dimensional space), not length (one dimensional).
If we set x = 4m/2s = 2 m/s, then x² = 16m²/4s² = 4 m²/s² = (2 m/s)².