Random question I came up with
Is there any defining point between infinity and real numbers?
A while back I just had a random thought: "If it takes an infinite amount of energy to make something with mass move the speed of light, where is the difference in energy between infinity and making something not move at all?" (Yes this is a random thought and the types of things I think about when I get bored)
Example: If an object with 1G of mass was moving at the speed of light, it'd take infinite energy to do so, but now what if it was moving 1 plank distance less than the speed of light? Would it still take infinite energy? Then you could keep going, for no matter how many times you subtract 1 from infinity, it's still infinity. So theoretically it takes an infinite amount of energy to make something to not move at all after subtracting some ludicrous number of plank distances.
[header2]Things to keep in mind[/header2]
The amount of Planck distance in 1 second of light speed: 1.85492292757841104x10^43 and not infinite
And Xeno's paradox is wrong because there's only 6.18735688x10^35 Planck distance in it.
Treat "Infinity" as a number with properties identical to the concept "Infinity"
Can someone disprove this or explain how this is wrong?
12 Comments • Newest first
definition of limit
[quote=Ponified]I see. Just another paradox then.[/quote]
It's not exactly a paradox.. but I guess you could call it that
[quote=zeck96]I've already beaten x/0. Quite simple really. Division is glorified subtraction, you just keep subtracting until you have nothing left, so what happens with you have 1-0? It's 1.
What if you 1-0 again? It's still one. This goes on PAST infinity into a term known as "Undefined" or you could argue that it is X because no matter how many times you subtract by 0 it's still X[/quote]
Well, its undefined because its not mathematically possible, but actually for f(x) = c/x, as x -> 0, f(x) approaches ∞.
[quote=Ponified]Since the speed of light is finite I don't see how it would take infinite energy in order to attain it. Care to explain?[/quote]
Because, special relativity tells use that as an object accelerates, it gains mass(Assuming it has mass to begin with). As you begin to start reaching the speed of light, your mass would spike up just like your speed reaching near infinite levels, and thus more energy is needed to push you. So once you get all the way up to.. lets say 50,000 meters per second, your mass would be so unbelievably high that the energy levels it took to push you were so great you'd turn into a black hole. But for funs sake, lets assume you don't, as you get closer and closer your mass would eventually reach infinity which is impossible on its own rights.. and so with infinite mass, you need infinite energy to push it.
E^2=(MC^2)^2+(pc)^2
E=Energy
M=Mass
C=Speed of light
P=Momentum of object
RELATED VIDEOS: http://www.youtube.com/watch?v=NnMIhxWRGNw
Well I meant "Subtract any number from infinity" and sadly I'm currently only in algebra 2 so I'm not too sure what -delta means exactly, I know the relativistic kinetic energy but delta is new to me
We need Numberphile in here.
EDIT: [url=http://www.youtube.com/watch?v=elvOZm0d4H0]Here you go.[/url]
[quote=zeck96]The only way it'd diverge is if it has a different mass, and if you subtract from infinity you still have infinity.
This tells us that either
A. It doesn't take infinite energy to move the speed of light
B. There's a point where numbers can turn into infinity
C. My conjecture is wrong (Most likely answer)
@ClementZ That's not exactly true, infinity has a special property(When treated as a number) that makes it so no matter what you do to it, it will stay as infinity or undefined. Regular numbers don't have that property.[/quote]
I'm not subtracting infinity from infinity. That makes no sense and is undefined for a good reason. I'm merely integrating from v to v-delta for the relativistic kinetic energy, where delta is Planck length as you've mentioned. Algebra can't handle infinity; calculus can.
Edit: Wait, v-delta for delta=Planck length makes no sense, either. Err, Planck length divided by c?
[quote=Quickjumper7]You're playing with dangerous stuff, kid. Many physics students have tried to reach infinity. Be warned, you may soon be tempted to attain this feat no matter what the cost, but it is not worth it! Whatever you do, don't put zero in the denominator. Men have gone mad attempting to divide by zero. Wrought with grief and stricken with the imcomprensible nature of their situation, they soon fade away to the same utter inexistence that plagues the very conundrum that they worked so hard to elucidate.
Sincerely, ∞[/quote]
I've already beaten x/0. Quite simple really. Division is glorified subtraction, you just keep subtracting until you have nothing left, so what happens with you have 1-0? It's 1.
What if you 1-0 again? It's still one. This goes on PAST infinity into a term known as "Undefined" or you could argue that it is X because no matter how many times you subtract by 0 it's still X
You're playing with dangerous stuff, kid. Many physics students have tried to reach infinity. Be warned, you may soon be tempted to attain this feat no matter what the cost, but it is not worth it! Whatever you do, don't put zero in the denominator. Men have gone mad attempting to divide by zero. Wrought with grief and stricken with the imcomprensible nature of their situation, they soon fade away to the same utter inexistence that plagues the very conundrum that they worked so hard to elucidate.
Sincerely, ∞
[quote=cb000]The work required to bring an object from c to c-delta will diverge, while any reduction from c-delta will produce finite results.[/quote]
The only way it'd diverge is if it has a different mass, and if you subtract from infinity you still have infinity.
This tells us that either
A. It doesn't take infinite energy to move the speed of light
B. There's a point where numbers can turn into infinity
C. My conjecture is wrong (Most likely answer)
@ClementZ That's not exactly true, infinity has a special property(When treated as a number) that makes it so no matter what you do to it, it will stay as infinity or undefined. Regular numbers don't have that property.
>Treat "Infinity" as a number with properties identical to the concept "Infinity."
That's the problem. Real numbers can go on and on to what is essentially infinity; there isn't any difference between the two.
The work required to bring an object from c to c-delta will diverge, while any reduction from c-delta will produce finite results.