Traveling .999999 reapeating the speed of light .

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Discussion Overview

The discussion revolves around the possibility of traveling at speeds approaching the speed of light, specifically at .999999999 repeating the speed of light. Participants explore the mathematical implications of repeating decimals and the physical constraints on massive objects reaching such velocities.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants question whether traveling at .999999999 repeating the speed of light is mathematically equivalent to traveling at the speed of light itself.
  • Others argue that achieving such speeds would require infinite energy or zero mass, referencing the kinetic energy formula and its implications as velocity approaches the speed of light.
  • There is a discussion about the distinction between .999999999 and .999999..., with some asserting that the latter is mathematically equal to 1.
  • One participant suggests that while you cannot travel at exactly .999999999... c, you can approach it with a finite number of 9s.
  • Another participant mentions that the limit of a series approaching .999... equals one, reinforcing the mathematical equivalence.
  • Questions arise about the maximum speed a massive object could theoretically achieve, with suggestions that it could get arbitrarily close to the speed of light.
  • There is speculation about utilizing all the energy in the universe to propel a massive object, implying a theoretical maximum speed that remains undefined.

Areas of Agreement / Disagreement

Participants express differing views on the mathematical interpretation of repeating decimals and the physical feasibility of massive objects reaching speeds close to the speed of light. No consensus is reached on the implications of these discussions.

Contextual Notes

Limitations include the dependence on definitions of repeating decimals and the unresolved nature of energy requirements for massive objects approaching light speed.

cragar
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Is it possible to travel .999999999 repeating the speed of light , because that would be a 1 in math .
 
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Sure. if you've got infinite enegy, or zero mass. If you are curious about the energy requirements the Kinetic energy required to reach a given velocity is given by:

[itex]\gamma m c^2 - m c^2 = \frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}} - m c^2[/itex] where m is the rest mass. Play around with it and you can get a sense of how the energy requirements increase to infinity as one approaches c.
 
Is this a math problem or a physics problem?


In any case, your question is really "Is it possible to travel at velocity c" and the answer is "yes, for light but not for any massive object".
 
cragar said:
Is it possible to travel .999999999 repeating the speed of light , because that would be a 1 in math .

And .999999999 doesn't equal 1, "in math". Those numbers differ by .00000001.
 
Vanadium 50 said:
And .999999999 doesn't equal 1, "in math". Those numbers differ by .00000001.

No, but ".999999 repeating" does. It seems clear that what he really means is the more conventional ".999999..."
 
negitron said:
No, but ".999999 repeating" does. It seems clear that what he really means is the more conventional ".999999..."
More precisely, the limit of the series 0.99, 0.99, 0.999, ... equals one.
 
And the limit of the series [tex]\frac{10}{\sqrt{19}},\frac{100}{\sqrt{199}},\frac{1000}{\sqrt{19<br /> 99}},...[/tex] (the time dilation factor for v = .9 c, .99 c, .999 c, ...) is infinite.
 
cragar said:
Is it possible to travel .999999999 repeating the speed of light , because that would be a 1 in math .

You can't travel at 0.999999999... c, but you can travel at 0.99999999...9c, where in the first case the ... means an unending string of 9s, and the in the second it means a finite but undetermined number of 9s.
 
Hootenanny said:
More precisely, the limit of the series 0.99, 0.99, 0.999, ... equals one.
Of course, that's exactly what "0.999 repeating" means.
 
  • #10
Well, since 0.999... and 1 are different representations of the same number (like 2-1 or 4/4), since a massive body can't travel at c, it can't travel at (0.999...)c either.
 
  • #11
i guess i should have said can something with mass travel at .99999 reapeating c and i guess it would be no , cause it is 1
 
  • #12
Correct. And just fyi, you can write that like this: .999...

The thre periods at the end (an ellipsis) indicates they repeat forever.
 
  • #13
so then what could be that fastest you could travel if you had mass .
 
  • #14
cragar said:
so then what could be that fastest you could travel if you had mass .
You can get arbitrarily close to C. Every time a new, bigger particle accelerator is built, they add a couple of more 9's to that.
 
  • #15
interesting
 
  • #16
cragar said:
so then what could be that fastest you could travel if you had mass .


Theoretically? Well I guess if one could estimate all the energy in the universe and if all that went into the kinetic energy of a single things of mass m. Which I imagine woud be a great many 9's
 

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