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Re: The Song of Lt. Cdr. Data

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Arindam Banerjee wrote:

> On Wednesday, September 13, 2017 at 2:06:56 PM UTC+10, sci.physics wrote:
>> How much energy will it take to get these spaceships to travel faster
>> than light?
>> 
>> Where does this energy come from?
> 
> If the acceleration of the ship is g or say 10m./sec^2 then from rest the
> ship will reach the speed of light

*You cannot reach the speed of light c using conventional propulsion* (i.e. 
not based on dynamic spacetime), because the kinetic energy you would need 
to generate approaches infinity.

Because in special relativity, the square of the total energy as derived 
from the norm of the 4-momentum P⃗ = (E∕c, p⃗), is:

  ||P⃗||² = −E²∕c² + p² = −m²c²

      E² = m² c⁴ + p² c²

where with 3-momentum for massive objects (m ≠ 0)

       p = γ m u

and Lorentz factor

       γ = 1∕√(1 − u²∕c²),

where u is the magnitude of 3-velocity, we find:

      E² = m²c⁴ + (γ m u)²c²
         = m²c⁴ + γ²m²u²c²
         = m²c⁴ + m²u²c²∕(1 − u²∕c²)
         = (m²c⁴ (1 − u²∕c²) + m²u²c²)∕(1 − u²∕c²)
         = (m²c⁴ − m²c²u² + m²u²c²)∕(1 − u²∕c²)
         = (m²c⁴)∕(1 − u²∕c²)
      E² = γ²m²c⁴
      E  = γ m c².

The rest energy is defined as the total energy when u = 0:

      E₀ = m c².

Since the total energy is the sum of the rest energy and kinetic energy –

       E = E₀ + Eₖ

– we find for the kinetic energy

      Eₖ = E − E₀
         = γ m c² − m c
         = m c² (γ − 1)
      Eₖ = m c² (1∕√(1 − u²∕c²) − 1)

    [the kinetic energy is zero at u = 0, proving that this is correct],

and therefore

  lim Eₖ = +∞.
  u→c

Likewise, the magnitude of the momentum that you would need to impart to a 
vehicle to for it to reach the speed of light c (see above) is

   lim p = +∞.
   u→c

Which is why *it cannot be done the conventional way*.

As you have referred to /Star Trek/:

Its creator(s), wanting to portray *science*-fiction, something that would 
be believable and entertaining to scientifically interested or even 
knowledgable people as to have some relation to current science, portraying 
a possible extension of current science, knew that (or learned it from the 
scientific advisors that they employed), and "invented" the “warp drive”: 

Inside a region of “warped” spacetime as created by the warp drive, relative 
to that “warp bubble” the starship never travels at speeds close to the 
speed of light (“thrusters” are at “station-keeping”), but the warp bubble 
can travel at any speed, as allowed by general relativity.  In effect, the 
ship would have an *apparent* speed that is faster than the speed of light.  
(This would also avoid time-dilation effects and enable interstellar 
alliances, but would not avoid dramatically useful violations of causality, 
such as with the “Picard maneuver”.)

Later, Miguel Alcubierre showed that the idea of the warp drive has a 
scientifically sound basis.  Later work by other scientists show that the 
practical difficulties, although still enormous, can be reduced:

<https://en.wikipedia.org/wiki/Alcubierre_drive>

> in c=gt or t=3*10^8/10 = 3*10^7 seconds
> That is 347 days.

Wrong.

> If the ship weighs 200,000 Kg then the force required will be 2 million
> Newtons.

No, as the magnitude of the force required is

  F = ∂p∕dt

it will be infinite, too:

  lim F = +∞
  u→c

Which is why *it cannot be done the conventional way*.

> F=LI^2 as per my derivation in IFE-7.

Then it is not even wrong.  You would probably realize that if you tried to 
publish a paper about it instead of only making YouTube videos.

> […]
> So a 100MW reactor operating for 347 days will raise a craft to light
> speed.

Not even remotely.

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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Thread

Re: The Song of Lt. Cdr. Data Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-20 13:37 +0200
  Re: The Song of Lt. Cdr. Data Arindam Banerjee <banerjeeadda1234@gmail.com> - 2017-09-20 06:26 -0700
    Failures of the Galilean transformation (was: The Song of Lt. Cdr. Data) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-20 17:23 +0200
      Re: Failures of the Galilean transformation (was: The Song of Lt. Cdr. Data) Arindam Banerjee <banerjeeadda1234@gmail.com> - 2017-09-20 16:19 -0700
        Re: Failures of the Galilean transformation Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-22 14:00 +0200
          Re: Failures of the Galilean transformation Arindam Banerjee <banerjeeadda1234@gmail.com> - 2017-09-22 05:10 -0700

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