Traveling faster than light. Limited by mass increment as predicted by Einstein's equations of relativity.

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FASTER THAN LIGHT [FTL]
Episode 2.02: The Dream of

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Then with your help, I will
become the first man on earth
to build a workable time-
machine!

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I see. You are so keen on
time travelling.
But frankly, how will you
travel in time?

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Ah hm . . . According to us
earthlings, one of the
plausible ways to travel in
time is by travelling faster
than light.
That means we have to travel
at a higher velocity than
300,000,000 meters per
second (186,000 miles per
second).

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Speed Limit
I know very well that there is
a universal speed limit set
by Dr. Einstein or his
predecessors.
But it was he who in the
early twentieth century
confirmed that the speed of
light is the ultimate one in
this universe and nothing
can travel any faster.
SPEED
LIMIT
𝑪𝑪

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However why did we say that
no one could move faster than
the speed of light?
Before the age of aviation,
people ventured to say that
no-one would be able to go
faster than sound.
But they were proven
wrong. We now have jets that
can travel three times above
the speed of sound.

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Now they are talking about that
no-one will ever go faster than
light. I am confident that someone
would one day succeed in flying
faster than light, once technology
has advanced to that stage.
I am lucky here to have a powerful
out-of-this-world technological
girl with me so that I can
overcome the speed limit.
We can break the light barrier as
we did with sound.

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LIMITED BY
ADDITIONAL
MASS
Episode 2.03

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Einstein did not give any
explanation to why there was the
limit other than telling us that the
limit was suggested by the equation
of Special Relativity.
RELATIVISTIC
EQUATION OF
MASS

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Mass Changes with
Speed
The Theory of Relativity
stipulated that the mass of
an object is not a fixed
quantity. It varies with its
velocity. The faster an object
gets, the heavier it will
become.

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The Relativity
Equation for Mass
The mass 𝑚𝑚 of a particle of
rest mass 𝑚𝑚𝑜𝑜moving with
speed 𝑣𝑣 is given by one of
the famous relativistic
equations on mass:
𝑚𝑚 =
𝑚𝑚𝑜𝑜
2
1 −
𝑣𝑣2
𝑐𝑐2
𝑚𝑚 =
𝑚𝑚𝑜𝑜
2
1 −
𝑣𝑣2
𝑐𝑐2
Mass of
particle at rest
Mass (variable)
of particle
Velocity (variable)
of particle

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Mass Proportional to
Speed
The energy equation
makes it pretty clear why
“relativistic mass”
increases with velocity.
Since the speed of light 𝑐𝑐
doesn't change, the mass
𝑚𝑚 should increase as the
velocity 𝑣𝑣 gets larger.
𝑚𝑚 =
𝑚𝑚𝑜𝑜
2
1 −
𝑣𝑣2
𝑐𝑐2
Variable
Constant
Variable

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The Two Ratios
We can move 𝑚𝑚𝑜𝑜 to the left
side and obtain an equation
relating the ratio of 𝑚𝑚/𝑚𝑚𝑜𝑜
to that of 𝑣𝑣/𝑐𝑐.
If we plot the two ratios
against each other in a
graph, we will see that the
𝑚𝑚/𝑚𝑚𝑜𝑜 ratio increases
dramatically as 𝑣𝑣/𝑐𝑐 is close
to 100%.
𝑚𝑚
𝑚𝑚𝑜𝑜
=
1
2
1 −
𝑣𝑣2
𝑐𝑐2
𝑚𝑚 =
𝑚𝑚𝑜𝑜
2
1 −
𝑣𝑣2
𝑐𝑐2

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Totalmassm/Restmass𝑚𝑚𝑜𝑜
Velocity (% of speed of light)
1357911
0 20 40 60 80 100
𝑚𝑚
𝑚𝑚𝑜𝑜
=
1
2
1 −
𝑣𝑣2
𝑐𝑐2

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Infinite Mass
As the speed approaches the
speed of light, 𝑣𝑣2
/
𝑐𝑐2approaches 1 and 1 −
𝑣𝑣2/𝑐𝑐2 becomes infinitely
small. As a result, the
particle's mass approaches
infinity.
It can be said that until close
to the speed of light the
object will be so heavy that an
infinite amount of energy is
needed to make it faster.
𝑚𝑚 =
𝑚𝑚𝑜𝑜
2
1 −
𝑣𝑣2
𝑐𝑐2
Approaches ∞
Approaches 𝑐𝑐

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Speed Barrier
Hence it should
be impossible to
accelerate an
object with rest
mass to the speed
of light.
This speed 𝑐𝑐 is
therefore
sometimes called
the “light speed
barrier”.
c

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Outsider Help
Now is our story.
May be with Zyrkonian
wisdom, we can do it.
Light at
speed 𝑐𝑐
Faster than 𝑐𝑐

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I wish to have some sort of explanation or
justification from your side - from some
of the ingenious touches of your
advanced civilization. Let us go ahead
and break the Einstein spell.

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I know what you mean. But first
of all: do you know where did
this equation come from?
𝑚𝑚 =
𝑚𝑚𝑜𝑜
2
1 −
𝑣𝑣2
𝑐𝑐2

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WHERE DID THE EQUATION COME FROM?
To be continued on: Episode 2.04
ABCC
𝑚𝑚𝑜𝑜 𝑚𝑚