From derivation in special relativity we already know that because the light itself have a velocity (speed) that does not depend on velocity of observer (not follow Galilean addition), then it follows that the velocity of light become the speed limit (maximum velocity for the object can achieve in this universe). Because of this factor: $$ \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} $$ But what if there is hypothetical object in this universe (that does not prevented by physics theory from existence), that its speed (let say $n$) behave like speed of light that is not follow Galilean addition. Then it is have same speed factor relative to other object given by: $$ \frac{1}{\sqrt{1 - \frac{v^2}{n^2}}} $$ So if this object exist, then we have two speed limit in this universe. But this is clearly a paradox, impossible we have two maximum value.

Any explanation?


closed as off-topic by StephenG, Gert, stafusa, John Rennie, WillO Dec 4 '17 at 2:08

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    $\begingroup$ There is no paradox, since this hypothetical object is your own invention, and does not exist in the physical world. $\endgroup$ – Dmitry Brant Dec 2 '17 at 19:28
  • $\begingroup$ But there is no something in physics theory that prevent this object from exist $\endgroup$ – Mohammad Fajar Dec 2 '17 at 19:31
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    $\begingroup$ There's nothing that prevents me from imagining that 2 + 2 = 5, but this is not a correct model for our universe. $\endgroup$ – Dmitry Brant Dec 2 '17 at 19:36
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    $\begingroup$ @MohammadFajar: Exactly the paradox which you constructed prevents such an object from existing. $\endgroup$ – Photon Dec 2 '17 at 19:38
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    $\begingroup$ What if there is a hypothetical number $N$ such that $N+8=10$ and $N+3 =3$ ? Then if I subtract the second equation from the first, I get $5=2$. But this is clearly a paradox! How can we possibly explain this? $\endgroup$ – WillO Dec 3 '17 at 2:01

Really, there's no paradox. First of all, what would be the reason to invent/define a new Speed "n"? The theory of relativity (special / general) already works perfectly, it is not necessary to postulate a new theory of Relativity v. 2.0 when you already have a theory that is consistent, works, describes, and quantify the reality very well, no? You also have to think that your argument is based on Lorentz's gamma factor $ \gamma $, precisely the theory of relativity is built under its postulates (https://en.wikipedia.org/wiki/Postulates_of_special_relativity), one of them is just the speed of light which is a universal constant. This is just one of the keys to relativity.

Like you must alreday know, in contrast with the classical mechanics :

Classical Galilean addition of velocities

$$ v + v = 2v $$

Addition of relativistic velocities (Lorentz)

$$ v + c = c $$

or, in the limit $ v \to c $

$$ c + c = c \not = 2c $$

So, in general, any particle or body whose mass at rest is 0 (like photons) will move at the speed of light $ c $, no more slow, not faster. Any observer in any reference frame will measured just $ c $

Therefore, the existance of this "object with speed n" is impossible because, if it existed, the speed of light would no longer be a constant for any observer, moreover, that we cannot have two "universal speed limits" because this would mean that one of them are not really a limit...

In short, your "New idea" cannot use arguments from a theory that by its construction does not make it compatible

I hope it helps you



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