The (relativistic) mass of an object measured by an observer in the $xyz$-frame is given by $$m = \frac{m_{rest}}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}.$$ Mathematically $v$ could be greater than the speed of light, but the mass $m$ would become imaginary. Physically we would have to get to the speed of light first i.e. $v = c$, which gives us an undefined value for $m$. So we believe that nothing moves faster than the speed of light because we do not like observables to be imaginary?
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Physically, you math guys aren't allowed to Note: But, there are some quantum mechanical solutions that allow negative masses like the expression for relativistic energy-momentum. Let's try not to make the subject more complicated. $$E^2=p^2c^2+m^2c^4$$ There are hypothetical particles (having negative mass squared (or) imaginary mass) always traveling faster than the speed of light called Tachyon. This was assumed by Physicists in order to investigate the faster than light case. So When $v>c$, the denominator becomes a imaginary. But, Energy is an observable. It should be some integer. A consistent theory could be made if their mass is made to be imaginary and Energy to be negative. Using these data in the E-p relation, we would arrive at a point $p^2-E^2=m^2$, where $m$ is real. This makes Tachyons behave a kind of opposite to that of ordinary particles. When they gain energy, their momentum decreases (which strongly disproves all our assumptions). The first reason that this investigation blown off is Cherenkov radiation where particles traveling faster than light emit this kind of radiation. As far as now, No such radiation has been observed in vacuum proving the existence of these..! It's like making a pencil to stand at its graphite tip. If it would stand, physicists would've to blow up their heads :-) There are tougher stories on the topic when you Google it out... |
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Actually, a quick search on Wikipedia shows that you have misinterpreted this formula: imaginary-mass particles do not propagate faster than the speed of light when you take quantum mechanics into account. A much better reason not to believe in faster-than-light particles is that they have never been observed to exist. Furthermore, if they were to exist, I could in principle do rather confusing things like cause the death of my own grandmother before my mother was even born. Generally, if something does not appear to exist, and it would cause everyone a massive headache if that something did exist, it is easier to assume that it doesn't! Likewise, I do not believe that an enormous colony of pixies living on the dark side of the moon is planning a surprise birthday party for me next year. Of course, someone, somewhere probably does believe that :) |
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The use of relativistic mass is deprecated in modern physics, which means that we can explain why nothing moves faster than the speed of light (in the contest of special relativity) without even mentioning relativistic mass. The special relativistic energy for a massive particle is $E^2=p^2c^2+m^2c^4$, where $m$ is mass [1]. Solving the Hamilton equation we obtain the velocity $v = pc^2/E$. It is evident that $v = c$ only when $E=|p|c$, which implies that $p$ has to be infinite: $\lim_{p \rightarrow \infty} (p^2c^2+m^2c^4) = p^2c^2$. Therefore you need infinite energy for accelerating a massive particle at the speed of light. The energy of all the observable universe is finite. You cannot break the c limit. For a massless particle, special relativistic energy is $E^2=p^2c^2$. Solving the Hamilton equation we obtain the velocity $|v| = c$, which is a constant. Therefore no matter what energy you give to a massless particle, it will be always moving at the speed of light. Again you cannot break the c limit. [1] This is standard notation but disagree with your notation. Relativistic mass is often denoted by $m_{rel}.$ |
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according to sudarsan, when particeles travel with velocity greater than that of light, the mass becomes negative or imaginary. they are called Tachons. I have shown in an earlier article that the mass becomes imaginary or negative. According to the method used in quatum mechanics, by multiplying by a complex conjugate [that is chaning -i to +i] one gets a positive mass but slightly less than the orignal |
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protected by Qmechanic♦ Mar 23 at 16:49
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