I assume this has something to do with general relativity, but i don’t exactly get it so
In: Planetary Science
It has to do with special relativity. Essentially, it takes an infinite amount of energy to accelerate a massive particle to the speed of light.
“Why can’t” type questions aren’t very easy to answer. Why can’t I cast magic spells? Is something stopping me from doing it? Not really, it just doesn’t work. Try thinking about it in terms of what actually happens if you try. Then at least we’re describing a world we live in.
in special relativity, the velocity of a massive is no longer proportional to momentum/energy. to closer you get to the speed of light, the more energy you need to invest to raise the velocity for the same amount. the energy cost asymptotically grows to infinity as you get closer.
on the other side, a massless particle can only travel at the speed of light and no other speed, because it has no moment of inertia. even if it has almost no energy, the velocity is still constant.
The easiest answer I can think of –
What we used to “know” was when you push on something it moves faster, push on something twice as hard, it moves twice as fast. etc. It’s important to note that in this view 100% of the “push energy” goes into the moving energy.
What we now “know” is that not all the push energy goes into the moving energy. Some %, let’s say X% gets “absorbed” by the thing your pushing and turns into mass.
Making it harder, X isn’t even consistent. Basically the faster the thing is moving the bigger X is. So in our daily lives where we don’t see things moving especially fast X is basically 0.0000001%, even bullets are “slow” in this regard.
But if you took a bullet and just kept pushing and pushing and pushing eventually it’s moving fast enough where X is 1% or 5% or 20%.
So at those speeds not only is a lot of your push “disappearing” and not becoming moving energy, ALSO the object is getting *heavier* meaning your next push is going to have less of an effect anyway.
So it’s two exponential problems – Problem 1: eventually all of your push is getting absorbed as mass and none is going to actually making the thing move faster and Problem 2: your thing is getting infinitely heavy as well so pushing it gets even harder until it’s impossible.
E=(mc^2)/(1-(v^2/c^2))
Here’s the special relativity energy equation, which will Taylor expand giving E= mc^2 + 1/2 mv^2 + ……..
As v approaches c, the denominator of the fraction in the equation gets smaller. The energy keeps increasing such that you would need an infinite amount of energy to actually reach the speed of light.
We can even explain it with special relativity. It takes infinite energy to do.
The lorentz factor, γ = 1/sqrt(1-v^(2)/c^(2)) approaches infinity as v approaches 0.
From the relativistic kinetic energy and momentum equations, we can get the following
v=pc^(2)/E
If we take the complete form of E=mc^2 (accounting for momentum)
E^(2)=(mc^(2))^2 + (pc)^2
Combining these two equations gives us
v=pc/sqrt((mc)^2 + p^(2))
As we can see, only when m=0 does v=c, and this is true for any momentum.
The derivation is left as an exercise for the reader
Massive particles need infinity energy to travel at c, and massless particles must travel at c.
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