# why need infinite energy if light has finite speed

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Why do you need infinite energy to get to light speed, if light speed is finite, and constant? It has a limit obviously right 186000 miles per second?

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The (very) short answer is that the faster you go, the more energy you need for the same acceleration. Or put in another way, adding more energy gives you less acceleration the faster you're going. This reaches a limit at light speed, so you can't ever reach it. Kind of like a Zeno's Paradox kind of thing.

This is a consequence of relativity, wherein the speed of light is always constant from your own reference frame. You see me going at 99% the speed of light past you and therefore think I just need that extra 1% to reach it. From my perspective, however, light still goes just as fast relative to me, and I'm not any closer to reaching it, because we experience time and length differently. So, in a certain sense, it's not possible to make ANY progress in getting closer to the speed of light, since it always has the same relative speed.

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then how do photons reach that speed?

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thay have no rest mass. since they have no rest mass, they can't go at anything but the speed of light.

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The shorter answer is that the relationship is not linear (or quadratic). The solution diverges at v = c.

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An explaination I readed is that , part of the energy is transformed in "relative mass" and having more mass make it harder to accelerate.

I think that the only experimental data on that come from particle accelerator where particle never reach c, no matter how much energy you add.

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• 2 weeks later...
This is a consequence of relativity, wherein the speed of light is always constant from your own reference frame. You see me going at 99% the speed of light past you and therefore think I just need that extra 1% to reach it. From my perspective, however, light still goes just as fast relative to me, and I'm not any closer to reaching it, because we experience time and length differently. So, in a certain sense, it's not possible to make ANY progress in getting closer to the speed of light, since it always has the same relative speed.

Are you saying that relative to your starting point you could accelerate to the speed of light?

But for you as a traveller the speed of light will still be ≈300000 m/s faster than you?

EDIT:

I always thought it was the mass of the vehicle increased requiring even more force to push it.

That does bring up another question though...

If you are carrying the fuel, won't it's mass increase and so give out more energy and more force to equal the increase in mass of the vehicle?

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• 1 month later...

Speaking of mass...How does the Mass of an object increase if matter can't be created or destroyed ? Is energy converted into matter? and if so...how?

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Speaking of mass...How does the Mass of an object increase if matter can't be created or destroyed ? Is energy converted into matter? and if so...how?

I always wondered about that myself. I think in math its correct if the equation for example reaches the same conclusion, such as 2+2=4 for example, if you could do the math the same but get the same answer then its good. I wonder if that applies in some small respect to the mathematical understanding physics applies sometimes in models is all. I mean in math you can literally get rid of parts of the equation sometimes, you can just minus out a galaxy in the universe though, it just sort of confuses me is all.

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an aside: It takes as much energy to decellerate an object with mass as it does to accelerate. One of the challenges with getting an object to move faster than we have to date is how to slow it down. For example, a technology infrastructure might be built one day just outside of the solar system to 'boost' an object via some energy source to get it moving at a 100th the speed of c but there would be no technology to slow it down unless it was 'on board'...(which would add too much mass and thus never get up to anything close to 100th the speed of c).

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Sisyphus gave you the 'correct' explanation as such...however many god questions arise and yes, the relation mathematically is very simple..

Relativistic mass (mass in motion) is defined as the rest mass (no velocity w.r.t a *very* arbitrary reference frame) plus additional mass due to velocity...

The equation from this is given in special relativity: m = m0(rest mass)/(1- [v/c]) if memory serves me correct. It is easy to see that with increasing v, m increases and if v = c you would have m0 / 0 = -> undefined or infinity as they state it.

Now, the question about how more mass comes about is due to another neat thing good ol' Onestone realised: E = mc^2 ... Thus to increase kinetic energy of something, energy must be added....(for example with fuel and yes, it would also increase in its mass, but in higher relativistic speeds, the energy density of the fuel would hmm either remain constant or would increase at a far lower rate than the increase of its mass).

Now, as energy is added, much of this energy would also be translated into mass as the last equation shows that mass and energy are interchangeable, or two sides of the same coin.

Does this help? (and for the question of mass, just like in another post i just sent, one needs to try and understand the inherent secrets of inertia )

lakmilis

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Speaking of mass...How does the Mass of an object increase...

Basically, that happens when you call the energy of a particle "mass" (some factors of c let aside). This alters the energy $E = \underbrace{m_0 c^2}_{=E(v=0)} + E_{kin}$ with $m_0$ being the (rest-)mass of the object and $E_{kin}$ being its kinetic energy into $E = m_\gamma c^2$ with $m_\gamma = m_0 + \frac{E_{kin}}{c^2}$ being the "relativistic mass" and dependent on the velocity of the particle. Due to being dependent on the particle's velocity, the relativistic mass is not a property of the particle anymore (velocity of a particle depends on the frame of reference), which is one of the reasons why it's less convenient to use than the rest-mass which is a particle property. Another reason is that $m_\gamma$ simply is the energy divided by c², wherefore it's simply another term for energy and a pointless concept (just call it energy!).

Is short: If you call the energy of a particle "mass" then if you understand that energy increases with increasing velocity (because of the increasing kinetic energy) it's pretty obvious that the so-defined mass must increase.

...if matter can't be created or destroyed ? Is energy converted into matter? and if so...how?

Afaik, that does, strictly speaking, not make any sense. The term "matter" lives on a completely different meaning-category than "energy" and "mass". Energy and mass are kinematic properties, whereas matter and non-matter are just classifications of particles. Particles being or consisting of leptons or quarks are called matter, other stuff (like light/photons) is non-matter. Both can have mass and energy.

So energy being converted into matter doesn't make much sense. Non-matter particles can decay into matter-particles. But what you probably meant is "is energy converted into mass?". This question also doesn't make much sense, since, as you can see from the 1st equation in my post, mass already is a term contributing to energy. One thing that can and does happen is that the different contributions to energy transform into each other. The/one point of colliding particles in large particle accelerators is to give the colliding particles are large kinetic energy so that during the collision heavy particles (particles with a larger mass) can be created. So kinetic energy transforms into mass, there. Different forms of energy transforming into each other is nothing really new. You already know that from things falling down where potential energy transforms into kinetic energy or things being thrown up where the reverse process happens.

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This is basically a consequence of relativity and what I am about to say may mirror what Atheist has said above but in a slightly different way.

For an object with a rest mass:

$E=\gamma mc^2$

Where $\gamma =1/\sqrt{1-v^2/c^2}$

Notice I can split the 1st equation into 2 components:

$E=mc^2+(\gamma -1)mc^2$

This shows the total energy being equalt to the rest energy+ the kinetic energy of the object in question. Notice we get the familiar equation for rest energy

$E=mc^2$

Notice from inspection what happens to gamma($\gamma$) as we increase v? When v is zero it equals 1. When $v\rightarrow c; \gamma \rightarrow \infty$. This causes our expressions for both total and Kinetic energy to tend towards infinity.

If you button bash with the calculator a little(or even turn gamma into a geometric series approximation) you will find that when v<<<c, we get that our expression for KE to a good aprroximation becomes:

$KE=(\gamma -1)mc^2\approx 1/2mv^2$

Which is our familiar expression for KE in classical mechanics which works pretty well at low velocities.

The most important question though is why these relations are true, and to really find out you need to study relativity, and start from the basic postulates, reasonig their justification and why they need to be true. Having done that the consequences of those postulates need to be followed, and eventually you get down to the algebraic relations relating quantities we can measure, like energy for example.

I hope that was clear as it was the main reason I posted, just try to give a clear impression of things using a little algebra(thats all this stuff is really).

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