Why does an object require infinite energy to travel the speed of light?

Question

Forgive my physics ignorance (I'm trying to introduce myself to physics through Stephen Hawking's book) and I see that, given E=mc^2, an object with infinite energy (req'd to travel at the speed of light) would have to have infinite mass, which is his argument against anything being able to travel at the speed of light. The blank I need filled in a little bit is why is it necessary to have infinite energy to travel the speed of light?

Answer 1

It's because...well, the whole equation isn't E=mc^2. That's just the short version to avoid explaining time dilation.

E=mc^2/(1-v^2/c^2)

Which is, if you've seen the time dilation formula, it looks very similar.

v is obviously velocity, so as you can see, as the velocity here approaches the speed of light, the bottom of the equation will approach 0, and thus the energy required to move faster approaches infinity (and for knowledge sakes, the degree of time dilation increases exponentially).


To get into it any further would make things unncessarily complex. So, blame the universe for making funky laws like this.

Answer 2

While other answers aren't completely wrong, saying that an object's mass increases is a bit misleading. Mass is the resistance to acceleration. However, if an object is moving near light speed, its resistance to acceleration is different depending on whether a force is applied parallel to its motion or perpendicular to it. So we can define two masses from this. There's other ways to define of mass, such as an object's momentum over its velocity, etc. These all yield the same results in classical physics, but not in relativity! So, physicists generally talk about mass as something that doesn't change, and define it in terms of the "rest mass". Now, to get to answering your question, the amount of kinetic energy that an object would have if it had mass, and were moving at light speed, would be infinite. Kinetic energy=mass*speed of light squared*(1/sqrt(1-v^2/c^2)-1) where v is the velocity. So, an object moving near the speed of light, if given more energy, would get closer to it, but would never reach it. If an object has zero mass, it must move at the speed of light. The kinetic energy equation then gives 0/0 as the energy. (When an equation gives 0/0, that simply means that you need to find the answer using some other method or equation.) EDIT: I usually don't like to trash other yahoo answerers, but the two answers below me are just plain wrong. (pearlsawme and goring) Please don't answer science questions unless you know what you're talking about.

Answer 3

In classical Physics there was no relation between the mass of a body and its speed.

Latter, it was known that the mass of any object increases when its speed increases.

If it is so, there must be a relation to find the mass of a body when it is moving with a particular speed.

Einstein postulated that there must be a maximum speed for any object and he took it to be equal to the value of the speed of light.

He postulated this, because the speed of light is measured as C in any moving reference frame irrespective of its speed.

In other words, the speed of light does not depend upon the motion of the observer or source.

Therefore, any object cannot move faster than the speed of light.

If any object moves faster than the speed of light, then the speed of light will vary for different reference frame, which is not true.

Latter his postulate was verified to be true.

A formula had to be formulated such that its mass must increase with its speed and at the same time the speed must have a maximum value of C.

Lorentz formulated this formula.

If Mo is the mass of an object when it is at rest with reference to a frame of reference and Mv is the mass when it is moving with a speed V, then the equation relating this two is:

(Mo / Mv) ^2 = {C^2 - V ^2} / C^2.

When the body approaches the velocity of light, the right hand side of the equation tends to zero.

Naturally Mv must tend to infinity as Mo is constant.

Latter the formula was experimentally verified to be true for particles nearing the speed of light.

Now the answer to your question is as follows.

There is a lot to understand in the meaning of the equation E = M C^2.

To make a mass Mo at rest to move with a velocity V, we must give it an energy which is given by the equation

E = (Mv - Mo) C ^2.
(Note that the equation E = MC^2 is not used, which is a general statement)

When the energy given is higher, the velocity attained by the object is high and the mass Mv is also high. The above equation does not give us the velocity of the object. We have to use a different formula to find the velocity. Remember, when velocity is increased the mass also increases.

As the velocity attained reaches the value of C, the mass Mv reaches infinity as already explained.

Using this in the above formula, we find that the energy needed to make a body move with a velocity C, infinite amount of energy is needed. In other words we cannot make a body move with a velocity C.

Answer 4

You need to look at another equation:

m' = m/(1-v^2/c^2)^(1/2)

This is taken from the Special Theory of Relativity and gives the relativistic mass (m') of an object moving at velocity v and with a "rest mass" of m.

In this equation, as v approaches c, the term

(1-v^2/c^2)^(1/2) approaches 0. Or,

m' approaches m/0, which is infinity.

Now, since kinetic energy is given by

K = 1/2*m*v^2, K will go to infinity if m does. This is why inifinite energy if required if v = c.

Answer 5

when an object moves it gains mass.the more mass an object has,the more energy is needed to move it or increase it's speed.this mass gain is calculated using a complex formula,and if you use the speed of light as the speed,the mass gain is infinite.if something has infinite mass,it needs infinit energy to move

Answer 6

So what is going to power the infinite mass?

Answer 7

cause you have to reach 0 gravity