Why does faster-than-light travel require infinite energy?

Question

I've read that faster-than-light travel of an object (i.e. spaceship) in a finite amount of time would require infinite energy, or a finite amount of energy in an infinite amount of time. I don't understand how this makes sense. The speed of light, like the speed of sound, is a finite value. It then makes sense that accelerating to a finite speed would require a finite amount of energy. Reaching the speed of sound doesn't take infinite energy, so why would lightspeed?

Answer 1

Einstein said it was impossible to travel faster than light. Since no one has yet even gone 1/2 of light speed I must agree with him

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

We were not able to disprove the formula so until that day it is assumed to be true, and taken at that.
E = MC^2
[ E = Energy]
[ M = Mass]
[ C = Speed Of Light in a vacum]

This is to say, that energy is equal to a mass accellerated to the speed of light squared. As we can see the right side gives a very large number. That is a nice way of saying to get a little bit of energy we need a mass accellerated to this speed.
However, it will take energy to get to that speed, which will increase the weight of the mass and that would reduce the speed.
So the only way you can do this is:
take your spaceship and load it up with fuel(energy) and attempt to accelerate to the speed of light, as described above tht will take an infinite amount of energy.
On the other hand, if you have a way to supply it with a finite energy it will take forever to reach the speed of light - you will never do it in other words.

1. infinite energy:
.. .. ..a. Spaceshipt is accellerated to speed of light but since the mass will produce a small amount of energy it will require more energy to further accellerte the mass but adding more energy is to increase the mass.
2. If you can continually supply a definite amount of energy to a mass in an attempt to accellerate to the speed of light, it will take forever because there will never be enough energy created by this defined total mass to reach that speed. Therefore, the time it will take is infinite.

Answer 4

Uncle Al and Skycat are both correct. While there are galaxies that are currently receding from us at .8 or so x light speed (relative to us), it would still take an infinite amount of energy to accelerate to light speed, even from that galaxy. This is because light speed is constant in both galaxies. As you accelerate toward light speed, your mass increases IAW the Lorentz transform. Since v^2 is usually insignificant relative to c^2, this is generally not observable. However, we have been successful in accelerating subatomic particles to .99 or so x light speed (by expending huge amounts of energy in an accelerator). When we do this, we find that, sure enough, the mass increases just as Einstein predicted. We also find that the half life of the subatomic particle increases, because time slows down for that particle, just as Einstein predicted. To get past light speed then should theoretically require an infinite amount of energy, especially for something that's pretty massive to start with (i.e. significantly larger than a subatomic particle).

Answer 5

Didn't problems arise with Einstein's equation? As an object accelerates Kinetic energy increases because the speed of light is constant. The mass of the object would increase. As the object approaches the speed of light it approaches an infinite mass. If it approaches an infinite mass then an infinite amount of energy will be used.

Answer 6

The speed of sound is no proble to attain, the speed of light is something else, it can't be attained, it can be approached but never attained. A mass nearing the speed of light absorbs the energy that is applied to it, this makes the mass more massive and more energy is required to raise the speed, if enough energy was available to get the mass to the speed of light the mass would become light.

Answer 7

As Per New revised relativity theory of Dr. Ricardo Carezani ,it is alluded that there are particle masses which moves up to twenty seven time the speed of light. Here we have a discovery which does not agree concerning infinite power which is the result of a large force moving at the velocity of light.

Atually to my understanding when a mass structure is pushed to move at the speed of light it would break apart into its basic component.So it would not be possible to propel a spaceship to the speed of light which would require such a power ,it would chalenge the structure of the vessell ,unless the vessel is built of supernatural atoms.
Very vely interesting question.

Answer 8

We know greater the energy that we give to an object greater is the velocity.

If we give infinite energy to a mass then it must have infinite velocity as per classical physics.

But we know that the speed of a material object has a limit namely the speed of light in vacuum.

As a particle approaches the speed of light, the energy that we do give is utilized more to increase its internal energy rather than the speed of the particle.

In simple words major part of energy given to a particle is used to increase its internal energy rather than to increase its kinetic energy.

In classical physics we believed that all the parts of energy given to an object can be fully utilized to increase the speed of an object.

In modern Physics part of the energy is used to increase the internal energy (mass) of the body when we try to increase the speed of the particle.

Answer 9

A massed body is subject to Lorentz invariance that scales as

beta = sqrt[1 - (v^2)/(c^2)]

mass = (mass_0)/beta
time = (time_0)beta
length in direction of translation = (L_0)beta (and Terrell rotation if it whooshes by rather than splats your nose)

Superluminal travel is not the problem (it has other problems re negative temps kelvin in population inversions). Getting through lightspeed which is a division by zero is the problem.

Answer 10

The mass is the variable.

To compare an object to light is where the mistake is being made.

The 0 mass factor represents the zero effect gravity has on this object allowing it to bend the rules of a different dimension.

Light... it's properties are unique. why compare.