Infinite mass?

[Anura]

Why would it take an infinite amount of mass or energy to push an object a finite speed? That finite speed being 186,000 miles a second.

[swansont]

Because of relativity, kinetic energy diverges as one approaches c, so any mass would require an infinite amount of energy to move at that speed.

 

http://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies

[vordhosbn]

Imagine, we are in a spaceship in Earth orbit.

 

Now we turn the ignition switch and the rocket's engines begin to work.

This means we have a constant force that propels our spaceship away, which results in acceleration (increase of speed over time). Now, you will say, it's only a matter of finite time and fuel to reach any speed.

 

However, due to special relativity consequences, the more our spaceship's speed increases (relatively to Earth), the more it's mass increases (relatively to Earth).

 

And therefore as the mass is greater, and the force remains the same, the resulting acceleration is smaller.

 

When our spaceship approaches the speed of light (relatively to Earth), it's mass (again r.t.E.) approaches infinity, and therefore to actually reach the speed of light, it requires infinite energy.

[michel123456]

Good question. IMO it is a wrong interpretation of the results of Relativity.

 

However, due to special relativity consequences, the more our spaceship's speed increases (relatively to Earth), the more it's mass increases (relatively to Earth).

 

Here is how I understand things, with all reservations.

 

The infinite increase of mass & energy is as seen from Earth, not as lived by the moving object. The astronaut on the spaceship can assume that the Earth is moving at near C speed, not him. Nothing strange happens to the spaceship, and it can increase its speed as the commander wishes without annoyance. But that is not what someone upon Earth will observe: this one will observe that the spaceship will never reach C.

[swansont]

The infinite increase of mass & energy is as seen from Earth, not as lived by the moving object.

 

In addition, it's the mass as measured using m = E/c^2, E being the total energy, which is not how mass is usually defined.

 

So the mass only increases for other observers, and only if you change the definition of mass.

[Johanluus]

"The infinite increase of mass & energy is as seen from Earth, not as lived by the moving object. The astronaut on the spaceship can assume that the Earth is moving at near C speed, not him. Nothing strange happens to the spaceship, and it can increase its speed as the commander wishes without annoyance. But that is not what someone upon Earth will observe: this one will observe that the spaceship will never reach C."

 

My question is this "how does the commander measure his speed"

relative to what ... he could theoretically be boosting his rockets and actually slowing down relative to a gravitational accelleration in the opposite direction. so he thinks he's going faster , but he may just be escaping some supermassive black hole ....what as his marker?If we on earth are discussing him we are his marker.. but thats only relative to us?

[vordhosbn]

He can measure his speed with relation to anything he wants. If he "sees nothing" in the Universe other than his ship, he can measure only his acceleration.

[Johanluus]

Yes he can measure his accelleration ,which is the rate of change of velocity .

But his velocity ( rate of change of distance) , had to be measured WRT somewhere "local". And only according to that reference frame, he may need infinite energy if he tries to reach c( according to that reference frame).

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"Why would it take an infinite amount of mass or energy to push an object a finite speed? That finite speed being 186,000 miles a second."

 

I think the origional question is a very valid one. As far as i can deduce it is a direct result of Einstein's 2nd Postulate

 

2: The speed of light in a vaccum is completely independent of the motion of the source emitting it.

 

And it is a constant.

[Nano]

My question is this "how does the commander measure his speed"

relative to what ... he could theoretically be boosting his rockets and actually slowing down relative to a gravitational accelleration in the opposite direction. so he thinks he's going faster , but he may just be escaping some supermassive black hole ....what as his marker?If we on earth are discussing him we are his marker.. but thats only relative to us?

 

I think that for relativistic effects to take place (time dilation, mass increase and lenght contraction) the spaceship have to travel close to c , relative to the space-time continuum. There is nothing special about earth, so why should the spaceships speed be measured relative to us?

[Johanluus]

Agreed there is nothing special about earth.But there is something special about who makes the measurment, because it will differ for different inhertial frames.

[swansont]

I think that for relativistic effects to take place (time dilation, mass increase and lenght contraction) the spaceship have to travel close to c , relative to the space-time continuum. There is nothing special about earth, so why should the spaceships speed be measured relative to us?

 

The space-time continuum is not a reference frame. You need to measure a speed in relation to a different frame, and in practical terms, something in that reference frame.

[Nano]

The space-time continuum is not a reference frame. You need to measure a speed in relation to a different frame, and in practical terms, something in that reference frame.

 

You are right offcourse. I am still in the learning process of relativity.

 

So a person inside a spaceship traveling close to c relative to us, would not "feel" any of the relativitsic effect? A watch carried by the captain would, in his opinion, click just normally? He would not gain any mass, or change his size?

 

If two spaceships leaves from earth traveling at a speed close to c but in in opposite directions relative to the earth, they would still travel extremely close to c relative to each other?

[swansont]

You are right offcourse. I am still in the learning process of relativity.

 

So a person inside a spaceship traveling close to c relative to us, would not "feel" any of the relativitsic effect? A watch carried by the captain would, in his opinion, click just normally? He would not gain any mass, or change his size?

 

Right. As far as the person is concerned, s/he is at rest.

 

 

If two spaceships leaves from earth traveling at a speed close to c but in in opposite directions relative to the earth, they would still travel extremely close to c relative to each other?

 

 

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html#c2

 

Two objects leaving at 0.8c will see each other as receding at 0.9756c