Mass Increase When Moving at Speed of Light?

[Visigoth]

Hello, I have a conundrum I cannot fathom a reasonable explanation to.

Suppose I were in a moving vessel at the speed of light (yes, I said it). If I were to get up and try to walk forward, I would have my velocity reduced since I cannot exceed the speed of light. Can I postulate then, by virtue of conservation of momentum, that my mass would increase?

Thanks!

 

[cjameshuff]

Suppose I were in a moving vessel at the speed of light (yes, I said it). If I were to get up and try to walk forward, I would have my velocity reduced since I cannot exceed the speed of light. Can I postulate then, by virtue of conservation of momentum, that my mass would increase?

From the parenthesized portion, I suspect you're expecting this, but the starting condition you describe is impossible. You can't move at the speed of light, no matter how good your spaceship is.

If you took off from Earth and accelerated to 0.9c, 0.99c, 0.999c, or however many 9's you want to add to your velocity relative to Earth, you would still find no change in your situation aboard the ship. You could operate a relativistic particle accelerator on board the ship, and it'll behave the same way it did during testing on Earth. You would find the outside universe to be quite distorted, but without looking at something outside the ship you would never be able to tell if you'd accelerated or not. Velocity is relative, and the velocities between parts of the ship have nothing to do with the velocity of the ship as a whole relative to other objects.

 

[Nabeshin]

You cannot move at the speed of light. There are uncountable threads on this forum discussing why, so if you're interested more in this look for one of those.

Any issues with momentum and relativity are solved if we note that normal momentum, p=mv, is not conserved but p=ɣmv is conserved, so we define momentum in this way. Some people call the quantity ɣm the "relativistic mass", but I (and many others) prefer to ignore this notation and just define momentum differently.

In light of this, do you still have a question?

 

[Passionflower]

Suppose I were in a moving vessel at the speed of light (yes, I said it). If I were to get up and try to walk forward, I would have my velocity reduced since I cannot exceed the speed of light. Can I postulate then, by virtue of conservation of momentum, that my mass would increase?

No, you cannot reach the speed of light.

 

[proculation]

Hello, I have a conundrum I cannot fathom a reasonable explanation to.

Suppose I were in a moving vessel at the speed of light (yes, I said it). If I were to get up and try to walk forward, I would have my velocity reduced since I cannot exceed the speed of light. Can I postulate then, by virtue of conservation of momentum, that my mass would increase?

Thanks!

Suppose you were in a vessel traveling at NEAR the speed of light, you would walk in your vessel normally, like anybody.

When you are walking in your vessel your are only "accelerating" when you make a move from your inertial frame. You would move like if your were stationary on Earth. Remember that 'c' is always constant.

 

[vociferous]

Consider this: you can reach the speed of light only if you have no rest mass, because if you have a >0 rest mass (even an infinitesimal amount of mass), then as you approach the speed of light, your relativistic mass approaches infinity. Since your mass approaches infinity, the amount of energy required to accelerate to the speed of light must also approach infinity.

So, when you think about it, your "spaceship" would have to be "built" of massless particles such as photons, so it really puts your question into a very different context, and you start getting into quantum weirdness that is way more difficult than special relativity.

It is not a dumb question though. Einstein himself started thinking about special relativity by asking what a photon would experience.

So, let us imagine you are traveling not at the speed of light, but at .999999999... c, very close to it. Basically, everything would behave normally in your frame of reference, though the outside universe might look strangely contorted. Einstein's brilliant realization was that all the physical laws (including electromagnetism: headlights and microwaves on your spaceship would behave as expected) would behave normally in your frame of reference.

Of course, if you insist on asking your original question, the answer is that there is no answer. Science can only deal with what is physically possible (the natural universe), so your question (as asked) would be like asking what an elephant (-)15 square meters in volume would eat for breakfast.

 

[Passionflower]

Einstein's brilliant realization was that all the physical laws (including electromagnetism: headlights and microwaves on your spaceship would behave as expected) would behave normally in your frame of reference.

At .999999999... c you would not need a microwave

 

[vociferous]

At .999999999... c you would not need a microwave

Like one of those rednecks that cooks a turkey in their engine block while they drive. You could just stick your turkey outside of your shielding for a fraction of a second.

 

[Visigoth]

Okay, wait, I'm still somewhat confused. So in my own frame of reference, nothing would be out of the ordinary, however the Universe around me would? So would that mean I would look contorted to the outside Universe?

Also, my intuition is failing me here: if I am moving at 99.9999999- % at the speed of light, and I begin walking forward (i.e. accelerating), is my velocity not greater than that of the vessel? Or does this have something to do with inertial frames of reference?

 

[Rasalhague]

if I am moving at 99.9999999- % at the speed of light, and I begin walking forward (i.e. accelerating), is my velocity not greater than that of the vessel?

Yes, it is. At low velocities, the ordinary rules of addition work fine, but when significant fractions of the speed of light are involved, you need to use the full relativistic addition formula ( http://en.wikipedia.org/wiki/Velocity_addition_formula ).

 

[Visigoth]

Yes, it is. At low velocities, the ordinary rules of addition work fine, but when significant fractions of the speed of light are involved, you need to use the full relativistic addition formula ( http://en.wikipedia.org/wiki/Velocity_addition_formula ).

Ah, thank you, this finally makes sense to me. It's rather fascinating how the Universe at it's extremes behaves so impertinently different from what the classical model predicts.

 

[psholtz]

Also, my intuition is failing me here: if I am moving at 99.9999999- % at the speed of light, and I begin walking forward (i.e. accelerating), is my velocity not greater than that of the vessel? Or does this have something to do with inertial frames of reference?

Your speed is only 99.999999% of c from an outside reference frame that is observing your motion.

Let's say this "stationary" reference frame is on Earth.

Relative to your reference frame (presumably, the one attached to the spacecraft moving at 99.99999% of c relative to Earth), you are (more or less) at rest, and then you begin walking forward at say 3 mph or something. It's better to imagine that you are walking in your spacecraft at a constant velocity, rather than "accelerating".. Accelerations rather mess up special relativity, which can only handle physics in inertial (i.e., non-accelerating) reference frames.

Technically speaking, in "your" reference frame, your "speed" is still zero, although in the reference frame attached to the ("moving") spaceship, your "speed" would be 3 m.p.h. Relative to the Earth-based reference frame which is observing the velocity of your spacecraft , your speed would be 99.99999% of c + 3 mph, added together using the Lorentz velocity addition formula, which result will always give you a speed smaller than c.

You could even shoot a bullet from the front of your spacecraft , which bullet moves relative to your spacecraft at 99.9999% of c. Relative to the Earth-based observer back on Earth, he'll detect that yes, the bullet is moving "faster" than the spacecraft which fired it, but no, both objects are still moving at a speed lower than c.