Speed of light question.

[SquishyDave]

OK, so I get most of the approaching speed of light marlarky. But as you approach the speed of light, your mass increases right?

Ok just past Pluto, there is planet X. It is traveling at roughly 0.8 c relative to Earth. That's quite fast. Now an intrepid space travelling guy launches his ship off planet X, and accelerates his craft 0.1 c. Relative to his planet, that's as fast as he is going. He thinks he is going 0.1 c

But when he comes flying past earth he sees us as going at 0.9 c. He will say "Wow, look at how fast that damn planets moving, it's mass must be HUGE!" Because as far as he's concerned he's travelling at 0.1 c. But we on earth would say "Damn, that guys space ship must wiegh a ton, poor bastard!"

What the hell is going on? Are both our masses big? Or what? IN THE NAME OF ALL THAT IS GOOD AND PURE, WHAT IS GOING ON?

To summarise. If two objects are approaching each other near light speed, and there is no way to tell if one is moving and one is not, or if both are moving to a lesser extent, how do you calculate the increase in mass of each of them?

 

[Xeriar]

Both of their masses are bigger, from the perspective of the other. Mr. Istg considers Earth's mass to be about triple normal, while his own mass is perfectly fine. Earth considers Istg's mass to be about triple normal, but of course, Earth is just fine.

Regarding the math, it's just the standard Lorentz contraction value. Ie, at .84 of c, your apparent mass (to those at rest) doubles, while the apparent distance to objects in front and behind you is halved (from your perspective).

 

[toddjh]

To summarise. If two objects are approaching each other near light speed, and there is no way to tell if one is moving and one is not, or if both are moving to a lesser extent, how do you calculate the increase in mass of each of them?

You're bumping into one of the biggest counterintuitive aspects of special relativity, which is that everything depends on your point of view. All calculations have to be done within a specific frame of reference, so there's no objective answer to how the calculations work out.

Saying "there is no way to tell if one is moving and one is not, or if both are moving to a lesser extent" implies the existence of what's called a "preferred frame" -- an outside, objective point of view, which is a big no-no in relativity. From the point of view of the spaceship, it is stationary and the planet is moving. From the point of view of the planet, it's just the opposite. Both are equally correct.

You could pick a third point of view (say, the position of the sun), and declare that both objects are moving, but that's just as arbitrary as either of the others. You really do just have to pick one and run with it.

So, that being the case, the answer to your question is that you can't always compare calculations from different frames. Rest assured that any discrepancies will be ironed out if you accelerate one body so that it becomes stationary in the other body's frame.

Jeremy

 

[SquishyDave]

OK, so what you are saying is it's not only time that's relative, but mass is also relative to the observer?

Now the equation (which I can't remember) that prevents two bodies travelling at 0.9c towards each other seeing the other as going faster than light, also prevents them seeing the other as having infinite mass, obviously.

So is there anything that isn't relative?

 

[toddjh]

So is there anything that isn't relative?

Just c.

Any two observers will always agree on how fast light is travelling, in any direction. They may disagree on how far it travels and how long it takes, but the speed will be a constant.

Jeremy

 

[SquishyDave]

Thanks guys, the piece of the puzzle I was missing was that Mass is relative also, I somehow thought it wasn't.

It all now makes sense to me, as much as it can anyway.

 

[Xeriar]

Just c.

Jeremy

Hahahaha.

That is to say, the speed of light is the same from all frames of reference. No matter how fast you go, c is c.

The electromagnetic force is also relativistic-invarient. That is, the magnetic pull of a particle is not affected by its velocity even at relativistic speeds.

 

[TobiasTheViking]

Hahahaha.

That is to say, the speed of light is the same from all frames of reference. No matter how fast you go, c is c.

The electromagnetic force is also relativistic-invarient. That is, the magnetic pull of a particle is not affected by its velocity even at relativistic speeds.

Yup, as your speed gets closer to C, time slows down so C still appears to be traveling at C in comparison to you.

That is the reason that time slows down when you get closer to C.

Even traveling at .9C, C will, for the traveler, still travel at C.

Sincerely
Tobias

Ah, i'm a teacher.

 

[toddjh]

The electromagnetic force is also relativistic-invarient. That is, the magnetic pull of a particle is not affected by its velocity even at relativistic speeds.

Ooh, right. It follows from what you said, but electric charge is also invariant.

Also, it should be noted that mass doesn't really increase as you approach the speed of light. What happens is that momentum increases faster than you'd expect from the Newtonian equation. They introduced a concept of "relativistic mass" as sort of a fudge factor so that the old equation could continue to be used.

At first, people thought that relativistic mass was the most "real" concept of mass, but when general relativity came onto the field, they realized that the normal concept of mass (or "rest mass") was more useful, and the term "relativistic mass" was mostly abandoned in favor of the more useful concept of "energy."

So, in modern terminology, an object at 0.9c will not have a higher mass than an equivalent object at rest, but it will have a higher energy.

Jeremy

 

[Hellbound]

Reminds me of a humorous sci-fi short story I read. A gentleman finally figured out how to built a light-speed drive. Big fanfare, etc, etc, as they get ready to test it. They launch, initiate the light speed drive, and trigger the collapse of the universe because it worked...

Mass increases to infinity as speed approaches c, so at c, mass is infinite (meaning so is gravitational force).

Hey, I thought it was funny

 

[Ziggurat]

OK, so I get most of the approaching speed of light marlarky. But as you approach the speed of light, your mass increases right?
...
What the hell is going on? Are both our masses big? Or what? IN THE NAME OF ALL THAT IS GOOD AND PURE, WHAT IS GOING ON?

In classical mechanics, momentum is given by
(1) p = m*v
where m is the mass of the object and v is the velocity. In special relativity, the momentum is given by
(2) p = m*v/sqrt(1-v^2/c^2)
where again, m is the mass. In this formula, m does NOT change, regardless of velocity. This is a messier formula (though note that if v << c, then (2) can be very well approximated by (1)). Some people don't like the messiness of (2), and rewrite it as
(3) p = m_v * v
m_v = m/sqrt(1-v^2/c^2)
where m is now the "rest mass" (the mass you'd measure in the object's own reference frame). (2) and (3) are mathematically equivalent, of course, but using m_v introduces the idea that mass is velocity-dependent. But really, you don't need m_v at all, it's only an occasionally convenient substitution. In other words, whether mass is velocity-dependent or not depends to some degree on how you define it (m_v is velocity dependent, m is not). But it's easy to define mass in a way that does NOT depend on velocity, and to my mind, that's the conceptually preferable approach. I'd much rather deal with an invariant mass, and complicated expressions for momentum than to try to simplify momentum at the cost of making mass velocity-dependent.

 

[Upchurch]

Ok just past Pluto, there is planet X. It is traveling at roughly 0.8 c relative to Earth. That's quite fast. Now an intrepid space travelling guy launches his ship off planet X, and accelerates his craft 0.1 c. Relative to his planet, that's as fast as he is going. He thinks he is going 0.1 c

But when he comes flying past earth he sees us as going at 0.9 c.

[nitpick]
Relativistic speeds are not simply additive. It isn't 0.8c + 0.1c = 0.9c. The actual calculation is more complex. Don't have time to write out the details, but it would probably be more like 0.82c or something.

To summarise. If two objects are approaching each other near light speed, and there is no way to tell if one is moving and one is not, or if both are moving to a lesser extent, how do you calculate the increase in mass of each of them?

As has been pointed out, the key to relativity is knowing from who's vantage point you are asking the question from and dropping the concept of simultaneity.

 

[69dodge]

So is there anything that isn't relative?

the invariant interval

or, more generally, the length of any 4-vector