So, as things approach relativistic speeds, their mass increases, correct? That’s why we can’t reach light speed because the mass we have to accelerate becomes too large.
Take a chemical rocket and accelerate to near light speed. The mass of the rocket increases, but so does the mass of the fuel. Seems like you still ought to get decent propulsion from kicking out something that heavy. Is the problem that the energy from the chemical reaction doesn’t increase? To an outside observer, is a very heavy ship pushing out very heavy exhaust very, very slowly?
Another question: Since mass increases the faster something goes, could I make a black hole by spinning a gyroscope really fast?
Incorrect. Despite what you may read in some books, the mass doesn’t change at all. What changes is the formula for things like energy and momentum. The longer you fire your rocket engines, the more momentum and kinetic energy your rocket will have, with no theoretical upper limit (provided you don’t run out of fuel first), but no matter how high your momentum and kinetic energy get, they still correspond to a speed less than the speed of light.
It’s worth remembering here, as everywhere in relativity, that if you’re on the rocket, everything on the rocket is still perfectly normal in your reference frame, and it’s the rest of the universe that’s moving past you.
Energy does increase the faster something spins, but a single gyroscope can’t become a black hole. There are strict fundamental limits on how much angular momentum a black hole can have, and trying to make a black hole out of a single gyroscope would violate those limits. In oversimplified layman’s terms, the centrifugal force of the spinning gyroscope would more than counteract gravity, causing it to fly apart rather than collapsing together.
You could, in principle, make a black hole out of a whole bunch of gyroscopes, all pointing in different directions, so most or all of the angular momentum cancels out. Practically, of course, it would be almost impossible to do, for many different reasons.
You’re using the phrase “too large” in the sense of “oh, man, this rocket is incredibly massive, and that makes it incredibly difficult to make it go fast.”
That is not why the rocket can’t reach light speed.
The reason it can’t reach light speed is this: If it did reach light speed, its mass would be infinite. Ponder the concept of infinity for a moment. We don’t simply mean that the rocket’s mass is incredibly large. We mean that the rocket’s mass is infinite. And that is a physical impossiblity. And that’s why reaching the speed of light is impossible.
A black hole is a global phenomenon. Relativistic mass, besides being a misnomer, is frame dependent.
If I move as fast as you, then to me you haven’t gained any mass. All this velocity dependent mass has been transformed away by the simple expedient of my going as fast as you are.
The OP is a perfect example of why the term relativistic mass belongs in the dustbin of physics.
Also, if an object really did gain mass due its velocity, then it could very well become a black hole in the longitudinal direction, but not in the transverse direction.
I thought that a black hole is also frame-dependent. Specifically, the people trapped in the black hole are unaware that this is so, because time has slowed down (from the perspective of the outside frame) and the people within think that things are still rather normal. They may be able to figure out that things are going badly and that they will soon be in the hole, but they don’t yet realize that it has already happened.
Am I mistaken? Or perhaps my problem arises from time distortion giving relativistic meanings to the words “soon”, “yet” and “already”.
So why do physicists talk about “rest mass”? As I understand it rest mass is an object’s mass in all frames of reference but that implies to me that an objects mass will be measured differently in different (i.e. accelerated) frames of reference.
IANAP (though I was an undergrad student many moons ago) but I think they use the phrase ‘rest mass’ just to make absolutely clear what they’re talking about. Because the concept of ‘relativistic mass’, whilst it is strongly deprecated, has not yet become completely extinct. If it was, there’d be no need for the phrase ‘rest mass’, but as long as there’s still the slightest hint of confusion (as evidenced by the OP, and a fair number of popular science books too), they keep the qualifier ‘rest’ in.
There’s no way, in general, to recognize an event horizon while you’re falling through it, but it’s still there. If you’re patient enough in taking your measurements, eventually everyone in the Universe (no matter what frame they’re in) will come to agree that there’s an event horizon, and where it was. At most, some observers will take longer to recognize it than others.
Thanks for all the responses. Things are clearing up a bit. So if relativistic mass isn’t really a correct term, what does my gravimeter measure when the ship goes blasting past it?
I once got curious what energy the relativistic increase in mass according to the formula m = m_0/sqrt(1-v^2/c^2) when v << c. I worked it out using the simple approximation sqrt(1 - x) = 1 - x/2, a good approximation when x is very small and discovered, to my great surprise (in retrospect it shouldn’t have been) that the energy was (1/2)m_0v^2. In other words the so-called kinetic energy is precisely the relativistic increase in mass. This relation will, of course, persist at near light speeds, except that it will be (1/2)mv^2.
That’s a more complicated question than it seems. The source of gravity isn’t a single simple number called “mass”, nor is the gravitational field a simple number, though in usual situations, it can be approximated that way. Things like flows of momentum and pressures can also contribute to gravity. All of these things are tensors, mathematical objects like vectors, but more complicated. Studying how these things relate to each other is what General Relativity is all about.
What used to be called the “relativistic mass” is just a fancy word for the total energy. The total energy of a moving object is its rest mass plus its kinetic energy, so indeed, the “extra mass” from relativity is just the kinetic energy, and at low speeds, will work out to the familiar 1/2 mv[sup]2[/sup].