Can’t say I really understand it, but:
from here: Mass in special relativity - Wikipedia
which is a quote from here: Spacetime Physics - Edwin F. Taylor, John Archibald Wheeler - Google Books
That is indeed what a lot of textbooks say, but it is and always was a very silly way to define things. In familiar Newtonian physics, the formula for momentum is p = m[sub]0[/sub]v , where m[sub]0[/sub] is the mass, and v is the velocity. In relativity, the formula for momentum is p = m[sub]0[/sub]gammav , where gamma is the relativistic dilation factor (which approaches infinity as speed approaches c). This apparently caused some heads to explode, when people said “No, wait, that’s not allowed! p = mv, just like my high school teacher said, and it can’t be any other way!”, and so they insisted that the “real” mass, m, must be equal to gammam[sub]0[/sub], where m[sub]0[/sub] is what’s called the “rest mass”. Now, it’s true that you can define the terms any way you wish, so in that sense this definition isn’t invalid, but it’s a very silly definition, since everything else in physics that depends on something we think of as “mass” (including the formation of black holes) is based on the rest mass.
And there’s very little motivation for defining things this way: Even if you’re so OCD that you insist that the formula for momentum must look like the Newtonian version, it makes much more sense to absorb the gamma into the v factor (which is after all closely related to gamma) rather than into the m factor (which has nothing to do with it): In this case, the formula is p = mu, where m (or m[sub]0[/sub], whichever you call it) is the one and only thing called “mass”, and u is something called the “proper velocity”, u = gammav. Doing this, in fact, not only doesn’t cause the host of complications you get from the “relativistic mass” version, but it actually considerably simplifies many problems.
This triggered a new (to me) thought: Velocity is relative, right? To say that I’m moving at .9c, that has to be measured against something that can be considered a fixed point. That seems to mean that mass is a relative concept? If I keep accelerating away from the Sun, at some point point the energy I apply becomes (very loosely, I’m sure) mass - let’s say that is around .9c for sake of argument. But if I’m chasing something that is already moving at .99c relative to the sun (and coasting), then the energy I’m applying will continue to accelerate me in that plane of reference?
My physics is pretty much non-existent, so am I missing something obvious? And I’m certainly using a lot of terms incorrectly in the previous paragraph.
Thank you for the explanation. A couple questions: Does what you point out above mean only momentum increases with speed? And, the example I learned (way back in school) where if you were able to weigh (or measure mass or whatever) of a passing relativistic object (close to c), it would have more mass than when it had zero velocity, that example is wrong?
Well, it depends on how you measure mass. If you measure mass by measuring momentum and velocity, and dividing one by the other, then yeah, it’ll go up. Measure it almost any other way, though, and it won’t.
Well, then what prevents something from attaining the speed of light if it isn’t increase of mass towards infinity? (not questioning you, just trying to reconcile what you are saying with my admittedly intro-level knowledge)
All I’ve read my entire life was “Mass increases as you approach the speed of light, that’s why you can’t get to the speed of light, because your mass will approach infinity” until i just read what you are saying in this thread.
Energy conservation. Or less glibly, you’d have to impart an infinite amount of kinetic energy to get something moving at the speed of light relative to you.
The energy of an object comes in two parts: the rest energy (or rest mass) which is a constant, and the kinetic energy which is a function of how fast the object is moving relative to the observer. The kinetic energy increases toward infinity as an object approaches c. So, to get something to c, you’d need to impart an infinite amount of energy into it in a finite amount of time.
Simply because gamma approaches infinity as velocity approaches c, as Chronos said.
I can understand that, but how do you measure gamma if you are the one increasing velocity?
Re: increase of non-mass with speed:
So the increase is not in the mass per se, but the rest of it? Cool! When I win the lottery, I’m going back to university to study this stuff.
In your frame of reference, gamma is one, because in your frame you’re not moving. In a sense, it’s impossible to even approach c, because no matter what speed you go, you’re always just as far away from it.
Well, I meant I was on a sled or whatever, accelerating. From what I read in this thread, as my velocity increases, SOMETHING (kinetic energy, mass, ??) increases and the value of gamma increases because of that SOMETHING, thereby making it harder to keep a constant acceleration. Up until this thread, i thought that SOMETHING was mass, but you are saying it’s not, do I have that right?
In your own frame of reference, it’s always equally easy to accelerate. If you apply a force sufficient to make you feel 1 g, then in your frame of reference, one second later, you’ll be going 9.8 m/s faster. It only gets harder to accelerate from the point of view of someone who isn’t accelerating.
so in my frame of reference, i can keep accelerating until I reach the speed of light?
No. In your frame of reference, you can keep accelerating until you’re stopped. Which is always.
can you maybe expand upon this? I’m not sure what you mean.
OK, so I’m in my rocket. What’s my velocity? Well, it depends on what frame of reference you’re asking in. How about my frame of reference? In that case, my velocity is zero.
Now, I fire up the engines, and accelerate. After I accelerate, what’s my velocity now? Again, in what frame of reference? In my current frame of reference, which is different from the one I had before, it’s again zero. Alternately, I could answer that question in terms of the same frame of reference I used the first time, in which case I have some nonzero velocity.
If I pick any one frame of reference and stick with it, then I will find that both the force of my rocket thrust and the magnitude of my acceleration, in that frame, will decrease as my velocity with respect to that frame increases, in such a way that no matter how long I fire my rocket, I’ll never reach c. If, however, I always use whichever reference frame I happen to be in at the moment, then I’ll find that my thrust and acceleration both remain constant (where acceleration here means the rate at which I’m changing which reference frame I’m using), but that my velocity in my reference frame du jour is always zero, and so I’ll still never reach c.
Sorry, forgot about this thread. Again, thanks for the explanations, and now it seems we are back to the original question. Above you say “force of rocket thrust” and “magnitude of acceleration” will decrease as velocity increases. I had previously learned that it was because mass increased, but you had previously said mass DOESN’T increase, so what causes the force and magnitude of acceleration to decrease?
Time dilation and length contraction.
I had read elsewhere that time dilation and/or length contraction could not be measured in your own reference frame, is that true?