I’m probably gonna regret asking this, ‘cuz there’s a good chance I won’t really understand the answers I get, but I’m feelin’ reckless today so I’m gonna ask anyway.
Why does mass increase the closer you get to light speed?
Try to dumb it down for us liberal arts majors, and thanks in advance to anyone bold enough to try to explain it.
OK. Mass is a form of energy - E=mc[sup]2[/sup] and all that agreed? In fact, the relativistic mass of a particle is simply the sum total of its energy. As you accelerate something up to the speed of light, you give it more energy, but for any non-zero mass particle, it takes an infinite amount of energy to accelerate the particle to light speed. So that energy being pumped into the particle must go somewhere - its mass. Basically, the more energy you put into a particle to try and accelerate it, the heavier it’;; get.
Its a bit of a circular argument I know, but that’s as simple as I can make it, without getting the textbook out.
E=mc[sup]2[/sup]
Remember, nothing can go faster than c, the speed of light. If more kinetic energy ( E) is added to an object approaching the speed of light, then the only alternative is for nature to direct the added energy towards an increase in mass (m).
Ummmm … so the energy used to accelerate the object adds to the mass? If I understand Grienspace at all, * after * the energy has contributed somewhat to acceleration, it has no where else to go, so it becomes part of the mass? I know that’s probably not an accurate way of stating it; perhaps it would be more accurate to say that the added energy both increases the acceleration and adds to the mass at the same time. In other words, you can’t add energy without adding mass without giving the energy some place to go (such as radiating the energy away as heat, maybe).
Thanks to you guys for putting up with a dumbass liberal arts major! 
Thanks for asking this. I wasn’t sure, but I think a light bulb just went on. Let me see if I can explain it, then have one of the smart people here say if I am right or not.
e=mc^2
You increase e as it is the energy to get to the speed of light. Now because you increased e you must add an equal amount to the other side of the equasion to keep it balanced. Can’t add to c because it is a constant(speed of light). So the only place left is m.
Right?
When you accelerate anything to any speed, it increases in mass, for reasons given above. Tape a dime to the shell of a snail and watch the snail crawl off; that dime’s infitesimally heavier than it was when it was just lying on the table. But the mode of calculating the difference in mass is such that it only becomes a significant portion of the whole at relativistic speeds.
Grienspace, a small but nitpicky correction. Nothing can be accelerated past (or to) light speed. Massless particles must travel at light speed; particles with mass at a speed under it (which can, of course, be zero, when they’re at rest). While there are arguments suggesting that tachyons (moving faster than light) do not exist, their existence is not contrary to the “light-speed limit law.” Rather, they would be forced to maintain a speed that, while variable, would always be faster than light.
(It’s worth remembering here that “light speed” refers to c, the speed of light in a vacuum, marginally less than 300,000 KM/sec – light travels at different speeds in air, water, glass, diamond, quartz, etc.)
I think it should be pointed out that while E = mc[sup]2[/sup] is probably a good means of understanding this phenomenon, it’s not how physicists understand it. Or at least, it’s not how Einstein understood it. Despite its popularity, the formula E = mc[sup]2[/sup] is not a fundamental equation in relativity - it’s derived using the mass dilation formula.
This seems like a good place for me to enter the discussion.
What is the mass dilation formula?
Go here:
http://www.1728.com/reltivty.htm
and it has a calculator to compute mass dilation
Just so you know, the vast majority of physicists do not subscribe to the concept of relativistic mass, they much prefer to stick with plain old invariant mass. RM causes confusion and all kinds of complexities.
If an object is travelling a .9c its mass has increased relative to you, but if you accelerate to the same speed its mass hasn’t increased at all. Relativistic mass has one value in the longitudinal direction, another value in the transverse direction and still others in different directions. It winds up being a matrix of some sort.
The relativistically correct equation for mass is
m[sup]2[/sup] = E[sup]2[/sup] - p[sup]2[/sup]
m = invariant mass
E = energy
p = momentum
c =1
What this equation says is if you increase the kinetic energy of the system you also increase the momentum by the same amount and the mass remains the same.
<minor hijack>
ok, so there’s all these ppl sayin that itd b highly impractical to accelerate some sort of craft to say, .9c , because the relativistic mass would have increased such that it would need HUGE amounts of energy to accelerate any appreciable amount.
but. and here’s where i expose my ignorance to the hungry lions…
say this craft had an onboard fuel source. as the craft’s mass increased, so would the fuel source’s mass. therefore the fuel yield, or output, would be increased in proportion to the mass increase, producing an overall effect of zero, no? this is all relative to a stationary(?) observer, of course.
relative to the craft, nothing would have really changed would it? in fact you could just say that if you were on the craft, YOU were the stationary one, just everybody else is goin reeeeeeeeal fast, so why can’t you accelerate?
Chagto
I am not saying it is impractical to accelerate a spaceship to .9c because of the problem of relativistic mass. The real problem would be in constructing a way to propel it continuously for almost a year so that it maintains an accelleration of 32 feet / sec[sup]2[/sup]
Ha, a very good question! The easiest way to answer it is by saying, “Well, you don’t have to worry about that if you look at it this other way.” but that doesn’t really contribute to your understanding. So I’ll try to answer it in terms of what you said. So I’m going to use m to mean relativistic mass here. Let’s be very clear to avoid any confusion - m is the mass that increases with speed.
When you apply a force to an object, relativistically speaking, you have to do two things. You have to increase its speed and you have to increase its mass. The energy for mass dilation doesn’t just happen - it has to come from the force that gets the mass up to speed.
Here’s how we know this mathematically. Take Newton’s second law:
F = d/dt(mv)
= v · dm/dt + m · dv/dt
= v · dm/dt + ma
Now, the second term we’re familiar with. It’s the non-relativistic form of Newton’s Second Law: F = ma. If this is all there was, and F increased with m like you have in mind, then it would work fine. However, there’s a new, first term: v · dm/dt. Notice that this term disappears if there’s no mass dilation (dm/dt = 0). It also disappears if the velocity v is very small, much less than c. So, this term becomes important when dealing with relativistic speeds in a relativistic setting. If you work it all out, the force equation becomes:
F = ma / (1 - v[sup]2[/sup]/c[sup]2[/sup])
As you can see, even if F and m increase proportionally, you have that pesky term on the bottom that makes it all impractical.
ahhhhh, ok, so thats wat the problem is.
oh, and when i said ‘all these ppl’ i didnt mean any1 on this board, i just meant in my personal experience.
so anyhow, say you COULD maintain an acceleration of 32 feet / sec squared, for MORE than a year, what exactly happens? i just hit 99.9999999999999% of c and then stop accelerating?
In special relativity the acceleration is not necessarily colinear with the force.
F = d/dt [ ( m[sub]0[/sub]*v )/( 1 – B[sup]2[/sup] ) ]
So m[sub]longitudinal[/sub] = m[sub]0[/sub] / ( 1- B[sup]2[/sup] )[sup]3/2[/sup]
And m[sub]transverse[/sub] = m*a / ( 1- B[sup]2[/sup] )[sup]1/2[/sup]
You’re right. I was dealing with one-dimensional motion only, for simplicity.
Would you mind explaining your last equation? I think I understand, but I’m not quite sure… Is that a acceleration?
Jeez, in the last two equations please substitute m longitudinal =, and m transverse =, with F longitudinal =, and F transverse =, and make the a in the third equation subbed transverse.
Or better yet ignore the entire post.
Achernar I didn’t see your question and I’m sorry for such a garbled post, if my last post isn’t clear please let me know. It’s definately time for me to go to bed.
Eh? 32 feet / sec[sup]2[/sup] is the acceleration of Earth’s gravity; there’s no reason why you can’t accelerate faster or slower than that if you want to, especially if you have the energy. But yes, getting something with positive mass to go faster than light does not work.
God, what a screwed up post. Here’s what I was trying to say:
In special relativity the acceleration is not necessarily colinear with the force.
F = d/dt [ ( m[sub]0[/sub]*v )/( 1 – B[sup]2[/sup] ) ]
And in fact the acceleration is only colinear in either the longitudinal or transverse directions.
So F[sub]longitudinal[/sub] = (m[sub]0[/sub] / ( 1- B[sup]2[/sup] )[sup]3/2[/sup])*a[sub]longitudinal[/sub]
And F[sub]transverse[/sub] = (m[sub]0[/sub] / ( 1- B[sup]2[/sup] )[sup]1/2[/sup])*a[sub]transverse[/sub]
To increase the amount of acceleration the human body can take, take, how about suspending the crew in a liquid-filled environment, in an (imaginary) oxygen bearing fluid allowing them to breathe;
this could allow a high acceleration to be more comfortable.
Alternatively the crew could be placed in partial or total biostasis;
(From Drexler’s Engines of Creation)(if feasible 
)
http://www.orionsarm.com/tech/nanostasis.html
ultimately they could become immobile solid blocks, easily stored in a relatively small space, and able to survive remarkable forces if necessary.