Mass and Velocity

[DanBlather]

A particle gains mass as it approaches light speed, right? How does that work. Don’t particles have a fixed mass?

Second question, if a particle is traveling near C relative to a star, that’s the same as the star moving at that speed relative to the particle. Does the gravitational pull on the particle increase because of the increased mass of the star? If the speed is close to C, and the mass gets really large, wouldn’t that make the force of gravity so strong that it would pull in any particle even remotely close?

Physics makes my head hurt.

[Ring]

@DanBlather

A particle gains mass as it approaches light speed, right? How does that work. Don’t particles have a fixed mass?

Second question, if a particle is traveling near C relative to a star, that’s the same as the star moving at that speed relative to the particle. Does the gravitational pull on the particle increase because of the increased mass of the star? If the speed is close to C, and the mass gets really large, wouldn’t that make the force of gravity so strong that it would pull in any particle even remotely close?

Physics makes my head hurt.

No, mass does not increase with an increase in velocity. This type of confusion is one of the main reasons the concept of relativistic mass has been discarded.

Mass is equal to the energy of a system that cannot be transformed away.

[Richard_Pearse]

This was covered fairly recently here.

[DanBlather]

@Richard_Pearse

This was covered fairly recently here.

Thanks, that was a great thread. It’s weird when you see stuff you were taught as a kid not being considered true today.

[Asympotically_fat]

These days mass is defined as the rest mass of an object/system, by definition this is invariant under a Lorentz boost (change of velocity).

Back in the early days of relativity (and it still hasn’t completely died out despite being widely thought of as ‘bad practice’) the term relativistic mass was used.

In the one dimensional case it is very easy to see why relativistic mass is used, you recover some well known relations from Newtonian physics such F = ma when ‘m’ is the relativistic mass.

However a closer examination reveals relativistic mass brings it’s on sets of problems. When you start to do things in more than two dimensions you need two types of relativstic mass, longitudinal mass and transverse mass. The contribution of each type of relativistic mass depends on the direction in which as force is acting relative to the direction of motion. So relativistic mass as a scalar becomes highly contextual.

So you can define mass in such a way that it increases with speed, but it’s not as straight forward as it may appear and for this reason it’s not the way things are done these days.

When you bring gravity in to the equation, it complicates things a little,mainly because general relativty is just complicated. But for example the relative velocity of a test particle in Schwarzchild spacetime doesn’t affect the metric, so it’s plain the simplistic view that an objetcs gravity increases with it’s velocity is false.

[Richard_Pearse]

@These are my own pants

These days mass is defined as the rest mass of an object/system, by definition this is invariant under a Lorentz boost (change of velocity).

Back in the early days of relativity (and it still hasn’t completely died out despite being widely thought of as ‘bad practice’) the term relativistic mass was used.

In the one dimensional case it is very easy to see why relativistic mass is used, you recover some well known relations from Newtonian physics such F = ma when ‘m’ is the relativistic mass.

However a closer examination reveals relativistic mass brings it’s on sets of problems. When you start to do things in more than two dimensions you need two types of relativstic mass, longitudinal mass and transverse mass. The contribution of each type of relativistic mass depends on the direction in which as force is acting relative to the direction of motion. So relativistic mass as a scalar becomes highly contextual.

So was it the case that relativistic mass was used for convenience to make some familiar equations work? Is it a bit like using an analogy to help understand a principle but then running into problems when stretching the analogy beyond what it was originally intended to be used for?

I think I just used an analogy as its own analogy, or something.

[Asympotically_fat]

@Richard_Pearse

So was it the case that relativistic mass was used for convenience to make some familiar equations work? Is it a bit like using an analogy to help understand a principle but then running into problems when stretching the analogy beyond what it was originally intended to be used for?

I think I just used an analogy as its own analogy, or something.

It’s really just a matter of definition. I imagine first of all it did seem like the most sensible definition of mass, but as the subject of relaticstic kinematics developed, it became clear that it wasn’t such a great defintion after all.

[Chessic_Sense]

In grade school, we’re given these basic definitions for concepts that are made for children to understand. I was taught that mass is “the amount of matter in an object.”*

But when we grow up to these bigger concepts, we’ve got to update our rolodexes of definitions. Relativistic mass made no sense to me. I was like “Where does the extra mass come from? Do the atoms just clone themselves? Do they dilate or something?” and it got really confusing.

Then I watched some video lectures and a student asked “What’s mass?” and the professor said that there were many definitions of mass but the one to use here, and the one to think about in relativity, is “Mass is a measure of the resistance to acceleration”. In other words, mass means how hard it is to move something.

Then it all makes sense! There’s no atom-cloning, there’s no increased gravity. But it is harder to accelerate…by definition. Aha!
And was taught that matter is anything that has mass. Good job, textbooks :rolleyes:

[Earl_Snake-Hips_Tucker]

@Chessic_Sense

In grade school, we’re given these basic definitions for concepts that are made for children to understand.

Yeah, sorta like the “solar system” diagram of the atom and Linnaean taxonomy. Not quite right, but good enough for high school.

[Asympotically_fat]

I don’t even know if it’s a matter of right or wrong, if you’re clear what you’re talking about it’s finw to use relatvistic mass it’s just a bit clunky and not in step with modern-day thinking.

I think the best illustartion of the deficits of relativstic mass is when you write out the relativistic equivalent of F = ma in full which is:
F = m[sub]0[/sub](1 - u[sup]2[/sup]/c[sup]2[/sup])[sup]-1.5/supu + m[sub]0[/sub](1 - u[sup]2[/sup]/c[sup]2[/sup])[sup]-0.5[/sup]a

Where m[sub]0[/sub] = rest mass, u = velocity, c = speed of light in a vacuum and a = acceleration.

There is no such scalar ‘m’ such that F = ma for all F and a.

When a and u are parallel the equation reduces to:

F = m[sub]0[/sub](1 - u[sup]2[/sup]/c[sup]2[/sup])[sup]-1.5[/sup]a

and m[sub]0[/sub](1 - u[sup]2[/sup]/c[sup]2[/sup])[sup]-1.5[/sup] is called the longitudinal mass.

When a and u are perpindicular then the equation reduces to:

F = m[sub]0[/sub](1 - u[sup]2[/sup]/c[sup]2[/sup])[sup]-0.5[/sup]a

and m[sub]0[/sub](1 - u[sup]2[/sup]/c[sup]2[/sup])[sup]-0.5[/sup] is called the transverse mass.

[Asympotically_fat]

So from the above it should be seen that it’s harder to move something along it’s direction of motion than it is to move something perpendicular to it’s direction of motion.

To work out the acceleration caused by a force in the ‘relativistic mass regime’ you have to work out the contributions from the longitundinal and transverse masses, with the end result that an acceleration is not always perpendicular to the force that causes it.

[Ring]

“Mass is a measure of the resistance to acceleration”. In other words, mass means how hard it is to move something.

Unfortunately, what you just described is relativistic mass, which is now a discredited concept.

Think of mass as equal to the energy of a system that cannot be transformed away. For instance, let’s say an object is moving at a high rate of speed with respect to you. Is its mass really greater than when it’s just sitting in front of you?

Of course not; all you have to do is move at the same speed as the object and all that additional mass disappears. In other words you can transform it away.

[GiantRat]

I apologize for being an English/Philosophy major (I should be working at StarBucks, I suppose). If anyone has any good (but semi-basic) sources for relativistic theory, atomic structures, etc, I’d be grateful. I believe that I once read Einstein for Dummies, or something like that. I’ve been convinced since about age 12 or so that everything in science boils down to physics on a certain level (not to dis chemistry), and that there’s potentially a universal parallel to all of these things (the elusive “theory of everything”).

Or maybe I have too much time on my hands lately. Either way, any good references would be appreciated.

[Asympotically_fat]

@These are my own pants

To work out the acceleration caused by a force in the ‘relativistic mass regime’ you have to work out the contributions from the longitundinal and transverse masses, with the end result that an acceleration is not always perpendicular to the force that causes it.

I should also be clear that this is the case in whatever regime you use and you get the same results as you would otherwise using relativistic mass.

[Chronos]

So was it the case that relativistic mass was used for convenience to make some familiar equations work? Is it a bit like using an analogy to help understand a principle but then running into problems when stretching the analogy beyond what it was originally intended to be used for?

To quote myself (with a slight edit) from the other thread:

The reason for the concept of relativistic mass in the first place is that some folks wanted to make the equations look the way they liked them, instead of the simplest way, and did a poor job of it, to boot. In Newtonian physics, the formula for momentum is P = mv. In relativistic physics, however, the formula is P = gammamv, where gamma = 1/sqrt(1-v[sup]2[/sup]/c[sup]2[/sup]) is a quantity that shows up in a lot of the relativity equations. Now, if you want to make this formula look like the familiar Newtonian formula, one way you could do it is by saying that there’s something called relativistic mass (which I’ll denote by a capital M) and say that M = gammam, and therefore in relativity, P = M*v. This makes that particular equation look nice, but then you really ought to ask if this “relativistic mass” behaves like we think mass ought to, in other ways. And the answer is, no, it doesn’t really (for instance, something won’t collapse into a black hole from having a “relativistic mass” that’s too high). You are, of course, free to define a quantity like that (you can define whatever you want), but it turns out it isn’t very useful at all.

Now, on the other hand, you could also decide to “clean up” the equation by absorbing the gamma into the velocity, instead of absorbing it into the mass. So you could define something called “relativistic speed”, or “proper speed” as it’s more commonly known, denoted by u. Then you’d have that u = gammav, and P = mu. This makes the equation just as pretty as in the relativistic mass version, but it has the benefit that proper speed really does behave like we’d expect speeds to behave in many different contexts, and many different sorts of equations get simpler when you use proper speed rather than regular speed in them.

[Asympotically_fat]

@GiantRat

I apologize for being an English/Philosophy major (I should be working at StarBucks, I suppose). If anyone has any good (but semi-basic) sources for relativistic theory, atomic structures, etc, I’d be grateful. I believe that I once read Einstein for Dummies, or something like that. I’ve been convinced since about age 12 or so that everything in science boils down to physics on a certain level (not to dis chemistry), and that there’s potentially a universal parallel to all of these things (the elusive “theory of everything”).

Or maybe I have too much time on my hands lately. Either way, any good references would be appreciated.

The Feynman Lectures is a good placee to start, I think the most relevant introductory chapters were released as part of ‘Six Easy Pieces’. Infact Six Easy Pieces is the book I’d recommend.

That said Special Relativity is not too challenging, there’s plenty of good resources on the web too. HyperPhysics is a good place to start