# Speed and mass

Ive Heard that things can get mass when moving in speeds Close to c. So I have question.

Lets say we have to objects, Object A and Object B.

Object A has twice the size of Object B.

Lets say these two objects where moving close to the speed of light. But Object B, who is twice as Little, moves a Little bit "faster". If I would measure these objects "mass", would it be possible for them to have equal mass? Object A is bigger, but not moving as fast as object B.

Drakkith
Staff Emeritus
Mass refers to "invariant" mass, which is the mass of an object as seen from its own inertial frame of reference. Moving objects do NOT gain more mass.

However, if we have two systems consisting of equal number of objects, where there is equal mass between the two systems, and in one of these systems the objects are moving faster than the masses in the other system, then the system where the objects are moving faster will have more energy and thus more mass than the other system. Note that this is the mass of the system as a whole, not of an individual object. As I said, individual objects do not gain mass from motion, as from their own frame of reference they aren't even in motion.

Mass refers to "invariant" mass, which is the mass of an object as seen from its own inertial frame of reference. Moving objects do NOT gain more mass.

However, if we have two systems consisting of equal number of objects, where there is equal mass between the two systems, and in one of these systems the objects are moving faster than the masses in the other system, then the system where the objects are moving faster will have more energy and thus more mass than the other system. Note that this is the mass of the system as a whole, not of an individual object. As I said, individual objects do not gain mass from motion, as from their own frame of reference they aren't even in motion.

1. So, more energy equals more mass? How does that work?
2. If object B moves faster, doesnt he have more energy?

Unfortunately, in the history of physics, the notion of a "relativistic mass" had been introduced. Nowadays, this is rather regarded as a kind of energy which increases inertia. "Relativistic mass" is not a scalar number as we may expect but a tensor: "relativistic mass" would vary with the direction a force is exerted ("longitudinal and transversal mass"). This is far from what we intuitively expect from a mass.
The new consensus is to reserve the term "mass" for the rest mass - as Drakhit had already pointed out.

Drakkith
Staff Emeritus
1. So, more energy equals more mass? How does that work?

The basic explanation is that energy and mass are related through Einstein's equation. e=mc2.
This is simply an observed property of the universe and as far as I know it has no underlying reason, though I could be incorrect.

2. If object B moves faster, doesnt he have more energy?

Yes, but this energy does not add mass to the object, but to the system as a whole.

Unfortunately, in the history of physics, the notion of a "relativistic mass" had been introduced. Nowadays, this is rather regarded as a kind of energy which increases inertia. "Relativistic mass" is not a scalar number as we may expect but a tensor: "relativistic mass" would vary with the direction a force is exerted ("longitudinal and transversal mass"). This is far from what we intuitively expect from a mass.
The new consensus is to reserve the term "mass" for the rest mass - as Drakhit had already pointed out.

How do we estimate invariant mass of electron? If an electron is Always moving, how can we know how much its weighs?

Maybe I should post that as a new topic...

The basic explanation is that energy and mass are related through Einstein's equation. e=mc2.
This is simply an observed property of the universe and as far as I know it has no underlying reason, though I could be incorrect.

Yes, but this energy does not add mass to the object, but to the system as a whole.

Drakkith, if it 1. can gain energy by moving faster, and 2. if it can gain mass by gaining energy, then that would mean that the object that is moving faster has = more energy, and therefore more mass. Then could they not have equal mass at a certain time? It would be a contradiction to say no.

In principle, magnetic fields are helpful to measure the mass of a charged particle. A magnetic field exerts the Lorentz force on a moving charge; the resulting acceleration may be measured and is inverse to the mass of the electron.
In practice, Penning traps are often used:
http://arxiv.org/ftp/arxiv/papers/0909/0909.1095.pdf

In principle, magnetic fields are helpful to measure the mass of a charged particle. A magnetic field exerts the Lorentz force on a moving charge; the resulting acceleration may be measured and is inverse to the mass of the electron.
In practice, Penning traps are often used:
http://arxiv.org/ftp/arxiv/papers/0909/0909.1095.pdf

So, if a atom loses 511 kev, a magnetic field would tell us that? I Think about the lost energy in a beta+ decay. What if a positron actually is a "part" of the electron, but smaller. Now, the positron moves "faster" then an electron. So, can it be "smaller" but moving faster, and have equal amount of energy (511 kev).

I actually dont even know what "kev" means (is it a measurment of energy?). But I am grateful for your answer.

KeV is "kilo electron volt": it is the amount of energy which an electron gains through acceleration by a voltage of 1000 V; see e.g.
http://en.wikipedia.org/wiki/Electronvolt

1. If an object would be smaller than an electron, and moving faster (accelerating faster), could it then, in theory, be possible for them to have the same amount of "kev"? An positron has 511 kev. An electron has 511 kev. But it would be possible for the smaller object to have 511 kev, if it was accelerated in a higher speed? (I am asking this question because positrons are said to have higher speeds). How do we know a positron has 511 kev?

2. When we accelerate a electron, do we make it travel faster than it would in a "natural" state in vacuum?

1. If an object would be smaller than an electron, and moving faster (accelerating faster), could it then, in theory, be possible for them to have the same amount of "kev"? An positron has 511 kev. An electron has 511 kev. But it would be possible for the smaller object to have 511 kev, if it was accelerated in a higher speed? (I am asking this question because positrons are said to have higher speeds). How do we know a positron has 511 kev?

The 511 KeV correspond to the rest mass of the electron. When you accelerate it, it gains additional kinetic energy (1/2)*m*v^2
You may accelerate a particle which is lighter than the electron to a higher speed such that the above term for the kinetic energy will yield the same number.

There is a theorem in physics which predicts same life-times and (rest-)masses for particles and their antiparticles. But of course, the mass of the positron has also been indepently measured.

2. When we accelerate a electron, do we make it travel faster than it would in a "natural" state in vacuum?

What do you mean by "natural state"??

The 511 KeV correspond to the rest mass of the electron. When you accelerate it, it gains additional kinetic energy (1/2)*m*v^2
You may accelerate a particle which is lighter than the electron to a higher speed such that the above term for the kinetic energy will yield the same number.

There is a theorem in physics which predicts same life-times and (rest-)masses for particles and their antiparticles. But of course, the mass of the positron has also been indepently measured.

What do you mean by "natural state"??

So, in theory it is perfectly possible for it to "yield the same number". I wish I had the scills in physics to show that with equations!

Another ting that is bothering me. We know that a electrons that are "closer" to the nucleus of the atom has less energy. The fotoelectric effect shows us that photons can make electrons "jump out" of the atom. Thats because they gain energy. So how do we know, that the electrons all have 511keV - when they have different amounts of energy to begin with?

PS. By "natural state" I meant its natural velocity in vacuum. Just like a photon moves with "c" in vacuum. I said "natural state", but I guess I am from Sweden, so we talk funny. We have good meat balls, though.

... The fotoelectric effect shows us that photons can make electrons "jump out" of the atom. Thats because they gain energy. So how do we know, that the electrons all have 511keV - when they have different amounts of energy to begin with?

We know it from measuring the rest mass of a free electron - "free" means "unbound".

PS. By "natural state" I meant its natural velocity in vacuum. Just like a photon moves with "c" in vacuum. I said "natural state", but I guess I am from Sweden, so we talk funny. We have good meat balls, though.

In contrast to the photon, the electron does not move with a "natural velocity". Arbitrary speeds are possible - you should also remember that speed is relative, i.e. it also depends on the state of the observer.

BTW, neither am I a native English speaker.

We know it from measuring the rest mass of a free electron - "free" means "unbound".

So we dont know how much rest mass it has in a atom. When we talk about a "free" electron, do we then know how an electron behave in vacuum? What I mean is, if no objects where around it, and if we would have observed it in vacuum, in its natural habitat (just as if the electron was in space), would it still have been an electron? Or do it "vanish"?

In contrast to the photon, the electron does not move with a "natural velocity". Arbitrary speeds are possible - you should also remember that speed is relative, i.e. it also depends on the state of the observer.

"speed is relative"... Well, the speed of light in vacuum isnt.

BTW, neither am I a native English speaker.

I guess you havnt tried meat balls.

Drakkith
Staff Emeritus
Drakkith, if it 1. can gain energy by moving faster, and 2. if it can gain mass by gaining energy, then that would mean that the object that is moving faster has = more energy, and therefore more mass. Then could they not have equal mass at a certain time? It would be a contradiction to say no.

I'll say it again: An object does NOT gain mass when it gains kinetic energy because it is not moving in its own frame of reference. This gain in energy is only seen when viewed from other frames where the object is seen as moving.

Consider the following:

You take a spaceship out into space, turn around, and accelerate to a very high speed. Upon passing the Earth you are moving at 99% the speed of light. According to special relativity, it is perfectly alright to claim that it is the Earth that is moving at 99% the speed of light and not you. Therefor you see the Earth with a great amount of kinetic energy. If an object gained mass just by having kinetic energy, then everyone on Earth would weigh several times what we do since all that energy would add to the mass of the Earth and increase the gravitational pull of the planet.

Obviously this does not happen, so as you can see objects do NOT gain mass simply by moving.

Also, note that the amount of kinetic energy an object has can be entirely different depending on how the object is moving according to different observers. An object moving at 99% the speed of light according to one observer may in fact be stationary to another observer who happens to be in motion at the same speed and in the same direction as the object. So how much energy does the object "actually" have? The answer is that it depends entirely on the frame of reference you are viewing it from.