# What exactly is relativistic mass?

And why does it increase as you travel faster and faster?

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Energy equals mass, E = mc^2. As a particle gains more and more energy, it's mass increases, because mass is energy.

Hi,
The concept of relativistic mass is confusing and leads to misunderstandings, and isn't ever really used any more. Nowadays, mass is reserved to mean the energy of a body when it is at rest, via the famous E=mc2. When that body is moving with momentum p, it will have total energy E, found by E2=m2c4+p2c2. 'Relativistic mass' is then basically the energy, the quantity E/c2, which makes it redundant. The strange statement that 'mass increases with speed' is then replaced with 'energy increases with speed', which is much more intuitive: it's just kinetic energy!

Oh ok, so there's really no such thing as relativistic mass? So as you travel faster, your mass does increase,since you need more energy to move faster, and energy is mass? But then you could say that mass doesn't increase since mass and energy is the same thing so energy increases, which makes much more sense than mass increasing.

ZapperZ
Staff Emeritus
Energy equals mass, E = mc^2. As a particle gains more and more energy, it's mass increases, because mass is energy.
This is a faulty use of the energy-mass equation. Please read the FAQ thread in the General Physics forum.

Zz.

What's wrong with it? and Where is the FAQ?

atyy
edguy99
Gold Member
And why does it increase as you travel faster and faster?
I am not sure relativistic mass is the best word here, invariant mass and/or inertial mass are often used and I am not sure if the definition is the same for all people.

The increase in mass is not because you are travelling faster and faster, it is because you are absorbing energy to travel faster. Ie. if you shot a laser at the front of a fast moving object, it would slow down and gain mass. If you shot a laser from behind a moving object, it would speed up and gain mass.

If you were a moving object and shot a laser out your back to speed yourself up, you would loss energy/mass and speed up. If you shot the laser out the front of yourself to slow down, you would loss energy/mass and slow down.

I am still not sure about the equations if the mass is falling (speeding up) in a gravity field. I am pretty sure it speeds up and losses mass, but I dont know the equations to try and calculate that one (but I would like to if someone has a link...).

atyy
I am still not sure about the equations if the mass is falling (speeding up) in a gravity field. I am pretty sure it speeds up and losses mass, but I dont know the equations to try and calculate that one (but I would like to if someone has a link...).
http://arxiv.org/abs/gr-qc/9909014 (I think that's not quite what you are thinking, but try this as a start.)

BruceW
Homework Helper
henry m got it right.
$$E^2 = m^2 c^4 + p^2 c^2$$
E is the total energy of the particle, and m is its rest mass (NOT its relativistic mass). p here is the relativistic momentum.
So, you can see that when the object isn't moving, p=0, so $E = m c^2$ Therefore the definition of the rest mass of the particle is simply that when measured in a reference frame where the particle isn't moving, the total energy of the particle equals the rest mass times c squared.
The relativistic mass of the particle $m_{rel}$ is equal to
$$\frac{E}{ c^2 }$$
And using the equation for E squared, we get:
$${m_{rel}}^2 = m^2 + \frac{ p^2 }{ c^2 }$$
So only in the special case when the particle has zero momentum, the rest mass and relativistic mass are equal.

I am not sure relativistic mass is the best word here, invariant mass and/or inertial mass are often used and I am not sure if the definition is the same for all people.

The increase in mass is not because you are travelling faster and faster, it is because you are absorbing energy to travel faster. Ie. if you shot a laser at the front of a fast moving object, it would slow down and gain mass. If you shot a laser from behind a moving object, it would speed up and gain mass.

If you were a moving object and shot a laser out your back to speed yourself up, you would loss energy/mass and speed up. If you shot the laser out the front of yourself to slow down, you would loss energy/mass and slow down.

I am still not sure about the equations if the mass is falling (speeding up) in a gravity field. I am pretty sure it speeds up and losses mass, but I dont know the equations to try and calculate that one (but I would like to if someone has a link...).
Can you explain the part about the laser being shot at the front of a fast moving object? I don't really understand what you're saying. Is it the laser that's slowing down or the truck? I'm guessing it's the truck though since light doesn't have mass.

The part about shooting a laser out your back etc, is that because the energy for the laser is in the form of mass so when you use it to power the laser, the mass turns into energy to power the laser?

BruceW
Homework Helper
Another expression for the relativistic mass $m_{rel}$ in terms of the rest mass m, is that:
$$m_{rel} = \frac{m}{ \sqrt{1 - \frac{ v^2 }{ c^2 }} }$$
Where v is the speed of the particle. So therefore, the relativistic mass depends on the speed of the object.

edguy99
Gold Member
Can you explain the part about the laser being shot at the front of a fast moving object? I don't really understand what you're saying. Is it the laser that's slowing down or the truck? I'm guessing it's the truck though since light doesn't have mass.

The part about shooting a laser out your back etc, is that because the energy for the laser is in the form of mass so when you use it to power the laser, the mass turns into energy to power the laser?
If you setup the laser in front of your house and shot it at a truck coming towards you, the truck would be slowed and the trucks mass would increase. If the truck was travelling away from you, the trucks speed would increase and its mass would increase. Ie. shooting the laser photons is just like shooting bullets, but you use the mass equivalent of the photons energy to add to the mass of the truck.

If you were to mount the laser on the truck and shoot photons out the back, the truck would tend to speed up and the mass of the truck/laser combo would be reduced by the energy equivalent of the photons you are shooting out the back.

The amounts are pretty small: consider the energy of a photon is often 1-2 evolts, the energy equivalent of an electron is 0.5MeV (500,000 evolts), a proton is almost 940Mev (940,000,000 evolts) and the truck is made out of a lot of protons and electrons, so it is pretty heavy compared to the photon.

Hope the example is of some use.

BruceW
Homework Helper
edgeguy99, you're right, but you should really use the term relativistic mass, or people will get it confused with the rest mass.

Thanks for all of your help everyone. One last question, if you was to tell someone what the definition of relativistic mass is, then what would you say?

Thanks for all of your help everyone. One last question, if you was to tell someone what the definition of relativistic mass is, then what would you say?
I would say: "It's the energy! So you should call it that...".

BruceW
Homework Helper
I agree with henry m, I find it stupid to use two words for the same thing.

Drakkith
Staff Emeritus