# What exactly is relativistic mass?

• TheJoninator
In summary, the concept of relativistic mass is a confusing and outdated one. The modern understanding is that mass is the energy of a body at rest, as described by the equation E=mc^2. When the body is in motion, its total energy is given by E2=m2c4+p2c2, where p is the momentum. The term "relativistic mass" is essentially redundant and has been replaced with the more intuitive idea that energy increases with speed, as seen in the equation for relativistic mass, m_rel = E/c^2. This increase in energy/mass is not due to the object's speed, but rather the absorption of energy to increase its velocity. The equations for mass and energy also
TheJoninator
And why does it increase as you travel faster and faster?

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.

silmaril89 said:
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?

TheJoninator said:
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 traveling 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 don't know the equations to try and calculate that one (but I would like to if someone has a link...).

edguy99 said:
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 don't 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.)

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.

edguy99 said:
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 traveling 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 don't 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?

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.

TheJoninator said:
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 traveling 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.

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?

TheJoninator said:
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...".

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

TheJoninator said:
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 tell them relativistic mass is an old term with no meaning anymore.

## 1. What is relativistic mass?

Relativistic mass is a concept in physics that describes the increase in mass of an object as it approaches the speed of light. It is also known as "relativistic mass increase" or "kinetic mass".

## 2. How is relativistic mass different from rest mass?

Rest mass is the mass of an object when it is at rest, while relativistic mass takes into account the increase in mass due to the object's velocity. As the velocity of an object approaches the speed of light, its relativistic mass increases significantly, while its rest mass remains constant.

## 3. What is the equation for calculating relativistic mass?

The equation for relativistic mass is m = m0/√(1-v^2/c^2), where m0 is the rest mass, v is the velocity of the object, and c is the speed of light.

## 4. How does relativistic mass affect the behavior of particles?

As particles approach the speed of light, their relativistic mass increases, which in turn requires more energy to accelerate them further. This leads to the phenomenon of time dilation and length contraction, where the passage of time and the length of objects appear to change for an observer moving at a different velocity.

## 5. Is relativistic mass a commonly used concept in physics?

Relativistic mass is a commonly used concept in the field of physics, particularly in the study of high-speed particles, such as those in particle accelerators. However, it is often replaced by the concept of "rest mass" in modern physics, as it can lead to confusion and is not always necessary for calculations.

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