Relativistic mass increase with velocity vs stationary & non stationary observer

[Circlotron]

From my limited understanding of the subject, when an object passes you by at a non zero velocity, it’s mass increases in proportion to it’s kinetic energy. What about the case when you are moving along at the same rate as the object, so that it appears stationary to you, so that you are both in the same reference frame. Does it’s mass increase to an outside observer, but be unchanged to you that is moving along with the mass?

I only have a basic YouTube level of understanding of the subject, so go easy!

[ejeffrey]

From my limited understanding of the subject, when an object passes you by at a non zero velocity, it’s mass increases in proportion to it’s kinetic energy. What about the case when you are moving along at the same rate as the object, so that it appears stationary to you, so that you are both in the same reference frame. Does it’s mass increase to an outside observer, but be unchanged to you that is moving along with the mass?

Yes.  If you are traveling at the same speed and direction as the object, your relative velocity is zero.  In that case, you would measure the object to have mass equal to its mass.  It might help to think of it not so much as the mass increasing, but the mass appears different to different observers, depending on their reference frame.  It's the same object and it hasn't fundamentally changed.

A very crude metaphor would be angular size.  Objects "look" smaller (take up less angular size) when viewed from far away, but the object hasn't actually changed.

[WatchfulEye]

Relativistic mass is just a convoluted way of describing the "total energy" of a system - the energy arising from its rest mass and its kinetic energy. Essentially, it is the rest mass with the same energy as the total (rest + kinetic energy) of the current system.  It is convenient in that it allows traditional Newtonian equations, such as the momentum (p= mv) to hold. Relativistic mass has been used as an educational tool, because it allows students to perform limited calcuations by using familiar equations (p=mv) together with the Lorentz transform.

It also has significant issues - such as being anisotropic. The relativistic mass is different in the direction of travel, to a direction perpendicular. This is not at all intuitive or helpful.

The modern approach to teaching special relativity tends to prefer the concept of mass as invariant, with momentum linked to total energy, and other relations (e.g. acceleration) arising from that. In other words, the fundamental equation is E^2 = m^2.c^4 + p^2.c^2

[Zero999]

Energy is relative. It's energy differences which produce relativistic effects, as well as having the potential to do work. If something is moving at the same speed as you, then it's stationary, from your perspective, even though you're whizzing by someone else at half the speed of light, or is it that they're stationary and you're the one who's moving, or are you both moving? Again, it doesn't matter, because it's differences which matter.

[coppercone2]

how do you measure the mass of something going that fast?

I imagined a space ship with arms shaking another one

[radiolistener]

In modern physics, the mass you are intuitively thinking of does not change with speed. An object has a single invariant (rest) mass, and it is the same in all inertial reference frames.

The idea that "mass increases with velocity" comes from an older concept called relativistic mass, which is largely avoided today because it tends to cause confusion and misunderstanding. What actually changes for observers in relative motion are the object’s energy and momentum, not its mass.

If you move along with the object so that it is at rest in your frame of reference, you measure its normal rest mass. An outside observer, who sees the object moving, measures a larger energy and momentum, but the mass itself remains unchanged.

A useful way to think about this is like observing an object through a camera lens. The object itself does not change, but depending on the lens settings, what you see on the camera output — its apparent size, perspective, or motion — does change. In this sense, the change happens in the transformation of the information about the object, not in the object itself. In relativity, different reference frames are like different "lens settings": they change the description of the object, but not the object itself.

[SteveThackery]

The idea that "mass increases with velocity" comes from an older concept called relativistic mass, which is largely avoided today because it tends to cause confusion and misunderstanding. What actually changes for observers in relative motion are the object’s energy and momentum, not its mass.

If you move along with the object so that it is at rest in your frame of reference, you measure its normal rest mass. An outside observer, who sees the object moving, measures a larger energy and momentum, but the mass itself remains unchanged.

Yep. To home in on one point: the resistance to acceleration increases, which at first glance would imply an increase in mass, but that is a misleading interpretation.