# Behavior of mass approaching the speed of light

I would like some clarification on the behavior of relativistic mass as it approaches the speed of light. I am a high school student with an interest in physics so chances are I will have a hard time understanding any formal math in special relativity but I appreciate it anyway.

In special relativity, an object at any non-zero velocity (within the universal speed limit) experiences a length contraction. I would like to know how a mass behaves when an object approaches high speeds, as relativistic mass increases and the length decreases (contracts). Thanks!

• What are you asking? You want to know how mass behaves in what respects? – Jim Mar 2 '15 at 21:02
• It's not clear what you want to know happens here. Do you mean what happens to "mass" as distinct from "relativistic mass"? My understanding is that "relativistic mass" is a concept that has fallen out of favor; everyone I know uses "mass" to mean "rest mass" and just keeps the extra factors of $\gamma$. The "rest mass" is the mass of an object in a frame where it is at rest and this does not change. – zeldredge Mar 2 '15 at 21:02
• From what I understand, relativistic mass is just mass of an object at an inertial reference frame. The title should be "relativistic mass" I guess because the object is not at rest. My question is how does the mass behave at high speeds, does it become more dense through contraction? if mass is increasing and length is contracting, what kind of relationship does that assume? – obliv Mar 2 '15 at 21:11
• As @SirElderberry said, relativistic mass is not a favoured interpretation. It's not actually the case that the mass of the object increases, it's that the momentum increases, which you can redefine in a way that looks like mass is increasing. – Jim Mar 2 '15 at 21:19
• What do you mean? If the equation states that m = p/c where p is increasing shouldn't m have to increase? Am I missing a deeper understanding of the subject? – obliv Mar 2 '15 at 21:20

In special relativity, an object at any non-zero velocity (within the universal speed limit) experiences a length contraction.

This isn't actually correct. The object does not experience length contraction since the object is at rest with respect to itself.

It is correct to say that, in an inertial reference frame (IRF) in which the object is uniformly moving, the observed length, in the direction of the motion, will be contracted from the length in the IRF in which the object is at rest.

But the object does not experience length contraction since uniform motion is relative. There are an infinity of relatively moving IRFs in which the object is in relative motion and each one observes a different length contraction.

I would like to know how a mass behaves when an object approaches high speeds,

Likewise, a mass is at rest with respect to itself. In an IRF in which the mass is uniformly moving, the total energy of the mass is given by

$$E = \sqrt{(pc)^2 + (mc^2)^2} = \gamma mc^2$$

where

$$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$

In the reference frame in which the momentum is zero (particle is at rest), this simplifies to

$$E = mc^2$$

That's really all there is to it. The invariant mass $m$ is the same for all observers.

There is a notion of relativistic mass which is just $\gamma m$ but some question if this notion is useful. From the Wikipedia article "Mass in special relativity":

Although some authors present relativistic mass as a fundamental concept of the theory, it has been argued that this is wrong as the fundamentals of the theory relate to space–time. There is disagreement over whether the concept is pedagogically useful. The notion of mass as a property of an object from Newtonian mechanics does not bear a precise relationship to the concept in relativity.

At any rate, as the relative speed $v$ approaches $c$, the relativistic mass $\gamma m$ goes to infinity since, as you can see from the expression for $\gamma$, the denominator approaches zero.

If it is just for the velocity: velocity is relative, so the moving mass considers itself at rest, no matter how fast it is. For this mass the rest of the world is moving, and therefore lenghtcontracted and timedilated.

If it is about acceleration, every acceleration acts like a force on objects with mass so the harder you accelerate an object, the more force you apply on it (and therefore you have to squish or stretch it if you are to push or pull it). But because you can apply low acceleration over a long time instead of high acceleration over a short time you can minimize the forces acting on the mass. If the forces are neglectable in its reference frame the rest of the world would be moving while it sees itself at rest.

In reality it also depends on how fast you move relative to surrounding air or even the cosmic microwave background, because if an objects moves with almost the speed of light, the low energy photons will in direction of motion blueshift to high energy gamma rays which at impact could easily destroy your spaceship.