The theory of relativity holds that as an object approaches the speed of light, it increases in mass.
If I have that right, what exactly does that mean? Does the object physically get bigger? More dense? What does it mean to have more mass?
Strictly, it is the multiplicative factor [symbol]g[/symbol] which increases, rather than the mass M or momentum Mv. Thus it behaves as though it had more mass, but it does not comprise any more actual atoms.
As I understand it, it’s due to the increased kinetic energy of the object and mass-energy equivalence. But I’m not swearing that I’m not totally wrong.
The rest mass of an object stays the same. The relativistic mass is, well, relative; it depends on the reference frame of the observer. The faster the object moves in the a reference frame, the greater its mass as observed in that reference frame.
As I recall, the use of the word “mass” to refer to relatvistic mass has fallen out of favor with physicists. “Mass” nowadays usually refers to rest mass. This article has more details.
[link]http://en.wikipedia.org/wiki/Relativistic_mass[/link]
(Note: I am not a physicist, and my understanding of relativity is limited to the few courses I took in special relativity.)
Argh, that should be
Relativistic mass refers to a perceived increase in mass of an object traveling at speeds comparable to the speed of light. In short, the amount of energy required to increase the velocity of an object by x at relativistic speeds is larger than that required to bring an object at rest up to velocity v. This was once explained by stating that the mass of the object at high speed has (apparently) increased, increasing the amount of kinetic energy required to speed it up.
I once read a more striking thought experiment demonstrating this principle. If I observe a vase at rest with respect to me fall and shatter, I know the physical reason the vase shattered was that its kinetic energy (.5mv^2) at the time it hit the floor was converted to stress energy, and this energy was large enough to shatter the vase. But If I am moving at relativistic speeds with respect to the vase, time dilation will make everything in the vase’s frame of reference appear to move more slowly. So the vase will be falling at a much slower apparent velocity, and therefor have a lower apparent kinetic energy. But the vase still shatters when it eventually strikes the floor; I must conclude that the vase’s kinetic energy is still the same, despite the lower apparent velocity. Since mass is the only variable I have left in the kinetic energy formula, the vase’s mass must have increased.
The problem with this interpretation is twofold: (1) the relativistic mass is measured kinematically (by its effects in dynamic experiments), but mass can also be measured gravitationally. The force of gravity, then, would depend on the speed of the observer, and I doubt anyone can offer a sensible interpretation of what that would look like. (2) In the thought experiment I am using my own time reference–my own clock–and applying it to a different frame of reference (i.e. using it to measure the velocity of the vase). While not technically wrong, it eventually makes things confusing.
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No, in fact it sort of appears smaller in that it will look shorter in the direction of travel than it did when it was at rest (at rest, that is, relative to you).
Not really, except as above.
It means that it will behave in a way that a body of more mass (at rest) would behave-- ie, it will take more force to give it an equal amount of acceleration. You have to think about what “mass” means in the first place.
Actually, this brings up a question about general relativity that I have occasionally wondered about. Let’s say there is an object of rest mass m and an observer at point p. Let’s say the object is traveling at a high velocity relative to the observer and passes through point p’, and the observer notes the gravitational pull from that object at the moment it passes through p’. Then, the object slows down, wanders back to p’, and stops there, again relative to the observer, who then notes the force produced by that object.
Will the observer feel identical forces for its two observations, because the object has the same rest mass at both points, or will the observer note a stronger pull when the object travels by at high speed, because its relativistic mass is larger then?
Just in case anyone wanted to calculate relativistic changes that occur as an object approaches light speed, here is a calculator:
http://www.1728.com/reltivty.htm
Gravitational mass and inertial mass are equivalent to each other. So an object in motion (in your reference frame) will exert a stronger gravitational force on you that it would if it were stationary.
Of course the object’s speed has to be a sizable fraction of c before the effect is anything to write home about. Relativistic mass is proportional to the factor gamma, which is very nearly 1 for all speeds in ordinary human experience.
The problem is that most physicists would take the term “inertial mass” to mean rest mass. The “relativistic mass” of an object in its direction of motion is different from its “relativistic mass” perpendicular to its direction of motion, which is very different from the way mass is expected to behave.
Unfortunately, this question can’t be addressed with special relativity alone. For objects traveling close to the speed of light, the Newtonian approximation to general relativity breaks down. Under general relativity, momentum and pressure have explicit effects on the curvature of space independent of mass. The force a quickly-moving object exerts on you will not behave precisely like an ordinary gravitational force.
This might seem more reasonable in light of the fact that the magnetic force is essentially the relativistic correction to the Coulomb static electric force. Because the charges of elementary particles are so enormous relative to their masses, the relativistic corrections for charge-dependent forces begin to become important at speeds far less than c.
One of the speed-dependent modifications to gravity is sometimes called “gravitomagnetism,” and a search for that term should yield more information on the subject. The upshot of all this is that the gravitational pull of a quickly-moving object will differ from that of a slowly-moving object in a complex way, and that its magnitude will neither stay the same nor increase in a fashion proportional to the object’s “relativistic mass.”