So what if I was in motion and tried to measure my own mass?

[NWH]

I was wondering, are mass and energy specific to a particular reference frame, as well as things like time? Let's say for example, there's two observers, one in motion (A) and another stationary (B) standing along side my path of direction. If I were in accelerated motion, observer B would witness my mass increase, right? So how would that reverse, would observer A witness no increase in his own mass and instead, it would appear as if observer B's mass had increased?

Or decrease perhaps?

 

[russ_watters]

Mass is a property of matter and is not specific to a reference frame. Energy is measured between two objects and is dependent on the reference frame.

Your thought experiment is a little confusing - are you observer A? In any case, since relative measurements require an outside reference, you don't ever measure anything changing about yourself except when measured against something else.

 

[NWH]

Well, I'm either observer really. I didn't word it properly when I said I am in accelerated motion, what I really should have said is observer A. But for it's use at that time, I was trying to imply that I am in observer A's frame of reference measuring observer A's mass.

I'll rephrase this a little. Observer A is in accelerated motion, observer B is stationary and they are measuring each other's mass. From observer B who's stationary, observer A will appear to have a mass increase because of his motion through space. So does that mean that from observer A's point of view, his mass is still the same amount as if he were stationary? It's instead observer B's mass which appears to change? If so, how does observer B's mass change? Is it equal and opposite? Would it increase or decrease?

SR is such a beautiful concept, it's easy to understand why mass increases with motion, but to think that almost every other thing in other reference frames around you is losing mass because of your action is quite something...

 

[DrGreg]

Well, I'm either observer really. I didn't word it properly when I said I am in accelerated motion, what I really should have said is observer A. But for it's use at that time, I was trying to imply that I am in observer A's frame of reference measuring observer A's mass.

I'll rephrase this a little. Observer A is in accelerated motion, observer B is stationary and they are measuring each other's mass. From observer B who's stationary, observer A will appear to have a mass increase because of his motion through space. So does that mean that from observer A's point of view, his mass is still the same amount as if he were stationary? It's instead observer B's mass which appears to change? If so, how does observer B's mass change? Is it equal and opposite? Would it increase or decrease?

SR is such a beautiful concept, it's easy to understand why mass increases with motion, but to think that almost every other thing in other reference frames around you is losing mass because of your action is quite something...

The subject of "mass" in relativity crops up regularly in this forum, and it necessary to point out the word has (at least) two different meanings in relativity

1. Relativistic mass includes within it the kinetic energy of the object, and so depends on the relative speed of the object to the observer. Different observers can ascribe different values of relativistic mass to the same object at the same time.
2. Invariant mass, also known as rest mass, excludes kinetic energy, and it a property of the object itself and does not depend on the observer.

Not all authors agree which of these two definitions to use when you say "mass" without further explanation. The modern convention amongst most physicists is to use definition 2, but there are still some people who use definition 1. Neither definition is technically wrong, but one reason 1 is considered unnecessary is because relativistic mass is really just another name for "energy" (via E = mc²). For an object that is stationary relative to the observer, the two definitions give the same answer.

Your question implies definition 1 but russ watters' reply implies definition 2.

If A and B are in relative motion, then A says that B's energy and relativistic mass are more than they would be if they were relatively stationary. B says that A's energy and relativistic mass are more than they would be if they were relatively stationary. Each measures their own energy and relativistic mass to be unchanged. And both agree that their rest masses never change at all.

The point is that energy and relativistic mass are observer-dependent concepts (just like length and time).

 

[NWH]

Wow, thanks. So, just to make sure I've got this right. Invariant mass is an objects definitive mass which is unchanging, a figure which remains the same and excludes "extra mass" which is applied to it through motion? Where as relativistic mass includes the invariant mass at rest, but also takes into account the "extra mass" which is added due to relativistic (and Newtonian?) concepts?

Lastly, assuming they're measuring each other, will the observer at rest observe an increase and the observer in motion will observe a decrease?

 

[jtbell]

Wow, thanks. So, just to make sure I've got this right. Invariant mass is an objects definitive mass which is unchanging, a figure which remains the same and excludes "extra mass" which is applied to it through motion? Where as relativistic mass includes the invariant mass at rest, but also takes into account the "extra mass" which is added due to relativistic (and Newtonian?) concepts?

Basically yes, except that Newtonian physics doesn't have any concept of "relativistic mass." In Newtonian physics, mass is mass, period.

Lastly, assuming they're measuring each other, will the observer at rest observe an increase and the observer in motion will observe a decrease?

According to each observer, the other's invariant mass stays the same, regardless of whether there is relative motion or not; whereas the other's relativistic mass increases over the invariant ("rest") mass.

Keep in mind that so long as the two observers are moving inertially (constant velocity), each one is entititled to consider himself as being at rest and the other as being in motion.

 

[DrGreg]

Wow, thanks. So, just to make sure I've got this right. Invariant mass is an objects definitive mass which is unchanging, a figure which remains the same and excludes "extra mass" which is applied to it through motion? Where as relativistic mass includes the invariant mass at rest, but also takes into account the "extra mass" which is added due to relativistic (and Newtonian?) concepts?

Yes, that's right. Relativistic mass is a relativistic concept only. Kinetic energy is both a Newtonian & relativistic concept (but the equations differ at high speed). In relativity only, the kinetic energy can be regarded as "extra mass" (although the modern view is just to call it energy rather than mass).

Lastly, assuming they're measuring each other, will the observer at rest observe an increase and the observer in motion will observe a decrease?

No, each will observe the other to increase. Remember that "at rest" and "in motion" are relative concepts only. Each regards themself at rest and the other in motion. And they are both right.

 

[NWH]

Wow, that's mind boggling. I understand what you're saying and discribing, but the concept of everything around you gaining mass (sorry, kinetic energy) purely because you're in motion is a hard one to fathom... Relativity discribes so much, but it also confuses the hell out of you...

 

[DrGreg]

Wow, that's mind boggling. I understand what you're saying and discribing, but the concept of everything around you gaining mass (sorry, kinetic energy) purely because you're in motion is a hard one to fathom... Relativity discribes so much, but it also confuses the hell out of you...

Note that conservation of energy only really applies within each single inertial frame. When you, the observer, change speed, you are switching into a different inertial frame where energy is measured differently. Nothing is "really" changing (in a sense), it's just that you're measuring it differently, relative to your new frame. (But that doesn't mean it's all an illusion either -- the measurements are valid measurements.)

One way of coping with this is to consider that an accelerating (non-inertial) observer has a notion of potential energy of other objects (due to their relative position) and that a gain in kinetic energy (or relativistic mass) is offset by a loss of potential energy. This is one of the ideas of general relativity, where acceleration of an observer is equivalent to gravity.

 

[ZikZak]

Wow, that's mind boggling. I understand what you're saying and discribing, but the concept of everything around you gaining mass (sorry, kinetic energy) purely because you're in motion is a hard one to fathom... Relativity discribes so much, but it also confuses the hell out of you...

But this concept is purely Newtonian. Even in Newtonian physics, energy is a frame-dependent quantity. It even depends on the location of the origin! What is the potential energy of this physics text sitting here on the table? Sure, it's mgh, but where are you measuring h from? The floor? The table? The ceiling? The amount of energy in the book depends on your answer. And more to the point, an observer driving by in a car assigns the book some nonzero velocity, so it has kinetic energy as well. None of this is Relativistic; it's all 1750s type stuff.