Increased mass origin?

[Chuck Norris]

Mass increases as you approach the speed of light. I have thought about the physical consuences of this and wondered how does what work? (not why does that work?) I mean does atoms just appear out of nowhere in even distributions or what?

[swansont]

Mass increases as you approach the speed of light. I have thought about the physical consuences of this and wondered how does what work? (not why does that work?) I mean does atoms just appear out of nowhere in even distributions or what?

 

It doesn't work. Mass, as it is usually defined, is the rest mass and is invariant. The term that is speed-dependent comes from misapplying the mass-energy relationship: using E=mc^2 rather than E^2 = p^2c^2 + m^2c^4. E=mc^2 is only true for an object at rest

 

Basically, "relativistic mass" becomes a proxy for kinetic energy. Kinetic energy increases with speed. Nobody seems to have a problem with that, nor should they — it's basically a tautology.

 

Lev Okun calls relativistic mass a pedagogical virus. I agree. In a broader picture, one has to make the distinction between models and the reality they represent. They aren't always the same thing. It might be convenient to use m=E/c^2 under some circumstances, even though the definition is artificial and there is no physical process involved to increase the mass with increasing speed.

[timo]

Do atoms just appear out of nowhere in even distribution or what?

That would be funny because speeds are different from different viewpoints/observers and hence the number of atoms in an object would depend on who is looking at it .

 

The bottom line is that there's two ways to interpret the infamous equation [math]E=mc^2[/math]. First, you can say that it only applies when the object is not moving. Hence, the increase of kinetic energy with the increase of speed will not say anything about the mass.

Alternatively, you can try to make the equation apply for all speeds. But then you should take it literal: If mass always is the same as energy (forget about the c² for a second) then mass is energy, i.e. both terms refer to the same thing. Now, if you call the mass energy, which I just argued that you could equally-well do, then you'd probably not expect new matter to appear just because the kinetic energy of an object increases. Depending on your personality you can then either consider the question answered, run away into the "but then our understanding of energy must be completely renewed, give me a few minutes to reinvent physics ..."-direction, or consider the unrestricted equality of mass and energy to be a bad idea. I consider the unrestricted equality of mass and energy to be a bad idea, btw.

 

I also wrote a slightly more technical post about the problem of defining mass some time ago: http://www.scienceforums.net/forum/showthread.php?t=38825 .

[Chuck Norris]

So mass doesn't increase at relativistic speeds?

[ajb]

So mass doesn't increase at relativistic speeds?

 

As swansont has said, the modern definition of mass is the rest mass and this does not change with speed.

 

The relativistic mass is not really a very natural thing and is simply not needed.

[Mr Skeptic]

So mass doesn't increase at relativistic speeds?

 

That depends on what you consider mass to be, and in any case is no surprise. If you consider mass to be the intrinsic, invariant mass, than it won't increase and no surprise. If you consider mass a form of energy, it does increase and again no surprise.

[timo]

If you consider mass to be the intrinsic, invariant mass, than it won't increase and no surprise. If you consider mass a form of energy, it does increase and again no surprise.

That's not fully correct or at least not complete. I do consider the invariant mass a contribution to energy (which is probably what you mean by "form of energy"). But a contribution to energy does not necessarily have to increase with velocity - think potential energy. An increase in mass with velocity only needs to happen when you consider mass being identical (up to constants) to an energy that includes kinetic energy (e.g. kinetic energy itself or total energy).

 

Btw: after thinking a bit about it, the idea of reading "E=mc²" as mass being equal to the total energy in every case does look even more strange to me than before: Most of us have learned that "E=mgh" is a contribution to energy. No one would start to argue stuff about mass or height of an object increasing with velocity from that. But when seeing the equation "E=mc²" that suddenly seems to sound like a great idea.

[Chuck Norris]

An epithany just hit me and I understand now.

[pioneer]

The relativistic mass is not really a very natural thing and is simply not needed.

 

Why did Einstein include it? I tend to think it was to make sure we didn't create relative reference illusions by avoiding an energy balance. If relativistic mass is equivalent to energy, one could only create relativistic mass by adding actual energy. We know absolute V by this.

 

For example, we have two rockets that are stationary. To rocket A we add energy until it reaches velocity V. We then ask each reference which is the moving reference. If we ignore relativistic mass and only use D, T, it is inconclusive, since motion appears relative. If we add the requirement of M we need to do an energy balance, since only one reference received any energy for motion. The E-Mc2 is not relative. The energy balances tells us which is stationary and which is moving. Without that energy balance we vote on it.

 

With relative reference we can create special effects, since there is no energy balance requirement. That pesky mass spoils the fun because it creates a reality check using an energy balance. Some have tried to get rid of it. Sometimes it is not easy to do an energy balance. If we have to include M in SR, we may have to say we are not sure which is which. But if we get rid of M, we can make bold statements that look real even without an energy balance.

 

For example, since motion is relative I have decided the moving reference will be stationary. In the reality of the energy balance, this reference has energy, but since I say it is stationary, this energy is now hidden. Now I can do a perpetual motion trick. If we include relativistic mass, since perpetual motion is not possible, I would know I was moving by this.

 

I often wondered how close is the assumption of relative motion in the universe, to the reality of an actual universal energy balance? If our assumption gives too much or too little energy, based on what is reality, we can create special effects.

[swansont]

Why did Einstein include it?

 

He didn't

 

http://blogs.scienceforums.net/swansont/archives/646

 

For example, since motion is relative I have decided the moving reference will be stationary. In the reality of the energy balance, this reference has energy, but since I say it is stationary, this energy is now hidden. Now I can do a perpetual motion trick. If we include relativistic mass, since perpetual motion is not possible, I would know I was moving by this.

 

No, you can't use this to do perpetual motion. Energy isn't invariant from frame to frame. It is conserved within each frame.

Edited March 12, 2010 by swansont
Consecutive posts merged.