1. Mar 29, 2007

### Littlepig

my point is:

How can we calculate invariant mass?? What is the still(inercial) state??

This question comes from several books and web sites that i've search about it, and my problem was; ok: with velocity, a body makes is m turn to M by Y factor, but, what can we assume is the m???? is the mass we calcule over volume and volumic mass? is the mass we height on earth using "g" aceleration??
because, as the earth itself is moving, then m is already being turned into M, and problaby, any other measurement is dependent of moving earth...

Another question about this is: considering E=Ymc^2 when v=/0, if a total aniquilation of a mass body hapens, what of this persons receive more E? A static person(considering referencial the mass body one), or a moving person?

My point of this question is: total energy depends on Y factor, so, if a mass body is still in relation to "A" and moving in relation to "B", "B" will receive more energy than "A" right? So in that case, the more faster we run from the explosion, the more energy we receive....:grumpy:

Once again, thanks...
Littlepig

2. Mar 29, 2007

### Mentz114

Briefly - every mass or body has something called 'rest mass', m0. This is the mass of the thing in its own frame of reference. The 'rest energy' of the thing is m0*c^2. Generally energy is not measured the same between inertial frames, because a moving mass has kinetic energy as well as rest energy.
It's done much better here -

http://www2.slac.stanford.edu/vvc/theory/relativity.html

3. Mar 29, 2007

### pervect

Staff Emeritus

There are at least two sorts of mass, which you appear to be confusing. Invariant mass is a property of the body itself, and does not change with speed. So called "relativistic mass" does change with speed (the gamma factor, i.e. $\gamma$. Because it changes with speed, it is not a property only of the body, but of the body and the observer.

4. Mar 29, 2007

### MeJennifer

Measuring the rest mass of an object is not as simple as it looks.

From the oustide an object could appear to be at rest but inside it is not. There can be cases where electrons reach relativistic speeds. For instance in the case of gold.

Obviously the difference is usually extremely small, so we don't have to worry that if we order 1kg of apples that we are cheated on because they sold us the relativistic instead of the rest mass.

5. Mar 29, 2007

### pmb_phy

Note: The term invariant mass is often meant to refer to the proper mass of a system of particles although many people use them to mean the same thing for the obvious reasons. Of course there is nothing wrong with this. I was een unaware of this until the author of one of my GR texts told me that's what he meant when he refered to invariant mass.

There was a time when this subject came up a lot. For that reason I created a web page to describe the topic. Not everything is in there because I wrote that several years ago and I've learned a lot about the topic so far.

Measurement is still something I've quite gotten yet. E.g. to measure invariant mass of a particle (e.g. the proper mass of a particle) then one might think that all you need is to measure the energy, E, and momentum, p of the body. Measuring the momentum doesn't seem troublesome to me but measuring the energy does see to be problem some since to determine the energy it appears that one needs to measure the rest mass, leading you into a circle. The measurements that are measued in particle accelerators is kinetic energy. IT appears that the the proper mass can be determined from the kinetic energy, hence no logical circle.

Anyone have thoughts on this? Thanks.

Pete

6. Mar 29, 2007

### Staff: Mentor

In any inertial reference frame you like, measure the object's momentum p and energy E. Its invariant mass is then

$$m_0 = \frac {\sqrt {E^2 - (pc)^2}} {c^2}$$

It doesn't matter which inertial reference frame you use. In different i.r.f's the energy and momentum have different values, but $m_0$ as calculated above always comes out to the same value. That's why we call it the "invariant mass."

7. Mar 29, 2007

### pmb_phy

How do you measure E without needing to know m0?

Pete

8. Mar 30, 2007

### pervect

Staff Emeritus
An experimental way to do it would be to do a curve fit. You can measure relative energies - so you just plot a curve of E_relative vs p, and look for the value of E_0 that makes E^2 - p^2 (in geometric units) constant.

9. Mar 30, 2007

### bernhard.rothenstein

mass relativity

Do you think that using for invariant mass, Newtonian mass would be confusing?
use soft words and kind arguments

10. Mar 30, 2007

### bernhard.rothenstein

I try to understand your point of view. When gold is in a state of rest relative to me i measure its rest mass which includes the equivalent of the kinetic energies of the electrons moving inside it, Where from could the difference you mention arrise.
use soft words and hard arguments:rofl:

11. Mar 30, 2007

### bernhard.rothenstein

mass relativity

The first place where I have met the ideea to fit experimental results is
Uri Haber-Schaim, 'The teaching of relativity in the senior high school."
The Physics Teacher February 1971 p.75
I think that it is worth to extend the ideea.

12. Mar 30, 2007

### pmb_phy

I don't understand. What is "E_relative" and how do you do to measure it? If a concrete example is needed then use an electron as an example.

Best regards

Pete

Last edited: Mar 30, 2007
13. Mar 30, 2007

### Littlepig

Yeahh, thats very nice...ahaha, and they said poetry were in languages curse...

however, M(relativistic mass) is what counts in inercia, reason why c is impossible to reach, as M tends to infinite...

another question is, in spacetime curvature(gravity expanation by general relativity), what counts? invariant or relativistic mass?
for instance, what curves more the space? a still apple or a moving one?
I read about matter curves spacetime, so can M(relativistic) be considered matter? or as it depends on observer, it isn't?

Another point, just to see if i'm right: measuring M and m of a 0.8c object, M=/m, however, if we manage to acelerate to 0.8c, as we aproach 0.8c, M tends to m...when we reach 0.8c, we actually measure that M=m. so basically we measure a decrease of object's relativistic mass has we acelerate...right?

thanks for all, and enjoy your weekend...

14. Mar 30, 2007

### MeJennifer

This is a very common misunderstanding. The reason you cannot reach c has nothing to do with relativistic mass going to infinite.
When you change relative speed you use the velocity addition formula. In this formula the velocity does not go to c in the limit, in fact it has no limit.

Motion is relative not absolute, so the question is meaningless.

Curvature does not depend on the observer, the curvature depends on the rest mass and energy.

Last edited: Mar 30, 2007
15. Mar 30, 2007

### JesseM

I think that for composite systems involving multiple particles like a gold atom, the "rest mass" is defined in terms of the system's resistance to acceleration in the frame of the object's center of mass (which is proportional to the system's total energy in that frame, including kinetic and potential energy as well as the rest mass energy of each particle)--so, for example, a heated brick is defined to have a greater "rest mass" than the same brick when cool, even though all the individual particles making it up have the same rest mass in both cases.

16. Mar 30, 2007

### robphy

It is better to say "In this formula, the [magnitude of the] velocity never reaches the upper-bound, c".

17. Mar 30, 2007

### MeJennifer

Well if it is the definition then there is nothing to argue I suppose.

Arguing definitions does not make anyone wiser.

18. Mar 30, 2007

### MeJennifer

Thanks Robphy!

19. Mar 30, 2007

### rbj

it's pretty hard to see something approaching infinite inertial mass to accelerate further. also $c^2$ times that relativistic mass (the mass as it appears to the "stationary" observer) is the total energy of the body as it appears to the same observer. putting in an infinite amount of energy to get the body to accelerate to the speed of $c$ also seems to be a problem. i don't think it's accurate to say it has nothing to do with it. there are different ways to look at it (that lead to the same conclusion).

20. Mar 30, 2007

### MeJennifer

An object accelerates from its rest frame, not from some other frame.

There are an infinite number of speeds that an object is traveling at when measured from an infinite number of frames of reference. But all these are completely irrelevant.

Right now, you and I are traveling at a speed very close to c in some frame of reference. Would we care for a minute that that is the case, and would it care if we accelerate?

If you accelerate for 10 million years you would still be at rest in your rest frame. And if you then accelerate even more, the prior 10 million years of accelerations would have no influence on it at all, it is as if you accelerate for the first time.

Last edited: Mar 30, 2007