The Relativity of Mass: Exploring the Concept of Relativistic Mass in Physics.

[baffledMatt]

E = m*c*c

No, the correct equation is:
[itex]
E^2 = m_0^2 c^4 + p^2 c^2
[/itex]
where p is the momentum of the particle.
[itex]
p = \gamma m_0 v
[/itex]
[itex]\gamma[/itex] is the lorenz factor and [itex]m_0[/itex] is the
rest mass.
The equation you have written down only applies in a particle's rest frame (ie when it is stationary).

v = root of ( E / M ) / k

Now, the energy of a particle can also be expressed by
[itex]
E = \gamma m_0 c^2
[/itex]
These equations lead to
[itex]
\frac{v}{c} = \frac{pc}{E}
[/itex]

F = mv

No, F = mass * acceleration. Is it possible you are confusing force with momentum?

Well, I guess this is enough to conclude that you haven't succeeded. Sorry

Matt

 

[Antonio Lao]

As for the three components. What type of matter is not constructed from energy ?

To me, the true quantum of nature is the square of energy. Matter is constructed from square of energy. The square of energy has two components: the potential and the kinetic. These give meaning to potential mass and kinetic mass. The square of energy is derived from the conservation of a Local Infinitesimal Motion (LIM) of one dimensional space. The LIM gives unique directional properties for all particles (fermions and bosons) in the universe. The LIM is the scalar (inner or dot) product of two vector (outer or cross) products of force and distance.

 

[baffledMatt]

The square of energy has two components: the potential and the kinetic. These give meaning to potential mass and kinetic mass.

Ok, but do you realize that these masses are not Lorentz invariant? For instance, I can always boost to a frame where the 'kinetic' mass is zero. This is why in relativity we only ever deal with the rest mass.

This whole 'relativistic mass equation' thing is a load of *ahem* anyway. I'm not sure how it worked its way into the literature, but it really has little meaning in SR. This is because whenever we talk about some quantity, be it mass, energy or acceleration, we have to think extremely carefully about how this quantity is measured. So how do you measure mass for a relativistic particle? I don't think the answer is at all trivial.

Matt

 

[Antonio Lao]

So how do you measure mass ...

In my research, I don't really measure by plugging numbers into equations. I determine the mass ratios of known particle such as proton and electron. To do that, I use matrices and their scalar factors.

 

[baffledMatt]

In my research, I don't really measure by plugging numbers into equations. I determine the mass ratios of known particle such as proton and electron. To do that, I use matrices and their scalar factors.

But I asked how do you measure these things? I mean, if I see a particle wizzing past me, what measurements can I make which will enable me to determine its mass?

Matt

 

[Antonio Lao]

Matt,

The measurement of an electron mass was done implicitly using angular momentum (deflections in EM field) and not just the linear momentum you envision in your last post (wizzing past me). But even in this technique, at best, we can only determine the charge to mass ratio of the electron. And then the unit of charge is determined by Millikan's oil drop experiment. The standard mass of 1 kilogram based on some metal bar is a macroscopic process (a very complicated process at that) which in reality must take into consideration of Avogadro's number in going into the microscopic domain(part of the science of chemistry).

 

[baffledMatt]

The measurement of an electron mass was done implicitly using angular momentum (deflections in EM field) and not just the linear momentum you envision in your last post (wizzing past me).

Ok, the point I was trying to make is that any 'increase in mass' you think you might observe for a relativistic particle (as implied by this 'relativistic mass' relation) is due to the fact that any experiment you make implicitely involves measuring the tragectory, speed and whatnot of the particle in an EM field and so you get all sorts of SR effects occurring. But it's not very useful to interpret these as due to 'relativistic mass'.

But even in this technique, at best, we can only determine the charge to mass ratio of the electron. And then the unit of charge is determined by Millikan's oil drop experiment. The standard mass of 1 kilogram based on some metal bar is a macroscopic process (a very complicated process at that) which in reality must take into consideration of Avogadro's number in going into the microscopic domain(part of the science of chemistry).

Yes, I agree completely. I guess I was being a little too subtle earlier.

Matt

 

[jcsd]

Ok, the point I was trying to make is that any 'increase in mass' you think you might observe for a relativistic particle (as implied by this 'relativistic mass' relation) is due to the fact that any experiment you make implicitely involves measuring the tragectory, speed and whatnot of the particle in an EM field and so you get all sorts of SR effects occurring. But it's not very useful to interpret these as due to 'relativistic mass'.

No it's got got nothing to do with measuremnt, in SR you can theroretically know all quantities with arbitary accuracy, no particular need for em fields either. The relativistic mass of a particle DOES increase with relative velocity. Relatvistic mass is pretty much equivalent to what we'd think of as mass in Newtonian physics (that is to say if we were to measure tha mass of a particle traveling at relativstic speeds, assuming Newtonian physics to be true, the quantity we would get would be the relativistic mass) , the main reaosn that relativistic mass isn't equated as mass is that it's not frame invariant unlike rest mass which is.

 

[baffledMatt]

No it's got got nothing to do with measuremnt

Indeed, SR is all about measurement.

in SR you can theroretically know all quantities with arbitary accuracy,

That is irrelevant (we are not talking about QM here!). SR tells us that if we are in an inertial frame we have no way of knowing whether or not we are in motion, we can only say if there is relative motion between our own and a different inertial frame. This is a simplified version of Einstein's relativity principle.

Now, when we start to think about what we can observe about moving objects we find that in fact there are odd things happening. For instance, we wish to measure the velocity of a passing spaceship so we have to do something like shoot a radio pulse at it or time how long it takes to pass between two points of fixed separation. This we can do and write nice equations for. However, this equivalence between the two frames means that there must be discrepancies between what we observe and what the person on the spaceship will observe. This leads to all sorts of things which have fancy names like 'time dilation' etc, but you must remember that these are simply due to comparing measurements in different inertial frames.

no particular need for em fields either.

How then do you propose measuring the mass of an electron? Or a passing spaceship in fact?

The relativistic mass of a particle DOES increase with relative velocity.

prove it.

that is to say if we were to measure tha mass of a particle traveling at relativstic speeds, assuming Newtonian physics to be true, the quantity we would get would be the relativistic mass

Ahh, now we are getting somewhere. So, your definition of 'relativistic mass' is the mass you would determine for a particle if you assume Newtonian mechanics?

This is very dangerous! First of all, if you want to build a consistent theory you must leave Newtonian mechanics way out of it. Second, in semiconductors it is found that electrons often behave as if they have an effective mass, [itex]m^*[/itex]. This again is the mass you would deduce they would have if simple Newtonian mechanics were to apply. Now, it is known exactly why this happens and it has nothing to do with the electrons actually becoming heavier, but is related to the band structure inside of the solid. We refer to it as an effective mass to make the maths more transparent, but everybody knows that this is not actually correct. Do you see the similarity?

the main reaosn that relativistic mass isn't equated as mass is that it's not frame invariant unlike rest mass which is.

Not only that, but it is perhaps the very reason why we don't seriously consider it at all.

Matt

 

[jcsd]

Indeed, SR is all about measurement.

No if anything it's about observation, when you talk about measurment you have to be careful as it's certainly not well-defined concept in relativity unlike other areas of physics where it's defined as an irreversible change.

That is irrelevant (we are not talking about QM here!). SR tells us that if we are in an inertial frame we have no way of knowing whether or not we are in motion, we can only say if there is relative motion between our own and a different inertial frame. This is a simplified version of Einstein's relativity principle.

The way you talked about measuremnt certainly made me think that you may of ghet some principles of QM and relativity mixed up. Yes I am aware of Einstein's first postulate.

Now, when we start to think about what we can observe about moving objects we find that in fact there are odd things happening. For instance, we wish to measure the velocity of a passing spaceship so we have to do something like shoot a radio pulse at it or time how long it takes to pass between two points of fixed separation. This we can do and write nice equations for. However, this equivalence between the two frames means that there must be discrepancies between what we observe and what the person on the spaceship will observe. This leads to all sorts of things which have fancy names like 'time dilation' etc, but you must remember that these are simply due to comparing measurements in different inertial frames.

Yes, I know this, but I fail to the relveance.

How then do you propose measuring the mass of an electron? Or a passing spaceship in fact?

You can collide them with objects of known mass, no need for em fields at all.

prove it.

Well I certainly don't know the proof of maths increase off by heart, it's not a particularly simple one (unlike the proof of time dialtion or length contraction), I rememebr a new variation of the proof was posted here a few months ago, so you could looi in archives. But if we accept that the defitnion of relativistic mass is [itex]M = \gamma m_0[/itex] then there's really no need for a proof.

Ahh, now we are getting somewhere. So, your definition of 'relativistic mass' is the mass you would determine for a particle if you assume Newtonian mechanics?

No it's not MY defitnion, nevertheless if we to try and cacualte the mass of a relativistic object using Newtomian physics we would obtain it's relativistic mass not it's rest mass.

This is very dangerous! First of all, if you want to build a consistent theory you must leave Newtonian mechanics way out of it. Second, in semiconductors it is found that electrons often behave as if they have an effective mass, [itex]m^*[/itex]. This again is the mass you would deduce they would have if simple Newtonian mechanics were to apply. Now, it is known exactly why this happens and it has nothing to do with the electrons actually becoming heavier, but is related to the band structure inside of the solid. We refer to it as an effective mass to make the maths more transparent, but everybody knows that this is not actually correct. Do you see the similarity?

relativistic mass and effective mass are synonyms.

Not only that, but it is perhaps the very reason why we don't seriously consider it at all.

Matt

Actually many did define relativistic mass as mass many years ago, howvere the common consenus is that rest mass is preferable as a defintion for mass as it's frame invariant, but you should realize the choice is in someways arbitary.

 

[baffledMatt]

No if anything it's about observation, when you talk about measurment you have to be careful as it's certainly not well-defined concept in relativity unlike other areas of physics where it's defined as an irreversible change.

Ok, I think this is just a little problem in semantics. You're right, we do have to be careful so we should probably define our terms a little better.

Would you accept that if we define:
Observation - the act of observing an event take place. (eg I observe that your clock stopped)
Measurement - a quantitative decription of an observation (eg I measured that your clock stopped at 10:31 by my clock)
then we would agree that SR is all about the fact that although two people in different inertial frames would have the same observations, their measurements would not necessarily agree?

You can collide them with objects of known mass, no need for em fields at all.

And how did you determine the mass of those objects of 'known' mass?

relativistic mass and effective mass are synonyms.

Actually many did define relativistic mass as mass many years ago, howvere the common consenus is that rest mass is preferable as a defintion for mass as it's frame invariant, but you should realize the choice is in someways arbitary.

Yes, I see what you're saying. I would argue that it is not correct to talk about relativistic mass by this definition as it requires Newtonian mechanics to define it. I just have one final question for you before I accept your last comment that the choice is arbitrary:

Mass is a scalar quantity but you argue that it transforms from one frame to another by means of the Lorentz transformation (LT). If this is the case then mass must be one component of a 4-vector, the length of which is invariant under LT. So what is the 3-vector which makes up the rest of the 4-vector?

Matt

 

[jcsd]

Ok, I think this is just a little problem in semantics. You're right, we do have to be careful so we should probably define our terms a little better.

Would you accept that if we define:
Observation - the act of observing an event take place. (eg I observe that your clock stopped)
Measurement - a quantitative decription of an observation (eg I measured that your clock stopped at 10:31 by my clock)
then we would agree that SR is all about the fact that although two people in different inertial frames would have the same observations, their measurements would not necessarily agree?

Even in Galiliean relativity not all measuremnts will agree because velocity is not absolute. Though you could certainly say that many quantities we think of as absolute in everyday life are infact frame dependnt in SR.

And how did you determine the mass of those objects of 'known' mass?

Well that's always going o be a feature of any measuremnt, if you decide to do it by deflections in an em field, how do you deterimine the charge etc.? The solution is simple: just define a unit mass.

Yes, I see what you're saying. I would argue that it is not correct to talk about relativistic mass by this definition as it requires Newtonian mechanics to define it. I just have one final question for you before I accept your last comment that the choice is arbitrary:

Mass is a scalar quantity but you argue that it transforms from one frame to another by means of the Lorentz transformation (LT). If this is the case then mass must be one component of a 4-vector, the length of which is invariant under LT. So what is the 3-vector which makes up the rest of the 4-vector?

Matt

Basically speaking: momentum

 

[baffledMatt]

Even in Galiliean relativity not all measuremnts will agree because velocity is not absolute. Though you could certainly say that many quantities we think of as absolute in everyday life are infact frame dependnt in SR.

ok. I tried to be careful not to specify which measurements would be the same and which wouldn't as I don't think we need to discuss that. So would you agree that we agree?

Well that's always going o be a feature of any measuremnt, if you decide to do it by deflections in an em field, how do you deterimine the charge etc.? The solution is simple: just define a unit mass.

Yes, but sooner or later you will want to relate mass to something else, which requires getting numerical constants which I don't think you can get without some other 'absolute' determination of mass.

Basically speaking: momentum

Ok. I have it that momentum makes a 4-vector with Energy. But the maths seems to work out the same so I'll agree with you that the choice does appear to be somewhat arbitrary.

Just bear this in mind next time you make a statement like

The relativistic mass of a particle DOES increase with relative velocity

Because it depends on which one of these (possibly arbitrary) formulations you have chosen.

Matt

 

[jcsd]

ok. I tried to be careful not to specify which measurements would be the same and which wouldn't as I don't think we need to discuss that. So would you agree that we agree?

I certainly think we agree what relativity is.

Yes, but sooner or later you will want to relate mass to something else, which requires getting numerical constants which I don't think you can get without some other 'absolute' determination of mass.

It's really a matter of semantics, both quantites still come out of the theory and can be transformed into one another by dividing/mutiplying by gamma, whether you prefer 'mass' to be Lorentz variant/invariant is a matter of practicaltiy

Ok. I have it that momentum makes a 4-vector with Energy. But the maths seems to work out the same so I'll agree with you that the choice does appear to be somewhat arbitrary.

Matt

[itex]p^0 = \gamma m_0 c[/itex], so to get energy you mutiply by a constant (i.e. c) and to get relativistic mass you divide by a constant (c again). This is anothe reason that relativistic mass isn't the preferred defintion of mass as it's directly proportional to energy, so the two are pretty much equivalent (there's no point in using two words for the same thing).

Just bear this in mind next time you make a statement like




Because it depends on which one of these (possibly arbitrary) formulations you have chosen.

Well, you seemed to be implying that the relatvistic mass didn't increase wiuth velocity, it does, otherwise I would of never even mentioned relativistic mass.

 

[baffledMatt]

Well, you seemed to be implying that the relatvistic mass didn't increase wiuth velocity, it does, otherwise I would of never even mentioned relativistic mass.

Yes, I see that now. Thanks for showing me this alternate point of view.

Matt

 

[jcsd]

Yes, I see that now. Thanks for showing me this alternate point of view.

Matt

You may well encounter the concept of relativistic mass in the future, though it is not *supposed* to be an oft-used term and it's use is discouraged it isn't completely moribund and merits a paragraph in most physics dictionaries and physics refernce sites (for example: http://scienceworld.wolfram.com/physics/RelativisticMass.html)

Also remember that the relativistic mass of an object in an inetrial reference frame is also it's inertial and hence (by the equivalence principle) it's gravitational mass.