what is Mass?

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paul.fr

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what is Mass?
« on: 11/05/2007 03:48:01 »
all things have mass, but what is mass and can it be manipulated? IE, reduced or increased.

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another_someone

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what is Mass?
« Reply #1 on: 11/05/2007 04:19:40 »
There are at least two answers to that.

Most simply, mass is just a measure of how difficult (how much force is required) to cause an object to change speed or direction - i.e. a measure of just how stubborn an object is going to be about continuing to do what it is doing.

More technically, mass is just another form of energy (E = mc2), and thus can be interchanged with other forms of energy (e.g. in an atomic bomb, where a small decrease in the mass of the bomb releases a huge amount of kinetic energy).

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Offline lightarrow

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what is Mass?
« Reply #2 on: 11/05/2007 13:21:44 »
all things have mass, but what is mass and can it be manipulated? IE, reduced or increased.
You need to loose weight? [;)]

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another_someone

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what is Mass?
« Reply #3 on: 11/05/2007 16:34:10 »
Another technical definition of mass can be a quantum definition, in terms of the wavelength of a quantum wave:



where
    h is Planck's constant, and
    p is the momentum of the object.
    λ is the DeBroglie Wavelength.

Where, at non-relativistic speeds, p = mV

where m = mass, and V = velocity.

Thus the above becomes:

λ = h/mV.

Thus:

m = h/λV

It gets more complex for relativistic speeds, but it still boils down to the mass being a function of the quantum wavelength of the particle.
« Last Edit: 11/05/2007 16:49:21 by another_someone »

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another_someone

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what is Mass?
« Reply #4 on: 11/05/2007 17:21:34 »
Most simply, mass is just a measure of how difficult (how much force is required) to cause an object to change speed or direction - i.e. a measure of just how stubborn an object is going to be about continuing to do what it is doing.

OK, leading on from here, I suppose the logical question is to define the object (i.e. matter) and the nature of force.

I suppose, if we go back to the earliest experiments with mass, the experiments that lead us to our most basic understanding of what mass is, it is really about two issues.

The simplest is we weigh objects, which tell us about the relationship between mass and gravity.

Secondly, we observe objects collide - but the objects we see collide are (in the early days) all composed of atoms, and what we are really seeing is the electrons around one group of atoms repelling the electrons around another group of atoms, so the force we see is really an electric force.

Thus, when we look at the relationship between mass when it is weighed, and mass in a collision, we are looking at the relationship between electrical and gravitational forces.

But, even when we are weighing an object, what we are really measuring is a form of of electrostatic collision - since the object whose weight we are measuring is composed of atoms which are repelling other atoms in order to apparently resist the force of gravity.

Thus, all of our modern concepts of mass ultimately derive from a notion of the interaction of electrostatic forces, and the inertia associated with the focii of these electrostatic forces.

We do now have more complicated ideas of subatomic particles that react to strange forces like the strong and the weak force, but these are all attempts to fit more recent observations into these early ideas that were born purely from the observations of electrostatic forces.

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Offline Batroost

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what is Mass?
« Reply #5 on: 11/05/2007 19:27:09 »

What you have pointed out is that the everyday concept of a solid object is flawed. What we precieve as a solid is , as you quite rightly say, merely electrostic repulsion between its atoms and ours.

But I don't think this invalidates our concept of inertial mass. A 'solid' ball of one isotope of lead could be constructed with the same number of atoms as one of a different isotope. The balls would appear physically identical and would certainly have the same number (rougghly!) of electrons and protons - both being lead - so the electrostatic forces between it and us would be the same when we pushed them. But we would be able to percieve/measure the difference in force that would have to be applied in order to give a specific acceleration.
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another_someone

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what is Mass?
« Reply #6 on: 11/05/2007 20:25:49 »

What you have pointed out is that the everyday concept of a solid object is flawed. What we precieve as a solid is , as you quite rightly say, merely electrostic repulsion between its atoms and ours.

But I don't think this invalidates our concept of inertial mass. A 'solid' ball of one isotope of lead could be constructed with the same number of atoms as one of a different isotope. The balls would appear physically identical and would certainly have the same number (rougghly!) of electrons and protons - both being lead - so the electrostatic forces between it and us would be the same when we pushed them. But we would be able to percieve/measure the difference in force that would have to be applied in order to give a specific acceleration.

Not sure that I was trying, as such, to invalidate anything - just to understand the limits of what we perceive and understand.  I was not trying to say that our model is right or wrong (although inherently all models are to some extent wrong, which is why we can so confidently predict that at some time in the future all models will be superceded by a new model).

That different atoms have different masses does not invalidate what I was saying, that our perception of solid matter is only through our perception of electrostatic forces (even the light we see is a manifestation of the electrostatic force).  That the electrostatic force of a the electrons around a lead atom may behave with different inertial characteristics, which we interpret as meaning that they are carrying different amounts of baggage (i.e. have different numbers of neutrons in the atoms) does not alter the fact that this is merely an interpretation of why the electrons are behaving as they are - we cannot actually observe the neutrons (o.k., we cannot actually observe the electrons - only the electric force they exert).

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Offline Batroost

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what is Mass?
« Reply #7 on: 11/05/2007 23:30:11 »
Ok - I see what you mean.

I was tempted to talk about the mass of non-atomic particles - or at least the observed masses calculated from experiment but then most of these experiments involve electromagnetic forces in one way or another.

Perhaps it's worth asking why electromagnetic effects have such a big effect on what we percieve? I think the answer is probably their high strength and long range compared with the other fundamental forces (at least as imagined by physicists):

Strong Force  - Short range  .. but eh the strongest!
Electromagnetic  about 1% as strong as the 'Strong' force but much longer range
Weak Force - 1/1,000,000,000 as strong and very Short range 
Gravitational Force - Long range but very, very weak (10-38 as strong as the stronng force).

So in everday life it is the electromagnetic effects we notice?
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another_someone

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what is Mass?
« Reply #8 on: 12/05/2007 00:11:48 »
Another interesting issue about electrostatic forces, they are the only force that comes in two polarities (i.e. the only force that is able to repel as well as attract).  If there was not this ability to repel, everything in the universe would collapse in on itself (excepting the issue of having to overcome inertia - but there would not be any force able to hold objects apart that have no inertial force pulling them apart).

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another_someone

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what is Mass?
« Reply #9 on: 12/05/2007 01:42:45 »
Strong Force  - Short range  .. but eh the strongest!
Electromagnetic  about 1% as strong as the 'Strong' force but much longer range
Weak Force - 1/1,000,000,000 as strong and very Short range 
Gravitational Force - Long range but very, very weak (10-38 as strong as the stronng force).

The point is that the strong force has a range of less that 10-14 metres, and the weak force has range of about 10-18 metres.  At this distance, we do not even know for sure that the gravitational force exists, and I am not sure that we know how consistently the laws of mass and inertia behave.  So it may even be (although maybe you will say there are experiments to the contrary - I don't know what does exist there) that mass only exists (in the form we understand it) at ranges of greater than the effect of the strong and weak force, and thus mass is only really pertinent to the electrostatic and gravitational forces.

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jolly

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what is Mass?
« Reply #10 on: 14/05/2007 01:30:50 »
More technically, mass is just another form of energy (E = mc2),

Sorry to be annoying but the maths Of E=MC2 is designed to give you the answer for the energy content of an object or whatever- not the mass!!!! To do the equation you need- the mass!

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another_someone

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what is Mass?
« Reply #11 on: 14/05/2007 03:42:38 »
More technically, mass is just another form of energy (E = mc2),

Sorry to be annoying but the maths Of E=MC2 is designed to give you the answer for the energy content of an object or whatever- not the mass!!!! To do the equation you need- the mass!

The point is that the equation provides an equivalence between mass and energy, such that you can create energy by reducing mass (as is done in an atomic bomb) and by inference can create mass from energy - thus the two are interchangeable.

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jolly

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what is Mass?
« Reply #12 on: 14/05/2007 14:28:05 »
More technically, mass is just another form of energy (E = mc2),

Sorry to be annoying but the maths Of E=MC2 is designed to give you the answer for the energy content of an object or whatever- not the mass!!!! To do the equation you need- the mass!

The point is that the equation provides an equivalence between mass and energy, such that you can create energy by reducing mass (as is done in an atomic bomb) and by inference can create mass from energy - thus the two are interchangeable.
More technically, mass is just another form of energy (E = mc2),

Well this is just not true mass is another form of energy!

The equation is E=MC2! right so under that equation mass and energy are considered distint and seperate! to work out the Mass you would have to do the equation

M=E/DIVIDED BY C2

The best bit is really... That you still dont know how to work out the mass or the energy of an object! and until you do you wont be able to check the maths in this equation...

but when you do you will realise it is utterly incorrect!!!
« Last Edit: 14/05/2007 14:30:59 by jolly »

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Offline Bored chemist

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what is Mass?
« Reply #13 on: 14/05/2007 15:04:40 »
Jolly,
If a=b then b=a
you don't need to specify which direction you are going in. If 2 things are the same it doesn't matter if you say this is the same as that or that is the same as this.
Rearanging the equation in terms of mass doesn't change it; it's still Einstein's relation between mass and energy.

And what, exactly do you mean by the last bit
"The best bit is really... That you still dont know how to work out the mass or the energy of an object! and until you do you wont be able to check the maths in this equation...

but when you do you will realise it is utterly incorrect!!!
"?
Please disregard all previous signatures.

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another_someone

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what is Mass?
« Reply #14 on: 14/05/2007 16:06:48 »
Well this is just not true mass is another form of energy!

The equation is E=MC2! right so under that equation mass and energy are considered distint and seperate! to work out the Mass you would have to do the equation

M=E/DIVIDED BY C2

Yes, it is correct that m = E/c2.

We have particle accelerators that can impart massive energy to a particle, and observe the increase in mass associated with that – so we know it works.

The best bit is really... That you still dont know how to work out the mass or the energy of an object! and until you do you wont be able to check the maths in this equation...

but when you do you will realise it is utterly incorrect!!!

Mass is merely a quantity that links energy, momentum, and force.

There are many ways of measuring force, energy, and momentum; and so calculate the mass.

I cannot believe you seriously think that we cannot work out how much energy it takes to lift a 1lb weight 1 foot in the air, or how much force your bathroom scales might have upon it when you stand upon it.

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Offline lightarrow

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« Reply #15 on: 15/05/2007 14:00:22 »
m = h/λV
It gets more complex for relativistic speeds, but it still boils down to the mass being a function of the quantum wavelength of the particle.
For relativistic speeds:
m = Sqrt[1 - (v/c)2]*h/λV
So, if you make the limit for V --> C, m --> 0.

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jolly

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what is Mass?
« Reply #16 on: 22/05/2007 11:33:11 »
Well magnetism and electricity are clearly linked! but I do not agree that mass and energy are! As a mass can hold varying amounts of energy, which flux; so under those circumstances how can you relate them!

Mass I do not believe realitively afects the amount of energy an object can hold!

The problem really is we still dont know what a mass is; or rather we need better understanding of what is classified/constiutues a mass!

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another_someone

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what is Mass?
« Reply #17 on: 22/05/2007 16:17:57 »
Well magnetism and electricity are clearly linked! but I do not agree that mass and energy are! As a mass can hold varying amounts of energy, which flux; so under those circumstances how can you relate them!

Mass I do not believe realitively afects the amount of energy an object can hold!

We are not actually saying that the mass in any way limits the amount of energy matter can hold, but rather the contrary, that the amount of energy a particle contains is manifest in the apparent mass of the particle, and that even at rest, that mass contains some energy.  Neither the mass nor the energy are limited (just as neither electricity nor magnetism limit each other, but they are nonetheless directly linked to each other).


The problem really is we still dont know what a mass is; or rather we need better understanding of what is classified/constiutues a mass!

I don't doubt this, but all that we can talk about is the current state of knowledge based upon experimental results and theories that try to explain those results.  There is no doubt that at some time in the future, new experiments will necessitate a reinterpretation of our understanding of mass, but the problem is that without having performed those experiments (and we don't even know what the experiment is likely to be until we try it, and suddenly find it returns a result not explained by current theory), then we have no basis upon which to make that reinterpretation.  Until that time, we can only work with what we know, not with what we do not know.

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Offline syhprum

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what is Mass?
« Reply #18 on: 24/05/2007 09:10:55 »
My priest says its where we celebrate the Eucharist
syhprum

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paul.fr

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what is Mass?
« Reply #19 on: 24/05/2007 09:42:18 »
My priest says its where we celebrate the Eucharist

Mass is a place!

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Offline BenV

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what is Mass?
« Reply #20 on: 24/05/2007 10:35:50 »
Well magnetism and electricity are clearly linked! but I do not agree that mass and energy are! As a mass can hold varying amounts of energy, which flux; so under those circumstances how can you relate them!

Mass I do not believe realitively afects the amount of energy an object can hold!

We are not actually saying that the mass in any way limits the amount of energy matter can hold, but rather the contrary, that the amount of energy a particle contains is manifest in the apparent mass of the particle, and that even at rest, that mass contains some energy.  Neither the mass nor the energy are limited (just as neither electricity nor magnetism limit each other, but they are nonetheless directly linked to each other).

Mass and energy are linked by the equation of mass-energy equivalence given in Einstein's theory of special relativity, e=mc2.

Mass is a place!

Wouldn't that be Mass. ?
« Last Edit: 24/05/2007 11:09:30 by BenV »

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Offline lightarrow

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what is Mass?
« Reply #21 on: 24/05/2007 21:18:45 »
An interesting feature of mass is this:
one photon has exactly zero mass.
Two photons, no!
(It's not a joke!).

Edit: two photons have mass if they don't move exactly in the same direction.
« Last Edit: 10/06/2007 12:26:57 by lightarrow »

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another_someone

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what is Mass?
« Reply #22 on: 25/05/2007 01:05:05 »
An interesting feature of mass is this:
one photon has exactly zero mass.
Two photons, no!
(It's not a joke!).

First I have ever heard about this.  Would you like to say (preferably in words of one, maybe two at most, syllables) how this comes about, and what it means?

Do you mean that two photons that are somehow bound, and it is the binding energy that has mass; or do you mean that even two independent photons are measured to have mass?

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Offline lightarrow

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« Reply #23 on: 25/05/2007 14:20:40 »
An interesting feature of mass is this:
one photon has exactly zero mass.
Two photons, no!
(It's not a joke!).
First I have ever heard about this.  Would you like to say (preferably in words of one, maybe two at most, syllables) how this comes about, and what it means?

1. Simple explanation.
If you know that a system has energy but no momentum, using simple relativistic considerations, you should easily conclude that it has rest mass, isnt'it?
Ok. Now, consider the system of two photons of exactly the same energy, travelling in opposite directions. This system has clearly non-zero energy but zero momentum (total p = p1 - p1 = 0). So, the system mast have a rest mass!

2. Just a bit less simple explanation.
The exact formula relating rest mass m, energy E and momentum p of a relativistic system of any kind, is:
(E/c)2 - |p|2 = (mc)2
So, if p = 0, then (E/c) = mc --> m = E/c2 ≠ 0 because E ≠ 0 (in this case, E = 2hν).

Quote
Do you mean that two photons that are somehow bound, and it is the binding energy that has mass; or do you mean that even two independent photons are measured to have mass?

Very good question! Don't know. I would say even two indipendent photons, but I'm not sure.
The fact is that if you observe the system of two photons I've described up, from a moving ref. frame, the two photons don't move in the described way, anylonger: you will see the two photons travelling away from each other forming an angle < 180°; but the rest mass of the system is invariant, so it's exactly the same in this new frame, so, I assume you can pick up any pair of travelling photons in the universe, with the prescription they are not travelling exactly in the same direction and sense (that is, their trajectories form a non-zero angle), and you'll have a non-zero rest mass system.

What all this could exactly mean, is a mystery to me.
« Last Edit: 25/05/2007 14:23:52 by lightarrow »

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another_someone

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« Reply #24 on: 25/05/2007 16:29:34 »
1. Simple explanation.
If you know that a system has energy but no momentum, using simple relativistic considerations, you should easily conclude that it has rest mass, isnt'it?
Ok. Now, consider the system of two photons of exactly the same energy, travelling in opposite directions. This system has clearly non-zero energy but zero momentum (total p = p1 - p1 = 0). So, the system mast have a rest mass!

2. Just a bit less simple explanation.
The exact formula relating rest mass m, energy E and momentum p of a relativistic system of any kind, is:
(E/c)2 - |p|2 = (mc)2
So, if p = 0, then (E/c) = mc --> m = E/c2 ≠ 0 because E ≠ 0 (in this case, E = 2hν).


It sounds to me simply to be a consequence of the notion that light can have energy, and momentum, and thus mass, while in motion, while having zero rest mass in the first place.  More specifically, it is down to the inevitable paradoxes one gets when one deals with infinities (the existence of light implies an assumption of zero rest mass multiplied by an infinite Lorenz factor because it is travelling at the speed of light - so don't be too surprised if you get quirky results).

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Offline lightarrow

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« Reply #25 on: 25/05/2007 19:22:19 »
It sounds to me simply to be a consequence of the notion that light can have energy, and momentum, and thus mass,

Here you are talking about relativistic mass, which is a concept physicists advice not to use anylonger. I was talking about rest mass of photons, which is 0 for one photon and non 0 for 2 of them!

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another_someone

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« Reply #26 on: 25/05/2007 20:14:01 »
It sounds to me simply to be a consequence of the notion that light can have energy, and momentum, and thus mass,

Here you are talking about relativistic mass, which is a concept physicists advice not to use anylonger. I was talking about rest mass of photons, which is 0 for one photon and non 0 for 2 of them!

Yes, but as I understand what you are doing is that you are taking the relativistic notions of energy and momentum, which implicitly include relativistic mass, and then back propagating to an implied rest mass.

Energy and momentum are thus:


where γ is the Lorentz factor.

Since both of those factors include both rest mass (zero) and the Lorenz factor (infinite when one is at the speed of light), so one inevitable has zero multiplied by infinity.

Clearly, with light, the situation is the converse to normal, in that we can measure energy and momentum, but cannot measure rest mass; so the equations are inverted, but you still have the fundamental mix of a measureable quantity divided by infinity returning an assumed zero.

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Offline lightarrow

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« Reply #27 on: 26/05/2007 15:00:40 »
Yes, but as I understand what you are doing is that you are taking the relativistic notions of energy and momentum, which implicitly include relativistic mass, and then back propagating to an implied rest mass.

Energy and momentum are thus:


where γ is the Lorentz factor.

With these formulas you would certainly have strange results, since they are simply wrong for photons (and for 0 mass objects in general). Those are only valid for non 0 mass  objects and travelling at v ≠ c.

The one valid for every object is (E/c)2 - |p|2 = (mc)2  as I've already written in the other post.

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another_someone

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« Reply #28 on: 26/05/2007 15:37:23 »
With these formulas you would certainly have strange results, since they are simply wrong for photons (and for 0 mass objects in general). Those are only valid for non 0 mass  objects and travelling at v ≠ c.

The one valid for every object is (E/c)2 - |p|2 = (mc)2  as I've already written in the other post.

Is there not a paradox here.

You are saying that you are using an equation that is only valid for massless particles to calculate that the particle is not massless (or, at least that the collections of particles are not massless).  If the particles are not massless, then how can you use an equation that is only valid for massless particles?

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« Reply #29 on: 26/05/2007 20:21:46 »
With these formulas you would certainly have strange results, since they are simply wrong for photons (and for 0 mass objects in general). Those are only valid for non 0 mass  objects and travelling at v ≠ c.

The one valid for every object is (E/c)2 - |p|2 = (mc)2  as I've already written in the other post.

Is there not a paradox here.

You are saying that you are using an equation that is only valid for massless particles to calculate that the particle is not massless (or, at least that the collections of particles are not massless).  If the particles are not massless, then how can you use an equation that is only valid for massless particles?

Probably I didn't express myself clearly.
The equation I use: (E/c)2 - |p|2 = (mc)2
is valid for all kinds of particles, massless and not massless, it's the most general one.

The equations you wrote:
E = γmc2
p = γmv
are valid only for not massless particles.

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another_someone

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« Reply #30 on: 27/05/2007 23:31:20 »
Probably I didn't express myself clearly.
The equation I use: (E/c)2 - |p|2 = (mc)2
is valid for all kinds of particles, massless and not massless, it's the most general one.

Sorry, I did misunderstand that.

On the other hand, if the equation is true for both massless and non-massless bodies; and for all such bodies, it can represent a mass for two objects that is different from the sum of the masses of the single objects, then should that not be just as true for tennis balls as for photons?
« Last Edit: 27/05/2007 23:33:09 by another_someone »

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Offline lightarrow

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« Reply #31 on: 28/05/2007 23:38:29 »
Probably I didn't express myself clearly.
The equation I use: (E/c)2 - |p|2 = (mc)2
is valid for all kinds of particles, massless and not massless, it's the most general one.
Sorry, I did misunderstand that.
On the other hand, if the equation is true for both massless and non-massless bodies; and for all such bodies, it can represent a mass for two objects that is different from the sum of the masses of the single objects, then should that not be just as true for tennis balls as for photons?
Yes, if the tennis balls are moving, but the effect is negligible at non-relativistic speeds, that is, m1 + m2 ≈ mass of the system of the 2 balls.
The effect is so striking with photons because they travel at c.

Let's make some computation.

we have 2 tennis balls, each having:

m = 100g = 0.1Kg; so m1 + m2 = 2m = 0.2Kg.
v = 30m/s

p = m*v = 0.1*30 = 3 Kg*m/s (actually, we should write p =m*v*γ, but it's easy to see that the result wouldn't change, at the level of accuracy we will find);

E = Sqrt[(cp)2 + (mc2)2]

and they travel in opposite directions.

be:
ms Es, ps the mass, energy and momentum of the system of 2 balls. We have:
Es = 2E because energy is additive;
ps = 0 because the 2 balls are travelling in opposite directions;
(msc2)2 = (Es)2 - (cps)2 = (Es)2
so:
ms = Es/c2 = 2E/c2 = 2 Sqrt[(cp)2 + (mc2)2]/c2 =

2 Sqrt[(p/c)2 + m2] = 2 Sqrt[(3/3*108)2 + (0.1)2] = 2 Sqrt(10-16 + 10-2) =

= 2*10-1 Sqrt( 1 + 10-14) ≈ 2*10-1 = 0.2Kg.

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another_someone

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« Reply #32 on: 29/05/2007 01:56:02 »
OK, I see what you are saying.

That for any particle or object, if two of them are moving antiparallel directions, they will have a greater calculated rest mass than if they travel in parallel; but that for low speed objects, most of the energy in the particle is bound up in the rest mass anyway, so the amount of kinetic energy is too insignificant to cause the confusion in rest mass.

So ant particle, be it massless or non-massless; if it has kinetic energy that is comparable to the zero velocity rest mass, then the calculated rest mass using that formula for particles that are antiparallel will differ from the rest mass of the same particles travelling in parallel.

As such, it does bring into question whether the equation can really be used to measure true rest mass, since true rest mass I would expect to be the mass of the object with zero kinetic energy, and if that equation causes a different answer to that, then the equation sounds wrong.

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Offline lightarrow

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« Reply #33 on: 29/05/2007 11:51:48 »
OK, I see what you are saying.
That for any particle or object, if two of them are moving antiparallel directions, they will have a greater calculated rest mass than if they travel in parallel; but that for low speed objects, most of the energy in the particle is bound up in the rest mass anyway, so the amount of kinetic energy is too insignificant to cause the confusion in rest mass.
So ant particle, be it massless or non-massless; if it has kinetic energy that is comparable to the zero velocity rest mass, then the calculated rest mass using that formula for particles that are antiparallel will differ from the rest mass of the same particles travelling in parallel.
Exactly.
Quote
As such, it does bring into question whether the equation can really be used to measure true rest mass, since true rest mass I would expect to be the mass of the object with zero kinetic energy, and if that equation causes a different answer to that, then the equation sounds wrong.
Infact, calling that m "rest mass" is not appropriate, in this case; some physicist call it, better, "invariant mass" and I agree with them. You could say that, in the case of two objects travelling in opposite directions with total p = 0, however, the system is "at rest" because it is its centre of gravity; however it would be very tricky to keep calling m "rest mass".
The term everyone should use is invariant mass simply because it doesn't change from a ref frame to another, and this is what really counts.

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another_someone

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what is Mass?
« Reply #34 on: 29/05/2007 16:02:51 »
Infact, calling that m "rest mass" is not appropriate, in this case; some physicist call it, better, "invariant mass" and I agree with them. You could say that, in the case of two objects travelling in opposite directions with total p = 0, however, the system is "at rest" because it is its centre of gravity; however it would be very tricky to keep calling m "rest mass".
The term everyone should use is invariant mass simply because it doesn't change from a ref frame to another, and this is what really counts.

In what way is it an invariant mass?

In fact, no mass is actually invariant; but the notion of 'rest mass' derives from the mass that an object would have in the absence of any kinetic energy, whereas the equation (E/c)2 - |p|2 = (mc)2 must include kinetic energy (otherwise there would not be any momentum, even for a lone particle, and thus the paradox we are talking about disappears).

In practical terms, what measurable quantity does this equation provide?  It does not show an apparent mass (because that would be the full relativistic mass), and it does not show the mass measured when the system is at rest - so what measurable quantity would relate to this number?

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Offline lightarrow

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what is Mass?
« Reply #35 on: 30/05/2007 14:17:08 »
Infact, calling that m "rest mass" is not appropriate, in this case; some physicist call it, better, "invariant mass" and I agree with them. You could say that, in the case of two objects travelling in opposite directions with total p = 0, however, the system is "at rest" because it is its centre of gravity; however it would be very tricky to keep calling m "rest mass".
The term everyone should use is invariant mass simply because it doesn't change from a ref frame to another, and this is what really counts.
In what way is it an invariant mass?
I wrote it:
"The term everyone should use is invariant mass simply because it doesn't change from a ref frame to another, and this is what really counts"
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In fact, no mass is actually invariant;
What do you mean? The m defined above is invariant.
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but the notion of 'rest mass' derives from the mass that an object would have in the absence of any kinetic energy,
But what do you mean with "kinetic energy"? For a single particle, kinetic energy is the energy due to the particle's movement, but for a system of two particles travelling in opposite directions with total p = 0, it is not: the system has no kinetic energy, just because total p = 0. Kinetic energy is cp.
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whereas the equation (E/c)2 - |p|2 = (mc)2 must include kinetic energy (otherwise there would not be any momentum, even for a lone particle, and thus the paradox we are talking about disappears).
In practical terms, what measurable quantity does this equation provide?  It does not show an apparent mass (because that would be the full relativistic mass), and it does not show the mass measured when the system is at rest - so what measurable quantity would relate to this number?
But m is the mass of the system in the ref. frame in which the system's kinetic energy is 0; it's only that it's difficult (for me, at least!) to call it "rest mass" for a system of two balls or particles that travels at high speed in opposite directions, you know what I mean?

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what is Mass?
« Reply #36 on: 31/05/2007 00:52:28 »
I wrote it:
"The term everyone should use is invariant mass simply because it doesn't change from a ref frame to another, and this is what really counts"

Not sure even this is true.

The equation (E/c)2 - |p|2 = (mc)2 will assume that |p|2 is zero in only one particular frame of reference.  If p = γmv for each of the two particles (which it will be is we are talking about non-massless particles at less than the speed of light), then it follows that p changes according to the frame of reference you use.

If you are in a frame of reference where you have two particles, each approaching you at equal velocity from opposite directions, then clearly the sum of the momentum of the two particles is zero.  But equally, you can choose a frame of reference where one particle is stationary in respect to you (and thus has zero momentum), while the other particle has a momentum:

p' = 2mv1/sqrt(1 – 4v12/c2)

Would not your calculated “invariant mass” be different in this reference frame?

What you do seem to be saying is that it is the “rest mass” of the system (i.e. the mass of the system when the sum of the velocity of the component parts of the system are zero, thus making the system as as a whole appear to be at rest relative to the observer), where the component parts of the system are not necessarily at rest (i.e. where all the component parts of the system may be in motion, but the total system itself is not in motion).

This would seem more sensibly to be regarded as a systemic rest mass, rather than any sort of reference invariant mass.  Thus, you are saying that a system of two photons can have a non-zero systemic rest mass, but that in any system, the rest mass of the system may be different from the sum of the rest masses of its component parts, if the component parts of the system are not at rest.

This is probably not unreasonable, since you are not actually measuring the rest masses of the component parts of the system, but the apparent masses as they occur within the system (i.e. the relativistic masses of the individual component parts).
« Last Edit: 31/05/2007 00:58:04 by another_someone »

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what is Mass?
« Reply #37 on: 31/05/2007 01:03:08 »
Ofcourse, if one follows the logic of the above, could all mass that we see merely be composed of “systemic rest masses” - i.e. could non-massless particles, such as electrons, really simply be systems composed of massless particles, and what we perceive as the rest mass of an electron, merely be the rest mass of the system of massless particles of which the electron is composed, and the component sub-particles within that system remain in motion, even as the system appears to be at rest?

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« Reply #38 on: 31/05/2007 13:39:46 »
I wrote it:
"The term everyone should use is invariant mass simply because it doesn't change from a ref frame to another, and this is what really counts"
Not sure even this is true.
The equation (E/c)2 - |p|2 = (mc)2 will assume that |p|2 is zero in only one particular frame of reference.  If p = γmv for each of the two particles (which it will be is we are talking about non-massless particles at less than the speed of light), then it follows that p changes according to the frame of reference you use .

Absolutely! But E also changes, and in such a way that (E/c)2 - |p|2 is invariant.
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This would seem more sensibly to be regarded as a systemic rest mass, rather than any sort of reference invariant mass.  Thus, you are saying that a system of two photons can have a non-zero systemic rest mass, but that in any system, the rest mass of the system may be different from the sum of the rest masses of its component parts, if the component parts of the system are not at rest.
Yes.
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This is probably not unreasonable, since you are not actually measuring the rest masses of the component parts of the system, but the apparent masses as they occur within the system (i.e. the relativistic masses of the individual component parts).
No, I talk about rest masses of the components, and rest mass of the system. (This is the only universally recognized useful concept of "mass").

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Offline Mr. Data

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what is Mass?
« Reply #39 on: 02/07/2011 15:47:19 »
What is mass?

Mass is a charge, fundamentally speaking, as a Higgs field interacts with a massless particle. Through a process of spontaneous symmetry-breaking, the photon (as an example of a massless particle) would obtain a mass by gobbling up a Goldstone Boson.

But what really is mass?

Mass is a concentrated form of energy. You can measure how compact the energy is if you apply the equation E=Mc2. This is non-relativistic, however, but the rest mass assures us that by using c2 as a scale factor, we can certainly get a lot of energy from a tiny bit of mass: because of this, energy must be a diffused state of matter.

So simply, mass the compact structure of a more concentrated energy - and this energy occupies the intrinsic structure of the particle, providing it with other interesting things, like charge, (or if absent of electric charge) some kind of magnetic dipole.
« Last Edit: 02/07/2011 15:49:32 by Mr. Data »

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« Reply #40 on: 05/07/2011 20:46:07 »
Wrong. According to your idea, a photon with total energy E and an electron with total energy E should have the same mass, but it's not.

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Offline Mr. Data

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« Reply #41 on: 05/07/2011 23:41:30 »
Wrong. According to your idea, a photon with total energy E and an electron with total energy E should have the same mass, but it's not.

No, you apply E=Mc2 to an individual particle system. Sure you can work out different values for mass, but for a photon, it does not even have a mass. But that's a whole different ball game involving more difficult field processes I doubt you could fully understand unless you sat down and learned this stuff.

But you would not have said what you did, if you had read my post and understood also what was said. I said E=Mc2 is non-relativistic, meaning it does not apply to particles travelling at or near light speed.

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Offline JP

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what is Mass?
« Reply #42 on: 05/07/2011 23:47:03 »
But you would not have said what you did, if you had read my post and understood also what was said. I said E=Mc2 is non-relativistic, meaning it does not apply to particles travelling at or near light speed.

That's an understatement, since it only applies in the rest frames of particles, which is as far from light speed as they can get.  That equation is wrong if the particle is moving in your reference frame--and of course light is always moving.

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Offline Mr. Data

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« Reply #43 on: 05/07/2011 23:51:45 »
But you would not have said what you did, if you had read my post and understood also what was said. I said E=Mc2 is non-relativistic, meaning it does not apply to particles travelling at or near light speed.

 
That's an understatement, since it only applies in the rest frames of particles, which is as far from light speed as they can get.  That equation is wrong if the particle is moving in your reference frame--and of course light is always moving.

This is an overstatement.

We are not talking about light. Light does not even have a mass - E=Mc2 is a relatively good estimate for particles travelling at non-relativistic speeds. In fact, the nature of speed, should not even be an issue here. The question is about mass, what mass is, and E=Mc2 was used to describe it. Now if we had been talking about photons (which I had not been, nor the OP) then the equation to worry about would have been E2=p2c2 + M2c4. But it wasn't needed.

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« Reply #44 on: 06/07/2011 00:24:42 »
Uh huh.  It's a good estimate. 

However, E2=p2c2 + M2c4 tells you a more complete story and includes the cases where the particle is moving or the particle happens to be a photon.

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Offline Mr. Data

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« Reply #45 on: 06/07/2011 00:41:58 »
Why would we want to talk about photons? They contain none of the relevent information to answer the question of what mass is...

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Offline Mr. Data

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« Reply #46 on: 06/07/2011 03:14:00 »
If you want a technical, mathematical explanation, then I will most happily write out some math tomorrow, or the next day and explain how photons and their fields predict the presence of a Higgs field in the presence of some symmetry-breaking. But you will need to know just some basics of partial differentiation for quantum fields, and whilst that part sounds difficult, it's really not.

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Offline Mr. Data

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« Reply #47 on: 06/07/2011 03:15:46 »
Whilst a Higgs field explains the presence of a mass, which is synonymous to a symmetry-breaking in something like a photon field, the photon alone does not answer what mass is - it, and it's field can answer for the presence of the Higgs Boson if you satisfy breaking the symmetries. Of course, however, the Higgs field does not exactly explain why inertia is experienced; all we can surmise from relativity is that inertial mass and gravitational mass are equal. The Weak equivalence.

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Offline lightarrow

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« Reply #48 on: 06/07/2011 10:09:40 »
Wrong. According to your idea, a photon with total energy E and an electron with total energy E should have the same mass, but it's not.

No, you apply E=Mc2 to an individual particle system. Sure you can work out different values for mass, but for a photon, it does not even have a mass. But that's a whole different ball game involving more difficult field processes I doubt you could fully understand unless you sat down and learned this stuff.

But you would not have said what you did, if you had read my post and understood also what was said. I said E=Mc2 is non-relativistic, meaning it does not apply to particles travelling at or near light speed.
About the concept of mass, I have understood to be quite careful and to make very precise statements, despite its seeming simplicity. You wrote:

"Mass is a concentrated form of energy"

and I reply:
mass is not "a form of energy", mass "is" energy. But that statement is not complete, because we have to add: "fixed a system in space". If it moves, then it's not true anylonger.
examples:
1) I heat a piece of iron which is "not moving in the frame of reference I have chosen", giving it an amount of thermal energy equal to ΔE; its mass increases of an amount Δm. It comes out that Δm = ΔE/c2.
2) That piece of iron has the shape of a spring. I give it the energy ΔE as elastic potential energy by compressing it of the appropriate amount. Its mass increases of Δm.
3) I give it ΔE as any other form of energy. Its mass increases of Δm.
4) I choose to consider a void volume of space. Its mass is zero. Then a beam of light goes through it, for a brief instant. During that instant, the mass of the system increases of Δm = ΔE/c2, if ΔE is the average light beam's energy in that volume of space during that brief instant of time.

It doesn't matter what form of energy ΔE I give to the piece of iron,
It doesn't matter what form of energy ΔE I give to the fixed system I am considering, its mass increases of Δm.
 
Conclusion: mass is not "a form of energy", mass "is" energy, provided the piece of iron or the system I'm considering doesn't move in space.

So, you don't have to explain what mass is, you already have an explanation.

Just to precise your statement.
« Last Edit: 06/07/2011 10:19:38 by lightarrow »

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Offline Mr. Data

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« Reply #49 on: 06/07/2011 10:21:45 »
Huh?

The word ''form'' does not imply a direct difference. The statement mass is a concentrated form of energy does not imply a difference either. ''Form'' is simply another word for ''structure''. Replace that with ''form'' in my sentence:

Mass is just a concentrated structure of energy.

The use of the word is not implying a difference between mass or energy. It is just as right as saying directly mass is energy and energy is mass. But saying it like the latter has less meaning than my statement, and I will leave it to you to figure out why.