Are the stings in string theory, considered to be matter?

[redhedkangaro]

Are the stings in string theory, considered to be matter?
Are the fundamental particles of the universe cnsidered to be matter?

 

[Nick89]

I think anything with mass is considered matter. So I suppose yes, that includes fundamental particles (except massless once such as photons (are they fundamental? no idea)).

No idea about strings, but I think strings are just considered energy.

 

[malawi_glenn]

matter is excitation modes of the strings.

The elementary particles are indeed considered as matter, even the massless entity called the photon. But matter is not a well defined subject as long as I understand it usage, it is according to me not a fundamental concept.

 

[redhedkangaro]

So matter and energy are diiferent or are they essentially one?

 

[malawi_glenn]

So matter and energy are diiferent or are they essentially one?

I don't think one should use the word "matter" since it is ambiguous - it depends on who you ask what matter is. A particle physicist (like me) would call photons (light) matter, but maybe not a atomic physicist - it is not a fundamental concept, it has no clear definition.

Mass and energy are the same thing, we had long such discussions like a month ago, would be good if you could find those old threads by using the "Search" function. We also had a discussion on what "pure energy" is, if you had the intentions to ask about it too.

 

[enotstrebor]

I don't think one should use the word "matter" since it is ambiguous - it depends on who you ask what matter is. A particle physicist (like me) would call photons (light) matter, but maybe not a atomic physicist - it is not a fundamental concept, it has no clear definition.

Mass and energy are the same thing, we had long such discussions like a month ago, would be good if you could find those old threads by using the "Search" function. We also had a discussion on what "pure energy" is, if you had the intentions to ask about it too.

Matter has mass (see http://en.wikipedia.org/wiki/Matter" ), but maybe it is different in your circle of friends.

However, energy and mass are not the same thing!

The photon has energy but no mass. A massed particle has energy but has massed properties which are different than photon properties. Mass can travel at any velocity less than "c" and requires energy to change its velocity, while the photon only wants to travel at "c''.

As massed energy and photon energy behave differently, energy and mass can not be the same thing.

E=mc^2 says that there is a relationship between the two not that they are the same.

 

[e3bm35]

Greetings! I'm new to this forum and I'm truly impressed with the quality of the discussions.
I especially enjoyed this thread. So the fine folks at Discovery had a contest for the best video explaining string theory in two minutes or less. I thought the winner (String Ducky) was decent. The contenders were pretty good as well.
Here's the link:
http://www.youtube.com/watch?v=AgwxJ-ki-f8"

 

[malawi_glenn]

Matter has mass (see http://en.wikipedia.org/wiki/Matter" ), but maybe it is different in your circle of friends.

However, energy and mass are not the same thing!

The photon has energy but no mass. A massed particle has energy but has massed properties which are different than photon properties. Mass can travel at any velocity less than "c" and requires energy to change its velocity, while the photon only wants to travel at "c''.

As massed energy and photon energy behave differently, energy and mass can not be the same thing.

E=mc^2 says that there is a relationship between the two not that they are the same.

There are several definitions of matter in that wiki article. Also think of this, a container with photon gas will have mass and a volume -> will one call the gas matter, and the constituients "non - matter" ? One has probably the same problem with the dark matter, we don't know what it is made up of - why do we call it matter then? Well it has mass and volume one might say, but that has the photon container also..

So, again to answer OP's question if the fundamental particles are considered as matter, it depends on what definition of matter you employ. The definition "everything that an atom is made out of" then only electrons, protons and neutrons are that for sure. But protons and neutrons are not fundamental particles, they are made up by three valence quarks each, and an "energy soup" of virtual quark- anti quark pairs and gluons (but virtual particles don't exists). Hence neutrinos, tau lepton, muon, photon etc, does not made up atoms are and are then not called 'matter' if one employs that definition.

Now energy, work in the units where c = 1, E = m .. got ya! (I work with them all the time..) What the equation tell you is the relation between mass and energy, energy can not be created nor be destroyed, it can only transfer between different KIDS of energy. Mass is one form of energy, angular frequency of electric and magnetic field waves propagating at the speed of light (E = \hbar \omega or, working in units of \hbar = 1, E = \omega). The c and hbar are just conversion factors in the SI system, but such constants are just a choice of gauge - physics is independent of such choices.

So what if 'massed' energy and 'photon' energy behaves differently, all forms of energy behaves differently in some way. What you have shown is just that an electron and a photon have different kinematical properties due to their rest mass. Nothing more.

I could impose that argument in a reverse order. "Now since photon energy behaves different that mass energy, photons can't be energy."

Late edit: Why u think one calls the equation E = mc^2 "mass–energy equivalence formula" ?

 

[Naty1]

Are the stings in string theory, considered to be matter?
Are the fundamental particles of the universe cnsidered to be matter?

yes, no, in the order asked.

The fundamental entities in string theory are strings, sometime multidimensional: one mode set of vibrations give rise to mass, another basic mode gives rise to energy, another to gravity, yet another is space...space would appear as, say, two dimensional branes and higher...evolving to Penrose spin networks in one formulation...a more energetic string in the right vibrational mode is heavier (more massive) than another similar mode with lesser energy.

 

[per.sundqvist]

Matter has mass (see http://en.wikipedia.org/wiki/Matter" ), but maybe it is different in your circle of friends.

However, energy and mass are not the same thing!

The photon has energy but no mass. A massed particle has energy but has massed properties which are different than photon properties. Mass can travel at any velocity less than "c" and requires energy to change its velocity, while the photon only wants to travel at "c''.

As massed energy and photon energy behave differently, energy and mass can not be the same thing.

E=mc^2 says that there is a relationship between the two not that they are the same.

To make a very simple answer of this: You are confusing the rest mass m0 with the total mass m. The more general version of E=mc^2 reads.

mc^2\equiv E=\sqrt{(pc)^2+(m_0c^2)^2}

where m is the definition of the total mass in terms of E (the equation you wrote actually). So if m0=0 (for the photon) you get: m=p/c, where p, the momentum is given from the de Broglie relation p=h/\lambda. Hence, the photon has BOTH mass and energy, by postulate (the equivalence principle E=m_{tot}c^2).

 

[lightarrow]

To make a very simple answer of this: You are confusing the rest mass m0 with the total mass m. The more general version of E=mc^2 reads.

mc^2\equiv E=\sqrt{(pc)^2+(m_0c^2)^2}

where m is the definition of the total mass in terms of E (the equation you wrote actually). So if m0=0 (for the photon) you get: m=p/c, where p, the momentum is given from the de Broglie relation p=h/\lambda. Hence, the photon has BOTH mass and energy, by postulate (the equivalence principle E=m_{tot}c^2).

No, the photon has energy but no mass. If you don't believe it, you can have a look at the Particle Data Group informations:
http://pdg.lbl.gov/2008/listings/s000.pdf

 

[Dmitry67]

no invariant mass - but it has a relativistic mass

 

[lightarrow]

no invariant mass - but it has a relativistic mass

Yes, I had understood what he intended .
Just a little consideration: if a photon of energy 511 KeV collides head-on with a still electron, since it has the relativistic mass = electron's mass, should it stop moving and give the electron all of its energy? No. Why this doesn't happen? Because relativistic mass concept is useful for nothing. Also, since relativistic mass has already a name: energy (divided by c^2), why do you want to give it another name?

 

[malawi_glenn]

what we are trying to demonstrate is that mass and energy is the same thing, that there are no such thing as 'pure energy'

 

[Dmitry67]

Yes, I agree with you, however, it leads toone misconseption we had recently discoered on this forum.

People got used that mass is a gravitational 'charge' and it works as a source of gravity.
Then people read that photons 'do not have mass' and they conclude that, for example, if matter annihilates with anitmatter and it is transformed into light the gravity suddenly dissapears.

 

[malawi_glenn]

I am planning to write about this in FAQ and in the science library.

 

[lightarrow]

what we are trying to demonstrate is that mass and energy is the same thing, that there are no such thing as 'pure energy'

I don't know what you intended with "pure energy", however a single photon has energy but not mass.

 

[lightarrow]

what we are trying to demonstrate is that mass and energy is the same thing, that there are no such thing as 'pure energy'

So you are not talking about "mass" in general, but specifically about "relativistic" mass.

 

[malawi_glenn]

I don't know what you intended with "pure energy", however a single photon has energy but not mass.

Energy must be bound to something, no thing as "pure energy" circles around in space. "Matter turns into energy" is a misconception.

 

[Dmitry67]

BTW, does the 'rest'/'invariant' mass have any sense at all ?
- knowing that it is just an illusion, a result or how strongly massless particles (electrons, quarks, ...) interact with the Higgs field? :)

 

[malawi_glenn]

It depends in what regime you are considering. One may also say that higgs field also is inaccurate since we have string theory and so on. What we can do is to discuss the validity and coherence of physical paradigms, such as theory of relativity, which we are doing now.

 

[per.sundqvist]

I think the absolute or as it has been called here, the "relativistic mass" has impact in reallity. Photons, even though without rest mass are affected by gravity, in a complicated way though (general relativity theory). This must be due to its "mass" and not since it is "pure energy".

The whole concept of mass and matter is bound to be little mysterious since the days Newton defined it, roughly as m=F/a and also as a source for gravity field F=G*m1*m2/r^2. It need a reference to define a mass or another fixed way to define the force F=m*a, but what is then m? and so on. Energy is derived from Newtons equation, and then a little generalized in relativity, but still relies on that change of momentum (force) is related to mass. I know no other way, all I want to say is that its a mess!

Note also that the mass of the proton, which we can measure, is not given by the quarks rest masses! It gains that mass, around 10 times bigger than rest masses, because of its extreme confinement. It is the total relativistic mass that we see as external observers. The same must be true for the photons (but their mass are extremely small, and we have to deal with GR as well to take it into account).

 

[lightarrow]

BTW, does the 'rest'/'invariant' mass have any sense at all ?
- knowing that it is just an illusion, a result or how strongly massless particles (electrons, quarks, ...) interact with the Higgs field? :)

About Higgs field, I cannot pronounce; about the rest, for what I see it, the distinction between (rest) mass and energy is simply the fact that in the first case, that is when a particle has (rest) mass, you can find a frame of reference in which the particle is stationary while in the second, when you have a particle with energy but no (rest) mass, you can't. So (rest) mass is nothing else than "energy that you can see when the particle is still".

 

[Dmitry67]

So (rest) mass is nothing else than "energy that you can see when the particle is still".

(to add even more confusion)
Are we talking about the mass of the "naked" particles? :)

 

[lightarrow]

(to add even more confusion)
Are we talking about the mass of the "naked" particles? :)

No, dressed, it's winter here in Italy

 

[enotstrebor]

To make a very simple answer of this: You are confusing the rest mass m0 with the total mass m. The more general version of E=mc^2 reads.

mc^2\equiv E=\sqrt{(pc)^2+(m_0c^2)^2}

where m is the definition of the total mass in terms of E (the equation you wrote actually). So if m0=0 (for the photon) you get: m=p/c, where p, the momentum is given from the de Broglie relation p=h/\lambda. Hence, the photon has BOTH mass and energy, by postulate (the equivalence principle E=m_{tot}c^2).

First, E=mc^2 (E=mc²) is universal for any velocity thus includes E=m₀c².

Second, momentum is different than mass, just as energy is different from mass. The equation p=h/\lambda applied to the photon is only true for mc^2=E=\sqrt{(pc)^2+(m_0c^2)^2} when in a vacuum and Thus Not A Fundamental Relationship For The Photon because;

the wavelength/momentum for the photon changes when not in a vacuum but the photon's energy does not.

As mc^2\equiv E=\sqrt{(pc)^2+(m_0c^2)^2} is not universally true, the mathematical relationship is misleading.

If you ignore the distictive behavioral differences you are ignoring the physics. Mathematics is not physics. Mathematical relationships are relationships and are often true only in certain circumstances. When a mathematical relationship is not true under all circumstances it is clearly phenomenological and not fundamental.

 

[enotstrebor]

So what if 'massed' energy and 'photon' energy behaves differently, all forms of energy behaves differently in some way. What you have shown is just that an electron and a photon have different kinematical properties due to their rest mass. Nothing more.

I could impose that argument in a reverse order. "Now since photon energy behaves different that mass energy, photons can't be energy."

Look up the definition of mass and the definition of energy. If you want to change the meaning and make the terms meaningless to you, feel free. They are not the same to the rest of the world and you are doing a disservice to those on this website by not acknowledging the difference.

Late edit: Why u think one calls the equation E = mc^2 "mass–energy equivalence formula" ?

It is called the "mass–energy equivalence formula" because it gives the euqivalent amount of energy held by a massed particle (mathematical energy value equivalence) if you could release all of the contained/particle energy. It does not say mass and energy are the same.

The fact that there is a 'E' (energy) term and a 'm' (mass) term in the equation is because the rest of the world understands that these are two different things. If they were the same there would not be two terms to mathematically describe them. QED

Because massed particles (one embodiment of energy) have different properties than photon particles (one embodiment of energy) we use different words to describe those differences of behavior (at least those who want clearity of thought and understanding).

"and words are grown so false I loath prove reason with them"

 

[malawi_glenn]

Look up the definition of mass and the definition of energy. If you want to change the meaning and make the terms meaningless to you, feel free. They are not the same to the rest of the world and you are doing a disservice to those on this website by not acknowledging the difference.



It is called the "mass–energy equivalence formula" because it gives the euqivalent amount of energy held by a massed particle (mathematical energy value equivalence) if you could release all of the contained/particle energy. It does not say mass and energy are the same.

The fact that there is a 'E' (energy) term and a 'm' (mass) term in the equation is because the rest of the world understands that these are two different things. If they were the same there would not be two terms to mathematically describe them. QED

Because massed particles (one embodiment of energy) have different properties than photon particles (one embodiment of energy) we use different words to describe those differences of behavior (at least those who want clearity of thought and understanding).

"and words are grown so false I loath prove reason with them"

Still I can measure mass in units of energy. The reason for bringing this up is to kill misconceptions of the kind "matter turns into energy".

Mass is one form of energy. If apple is one kind of fruit, the apple is fruit. But not all fruits are apples. Hence mass is energy, but not all energy is mass.

And if photons have mass: A container with photon gas will have mass, that is for sure. What is the definition of mass? It can not be the quantity referred to in Newton's 2nd law since Newtonian dynamics is not fundamental. Same with energy, energy is often defined as the amount of work it can produce by asserting a force to something. But the concept of force is not used in quantum mechanics, there Energy is the fundamental thing (in the Lagrangian and Hamiltonian).

 

[The Dagda]

I think the absolute or as it has been called here, the "relativistic mass" has impact in reallity. Photons, even though without rest mass are affected by gravity, in a complicated way though (general relativity theory). This must be due to its "mass" and not since it is "pure energy".

The whole concept of mass and matter is bound to be little mysterious since the days Newton defined it, roughly as m=F/a and also as a source for gravity field F=G*m1*m2/r^2. It need a reference to define a mass or another fixed way to define the force F=m*a, but what is then m? and so on. Energy is derived from Newtons equation, and then a little generalized in relativity, but still relies on that change of momentum (force) is related to mass. I know no other way, all I want to say is that its a mess!

Note also that the mass of the proton, which we can measure, is not given by the quarks rest masses! It gains that mass, around 10 times bigger than rest masses, because of its extreme confinement. It is the total relativistic mass that we see as external observers. The same must be true for the photons (but their mass are extremely small, and we have to deal with GR as well to take it into account).

Are you saying photons have mass? I always thought that was an open question.

Also the equations of GR as I was told recently deal with the bending of space, according to energy, so I suppose mass is superfluous in terms of photons?

 

[per.sundqvist]

First, E=mc^2 (E=mc²) is universal for any velocity thus includes E=m₀c².

Second, momentum is different than mass, just as energy is different from mass. The equation p=h/\lambda applied to the photon is only true for mc^2=E=\sqrt{(pc)^2+(m_0c^2)^2} when in a vacuum and Thus Not A Fundamental Relationship For The Photon because;

the wavelength/momentum for the photon changes when not in a vacuum but the photon's energy does not.

As mc^2\equiv E=\sqrt{(pc)^2+(m_0c^2)^2} is not universally true, the mathematical relationship is misleading.

If you ignore the distictive behavioral differences you are ignoring the physics. Mathematics is not physics. Mathematical relationships are relationships and are often true only in certain circumstances. When a mathematical relationship is not true under all circumstances it is clearly phenomenological and not fundamental.

Clearly mathematics is not physics, but you must admit that "the power of the equality sign" has been quite successful so far!

1) p=h/\lambda (waves has a momentum) \rightarrow\;\lambda=h/p -> matter are waves!
2) E=mc^2 (mass contains energy) \rightarrow\;m=E/c^2 matter can be PRODUCED by any kind of energy!

2) is the most fruitful result by Einstein, not E=mc^2.

You would agree in that charge is conserved in a reaction, like 0=-e+e, but not mass? My answer is that Yes, the photon has mass. If a container with photon gas has mass, why should not a single photon has mass?

Perhaps I have misunderstood things here, but If it is the Higgs particle that GIVES particles their mass, Its would not exist -> Quite extreme prediction these days... But if it only intermediate mass in some way (like Feynman diagram Kirchoff current of mass) its OK, but why don't predict a "particle" that intermediate momentum and angular momentum at the same time? I here predict the momentum particle in the case you find the Higgs particle.

 

[lightarrow]

You would agree in that charge is conserved in a reaction, like 0=-e+e, but not mass? My answer is that Yes, the photon has mass. If a container with photon gas has mass, why should not a single photon has mass?

Because mass is not additive...

 

[The Dagda]

Clearly mathematics is not physics, but you must admit that "the power of the equality sign" has been quite successful so far!

1) p=h/\lambda (waves has a momentum) \rightarrow\;\lambda=h/p -> matter are waves!
2) E=mc^2 (mass contains energy) \rightarrow\;m=E/c^2 matter can be PRODUCED by any kind of energy!

2) is the most fruitful result by Einstein, not E=mc^2.

You would agree in that charge is conserved in a reaction, like 0=-e+e, but not mass? My answer is that Yes, the photon has mass. If a container with photon gas has mass, why should not a single photon has mass?

Perhaps I have misunderstood things here, but If it is the Higgs particle that GIVES particles their mass, Its would not exist -> Quite extreme prediction these days... But if it only intermediate mass in some way (like Feynman diagram Kirchoff current of mass) its OK, but why don't predict a "particle" that intermediate momentum and angular momentum at the same time? I here predict the momentum particle in the case you find the Higgs particle.

Well considering that the photon appears to be a special case, and that no one in fact knows for sure if its mass is 0, or it is beneath the Planck scale, or tinier still. Suffice to say without a method of measuring it, photons having particular mass is an entirely hypothetical concern. I doubt it having 1x10^-67kg mass would bother the theory all that much either but there you go.

Mass and energy are equivalent but they are not the same thing exactly, we have different ways of modelling mass particles and waves. Is it possible for something to be pure energy? Yes, is it possible light isn't? Yes, who knows...

 

[malawi_glenn]

The very confusion could perhaps lie in the definition of mass and matter - that is why there is such confusion. We have both quantum physics, general relativity and special relativity.

Trying to be diplomatic here ;-)

 

[Dmitry67]

Because mass is not additive...

Again confusion between relativisitc and rest mass...
Before the post I recommend adding what do you mean by 'mass'
Otherwise it is not a mass, but a mess :)

 

[per.sundqvist]

Because mass is not additive...

Well again, its the relativistic mass I was talking of and you are talking of rest mass?

According to the textbook "Introduction to special relativity" by Rindler we have such mass conservation:

\sum*m=0 (* means - for outgoing + for incoming etc)

but he also mention that E=mc^2, here meaning the equivalence of energy and mass is part of a hypothesis from Einstein, but which so far has been shown to be right. About light he write (chap 27):
If every form of energy has mass, we would expect light to have mass and thus bend in a gravitational field like that of the sun. Indeed, this has been observed. The radiation which the sun itself pours into space represents a mass loss to it of more than four million tons per second!

I agree that its a mess with matter and mass... But assume you create a electron positron pair with light you get: " something=m1+m2", what is something? Mass does not appear out of nowhere, it comes from the photon, but it change its manifestation, from being bound in an EM-field to be bound in two point particles.

 

[lightarrow]

Well again, its the relativistic mass I was talking of and you are talking of rest mass?

You don't need to talk about relativistic mass: in a confined space, it's *invariant* mass of the photons to be non-zero, probably it's this that you and others have missed.

 

[Dmitry67]

*invariant* mass of a photon is non zero?
something really new...
In Standard Model it is 0

 

[lightarrow]

*invariant* mass of a photon is non zero?
something really new...
In Standard Model it is 0

Read well what I wrote: not "one photon", but "photons".
In a confined space, for example a box with perfectly reflecting internal walls, you will have stationary EM waves and so no net wave's momentum. Then put p = 0 in E^2 = (mc^2)^2 + (cp)^2 and you get that the total invariant mass of the EM wave is E/c^2 and so non-zero.

 

[Dmitry67]

If this box is big enough then it is just a photon gas - photons moving in all directions.

If walls are close enough (in comparison with a wavelength) then if fact it can be described as a stationary wave, however, in that case you can not analyze just the wave, you need to analyze the whole system: walls plus wave.

 

[Phrak]

If this box is big enough then it is just a photon gas - photons moving in all directions.

If walls are close enough (in comparison with a wavelength) then if fact it can be described as a stationary wave, however, in that case you can not analyze just the wave, you need to analyze the whole system: walls plus wave.

If it's a boson gas, it's still nonzero. But if we knew the position of each phton fairly well, so that they don't overlap too much, the mass would tend to zero. It seems mass is observer dependent.

 

[enotstrebor]

The very confusion could perhaps lie in the definition of mass and matter - that is why there is such confusion. We have both quantum physics, general relativity and special relativity.)

Mass is the property of a resistance to a change in linear velocity (and associated requirement to apply a force to change a massed particles velocity). The massed particle in a vacuum can have any velocity between zero and up to but not including ``c''.

This is true in quantum physics, general relativity and special relativity.

Massed particles also exhibit other properties related to their environment as given by quantum physics, general relativity and special relativity.

The mass values is thus measured via its resistance to a change via a fource (see http://en.wikipedia.org/wiki/Mass" ) ``In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force.''


Matter (see http://simple.wikipedia.org/wiki/Matter" ) ``is the substance or material of which all things are made. Matter has mass. Most matter has volume. All things we can touch, taste or smell are matter.''

``Not Matter'' (see http://simple.wikipedia.org/wiki/Matter" )
``heat is not matter, it is also known as infrared radiation, or another form of light
light is not matter
sound is not matter, it is vibrations of molecules in the air''.

Then there is the photon whose velocity in a vacuum is only ``c''. The photons velocity is only dependent on the media through which it travels. The photon has no invariant mass as it does not have mass.

The fact that the path of a photon around the sun (according to GR) does not mean that it has mass as the path curvature has nothing to do with the property of mass (which is the resistance to a change in linear velocity), but reaction of the photo to the curvature of space. If my memory is correct, the reaction of a massed particle to the curvature of space is also different than the reaction of the photon (but I wouldn't bet my life and can't give a reference).

There are some who want to give the massless photon ``mass'' for the sake of their theoretical beliefs. But there is no physical experimental evidence to indicate the photon has mass.

 

[lightarrow]

If this box is big enough then it is just a photon gas - photons moving in all directions.

If walls are close enough (in comparison with a wavelength) then if fact it can be described as a stationary wave, however, in that case you can not analyze just the wave, you need to analyze the whole system: walls plus wave.

Ok, then let's consider the first case (very big box) and, inside of it, two photons with the same energy E traveling in opposite directions: this system has invariant mass (=2E/c^2). If these two photons will hit the walls of the box an hour later, does it make any difference?

 

[Dmitry67]

Ok, then let's consider the first case (very big box) and, inside of it, two photons with the same energy E traveling in opposite directions: this system has invariant mass (=2E/c^2). If these two photons will hit the walls of the box an hour later, does it make any difference?

Such system with 2 photons has RELATIVISTIC mass of 2E/c^2 (in the frame of the box, as relativistic mass is not invariant). Invariant (rest) mass is 0.

 

[per.sundqvist]

Mass is the property of a resistance to a change in linear velocity (and associated requirement to apply a force to change a massed particles velocity). The massed particle in a vacuum can have any velocity between zero and up to but not including ``c''.

This is true in quantum physics, general relativity and special relativity.

Massed particles also exhibit other properties related to their environment as given by quantum physics, general relativity and special relativity.

The mass values is thus measured via its resistance to a change via a fource (see http://en.wikipedia.org/wiki/Mass" ) ``In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force.''


Matter (see http://simple.wikipedia.org/wiki/Matter" ) ``is the substance or material of which all things are made. Matter has mass. Most matter has volume. All things we can touch, taste or smell are matter.''

``Not Matter'' (see http://simple.wikipedia.org/wiki/Matter" )
``heat is not matter, it is also known as infrared radiation, or another form of light
light is not matter
sound is not matter, it is vibrations of molecules in the air''.

Then there is the photon whose velocity in a vacuum is only ``c''. The photons velocity is only dependent on the media through which it travels. The photon has no invariant mass as it does not have mass.

The fact that the path of a photon around the sun (according to GR) does not mean that it has mass as the path curvature has nothing to do with the property of mass (which is the resistance to a change in linear velocity), but reaction of the photo to the curvature of space. If my memory is correct, the reaction of a massed particle to the curvature of space is also different than the reaction of the photon (but I wouldn't bet my life and can't give a reference).

There are some who want to give the massless photon ``mass'' for the sake of their theoretical beliefs. But there is no physical experimental evidence to indicate the photon has mass.

It seems you have a classical view of mass (similar to m=F/a). In this sense m=0 since v=c and cannot change. This corresponds to the rest mass m0, but not with m=E/c^2.

Deflection of light can be predicted by Newtons theory assuming the Force interaction
F=G*m1*m2/r^2 and letting v=c. GR correct the deflection angle by a factor of 2.

All relies on that there, in the Newton case, m1>0 (the photon), but also in the GR-case since there would be no space-time curvature for an object that does not have mass! Even if the mass of the object don't appear in the final result, the very extreme exact case m=0 (not the limit m->0) would lead to a straight line (no bending)!

 

[jtbell]

Such system with 2 photons [moving in opposite directions] has RELATIVISTIC mass of 2E/c^2 (in the frame of the box, as relativistic mass is not invariant). Invariant (rest) mass is 0.

No, the invariant mass is not zero. The invariant mass of a system is

m c^2 = \sqrt {E_{total}^2 - (\vec p_{total} c)^2}

For two photons with equal energy E, moving in opposite directions, the total energy is 2E and the total momentum is zero. Therefore, for this system, m c^2 = 2E.

More generally, for a "gas" of many photons in a stationary box,

m c^2 = \sqrt {(E_{photons} + E_{box})^2 - (\vec p_{photons} c + \vec p_{box} c)^2}

m c^2 = \sqrt {(E_{photons} + m_{box} c^2)^2 - (0 + 0)^2}

m c^2 = E_{photons} + m_{box} c^2

because the total vector momentum of the photons is negligible for any realistic number of photons moving in random directions.

(I use m instead of m_0 for invariant mass here to simplify the notation.)

 

[lightarrow]

No, the invariant mass is not zero. The invariant mass of a system is

m c^2 = \sqrt {E_{total}^2 - (\vec p_{total} c)^2}

For two photons with equal energy E, moving in opposite directions, the total energy is 2E and the total momentum is zero. Therefore, for this system, m c^2 = 2E.

More generally, for a "gas" of many photons in a stationary box,

m c^2 = \sqrt {(E_{photons} + E_{box})^2 - (\vec p_{photons} c + \vec p_{box} c)^2}

m c^2 = \sqrt {(E_{photons} + m_{box} c^2)^2 - (0 + 0)^2}

m c^2 = E_{photons} + m_{box} c^2

because the total vector momentum of the photons is negligible for any realistic number of photons moving in random directions.

(I use m instead of m_0 for invariant mass here to simplify the notation.)

Perfect, Jtbell

 

[enotstrebor]

It seems you have a classical view of mass (similar to m=F/a).

That is the definition and how it is measured. It is not a view of mass it is the definition (period). You seem to want some other definition, so just let's all make up our own.

In this sense m=0 since v=c and cannot change. This corresponds to the rest mass m0, but not with m=E/c^2.

m=E/c^2 is not a definition of physic(s)al equivalence. Mathematic equivalence is not physics equivalence.

m=E/c^2.

I have two energy forms. One a two ton object rotating with rotational energy E_R. One a two ton object traveling with a velocity and translational energy E_L.

The rotational and linear velocities are such that:

E_R=E_L

I will stand in front of the rotating velocity object and you in front of and along the direction of the linear velocity object.

The difference between mathematics and physics will (hopefully) become clear to you before you die.

 

[Phrak]

It seems you have a classical view of mass (similar to m=F/a). In this sense m=0 since v=c and cannot change. This corresponds to the rest mass m0, but not with m=E/c^2.

It may be classical, but it is correct. F/a is a perfectly valid measure of mass, where abstract equations become an experimental science, as you can actually F/a.

Deflection of light can be predicted by Newtons theory assuming the Force interaction F=G*m1*m2/r^2 and letting v=c. GR correct the deflection angle by a factor of 2.
All relies on that there, in the Newton case, m1>0 (the photon), but also in the GR-case
since there would be no space-time curvature for an object that does not have mass! Even if the mass of the object don't appear in the final result, the very extreme exact case m=0 (not the limit m->0) would lead to a straight line (no bending)!

As you've noted, Newtonian gravity may predict the deflection of a photon, but it predicts it incorrectly. So, it lends no supporting evidence to photon mass, one way or the other.

In the case of General relativity, the particle or photon appearing deflected by the influence of a planet is not a result of the curvature of spacetime about the object by the object, but the curvature of spacetime by the planet. Massive and massless objects behave in the same way; following geodesics. Again, no evidence for or against. The difference in the case of gravity is that light follows "null geodesics," but this is the same in Minkowski space.

 

[Phrak]

No, the invariant mass is not zero. The invariant mass of a system is

m c^2 = \sqrt {E_{total}^2 - (\vec p_{total} c)^2}

For two photons with equal energy E, moving in opposite directions, the total energy is 2E and the total momentum is zero. Therefore, for this system, m c^2 = 2E.

More generally, for a "gas" of many photons in a stationary box,

m c^2 = \sqrt {(E_{photons} + E_{box})^2 - (\vec p_{photons} c + \vec p_{box} c)^2}

m c^2 = \sqrt {(E_{photons} + m_{box} c^2)^2 - (0 + 0)^2}

m c^2 = E_{photons} + m_{box} c^2

because the total vector momentum of the photons is negligible for any realistic number of photons moving in random directions.

(I use m instead of m_0 for invariant mass here to simplify the notation.)

I was preparing to argue with you as I assumed you buried a factor or 2 somewhere, as your results differ from the Komar mass which would double the result. After some quick edgikation, I see that general relativity throws a new curve into this mass vs. mass business, even where the total mass of an object is very small on human scales.

The results from the general theory differ from the special theory.

Unless I'm mistaken, we can treat the light in a laser cavity as a one dimensional box. The norm of the energy momentum vector of light contributes an amount of mass equal to what you derrived. The internal pressure of the light contributes an identical amount, doubling what we should expect between the mirrors. And the mechanical arrangment holding the two mirrors together loses this same amount due to the resultant tension.

The total mass is the same, it's location has changed. ...but somehow, I think you already knew this...

 

[enotstrebor]

No, the invariant mass is not zero. The invariant mass of a system is

m c^2 = \sqrt {E_{total}^2 - (\vec p_{total} c)^2}

...

m c^2 = \sqrt {(E_{photons} + E_{box})^2 - (\vec p_{photons} c + \vec p_{box} c)^2}

m c^2 = \sqrt {(E_{photons} + m_{box} c^2)^2 - (0 + 0)^2}

m c^2 = E_{photons} + m_{box} c^2

because the total vector momentum of the photons is negligible for any realistic number of photons moving in random directions.

(I use m instead of m_0 for invariant mass here to simplify the notation.)

What does it take for you to understand that photon energy is not mass!

Therefore photon energy can never contribute to the invariant mass of a system!

The equation you keep using is a statement about the energy value equivalence of a massed object, it is not a physics equivalence.

See my last posting, though it appears you will die first before recognition of the differnce between mathematical equivalence and physics equivalence.