[erickejah]

really interesting.  []

[yor_on]

Ah Sophie, you are a voice of reason:)
And I'm not joking there.

How would I dare disagree with such logic?
But I will try, not so much disagreeing, more like not being fully satisfied:)

Tell me Sophie, if you pinch your self, does it not hurt?
And that skin of yours, is it then not different from bone, from stone?

So if all is explainable as waves what about invariant mass?

[lyner]

All I was implying is that treating photons as little bullets is very blinkered. Treating them as small helpings of Energy (the original reason for introducing the concept), constrained by a wave gives rise to no problems yet resolves a lot of apparent paradoxes.

Where does invariant mass prove to be a problem in this respect? Perhaps you could include 'what mass is' in that explanation.

[yor_on]

Sophie, to me it is a constant source of consternation.
Most things in QM can be explained, as you write, as "small helpings of Energy (the original reason for introducing the concept), constrained by a wave".
But then we have 'matter' (invariant mass) and to me it is to its 'nature' definitely unlike any of those concepts:)
It's not energy, even though it can be 'expressed' as it and 'transformed' into it.
It have an equivalence, but is a totally different 'state' if you see how i think.
And I can't reconcile it with waves only.

And I would love to be able to "include 'what mass is"

[lightarrow]

Sophie, to me it is a constant source of consternation.
Most things in QM can be explained, as you write, as "small helpings of Energy (the original reason for introducing the concept), constrained by a wave".
But then we have 'matter' (invariant mass) and to me it is to its 'nature' definitely unlike any of those concepts:)
It's not energy, even though it can be 'expressed' as it and 'transformed' into it.
It have an equivalence, but is a totally different 'state' if you see how i think.
And I can't reconcile it with waves only.

And I would love to be able to "include 'what mass is"

Take a ray of light and confine it in a fixed space (for ex. a box). Now the light has mass.

[yor_on]

Good one, but nah:)
The light still only has 'momentum'

The box though, if clad in a totally reflective material, will exhibit an added mass.
But it sure phreaks me out:)

[lightarrow]

Good one, but nah:)
The light still only has 'momentum'

The box though, if clad in a totally reflective material, will exhibit an added mass.
But it sure phreaks me out:)

A couple of photons not travelling in the same direction has mass, because you can find a reference frame where the total momentum of the system is 0:

E² = (Mc²)² + (cP)²

E = energy of the two photons' system = E₁ + E₂ = 2E₁, with two equal photons, where E₁ is a single photon's energy (energy is additive).
M = mass of the two photons' system.
P = momentum of the two photons' system = P₁ + P₂ where P₁ and P₂ are the momenta of the  photon 1 and 2, respectively.

A single photon's momentum is, in modulus: |P₁| = |P₂| = E₁/c.

So, if the two photons are not travelling in the same direction:

|P| = |P₁ + P₂| < 2|P₁| = 2E₁/c

so

P² = |P|² < 4E₁²/c²   →   -P² > -4E₁²/c²

(Mc²)² = E² - (cP)² = (2E₁)² - c²P² > 4E₁² - c²4E₁²/c² = 0

so

(Mc²)² > 0

that is:

M > 0.

So it's light which has mass when confined in a fixed space.

[yor_on]

lightarrow, are you referring to momentum as mass?
As that, as I see it, is what gives the box the added 'weight'
And do you see it as being 'invariant' mass?

You wrote 'A couple of photons not traveling in the same direction has mass, because you can find a reference frame where the total momentum of the system is 0:'
If you by that mean that photons 'meeting' each other will, when treated as a 'whole system', take out each others momentum as seen inside that system?
I think I will agree
(Thinking of that proficiency shown in your math, it would be downright suicidal to do otherwise, right:)
Ahh, a small Joke there...Innocent Sir, totally innocent I insist.

But yes that's true.
Rather elegant in fact:)
But doesn't that negate mass too then?

[lightarrow]

lightarrow, are you referring to momentum as mass?

No.

And do you see it as being 'invariant' mass?

Exactly. Weird, isnt'it?

You wrote 'A couple of photons not traveling in the same direction has mass, because you can find a reference frame where the total momentum of the system is 0:'
If you by that mean that photons 'meeting' each other will, when treated as a 'whole system', take out each others momentum as seen inside that system?

They can "meet" each other or recede.

I think I will agree
(Thinking of that proficiency shown in your math, it would be downright suicidal to do otherwise, right:)

I had already done the computations in another thread on this forum, some months ago... []

I think I will agree
(Thinking of that proficiency shown in your math, it would be downright suicidal to do otherwise, right:)
Ahh, a small Joke there...Innocent Sir, totally innocent I insist.

But yes that's true.
Rather elegant in fact:)
But doesn't that negate mass too then?

Mass (of every kind) is just energy confined in a fixed space, nothing more than this.

[yor_on]

Yes it's very weird.
Where does this 'transformation' take place?
And how can it do it.

Normally when you think of 'energy' or spacetime creating particles there has to be a lot of energy involved right, if we're not talking virtual partickles.
But here you just need to 'enclose' a photon, or if you like, wavepacket, oh ok, a lightquanta then, qubits? Ahhhhhh...(running away into the wilderness, while repetitively calling 'Glooria')

[lightarrow]

Yes it's very weird.
Where does this 'transformation' take place?
And how can it do it.

Do you mean the "transformation" mass <--> energy?

Normally when you think of 'energy' or spacetime creating particles there has to be a lot of energy involved right, if we're not talking virtual partickles.
But here you just need to 'enclose' a photon, or if you like, wavepacket, oh ok, a lightquanta then, qubits? Ahhhhhh...(running away into the wilderness, while repetitively calling 'Glooria')

About composed systems, for example an atom, you find that part of the energy (and so part of the mass) is present in the form of the field binding the electrons to the nucleus. About elementary particles we still don't have models (apart from string theory) describing them as made of some kind of confined fields. Just as curiosity, some times ago I saw a model of the electron as made of electromagnetic radiation interacting in a strange way with itself (the wave is "warped around" a small region of space, so that to canceal the magnetic field by destructive interference but not the electric field and so giving rise to the electric charge!) but it was just a speculation. (Now the author will write me and say "What speculation? It's a serious theory!"  []).

[yor_on]

Nope;)
He will write you and congratulate you to your show of common sense, as you now at last admit to his theory's inherent strength and beauty.
And wait until you see mine...

As an small appetizer I will confide in that it involve AVGP instead of a BB.
Yes A...V...G...P!!!
 

[Soul Surfer]

Lightarrow.  Mass (of every kind) is just energy confined in a fixed space, nothing more than this.

An interesting thought. Does the size of the fixed space matter.  Suppose our universe was a fixed space that confined the energy in the universe (like the inside of a black hole) could that mean that the total electromagnetic energy in the universe reperesented a significant effective mass?

[lightarrow]

Lightarrow.  Mass (of every kind) is just energy confined in a fixed space, nothing more than this.

An interesting thought. Does the size of the fixed space matter.  Suppose our universe was a fixed space that confined the energy in the universe (like the inside of a black hole) could that mean that the total electromagnetic energy in the universe reperesented a significant effective mass?

This is not bad too as thought  [] I suppose it should be so.

[labview1958]

My hunch is that mass bends space. A magnet has mass thus bends space. However if a North pole of a magnet is brought near another North pole, space is bend in a way as to "repel" them. Similarly if unlike poles are brought together space is bend another way as to "attract"

[lightarrow]

My hunch is that mass bends space.

Of course.

A magnet has mass thus bends space.

There are many things which have mass, not only a magnet: stones, trees, ants, you...Probably you intended to talk about "magnetic field"?

[nicephotog]

..."invariant mass?"... shell orbit level by charge...
Wave mechanics and Geometry!!!, my favourite, if i ever get out of the old kingdom and intermediate one for my Dingos which probably came from Ancient Chinese explorerers not Egyptian war dogs bred on another continent for Pharoah, i can have some mathematical fun not encryptive decyphering by block interpretations.
http://www.nicephotog-jsp.net/Dingone.pdf
http://www.awarenessquest.com/research.htm

[yor_on]

A V G P

Well, ah 'somebody' gave birth to our universe via it.
And indeed it was, and is, a very good party.
And thats the truth about AVGP:)

[labview1958]

I am implying a magnet of 1 kg.  bends space in a certain way. These bending is different from a  1 kg of non-magnet material.

[lightarrow]

I am implying a magnet of 1 kg.  bends space in a certain way. These bending is different from a  1 kg of non-magnet material.

So you are talking about the magnetic field, not the magnet.