How does mass increase at higher speeds?

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #50 on: 22/12/2012 01:23:46 »
Quote from: Phractality
I don't accept the claim that a photon has no mass.
Smart man! :)

If that is your opinion then you might enjoy reading my article on the subject. It’s at
http://arxiv.org/abs/0709.0687

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #51 on: 22/12/2012 01:27:23 »
Quote from: lightarrow
You can't localize a photon, so you can't do that.
Everything I’ve seen in this thread speaks mostly about classical physics, e.g. relativity. In relativity one uses classical photons, which is basically a point particle having a classical trajectory but zero proper mass. Such a thing can be localized.

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Offline yor_on

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Re: How does mass increase at higher speeds?
« Reply #52 on: 22/12/2012 06:17:40 »
Maybe I am unclear?

Are you telling me that gravity is observer dependent?
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Offline yor_on

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Re: How does mass increase at higher speeds?
« Reply #53 on: 22/12/2012 06:30:05 »
As for why I doubt it is that all experiments in a uniformly moving body is said to act out the same, meaning that whatever relative motion you achieve does nothing to change it. If I now assume that the relative motion indeed is non-relative, meaning that there is a definite change in the gravitational field locally measured then that should invalidate that statement. If we on the other hand treat gravity as something locally unchanging, but when involving two bodies measuring one, observer dependent? I need to think about that one, a damn lot. My original thought is that gravity is constantly dynamically updated in a universe, obeying 'c' as information between relatively moving bodies, but not that they also will measure a different gravity, depending on from where you do the measurement? That would hurt my head terribly to assume :)
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Offline yor_on

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Re: How does mass increase at higher speeds?
« Reply #54 on: 22/12/2012 07:08:30 »
Or maybe not? But I still need to think about it :) One could assume that the 'energy' of a universe is a constant one, the same no matter what observer dependencies exist, and then include gravity into that. But it still makes my head ache a little.
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Offline yor_on

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Re: How does mass increase at higher speeds?
« Reply #55 on: 22/12/2012 22:46:41 »
Actually been thinking a little and I think it must be correct. Gravity is observer dependent, meaning that when you measure the gravity of other uniformly moving objects that should change with your relative speed. But locally it won't change for you, meaning that different uniform motions, locally measured, won't change your weight, as you measuring it on a weight scale. Then there is this other type of description in where some solutions to a non-rotating black hole present you with a 'infinite space' and so a weaker gravity, as observed inside the event horizon (locally). Can that also be called a observer dependency? I guess it can :) thinking of it.

If now that was what you meant?
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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #56 on: 23/12/2012 00:09:01 »
Maybe I am unclear?

Are you telling me that gravity is observer dependent?
Depending on what youi mean by "gravity" yes.

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #57 on: 23/12/2012 15:59:12 »
Quote from: lightarrow
You can't localize a photon, so you can't do that.
Everything I’ve seen in this thread speaks mostly about classical physics, e.g. relativity. In relativity one uses classical photons, which is basically a point particle having a classical trajectory but zero proper mass. Such a thing can be localized.

Classical photons? Which movie is it?  [:D]

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #58 on: 27/12/2012 06:25:21 »
Quote from: lightarrow link
Classical photons? Which movie is it?  [:D]
I don't understand what you mean, "Which movie is it?"

lightarrow - Have you ever heard of the terms "classical photon" and "classical electron"? Perhaps some use the term “scalar photon” or “scalar electron” instead. I read an article where similar such term(s) were used, rather than forcing someone to explain that what it means. While you may be using it as some sort as slang, I have no idea what it means which means that other people don’t either. It you mean photon then please say photon and he same with electrons. We then won’t have to waste space by trying to explain terms or explain what was a joke and then razz the person who didn’t get the joke.

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #59 on: 27/12/2012 18:32:10 »
Quote from: lightarrow link
Classical photons? Which movie is it?  [:D]
I don't understand what you mean, "Which movie is it?"

lightarrow - Have you ever heard of the terms "classical photon" and "classical electron"?
"classical electron": yes
"classical photon": no. The reason is because of qm history: a classical electron was a starting point for Bohr and Sommerfeld when they described the atom. But a classical photon couldn't have any meaning, because m = 0 in this case.
But that was history. Now we know that a precise trajectory of particles is impossible, they don't have at all. Wavefunctions are wat replaced them.

Phractality wrote about defining the centre of a system of two photons: you don't even know where is a photon, and you want to find such a thing?

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #60 on: 28/12/2012 01:18:49 »
I believe a "classical photon" would be a ray.  You get ray optics from light waves using the same procedure that you can use to get particle-like electrons from a more thorough quantum wave theory.  But it sounds like Pmb's classical photons are like little bullets, not rays.  I'm not sure how to get to those from the wave theory.

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #61 on: 28/12/2012 21:13:46 »
Geometrical optics is the (classical) limit of em radiation when frequency goes to infinite. While this gives a perfect geometrical ray (no diffraction, possibility to create infinitely thin rays) it's a mistake talking of "classical photons" even in this case because you can never know where exactly the photon is along the ray.

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #62 on: 29/12/2012 00:37:48 »
I agree that a ray isn't a photon.  You can hand wave a bit and define the ray as carrying a density of photons proportional to the power transported along it (divided by frequency, perhaps?), but I don't see how you can define a single photon in this way.

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #63 on: 29/12/2012 00:58:03 »
Quote from: lightarrow link
Classical photons? Which movie is it?  [:D]
I don't understand what you mean, "Which movie is it?"

lightarrow - Have you ever heard of the terms "classical photon" and "classical electron"?
"classical electron": yes
"classical photon": no. The reason is because of qm history: a classical electron was a starting point for Bohr and Sommerfeld when they described the atom. But a classical photon couldn't have any meaning, because m = 0 in this case.
A classical photon is defined as a point particle whose energy i related to its momentum by E = pc, whose speed is c, and whose momentum is p = Mv = mc where M = E/c^2. M is defined as the photon's inertial mass.

Worrying about m = 0 is confusing inertial mass (a pre-relativistic notion) with proper mass (a relativistic notion)

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #64 on: 29/12/2012 01:00:36 »
I believe a "classical photon" would be a ray.  You get ray optics from light waves using
 the same procedure that you can use to get particle-like electrons from a more thorough
quantum wave theory.  But it sounds like Pmb's classical photons are like little bullets, not rays.
 I'm not sure how to get to those from the wave theory.
A ray would be approximated as a stream of classical photons. Picture a laser beam as an approximation
of a ray.

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #65 on: 29/12/2012 14:47:50 »
But a beam isn't a point particle.  I understand that you can express a beam roughly as a density of classical point particle photons moving along raytrajectories at the speed of light, but the case of two classical photons seems a rather unphysical approximation to me.  Can you point out a case that is well approximated by two classical photons?

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #66 on: 29/12/2012 18:29:47 »
A ray would be approximated as a stream of classical photons. Picture a laser beam as an approximation of a ray.
It's the same mistake that one makes stating that an electron's track in a bubble chamber means that elementary particles have a precise trajectory. QM teaches us they actually don't have.

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #67 on: 30/12/2012 01:11:14 »
But a beam isn't a point particle.
Since nobody suggested or inferred otherwise this comment confuses me. Can you elaborate please?

I understand that you can express a beam roughly as a density of classical point particle photons moving along raytrajectories at the speed of light, but the case of two classical photons ...
Where did you get the idea of using only two photons from?

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #68 on: 30/12/2012 01:20:25 »
A ray would be approximated as a stream of classical photons. Picture a laser beam as an approximation of a ray.
It's the same mistake that one makes stating that an electron's track in a bubble chamber means that elementary particles have a precise trajectory. QM teaches us they actually don't have.
Hence the term "approximation". In classical mechanics we're most often concerned with physics only down to, perhaps, the micron level. At that level and over small distances such as a mile we don't much need to worry about the non-exact nature of the trajectory of the photons.
I've been thinkig of this stream of photons as a laser beam and when I studied ray optics as an undergrad I always had a laser beam in mind.
I never worried about the cross sectional area of the laser beam either.

This is getting off course of the reason I mentioned classical photons.

As I said, in relativity one uses classical photons, which is basically a point particle having a classical trajectory but zero proper mass. Such a thing can be localized.

I had in mind this notion when I was reading Exploring Black Holes and working with GR and SR and when they used photons. Never in that work does anybody ever worry about te photon being localized or it not having a classical trajectory.

Remember this is an analogy which, by definition, means that its alike in some ways and not alike in other ways.
Let is not forget why it was brought up rather than dwell on what each of us knows all to well about how real photons behave,shall we? Otherwise it gets over pedantic and that's when I go back to watch my brand new 60" plasma TV :)

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #69 on: 30/12/2012 01:32:10 »
Heh :)

I can see you and Pete gearing up to a argument Lightarrow :)
Ain't gonna happen. I had several months of too much quite to come out and worry about such trivia.

There are many terms in physics for which you must know the context and perhaps the authors views in order to determine the precise definition of a term. E.g when some people use the term "weight" they refer to the quantity mg. Others refer to weight only when the object of mass m is being supported at rest in the field while only defining weight as mg could mean that a body in free-fall has weight.

Then there is the definition of momentum. In Newtonian physics it means p = mv. In analytical mechanics and quantum mechanics it means canonical momentum. And you have to know that when reading QM material - the authors won't just tell you.

So nope. Nore more debating things anymore for me. I have no desire to let people know the complete picture of things. If they think they're gonna get a complete picture on the internet then they deserve whatever it is they get.

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #70 on: 30/12/2012 01:42:53 »
[quote author=PhractalityI'm wondering, now, if I should consider the center of the two-photons to be the center of energy; equivalent to center of mass. Applying inverse square law to the energy of each photon to get a ratio of each photon's distance from the center. My brain hurts; maybe I'll just play solitaire, instead.  :-\
[/quote]
If you're speaking of the geometric center of the two photons then no. The center of enegy is not the same as the geometric center of the two photons.

Note - See http://home.comcast.net/~peter.m.brown/sr/center_of_mass.htm

I see that this is where all this photon stuff started. This was a discussion of a classical photon and not a quantum mechanical one. Don't sweat the small stuff. Look how far off track it took this thread even though everyone knew what was meant by a classical and quantum photons.

In relativity we speak of point particles such as electrons, protons etc. even when we're speaking about classical relativity (since there is no quantum theory of relativity yet). When talking classical relativity and one is speaking of photons then what is being discussed is trivially simple: A classical particle having a well-defined trajectory, having its energy related to its mometum by E = pc and whose mass is given by p = mv = mc or E = mc^2.

This is how we speak of all particles in relativity. If you see a relativity text or article speaking of electrons, protons etc then they are treating them as classical particles. There is no difference with photons.

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #71 on: 30/12/2012 12:52:35 »
It's the same mistake that one makes stating that an electron's track in a bubble chamber means that elementary particles have a precise trajectory. QM teaches us they actually don't have.
Hence the term "approximation". In classical mechanics we're most often concerned with physics only down to, perhaps, the micron level.
No. When interactions among elementary particles are involved, you have to use the full wavefunctions treatize of QM, so: diffraction, interference, non existence of an exact trajectory. Ask particle physicists. Classical limits are used in macroscopic system *of non zero mass*, so singular photons are excluded by definitions. About lasers, you are using the geometrical optics approximation, so you are not talking of singular photons by definition.

--
lightarrow

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #72 on: 30/12/2012 15:50:20 »
Quote from: lightarrow
No. When interactions among elementary particles are involved, ...
Then you have to use QM. You did understand, didn't you, that I was speaking about classical relativity? I wasn't speaking of quantum relativity since it doesn't exist yet. If you have a problem which requires QM then you have to use QM. The context of my post tells you that I was referring to classical mechanics problems, not QM problems.

In relativity one speaks of light cones. In a 2-D spacetime diagram a photon moves on a straight worldline, i.e. a straigh in spacetime. We don't speak about quantum trajectories in classical relativity. When QM is required then we've gone outside the realm of classical relativity. In classical relativity one assumes that whatever we are speaking above can be approximated to move on worldlines, and that includes elementary particles too.

Clearly, when one is speaking of a particle moving on a null geodesics one is thinking about classical luxons. And that's what I've been explaining here.
« Last Edit: 30/12/2012 15:58:27 by Pmb »

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #73 on: 31/12/2012 10:30:58 »
Quote from: lightarrow
No. When interactions among elementary particles are involved, ...
Then you have to use QM. You did understand, didn't you, that I was speaking about classical relativity?
So you can't speak of photons...
Quote
I wasn't speaking of quantum relativity since it doesn't exist yet.
You are joking! It was created in the 30' of the previous century, one of the first was Dirac, have you haver heard of "Dirac equation"? Have you ever heard of QED quantum electrodynamics?
Maybe you intended "quantum gravity", that is, a theory who would unify quantum mechanics and *general* relativity. But we are talking of laser beams, so we don't need gravity here.
Quote
Clearly, when one is speaking of a particle moving on a null geodesics one is thinking about classical luxons. And that's what I've been explaining here.
Don't know what they are, but certainly they are not photons.
« Last Edit: 31/12/2012 10:34:43 by lightarrow »

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #74 on: 31/12/2012 13:27:53 »
Quote from: lightarrow
So you can't speak of photons...
While I disagree with you last post I've decided to end my contribution of quantum/photon thing since I've basically lost interest (of course I'm always available inPM for anything).

Plus I don't like endless debates on subjects, especially when most of it contains rephrasing of statements already made.

I'll end this with one reference: Inertia of energy and the liberated photon by Adel F. Antipa, Am. J. Phys., Vol (44) No.(9) Sep. 1976
Quote
Abstract
We follow through the different variants of Einstein's intuitive photon-in-a-box derivation of the inertia of the inertia of energy, then  end with a very simple "radiating atom" derivation
See section 7. The Radiating Atom

This article is basically a modern derivation of Einstein's famous "Photon in a Box" experiment. See my web site at
http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

In the first section I outline Einstein's derivation. In the later section I outline Atipa's derivation.

Einstein uses a pulse of radiation to prove the mass-energy relation while Antipa uses an atom and a photon.
In both cases the center-of-mass is calculated and used.

The more general definition of center of mass of radiation is given in my web page at
http://home.comcast.net/~peter.m.brown/sr/conservation_laws.htm

The center of mass is in Eq. (15).

« Last Edit: 01/01/2013 01:47:51 by Pmb »

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Re: How does mass increase at higher speeds?
« Reply #75 on: 01/01/2013 17:35:36 »
I had another thought. In the physics literature one runs into terms like "classical electron" etc. In fact Fritz Rohrlich's book is called Classical Charged Particles. I know that saying "Classical Photon" caused some confusion here. But I'd like to end my contribution of this side bar by saying that in classical relativity one works with three classes of particles. They are defined as follows

(1)   If the speed of the particle is always v < c then the particle is classified as a Tardyon.
(2)   If the speed of the particle is always v > c then the particle is classified as a Tachyon.
(3)   If the speed of the particle is always v = c then the particle is classified as a Luxon.

There shouldn't be any problems now since these are well defined terms and used in the classical relativity literature.

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #76 on: 01/01/2013 22:22:58 »
Would you folks be interested if I started and/or split off a thread with a title along the lines of "Is there such a thing as a "classical" photon?" or are you OK with this thread being used for discussion?

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #77 on: 01/01/2013 22:41:33 »
Would you folks be interested if I started and/or split off a thread with a title along the lines of "Is there such a thing as a "classical" photon?" or are you OK with this thread being used for discussion?
Makes no difference to me, JP. I think we’ve all said what we wanted to say and learned what we wanted to learn at this point. But if you want to start a new thread on it then please feel free to do so.

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #78 on: 02/01/2013 17:19:25 »
I think Pmb has explained what he intended with that term in its previous post, so I can stop here too.

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #79 on: 02/01/2013 22:23:43 »
Fair enough.  :)

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Offline Bill S

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Re: How does mass increase at higher speeds?
« Reply #80 on: 03/01/2013 17:09:43 »
JP, as a "hitch-hiker" where science is concerned, I got a bit bogged down in this thread.  In general, I find your explanations reasonably easy to follow, as long as you don't wax too technical, so if you are going to say a bit more about the idea of "classical photons" I'll follow with interest.
There never was nothing.

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #81 on: 04/01/2013 11:12:31 »
JP, as a "hitch-hiker" where science is concerned, I got a bit bogged down in this thread.  In general, I find your explanations reasonably easy to follow, as long as you don't wax too technical, so if you are going to say a bit more about the idea of "classical photons" I'll follow with interest.
Regarding the term I coined, i.e. “classical photon.” There is nothing special or new about this concept. In the physics literature you’ll find two kinds of “particles” spoken of. One type of particle has its position and momentum simultaneously determined and moves on a classical trajectory. Such particles are called “classical particles.” The other kind of particle has its position and momentum constrained by the Heisenberg uncertainty relation. Such particles are called "quantum particles."

A classical particle whose energy E and momentum p is related by E = pc and whose nature is electromagnetic in origin (i.e. can scatter off a classical charged particle such as a classical electron) is what I had in mind when I referred to a “classical photon”.

Pete

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #82 on: 04/01/2013 19:31:36 »
Thanks, Bill.  It's good to know my explanations (sometimes) make sense.  :)

I think this debate has been over two things: whether you can accurately model light with classical particles traveling at the speed of light and whether, if you can, you should call them "classical photons."

To answer the first question, you can in some cases.  Whether you use Maxwell's equations (which are accurate, but don't include quantum effects) or quantum optics (in which light is treated more rigorously as individual quantum mechanical photons), you're dealing with waves.  Either the light itself is a continuous wave (Maxwell) or the photons are waves (quantum optics).  In certain cases, you can approximate waves over space and time by classical trajectories through space and time.  This is an approximation whose validity depends on how rapidly the waves are oscillating over space and time (faster oscillation makes this approximation more accurate).

In the case of Maxwell's equations, these trajectories are rays which carry energy at some rate.  You could divide this energy up into packets, each moving at the speed of light, and you'd have something like a "classical photon."  Alternatively, if you use the Feynman path integral formulation of quantum mechanics, you can compute the effect of the emission and absorption of a photon by accounting for all possible paths the photon can take between emission and absorption.  The analogous trick to finding rays should be to find the most probable path for the photon to take.  I believe you could call this the "classical photon" trajectory.  Its important to remember that these are approximations to more rigorous models, but they should be accurate enough in many cases.

As for whether "classical photon" is a good term for these approximations--It probably isn't, as is evident from the confusion here.  However, it is clear that what Pmb means is a model for light as particles moving along a definite trajectory at the speed of light, and as I noted above, that model is an approximation, but can be accurate in some cases.

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #83 on: 04/01/2013 21:01:30 »
JP - When the wave nature of light is important I can't see how photons can be used. In fact that's what led to the wave-particle duality. When the wave aspect is important I'd say forget all about particles moving on worldlines. At that point you're stuck with waves in spacetime. When you use Maxwell's Theory instread of quantum field theory is another conversation in itself.

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #84 on: 05/01/2013 15:51:21 »
Yes, Pmb, you need to go a bit beyond the idea of a classical "little bullet" of energy to describe light when wave effects are important.  There are many ways to do so, but none of these "modified bullets" has all the properties of a classical particle unless wave effects are negligible. 

I'll spare you the details, but the Wigner distribution function is one way of thinking of a wave as particles moving along classical trajectories.  If you read through that, you'll find that the particles in non-classical states (those where wave effects are important)  have some odd properties such as appearing to carry negative energy or probability, which ends up being required for particles to model waves: http://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution
« Last Edit: 05/01/2013 15:55:07 by JP »

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #85 on: 12/01/2013 11:52:39 »
Quote from: fertilizerspike
It does not happen.
In this forum we've beat that horse dead many times over. In the end whether "mass" = m, depends on speed ultimately depends on how one defines the term. And there are two well-known, but different definitions used in relativity today. One were m is a scalar. It's then given the full name with the qualifier "proper" to end up with "proper mass". When one starts with the laws of physics where in the 3+1 viewpoint F = dp/dt and m is defined as the m in p = mv where p = 3-momentum (linear mechanical) and t = coordinate time. It's then given the full name with the qualifier "inertial" to end up with "inertial mass"

So mass can and does mean either (1) inertial mass or (2) proper mass. While you seem to have used it as a conceptual crutch I know that I haven't. That's not why I prefer it when appropriate.

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #86 on: 12/01/2013 12:10:40 »
JP - When the wave nature of light is important I can't see how photons can be used. In fact that's what led to the wave-particle duality.
I hope not to offend you, but this sentence means you haven't understood a lot of QM, or about photons, at least.
1. A photon, as well as any other elementary particle, it's not a corpuscle; when in QM we talk of a "particle" we intend an entity which is described with a wave equation and which is detected as a corpuscle, so it has *both* a corpuscolar and a wave behaviour *by definition* (I'm referring to the QM postulates).
2. You want to see light waves and light corpuscles in a single experiment? Send individual photons trough a doble slit and detect them in a screen. You will see individual flashes on the screen (light corpuscles) distributed according to a diffraction pattern (light waves).
3. In particle/particle collision experiments in a collider, you have individual particles colliding and the result of that (particles, energies, ecc.) is something  that you can compute *only* using the wave nature of them (= wavefunctions = quantum mechanics).

Conclusion: if you use the word "photon" you are talking of quantum mechanical description by definition.

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #87 on: 14/01/2013 02:55:46 »
Quote from: lightarrow
Conclusion: if you use the word "photon" you are talking of quantum mechanical description by definition.
I disagree.

First off JP knows his QM quite well so one would be quite off the mark and misleading themselves to think that he doesn’t understand QM a great deal.

The term photon is often used in areas of physics where it’s treated like a classical particle. The same holds for any other particle that we know since what you can say about a photon regarding its properties as a particle you can say about any elementary particles in nature. That’s why we quit often use the term photon in relativity,

What you spoke about above also holds true for electrons and when you use the term “electron” it doesn’t mean that you’re talking about a quantum mechanical description. We use the term “electron” in classical electrodynamics which by definition is a classical, not a quantum, branch of physics. .

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #88 on: 14/01/2013 13:17:11 »
What you spoke about above also holds true for electrons and when you use the term “electron” it doesn’t mean that you’re talking about a quantum mechanical description. We use the term “electron” in classical electrodynamics which by definition is a classical, not a quantum, branch of physics.
But in those cases you neglet the wave aspect of the particle. Instead you intended to discuss exactly the case of the wave aspect of particles, infact you wrote:
"When the wave nature of light is important I can't see how photons can be used".

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #89 on: 14/01/2013 18:01:30 »
Quote from: lightarrow
But in those cases you neglet the wave aspect of the particle.
Of course. That’s entirely the point. Maybe that’s what has you confused. You must have thought that somewhere someone was making the claim that under all conceivable scenarios the photon can always be treated as a classical particle.  Not true. If you thought that someone made such an assertion then you were mistaken.

When one is considering only those experiments in which the limits of the experiments/observations are such that one can describe the motion of a photon using a classical trajectory and thus a worldline in spacetime (null worldline to be exact).

Not all experiments and observations pertain to the wave aspects of photons. Those experiments and/or observations which treat the photon as a particle and for which the limits of accuracy of the experiment are such that one can ignore the limitations imposed by the uncertainty principle can one treat the photon as a classical particle.

When one is, say, analyzing photons in Young's double slit experiment then one is going outside the scope of classical relativity since a classical trajectory cannot be used to describe the motion of the photon.

However in other circumstances, say, when one is tracing a photon as a particle bouncing off mirrors which are moving in a vacuum or are being emitted and detected by photon emitters and detectors then one can use classical relativity and classical trajectories. If you want a good example of a photon being treated as a classical particle in special relativity then crack open “Gravitation” by Misner, Thorne and Wheeler. I know of a particular example of a photon being treated as a classical particle in that text. If you have the text and want to read it then I’ll try to find if for you.

Another treatment of a photon as a classical particle (in fact in a derivation where a photon is used in a center of mass calculation) see the article Inertia of energy and the liberated photon, Adel F. Antippa, Am. J. Phys. 44(9), September 1976. I have this article and if you’d like to read it I can make it available on my website for you to download and read.

The new version “Exploring Black Holes – Second Ed.” has examples where photons are treated as classical particles. This version of the book should be out later this year.

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #90 on: 14/01/2013 19:34:05 »
Quote from: lightarrow
But in those cases you neglet the wave aspect of the particle.
Of course. That’s entirely the point. Maybe that’s what has you confused. You must have thought that somewhere someone was making the claim that under all conceivable scenarios the photon can always be treated as a classical particle. 
I have never thought it. The point is that the photon can never be treated as a classicle particle  [:)]

When at a certan point you talked of "luxons" I believed to have understood that you intended this, with "classical photon", and I accepted to end the discussion. But I see you insist   [:)]
Quote
Not all experiments and observations pertain to the wave aspects of photons.
If you want to talk about photons in that sense, you can do it only if you talk of the interaction energy and not when you talk of "something in fly between source and detector" which was what I was discussing with (I don't remember who) because he was talking of "the centre of a two photons system".
You can talk of the centre of two heavy atoms, if they are not cooled down to low temperatures, because they are still almost classical particles, maybe in some cases you could even talk of classical electrons, but absolutely not about photons; if there is an example you can't talk of classical particles is just that...
Quote
When one is, say, analyzing photons in Young's double slit experiment then one is going outside the scope of classical relativity since a classical trajectory cannot be used to describe the motion of the photon.

However in other circumstances, say, when one is tracing a photon as a particle bouncing off mirrors which are moving in a vacuum or are being emitted and detected by photon emitters and detectors then one can use classical relativity and classical trajectories.
Yes. But then you talk of *light rays and geometrical optics or classical electromagnetism*, *not* photons, until they are detected.

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #91 on: 14/01/2013 19:58:05 »
Quote from: ]
[
I have never thought it. The point is that the photon can never be treated as a classicle particle  [:)]
Your point is wrong. And its often treated as such.

Please post a proof demonstrating that a photon can never be treated as a classical particle.

While I'm waiting for that I'll show you examples of how physicists actually do treat photons as classical particles.

Examples are under my website at
See - http://home.comcast.net/~peter.m.brown/sr/light_clock.htm
and - http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm
and - http://home.comcast.net/~peter.m.brown/sr/lorentz_contraction.htm (substitute "photon" where you see "light"
and - http://home.comcast.net/~peter.m.brown/sr/lorentz_contraction_2.htm
and - http://home.comcast.net/~peter.m.brown/sr/spacetime.htm
and - http://home.comcast.net/~peter.m.brown/sr/relativistic_optics.htm (substitute "photon" where you see "beam")

Here's an example of how one treats an electron as a classical particle
http://home.comcast.net/~peter.m.brown/sr/cyclotron.htm

In real life, strictly speaking that is, electrons are quantum particles just like in real life, strictly speaking that is, photons are quantum particles.

Those are examples of how this is actually done by physicists (including myself), contrary to your claim that it can't be done.

You have yet to post a valid reason why one can't treat photons as classical particles in certain cases. You've made assertions to that effect but statements of facts are not considered to be a proof of that fact.

When I write the expression for a null worldline, i.e. x(t) = cos(theta) ct, y(t) = sin(theta) ct. These are the parametric equations of a photon moving in the xy-plane at an angle of theta from the x-axis. That's a null worldline and this is a classical statement.
Anytime a relativist is speaking of the null geodesic that a photon is moving on then he's speaking of a classical photon.

And that, my dear lightarrow, is how its done. :)
« Last Edit: 14/01/2013 20:28:04 by Pmb »

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #92 on: 15/01/2013 07:11:42 »
Quote from: Phractality
I'm wondering, now, if I should consider the center of the two-photons to be the center of energy; equivalent to center of mass. 
Yes. In fact please see http://en.wikipedia.org/wiki/Two-photon_physics

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #93 on: 16/01/2013 17:15:53 »
Quote from: ]
[
I have never thought it. The point is that the photon can never be treated as a classicle particle  [:)]
Your point is wrong. And its often treated as such.
Please post a proof demonstrating that a photon can never be treated as a classical particle.
It's very simple, and I let you do it: define "photon".

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Re: How does mass increase at higher speeds?
« Reply #94 on: 16/01/2013 19:09:39 »
Lightarrow – In what follows, please do not confuse “frustration” with “irritation.” While I am frustrated by what appears to be being ignored in the examples I’ve posted or that you’ve only posted assertions without proofs, I’m not irritated in the sense that I’m angry at you. I mention this because it seems that some people in physics forums read certain emotions or intentions into posts that aren’t really there. They seem to be based on what the reader assumes about the person who’s doing the posting. Okay?


Quote from: lightarrow
It's very simple, and I let you do it: define "photon".
I gotta tell ya, lightarrow, I'm quite baffled as to why you’ve been ignoring the examples I've posted for you. I'm not posting them for my health ya know. :)  They are meant as counter arguments to the assertions that you've been sticking to. If you ignore them then I see no reason to discuss the physics anymore.

You also seem to be ignoring the fact when I explained that when photons are used in classical derivations its always an approximation to real life, i.e. quantum effects or precision is either ignored or not important.. Such approximation are not unique to photons or the examples I've posted but apply to ever classical treatment in physics that there exists since all real life particles have real life uncertainties in their locations. Why you've singled out photons among other particles such as electrons and protons and why you've been ignoring the usage of classical trajectories such as those in particle physics like tacks in bubble chambers of elementary particles is something I don’t understand.

Anyway … asking for the definition of the term "photon' is not a proof that they can’t be used in the manner which you say they can’t. When photons were first discovered by Einstein and Planck there was no uncertainty principle in existence and there was no need for such even though the particle nature of photons has been used long before the term "photon" was invented. Einstein and Planck came up with the concept of "bundle of energy" long after the first thoughts of "particles of light" were first being thought of and before they knew of the exact nature of them.

In any case the definition of Photon is - a discrete bundle (aka "quantum") of electromagnetic radiation where its kinetic energy E is related to its momentum p by E = pc. Einstein called these discrete bundles "light quanta". When the term “photon” was actually first defined by Gilbert Lewis they didn't have the same properties that we now assign to them.

Here the term "bundle" does not mean that they have a finite extension in space that one might visualize when one hears the term "bundle." The term “bundle” means "finite amount," nothing more and nothing less.

Also I’ve used the term “classical photon” or referred to the use of photons in a classical setting as approximations to the more exact expressions given in quantum mechanics. In your responses its like you’re not reading the parts of my posts which clarifies this point. When the wave aspect of the photon is under consideration or more precise measurements are being considered then the classical approximation of the photon is no longer being used.

I've already given you many examples of how and where photons are used in derivations using the conservation of center-of-mass. In particular, they are used in the article

Inertia of energy and the liberated photon by Adel F. Antippa, Am. J. Phys. 44(9), September 1976

A similar derivation is given in Special Relativity by A.P. French on pages 17 and 27.

In each version of the derivation the correct results are obtained.

I'd like to remind you that it was you who first claimed that the center of energy of a system of photons couldn’t be defined because you claimed that photons couldn’t be localized. In that response you had your mind fixed on quantum mechanics and were ignoring the sense in which that person was using the concept of photons. To be 100% accurate, nothing in the universe can be localized to a mathematical point. What you failed to mention was the fact that any particle can be localized to a finite region of space. If that weren’t true then nobody would have ever referred to anything in physics, quantum or classical, as a “particle.”  In fact even in quantum mechanics photons can be localized to an arbitrarily small region of space. One just has to give up some uncertainty in the knowledge of the photons momentum. If we were to take your response literally then you would have said that the center of mass of electrons, protons, neutrons etc. couldn’t be defined because no elementary particle can be localized in space. I’m rather baffled at where you got the notion that photons can’t be localized. No treatment of quantum mechanics would ever make such an assertion. Perhaps you made the mistake of thinking that “localized” meant “located at a mathematical point.” If so then no elementary particle can be localized. But that’s not what is meant by “localized” in quantum mechanics.

I think this point needs to be clarified more (Let’s use the double slit experiment and for purposes of illustration we’ll only look at the x-component). When one is considering experiments like Young’s double slit experiment then what is observed under low enough intensity of the light source are photons hitting the screen at finite locations. That means that if the screen were made of a huge amount of very small pixels (let’s say 0.001 mm) then only one pixel at a time is illuminated at one time. The location of that pixel is then recorded. After a large number of photons hit the array of pixel what you’ll have a bunch of numbers that denote locations where the photons were localized to a region 0.001 mm long. If you were to plot the number of photons at a particular x-location verses the x-coordinate what you’ll have is a graph which has the general shape of a bell curve. Let the width of that curve be dx. This is the dx that the uncertainty principle uses, not the size of a pixel. That is precisely what it means to localize a photon and precisely why photons are said to behave like particles in this experiment.

In case you ignore my previous posts and explanations (since you failed to explain why you’re claiming that all these physicists who use these explanations got them all wrong) I’ll have to repeat myself. I showed you how physicists are and have used photons in a classical context. You didn’t acknowledge the derivations that I’ve shown you. They are at  - http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

Go down to below Eq. (8) and you'll see how they are used in the classical sense, i.e. by using them in the center of mass theorem. This is how Antippa and French used them.

Other uses are when physicists draw spacetime diagrams and show the worldliness of photons. Such worldliness are classical approximations to what photons actually do on a small scale. When such diagrams are drawn the worldliness used as example are often of the order of a meters. The uncertainty of the photon’s location along such paths is negligible when drawing such diagrams. Thus the width of the worldline is approximated to be zero rather than the real life finite width one would get in experimental data. When one draws a classical trajectory like this for a particle then, in all cases, one is using an approximation. Just like when the path of an electron is drawn as a circle in a cyclotron. That path is also an approximation to real life.

From now on I’ll have to wait until you give a proof and a valid reason why the above approximations cannot be used. Until then I won’t respond to any other post of yours in this thread since all you’ve been doing is making a claim that they can’t be used with no acknowledgement that (1) I’ve been referring to approximations and (2) that they are indeed used by physicist and appropriated so and without error in their derivations.

One last comment before I end this post: To drive this point home let me remind you that what I’ve been, i.e. what I’ve labeled a “classical photon” which you seem to keep mistaking for a “quantum photon” which has a wavelength L related to its momentum p by p = h/L and whose position and momentum satisfy the uncertainty relationship.  Now recall what a “classical electron” is. It’s a particle with charge e = 1.60x10^(-19) C, a proper mass of 9.11x10^(-31)kg which moves on a well-defined trajectory. This is different than a “quantum electron” which has a wavelength L related to its momentum p by p = h/L and whose position and momentum satisfy the uncertainty relationship.

With this in mind recall the definition of "classical photon" a quantum of radiation whose kinetic energy is related to its momentum by E = pc which moves on a well-defined trajectory. From this definition it follows that the proper mass of a photon is zero.

Do you understand what I meant by "classical photon" now?
« Last Edit: 16/01/2013 23:58:03 by Pmb »

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Re: How does mass increase at higher speeds?
« Reply #95 on: 17/01/2013 00:06:40 »
... "Is there such a thing as a "classical" photon?" …
The answer is “No.” Does that mean that the concept is not useful or that it’s not being used in the physics/relativity literature? The answer to that is “No” as well. Then again there is no such thing as a “classical electron” since no particle exists that has the same properties of a “quantum electron” and also does not move on  a well-defined trajectory. Also no “classical electron” satisfies the uncertainty principle. That also doesn’t mean that the concept is not useful or that it’s not being used in the physics/relativity literature.

A classical photon is an approximation to a real photon just as a classical electron is an approximation to a real electron.

Compare this with the Earth’s gravitational field. Does a particle of mass m moving in the Earth’s (Earth mass = M) gravitational field a distance r from its center have a force on it given by F = GMm/r^2. The answer is no. This is true because the Earth is not a perfect sphere and F = GMm/r^2 only holds for a particle moving in the gravitational field of a perfectly spherical body. To say that this is not a useful approximation would be quite wrong.
« Last Edit: 17/01/2013 00:09:18 by Pmb »

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Offline lightarrow

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Re: How does mass increase at higher speeds?
« Reply #96 on: 18/01/2013 11:31:42 »
... "Is there such a thing as a "classical" photon?" …
The answer is “No.” Does that mean that the concept is not useful or that it’s not being used in the physics/relativity literature? The answer to that is “No” as well. Then again there is no such thing as a “classical electron” since no particle exists that has the same properties of a “quantum electron” and also does not move on  a well-defined trajectory. Also no “classical electron” satisfies the uncertainty principle. That also doesn’t mean that the concept is not useful or that it’s not being used in the physics/relativity literature.
But there is a difference because you can treat electrons as classical particles in some cases, for example in Maxwell's electromagnetic description you can consider electrons as point charges. Furthermore, considering the electron as a classical particle, you can describe the most important features of the hydrogen atom; in which case you can do something similar with the photon?

http://en.wikipedia.org/wiki/Photon
<<A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation,>>

just the term "quantum" removes every "classical" description *by definition*. A photon is the quantum of the electromagnetic field, that is a quantum object that comes from the QED "quantum electrodynamics", it doesn't have a classical origin as the electron, it borns quantum....

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Offline Pmb

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Re: How does mass increase at higher speeds?
« Reply #97 on: 18/01/2013 14:37:13 »
Quote from: lightarrow
But there is a difference because you can treat electrons as classical particles in some cases, ...
Just as you can treat a photon as a classical particle in some cases.

Quote from: lightarrow
Furthermore, considering the electron as a classical particle, you can describe the most important features of the hydrogen atom; in which case you can do something similar with the photon?
Already done in the examples which you continue to ignore.

Quote from: lightarrow


http://en.wikipedia.org/wiki/Photon
<<A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation,>>

just the term "quantum" removes every "classical" description *by definition*. A photon is the quantum of the electromagnetic field, that is a quantum object that comes from the QED "quantum electrodynamics", it doesn't have a classical origin as the electron, it borns quantum....
You’re mistaken. All the term “quantum” means is discreteness. Period. That’s all. That photons first arose in the photoelectric effect in no can be interpreted that they can only be used in a quantum context. Electrons arose in a classical context but it was later shown that they can’t be used in all classical situations. And it’s quite clear that an electron can be referred to as a quantum of charge.

So I see that you once more have nothing to add other than making unfounded assertions and you keep ignoring the counter examples given to you which prove you wrong. You certainly can’t back up your position merely by repeating yourself and making statements that you can’t back up.
« Last Edit: 18/01/2013 14:39:33 by Pmb »

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Offline JP

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Re: How does mass increase at higher speeds?
« Reply #98 on: 18/01/2013 16:57:37 »
If you look at the Standard Model of particle physics, photons are a quantum of the electromagnetic field, and electrons are a quantum of the electron field: this symmetry between matter and fields is a major part of the Standard Model.  We know that we can take a classical limit of the quantum description for electrons and arrive at classical electrons.  I've never seen it done explicitly, but I suspect you could do the same for photons and arrive at a classical limit for photons--i.e. the classical photons Pmb brings up.  Maybe there's a reason why you can't, but based on my (admittedly limited) understanding of the Standard Model, I don't see why this would be.

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Re: How does mass increase at higher speeds?
« Reply #99 on: 18/01/2013 22:09:30 »
If you look at the Standard Model of particle physics, photons are a quantum of the electromagnetic field, and electrons are a quantum of the electron field: this symmetry between matter and fields is a major part of the Standard Model.  We know that we can take a classical limit of the quantum description for electrons and arrive at classical electrons.  I've never seen it done explicitly, but I suspect you could do the same for photons and arrive at a classical limit for photons--i.e. the classical photons Pmb brings up.  Maybe there's a reason why you can't, but based on my (admittedly limited) understanding of the Standard Model, I don't see why this would be.
The reason I know why we can is because I see it done all the time with success. Especially when it comes to calculating the deflection of light past the sun and deriving E = mc^2 using the conservation of the center of mass of a atom-photon system. In the case of the former one generates a null worldline a particle of zero proper mass that is passing by the sun and calculates its trajectory and the correct value of deflection is obtained. In the later case one assigns a position vector to both the atom and the photon and the results yield E = mc^2. I’ve never done the former on my web site (perhaps I did it on paper) but the later  I did in two ways on my website which is at http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

Scroll to just past Eq. (8) and follow the derivation. You’ll notice that the properties of the photon are used and the result is valid