How does mass increase at higher speeds?

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lightarrow

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Re: How does mass increase at higher speeds?
« Reply #100 on: 19/01/2013 02:03:54 »
Why do you need a photon for this? A light pulse wouldn't work?

Pmb

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Re: How does mass increase at higher speeds?
« Reply #101 on: 19/01/2013 03:28:53 »
Why do you need a photon for this? A light pulse wouldn't work?
Who said a photon was needed? Einstein used a "burst of radiation". In any case it's sufficient, to use a photon, not neccesary. If you read the derivation I pointed to by Antippa below Eq. ( they you'd see that it uses an atom emitting a photon. You can't have an atom emitting light, pe se
« Last Edit: 19/01/2013 09:10:42 by Pmb »

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #102 on: 19/01/2013 14:13:05 »
Ok, anyway, if you want to use the term "photon" because it's emitted or absorbed by an atom, you can't say it can be localized in flight. Either is a photon, with its quantum properties, or is a classical pulse of light; you can't mix the two in a sort of "chimeric" beast.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #103 on: 20/01/2013 14:05:14 »
Ok, anyway, if you want to use the term "photon" because it's emitted or absorbed by an atom, you can't say it can be localized in flight. Either is a photon, with its quantum properties, or is a classical pulse of light; you can't mix the two in a sort of "chimeric" beast.
I'm afraid that you’ve made the same mistake here that you’ve made in your previous posts.  You say it can’t be done but give no proof. In this case you claim “you can't say it can be localized in flight” but don’t explain what that means or why you can’t say it and what it means not to be able to say something when in practice (i.e. in practical examples, math and all) it works just fine.

I feel like I’ll just be repeating myself here so I’m ending my contribution in this thread and am as such agreeing to disagree. That means I won’t respond to any further assertions you make even if I  know them to be wrong.

I rest easy in the knowledge that has been done successfully on numerous occasions by many physicists in many textbooks and at least some journal articles. Most notably its now being used in the new version of Exploring Black Holes. I’d like to note that one of the authors of that text, Edwin Taylor, is also co-author of the MIT Introductory Physics Series Quantum Mechanics text.
« Last Edit: 20/01/2013 14:46:04 by Pmb »

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #104 on: 21/01/2013 12:43:57 »
Ok, anyway, if you want to use the term "photon" because it's emitted or absorbed by an atom, you can't say it can be localized in flight. Either is a photon, with its quantum properties, or is a classical pulse of light; you can't mix the two in a sort of "chimeric" beast.
I'm afraid that you’ve made the same mistake here that you’ve made in your previous posts.  You say it can’t be done but give no proof. In this case you claim “you can't say it can be localized in flight” but don’t explain what that means or why you can’t say it and what it means not to be able to say something when in practice (i.e. in practical examples, math and all) it works just fine.
When I answered to the question of what is the "centre" of a system of two photons (question intended in the sense that the photons were emitted but not yet absorbed) I said that it's not possible because you can't say where a photon is exactly in flight, that is after emission and before detection.
The proof is very simple, it only needs the Young experiment with two slits and photons emitted one at a time: if you can say which slit the photon passed through, the interference pattern disappears...

JP

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Re: How does mass increase at higher speeds?
« Reply #105 on: 21/01/2013 16:43:56 »
Lightarrow, is there any reason why you can't take a classical limit of the quantum theory to come up with classical photons like Pmb claims?  That approach is certainly valid for electrons (and explains why we have "classical" electrons" when we know they also behave like waves in the 2 slit experiment).

AndroidNeox

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Re: How does mass increase at higher speeds?
« Reply #106 on: 21/01/2013 17:44:02 »
All matter and energy has mass. Even the kinetic energy of an object has mass. In fact, when you compress a spring, its mass increases... not detectably, but the potential energy added to the spring has its own contribution to the total mass.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #107 on: 21/01/2013 19:09:31 »
Lightarrow, is there any reason why you can't take a classical limit of the quantum theory to come up with classical photons like Pmb claims?  That approach is certainly valid for electrons (and explains why we have "classical" electrons" when we know they also behave like waves in the 2 slit experiment).
When you take the classical limit for a photon (h --> 0) it gets zero energy, so it disappears.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #108 on: 21/01/2013 19:12:37 »
All matter and energy has mass. Even the kinetic energy of an object has mass.
If you mean relativistic mass, ok. If you mean "mass", with this term it's usually intended "invariant" mass and then it's false, unless the object rotates around a fixed point.
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In fact, when you compress a spring, its mass increases... not detectably, but the potential energy added to the spring has its own contribution to the total mass.
Correct.

JP

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Re: How does mass increase at higher speeds?
« Reply #109 on: 21/01/2013 20:32:40 »
Lightarrow, is there any reason why you can't take a classical limit of the quantum theory to come up with classical photons like Pmb claims?  That approach is certainly valid for electrons (and explains why we have "classical" electrons" when we know they also behave like waves in the 2 slit experiment).
When you take the classical limit for a photon (h --> 0) it gets zero energy, so it disappears.

Good point.  After reading that and a bit more thinking, I believe that what's going on with these "classical photons" is two limits.  If we have a field made of photons, the classical limit does not correspond to taking h->0, but rather to taking many photons.  In this limit, you recover Maxwell's equations, but you've lost information about the behavior of individual photons.

Then you take a second limit corresponding to wavelength->0 which gets you ray optics.  So essentially, your "classical photon" is an arbitrary packet of energy assigned to propagate along a ray.  It's related to real photons only insofar as the sum over many photons gets you the classical field, which you then use to define rays.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #110 on: 21/01/2013 22:57:47 »
Quote from: lightarrow
When you take the classical limit for a photon (h --> 0) it gets zero energy, so it disappears.
(sigh!) I'm clearly sorry that I asked.

That's wrong. If you were right then no classical particles exist in the classical limit. Don't forget what h physically means. I means that for every quantum mechanical particle that has inertial energy (defined as E = K + E0 = Kinetic Energy + Rest Energy) has an associated frequency given by the relationship E = hf. What does it mean to take h -> 0 for an electron? It means that there is no associated wavelength.

Recall that in classical electrodynamics one can have a very small packet/burst of radiation (which can be described by a Fourier integral) which has enegy and momentum p. The relationship between them is a non-quantum mechanical relationship, i.e. E = pc. The shape of the light pulse can be selected such that the spatial extention is small enough for all practical purposes.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #111 on: 21/01/2013 23:02:06 »
Quote from: lightarrow
If you mean relativistic mass, ok.
You know that its relativistic mass from the context in which he used it. Its not wise to assume that everyone who uses the description that he does needs to be reminded of these facts. To assume so is condescending to the poster because we're assuming that he doesn't know what he's talking about and we need to correct them.

I recommend that if someone says "mass depends on speed/energy etc." then we simply assume that by "mass" they mean relativistic mass. Having to remind people all the time is a waste of everybody's time. People can get irritated when someone has to comment on it every time they use the concept, don't you think

JP

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Re: How does mass increase at higher speeds?
« Reply #112 on: 22/01/2013 03:57:26 »
Recall that in classical electrodynamics one can have a very small packet/burst of radiation (which can be described by a Fourier integral) which has enegy and momentum p. The relationship between them is a non-quantum mechanical relationship, i.e. E = pc. The shape of the light pulse can be selected such that the spatial extention is small enough for all practical purposes.

Yep, and a photon is usually defined similar to a Fourier component (monochromatic plane wave) of a pulse.  It has a well-defined frequency, momentum and polarization, but no simple position representation (much as a plane wave has a well-defined frequency, direction and polarization, but exists over all space).  Just like a pulse which has a confined position can be expressed as a superposition of many plane waves, a classical beam which has a limited area in space can be expressed as a state consisting of many photons.  Once you have that state, you can invoke geometrical optics or similar approximations to make it appear like a classical particle, but you've taken two approximations: many photons->classical pulse->geometrical/partical approximation to Maxwell's equations.

I've no doubt that you can make these two approximations in that order because I know the math fairly well.  So if "classical photon" means (essentially) classical approximation to a solution of Maxwell's equations, which are themselves a many-photon approximation to a quantized field, then yes--"classical photons" are a thing.

What I'm less sure of is this: can you go directly from the mathematical description of a photon and, by expanding in powers of h, (presumably by expanding the action?) get to a classical particle description?  Or is there something about photons that prevents you from doing this directly?  I know, for example, that photon wave-functions are controversial and unlike those of massive particles (http://arxiv.org/pdf/quant-ph/0508202v1.pdf).

Pmb

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Re: How does mass increase at higher speeds?
« Reply #113 on: 22/01/2013 13:41:39 »
Quote from: JP
Yep, and a photon is usually defined similar to a Fourier component (monochromatic plane wave) of a pulse.
Huh? What is a "Fourier component (monochromatic plane wave) of a pulse."?

JP

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Re: How does mass increase at higher speeds?
« Reply #114 on: 22/01/2013 15:06:20 »
A monochromatic plane wave is a solution to the wave equation that has both a definite direction and frequency.  You can write it as
$$\exp[\mathrm{i}(\mathbf{k}\cdot\mathbf{x}-\omega t)],$$
where k is wave vector (2*pi/lambda*direction), x is position, omega is (angular) frequency and t is time.  Each of these solutions satisfies a wave equation, so any pulse built from these satisfies the wave equation.  Since they're exponential solutions, the integral is a Fourier integral that takes a weighting function in k and omega to x and t.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #115 on: 23/01/2013 17:24:46 »
Quote from: lightarrow
When you take the classical limit for a photon (h --> 0) it gets zero energy, so it disappears.
(sigh!) I'm clearly sorry that I asked.

That's wrong. If you were right then no classical particles exist in the classical limit. Don't forget what h physically means. I means that for every quantum mechanical particle that has inertial energy (defined as E = K + E0 = Kinetic Energy + Rest Energy) has an associated frequency given by the relationship E = hf. What does it mean to take h -> 0 for an electron? It means that there is no associated wavelength.
I have already replied you (in a previous post of this or another similar thread, don't remember) that a photon is different because has zero mass. For an electron, you can have non-zero momentum p even at very low speeds, because of its non-zero mass. Then De-Broglie relationship: $$\lambda$$ = h/p tells that, in the limit h --> 0, $$\lambda$$ = 0, that is, frequency should be infinite.
For a photon you can't do it, because its momentum p too would vanish, in the limit h --> 0.
« Last Edit: 23/01/2013 17:27:34 by lightarrow »

AndroidNeox

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Re: How does mass increase at higher speeds?
« Reply #116 on: 23/01/2013 20:38:27 »
All matter and energy has mass. Even the kinetic energy of an object has mass.
If you mean relativistic mass, ok. If you mean "mass", with this term it's usually intended "invariant" mass and then it's false
[/quote]

Naturally I'm referring to relativistic mass, since that's what the question is about. The rest mass doesn't change because it's never in motion and has no kinetic energy. I was specifically referring to kinetic energy having mass.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #117 on: 23/01/2013 21:19:32 »
All matter and energy has mass. Even the kinetic energy of an object has mass.
If you mean relativistic mass, ok. If you mean "mass", with this term it's usually intended "invariant" mass and then it's false
Naturally I'm referring to relativistic mass, since that's what the question is about. The rest mass doesn't change because it's never in motion and has no kinetic energy. I was specifically referring to kinetic energy having mass.
Certainly. However we should be more precise when we discuss this subject because it's very easy to make confusion. For example, saying "All matter and energy has mass. Even the kinetic energy of an object has mass" is very confusing: in the first sentence, matter has invariant mass, "energy has mass" is incorrect, since energy is "a property" of a body, and a property cannot have mass (as if I would say that a number has a colour); we should say instead that "a body which has energy has mass", but in this case is not always invariant mass...
As you see, things are not so simple.
« Last Edit: 23/01/2013 21:21:48 by lightarrow »

AndroidNeox

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Re: How does mass increase at higher speeds?
« Reply #118 on: 23/01/2013 21:32:15 »
Certainly. However we should be more precise when we discuss this subject because it's very easy to make confusion. For example, saying "All matter and energy has mass. Even the kinetic energy of an object has mass" is very confusing: in the first sentence, matter has invariant mass, "energy has mass" is incorrect, since energy is "a property" of a body, and a property cannot have mass (as if I would say that a number has a colour); we should say instead that "a body which has energy has mass", but in this case is not always invariant mass...
As you see, things are not so simple.

Energy does have gravitational mass. Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #119 on: 24/01/2013 09:04:56 »
Certainly. However we should be more precise when we discuss this subject because it's very easy to make confusion. For example, saying "All matter and energy has mass. Even the kinetic energy of an object has mass" is very confusing: in the first sentence, matter has invariant mass, "energy has mass" is incorrect, since energy is "a property" of a body, and a property cannot have mass (as if I would say that a number has a colour); we should say instead that "a body which has energy has mass", but in this case is not always invariant mass...
As you see, things are not so simple.
Energy does have gravitational mass.
1. Energy *cannot* have mass, or charge, or lenght, colour, as a number cannot have mass, charge, lenght, or colour. I've already written it but you probably still haven't understood it. Energy is *a property* of a body, and *not a body itself*. What would you answer to someone who stated that his "age" has "weight"?
Please, answer this question, before stating another time that energy has mass.
2. Even when your statement is correctly written, that is: "a body which has energy
also have gravitational mass" is not exact because a photon, by itself, doesn't have gravitational mass (before you contest this, think to a physics book where this is written). Instead "a region of space which has electromagnetic energy" does have.
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Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.
Correct, but it doesn't confirm your statement.
By the way, there is no need of matter and antimatter and not even of light in a box,  two photons are enough, because such a system have a non-zero mass (I mean invariant mass, not relativistic mass), I have already showed it in a recent thread and in several others, during the years.
« Last Edit: 24/01/2013 09:11:36 by lightarrow »

Pmb

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Re: How does mass increase at higher speeds?
« Reply #120 on: 24/01/2013 13:50:43 »
That's wrong. I have already replied you (in a previous post of this or another similar thread, don't remember) that a photon is different because has zero mass.
I can see that you’re not one who is much for agreeing to disagree, huh? Okay.

For an electron, you can have non-zero momentum p even at very low speeds, because of its non-zero mass. Then De-Broglie relationship: $$\lambda$$ = h/p tells that, in the limit h --> 0, $$\lambda$$ = 0, that is, frequency should be infinite.
And since the product of wavelength and momentum has to remain the same in that relationship it means that it’s an improper limit since as ones going down, the other is going up.

In any case you keep forgetting that we’re treating it as a classical particle for which the relationship: $$\lambda$$ = h/p ignored. Thus it means nothing in the classical sense to take a classical limit of a photon. JP and myself explained how it works in a classical sense.  You insist on ignoring its defining properties. It’s a classical description of a Fourier integral description of a sharp pulse of radiation. Since JP and I both have our convictions I’m wondering what it is that you hope to gain into continuing this? You certainly can’t change the textbooks or change the usage of the center of mass of a two photon system in the textbooks. As I have asked too many times now with no response – why do people insist in using the scenario I’ve described and never came to a wrong answer.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #121 on: 24/01/2013 17:11:34 »
I can see that you’re not one who is much for agreeing to disagree, huh? Okay.
It depends. Because of my nickname, I like to talk about light and photons [], so I've studied this subject and discussed it in the forums, for several years.
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For an electron, you can have non-zero momentum p even at very low speeds, because of its non-zero mass. Then De-Broglie relationship: $$\lambda$$ = h/p tells that, in the limit h --> 0, $$\lambda$$ = 0, that is, frequency should be infinite.
And since the product of wavelength and momentum has to remain the same
? We are making the limit h-->0, so it doesn't remain the same!
Quote
In any case you keep forgetting that we’re treating it as a classical particle for which the relationship: $$\lambda$$ = h/p ignored.
But the point is that *you have to prove* treat it can be treated as a classical particle.
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Thus it means nothing in the classical sense to take a classical limit of a photon.
Exactly! Read again what you have written here   []
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JP and myself explained how it works in a classical sense.
JP wrote this:
<<Good point.  After reading that and a bit more thinking, I believe that what's going on with these "classical photons" is two limits.  If we have a field made of photons, the classical limit does not correspond to taking h->0, but rather to taking many photons.  In this limit, you recover Maxwell's equations, but you've lost information about the behavior of individual photons.

Then you take a second limit corresponding to wavelength->0 which gets you ray optics.  So essentially, your "classical photon" is an arbitrary packet of energy assigned to propagate along a ray.  It's related to real photons only insofar as the sum over many photons gets you the classical field, which you then use to define rays.>>

So JP, essentially, says: OR you recover classical electromagnetism, and you have lost information about the behaviour of individual photons, OR you come up with the geometrical optics approximations and you can talk about packets of energy assigned to propagate along a ray.
But this is exactly what I've already written to you in previous posts  []
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You certainly can’t change the textbooks
Sincerely I have never read "classical photon" in a book of physics.
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or change the usage of the center of mass of a two photon system in the textbooks. As I have asked too many times now with no response – why do people insist in using the scenario I’ve described and never came to a wrong answer.
Please explain, in detail if you please, what it means when you say “You can’ do that!” when so many people do it,
"So many people" are able to localize a photon in flight? Forget it...
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and very successfully too I might ad. You imply that you can’t draw a worldline of a photon in a spacetime diagram and yet physicists do it all the time.
How do you draw a photon's worldline between (0,0,0,0) and (1,1,0,0)? Just for curiosity.
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E.g. referring to finding the center of mass of two photons you claimed “You can't localize a photon, so you can't do that.” When in fact derivations based on the localizability of property of a photon that plays a crucial role in its use in the derivation, you know, the one you claimed can’t be done. While you’re at it please state in detail what you mean whey you say “You can’t localize a photon”.  Again you claimed that just because I was speaking about classical physics you claimed that I was speaking about quantum mechanics, again with no proof provided. I suggest that you take a look at the derivation again http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm just pas Eq. (. Nothing about a quantum nature about anything is mentioned in there. Easy as cake. Over and over again you keep making the unfounded assertion that you can’t localize a photon but then never state what that means in practice. Then you later claim that you “so you can’t speak of photons”. Then you go on an claim I don’t know a lot about QM just because you didn’t understand what I wrote and you didn’t appear to go back to JPs post to see the context in which I made the statement which makes you think I don’t understand QM. As JP says and I believe him 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.
I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.
« Last Edit: 24/01/2013 17:14:29 by lightarrow »

JP

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Re: How does mass increase at higher speeds?
« Reply #122 on: 24/01/2013 18:49:36 »
I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.

This sums it up nicely: you two disagree on what you call a photon.  Pmb's photons are not at all the quantized photons of quantum optics.  If I were writing the textbooks, I'd side with Lightarrow on this and reserve photon to mean a very specific thing in quantum mechanics that has no classical analogue: the state resulting from an exitation of hbar*omega of energy in the EM field.  However, as I'm not the President of Physics, I can't do this, and I've noticed that many physicists use the term in a sense similar to what Pmb is doing, and this works out pretty well.  The problem arises when compare the properties of these different uses of "photon" and realize they're talking about two completely different things with completely different properties, and that there is no classical limit of a single-photon Fock state.

Perhaps the solution should be to elect me the President of Physics and I'll rewrite all the textbooks to clear this up?

Pmb

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Re: How does mass increase at higher speeds?
« Reply #123 on: 25/01/2013 02:32:57 »
Quote from: lightarrow
I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.
If that is your response then you weren't paying attention to what I was saying. You consistently keep forgetting the approximation and what it would mean to put the photon's position vector inside the area of uncertainty according to how the wave function would average the position. I gave you an example of a pixel of 0.001 mm in width a length and when it detects the photon then its localized in that area and the location of the photon is the location of the pizel) e.g. geometric center.

You youy insist on ignoring every single thing I've said regarding approximation then there is no use to continue this conversation. Why should I post something I know you're going to igore?

While you're at it it wouln't hut you to finally state what it is you mean by saying something can or can't be localized. E.g. find a QM texbook and quote the definition of "localized" or "localize" so you won't be vauge anymore.
« Last Edit: 25/01/2013 02:50:38 by Pmb »

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #124 on: 25/01/2013 11:39:01 »
Quote from: lightarrow
I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.
If that is your response then you weren't paying attention to what I was saying. You consistently keep forgetting the approximation and what it would mean to put the photon's position vector inside the area of uncertainty according to how the wave function would average the position. I gave you an example of a pixel of 0.001 mm in width a length and when it detects the photon then its localized in that area and the location of the photon is the location of the pizel) e.g. geometric center.

You youy insist on ignoring every single thing I've said regarding approximation then there is no use to continue this conversation. Why should I post something I know you're going to igore?

While you're at it it wouln't hut you to finally state what it is you mean by saying something can or can't be localized. E.g. find a QM texbook and quote the definition of "localized" or "localize" so you won't be vauge anymore.
It's you that don't pay attention to what I wrote. I've already written that "saying to have exactly localized a photon is the same mistake of saying to have perfectly localized a particle' path in a cloud chamber".
And, again, you don't need to talk of photons, if you intend to make such coarse approximations, you can talk of pulses of light.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #125 on: 26/01/2013 15:45:19 »
I pay close attention. You just never make any sense and you ignore all the derivations provided to you. You're the one who insists on refusing to explain how physicists, in physics journals none the less, do what you claim can't be done and yet get the correct results.

Is there a good reason why you keep refusing to provide a definition of the term "localized" as you insist on using it? I case your response is to claim that you already have please post the time and day of your response.
« Last Edit: 26/01/2013 15:48:52 by Pmb »

JP

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Re: How does mass increase at higher speeds?
« Reply #126 on: 26/01/2013 15:49:41 »
Is there a good reason why you keep refusing to provide a definition of the term "localized" as you insist on using it? BTW photons are always localized when their position is measured

But a photon that's been measured is no longer a photon.  The entirety of this argument comes down to the fact that Lightarrow uses photon to mean a single photon Fock state, which cannot be localized by definition, and you're using photon to mean a classical pulse.  A measured photon is no longer in a Fock state, so it is no longer a photon by that definition.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #127 on: 26/01/2013 16:51:32 »
Quote from: JP
But a photon that's been measured is no longer a photon.
I’m aware of that, of course. I wasn’t sure he was aware that when a photon’s position is measured that it was localized.

Quote from: JP
The entirety of this argument comes down to the fact that Lightarrow uses photon to mean a single photon Fock state, which cannot be localized by definition, and you're using photon to mean a classical pulse..
Sorry, but I don’t know what a Fock state is.

In any case, that’s not what I meant by a “classical photon.” Recall the definition that I used. A classical photon is a particle whose inertial energy is related to its momentum by E = pc and interacts with charges via the electromagnetic interaction. There is no associated wavelength since that’s a quantum property just as a classical electron has no wavelength. By this definition it moves on a classical trajectory, has a position vector, etc.  This is what they use in the derivations for the mass-energy equivalence relationship where they use the conservation of the center of momentum. It’s also what relativists use when they draw a worldline of a photon.

It doesn’t matter at this point. I don’t want to discuss it anymore. I merely wanted to see what lightarrow thinks “localized” means. I've already had enough of his broken record responses.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #128 on: 26/01/2013 17:05:54 »
I checked all my texts on quantum mechanics and none of them mentioned Fock space. However a friend of mine just gave me his text Quantum Mechanics II: A Second Course in Quantum Theory by Rubin H. Landau.

I guess this is where this second quantinization stuff I hear about so often is addressed. I've never studied QM at this level before. Thanks for mentioning it. It'll give me a goal to reach after I refreshen my quantum mechanics in the next few months.

JP

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Re: How does mass increase at higher speeds?
« Reply #129 on: 26/01/2013 19:20:57 »
I guess this is where this second quantinization stuff I hear about so often is addressed. I've never studied QM at this level before. Thanks for mentioning it. It'll give me a goal to reach after I refreshen my quantum mechanics in the next few months.

It's interesting stuff.  I've studied the basics, but haven't really applied it to anything.  A single Fock state can't be localized, but physics can and do write approximate photon wave functions when considering photons emitted by a source and absorbed by a detector.  I briefly read a section on this in Optical Coherence and Quantum Optics in Mandel and Wolf when this question came up previously, but I didn't have the time to really dig into the details.  Again, I'm not going to wade into the argument of whether we should call localized wave functions that aren't single-photon Fock states "photons," but some physicists definitely do so in practice.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #130 on: 26/01/2013 21:55:15 »
I guess this is where this second quantinization stuff I hear about so often is addressed. I've never studied QM at this level before. Thanks for mentioning it. It'll give me a goal to reach after I refreshen my quantum mechanics in the next few months.

It's interesting stuff.  I've studied the basics, but haven't really applied it to anything.  A single Fock state can't be localized, but physics can and do write approximate photon wave functions when considering photons emitted by a source and absorbed by a detector.  I briefly read a section on this in Optical Coherence and Quantum Optics in Mandel and Wolf when this question came up previously, but I didn't have the time to really dig into the details.  Again, I'm not going to wade into the argument of whether we should call localized wave functions that aren't single-photon Fock states "photons," but some physicists definitely do so in practice.
What we were talking about was the position vector of a single photon in a system of only a few photons. Can that be done by using some sort of centroid?

JP

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Re: How does mass increase at higher speeds?
« Reply #131 on: 26/01/2013 23:43:47 »
The short answer is yes.  I found part of the book I was talking about on Google books:

They come back to the plane wave description I was giving earlier: if you have a single plane wave it is not localized in space and time, but if you have many added together, it can be localized.

In the same way, if you have a single Fock state, it cannot be localized, but if you add many single-photon Fock states together, it can be.  But since this is quantum, the addition of many Fock states can be a single-photon state, since each Fock state represents a configuration of a photon, and the whole state describes the probability of finding that photon in each configuration.

But as they say, you have to be careful when interpreting "localized" photons, since they are defined from second quantization of the field, and do not have all the properties of a particle such as an electron, which can be described in terms of first quantization of a particle.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #132 on: 27/01/2013 00:12:23 »
Thanks JP. Speaking about electrons, I just read an iteresting comment in French and Taylor's QM text on page 9
Quote
Millikan demonstrated very directly what he called the "unitary nature of electricity," the fact that electric charge is quantized and transferred in multiple integrals of e.
So lightarrows attempt to use the term "quantized" as part of the definition of photon has the defining "quantum mechanical" property is flawed since we know that referred only to it being a discrete amount of something and not as "quantum mechanical" also finds its use as in the defining property of the electron as well. In fact they use it to first describe the electron and only much later to describe the photon. As I said before, you have to be careful of how you interpret the use of the term "quantized" or "quantum." For the most part it refers to discrete lumps of matter more that it does to the name of a theory.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #133 on: 27/01/2013 02:24:00 »
Quote from: Pmb
Recall the definition that I used. A classical photon is a particle whose inertial energy is related to its momentum by E = pc and interacts with charges via the electromagnetic interaction.
This has been bothering me recently. It appears to me now that such a classical photon cannot interact with other particles in such a way that it would change its energy E. There’s no way for such a particle to change its energy so when a charged particle interacts with it it can’t change its energy. So a classical photon can’t change its kinetic energy, since E = kinetic energy. A quantum photon can change its kinetic energy by changing its wavelength. So a classical photon cannot change its speed.

Since the uses I've seen for such a particle never invoke a change of energy this isn't a serious limitation.

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Re: How does mass increase at higher speeds?
« Reply #134 on: 27/01/2013 17:04:34 »

Quote
Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.
Correct, but it doesn't confirm your statement.
By the way, there is no need of matter and antimatter and not even of light in a box,  two photons are enough, because such a system have a non-zero mass (I mean invariant mass, not relativistic mass), I have already showed it in a recent thread and in several others, during the years.

It's both correct and does prove my statement.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #135 on: 27/01/2013 17:50:48 »

Quote
Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.
Correct, but it doesn't confirm your statement.
By the way, there is no need of matter and antimatter and not even of light in a box,  two photons are enough, because such a system have a non-zero mass (I mean invariant mass, not relativistic mass), I have already showed it in a recent thread and in several others, during the years.

It's both correct and does prove my statement.
Forget what he's been saying. He has a way of confusing the poperties of mass with those of proper mass. There are three aspects of mass given three names and each are merely just called "mass" because they all have the same value

(1) inertial mass - m = p/v. The higher the inerial mass the harder it is to change its momentum.

(2) passive gravitational mass - The property of matter to respond to a gravitational force.

(3) active graivtational mass - The property of matter to generate a gravitational field.

proper mass (i.e. what lightarrow is always referring to when he sees the word "mass") has little or nothing to do with the defining characteristics of mass. A photon has zero proper mass but has inertial mass, passive gravitational mass and active gravitational mass.

JP

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Re: How does mass increase at higher speeds?
« Reply #136 on: 27/01/2013 20:10:03 »
proper mass (i.e. what lightarrow is always referring to when he sees the word "mass") has little or nothing to do with the defining characteristics of mass.

That's because you're defining mass to preclude the use of invariant mass.  Plenty of physicists (mostly in high energy physics) use "mass" to mean invariant mass, which also has desirable properties.
(1) Invariant mass properly satisfies m=p/v when you use 4-momentum and 4-velocity, while inertial mass doesn't
(2) Invariant mass is invariant when you change inertial reference frames, which is a very elegant property.

I can't comment on your points (3) and (4), since I'm not up to speed on my general relativity.  They probably don't matter much to most particle physicists, since they don't deal with gravity.

It's also important to note that we all agree on the properties of mass in the non-relativistic limit, but all these definitions of mass agree in that limit, so we can't use that as a basis for picking the "best" one.

There is legitimate controversy in the teaching of physics over which definition to use.  It's my impression that invariant mass is generally winning insofar as it's being adopted in introductory textbooks.  http://en.wikipedia.org/wiki/Mass_in_special_relativity#Controversy

Pmb

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Re: How does mass increase at higher speeds?
« Reply #137 on: 27/01/2013 23:20:36 »
Quote from: JP
Quote from: Pmb
proper mass (…) has little or nothing to do with the defining characteristics of mass.
That's because you're defining mass to preclude the use of invariant mass.
Not at all. I’ve chosen to state the definitions (not to define them since they were defined waaaay before I was even a gleam i m'daddy's eye! lol!) of mass that describe dynamics. I’m not choosing one particular definition of mass over another to state because I wish to preclude the use of invariant mass. Invariant mass is quite useful. I’d hate to try to work out your typical particle physics problems without it. Proper mass is also a defining property of a particle in that it is the unique limit of inertial mass for low v, i.e. m = M(v) as v->0.

Quote from: JP
Plenty of physicists (mostly in high energy physics) use "mass" to mean invariant mass, which also has desirable properties.
(1) Invariant mass properly satisfies m=p/v when you use 4-momentum and 4-velocity, while inertial mass doesn't
(2) Invariant mass is invariant when you change inertial reference frames, which is a very elegant property.
Absolutely (Noting that #1 fails for all luxons). Please don’t misinterpret my comments to mean that proper mass is not useful. That would be an outrageously inaccurate assumption.

Quote from: JP
I can't comment on your points (3) and (4), since I'm not up to speed on my general relativity.  They probably don't matter much to most particle physicists, since they don't deal with gravity.
Its my opinion that there are many more particle physicists than other kinds of users of relativity so that the majority of use is mass = proper mass. However that is merely a game of numbers and what’s currently a popular area of research.

Quote from: JP
It's also important to note that we all agree on the properties of mass in the non-relativistic limit, but all these definitions of mass agree in that limit, so we can't use that as a basis for picking the "best" one.
Except when it comes to photons where there is no such limit, of course.

Quote from: JP
There is legitimate controversy in the teaching of physics over which definition to use.

Oh yes. That horse has been thoroughly beat upon in virtully every physics forum on the internet ever time the subject of mass comes up. Its become a virus which derails most threads merely because when people say “mass depends on speed” the non rel-mass people have to change it to debate against rel-mass rather than jus think to themselves  “Okay. By ‘mass’ that person means rel-mass.” and then moves on with the discussion. Never happens in practice thought. The problem is that it causes tons of confusion because you then have to explain why light can generate a gravitational field. When it comes to defining mass density for a uniform magnetic field it becomes very dicey.

By the way, I’ve changed my mind on the only properties of a classical photon being its energy and momentum. It’s mass is the real physical property. While in QM the wavelength changes giving a corresponding change in energy in classical mechanics it’s the mass that changes giving a corresponding change in energy, same as in QM but phrased in terms of classical properties.
« Last Edit: 28/01/2013 04:12:41 by Pmb »

JP

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Re: How does mass increase at higher speeds?
« Reply #138 on: 28/01/2013 05:02:24 »
Quote from: JP
Quote from: Pmb
proper mass (…) has little or nothing to do with the defining characteristics of mass.
That's because you're defining mass to preclude the use of invariant mass.
Not at all. I’ve chosen to state the definitions (not to define them since they were defined waaaay before I was even a gleam i m'daddy's eye! lol!) of mass that describe dynamics. I’m not choosing one particular definition of mass over another to state because I wish to preclude the use of invariant mass.

I'm just taking issue your one line above that I quoted.  Invariant mass has plenty to do with the definition of mass, since it agrees completely with non-relativistic mass in the non-relativistic limit, just as inertial mass does.  It's all a matter of the way you choose to extend that definition into a relativistic framework, and both invariant and inertial mass are useful extensions.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #139 on: 28/01/2013 06:13:29 »
Quote from: JP
I'm just taking issue your one line above that I quoted.
I smell a debate about proper mass vs rest mass in the air. That's when I must leave the room. Methinks it be bad juju!
« Last Edit: 28/01/2013 06:15:46 by Pmb »

JP

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Re: How does mass increase at higher speeds?
« Reply #140 on: 28/01/2013 14:31:45 »
Quote from: JP
I'm just taking issue your one line above that I quoted.
I smell a debate about proper mass vs rest mass in the air. That's when I must leave the room. Methinks it be bad juju!

I wasn't the one telling posters that proper mass has little or nothing to do with the definition of mass!  I'm content to call them "invariant/proper mass" and "inertial/relativistic mass" and skip the arguing phase over which meets the definition of mass.

Pmb

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Re: How does mass increase at higher speeds?
« Reply #141 on: 28/01/2013 16:48:34 »
Quote from: JP
I'm just taking issue your one line above that I quoted.
I smell a debate about proper mass vs rest mass in the air. That's when I must leave the room. Methinks it be bad juju!

I wasn't the one telling posters that proper mass has little or nothing to do with the definition of mass!  I'm content to call them "invariant/proper mass" and "inertial/relativistic mass" and skip the arguing phase over which meets the definition of mass.
Don't get me wrong.I wasn't blaming anyone for anything about that. More later. Gotta go to pain clinic.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #142 on: 28/01/2013 21:57:50 »
Perhaps the solution should be to elect me the President of Physics
[]
Quote
and I'll rewrite all the textbooks to clear this up?
I like your kind of humour.

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #143 on: 28/01/2013 22:22:34 »
Quote from: lightarrow
I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.
If that is your response then you weren't paying attention to what I was saying. You consistently keep forgetting the approximation and what it would mean to put the photon's position vector inside the area of uncertainty according to how the wave function would average the position. I gave you an example of a pixel of 0.001 mm in width a length and when it detects the photon then its localized in that area and the location of the photon is the location of the pizel) e.g. geometric center.
Ah, yes, localized after detection, of course. The problem is, and this is not the first time I write it, I was talking of localizing it in flight, between source and detector.
Quote
You youy insist on ignoring every single thing I've said regarding approximation then there is no use to continue this conversation. Why should I post something I know you're going to igore?
While you're at it it wouln't hut you to finally state what it is you mean by saying something can or can't be localized. E.g. find a QM texbook and quote the definition of "localized" or "localize" so you won't be vauge anymore.
Have a look also here:

http://stochastix.files.wordpress.com/2008/05/what-is-a-photon.pdf

<<What is a photon?
Rodney Loudon
University of Essex, Colchester, UK>>
...
<<A one-photon excitation in such a mode again carries an energy
quantum ¯hω distributed over the entire interferometer,
including both internal paths. Despite the absence of any localization
of the photon
, the theory provides expressions for
the distributions of light in the two output arms, equivalent to
a determination of the interference fringes.>>
« Last Edit: 28/01/2013 23:27:30 by lightarrow »

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #144 on: 28/01/2013 22:45:31 »
Sorry, but I don’t know what a Fock state is.

In any case, that’s not what I meant by a “classical photon.” Recall the definition that I used.
Do you mean it's a definition invented by you? It's just a question.
Quote
A classical photon is a particle whose inertial energy
"inertial energy"? Sorry but I've never read this term; it's not another of "your definitions", isnt'it?
Quote
is related to its momentum by E = pc and interacts with charges via the electromagnetic interaction. There is no associated wavelength since that’s a quantum property just as a classical electron has no wavelength. By this definition it moves on a classical trajectory, has a position vector, etc.
Ok. What you have described here is simply a classical pulse of light: an electromagnetic wavepacket. Why do you call it "classical photon"? Well, if I will find it in books of physics, I will conform to it, no problem; don't see any problem in using that term, as soon as it will be defined.
Quote
This is what they use in the derivations for the mass-energy equivalence relationship where they use the conservation of the center of momentum. It’s also what relativists use when they draw a worldline of a photon.
If they use the term "photon" it's a misuse and they could simply talk of an electromagnetic wavepacket. I suspect some relativists don't actually now what "a photon" exactly is; I don't mean I know it well, but it's a lot of time I discuss this specific subject with physicists, at university, first and in the forums.
« Last Edit: 28/01/2013 23:27:00 by lightarrow »

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #145 on: 28/01/2013 23:06:11 »

Quote
Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.
Correct, but it doesn't confirm your statement.
By the way, there is no need of matter and antimatter and not even of light in a box,  two photons are enough, because such a system have a non-zero mass (I mean invariant mass, not relativistic mass), I have already showed it in a recent thread and in several others, during the years.

It's both correct and does prove my statement.
If you say so...

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #146 on: 28/01/2013 23:13:21 »
Forget what he's been saying. He has a way of confusing the poperties of mass with those of proper mass.
[]  Sorry, I wasn't.
Quote
There are three aspects of mass given three names and each are merely just called "mass" because they all have the same value
(1) inertial mass - m = p/v. The higher the inerial mass the harder it is to change its momentum.
(2) passive gravitational mass - The property of matter to respond to a gravitational force.
(3) active graivtational mass - The property of matter to generate a gravitational field.
proper mass (i.e. what lightarrow is always referring to when he sees the word "mass") has little or nothing to do with the defining characteristics of mass. A photon has zero proper mass but has inertial mass, passive gravitational mass and active gravitational mass.
Just "Four" kinds? My God, where has gone your creativity? From you I expected at least a hundreds kinds  []
You still have a lot of work to do, if you want to write since-fiction books  []

yor_on

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Re: How does mass increase at higher speeds?
« Reply #147 on: 29/01/2013 04:06:03 »
This one does a nice job of explaining the history of mass, and how the idea of passive and active mass came to be. The Equivalence Principle: A Question of Mass
"BOMB DISPOSAL EXPERT. If you see me running, try to keep up."

lightarrow

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Re: How does mass increase at higher speeds?
« Reply #148 on: 29/01/2013 08:40:06 »
This one does a nice job of explaining the history of mass, and how the idea of passive and active mass came to be. The Equivalence Principle: A Question of Mass
History is interesting, but once physics has established the equivalence of those masses, there is no need to talk about them any longer, there is just one.

yor_on

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Re: How does mass increase at higher speeds?
« Reply #149 on: 29/01/2013 17:34:02 »
I think the point of it has to do with light quanta. "A photon has zero proper mass but has inertial mass, passive gravitational mass and active gravitational mass." The 'passive' being what is acting on it, the 'active' being the way it will act on other, the inertial mass being its resistance to change, all as I think of it. But if it is a field then? How many degrees of freedom would be needed to create a static field in where you have the illusion of a arrow, waves/particles, gravity and motion, and all of it being observer dependent?
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