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Author Topic: Does a photon have mass equivalent to its energy?  (Read 25761 times)

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #50 on: 13/05/2012 15:54:43 »
Those who insist on calling m what was once called "relativistic mass" don't explain that this term is just another name for "total energy" (divided by c2).
Since this concept has already a name, that is "Energy", why using a new one?

The reason in physics it is used the term "mass" intending "invariant mass" (or "proper mass") is in its very name: it is INVARIANT.
In relativity is extremely useful to use quantities which are INVARIANT; every one who has solved meaningful problems on the subject, understands it. Another example of invariant quantity is "interval" or "proper time" (interval divided by c2).

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Offline Phractality

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Re: Does a photon have mass equivalent to its energy?
« Reply #51 on: 13/05/2012 19:44:51 »
 We expect religious fundamentalists to fight over a word. Scientists should be a bit more tolerant and understanding.

Confusion over the term "mass" and it's various symbols and abbreviations results from a lack of consensus and authority. Until all leading international governing bodies pass a resolution, binding on their members, to adhere strictly to an accepted nomenclature, the controversy will continue. Authors will be free to use their own favorite nomenclature. We can only hope that each author will make it clear what he means by "mass" and the letter "m", or whatever letter he uses.

I've gotten into the bad habit of using the terms "mass" and "m" without distinguishing which kind of mass I'm talking about. I've been doing it since my first intro to physics as a college freshman, before I learned about relativity. It's a hard habit to break, but I shall make an effort to do so.
I won't attack those who disagree with me, but I will argue in favor of my preference. I prefer to define "inertial mass", mi, as a measure of how much momentum changes per unit change in velocity in a given reference frame; mi = dp/dv. By that definition, the mass of a particle depends on the reference frame. The opposite camp in this controversy defines mass as the momentum change for the first small increment of velocity change beginning at rest. By that definition, the mass of a particle is the same in all inertial reference frames.

[EDIT 2012-05-16: I see a problem with my definition of mi. It works for particles with a rest mass, but not for photons. A photon's momentum changes as it passes thru a gravity well, but in GR a photon's velocity is constant. In Minkowski space-time, the path of light is the definition of a straight line, so a photon can't change direction. In GR, dp/dv for a photon would be infinite.
What's needed is a definition of inerial mass that works for photons as well as for particles with rest mass. I'll give this some more thought and get back to you.]
 
Since "m" has been used in the literature to represent both kinds of mass, perhaps the best solution is to abandon "m" altogether (except where relativity is clearly not an issue) and use only symbols that, historically, have been used only to mean one kind of mass or the other. I like the term "m0" for rest, invariant or proper mass, and I like the term "mi" for relativistic inertial mass. PMB likes to use "μ" instead of "m0" and "m" instead of "mi". I guess Lightarrow prefers "m" instead of "m0" and "γm" instead of "mi". I will be happy with any nomenclature that is unambiguous until such time as the international governing bodies make a unanimous ruling on the matter. [Edited to change "mr" to "mi".]
 
I define "gravitational mass", "mg", in terms of a slightly modified Newton's universal law of gravitation; f = dp/dt = G(mg1mg2 / r2). I believe that mg ≠ mi at relativistic speeds because time dilation makes planets orbit slower, not faster. Time dilation of planetary orbits is consistent with mg = m0 and mi = γm0. I haven't yet figured out whether mg = m0, or mg = mi when one body is stationary in the reference frame and the other is moving at relativistic speed.
 
I see no reason to distinguish between active and passive gravitational mass, as PMB does. While PMB is not saying they differ, simply giving them different names hints that they could differ. If they're not equal, momentum is not conserved, and conservation of momentum is one of a physicist's favorite security blankets. Please; leggo my security blanket! Waaaah! 
« Last Edit: 16/05/2012 19:19:45 by Phractality »
 

Offline imatfaal

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Re: Does a photon have mass equivalent to its energy?
« Reply #52 on: 14/05/2012 10:07:48 »
We expect religious fundamentalists to fight over a word. Scientists should be a bit more tolerant and understanding.

Nicely said.  Let's have no more wrangling over terminology please Ladies and Gentlemen
 

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #53 on: 14/05/2012 14:24:04 »
We expect religious fundamentalists to fight over a word. Scientists should be a bit more tolerant and understanding.

Confusion over the term "mass" and it's various symbols and abbreviations results from a lack of consensus and authority. Until all leading international governing bodies pass a resolution, binding on their members, to adhere strictly to an accepted nomenclature, the controversy will continue. Authors will be free to use their own favorite nomenclature. We can only hope that each author will make it clear what he means by "mass" and the letter "m", or whatever letter he uses.

I've gotten into the bad habit of using the terms "mass" and "m" without distinguishing which kind of mass I'm talking about. I've been doing it since my first intro to physics as a college freshman, before I learned about relativity. It's a hard habit to break, but I shall make an effort to do so.
I won't attack those who disagree with me, but I will argue in favor of my preference. I prefer to define "inertial mass", mi, as a measure of how much momentum changes per unit change in velocity in a given reference frame; mi = dp/dv. By that definition, the mass of a particle depends on the reference frame. The opposite camp in this controversy defines mass as the momentum change for the first small increment of velocity change beginning at rest. By that definition, the mass of a particle is the same in all inertial reference frames.
 
Since "m" has been used in the literature to represent both kinds of mass, perhaps the best solution is to abandon "m" altogether (except where relativity is clearly not an issue) and use only symbols that, historically, have been used only to mean one kind of mass or the other. I like the term "m0" for rest, invariant or proper mass, and I like the term "mi" for relativistic inertial mass. PMB likes to use "μ" instead of "m0" and "m" instead of "mi". I guess Lightarrow prefers "m" instead of "m0" and "γm" instead of "mi". I will be happy with any nomenclature that is unambiguous until such time as the international governing bodies make a unanimous ruling on the matter. [Edited to change "mr" to "mi".]
Ok. Anyway, in favour of my...school of thought  :) I just want to ask you a simple question: at school or university or at work, you have to solve a written problem where you find the symbol "me" and the text explain is the "electron mass" (see any book of physics for it).
Which value do you give it? Where do you look up for that value or how do you compute it?

 

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #54 on: 14/05/2012 14:32:27 »

Since "m" has been used in the literature to represent both kinds of mass, perhaps the best solution is to abandon "m" altogether (except where relativity is clearly not an issue) and use only symbols that, historically, have been used only to mean one kind of mass or the other. I like the term "m0" for rest, invariant or proper mass, and I like the term "mi" for relativistic inertial mass.
Maybe, the fact  people used the term "relativistic mass" and a symbol "m" for it, is because a lot of physicists still believe there is a difference between that mass and energy.

Some still make confusion about mass and energy and talks about "converting mass into energy", for example when they talk about the energy freed in a nuclear reaction.

I also talked in that terms, in the past, but it's incorrect. I have to thank a professor of physics for having (with difficulty) understood it. Actually, it's quite easy to understand; the difficult part is to accept it...

--
lightarrow

Edit:
Let's make a simple example: a nucleus of rest  mass m = 10-25 kg  undergoes nuclear fission and two equal fragments are shoot away in opposite directions.

Let's say the total kinetic energy of the fragments is 1/1000 the energy of the initial nucleus: 0.0001*m*c2 = 0.001*10-25*(3*108)2 Joule

Question: compute the *Rest* mass of the system before and after the nuclear reaction.

Rest mass of the system before reaction: 10-25 kg
Rest mass of the system after reaction: 10-25 kg

There are no mistakes.

Now I ask again: why using a different concept of mass different from rest mass?

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lightarrow
« Last Edit: 14/05/2012 14:51:32 by lightarrow »
 

Offline JP

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Re: Does a photon have mass equivalent to its energy?
« Reply #55 on: 14/05/2012 17:54:46 »
Not to mention that invariant mass is an extremely elegant quantity in the geometric formulation of special relativity.  The motion of an object with respect to an observer can be characterized by a 4-vector in space and time, which has length equal to invariant mass, and whose direction specifies the motion of the object in the observer's reference frame.  Changes of reference frame are accounted for by rotating this vector rather than using cumbersome formulas. 

Ok, so invariant mass is elegant and useful and agrees with the non-relativistic definition of mass in the appropriate limit.

What about relativistic mass makes it elegant or useful?  Does it have properties that energy alone does not?  I'm legitimately curious--I have used invariant mass in computations and know enough about its use in modern physics that I can see its virtue.  I can't say the same for relativistic mass, but I'd be interested in hearing where it still finds use.
 

Offline Phractality

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Re: Does a photon have mass equivalent to its energy?
« Reply #56 on: 14/05/2012 19:24:17 »
 

 Maybe, the fact people used the term "relativistic mass" and a symbol "m" for it, is because a lot of physicists still believe there is a difference between that mass and energy.
 
 Some still make confusion about mass and energy and talks about "converting mass into energy", for example when they talk about the energy freed in a nuclear reaction.
 
 I also talked in that terms, in the past, but it's incorrect. I have to thank a professor of physics for having (with difficulty) understood it. Actually, it's quite easy to understand; the difficult part is to accept it...
I totally agree that rest mass (or proper mass) is captive energy. Any energy that is bound within a system, by any attractive force, is captive energy; it contributes to the rest mass of the system. Any energy has both gravitational and inertial mass, whether it is bound within a system or not. Both kinetic energy and photons have mass.


Edit:
 Let's make a simple example: a nucleus of rest mass m = 10-25
kg undergoes nuclear fission and two equal fragments are shoot away in opposite directions.
 
 Let's say the total kinetic energy of the fragments is 1/1000 the energy of the initial nucleus: 0.0001*m*c2 = 0.001*10-25*(3*108)2 Joule
 
 Question: compute the *Rest* mass of the system before and after the nuclear reaction.
 
 Rest mass of the system before reaction: 10-25 kg
 Rest mass of the system after reaction: 10-25 kg
 
 There are no mistakes.
 
 Now I ask again: why using a different concept of mass different from rest mass?
 
 --
 lightarrow
 
Assuming that the split was spontaneous and not triggered by any external particle, the sum of rest masses of the two halves after the split must equal the original rest mass MINUS the kinetic energy of the fragments. Kinetic energy is the difference between relativistic mass and rest mass.
 
The key word in your argument is "system". If the two halves are bound by opposite electric charges, they are a system. Then, you are correct about the rest mass of that system. The rest mass of the system is the sum of rest masses of the two halves PLUS their kinetic energy. The kinetic energy of the halves is 10-28 kg; the kinetic energy of the system is zero. Kinetic energy of the two halves is captive within the system; captive energy is mass. [edited from 10-27]
 
If their kinetic energy is too great to be bound by electrostatic attraction, then I would consider the halves to be two independent systems. The sum of rest masses of the two systems would be 9.999 * 10-26 kg. [edited from 10-24]
« Last Edit: 14/05/2012 22:59:21 by Phractality »
 

Offline yor_on

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Re: Does a photon have mass equivalent to its energy?
« Reply #57 on: 14/05/2012 20:45:12 »
Sweet idea and I agree.

"A photon can accelerate by the way. It does so by scattering off, say, an electron  as in Compton Scattering. The magnitude of the photon's velocity remains constant. It's the change in direction that changes, which means that velocity changes, i.e. the photon accelerates."

By definition everything outside of a geodesic should be accelerating as I understands it. And there both Newton and Einstein agree. So :)

Does our earth accelerate more ways than one?
Well, sort of.
That's the equivalence principle when comparing a acceleration relative a 'mass' or 'proper/invariant mass'
Then we also have the fact that it is rotating, which should introduce another acceleration for all.

And it's pretty weird that the ('dynamic' as in using a 'motion' measured in time, as our earth spinning) geometry can be defined as creating a mass.

Where does the mass come from in a spin? And for a 'rotational mode' it don't matter if the spinning object is in a constant uniform spin, does it? It still should be seen to generating a 'mass' if I use the equivalence principle.

That is if I'm thinking right here :)
 

Offline yor_on

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Re: Does a photon have mass equivalent to its energy?
« Reply #58 on: 14/05/2012 20:50:46 »
The argument against it might be that you seem to be defining it from a 'wave picture' here Pete? As in a 'perfect reflection' of a wave as I think of it. If you instead use a 'particle' as a 'photon' it should interact with the material/atoms/electrons and annihilate as its interaction present us with a new 'photon'?
=

But no matter that, it doesn't change the way a uniformly spinning object 'accelerates' and so should gain a 'mass', as I think of it. Which should be a very strong argument for 'gravity' being a 'geometry', in some weirdly mysterious way. The Higgs field/bosons, what does that have to say about uniform spins?
« Last Edit: 14/05/2012 20:59:12 by yor_on »
 

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #59 on: 14/05/2012 21:09:57 »
I totally agree that rest mass (or proper mass) is captive energy.
 
You don't need the new term "captive energy", since you can call it "binding energy".
Quote

Any energy that is bound within a system, by any attractive force, is captive energy; it contributes to the rest mass of the system.
But this definition is very sneaky: as soon as you change the definition of which is the system, you have to change the phrase "it contributes to the rest mass of the system" to "it doesn't contributes to the rest mass of the system"  :) You see that it's impossible to separate the two concepts of mass and of energy, in some cases; also to avoid confusion, I prefer to talk about invariant mass, total energy, kinetic energy, without talking of which energy "contributes" to mass or of "mass converted into energy".
Quote

Any energy has both gravitational and inertial mass, whether it is bound within a system or not. Both kinetic energy and photons have mass.
But now you are again talking about relativistic mass...
Quote

Edit:
 Let's make a simple example: a nucleus of rest mass m = 10-25 kg undergoes nuclear fission and two equal fragments are shoot away in opposite directions.
 
 Let's say the total kinetic energy of the fragments is 1/1000 the energy of the initial nucleus: 0.0001*m*c2 = 0.001*10-25*(3*108)2 Joule
 
 Question: compute the *Rest* mass of the system before and after the nuclear reaction.
 
 Rest mass of the system before reaction: 10-25 kg
 Rest mass of the system after reaction: 10-25 kg
 
 There are no mistakes.
 
 Now I ask again: why using a different concept of mass different from rest mass?
 
 --
 lightarrow
 
Assuming that the split was spontaneous and not triggered by any external particle, the sum of rest masses of the two halves after the split must equal the original rest mass MINUS the kinetic energy of the fragments. Kinetic energy is the difference between relativistic mass and rest mass.
The key word in your argument is "system". If the two halves are bound by opposite electric charges, they are a system. Then, you are correct about the rest mass of that system. The rest mass of the system is the sum of rest masses of the two halves PLUS their kinetic energy. The kinetic energy of the halves is 10-27 kg
10-28 kg, but just to be picky... ;)
Quote
; the kinetic energy of the system is zero. Kinetic energy of the two halves is captive within the system; captive energy is mass.
 
If their kinetic energy is too great to be bound by electrostatic attraction, then I would consider the halves to be two independent systems. The sum of rest masses of the two systems would be 9.999 * 10-24 kg. [/font]
Ok.
 

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #60 on: 14/05/2012 21:20:21 »
"A photon can accelerate by the way. It does so by scattering off, say, an electron  as in Compton Scattering. The magnitude of the photon's velocity remains constant. It's the change in direction that changes, which means that velocity changes, i.e. the photon accelerates."
I answer just this because the rest is too complicated for me and I don't want to get a headache  :)

I am not so sure we can talk of a single photon changing direction; I prefer to see it in terms of an incoming photon from a direction which interacts with the atom (or molecule) and then another photon being emitted by the atom in another direction.

Just because the idea of accelerating a photon gives me "cold sweat"
  :).
 

Offline yor_on

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Re: Does a photon have mass equivalent to its energy?
« Reply #61 on: 14/05/2012 21:29:37 »
And what about those rotating black holes 'frame dragging'?
That should create a mass too, shouldn't it?

And they seem to be spinning close to 'c', some of them? Which either should be incredibly energy consuming, assuming that a spinning geometry as defined from us on earth observing, can't be a uniform motion and so somewhere must create 'energy' constantly, or else bleed that spin of?

All of it assuming a spin to be equivalent to mass, as it is a acceleration. That one has bothered me before and it keeps bugging me :) Because all 'uniformly constant' spins should lose energy if this is correct, shouldn't they?

Ouch, been away for some time here.

Also, if it is true then we have a definition of something maybe possible to prove from only one frame of reference. As a rotating mass in a otherwise 'empty universe', as long as 'they' had a knowledge of relativity, but that may only become a academic question in that case, as they would define the 'energy' relative whatever  'mass' they found anyway. But then it should differ depending on diameter, shouldn't it?
The closer you get to the center mining the more 'energy' in a interaction, if I'm thinking right?

Maybe it would work for a sf :)

Yeah, the equivalence principle is weird, but it seems to be correct as far as I know..

Although. http://news.softpedia.com/news/The-First-Test-That-Proves-General-Theory-of-Relativity-Wrong-20259.shtml   argues somewhat otherwise, possibly
 :)

But I suspect they got that one slightly wrong myself, although I would dearly like to see it tested, once and for all.
 

Offline yor_on

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Re: Does a photon have mass equivalent to its energy?
« Reply #62 on: 14/05/2012 21:42:16 »
It's an 'acceleration' to me lightarrow :) if we assume a wave picture for it, although I'm also questioning all 'motion' there is I'm afraid? And if you do so there it becomes no big deal calling it a 'acceleration' as 'motion' itself is misunderstood, well, possibly so?

I think it is anyway, eh, possibly :) When I think of it I believe we 'see things' from a instinctive definition, making sense to us, using a linear description inside a arrow, and that is the best working hypothesis we have. But it doesn't tell the whole truth, just the truth when looked at from one direction.

But I'm pretty weird :)
 

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #63 on: 15/05/2012 08:04:41 »
And what about those rotating black holes 'frame dragging'?
That should create a mass too, shouldn't it?
In GR the concept of mass becomes infinitely more smooth and vague:
http://en.wikipedia.org/wiki/Mass_in_general_relativity

(they say "more complex" but it's euphemistic  :))

As long as we stay in SR, I can talk about something; in GR, mass or energy is still...science fiction for me.
« Last Edit: 15/05/2012 08:06:45 by lightarrow »
 

Offline Phractality

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Re: Does a photon have mass equivalent to its energy?
« Reply #64 on: 15/05/2012 18:36:22 »
And what about those rotating black holes 'frame dragging'?
That should create a mass too, shouldn't it?
In GR the concept of mass becomes infinitely more smooth and vague:
http://en.wikipedia.org/wiki/Mass_in_general_relativity

(they say "more complex" but it's euphemistic  :) )

As long as we stay in SR, I can talk about something; in GR, mass or energy is still...science fiction for me.
If you want to get technical about it, mass doesn't belong in special relativity, at all. Mass has no meaning apart from gravity and acceleration, and the absence of gravity and acceleration is what makes SR "special". Einstein was bending the rules when he gave us a formula for relativistic mass.

When you talk about chemical processes (at the molecular level) and oscillating springs, you're talking about accelerations. At the atomic level, time can be reckoned in terms of electrons accelerating around a nucleus. The only sort of clock that doesn't involve acceleration is the theoretical light clock, in which light reflects back and forth between ends of a vacuum tube.

When we discuss mass in the context of SR, we also must bend the rules to include minimal gravity and acceleration within a bound system which has relativistic motion in the observer's reference frame. That's how I am able to talk about time dilation of a planetary system. The bodies accelerate toward one another, due to their mutual gravitational attraction. As long as motion within the planetary system is not a significant fraction of the speed of light, the formulas of SR can be applied to the planetary system which has relativistic speed in the observer's reference frame.

If the barycenter of a planetary system is moving at gamma = 10 in Frame A, time dilation slows the orbital period to 1/10th of what it is to an observer in Frame B, moving with the barycenter. So in Frame A, the acceleration is 10th normal. If both the gravitational mass and the inertial mass were 10 times normal, the attractive force would be 100 times greater, and the acceleration and orbital period would be 10 times faster, not 10 times slower.
(The problem is simple if the orbital plane is perpendicular to the line of relative motion of the barycenter in Frame A. For other orientations of the orbital plane, you have to take length contraction into account.)
 

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #65 on: 15/05/2012 20:00:07 »
If you want to get technical about it, mass doesn't belong in special relativity, at all. Mass has no meaning apart from gravity and acceleration, and the absence of gravity and acceleration is what makes SR "special".
Then you shouldn't even talk about energy and not even momentum, in SR. What you are left with? No mechanics at all, just kinematics. So long Galileo, so long Newton... :)
As long as the spacetime curvature introduced by the mass-energy is negligible (and notice that this is not just a rough way of proceding, all physics is based on this concept) you can use SR and treate even infinite accelerating bodies.
Anyway, if you find a simple concept which generalizes and unites all the various concepts of mass in GR, I will be very honoured to know it (and I say seriously).

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lightarrow

Quote
Einstein was bending the rules when he gave us a formula for relativistic mass.

When you talk about chemical processes (at the molecular level) and oscillating springs, you're talking about accelerations. At the atomic level, time can be reckoned in terms of electrons accelerating around a nucleus. The only sort of clock that doesn't involve acceleration is the theoretical light clock, in which light reflects back and forth between ends of a vacuum tube.

When we discuss mass in the context of SR, we also must bend the rules to include minimal gravity and acceleration within a bound system which has relativistic motion in the observer's reference frame. That's how I am able to talk about time dilation of a planetary system. The bodies accelerate toward one another, due to their mutual gravitational attraction. As long as motion within the planetary system is not a significant fraction of the speed of light, the formulas of SR can be applied to the planetary system which has relativistic speed in the observer's reference frame.

If the barycenter of a planetary system is moving at gamma = 10 in Frame A, time dilation slows the orbital period to 1/10th of what it is to an observer in Frame B, moving with the barycenter. So in Frame A, the acceleration is 10th normal. If both the gravitational mass and the inertial mass were 10 times normal, the attractive force would be 100 times greater, and the acceleration and orbital period would be 10 times faster, not 10 times slower.
(The problem is simple if the orbital plane is perpendicular to the line of relative motion of the barycenter in Frame A. For other orientations of the orbital plane, you have to take length contraction into account.)
 

Offline yor_on

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Re: Does a photon have mass equivalent to its energy?
« Reply #66 on: 16/05/2012 00:27:05 »
"the idea of accelerating a photon gives me "cold sweat""
Yep, somehow the universe seems to steered by equivalences, symmetries and?

That we find 'rules and regulations' is a very strong indication of there being real 'constants' to me. The question is what those constants are. I find 'c' to be the one relativity is built on, and 'c' is defined through SR.

It discuss a two way (mirror) experiment of reflected light in a vacuum, ignoring 'gravity' bending 'space', instead assuming a 'flat space'. And it seems to be correct? 'c' I mean, we've found all sorts of evidence for it, from frame dragging to ... Because what GR does is to add gravity 'distorting/bending/reshaping the 'space' that light 'propagates' in.

And that reshaping is equivalent both to a acceleration, and a 'weight'. But the spinning disk?? How does it create a mass? And why?
 

Offline lightarrow

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Re: Does a photon have mass equivalent to its energy?
« Reply #67 on: 16/05/2012 11:58:10 »
"the idea of accelerating a photon gives me "cold sweat""
Yep, somehow the universe seems to steered by equivalences, symmetries and?

That we find 'rules and regulations' is a very strong indication of there being real 'constants' to me. The question is what those constants are. I find 'c' to be the one relativity is built on, and 'c' is defined through SR.

It discuss a two way (mirror) experiment of reflected light in a vacuum, ignoring 'gravity' bending 'space', instead assuming a 'flat space'. And it seems to be correct? 'c' I mean, we've found all sorts of evidence for it, from frame dragging to ... Because what GR does is to add gravity 'distorting/bending/reshaping the 'space' that light 'propagates' in.

And that reshaping is equivalent both to a acceleration, and a 'weight'. But the spinning disk?? How does it create a mass? And why?

Sincerely I have understood...nothing of what you wrote (but it's probably me...) but maybe you ask how spacetime would be distorted in presence of a particular accelerating field, that is a centrifugal field? If it were 2-dimensional, you can imagine a sort of dome-shaped surface. But we are entering...esotericism here.
 

Offline JP

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Re: Does a photon have mass equivalent to its energy?
« Reply #68 on: 16/05/2012 13:11:59 »
Yor_on, if I understand you correctly, I believe you have to think not about energy or mass or momentum creating gravity/bending space-time.  You have to think about the stress-energy tensor as a source of gravity.  The stress energy tensor not only contains information about how much mass/energy/momentum an object has, but how that mass/energy/momentum flows over space and time, so the motion of objects causes gravitational effects that are different from if the objects were stationary.

The field of gravitomagnetism (http://en.wikipedia.org/wiki/Gravitomagnetism) deals with this, and likens gravity to electromagnetism: stationary masses emit a gravitational field, but moving masses generate a different gravitational field (much in the same way that stationary charges emit an electric field, but moving charges emit a magnetic field).
 

Offline yor_on

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Re: Does a photon have mass equivalent to its energy?
« Reply #69 on: 17/05/2012 10:14:52 »
There is a subtle difference to my thinking between uniform and accelerated 'motion'. And a spin can be perfectly uniform and still become a 'acceleration' as I see it. And then it must create a added mass, but from where would that very real mass come? The stress energy tensor?

How?

If that is correct I dearly wonder how you would explain define that from a Higgs boson, as we still see a uniform motion? In China they used to say that demons can't take angles, maybe that is it? Which ever way you look at it the geometry must have a importance for what is a acceleration. Using an idea of a 'field' you might formulate it differently though? And all respect for those gravitomagnetic analogues JP but to me gravity is a geometry, not 'forces'. And that makes it a real headache, because then we have 'fields' although not 'forces' acting.
 

Offline yor_on

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Re: Does a photon have mass equivalent to its energy?
« Reply #70 on: 17/05/2012 10:22:02 »
Maybe you could use the arrow for defining it? After all, it do have a 'direction' for us, and as far as I know there is no evidence for it being able to be 'played backwards', although we do find a temporal symmetry to it? Because without 'forces', what do we have?
==

Here is two interesting guys discussing 'gravity'.

http://www.einstein-online.info/spotlights/scalar-tensor
http://www.mathpages.com/home/kmath613/kmath613.htm
« Last Edit: 17/05/2012 10:30:32 by yor_on »
 

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Re: Does a photon have mass equivalent to its energy?
« Reply #71 on: 17/05/2012 13:07:41 »
There is some more points one seems to be able to make. Consider something 'weighlessly' orbiting our earth, their weigh and so gravity itself transformed away in their 'free fall'. Weight can't be mass even though it is 'coupled' to mass. So is the mass for those astronauts increased by them spinning around us? It can't be, they should be following a geodesic there, which can be expressed as the 'straight paths' of SpaceTime.

But it is still a spin to us observing them.
So what would consist a spin in SpaceTime?

Something that breaks a geodesic.
==

So how do you break a geodesic?

You need invariant mass for it. Bosons do not break geodesics. And you can't assume that something spinning in space as observed by you is breaking that geodesic. You need something like that plate spinning, confined in its mass.
« Last Edit: 17/05/2012 13:24:33 by yor_on »
 

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Re: Does a photon have mass equivalent to its energy?
« Reply #72 on: 23/05/2012 12:02:29 »
Quote from:  “Phractality”
PMB likes to use "μ" instead of "m0" and "m" instead of "mi".
I prefer to use what is best at the time I use it. Last night I was working on the basic derivations of SR such as E = pc for a photon and in general E^2 – (pc)^2 = (mc^2)^2jsyr.

Note: "μ" is sometimes used as proper mass density so I try to try

Notice that here I used m to mean proper mass. Otherwise its hard on my eyes for some reason.  ;D

only chose to use the letter "μ" in my paper. It was for two reasons

(1) There are many different concepts floating around in that apper I wanted to make sure it was a clear as could be.

(2) Greek letters are often used when people name proper quantities such as proper distance and proper time.
« Last Edit: 24/05/2012 12:24:46 by Pmb »
 

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Re: Does a photon have mass equivalent to its energy?
« Reply #73 on: 24/05/2012 15:28:27 »
Pete, perhaps you could clear up a question I've had.  I've done some work in quantum mechanics and a little in (special) relativistic quantum mechanics.  In that case, invariant mass is the mass of choice because it's generally easier in the math to deal with quantum particles in terms of their energy-momentum four vector by describing it in terms of rapidity (essentially an angle in space-time specifying its velocity in the lab frame) and its length (the invariant mass).

Could you comment on where relativistic mass sees use in physics?  Where do calculations get simplified by its use? 
 

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Re: Does a photon have mass equivalent to its energy?
« Reply #74 on: 24/05/2012 17:35:10 »
Pete, perhaps you could clear up a question I've had.
I'll do my best!

I've done some work in quantum mechanics and a little in (special) relativistic quantum mechanics.
The only relativistic quantum mechanics I've had touch with is towards the end of Liboff's Quantum Mechanics. So I don't feel qualified to comment there. Relativist mass obviously has no place in non-relativistic quantum mechanics. But I say that one should go with what they find easier to use. I know experts who teach rel-mass but who don't use in a great deal in their scientific publications. They tell me that they find it useful to think of, say, light having mass. I recommend not assuming that what one uses is practice is not what they use on the path to getting there. Texts on the Philosophy of Science point this kind of thing out. I'll scan that portion of my undergrad text in to a PDF file and make it available for you to read if you're interested.

Could you comment on where relativistic mass sees use in physics?  Where do calculations get simplified by its use? 
Moslty its not about calculations. Did you read my paper on the concept of mass in relativity? In the abstract I wrote
Quote
Although I argue for the usage of relativistic mass I do not argue that proper mass is not an important tool in relativistic dynamics.
So I'm not really disagreeing with you for the most part. The article explains much more than I can lay out here. For a compete answer please see and read http://arxiv.org/abs/0709.0687

I'll do my best in this post.

A lot of my paper discusses bulk systems with extended bodies instead of systems which are only systems of particles.

JP - Have you ever used special relativity in any other cases other than systems of particles? Consider this
Quote
Measuring the active gravitational mass of a moving object, D.W. Olson and R.C. Guarino, Am. J. Phys. 53(7), July 1985

If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that
 M_rel = \gamma(1 + \beta)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not \gammaM  but is 2\gammaM

As far as reasons people use rel-mass goes, I've aleady explained what I know in the paper I wrote and is located here and mentioned in this thread. It's online at http://arxiv.org/abs/0709.0687

I wrote a paper on this because it deserves a full treatment in all generality. Most people who ask the question you just did seem to have only systems of particles in mind and then only closed systems.

Special relativity is much richer than just using it in particle physics. Particle physicists seem therefore to never consider anything besides systems of particles.

The world is composed with continuos systems of matter. Such systems are described by the stress-energy-momentum tensor.

Take a look at Physical Principles of Cosmology by Peebles. It shows the density of active and passive gravitational mass as well as inertial mass densities. They are not the same! I.e. the density of active gravitational mass is different than the density of passive gravitational mass (this addresses a question someone was wondering about above). Inertial mass density is the same as the density of passive gravitational mass. Schutz rigorously derives the inertial mass density and shows that it's a function proper mass density and pressure.

Schutz's book touches on this in his text Gravity from the Ground Up so if you have that text look uo those terms.

In general, SR can be applied to anything in an inertial frame of reference in flat spacetime. It covers systems which are fully described by the stress-energy-momentum tensor. In Gravitation by Misner, Thorne and Wheeler, the authors use relativistic mass (which they simply call "mass") in their proof that the stress-energy-momentum tensor is symmetric. Schutz does the same thing in his GR text.

I considered a simple system which consists of a rod which was cooling down by radiating energy in the form of emitting photons/EM radiation. The question was to find the momentum of the rod using the relation  P = \gamma*m*v. If one tried to use that relation from a frame moving with respect to the rod then they'd get an error. I was finally able to get this page online yesterday. Please see

http://home.comcast.net/~peter.m.brown/sr/invariant_mass.htm

Please scroll down to where it says An Incorrect Application of Invariant Mass

Here's another web page I wrote on this subject to demonstrate how physicists - Well known physicists I mnight add - use the concept.
http://home.comcast.net/~peter.m.brown/ref/relativistic_mass/relativistic_mass.htm

Here is a list of articles I've read (at least most of them - I just can't recall which ones and iof I did read them all) on the concept of mass.
http://home.comcast.net/~peter.m.brown/ref/mass_articles/mass_articles.htm

Also take a look at the web pages at
http://home.comcast.net/~peter.m.brown/sr/sr.htm

Many of them use rel-mass to derive many SR relationships. They can all be derived using proper mass. However I myself found it easier using relativitic mass. All of our brains work differently and, to me anyway, its irrational to assume that all people think alike and therefore some people will find it easier and some will find it harder. I'm one of the people who finds it easier.

Here is something Guth told meto my face - He finds it easier somtimes to think of light as having mass.

Thinking about physics is much much more than deriving equations. Have you ever heard of Wheeler's First Moral Principle? It states
Quote
Never make a calculation until you know the answer. Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. Courage: No one else needs to know what the guess is. Therefore make it quickly, by instinct. A wrong guess brings refreshment of suprise. In either case life as a spacetime expert, however long, is more fun!
 

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Re: Does a photon have mass equivalent to its energy?
« Reply #74 on: 24/05/2012 17:35:10 »

 

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