[mxplxxx (OP)]

The famous e=mc2 equation seems to imply that mass and energy are interchangeable. Most people have this view. However, most bosons in the standard model are massless but do contain energy. This seems to strongly refute the interchangeability theory. I have also read recently that e=mc2 is just a conversion of mass units into energy units. This makes just so much sense when you try and think where the weird "speed of light squared" fits into the picture. So it may be that the equation is all about concepts rather than reality.

Also, can anyone tell me where I can obtain a picture of the standard model that contains how many quanta  (these will be whole numbers) are present in each particle in the table? And also, how do I convert quanta into mass?

[JP]

That equation only works for masses at rest with respect to you (the observer) and indicates the energy content of the mass of that object if you were to measure it at rest.  However, you're right that a Boson has zero mass, so how can it have energy?  Well, a zero-mass Boson can't be at rest!  So this equation doesn't hold for moving particles.  The correct form of the more general equation is:


E²=m²c⁴+p²c²

where p is momentum.  So a moving Boson can (and does) have momentum and therefore energy, even though its mass is zero.

[lightarrow]

The famous e=mc2 equation seems to imply that mass and energy are interchangeable. Most people have this view. However, most bosons in the standard model are massless but do contain energy. This seems to strongly refute the interchangeability theory. I have also read recently that e=mc2 is just a conversion of mass units into energy units. This makes just so much sense when you try and think where the weird "speed of light squared" fits into the picture. So it may be that the equation is all about concepts rather than reality.

Also, can anyone tell me where I can obtain a picture of the standard model that contains how many quanta  (these will be whole numbers) are present in each particle in the table? And also, how do I convert quanta into mass?

In addition to what JP wrote:
1. "it may be that the equation is all about concepts rather than reality" is nonsense in physics: either an equation is valid in a certain domain (and so it describes physical reality in that domain) or is not.
2. You cannot convert quanta into mass for the reason explained JP: massless particles can have energy (and so quanta of it) but, indeed, zero mass.
3. You cannot even find the number of quanta of energy in a particle of which you know the energy, if you don't have other informations. For example, for the quanta of electromagnetic field (photons) you have, at least, to know also the frequency of the field.

--
lightarrow

[mxplxxx (OP)]

That equation only works for masses at rest with respect to you (the observer) and indicates the energy content of the mass of that object if you were to measure it at rest.  However, you're right that a Boson has zero mass, so how can it have energy?  Well, a zero-mass Boson can't be at rest!  So this equation doesn't hold for moving particles.  The correct form of the more general equation is:


E²=m²c⁴+p²c²

where p is momentum.  So a moving Boson can (and does) have momentum and therefore energy, even though its mass is zero.

Thx JP. Problem with this equation is that p is momentum which is mass * velocity and many bosons do not have mass.

[chiralSPO]

momentum is not always defined as: p=m*v. In the case of a photon, p=h/λ.

[mxplxxx (OP)]

momentum is not always defined as: p=m*v. In the case of a photon, p=h/λ.

Thx for that. p=h/λ in units is Kg m/s=Joules.second/metres which seems on first glance to not make much sense at all (lets face it, what is Joules.sec anyway - I have an interesting post on this at http://www.thenakedscientists.com/forum/index.php?topic=41125.0). Bye the bye, getting units for all these types of equations is ridiculously hard.

[mxplxxx (OP)]

In a computer, reality is basically the digits (0/1) that make up the memory and the ability to manipulate the memory. Computer languages  translate concepts into digits. Reality appears to be made up of space, time and fields (energy being a property of a field) plus, maybe, a meta-field. Everything else seems to be some kind of an abstraction (concept) of these basic elements, much like a computer.  Hope I am not making a fool of myself here:).

What do you think of the possibility that e=mc2 is just a units of mass to units of energy conversion?

[mxplxxx (OP)]

3. You cannot even find the number of quanta of energy in a particle of which you know the energy, if you don't have other informations. For example, for the quanta of electromagnetic field (photons) you have, at least, to know also the frequency of the field.

Thx lightarrow. My reading of a quantum is that h equals energy times 1 second. The energy, e, in e=hf is energy per second. All quanta, no matter what their frequency contain h amount of energy in total. The frequency relates to the power of a quantum, i.e. how fast the h amount of energy is transferred. Energy is a constant but power varies.

[alancalverd]

Yes.

Energy-mass-energy conversion is an everyday phenomenon. If a sufficiently energetic (> 1.02 MeV) photon interacts with a nucleus it can produce an electron-positron pair (1.8 x 10^-30 kg) which then self-annihilates to generate two 511 keV photons.

This phenomenon is exploited in radionuclide imaging.

[mxplxxx (OP)]

Yes.

Energy-mass-energy conversion is an everyday phenomenon. If a sufficiently energetic (> 1.02 MeV) photon interacts with a nucleus it can produce an electron-positron pair (1.8 x 10^-30 kg) which then self-annihilates to generate two 511 keV photons.

This phenomenon is exploited in radionuclide imaging.

Thx alancalverd. Interesting stuff.

[lightarrow]

That equation only works for masses at rest with respect to you (the observer) and indicates the energy content of the mass of that object if you were to measure it at rest.  However, you're right that a Boson has zero mass, so how can it have energy?  Well, a zero-mass Boson can't be at rest!  So this equation doesn't hold for moving particles.  The correct form of the more general equation is:
E²=m²c⁴+p²c²
where p is momentum.  So a moving Boson can (and does) have momentum and therefore energy, even though its mass is zero.

Thx JP. Problem with this equation is that p is momentum which is mass * velocity and many bosons do not have mass.

That equation has no problems: if you put m = 0 in it (photons, gluons) then E = c*p: the energy of a photon is c times its momentum (light has momentum even in classical electrodynamics).

--
lightarrow

[lightarrow]

3. You cannot even find the number of quanta of energy in a particle of which you know the energy, if you don't have other informations. For example, for the quanta of electromagnetic field (photons) you have, at least, to know also the frequency of the field.

Thx lightarrow. My reading of a quantum is that h equals energy times 1 second. The energy, e, in e=hf is energy per second. All quanta, no matter what their frequency contain h amount of energy in total. The frequency relates to the power of a quantum, i.e. how fast the h amount of energy is transferred. Energy is a constant but power varies.

I answer to what I have underlined of your post.
No! First, h is not energy, is "action". Second, the quantum of energy in the EM field is h*f where f is the frequency, so the value of the quantum *does* depend on its field frequency.
Example: in a blue laser beam with (exact) wavelenght = 400 nm, every photon has an (exact) energy of 3.1 eV; in a red laser beam with (exact) wavelenght = 700 nm, every photon has an (exact) energy of 1.77 eV.

--
lightarrow

[lightarrow]

In a computer, reality is basically the digits (0/1) that make up the memory and the ability to manipulate the memory. Computer languages  translate concepts into digits. Reality appears to be made up of space, time and fields (energy being a property of a field) plus, maybe, a meta-field. Everything else seems to be some kind of an abstraction (concept) of these basic elements, much like a computer.  Hope I am not making a fool of myself here:).

It's always difficult to discuss about what reality is or should be; I am talking about physical reality, that is what can be measured, directly or indirectly, in the physical world.

What do you think of the possibility that e=mc2 is just a units of mass to units of energy conversion?

It is something more than that: it tells you (if you have already applied the equation: E² = (cp)² + (mc²)² with p = 0) that, in a frame of reference where the system has total momentum = zero, its total energy is m times c².
But if the system has not zero momentum, for example a car which is moving at speed v, then its total energy is not m times c², so, mass and energy are not interchangeable in that case.

--
lightarrow

[PmbPhy]

The famous e=mc2 equation seems to imply that mass and energy are interchangeable.

It depends on what you mean by that. To understand what it means you should follow the derivation at http://home.comcast.net/~peter.m.brown/sr/mass_energy_equiv.htm

I wrote a very highly detailed article on mass. It's online at
http://arxiv.org/abs/0709.0687

See also
http://home.comcast.net/~peter.m.brown/sr/inertial_mass.htm
http://home.comcast.net/~peter.m.brown/sr/invariant_mass.htm
http://home.comcast.net/~peter.m.brown/sr/einsteins_box.htm

 Here is what it means. If you have an object which is at rest in your frame of reference and its energy decreases by the amount dE then the mass decreases by the amount dm where dE = dm*c². Energy is never converted to mass and mass is never converted to energy because if there is a conversion process going on then there must be a change in energy. However since energy is a conserved quantity it means that no conversion can possibly take place. What is actually going on is that things like photons are created from particles which have non-zero proper mass and vice versa.

Most people have this view.

Not the ones who know what they’re talking about. One has to be very careful when discussing this subject because its easy to go astray. This is all explained very carefully in the article Does nature convert mass into energy? by Ralph Baierlein, Am. J. Phys., 75(4), Apr. (2007). The abstract reads

First I provide some history of how the equationE=mc 2 arose, establish what “mass” means in the context of this relation, and present some aspects of how the relation can be understood. Then I address the question, DoesE=mc 2 mean that one can “convert mass into energy” and vice versa?

However, most bosons in the standard model are massless but do contain energy. This seems to strongly refute the interchangeability theory.

It has to do with not being careful on the definition of mass. I’ve read your posts and it’s clear to me that when you use the term “mass” you mean “relativistic mass” since that’s define as the M in p = Mv. When defined like that even a photon has mass by virtue of its momentum. If this seems strange to you then don’t worry about it. I know what I’m talking about and can site you all the references in the best relativity textbooks that are out there to confirm what I’m saying. When you say ”The mass of a photon is zero.” What you’re really doing is contradicting what you said elsewhere since you used a different definition of mass when you said it. You meant the same thing that JP did when he defined mass. When you plug in the relationship between momentum and energy in his equation you’ll get zero.

I have also read recently that e=mc2 is just a conversion of mass units into energy units.

Whoever said that doesn’t know what they’re talking about.

This makes just so much sense when you try and think where the weird "speed of light squared" fits into the picture. So it may be that the equation is all about concepts rather than reality.

And also, how do I convert quanta into mass?

Please explain what you mean by this

Thx JP. Problem with this equation is that p is momentum which is mass * velocity and many bosons do not have mass.

Your dilemma is easily resolved when it is realized that the term mass hasn’t been defined yet and there are definitions being used here, one by you and one by JP.

Mxplxxx: the M in p = Mv

JP: the m in E² = m²c⁴ + p²c²

The two are related by the expression

M = m/sqrt[1 – (v/c²)]

If you’d like to see a list that someone put together regarding a sampling of books on special and general then I recommend looking at On the abuse and use of relativistic mass by Gary Oas, Education Program for Gifted Youth, Stanford University, Feb 2, 2008. It’s online at http://arxiv.org/pdf/physics/0504110.pdf

As you can see most of the authors in that list in the years leading up to the publication of the articleuse relativistic mass. If an author uses the term in his text or a book then it doesn’t necessarily mean that they use it in their professional work. However it seems to me that they probably think in those terms at times. For example; a friend of mine is a well-known cosmologist who doesn’t use it in his work but uses it in his lecture notes at one point. He told me that “Sometimes its useful to think of photons has having mass.” For example; if you were to look at Principles of Physical Cosmologyby P.J.E. Peebles, Princeton University Press, (1993), page 643, Peebles states the expansion rate equation in Eq. (25.60) and refers to the second term as the relativistic mass in radiation…

Before I go on to addressing the question at hand I want to explain why JP wrote That equation only works for masses at rest with respect to you? He wrote this because he’s using a different definition of mass than you are.

Any questions?

[PmbPhy]

I should point out that what's going on in situations like pair annihilation/production is that the form of the matter is what's being converted.

[mxplxxx (OP)]

3. You cannot even find the number of quanta of energy in a particle of which you know the energy, if you don't have other informations. For example, for the quanta of electromagnetic field (photons) you have, at least, to know also the frequency of the field.

Thx lightarrow. My reading of a quantum is that h equals energy times 1 second. The energy, e, in e=hf is energy per second. All quanta, no matter what their frequency contain h amount of energy in total. The frequency relates to the power of a quantum, i.e. how fast the h amount of energy is transferred. Energy is a constant but power varies.

I answer to what I have underlined of your post.
No! First, h is not energy, is "action". Second, the quantum of energy in the EM field is h*f where f is the frequency, so the value of the quantum *does* depend on its field frequency.
Example: in a blue laser beam with (exact) wavelenght = 400 nm, every photon has an (exact) energy of 3.1 eV; in a red laser beam with (exact) wavelenght = 700 nm, every photon has an (exact) energy of 1.77 eV.

--
lightarrow

Judging by the number of people in physics asking the meaning of e=hf, it is reasonable to ask if the equation is correct. Many in the physics community are deciding that it is not. I explain why in http://www.thenakedscientists.com/forum/index.php?topic=41125.0. The post has been viewed by 1537 people and only one reply has been forthcoming. Not certain what this means but am sure if I was talking rubbish I would get many challenges. Basically, the proposition being put by many physicists (and me) is that the quantum is one of energy, not action. This proposition takes so much weirdness out of quantum mechanics. Lets face it, no one really knows how a quantum of action relates to reality.

[PmbPhy]

My reading of a quantum is that h equals energy times 1 second.

That's quite wrong. If you wrote it out then you'd see that your statement is dimensionally incorrect. I.e. Let

J = Joule = dimension of energy
S = Second = dimension of time

E = hf ==> E[J] = h[J*S] f[1/S]

h = E/f ==> h[J*S] = E[J]/f[1/S] = (E/f) [J*S]

That’s how you’d check to see whether an expression is dimensionally correct. Let’s try your assertion. You claim that if you multiplied Planck’s constant, h, by 1s then you’d get energy (although you never told us what this quantum is. Is it a photon?). Let’s try it

h[J*S] 1s = h [J*S^2]

which is wrong. QED

Here is what E = hf means. First off it applies to zero mass particles only.

The energy, e, in e=hf is energy per second.

That is incorrect. That expression has units of energy, not power. It is the energy of one quantum. For example; if there is a photon whose frequency is f then the energy that the photon has is E = hf

All quanta, no matter what their frequency contain h amount of energy in total.

That’s incorrect. h is not an amount of energy. You’ve never studied quantum mechanics, have you?  Let’s take photons an example. Different quanta can have different values of energy. You’re incorrectly claiming that’s wrong. The expression E = hf is the expression which tells you how much energy a photon has given the frequency of the photon. The greater the frequency of the photon the greater the photon’s energy. What you said above is quite wrong

The frequency relates to the power of a quantum, i.e. how fast the h amount of energy is transferred. Energy is a constant but power varies.

No. You have it all wrong. See above. Energy is delivered in lumps, not the way you think it does.

Where on Earth did you get these ideas from?

[PmbPhy]

Judging by the number of people in physics asking the meaning of e=hf, it is reasonable to ask if the equation is correct. Many in the physics community are deciding that it is not.

That's quite untrue. That postulate has been around for nearly 105 years now and is has been born out buy experiment countless times during the last 105 years. No professional physicist would ever make such an assertion.

I explain why in http://www.thenakedscientists.com/forum/index.php?topic=41125.0.

Seriously flawed. That it has to be in the New Theories forum tells us as much. I read that page and it's clear that it's written by someone who never sat down and studied physics head to toe but only picked up small disconnected peices all over the place and can't make heads or tales out of it as a result.

The post has been viewed by 1537 people and only one reply has been forthcoming.

That's because it's meaningless.

Not certain what this means but am sure if I was talking rubbish I would get many challenges.

No. That's not the reason. The reason is that we recognize that you'd be unable to understand the responses. After many years experience in doing this we've come to see first hand what happens when we tried and it's never pretty. So we stop trying. For example:

"A photon IS one cycle of an electromagnetic wave."

All physicists know that one of the reasons that classical EM fails on the subatomic level is that such a continuos electromagnetic wave interacting with atoms doesn't behave in the way that it's predicted to when one does the calculation. We know that photons don't behave like electromagnetic waves. Your comment here shows us that you're not taking that into account and are ignoring experimental facts.

Basically, the proposition being put by many physicists (and me) is that the quantum is one of energy, not action.

I find that impossible to believe. If what you claim is true for "many" physicists then you should be able to name just one. Please do so.

This proposition takes so much weirdness out of quantum mechanics. Lets face it, no one really knows how a quantum of action relates to reality.

Total nonsense. All physicists know what Planck's constant is and how it relates to reality.

No wonder I don't like this subforum.

[mxplxxx (OP)]

Total nonsense. All physicists know what Planck's constant is and how it relates to reality.

Hi PmbPhy. I was talking about the Quantum of Action. If you can define and explain this entity, then I take my hat off to you. Care to have a try? You are aware, I assume, that all quanta contain the same amount of action. I am sorry to say that many physicists do not understand Planck's constant - at least that is what I glean from my adventures on physics forums. In fact, many physicists seem unaware of the Quantum of Action (this discussion of mine on Physics Forums makes this quite clear http://www.physicsforums.com/showthread.php?t=367434).

[mxplxxx (OP)]

I find that impossible to believe. If what you claim is true for "many" physicists then you should be able to name just one. Please do so.

Juliana Brooks Mortenson at generalresonance.com