Electromagnetic Wave have momentum

[iNow]

Where do morals come from if you're atheist?

[Mr Skeptic]

Pete, thanks for the link to your paper. I am still going through it. Oh, and I can't see where there should be an [math]m_0[/math] in your paper. It appears to me as a box. When I get home I'll find out whether it is the stupid college computers or not, that is the reason.

 

Perhaps it is time that we use the terms [math]m_0[/math] for proper mass, and [math]\vec m_p[/math] or something for relativistic mass, rather than using m, to avoid all this confusion. Then we can let the lexicographers argue.

[Pete]

I've changed my mind for the moment. I've decided to PM people when I want to mention this subject. Otherwise I'll avoid the subject. I have to say that this cencorship is a poor way to run a forum though.

Pete, thanks for the link to your paper. I am still going through it.

You're very welcome. Due to the censorship mentioned above I've decided that is how I will be handling things like that in the future, i.e. not in open forum but in PM

Oh, and I can't see where there should be an [math]m_0[/math] in your paper. It appears to me as a box. When I get home I'll find out whether it is the stupid college computers or not, that is the reason.

Please let me know. Its probably a problem with the font. I had struggled with what symbols to use. I wanted the reader to focus on the subject and not be worried about notation and whether they symbols used were "pretty" or not. There were even times when I chose to use [math]\mu[/math] for [math]m_0[/math]. There is a general tendancy to replace write proper quantities with the associated Greek letter. Thus [math]\tau[/math] is used for t and [math]\sigma[/math] is used for s. [math]\mu[/math] is theGreek letter for m.

Perhaps it is time that we use the terms [math]m_0[/math] for proper mass, and [math]\vec m_p[/math] or something for relativistic mass, rather than using m, to avoid all this confusion. Then we can let the lexicographers argue.

I dislike that notaton myself. Mass is not a vector quantity. The complete definition of mass requires a second rank tesor to fully describe it, i.e. the stress-energy-momentum tensor. From that tensor one can see that pressure is also a source of inertia. If you have Schutz's book on GR then you can see how it is derived. Schutz has a nice GR book. Have you read it?

 

iNow - In case you forgot I placed you on my ignore list. You should keep that in mind in case you were expecting me to either read your post or post a response.

Edited November 12, 2008 by Pete

[swansont]

I've changed my mind for the moment. I've decided to PM people when I want to mention this subject. Otherwise I'll avoid the subject. I have to say that this cencorship is a poor way to run a forum though.

 

Which definition of "censorship" are you using? I see absolutely no evidence of any censorship going on here.

[Pete]

Which definition of "censorship" are you using? I see absolutely no evidence of any censorship going on here.

Huh? Who said that there was? I sure didn't. I was referring to what Martin indicated would be the case in the future regarding the definition of mass. Recall Martin's comment

You are trying to promote a minority word usage, and I would recommend that you stop voluntarily, or that all links to your site be deleted.

I consider things like deleting those links (which are URLs to references, derivations and "textbook" definitions) as being censorship.

 

I've already decided what to do in the future so there is no longer a problem. Let's let this die shall we?

[iNow]

Which definition of "censorship" are you using? I see absolutely no evidence of any censorship going on here.

 

Pete's definition appears to be one where the "censorship" is perceived-only, and further, only the possibility of censorship which might happen in the future.

 

I guess it's the non-realized perceptual-potential censorship definition... You know, the standard definition.

[Severian]

Yes. It is. Please do more than merely say "No its not." since merely objecting helps nobody.

 

You made a claim that there was no way to define (proper) mass in all cases. I gave you a counter example.

 

When are you restricting the definition to a the very specific case of elementary particles rather than being as general as possible? Especially in those cases when a body is under stress as in the example I gave.

Everything is made up of elementary particles, so it seems a reasonable place to start. Of course, when you have composite systems, you then have to take into account the interactions within the system. The proton mass for example is not just the mass of the quarks summed up - you have a contribution from the strong force too. (Technically, the mass of the proton is the coefficient of the bilinear term in the effective Lagrangian.)

 

However, I had made the reasonable assumption that we were talking about free bodies with no external forces. If you are present when a friend weighs themselves, do you put your foot on the scales? In your "proof", you apply an external force so it is not surprising you get different answer. If you set the external force to zero, then your own equations have [math]E=\gamma mc^2[/math] and [math]p=\gamma m \beta c[/math] (I have taken the liberty of rewriting the "m" in your equations in terms of the (what you would call the "proper") mass [math]m[/math]), so that (lo and behold!) [math]E^2-p^2c^2=m^2c^4[/math].

 

For the record, I have no objection to using the quantity [math]\gamma m[/math] in any calculations or physics discussions. My objection is to the name you use (mass) and the symbol [math]m[/math], because it causes no end of confusion. At the very least, you should quote the frame of reference in any name for [math]\gamma m[/math] since it is frame dependent, so I would even object to calling it "relativistic mass". Something like "the effective mass in frame S" would be OK though. (Also not that I never said Gilded post was wrong - I just said it was a horrible way of expressing it.)

[Pete]

You made a claim that there was no way to define (proper) mass in all cases. I gave you a counter example.

As I've already stated, your counter example is flawed. Is there a reason why you ignored the explanation I gave as to why?

However, I had made the reasonable assumption that we were talking about free bodies with no external forces.

I don't follow. When exactly did you make this assumption? Was it before or after I gave a proof? And why would you make such an assumption? You asked for proof of my assertion so I provided a proof by giving a counter example which clearly stated that there were external forces acting on the body.

If you are present when a friend weighs themselves, do you put your foot on the scales?

I don't follow. How is that relevant to the example I gave?

In your "proof", you apply an external force so it is not surprising you get different answer.

Why do you think that "it is not surprising"? From your comments it seems to me that we're not talking about the same thing. I had stated that one cannot define proper mass for a body in all possible cases. To prove such an assertion one merely has to provide an example where a proper mass can't be defined and that is exactly what I did.

If you set the external force to zero, then your own equations have [math]E=\gamma mc^2[/math] and [math]p=\gamma m \beta c[/math] (I have taken the liberty of rewriting the "m" in your equations in terms of the (what you would call the "proper") mass [math]m[/math]), so that (lo and behold!) [math]E^2-p^2c^2=m^2c^4[/math].

Its the stress that is non-zero. The total force on the body could very well be zero though. I neglected to mention that fact. I.e. that even when the total external forces on the object is zero the example I gave still holds.

 

Let me be more concrete example: Consider an inertial frame of reference S in which there is a rod lying at rest along the x-axis. Let there be applied a force to each end of the rod (these forces are parallel to the x-axis) which are equal and opposite. The total force is zero but now there is stress in the rod. Now transform to the inertial frame S' which is in standard configuration with S. The rod is moving in this frame with speed v. The inertial mass of a body is defined as m = p/v. The rest mass is defined in the limit as v -> 0. If the stressed rod were lying parallel to the y-axis rather than the x-axis then m would have a different value.

 

 

It is important to keep in mind here that in such a case the relation E = mc² no longer holds. If E is the total inertial energy of the rod (defined as the kinetic energy plus kinetic energy) and p is the total momentum of the rod then the quantity (E,p) will not be a 4-vector and, contrary to your assumption, the magnitude will not be invariant and thus no proper mass can be defined. I.e. there does not exist a 4-momentum for the object in such a case. Since there is no 4-momentum one can't define a magnitude for it and thus one cannot define a proper mass.

 

A similar case is to consider the mass of a gas which is contained in a box. The inertial mass of the gas will be a function of the pressure of the gas. To be precise the inertial mass density of the gas is given by

 

Inertial mass density = [math]\rho + p/c^2[/math]

 

This is an example when the 4-momentum won't give you the inertial mass of quantity and one must use the stress-energy-momentum tensor.

 

At the very least, you should quote the frame of reference in any name for [math]\gamma m[/math] since it is frame dependent, ..

The frame is always implied. There is little use in stating "As measured in frame S" since it is implied that one is refering to a particular frame of reference. This is normally true whenever any frame dependant quantity is being discussed.

 

In case anyone is wondering whether this all merely academic or not, consider the fact that when one calculates mass density in such applications such as calculating active gravitational mass. In cosmology there are objects known as a vacuum domain wall and the better known cosmic strings. A domain wall has tension in it (negative pressure) which acts to oppose the positive mass-energy and gives a net result of a negative active gravitational mass. This means that a vacuum domain wall gravitational repels objects away from it (these objects are described in Peebles book on cosmology).

[Severian]

As I've already stated, your counter example is flawed. Is there a reason why you ignored the explanation I gave as to why?

 

OK - I'll be nice, tolerant and cuddly. Let's go through your "proof" at http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm one step at a time.

 

"Consider a square box at rest"

 

What do you mean by this? What is a "box"? Is it defined just as a volume of space? Is it a collection of interacting particles which just happen to fill a box? Is it a rigid body? What is this box?

[Pete]

OK - I'll be nice, tolerant and cuddly.

As opposed to what?

Let's go through your "proof" ..

Why do you keep putting proof in quotes?

What do you mean by this? What is a "box"? Is it defined just as a volume of space? Is it a collection of interacting particles which just happen to fill a box? Is it a rigid body? What is this box?

You're telling me that you don't know what a box is? When following a derivation one starts with basic knowledge (like what a box is. If you can't figure out what a box is then look the term up in a dictionary) and goes from there. If, during the process, the construction of the box becomes important then one becomes more precise at that time. I'll give you a hint - What I mean by "box" is identical to what the author of this paper means

 

The mass of a gas of massless photons, H. Kolbenstvedt, Am. J. Phys. 63(1), January 1995

 

I can upload this onto my website if you are unable to figure out what a box is. If you have Schutz's new book Gravity from the Ground Up then crack it open since he means the exact same thing. A box is a box is a box. A box is rigid by definition.

 

In any case the example I gave was about a rod, not a box. And the expression for the energy-momentum tensor can easily be ontained merely by transorming the tensor from a frame of rest to a moving frame using a Lorentz transformation

[Severian]

A box is rigid by definition.

 

Are you aware that there is no such thing as a rigid body in relativity?

 

Since you like Rinder so much, let me quote him on page 36:

 

"One consequence of the relativistic speed limit is the "rigid bodies" and "incompressible fluids" have become impossible objects, even as idealizations or limits."

 

So are you sure your box is rigid?

[Pete]

Are you aware that there is no such thing as a rigid body in relativity?

Yes. I'm very aware of that fact. But so what? Why do you mention it? Nothing in what I've said so far has anything to do with the problems of rigidity. A box with a gas in it is in dynamic equilibrium.

 

Do you understand what Rindler means when he speaks of the problems of the rigidity of an object? He is not referring to any problem with a box having rigid walls and thus can contain a gas and maintain the shape of a box. He's referring to the fact that it a disturbance on an object does not propagate instantaneously throughout the body.

Since you like Rinder so much, ..

Rindler is a supurb author and relativist. His books are very good in that they are quite comprehensive. They address subtleties that most other texts ignore.

So are you sure your box is rigid?

By rigid I'm refering to the fact that the walls of the box are sturdy (i.d. they are not made out of rubber).

 

Now that I've answered your questions perhaps you'll answer mine.

 

Why do you keep putting proof in quotes?

[swansont]

Why do you keep putting proof in quotes?

 

I imagine it's because Severian thinks it invalid.

 

Can we dispense with the melodrama and stick to the physics?

[YT2095]

As you may be aware light bends around a dent in the spatial fabric. It responds to the presence of mass,that is to gravity.

 

actually I always thought that it was Space that bends due to gravity and that the light within that space was traveling in a straight line?

[swansont]

actually I always thought that it was Space that bends due to gravity and that the light within that space was traveling in a straight line?

 

Basically saying the same thing. Mass/energy bends space, and light follows a geodesic.

[Pete]

I imagine it's because Severian thinks it invalid.

That was my point and he should merely state that and then he should look the derivation up in a text like Rindler's or Tolman's. This is not new physics or something I created/imagined. When people do things like this (put terms like "proof" in quotes) it tends to indicate that they're not taking the subject seriously.

Can we dispense with the melodrama and stick to the physics?

melodrama ? What makes this a melodrama? Is it because I wanted to know why Severian has this attitude before he starts attempting to follow a derivation? It will just make it harder for him to follow. Its not wise assuming something is in error before you start to follow it.

 

If Severian figures out what a box is and why rigidity has nothing to do with the topic/derivation then we can move forward. Its not as if boxes (or box-like objects such as a cylinder) haven't been used in relativity thought experiments before. Einstein was the first to do so in fact in what has come to be known as Einstein's famous "photon in a box" experiment.

 

Severian - If you have Rindler's SR text then I suggest that you read the chapter on continuum mechanics and learn this material from there or perhaps even from Tolman's SR/GR text. Do you have either of these books?

Edited November 15, 2008 by Pete

[swansont]

melodrama ? What makes this a melodrama? Is it because I wanted to know why Severian has this attitude before he starts attempting to follow a derivation? It will just make it harder for him to follow. Its not wise assuming something is in error before you start to follow it.

 

Derailments such as this. Inquiries about attitude and motivation. One can ignore them and get on with the proof. Or not. I prefer the former.

[Pete]

Derailments such as this. Inquiries about attitude and motivation. One can ignore them and get on with the proof. Or not. I prefer the former.

 

Its annoying when a moderator asserts that someone is being melodramatic when they ask a question to someone who doesn't seem to be taking a derivation/proof seriously. Such comments have an effect which is opposite to the desired one. Have you ever considered using Pm for such comments?

Edited November 16, 2008 by Pete

[swansont]

Its annoying when a moderator asserts that someone is being melodramatic when they ask a question to someone who doesn't seem to be taking a derivation/proof seriously. Such comments have an effect which is opposite to the desired one. Have you ever considered using Pm for such comments?

 

Yes. I also considered infractions. I chose neither.

 

All of the sudden I feel like it's the scene in My Cousin Vinny where Pesci refuses to say "Not Guilty."

 

How about we focus on the physics?

[Pete]

I also considered infractions.

Infraction regarding what? Asking why someone posted something the way they did or for objecting to certain assertions that were made?

How about we focus on the physics

I'm not the one who isn't focusing on the physics.

Edited November 16, 2008 by Pete

[swansont]

I'm not the one who isn't focusing on the physics.

 

No? How much physics is contained in your last three posts? Why has discussion of your proof stalled? We have a box. That's it.

[Pete]

No? How much physics is contained in your last three posts?

You're the one who keeps posting these provoking non-physics comments. How much physics has been in your last few posts? If you had instead chosen to simply let my question to Severian alone then the thread wouldn't have taken this turn. Your actions have consequences you know.

Why has discussion of your proof stalled?

It hasn't stalled. Severian has probably chosen not to pursue it any further. Did you consider that perhaps he took my advice and looked the proof up in Rindler's text?

 

The entire proof is contained in the web page I posted the URL to and from which Severian was quoting. The web page is at http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

 

Perhaps Severian merely chosen not to pursue this subject any further. In any case the proof is on that web page for all to follow. All Severian asked me was what a box is and that's not something that needs an explanation. I assumed a certain level of knowledge of the reader and that includes what a three year old should know, i.e. what a box is. I replied by using the term "rigid" which was a poor choice of a word. I should have used the term "solid" instead.

We have a box. That's it.

Wrong. The derivation has everything that one needs to know in order to follow it. How can you make such a statement if you read that page? If you didn't read the page when why are you assuming that there is lack of proof or a stalled proof? Edited November 16, 2008 by Pete

[iNow]

assumed a certain level of knowledge of the reader and that includes what a three year old should know

Speaking of 3 year olds, Pete... Geeez... Come on already.

[swansont]

You're the one who keeps posting these provoking non-physics comments. How much physics has been in your last few posts? If you had instead chosen to simply let my question to Severian alone then the thread wouldn't have taken this turn. Your actions have consequences you know.

 

My user name is in blue. That has implications, you know.

[Pete]

My user name is in blue. That has implications, you know.

That's a pretty lame response. When you post comments as you keep insisting on doing which are intended to provoke (or don't you realize that what you are posting are provoking comments?) then you should be prepared to accept the responses that you get when you take such action and not constantly whine about them as you keep doing. Are you so ignorant that you couldn't figure that out and instead responed with a totally irrelavant comment as you have in your last response? Edited November 16, 2008 by Pete
multiple post merged