Exploring Relativistic Mass with pmb_phy: A Conversation on Its Relevance

[Aer]

I wish to converse with you on your brand of relativistic mass.

Pervect, can you direct me to the thread where pmb_phy convinced you relativistic mass was useful?

 

[pmb_phy]

I wish to converse with you on your brand of relativistic mass.

Pervect, can you direct me to the thread where pmb_phy convinced you relativistic mass was useful?

There is no thread that convinced me of anything. I doubt there is one thread that can/should convince anyone of anything. Being that mallable on one's ideas in physics (science) is never a good idea. I came across this debate (not really much of a debate really) back about 15 years ago. Later in about 1997 some people were swearing by it and claiming everone used it and how rest mass was the only "real" mass yadda yadda yadda. I spent the following 7 years studying the subject to form an opinion. My opion is that if you want to give a meaning to the word "mass" then the term which posseses the inertial, passive gravitational and active gravitational mass then it is what you refer to as "relativistic mass."

If you want the details then read this
http://www.geocities.com/physics_world/mass_paper.pdf

Warning - I poorly proof read that work. It took so long to write that it had a ton of errors in it (few conceptual errors. only one that I'm aware of. just repetition and poor phrasing etc). I haven't gotten time to rerwrite it. Have fun - Warning. Its over 80 pages long.

The error I mention I am my paper is when I made the assumption that E = mc^2 in all cases. A counter example is here
http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

For more on why E != mc^2 in all cases see Rindler's text if you have a copy of it or access to it.

For other stuff see http://www.geocities.com/physics_world/misc/relativistic_mass.htm
http://www.geocities.com/physics_world/misc/mass_articles.htm

As far as anything else I'm pretty talked out of this topic and will simply be referring to that stuff inn the future. I've been rather sick for a while and don't have the strength for much posting.

Pete

 

[ohwilleke]

You have our best wishes to get well. Take care.

 

[pmb_phy]

However there is Wheeler's First Moral Principle which states "Never make a calculation until you know the answer[/i]. This implies that you should seek ways of thinking such that you have an idea of what the answer should be and if you get something totally unexpected then you need to rethink or be happy in your surprise. For example; I read a paper which did a rather round about calculation to find an answer for the deflection of a particle. The reason for the answer didn't seem right. However when looked at with gravitomagnetism keeping in mind that the active gravitational mass = relativistic mass, then the reason be comes clear.

If you can get a good idea of an amount without calculation then you've made a good jump in your knowledge and understanding of a subject.

Peter

 

[Aer]

There is no thread that convinced me of anything.

Perhaps your reading comprehension needs a little adjusting.

I doubt there is one thread that can/should convince anyone of anything.

Well, we shall create one.

Being that mallable on one's ideas in physics (science) is never a good idea.

Being completely wrong is never a good idea either.

I came across this debate (not really much of a debate really) back about 15 years ago. Later in about 1997 some people were swearing by it and claiming everone used it and how rest mass was the only "real" mass yadda yadda yadda. I spent the following 7 years studying the subject to form an opinion. My opion is that if you want to give a meaning to the word "mass" then the term which posseses the inertial, passive gravitational and active gravitational mass then it is what you refer to as "relativistic mass."

Tell me, what is your definition of mass? Just mass, no adjectives or anything - I just want to know your definition of mass so we can work from there.

If you want the details then read this
http://www.geocities.com/physics_world/mass_paper.pdf

I've seen your paper and do not agree with it. So like I said, let's start with the definition of mass. Give me your definition.

Have fun - Warning. Its over 80 pages long.

Yeah, let's not refer to long winded discussions on the internet. You should be able to back up any argument on your own without referring to authority or your own work published elsewhere. I mean, we are talking about one basic concept - mass. So, what do you define mass to be - a concise answer is what I am looking for.

 

[εllipse]

Objects have proper lengths and clocks measure proper times, but we don't throw out the idea of relative lengths and times. Although a meter stick may still be a meter in your reference frame, if it's moving relative to me, it will have a relative length which is smaller. It's the same with mass. Invariant mass may be the most helpful concept from one viewpoint or relativistic mass may be the most helpful from another.

 

[Aer]

Objects have proper lengths and clocks measure proper times, but we don't throw out the idea of relative lengths and times.

The proper length and contracted length are defined through the lorentz transformations. These are meaningful when dealing with "events" that happen in space-time.

To quote Einstein himself:

"It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

 

[EnumaElish]

Aer -- I "hear" doctor Einstein's quote. But on a purely technical note, one can define relativistic mass through a similar transformation: $M = \gamma \times m$, right? The concept may be misapplied, misdirected, improperly used, unbecoming of a physicist, auxiliary at best, etc., but there is a narrow technical sense in which one cannot say that M is ill-defined.

 

[Aer]

but there is a narrow technical sense in which one cannot say that M is ill-defined.

How wrong you are - it is technically an ill-defined quantity if it is in anyway referred to as "mass". Then we have people like pmb_phy claiming a contained gas's weight is a measure of the rest mass of the particles PLUS the kinetic energy they possess. UMMM - NO! That's wrong, the weight is only a measure of the rest mass of the particles and nothing more.

 

[EnumaElish]

One wonders, though, why and how could anyone come up with such a grand misconception? I mean, confusing mass and energy?! Thinking they could be the same? At best this is alchemy, if not outright heresy! Even I can understand something's wrong there, although I am no Einstein

Sorry, I couldn't contain myself.

 

[Aer]

I mean, confusing mass and energy?! Thinking they could be the same?

Well, mass is a form of energy, yes. But mass has nothing to do with kinetic or potential energy.

 

[learningphysics]

How wrong you are - it is technically an ill-defined quantity if it is in anyway referred to as "mass". Then we have people like pmb_phy claiming a contained gas's weight is a measure of the rest mass of the particles PLUS the kinetic energy they possess. UMMM - NO! That's wrong, the weight is only a measure of the rest mass of the particles and nothing more.

pmb_phy is completely right. This has nothing to do with ill defined quantities.

When you measure your own weight on a scale... the number you get is not the sum of the rest masses of all the particles that make up your body... the number you get is much much higher than that.

The rest mass of a "set of particles" is not the sum of the rest masses of the constituent particles.

 

[learningphysics]

Perhaps your reading comprehension needs a little adjusting.

You really shouldn't insult someone who took the time to respond to your post despite the fact that he was tired of the topic.

Yeah, let's not refer to long winded discussions on the internet. You should be able to back up any argument on your own without referring to authority or your own work published elsewhere.

Why should he bother? He's not trying to make any argument here... You asked for his input and he gave it to you. Then you turn around and insult him for it.

 

[Aer]

learningphysics - based on my previous experience with you, I am going to assume you have no idea what you are talking about.

OK, I don't have to assume from memory anymore, here is a quote by you:

link to your post

Relativistic mass = inertial mass

NO! And I am going to assume your misunderstanding stems from reading posts/websites by pmb_phy.

 

[Aer]

Why should he bother? He's not trying to make any argument here... You asked for his input and he gave it to you. Then you turn around and insult him for it.

I merely asked for his definition of mass. He can freely choose to ignore if he wishes.

 

[JesseM]

Then we have people like pmb_phy claiming a contained gas's weight is a measure of the rest mass of the particles PLUS the kinetic energy they possess. UMMM - NO! That's wrong, the weight is only a measure of the rest mass of the particles and nothing more.

Are you sure about that? the last question from this FAQ says that the apparent inertia of a black box filled with a gas will increase as the temperature increases, which I would think would mean the weight would increase as well:

If you set up a "black box" (box you can't see into) containing some atoms, the total mass of the box and its contents will be equal to the sum of the mass of the box and mass of the individual atoms in the box. If you heat the box to a high temperature (so the atoms are moving around at high speed in the box, and thus have high energy), then the total mass of the box and its contents will be larger than if the temperature of the box is lower. Why? Because, the higher energy atoms contribute more mass to the total mass than before the box was heated. So, if you try to push on the box, you will discover that its inertia will be larger (it won't accelerate as quickly).

In a practical setup of this box containing gas, the actual change in inertia of the box (due to heating it) will be small. But, in principle, if the atoms are made to move at speeds nearing the speed of light, the mass of the box can be made very large --- even approaching infinity.

Also, in a post on this thread "Tom Roberts" describes the definition of rest mass for a composite object:

The nomenclature is simple and obvious: the mass of an object is its
total energy in its rest frame. For composite objects this includes any
motion of its constituents in this frame, their binding energy in this
frame, etc. Note that a composite object need not be bound, and this
still applies (e.g. one can measure the mass of a gas in a given
volume), but sometimes this leads to weird situations (e.g. what is the
mass of the "object" consisting of two rocket ships headed in different
directions?). So it is really only useful for objects for which one can
identify an obvious rest frame, and all parts of the object are
localized in that frame.

So, this would indicate that the rest mass of a box of gas is defined to be simply the sum of the relativistic masses of all the atoms in it, since this is equal to the total energy (assuming energy in other forms, like the potential energy between the particles that make up the atoms, can be ignored).

 

[Aer]

Are you sure about that? the last question from this FAQ says that the apparent inertia of a black box filled with a gas will increase as the temperature increases, which I would think would mean the weight would increase as well:

From that same FAQ, that answer is to the following question: "Einstein said that if something could travel at light speed its mass would duplicate".

Einstein said that? No he didn't. That is just something that other people have wrongly interpreted from his equations.

If you wish to read something Einstein actually said:

"It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

If you are going to refer to authority, do so correctly next time.

 

[JesseM]

From that same FAQ, that answer is to the following question: "Einstein said that if something could travel at light speed its mass would duplicate".

Einstein said that? No he didn't. That is just something that other people have wrongly interpreted from his equations.

Yes, but FAQ questions do not represent the point of view of the author, only the answers do. And see the thing about the definition of the rest mass of a composite object I added in an edit.

 

[Aer]

Yes, but FAQ questions do not represent the point of view of the author, only the answers do. And see the thing about the definition of the rest mass of a composite object I added in an edit.

Who answered these questions? Was this person qualified? It would seem he is not qualified if he didn't correct the person asking the question as to what Einstein actually said.

 

[learningphysics]

learningphysics - based on my previous experience with you, I am going to assume you have no idea what you are talking about.

OK, I don't have to assume from memory anymore, here is a quote by you:

link to your post
NO! And I am going to assume your misunderstanding stems from reading posts/websites by pmb_phy.

Well here's another post of mine:

https://www.physicsforums.com/showpost.php?p=688394#post688394

I've posted links to course notes using the same definition of inertial mass.

 

[Aer]

Also, in a post on this thread "Tom Roberts" describes the definition of rest mass for a composite object:

You are standing in very thin waters if you think this any authority in relativity.

the mass of an object is its total energy in its rest frame

should be "the mass of an object is the sum of all its constituents' rest masses".

 

[Aer]

Well here's another post of mine:

https://www.physicsforums.com/showpost.php?p=688394#post688394

I've posted links to course notes using the same definition of inertial mass.

One thing is for sure, the wikipedia article you linked to which was your reference for inertial mass did not define inertial mass as relativistic mass. If it is defined that way elsewhere, it is a conflict of definition.

 

[JesseM]

Who answered these questions? Was this person qualified? It would seem he is not qualified if he didn't correct the person asking the question as to what Einstein actually said.

The top of the FAQ says "Compiled by Dr. John Simonetti of the Department of Physics at Virginia Tech." Perhaps the questions were submitted by students, I don't know. And he did correct the questioner in a way: he said "Actually, here's the way it should be said: energy and mass are related."

Just to be clear, are you claiming for sure that the inertia of a black box filled with gas won't appear to increase when the temperature increases, or are you just not certain either way?

 

[Aer]

Just to be clear, are you claiming for sure that the inertia of a black box filled with gas won't appear to increase when the temperature increases, or are you just not certain either way?

OK - let me state that I cannot be certain, but according to mass as it is defined, the answer would be that the mass of the gas would not appear to increase.

 

[learningphysics]

You are standing in very thin waters if you think this any authority in relativity.

should be "the mass of an object is the sum of all its constituents' rest masses".

Aer, this is totally wrong. Hopefully someone else will post and correct you since you won't take my posts into account.

The rest mass of an object is the (total energy of the object in the rest frame)/c^2

This need not be the sum of the rest masses of the constituent particles.

The rest frame is the frame where the center of mass of the object is at rest.

 

[JesseM]

should be "the mass of an object is the sum of all its constituents' rest masses".

No, not if you use the definition given by Tom Roberts, where the "rest mass" of a composite object is defined as its total energy (divided by c^2, presumably) in the center-of-mass frame. In this frame, most of the individual particles will have nonzero velocity, so their energy will be greater than just c^2 times their rest mass, it will be c^2 times their relativistic mass.

Here is another page (from mathpages.com, a pretty reliable internet resource) that says that the inertia of a composite object (its resistance to being accelerated) will be a function of its total energy, not just the energy of the rest mass of all the constituent particles:

Another derivation of mass-energy equivalence is based on consideration of a bound "swarm" of particles, buzzing around with some average velocity. If the swarm is heated (i.e., energy E is added) the particles move faster and thereby gain both longitudinal and transverse mass, so the inertia of the individual particles is anisotropic, but since they are all buzzing around in random directions, the net effect on the stationary swarm (bound together by some unspecified means) is that its resistance to acceleration is isotropic, and its "rest mass" has effectively been increased by E/c^2. Of course, such a composite object still consists of elementary particles with some irreducible rest mass, so even this picture doesn't imply complete mass-energy equivalence.

Do you have any sources to back up your claim that the inertia of a composite object is dependent only on the rest masses of its constituent particles? If not, why are you so confident about this?

 

[Aer]

Apparently you all need a little refresher course, I hope this helps.

The total energy of a particle is:

$$E = \gamma m c^2$$

where $\gamma$ is the Lorentz factor, m is the particle's rest mass and c is the speed of light.

We can also write:


$$E = E_0 + K$$

where K is the particle's kinetic energy and $E_0$ is the particle's rest energy. That is:

$$E_0 = m c^2$$

The relativistic kinetic energy is then easily seen to be:

$$K = (\gamma - 1) m c^2$$

which for $\gamma$ close to 1 (v << c) reduces to approximately

$$K = 1/2 m v^2$$

the usual Newtonian expression for kinetic energy.

 

[Aer]

No, not if you use the definition given by Tom Roberts, where the "rest mass" of a composite object is defined as its total energy (divided by c^2, presumably) in the center-of-mass frame.

Very well, then his definition of "rest mass" is not the proper definition of "rest mass" :zzz:

 

[Aer]

that says that the inertia of a composite object (its resistance to being accelerated) will be a function of its total energy, not just the energy of the rest mass of all the constituent particles:

The acceleration of an object is only properly measured in it's rest frame which implies the total energy is the rest energy.
:zzz:

 

[JesseM]

Apparently you all need a little refresher course, I hope this helps.

The total energy of a particle is:

$$E = \gamma m c^2$$

where $\gamma$ is the Lorentz factor, m is the particle's rest mass and c is the speed of light.

Uh, yes, and this is the same as E=Mc^2, where M is the relativistic mass which equals gamma*m. So the total energy of a collection of particles (again, ignoring potentials--assume the particles don't interact much) is equal to the sum of their relativistic masses times c^2. Thus, if you define the "rest mass" of a composite object as the total energy in its center-of-mass frame divided by c^2, then the rest mass of a composite object will be the sum of the relativistic masses of all the particles that make it up. That brings us to the issue of whether this is in fact the standard definition of "rest mass" for a composite object:

No, not if you use the definition given by Tom Roberts, where the "rest mass" of a composite object is defined as its total energy (divided by c^2, presumably) in the center-of-mass frame.

Very well, then his definition of "rest mass" is not the proper definition of "rest mass"

What makes you so sure? Do you have any sources that tell us how "rest mass" should be defined for a composite object made up of many individual particles which are in motion relative to each other?

And aside from the issue of definitions, that mathpages.com page confirmed that the resistance to acceleration (inertia) of a composite object will be proportional to its total energy, so the inertia of a box filled with gas will increase as the gas is heated. Do you have any source that says otherwise? Have you actually done a calculation to see how a box filled with moving objects would react to external forces? If not, why are you so confident, when multiple sources say otherwise?

 

[JesseM]

The acceleration of an object is only properly measured in it's rest frame which implies the total energy is the rest energy.
:zzz:

Uh, but again, we're talking about a composite object. Even in the center-of-mass frame of a box filled with moving gas molecules, most of the individual molecules will not be at rest. Unless all the molecules are moving at the same speed and in the same direction (which would be a thermodynamic miracle) there is no frame where all the molecules are at rest. And in the center-of-mass frame, the total energy of a box of gas will be the sum of the relativistic masses of all the gas molecules (assuming the energy in the walls is negligible)--do you deny this?

 

[Aer]

Uh, yes, and this is the same as E=Mc^2, where M is the relativistic mass which equals gamma*m.

! There is clearly no getting through to you. The concept of relativistic mass is not physical - it only exists in frames other than the frame of the actual object. You have an infinite number of "relativistic masses" according to your definition. What makes you think "relativistic mass" is any type of measure of "actual mass" (i.e. the weight an object would feel in a gravitational potential)?

 

[Aer]

What makes you so sure? Do you have any sources that tell us how "rest mass" should be defined for a composite object made up of many individual particles which are in motion relative to each other?

I already did! It is the sum of all the constituents own rest masses.

 

[Aer]

If I have objects in my car moving at .9999999999999999999999999999999999999999999999c bouncing all over the place, what is the mass of my car?

 

[JesseM]

! There is clearly no getting through to you. The concept of relativistic mass is not physical - it only exists in frames other than the frame of the actual object.

It's just as physical as energy--in fact it is simply the energy divided by c^2. If you prefer, we can ignore the concept of "relativistic mass" altogether and just talk about the total energy of a composite object in its center-of-mass frame.

You have an infinite number of "relativistic masses" according to your definition.

No, because the definition specifies that you're looking at things in a particular frame, the center-of-mass frame of the composite object.

What makes you think "relativistic mass" is any type of measure of "actual mass" (i.e. the weight an object would feel in a gravitational potential)?

Again, forget relativistic mass and just talk about energy. The reason I think it's the total energy rather than the sum of all the rest masses that determines weight is because I have several sources written by experts which say that it's the total energy that determines resistance to acceleration (inertia). What makes you think that the inertia of a composite object is proportional only to the sum of the rest masses of the particles that make it up rather than proportional to the total energy of the particles that make it up, when several sources written by experts say otherwise?