Idea of increased mass at relativistic speeds

[Doc Al]

I have a relatively simple question I would like to bring up...According to Leo Satori, as a rocket ship leaving Earth for the stars picks up speed, "Acceleration initially has the Newtonian value F/m, but then decreases steadily and approaches zero as the speed approaches c.."

Satori is referring to the acceleration as measured by observers on the Earth. Observers on the ship measure the ship's acceleration (with respect to an inertial frame with the same instantaneous speed as the ship) as being constant.

But, what I wonder about, is how do the travelers on the ship observe this matter of increasing velocity? If they are aware that more fuel is required for less acceleration, then would they not be able to calculate their velocity in absolute terms?

Even though the rocket's acceleration is constant (in the sense defined above), due to relativistic addition of velocities, a given burst of speed (with respect to that instantaneously co-moving inertial frame) produces a smaller and smaller increase in the relative velocity of the rocket with respect to some object, say the earth, as that speed increases.

In other words: As the rocket's speed with respect to the Earth increases, a one (rocket) second burst of speed has less and less of an effect in increasing that relative speed. All you can determine with this is the rocket's speed with respect to the Earth, a relative not absolute speed.

(Look up references to the "relativistic rocket equation" for more.)

 

[robert Ihnot]

Dear Doc Al, thank you for the reply. Assumedly then if you were on the rocket ship, the feeling you experience as a passenger is constant acceleration, right? That is, the “bang for the buck,” seems to remain constant.

 

[Doc Al]

Assumedly then if you were on the rocket ship, the feeling you experience as a passenger is constant acceleration, right? That is, the “bang for the buck,” seems to remain constant.

Exactly right.

 

[pmb_phy]

Can't the two sides of the mass debate agree to differ?

Like it or not, historically [at least] two different notions of mass have both been extensively used, and both are still in use today in different contexts.

"Relativistic mass" and "proper mass" (= "invariant mass" = "rest mass") are just two different tools in the relativist's toolbox. Each practitioner has their favourite tool and many will work exclusively with one tool and ignore the other. Each tool has its own merits and it doesn't matter which tool you use as long as it is fit for your particular task and you use it correctly. You will get into trouble if you try to use one tool as if it were the other.

You may well feel that your preferred tool is far superior to the other tool and that the other has no use. You are entitled to your opinion.

But surely we must all take a pragmatic view and accept that both tools have been used and are still in use? Anyone who wishes to read around the subject of Relativity needs to be aware that both tools exist and what is the difference between them. Otherwise you will have difficulty in understanding someone else who prefers a different tool to yours.

Unfortunately some people insist on referring to their preferred tool as "mass", rather than give the tool its full name of either "relativistic mass" or "proper mass" (or whatever). This can cause much confusion. Whenever you read about "mass", you need to know which of the two types is being referred to.

Neither side of the argument is going to admit defeat, so can't we just agree that there are multiple notions of mass and that we will always specify which we are talking about?

Wow! I (almost) couldn't have said that any better myself!

 

[pmb_phy]

The derivation of the quadratic energy-momentum relation follows from the fact that the norm of the 4-momentum is a Lorentz scalar. See Jackson's Classical Electrodynamics, 2ed, p 531 for a brief discussion.

Tom. What was Aer talking about when he stated

No, that is how it was derived when I it was taught to me in a physics class on the university level. If you have another derivation, please provide it - I'd love to see it.

i.e. What is the "that" which Aer was referring to? I do note that what he's referring to is not a derivation of anything, merely a rearrangement of p = \gamma m_0 c^2.

Go take a course in logic. Any result you derive is only as strong as the antecedent conditions allow. In this case you started with relations that are only valid for massive particles. It obviously follows (obvious for anyone with at least a pair of brain cells to rub together) that you can only apply your result to massive particles, based on the reasoning you provided.

Its unfortunate that many relativists use a "limiting" process to obtain the expression of relations for a photon. Thorne's new text as well as Rindler's new text uses this notion.

Again: Those are valid for massive particles only.

They are also valid for systems of free particles and for objects which are isolated.


Seems quite clear to me that Aer has no idea what he's saying when he claimed

'the definition of relativistic mass is wrong'

He's claiming what dw used to claim, i.e. that the term "relativistic" when followed bu the word "mass" refers to the term "mass" as it is used by some in SR. Clearly that is a misuse of the term "relativistic mass."

re - "Now tell me Tom, who am I to believe on this matter in physics?"

I say that one should believe Einstein first, then everyone else.

re - "The collect majority of Physics professors or a single Math/Engineering Professor?"

It one is to "believe" i.e. take on blind faith then I say use as the SR bibles e.g. Feynman, Rindler, Goldstein, etc.

re - "BTW, do you have a degree in math or engineering? "

In my case I have a BA in both physics and math. My graduate work is in physics (that much I could finish until Mom got ill and needed her favorite sone, good ole me, for help - later the school on the "infinite wisdom" decided to hold night classes during the day time! )

re - "I've never said that is the procedure, I've correctly stated that those equations are undefined for a photon."

Extremely ignorant response. The correct definition of rel-mass, m, is m = p/v/. This holds in all possible cases for a free-particle.

re - "I suppose all physicists are crackpots according to you?"

Einstein just proverbaly rolled over in his grave!

Pete

ps - I wonder if its a coindidence that I live in Mass and that MIT is on Mass ave (MIT is where I confirmed almost all I've mentioned here)?

 

[pmb_phy]

I wonder if everyone here who noted that Aer (whom I assume claims rel-mass is useless??) actually referenced a page which employs relativistic mass in the derivation!

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html

Too funny!

Pete

 

[quantumdude]

Tom. What was Aer talking about when he stated
i.e. What is the "that" which Aer was referring to? I do note that what he's referring to is not a derivation of anything, merely a rearrangement of p = \gamma m_0 c^2.

The "that" is E^2=(pc)^2+(mc^2)^2.

 

[selfAdjoint]

1) The momentum-energy four-vector has component in the time direction E, its extension in the space directions is c times the 3-momentum vector, magnitude pc, and its magnitude as a four-vector is mc^2.

2)The magnitude of a four vector is a Lorentz invariant.

3)If you do the Minkowski version of the Pythogorean theorem:
(4-magnitude)^2 = (time)^2 - (3-space-magnitude)^2.
This equation will be covariant (true in every frame) because of (2).

4)This works out to
(mc)^2 = E^2 - (pc)^2
or rearranging terms, you get what Tom posted. It is the covariant energy equation for particles. The terms have different values in different frames, but the equation is always true; it is even true for light: m = 0 => E = pc.

 

[cybermambo]

You are completely correct selfAdjoint. The 4 vector derivation follows precisely as:

Start with the vector:

(cdt,dx,dy,dz)

Divide by proper time dτ=dt/γ and define as V:

V ≡ γ(c,dx/dt,dy/dt,dz/dt) = (γc,γv)

Multiply by m and define as P:

P ≡ (γmc,γmv)

Multiply by c:

Pc = (γmc²,γmvc) = (E,pc)

Take the inner product of Pc·Pc:

Pc·Pc = (γmc²)² - (γmvc)²

The value of the inner product is invariant and can be found most easily by choosing v=0:

(γmc²)² - (γmvc)² = (mc²)²

Rearrange and we get:

E² = (pc)² + (mc²)²

 

[pmb_phy]

The "that" is E^2=(pc)^2+(mc^2)^2.

Oy! Too bad he refused to read what I posted. I wrote a paper on all the aspects of this topic in mass. Had he read it he'd have seen it there. I guess it was far too much to expect?

For the curious please see "On the concept of mass in relativity" which has a link to it at

http://www.geocities.com/physics_world/

For the really brave see
http://www.geocities.com/physics_world/ma/invariant.htm

Pete

 

[pmb_phy]

You are completely correct selfAdjoint. The 4 vector derivation follows precisely as:

Start with the vector:

(cdt,dx,dy,dz)

Divide by proper time dτ=dt/γ and define as V:

V ≡ γ(c,dx/dt,dy/dt,dz/dt) = (γc,γv)

Multiply by m and define as P:

P ≡ (γmc,γmv)

Multiply by c:

Pc = (γmc²,γmvc) = (E,pc)

Take the inner product of Pc·Pc:

Pc·Pc = (γmc²)² - (γmvc)²

The value of the inner product is invariant and can be found most easily by choosing v=0:

(γmc²)² - (γmvc)² = (mc²)²

Rearrange and we get:

E² = (pc)² + (mc²)²

Note - Don't be too surprised if you see this relation in an SR text with the E missing. Sometimes the authors leave the m (rel-mass) in and leave out the E

Pete

 

[cybermambo]

Missing the E? The entire point was to get the relation E² = (pc)² + (mc²)². I am not sure what you mean by "missing the E". Sometimes the c is left out because we are free to choose c=1.

 

[quantumdude]

It should also be noted that the derivation posted by cybermambo doesn't justify the use of the energy-momentum relationship for photons, since the expressions he used don't apply to photons. It has to be determined independently that E=pc for photons, and indeed it does.

 

[pmb_phy]

It should also be noted that the derivation posted by cybermambo doesn't justify the use of the energy-momentum relationship for photons, since the expressions he used don't apply to photons. It has to be determined independently that E=pc for photons, and indeed it does.

Ummmm ... Tom - Let us not forget that Thorne and Blanchard and well as Rindler have already argued that the relationship m = \gamma m_o can be applied to zero proper mass particles in the limit m₀ -> 0. No - I don't agree with them. But I at least followed their argument before I disagreed with them. I assume you'd give them the same honor that they deserve, right? Then you can disagree with them with my blessings.

E.g. see
http://www.pma.caltech.edu/Courses/ph136/yr2002/chap01/0201.2.pdf

page 16. It is arguements like this which justifies the use of the term zero rest mass for particle's like photons.

Pete

 

[mitchellmckain]

How right you are!
Very good explanation. You obviously must be a qualified physicist unlike most on this forum.

You are the first person on this forum that I've seen correctly explain the issue of relativity and mass. Good work

Thank you. Yes, I have a masters in physics and I teach physics online. My expertise in relativity derives from the relativistic space-flight simulator that I spent the last three years writing. http://www.relspace.astahost.com

Actually, it was not concocted as an explanatory tool. In the old days, it was believed the relativistic mass was the real mass.

Thank you for you correction. I am certainly not an expert on the history of relativity. That was simply my impression from texts that I have read.

http://www.geocities.com/pmb_phy/mass.pdf
I've referred to it many times and guess what? Nobody has read the whole thing I bet.

Quite frankly, they'd be better off not clicking it, which consequently is my recommendation for everyone reading this thread.

I read the whole thing and found it quite enlightening, so I disagree with your assessment Aer. However, what I learned from it was not what pmb_phy intended, and the fact that he uses this as his authoritative support says a lot about pmb_phy. You can see my earlier critique for details (2nd page of posts).

There seems to be a growing trend to indulge in pseudo-science which approaches the concepts of science with the techniques of rhetoric. Creationism is probably the biggest and most well established of these pseudo-sciences, but the phenomena seems to be growing rapidly everywhere.

 

[reilly]

Mr. M -- How do you explain the observed increase in inertial mass of electrons in accelerators?
Regards,
Reilly Atkinson

 

[Chronos]

[Originally Posted by pmb_phy
http://www.geocities.com/pmb_phy/mass.pdf
I've referred to it many times and guess what? Nobody has read the whole thing I bet.]

I read the whole thing and found it quite enlightening, so I disagree with your assessment Aer. However, what I learned from it was not what pmb_phy intended, and the fact that he uses this as his authoritative support says a lot about pmb_phy. You can see my earlier critique for details (2nd page of posts).

Indeed, it does say a lot about pmb phy, since he is the author of that source. It's kind of ironic that he asserted nobody read the whole thing. Had you done so, I'm guessing you would not made such an internally inconsistent statement.

 

[mitchellmckain]

Mr. M -- How do you explain the observed increase in inertial mass of electrons in accelerators?
Regards,
Reilly Atkinson

I would have to see a reference to the observation you are talking about in order to comment.

 

[pmb_phy]

However, what I learned from it was not what pmb_phy intended, and the fact that he uses this as his authoritative support says a lot about pmb_phy.

Can you clarify for me what this means when you say "the fact that hhe uses this as his autthoritative support says a lot about pmb" is supposed to mean?

There has never been a word that came from my kegyboard which has ever meat to me taken as an "authoritative support." I've spent a very long time looking into all the objections I've seen in alkl the physics journal articles and texts against this concept as well as for the concept.
I ttied everything I cold thik of to break eiher notion and I've alwayhs found that I cpould take the "mass = proper mass" notion and break it ut I could never take the "mass = relatvistic mass notion and break it. After this was all said and done there was too much to say that could be placed in one post or in one web page. The only alternative to this was to write an article and place it on my website and let thos interested inn this subject and make up thheir own minds about it. It was 80 pages long so there's no way I'd say in one thread why I like one over the other had I been forced to under threat of death to make a choice.

So who is this "authoirity" you speak of? Are you saying that if I find something too long to present in any other format/presentation and I therefore make it into a PDF file and place it on my website that makes me claim I'm an authority on the topic? You may think that's the case but I do not.

And its not finished. I didn't like it so I plan on starting fresh.

Pete

 

[pmb_phy]

I would have to see a reference to the observation you are talking about in order to comment.

What is it about your teaching experience at ITT (How lo\ng have you been teaching there?) that makes you an authority on SR. And if you don't know what Reily meant and you need him to explain it o you then trulyh don't have a complete understaning of relativistic mass. You can leave he insulting/condescennding comments/attitude out of your posts direced towards me and the conversation will still be able to conntinue. You do understand that this is a moderated board and that comments of an irritating nature are unwelcome, right?

Pete

Note - For the next several days I'll be in the hospital due to a serious infection in my incision. If I mispell or something of that nature more often then not then its because this room is freezing and my jolints don't work and the screen is too small and I don't have my glasses with me (the prescription is out of date and invalid anyway).

 

[vanesch]

Allright, boys and girls, let's keep the discussion here scientific and let's refrain from putting in question personal reputations, "I'm right and you're wrong" contests, and other unnecessary a-social behaviour please...
Otherwise the key will go on this thread!

 

[pmb_phy]

Allright, boys and girls, let's keep the discussion here scientific and let's refrain from putting in question personal reputations, "I'm right and you're wrong" contests, and other unnecessary a-social behaviour please...
Otherwise the key will go on this thread!

Sure. As long as people stay on topic and don't get personal - That's all I can ever ask for. But the person I responed to made a remark which scientifically meant nothning to me so I wanted an answer as to what his remark meant. However I remembered what a moderator told me to do in those cases so that's what I did.

Regarding mass - There are only very few relativists who truly understand the subject as it is known in relativity. The energy-momentum 4-vector invariant people love to call "mass" as an exremely limited use and is not valid in all cases. Since this is a relativity forum when poeople ask about rel-mass I tell them the most general definition there is, i.e. one that works in all cases and not the extremely limited nbumber of cases that is only discussed in this forum. That's why I want a detailed description of mitchellmckain's apparentlt clandestine remark on my paper rather than a broad insulting comment. People who refuse to state the specifics and be exact usually do so when they don't understand a topic. That seems to be the case here with mitchellmckain. So let's get to the physics mitchellmckain - state what part of the paper you have a poroblem with or exactly what your problem is with me and the paper please.

Pete

 

[vanesch]

So let's get to the physics mitchellmckain - state what part of the paper you have a poroblem with or exactly what your problem is with me and the paper please.
Pete

Eh, just limit it to the paper

 

[pmb_phy]

Eh, just limit it to the paper

Sorry. That's all I intended to say.

Right now I'm in a very bad sate of mind. I'm in the hospital fighting an infection that my incision that was left over from my spinal surgery. I'm not my normal happy go luck happy chap that I usually am.

Chronos - Please PM me annd let me know what your thoughts are on the subject. I have a pretty nifty little example which blows this whole "mass = proper mass" put of the water. Also let me know in the PM if you read the paper in part or in whole and let me know what you think/thought.

Pete

 

[pmb_phy]

Relativistic mass is unnecessary, cumbersome and undesirable upon close examination.

Can you please elaborate on what you mean by "close examination"? E.g. give an example where it is undesirbable other than simply being confusing to someone. Confusion is the fault of the user which is a result of an unwillingnness to actually learn the subject cold.

Here's an example: May people define "mass" as the m in

p = M(v)v

m == limit as v->0 M(v). Actually what happens is that this defines both p and M/m because you demand that the quantity Mv be conserved. You then define p as p = Mv. Its for this reason m can't be defined as the magntude of the 4-momentum since p and m are both undefined there.

If you try to define m in this way then it only works for a particle. If you try to use it to define the mass density of the EM field the definition of m falls apart. This is because, as particle physicists define "m" it onl works in a limited number of cases (for details see Rindler 1982)

Pete

 

[Hans de Vries]

I'm in the hospital fighting an infection left over from my spinal surgery.
Pete

Pete,

I wish you all the best. I hope you'll recover soon.

Have you ever considered this issue by taking a bit of QM into account?
This brings some extra very interesting insights. Mass is given by the
frequency f of the wave function. m = hf/c²Rest mass.
Just m_0

Relativistic mass or "Hamiltonian" mass
m_0 \gamma\ \ \ \approx\ \ m_0 + \frac{1}{2}m_0 v^2/c^2 \ \ \ \ (v<<c)

"Lagrangian" mass
m_0/ \gamma\ \ \approx\ \ m_0 - \frac{1}{2}m_0 v^2/c^2 \ \ \ \ (v<<c)

The difference between the latter two is how you measure the frequency.
It's either measured over the t or t' axis (for the relativistic mass and the
"Lagrangian" mass respectively). The mass seems increased when measured
over the t-axis while it seems decreased when measured over the t' axis.

The measurement over the t-axis corresponds to how the particle interacts
with objects in the rest frame. The measurement over the t' axis measures
the frequency over the trajectory of the particle itself. Here we see what
we expect from the Time Dilation, a decreased frequency corresponding to
a slower aging particle:

If time passes 1 second in the rest frame, the moving particle will move over
the t' axis and will undergo f/\gamma phase changes: The frequency over the
trajectory is f/ \gamma corresponding to a mass of m_0/ \gammaI called these masses "Hamiltonian" and "Lagrangian" because this is exactly
the origin of these two formalisms which are rather abstract classically but
have a very physical meaning in relativistic QM. The Hamiltonian is typically
defined in the rest coordinates while the Lagrangian is taken over the trajectory
of the particle (Principle of Least Action, Feynman path integral)Regards, HansThere's some more here: http://www.chip-architect.com/physics/deBroglie.pdf

 

[Hans de Vries]

This is intended to illustrate the points of the post above. The drawing shows
a Minkowsky diagram with a de Broglie wave form blended upon it (the bands
run parallel to the x' axis)

It illustrates two points:

1) The frequency "paradox"

The "paradox" is that a relativistic particle has a higher mass and thus should have
a higher frequency according to E=hf while at the other hand it ages slower due
to time dilation and thus should have a lower frequency.

The solution is is that the higher frequency f \gamma is measured over the t-axis while the
actual trajectory of the particle is over the t'-axis. We thus must count phases over
the t'-axis and see that the frequency of the particle is f / \gamma, which is the lower
frequency.

2) Hamiltonian vs Lagrangian.

The difference of the two frequencies (= masses = energies) comes down to \pm \frac{1}{2} m_0 v^2
in the non-relativistic limit corresponding to the difference in the definition of the
classical Hamiltonian and Lagrangian:

\ H\ \ \ =\ \ V\ +\ T\ \ \ \ =\ \ \ V\ +\ \frac{1}{2}mv^2\ \ \ \ \ \ \ \ \mbox{(Hamiltonian)}
-L\ =\ \ V-T\ \ =\ \ V-\frac{1}{2}mv^2\ \ \ \ \ \ \mbox{(Lagrangian)}

The Lagrangian is used when we integrate over the trajectory of the particle, which is
the t'-axis (Principle of Least Action, Feynman path integral) Regards, Hans(PS: note the minus in the historical definition of L)

 

[mitchellmckain]

Can you clarify for me what this means when you say "the fact that hhe uses this as his autthoritative support says a lot about pmb" is supposed to mean?
There has never been a word that came from my kegyboard which has ever meat to me taken as an "authoritative support." I've spent a very long time looking into all the objections I've seen in alkl the physics journal articles and texts against this concept as well as for the concept.
...
Pete

Sorry, sorry, I apologize. I wrote this a while ago and you are right it is over the top and un-called for. I certainly did not mean it to be quite as caustic as it must have sounded to you. But you had left the discussion and you never responded to my critique of your paper on page 2 of this thread, so I was (over)sympathizing with Aer while disagreeing with him about your paper being worth reading. I really hate making things personal myself and find that it is best to ignore such things. So forgive me for not responding to your request to explain myself and your righteous retaliation. My choice of words were, shall we say, careless and unfortunate.

If you want you can find the response I first made to your paper on page 2 of this thread, though I had no idea when making this response that you were its author. To summarize, I found the paper interesting and even enlightening but came away from it even more convinced of the initial position I took when I started this thread.

P.S. It is difficult for me handle the alternation of no activity for months on this topic with this sudden barage.

 

[pmb_phy]

Sorry, sorry, I apologize. I wrote this a while ago and you are right it is over the top and un-called for.

Appology accepted. I'm not sure why I didn't respond to your comments. I believe it was because right after I posted that I got a call from my surgeon's office because they mmoved up my scheduled spinal surgeryh to the 19th and I had a ton of stuff to do before the 19th. Then there was the recovery period where I was in tons of paiin and not too focused on posting. Then there is this past alf week when I got an infection in my incision and had to be admitted to th e hospital agaqin and be pumped full of anti-biotics. Then they put a pic in my arm last night, which is a horrible thing to be awake and watch them do. They shove this wire into your arm into a vein and then right outside the heart etc. I then needed to blow off steam and came here and when I saw that this suject was still active I read your response and was confused and irritated - it seems people love to attack me for my opinion on this. I didn't realize that people wouldn't know that it was my paper. In any case I think its good if a work can stand on its own without the need to know who the author is. All references are online at my we b page.

I will be rewriting this paper soon since I made a few mistakes which I need to mend as well as to shrink it and add in a very simple example of when E = gamma *m*c^2 (m = proper mass) doesn't hold true. In fact if you ask pervect ha may be able to show you where on my web page I gave that example. Right now its too hard to type. Due to the infection I have to wear gloves to type and the number of mistakes I make typing with surgical gloves is enorm ous.

Thanks for your response and retraction. It is greatly appreciagted. And there was no way that you coul,d have deduced something as serious as I had expained had happened to me so don't worryh about it. I'll be home soon (today->tom mmorow) and we can dig into this.

Please note: I try not to claim one is better than the other because that is opinion. All I do is argue that one is not being ignorant for using rel-mass. In fact at times it has to be used. More later

Pete

Addendum - I just found out that I can't go home for a while. Perhaps a week or two. All because of some darned bug!

Addendum 2 - I just found out that I'm going home tonight! Yay! So we can talk then. mitchellmckain - I do have a request. For the pereliminary sgtuff ca n we talk in PM or e-mail? That way we don't have to jam the place up with catching up with each other. Should take only 1 or 2 PMs. Then I'd love to hear any critiques you have on the paper because I'll be changing it. I'd enjoy hearing all objections to rel-mass that you didn't see in the paper. When I get home tonight I'll show you where the article's referenced in the paper are in PDF format on my web site

 

[Longstreet]

I don't have much experience with special relativity, but it seems to me that the concept of rest-mass and relativistic mass are equally pathological. If you confine (in say a box) a particle at relitivistic speeds, or at c in the case of photons, you can say the box has some mass related to the total energy (i.e. relativistic mass). You could then just call this mass the rest mass of the box, even though the rest mass is really a product of the relativistic energy of the particle contained within.

However, doing this loses information about the origional mass and velocity, which begs the question of what mass is the "proper" mass. You can imagine a scenario of nesting dolls where you open the box to find the proper mass only to find another box. So all this has done is redefine the relativistic mass as the rest mass around an arbitrary average velocity, and then use that for the change in the average velocity of the box.

Thanks,