Idea of increased mass at relativistic speeds

[Aer]

I said that quantum theory and special relativity have been completely unified, and that is true. The status of quantum theories of gravity is irrelevant to that statement.

I am talking about QM and Relativity, not QM and 'special relativity'. Relativity is in fact 'general relativity' because 'special relativity' is nothing but a special case of 'general relativity'. Now let's be thorough here. The special relativity equations are recovered in general relativity when spacetime is considered to be flat. So, the special case that is 'special relativity' is flat spacetime. Any unification of special relativity and QM should inherently include the general case which is general relativity. Do you disagree with the fact that special relativity is a special case of general relativity?

No, it isn't. If that were true then the energy of all photons would be undefined, which it isn't.

Very good, this is true - the energy would be undefined according to the relativity equation E=\gamma m c^2

In relativity the energy of a photon is given by E=pc.

Yes, from the equation I gave below - I already mentioned this, why did you need to pretend like I didn't know?

or

E^2 = (pc)^2 + (mc^2)^2

which consequentyly is derived from E = \gamma m c^2 and p = \gamma m v.

The first equation is not derived from the second and third equations at all.

Oh yeah? You'll have to forgive me then for providing the derivation of E^2 = (pc)^2 + (mc^2)^2

Start with the definition of p:
p = \gamma m v
Multiply by c and square both sides:
(pc)^2 = \frac{(m v c)^2}{1-v^2/c^2}
Divide and multiply the right side by c²
(pc)^2 = \frac{m^2 \frac{v^2}{c^2} c^4}{1-v^2/c^2}
Subtract and add the quantity \frac{m^2 c^4}{1-v^2/c^2}:
(pc)^2 = \frac{m^2 c^4 (\frac{v^2}{c^2}-1) }{1-v^2/c^2} + \frac{m^2 c^4}{1-v^2/c^2}
Simplify:
(pc)^2 = -m^2 c^4 + \frac{m^2 c^4}{1-v^2/c^2}
Plug in \gamma^2 = 1/(1-v^2/c^2):<br /> (pc)^2 = -m^2 c^4 + \gamma^2 m^2 c^4<br /> Using the definition of E=\gamma m c^2:<br /> (pc)^2 = -m^2 c^4 + E^2<br /> And viola:<br /> E^2 = (pc)^2 + m^2 c^4<br /> <br /> You were saying?<br /> <br /> <br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> The second and third equations only applie to massive particles, while the first applies to all particles, even those with zero mass. </div> </div> </blockquote> That is the ad-hoc nature of taking the result from QM of pc=hf for a photon and throwing it into the relativity equation. It works only if you forget the definition of p = \gamma m v used to derive the equation. That is what I am saying - it is very ad-hoc in nature. You call it unify... I call it ad-hoc. Unification <i>should</i> be all the results from relativity being described in QM.<br /> <br /> Forgive my ignorance, but how does QM explain the relativity of simultanteity? I will admit that I do not know the answer to this and would like for you to tell me since you said special relativity and QM are completely unified.<br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Right, the explanation comes from the unification of special relativity and quantum theory, which has been done, despite the fact that you claim otherwise. </div> </div> </blockquote> I told you I already know how the result is arrived at, but it is not from &quot;unification&quot;. True, you use both theories, but that is not what I meant by unification and is not what I think most people mean by unification (though I could be wrong - in which case, I need another word for what I am talking about).<br /> <br /> <br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Why would I need to explain quantum gravity, in order to defend my point? </div> </div> </blockquote> Well, my point was the original point of contention. And my point was: QM and Relativity are not unified. When I say &quot;Relativity&quot; with no prefix, I mean General Relativity. Sorry for the confusion. And it is for that reason that I believe my point about gravity is relevant.<br /> <br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> I didn&#039;t forget to do anything. You can, in fact, write force as F=dM/dτ. </div> </div> </blockquote> I didn&#039;t say you couldn&#039;t do it (actually, I believe you mean F=d(Mv)/dτ but that is beside the point), but if you actually want to take that derivative, you must expand it out, no?<br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Obviously, the use of M in that particular equation was to make the relationship more compact. Is that really too difficult to see? </div> </div> </blockquote> What is wrong with just leaving it in the compact form F=dp/dτ?<br /> <br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> If by a &quot;non-gravitational energy&quot; term you mean a term that describes &quot;energy that does not contribute to gravitation&quot;, then kinetic energy is not one of them. </div> </div> </blockquote> So a particle with kinetic energy has a greater effect on the curvature of spacetime? That is what you mean do you not? In which frame must the kinetic energy be calculated so that the curvature of spacetime that our particle creates can be known?<br /> <br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> I said that all energies are put into the energy-momentum tensor, and that is a fact. Nothing you have referred to disagrees with anything that I said. </div> </div> </blockquote> I did not raise any disagreement with that part of your statement.<br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Unfortunately, you don&#039;t have a single good reason for holding that opinion. </div> </div> </blockquote> Name one good reason you have for holding the opinion that <a href="http://en.wikipedia.org/wiki/Relativistic_mass" target="_blank" class="link link--external" rel="nofollow ugc noopener">relativistic mass is useful</a>. I have one, it is highlighted in red:<br /> <br /> In the earlier years of relativity, it was the relativistic mass that was taken to be the &quot;correct&quot; notion of mass, and the invariant mass was referred to as the rest mass. Gradually, as special relativity gave way to general relativity and found application in quantum field theory, it was realized that the invariant mass was the more useful quantity and scientists stopped referring to the relativistic mass altogether.<br /> <br /> The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only &quot;mass&quot;, while the concept of energy has replaced the relativistic mass. In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity.<br /> <br /> However, I don&#039;t think it is a good idea to use it at all because of the confusion it generates.<br /> <br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> Aer, you have been trying the patience of the staff with your insulting tone to others, and we have been watching. </div> </div> </blockquote> I know that you have been watching and that you have been called here.<br /> <br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> But in this post not only have you been patronizing, but you have descended into abject crackpottery. </div> </div> </blockquote> Name one thing I&#039;ve said that is crackpottery? I can tell you one thing, the only person I agree with in this thread is the thread starter whom just happens to be a qualified physics instructor. Ho-hum, and I am a crackpot?<br /> <br /> <blockquote data-attributes="" data-quote="Tom Mattson" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-title"> Tom Mattson said: </div> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> I must insist that you stop doing it. </div> </div> </blockquote> I will agree to stop pushing any crackpot ideas because I&#039;ve yet to do so.<br /> <br /> Now I am just curious, are you just as qualified or more qualified in physics than the thread starter?

 

[roger]

Quite wrong, laddy. There are at least two ways to define "mass" and each has its merits. Defined as m = p/v = mass, can be found in many places.

How can mass be defined as p/v ?

I don't understand


Roger

 

[Aer]

How can mass be defined as p/v ?

I don't understand


Roger

The definition of momentum is p = \gamma m v where \gamma is the Lorentz factor, m is the rest mass, and v is the velocity relative to some inertial frame.

pmb_phy likes to define m as relativistic mass so that \gamma m in the equation above just becomes m. Unfortunately, relativistic mass has no fundamental meaning as wikipedia says here so mass would be more correctly defined as: m = p / (\gamma v).

But as you can see, this is just a reordering of terms from the definition of momentum, p.

 

[quantumdude]

I am talking about QM and Relativity, not QM and 'special relativity'. Relativity is in fact 'general relativity' because 'special relativity' is nothing but a special case of 'general relativity'.

You claimed that QM had not been unified with SR/GR in any way.

Your original statement, as written, is false.

Now let's be thorough here. The special relativity equations are recovered in general relativity when spacetime is considered to be flat. So, the special case that is 'special relativity' is flat spacetime. Any unification of special relativity and QM should inherently include the general case which is general relativity.

First, this is a simple non-sequitir. Just because SR is a special case of GR, that doesn't imply that the existence of (special) relativistic quantum mechanics should imply the existence of (general) relativistic quantum mechanics.

And second, you can in fact do QM and QFT in curved spacetime. This unification of QM and GR has nothing to do with quantum gravity theories.

Do you disagree with the fact that special relativity is a special case of general relativity?

No, I disagree with your flawed logic and bad information.

Very good, this is true - the energy would be undefined according to the relativity equation E=\gamma m c^2

Yes, from the equation I gave below - I already mentioned this, why did you need to pretend like I didn't know?

I didn't pretend anything. I explicitly said that your error was the application of the formulae for energy and momentum of massive particles to photons.

Oh yeah? You'll have to forgive me then for providing the derivation of

(snip)

All you did was show that the relations for energy and momentum of massive particles satisfy the quadratic energy-momentum relation. Your "derivation" is consequently only valid for massive particles. Nothing in your logic justifies the application of the quadratic energy-momentum relation to photons.

To justify that, you would have to really derive it, without making reference to relations that are specific to massive particles.

You were saying?

So as I was saying: You cannot derive the quadratic energy-momentum relation (the one that applies to both massive and massless particles) from the expressions you quoted.

That is the ad-hoc nature of taking the result from QM of pc=hf for a photon and throwing it into the relativity equation. It works only if you forget the definition of p = \gamma m v used to derive the equation.

p=\gamma mv is not used to derive the equation.

That is what I am saying - it is very ad-hoc in nature. You call it unify... I call it ad-hoc. Unification should be all the results from relativity being described in QM.

Now you are changing your tune. You went from saying that QM and SR/GR have not been unified in any way before to saying that they haven't been unified in a way that does not involve ad hoc hypotheses.

But in any case you are wrong. When two theories are "unified" it is not the case that this entails that one theory completely contains the other. It means that there exists a single theory that is a superset of the two original theories.

And in this case, that theory is quantum field theory.

Forgive my ignorance, but how does QM explain the relativity of simultanteity? I will admit that I do not know the answer to this and would like for you to tell me since you said special relativity and QM are completely unified.

The answer to that question would be no different from that of SR itself. QFT is built out of both QM and SR. Since the explanation of relativity of simultaneity is not quantum theoretic, it only makes sense that SR retains that part of its "identity" when merged with quantum theory.

I told you I already know how the result is arrived at, but it is not from "unification". True, you use both theories, but that is not what I meant by unification and is not what I think most people mean by unification (though I could be wrong - in which case, I need another word for what I am talking about).

Most people who know what they are talking about consider relativistic QM and QFT to be unifications of quantum theory and special relativity. Look into it.

Well, my point was the original point of contention. And my point was: QM and Relativity are not unified. When I say "Relativity" with no prefix, I mean General Relativity. Sorry for the confusion. And it is for that reason that I believe my point about gravity is relevant.

OK, but you didn't say that QM and Relativity are not unified. You said that QM and SR/GR are not unified in any way, and that statement is wrong.

I didn't say you couldn't do it (actually, I believe you mean F=d(Mv)/dτ but that is beside the point), but if you actually want to take that derivative, you must expand it out, no?

Yes, I meant F=d(Mv)/dτ, and yes you have to expand it out when you take the derviative.

You still haven't answered my initial questions though. You have done just about everything you possibly could to avoid answering them, in fact.

What is wrong with just leaving it in the compact form F=dp/dτ?

Nothing. I've never said otherwise.

So a particle with kinetic energy has a greater effect on the curvature of spacetime?

Yes, that's what I mean.

That is what you mean do you not? In which frame must the kinetic energy be calculated so that the curvature of spacetime that our particle creates can be known?

You would use the same frame that you would use for all of the other forms of energy that you put in. What else would you use?

I did not raise any disagreement with that part of your statement.

LOL, No you simply rewrote my statement to say something that I did not say.

Name one good reason you have for holding the opinion that relativistic mass is useful.

I never made a claim one way or the other on the subject. That is just you putting words into my mouth, once again.

What I claimed is that it is not incorrect to use relativistic mass, and that is a fact. I am still waiting for you to demonstrate why it is incorrect.

I have one, it is highlighted in red:

Irrelevant.

However, I don't think it is a good idea to use it at all because of the confusion it generates.

Again: Irrelevant. I didn't ask you why you don't like it, I asked you why you say that it's wrong.

Either answer the question or admit that you can't. But please stop the evasive tapdancing.

Name one thing I've said that is crackpottery?

I'll name 3.

1. That relativistic mass is incorrect.

2. That the procedure for determining photon energy and momentum that is prescribed by relativity is to use the relations for massive particles.

3. That you can derive the quadratic energy-momentum relation from the relations for massive particles and then turn around and apply the result to photons.

I can tell you one thing, the only person I agree with in this thread is the thread starter whom just happens to be a qualified physics instructor. Ho-hum, and I am a crackpot?

Yes.

I will agree to stop pushing any crackpot ideas because I've yet to do so.

Wishful thinking on your part, I'm afraid.

Now I am just curious, are you just as qualified or more qualified in physics than the thread starter?

Don't know him, so I can't say.

How about you just stick to dealing with my statements, instead of my personal qualifications?

 

[pmb_phy]

The definition of momentum is p = \gamma m v where \gamma is the Lorentz factor, m is the rest mass, and v is the velocity relative to some inertial frame.

pmb_phy likes to define m as relativistic mass so that \gamma m in the equation above just becomes m. Unfortunately, relativistic mass has no fundamental meaning as wikipedia says here so mass would be more correctly defined as: m = p / (\gamma v).

I really hate it when people put words into my mouth. If I were writing a paper on particle physics or I was doing calculations of particle collosions then I'd hate to use the notation m₀. Its a huge pain in the butt. Since in most equations on particle dynamics there are more than one particle it because yucky to start writint things like m₀₁. This is not to say that people don't do it. Use the notation that is easy to read.

That article in wikipedia is wrong as most such articles are. Such comments are rooted in ignorance. Asking me to prove why relativistic mass is useful is like asking me why F = dp/dt is useful. Its a very silly question.

I recall some wiseguy in the sci.physics.relativity newsgroup "proving" to me that rel-mass is not useful and is "outdated" by pointing me to David Morin's text. David is a physics professor at Harvard. Taking that as a challenge I wrote a letter to David and later e-mailed him. After a small amount of e-mail exchanges David proved that he's a very sharp and very reasonable physicist. Later on this year (a month or two?) David will update his text to change that comment. I'll let you know when the new comment is there.

I recommend that you naysayers actually try to learn relativity the correct way and STOP limiting yourselves to objects which you're treating as pointlike particles. Read Rindler's text Introduction to Special Relativity, Wolfgang Rindler, Oxford Science Press, 1982. Pay close attention to Chapter VII Relativistic Mechanics of Continua. Einstein knew all this extremely well. That's why he stated in no uncertain terms that mass is completely described buy the energy-momentum tensor.

If you are going to keep whining about "useful" then defined that term and prove why rest mass is "useful" (which, of course, it is).

I can tell you one thing, the only person I agree with in this thread is the thread starter whom just happens to be a qualified physics instructor.

So what? That is a baseless assertion since erroneously assumes that all physics instructors agree with him. Its a fact that not all do. Whom am I speaking about you say? Take a gander

http://www.geocities.com/physics_world/misc/relativistic_mass.htm

Note the accelerator labs

Cern
Argonne National Laboratory
Lawrence Berkeley National Laboratory
University of Wisconsin-Madison

Are they allowed to have an opinion? Are they as dumb as you're claiming?

Then there's Einstein (Do you claim that he's dumb too? Ae not as smart since after all he's dead?)

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

Pete

 

[Aer]

You claimed that QM had not been unified with SR/GR in any way.

I still stand by my claim because I have a different definition of unification than you do. My definition would most closely be defined as: the act of combining into one. Now this is still a bit vague, so let me put it into context of the unification of Relativity (for our purposes here, we'll just say special relativity and disregard general relativity since we both seem to agree that QM and general relativity are not unified). So when I say the unification of QM and SR, I mean that we have one coherent theory that describes all the phenomena in both QM and SR. Now, you have presented little tid-bits of QM in relative frames, but that is a far cry from a unification theory. That is why QM and SR are still separate theories. At the least, you've presented compatibility, but not unification.

So, I believe:

Your original statement, as written, is false.

my original statement, as I intended, is true.

I disagree with your flawed logic and bad information

What bad information? I think you just misunderstood me is all.

Oh yeah? You'll have to forgive me then for providing the derivation of

(snip)

All you did was show that the relations for energy and momentum of massive particles satisfy the quadratic energy-momentum relation.

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. If you don't believe my derivation, find it here and check out what Wikipedia has to say on the matter:

The relativistic energy-momentum equation

The relativistic expressions for E and p[/color] above can be manipulated into the fundamental relativistic energy-momentum equation:

Now, what are the relativistic expressions for E and p you ask? The very ones that I provided and you say have nothing to do with the relativistic energy-momentum equation.

Relativistic expressions for E and p:

E=\gamma m c^2
p=\gamma m v

Now a lot of people come here to learn, so please stop stating your false claim that the relativistic equations for E and p are not used to derive the relativistic energy-momentum equation. Now I am not totally sure, but aren't you an owner or at least super moderator of physicsforums? I would think you'd want to keep false claims off your site considering your past history on such issues. You seem to be a bit of a hypocrite from my perspective. Of course you'll probably take offense to that, but I am not in the wrong here and you are.

Now you are changing your tune. You went from saying that QM and SR/GR have not been unified in any way before to saying that they haven't been unified in a way that does not involve ad hoc hypotheses.

Actually, I am not changing my tune, you just misunderstood what I meant. I've discussed the very nature of these ad-hoc QM->SR jobs elsewhere. I am aware of them and did not think of them as "unification" in the way you do. We just have a semantics issue here, I tried to resolve that in my opening paragraph of this post.

But in any case you are wrong. When two theories are "unified" it is not the case that this entails that one theory completely contains the other. It means that there exists a single theory that is a superset of the two original theories.

I agree that unification means that a single coherent theory should describe the original two. But that is not what you have shown with your examples of "unification" which are more or less "compatibility".

And in this case, that theory is quantum field theory.

Quantum field theory is an attempt, it has not been fully developed into a unified theory of QM and relativity.

Most people who know what they are talking about consider relativistic QM and QFT to be unifications of quantum theory and special relativity. Look into it.

I was not referign to Quantum Field Theory when I made my statement. I was referring to the energy of a photon which is defined from pc=hf from QM and then manipulated in the relativistic energy-momentum equation to mean E=hf. Now, there should be one Energy equation in which we should be able to get E=hf without an ad-hoc treatment of forgetting the definition of p and redefining pc for a photon. A unification should end in one equation, not an algorithm, which consequently is all we have with the above treatment of energy for a photon.

OK, but you didn't say that QM and Relativity are not unified. You said that QM and SR/GR are not unified in any way, and that statement is wrong.

Once again, this is an issue of semantics, I believe what you are referring to is compatibility, unification means something entirely different - such as, with unification, we'd have one energy equation for all results in relativity or QM.

You still haven't answered my initial questions though. You have done just about everything you possibly could to avoid answering them, in fact.

Which question? I assume you are referring to when I said 'the definition of relativistic mass is wrong', in that case, I already have answered you, and I did so indepth which is probably why the answer got lost. Anyway, I'll summarize:

My first mistake was when I said " OK, I should have been more thorough in what I was saying. Relativistic mass was defined as γm since it was shown that E=γmc2 and from this definition, physicists thought relativistic mass was the true mass." because when I introduced the word "true mass" you did not know what I was referring to and thought my answer was a dodge.

Now let me restate everything: When I said the definition was wrong, I meant that the definition that physicists attributed to relativistic mass when it was first conceived was wrong which was that relativistic mass was the "correct" notion of mass. Some people still hold on to the notion that the correct notion of mass is the relativistic mass. I did not mean to imply that the mathematical definition of relativistic mass was in any way wrong. Pretty much, you can make any mathematical definition you want, I never meant to imply that a mathematical definition is invalid. However, mathematical definitions are usually for a good reason and with relativistic mass, there doesn't really appear to be any good reason for the mathematical definition. That was the opinion of my physics professors, that is the opinion of the physics professor (instructor? I don't believe he has a Ph.D) that started this thread and is the collective opinion of the contributors to the relativistic mass page on wikipedia, which for me, seems to be the most reliable source on the internet for a general consensus for such matters.

Now tell me Tom, who am I to believe on this matter in physics? The collect majority of Physics professors or a single Math/Engineering Professor? BTW, do you have a degree in math or engineering? I've known some engineering professors to have a degree in math, but not the other way around - and I assume that to be the case for good reasons. If you don't wish to answer just like you dodged my question on your qualifications in physics, then that is fine - I was just curious. You could PM it if that suits.

Name one good reason you have for holding the opinion that relativistic mass is useful. I have one, it is highlighted in red:
In popular science and basic relativity courses, however, the relativistic mass is usually presented, most likely due to its conceptual simplicity.[/color]

Irrelevant.

Oh? Irrelevent you say. But that was my entire point. I will give you this: I chose the wrong wording when I made my first claim. But I quickly corrected it in the next post and you took that to be a dodge as you are still looking for me to answer how a mathematical definition (I never said mathematical in my initial claim by the way - you just interpreted that) can be incorrect. Well, I told you above that I too believe any mathematical defintion certainly must be correct -by definition-. And again, I am sorry that I am not always the best at choosing my words, but surely you can take my word for it that what I in fact meant is what I say I meant.

I asked you why you say that it's wrong.

Either answer the question or admit that you can't. But please stop the evasive tapdancing.

Again, I answered this in the paragraph above as well I might add, I corrected the interpretation you attributed to my claim in my 2nd response to you in this thread.

Name one thing I've said that is crackpottery?

I'll name 3.

1. That relativistic mass is incorrect.

We've already been over this. I never said the mathematical definition of relativistic mass is incorrect, nor did I ever intend this.

2. That the procedure for determining photon energy and momentum that is prescribed by relativity is to use the relations for massive particles.

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

3. That you can derive the quadratic energy-momentum relation from the relations for massive particles and then turn around and apply the result to photons.

That is the only way that I am aware of that the energy-momentum equation is derived. It is how it was taught by my physics professor on the very subject. Now you attribute the name 'relations for massive particles' for the relativistic energy and momentum relations. While it is true that the relations are only defined for such objects with mass, it is not true that those equations have nothing to do with the general quadratic energy-momentum relation.

I can tell you one thing, the only person I agree with in this thread is the thread starter whom just happens to be a qualified physics instructor. Ho-hum, and I am a crackpot?

Yes.

I suppose all physicists are crackpots according to you?

How about you just stick to dealing with my statements, instead of my personal qualifications?

Well your statements should be backed up in some way. If you are not personally qualified, you should be providing references for what you say. I think that is a reasonable rule to abide by, don't you?

 

[Aer]

Since in most equations on particle dynamics there are more than one particle it because yucky to start writint things like m01

Well, you can adopt the notation of others and simply use m as rest mass and not use m₀.

That article in wikipedia is wrong as most such articles are.

So Wikipedia is full of a bunch of know-nothing idiots I see.

I recall some wiseguy in the sci.physics.relativity newsgroup "proving" to me that rel-mass is not useful and is "outdated" by pointing me to David Morin's text.

I do not know the background on your little story here.

If you are going to keep whining about "useful" then defined that term and prove why rest mass is "useful" (which, of course, it is).

Your only argument so far has been that relativistic mass makes notation easier. I really don't see how. If I run across m/γ I might forget that that could simplify. OR if I have to take the derivative of m, then I must first expand it into γm₀ to proceed, compactness can be nice - but not if it sacrifices clarity. Personally, I think compacting 1/\sqrt{1-v^2/c^2} is good enough. Further compacting of two variables multiplied by each other into a single variable that is very similar to one of the variables in which was compacted is not a very good idea and loses clarity.

 

[pmb_phy]

Well, you can adopt the notation of others and simply use m as rest mass and not use m₀.

I see you weren't paying close attention. This is for a system of free particles. This is not meaningful otherwise in the general case.

So Wikipedia is full of a bunch of know-nothing idiots I see.

So what you're saying is that if a person (the person who wrote that article) is not an expert on on specific and highly specialized subject then he's an idiot?

With that logic I can't see the benifit of continuing this conversation. Apparently Tom is write and you don't have a great capacity of listening to propopnents of the otherside of a topic. Had you been willing then you'd know that this is not a new debate but one that dates back many decades, at least to the mid 60s.

Pete

ps - Tom, he/she's all yours.

 

[robert Ihnot]

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.."

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?

 

[quantumdude]

I still stand by my claim because I have a different definition of unification than you do. My definition would most closely be defined as: the act of combining into one. Now this is still a bit vague, so let me put it into context of the unification of Relativity (for our purposes here, we'll just say special relativity and disregard general relativity since we both seem to agree that QM and general relativity are not unified). So when I say the unification of QM and SR, I mean that we have one coherent theory that describes all the phenomena in both QM and SR. Now, you have presented little tid-bits of QM in relative frames, but that is a far cry from a unification theory. That is why QM and SR are still separate theories. At the least, you've presented compatibility, but not unification.

I told you that relativistic QM and QFT are considered a unification of QM and SR, and I told you to look into it. I can't help it if you are determined to remain ignorant willfully.

So, I believe:
my original statement, as I intended, is true.

Well your original statement, as you wrote it, is false. Say what you mean, and mean what you say.

What bad information? I think you just misunderstood me is all.

I've been pointing it out along the way. Go back and find it.

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.

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.

If you don't believe my derivation, find it here and check out what Wikipedia has to say on the matter:

The relativistic energy-momentum equation

The relativistic expressions for E and p[/color] above can be manipulated into the fundamental relativistic energy-momentum equation:

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.

There is a way to justify that relation without referring to relations that are specific to massive particles, but you have yet to realize it.

Now, what are the relativistic expressions for E and p you ask? The very ones that I provided and you say have nothing to do with the relativistic energy-momentum equation.

You are a liar, and have been throughout our discussion. I did not say that they have nothing to do with the relativistic energy-momentum relation. I said that they SATISFY it.

Relativistic expressions for E and p:

E=\gamma m c^2
p=\gamma m v

Again: Those are valid for massive particles only.

Now a lot of people come here to learn,

Too bad you aren't one of them. You clearly need it.

so please stop stating your false claim that the relativistic equations for E and p are not used to derive the relativistic energy-momentum equation. Now I am not totally sure, but aren't you an owner or at least super moderator of physicsforums? I would think you'd want to keep false claims off your site considering your past history on such issues. You seem to be a bit of a hypocrite from my perspective. Of course you'll probably take offense to that, but I am not in the wrong here and you are.

You are a crackpot, and my only concern as a Super Mentor is to keep you and your false claims in check. Since you did not adjust your behavior after the warnings I issued and the correction I gave, you are going to have to take a powder from Physics Forums.

This is not sciforums. If you can't be reasoned with, then you will be banned from here. It's as simple as that.

Actually, I am not changing my tune, you just misunderstood what I meant.

I've discussed the very nature of these ad-hoc QM->SR jobs elsewhere. I am aware of them and did not think of them as "unification" in the way you do. We just have a semantics issue here, I tried to resolve that in my opening paragraph of this post.

I agree that unification means that a single coherent theory should describe the original two. But that is not what you have shown with your examples of "unification" which are more or less "compatibility".

Again: Go study relativistic QM and QFT. I have neither the time nor the inclination to discuss it with someone who is only interested in being "right".

Quantum field theory is an attempt, it has not been fully developed into a unified theory of QM and relativity.

It is a fully unified theory of QM and SR, which is all I've ever claimed.

Which question? I assume you are referring to when I said 'the definition of relativistic mass is wrong', in that case, I already have answered you, and I did so indepth which is probably why the answer got lost. Anyway, I'll summarize:

(snip)

You're changing your tune again. Your earlier posts indicate that you think that it is incorrect to define mass in that way. You called it misguided and unfounded physics. I asked you why it is wrong, and which predictions of relativity come out wrong if you use that definition. You have yet to answer. All you are doing here is a long-winded back peddle, saying that the idea isn't really wrong, but that you don't find it useful (in other words, you just don't like it). Why can't you just retract the claim straightforwardly?

Come on, it won't kill you. Say it with me, "I was wrong, Tom."

Now tell me Tom, who am I to believe on this matter in physics? The collect majority of Physics professors or a single Math/Engineering Professor?

Since you've shifted your claim, I find this quite disingenuous. But the answer to the general question, "who should I believe?" in matters of physics is always the same:

Don't believe anyone. Go study up on it for yourself.

BTW, do you have a degree in math or engineering? I've known some engineering professors to have a degree in math, but not the other way around - and I assume that to be the case for good reasons. If you don't wish to answer just like you dodged my question on your qualifications in physics, then that is fine - I was just curious. You could PM it if that suits.

I didn't dodge your question, I simply declined to answer it. There's a difference. Dodging a question is giving an overly verbose response to a question which doesn't really give a direct answer, and then pretending that an answer really was given.

Just like you do.

If you really want to have this pissing contest then you're on your own. You can find out all the personal information about me that I have chosen to reveal online by reading my journal.

Oh? Irrelevent you say. But that was my entire point.

No, your entire point was that the definition of relativistic mass is wrong. Now that you've (sort of) admitted that it isn't, there's nothing left to say.

We've already been over this. I never said the mathematical definition of relativistic mass is incorrect, nor did I ever intend this.

Yes you did say it. Go back and read your posts.

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

You said that that is how it would be done in relativity. Go back and read your posts.

That is the only way that I am aware of that the energy-momentum equation is derived. It is how it was taught by my physics professor on the very subject. Now you attribute the name 'relations for massive particles' for the relativistic energy and momentum relations. While it is true that the relations are only defined for such objects with mass, it is not true that those equations have nothing to do with the general quadratic energy-momentum relation.

Good grief, you're dense.

I suppose all physicists are crackpots according to you?

You aren't a physicist.

Well your statements should be backed up in some way. If you are not personally qualified, you should be providing references for what you say. I think that is a reasonable rule to abide by, don't you?

My statements are backed up by knowledge that is common to any beginning graduate student in physics. Go learn, boy.

 

[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 &equiv; γ(c,dx/dt,dy/dt,dz/dt) = (γc,γv)

Multiply by m and define as P:

P &equiv; (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&lt;&lt;c)

"Lagrangian" mass
m_0/ \gamma\ \ \approx\ \ m_0 - \frac{1}{2}m_0 v^2/c^2 \ \ \ \ (v&lt;&lt;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,

 

[daniel_i_l]

The real problem with dilation is that no real experiments have been done. We know how single particles behave, but if large objects carry their own inertial frame they may simply ignore relativity completely. The physics of large objects at relativistic speeds is basically completely unknown.

Of course there have been experiments done! Such as the experiment with the atomic clocks - one in a plane and one on the ground.

If Einstein is truly correct then Quantum entanglement cannot exist

No information can be sent with QE.

A very interesting thing happens if you make c infinite - relativity becomes linear - Newtonian!

How exactly do you do that?

 

[Longstreet]

Also, the GPS (global positioning system) has to compensate for time differences caused by both it's velocity and gravitational field differences between it and the surface of the Earth in calculating position so accuratly.

The c boundary is not so much that things become imaginary, but to even get an imaginary number you have to go through infinity. Even in quantum mechanics particles could never penetrate such a boundary. You would have to have infinite uncertainty in the energy and momentum of the particle, which means you could never detect it.

 

[pmb_phy]

No information can be sent with QE.

That may not be true. There has been theoretical research in this area and published in journals such as American Journal of Physics. References provided upon request.

Pete

 

[Longstreet]

Is it that no information can be sent, or that it can't be sent faster than light? I'd be interested to learn more about that because one might argue that in seperating two entagled particles to such a distance where the speed of light becomes significant, you still have to carry the particle (ie the information) less than c and so nothing is really violated.

 

[pmb_phy]

Is it that no information can be sent, or that it can't be sent faster than light? I'd be interested to learn more about that because one might argue that in seperating two entagled particles to such a distance where the speed of light becomes significant, you still have to carry the particle (ie the information) less than c and so nothing is really violated.

If a signal can travel faster than the speed of light then you can devise a situation where causality is violated.

Pete

 

[sequence]

That may not be true. There has been theoretical research in this area and published in journals such as American Journal of Physics. References provided upon request.
Pete

provide them.

 

[pmb_phy]

References:
Faster than Light?, Chiao et al, Scientific American, Aug. 1993

Can EPR-correlations be used for the transmission of superluminal signals?, P. Mittlestaedt, Ann. Phys., 7, 1998, 711-715

Superluminal signal velocity, G. Nimtz, Ann. Phys., 7, 1998, 618-624

Bell's theorem: Does quantum mechanics contradict relativity?, L.E. Ballentine, Am. J. Phys., 55(8), Aug. 1987

Possibility of Faster-Than-Light Particles, G. Fienberg, Physical Review, Volume 159, No. 5, July 25, 1987 (this is the paper which postulated the posibility of tachyons)

Pete

 

[Intuitive]

If We have two Atoms.

1. Atom A. is a Hydrogen Atom at rest.
2. Atom B. is a Hydrogen Atom traveling at half the speed of light or 93,141 miles a second.

Question is, How big is Atom B. compared to Atom A. Exactly?

What are their size differences?

 

[pmb_phy]

If We have two Atoms.
1. Atom A. is a Hydrogen Atom at rest.
2. Atom B. is a Hydrogen Atom traveling at Light speed.
Question is, How big is Atom B. compared to Atom A. Exactly?
What are their size differences?

Nothing can travel at the speed of light so please rephrase your question. Thanks.

Pete

 

[jtbell]

What is it with physicists? This almost religious conviction that Mr Einstein must MUST be right. In reality relativity is a pretty fragile beast,

Not every single prediction of relativity has been tested, for example I don't know of any observations of length contraction (which would be rather difficult in practice). However, practically all tests so far have supported predictions of relativity, and the few that apparently don't, have problems:
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html