Idea of increased mass at relativistic speeds

[omnipotent]

Mass and momentun are tools for calculations and lollypops for children. In classical mechanics we use inertial force to balance equations as a "pseudo force". Though we could consider inertial force as a "pseudo force" long ago, we cannot still consider mass as something "pseudo" (or if you like it - "relative"). Just as velocity is not an intrinsic property of an "object" and is irrelevant unless another object with a relative velocity is present as a reference; mass, momentum, energy all show up in calculations when some accident occurs, they are not intrinsic properties of "objects" . They are not realities in themselves but are measurable effects of some other realities.

 

[pmb_phy]

Because mass can be converted to energy.

So what. Nobody seemed to care about the relationship between mass and energy. Why is E = mc^2 a good/meaningful response to "But it is not interchangeable and defining it to be so is not a useful thing to do."?

Pete

ps - Its not quite correct to say that mass can be converted into energy. E.g. Neither mass nor energy changes in a nuclear reaction. What changes is the partioning of the energy from mass-energy to other forms of energy such as kinetic energy or potential energy.

 

[Entropy]

I don't know why you are getting all pissy about this. You're acting like I said something offensive.

So what. Nobody seemed to care about the relationship between mass and energy.

That is what this whole topic is about.

Why is E = mc^2 a good/meaningful response to "But it is not interchangeable and defining it to be so is not a useful thing to do."?

Because matter and energy are inchangeable. That equation shows it.

Its not quite correct to say that mass can be converted into energy. E.g. Neither mass nor energy changes in a nuclear reaction. What changes is the partioning of the energy from mass-energy to other forms of energy such as kinetic energy or potential energy.

"Mass-energy?" Stop playing word games and just call it "mass." I'm not sure what point you're trying to make here. Calling something by a different word doesn't change what it is.

 

[pmb_phy]

I don't know why you are getting all pissy about this. You're acting like I said something offensive.

You have read something into my posts which was definitely not there. Please try not to put words into my mouth or intentions into my tone.

"Mass-energy?" Stop playing word games and just call it "mass."

Nothing I post is ever a game unless I specifically state so. If I say something then I'm very serious about it. This is especially for this topic, i.e. "mass." Here you seem to be assuming that in all cases E = mc² and this seems to have led you to this "correction" of yours and your comment regarding "word games." Quite untrue. That equation is valid only in certain special cases, e.g. for single particles and for systems of free particles. It is not generally valid for constrained systems. Thus the claim that mass is identical to mass-energy is invalid.

You may want to think of this as silly semantics but that is your choice and your opinion. I'm very very serious about terminology and nothing I post is any sort of "game."

Let me clarify - The way we think is deeply entrenched in the language we use. Different language -> different ways of thinking. As Einstein once wrote

The greated part of our knowledge and beliefs has been communicated to us by other people through the medium of a language which others have created. Without language our mental capacities would be poor indeed, comparable to those of higher animals; ...

I'm going to take a guess and assume that you think that this is all nonsense and that differences in language has little to do with differences in ideas. To that point please recall the language of the Hopi indian. In the language of the Hopi there is no word for time. The language contains no referance to "time," either explicit or implicit.

Oh how I wonder how a text on special relativity would be translated into the language of the Hopi!

Pete

 

[Entropy]

Quite untrue. That equation is valid only in certain special cases, e.g. for single particles and for systems of free particles. It is not generally valid for constrained systems. Thus the claim that mass is identical to mass-energy is invalid.

Alright then help me out here. What do you mean by mass-energy.

 

[Aer]

Not only is it completely unnecessary but I think it creates more confusion than understanding.

How right you are!

The idea of mass increasing at relativistic velocities leads to the unavoidable conclusion that mass is relative just like velocity, which I find absurd. Reading some of the other post I see that it also leads to the conclusion that mass is different in different directions, which is even more absurd.

Yes and yes.

The total energy of a mass m at a relative velocity v and thus lorentz contraction factor gamma is given by E = gamma m c^2.

Yes.

Well what about kinetic energy? [...]
To handle the relativistic correction, we typically write
E = m c^2 + (gamma-1) m c^2
and we say that the first term is the mass energy (or rest energy) and the second term here is the relativistic kinetic energy, KE = (gamma-1) m c^2

Yes.

In this case we are obviously not thinking that the mass has increased by a factor of gamma at all, because the energy associated with mass has not changed. To say that the mass has increased by a factor of gamma would mean that all of the energy is a part of the mass and there is no energy of motion, and I don't think this helps in understanding special relativity at all.

Correct.

I guess the only way to make what I am saying clear is to look at an example. Suppose you accelerate a big ship to 1/2 the speed of light relative to the earth. If you have a medium ship inside the big ship then you can accelerate that medium ship to 1/2 the speed of light relative to the big ship. Then if you have a small ship inside the medium ship you can accelerate the small ship 1/2 the speed of light relative to the medium ship.

The energy requirements of all these acceleration depend on the rest masses of these ships (lets call them mbig, mmed, and msmall) in exactly the same way, using the KE shown above KE = (gamma-1) m c^2.
In each of the three cases gamma = 1/sqrt(1-.25) = 1.1547
First acceleration: energy required was KE = .1547 mbig c^2
Second acceleration: KE = .1547 mmed c^2
Third acceleration: KE = .1547 msmall c^2

If you want to talk about the resulting velocity with respect to the Earth then you need the velocity addition formula v3 = (v1+v2)/(1+ v1 v2/c^2).
So the velocity of the medium ship with respect to the Earth is (c/2+c/2)/(1+.25) = 0.8 c, and the velocity of the small ship with respect to the Earth is (.8 c + .5 c)/(1+ .8x.5) = .92857 c. If you look carefully at the velocity addition formula you will see that if both v1 and v2 are less than c then v3 will be less than c, but if either v1 or v2 is equall to c then v3 will also be c.

The point is there is no increase of mass in this explanation nor should there be. The idea of mass increase promotes a misconception that something changes as you accelerate making an increase of speed more difficult. Absolutely nothing changes. The only limit is on relative velocity at which you see objects receding behind you. It does not even limit how fast you can travel to a destination.

Very good explanation. You obviously must be a qualified physicist unlike most on this forum.

The speed of light is unreachable because it is like an infinite speed in the sense that if you chase after a light beam your accelertion never reduces the relative velocity between you and the light beam you are chasing, the light continues to speed away from you at 3x10^8 m/s. You cannot catch the light no matter how fast you go, just as if the light were traveling infinitely fast. In fact, we know from the relativity of simultaneity that any travel faster than light would be equivalent to arriving at your destination before you left, leading to the same paradoxes as in time travel. Also if you think of the infinite speed as the limiting case where you get to your destination in no time at all, the speed of light is exactly such a limiting case.

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

 

[Aer]

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. Sayang one is the correct one and the other incorrect is nonsense. And I don't really care if paticle physicist is bothered by it or not.

m=p/v is incorrect for relativity. m=p/(γv) is correct for relativity. The former can only be used when v<<c and I hope is the only "many places" you are referring to, otherwise your sources are wrong.

Please provide proof that was increasing mass was concocted as an explanatory tool

Actually, it was not concocted as an explanatory tool. In the old days, it was believed the relativistic mass was the real mass. It wasn't until quantum physics that physicists realized that invariant mass was the real mass. Since then, relativistic mass has all but been forgotten except in elementary physics classes - and even at a good university, it isn't included in the elementary physics classes either. Relativistic mass however is still very prevalent on the internet and with some older generation physicists.

Physicists Einstein included, never intentionaly fool someone or "concoct" something for a teaching tool.

Einstein is included in the "early days" when relativity was new and the concept of relativistic mass was not fully understood to be the incorrect concept we know it to be today.

I'll await proof for said claims.

How about you try to read an up-to-date text on relativity.

This is your basic assumption? You don't like it so it must be wrong huh?

That would make you, as a person, wrong; so I wouldn't say that was his assumption. He hasn't assumed anything in fact, he is merely trying to teach you modern relativity.

So. Did you read my entire paper? My website? Give it a whirl.

I've seen your website, the website would be better whirled down the toilet.

In pre-Einstein physics rods don't contract, volumes don't change and there is non-similaneity is gone. Therefore do you wish to get rid of these thinhgs too?

Those are all direct results of the lorentz transformations. Relativistic mass was a definition that was incorrect.

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.

The rest of your posts are so far off the mark it is just incredible

 

[quantumdude]

Those (edit: length contraction, non-simultaneity, etc) are all direct results of the lorentz transformations.

Yes, that's true. It's also true that relativistic mass is not a consequence of the Lorentz transformations.

Relativistic mass was a definition that was incorrect.

Er...How can a definition be incorrect?

What predictions turn out wrong if you use the older convention?

 

[Aer]

Er...How can a definition be incorrect?

What predictions turn out wrong if you use the older convention?

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.

Now what is meant by true mass? Well that's very hard to say because of all of the different definitions people seem to attribute to mass. From quantum mechanics, it was found that invariant mass was the only useful quantity, but I would argue that this is just because QM doesn't deal with frames, which consequently is why QM and GR/SR are not unified in anyway. However, if we stick to just relelativity, we see also that the definition of m_r=γm has less use than just the invariant mass as well. The only time γm really has any use is when dealing with the energy equation. The force equation for example would be F=*gamma;³ma, so "relativistic mass" doesn't really help out here any either.

Now let's get back to what was originally assumed when relativistic mass was defined:
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. So we want to know what is true mass. I would put forth that an object, or series of objects (a la compound objects) true mass is proportional to the gravitational field it/they produce. Now when dealing with the curvature of spacetime, the kinetic energy of an object does not increase the curvature of spacetime around it, so relativistic mass in this way would not be considered true mass. Also, concerning thermal energies, thermal energy is just a term for the kinetic energy of atoms. In this way, thermal energy can be thought of as a compound object with constituent parts each having kinetic energies. So in this way, I don't think it makes much sense to say that thermal energy increases the "true mass" of an object either.

What we are left with (this is my personal opinion) is that "true mass" is a form of energy and not simply interchangable with energy. That is, mass and energy are only interchangable on the quantum level in which only quantum physics would be able to explain IMO.

 

[quantumdude]

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.

Well, I'd ask them the flip side of my question: How can a definition be considered undeniably true? You can't show a definition to be either true or false.

Now what is meant by true mass? Well that's very hard to say because of all of the different definitions people seem to attribute to mass. From quantum mechanics, it was found that invariant mass was the only useful quantity,

That's very cute, the way you take your opinion and impute to it nothing less than the authority of quantum mechanics. But it is obivously not true that your opinion follows from QM, so let's not pretend like it does, OK?

but I would argue that this is just because QM doesn't deal with frames, which consequently is why QM and GR/SR are not unified in anyway.

Say what? Have you not heard of the Klein-Gordon equation? Or of the Dirac equation, or any of its higher-spin analogs? Or of QFT?

Quantum theory and special relativity have been completely unified. And even if they hadn't, your statement would still be wrong. I've "dealt with frames" even with the plain vanilla Schrodinger equation. There is nothing stopping you from performing a Galilean boost to find out how QM predictions in one inertial frame are related to those in another.

However, if we stick to just relelativity,

Yes, I think that would be for the best!

we see also that the definition of m_r=γm has less use than just the invariant mass as well. The only time γm really has any use is when dealing with the energy equation. The force equation for example would be F=*gamma;³ma, so "relativistic mass" doesn't really help out here any either.

That's a bit uncharitable of you. You could define momentum as $p=(\gamma m)v=Mv$ and state that the force is $F=\frac{dp}{d\tau}=\frac{d(Mv)}{d\tau}$.

Now when dealing with the curvature of spacetime, the kinetic energy of an object does not increase the curvature of spacetime around it, so relativistic mass in this way would not be considered true mass.

Kinetic energy does, in fact, contribute to gravitation. All sources of energy and momentum are put into the energy-momentum tensor in GR.

You never did answer my questions on either how a definition could be considered wrong, or what predictions turn out wrong if the older convention of relativistic mass is used. But at least you admitted towards the end there that you are expressing your personal opinions about certain things.

Some things are simply a matter of opinion, and I think that the correctness or even the usefulness of relativistic mass is one of them.

 

[Aer]

Well, I'd ask them the flip side of my question: How can a definition be considered undeniably true? You can't show a definition to be either true or false.

I didn't claim that it was a true definiton.

That's very cute, the way you take your opinion and impute to it nothing less than the authority of quantum mechanics. But it is obivously not true that your opinion follows from QM, so let's not pretend like it does, OK?

You read too much into the issue of bringing up QM. And it is not my opinion, it is the opinion of those that deal with QM that invariant mass is the only useful quantity - NOT MINE. Do not try to push that claim on me as if it is my opinion.

Quantum theory and special relativity have been completely unified.

No, you talk only of special cases, there is no complete unification. Gravity is unexplained in QM for example.

To see how QM and Relativity are not completely unified, we need not even consider the gravity issue, one only needs to consider a photon. In relativity, the energy of a photon is given by:

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

or

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

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

Now pc in relativity for a photon would be: $$pc = \gamma m v c = \gamma m c^2$$, the familiar energy equation. However, $\gamma m$ is undefined for a photon because $\gamma$ is 1/0 where the denominator is exactly 0, which makes it undefined. If the denominator was only approximately 0, then it could be argued that γ is infinity for a photon, but that is not the case in current relativity theory. $\gamma$ is undefined for a photon. So the QM result that pc=hf cannot be explained in relativity for this very reason.

However, if one forgets the definition of p = γ m v, in which γ is undefined for a photon, and plugs pc = hf into the energy equation $$E^2 = (pc)^2 + (mc^2)^2$$, then one gets the correct result that E=hf. But this is an ad-hoc job because pc is undefined for a photon in relativity as I've repeated over and over so that you would understand.

Yes, I think that would be for the best!

No, let's consider more QM examples. Explain to me how QM explains gravity. I am aware of possible canidates that you will no doubt try to pass off as generally accepted, but I know better - in truth, they are just candidate theories and have problems when trying to unify the two theories.

That's a bit uncharitable of you. You could define momentum as $p=(\gamma m)v=Mv$ and state that the force is $F=\frac{dp}{d\tau}=\frac{d(Mv)}{d\tau}$.

You forgot to keep going... $$F=\frac{dp}{d\tau}=\frac{d(Mv)}{d\tau}=\frac{d(mv/ \sqrt{1-(\frac{v}{c})^2})}{d\tau}$$.
Remember, you need all terms that are going to differentiate with $\tau$ to be expanded out. I ask again, what was the use of M in the above? I could have just skipped to the last step if I never defined an M...

Kinetic energy does, in fact, contribute to gravitation. All sources of energy and momentum are put into the energy-momentum tensor in GR.

They are all put in, but some are referred to as "non-gravitational energy". Ho-hum, this disagrees with what you said about all energies contributing to gravitation:

The components T0b can therefore be interpreted as the local density of (non-gravitational) energy and momentum. The spatial components Tij correspond to components of local non-gravitational stresses, including pressure. This tensor is the Noether current associated with spacetime translations.Source: wikipedia

Some things are simply a matter of opinion, and I think that the correctness or even the usefulness of relativistic mass is one of them.

My opinion is that you are wrong, ok?

 

[DrGreg]

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?

 

[Aer]

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

I can agree to differ with the other side with the added context that the other side is just wrong.

"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.

You are correct to say that one may use proper mass and ignore relativistic mass forever and for every situation. However, the converse is not true. One using relativistic mass cannot ignore proper mass as it is in the definition of relativistic mass! Furthermore, when doing any detailed analysis, one is required to break relativitistic mass, M into &gamma; and m, as is even apparent in Tom's example of d(Mv)/dt above.

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.

One using relativistic mass is not free to not use proper mass in any context!

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?

There are not multiple notions of mass, there is only one correct notion of mass and that is proper mass, rest mass, invariant mass (all the same thing).

 

[quantumdude]

I didn't claim that it was a true definiton.

And I clearly said that I would ask "them" (meaning "those physicists who thought that relativistic mass was the true mass").

You read too much into the issue of bringing up QM. And it is not my opinion, it is the opinion of those that deal with QM that invariant mass is the only useful quantity - NOT MINE. Do not try to push that claim on me as if it is my opinion.

You stated the opinion, and you did not attribute it to anyone else. Any naitive English speaker would have concluded that the opinion is yours.

But fine: Let's not pretend that "their" opinion follows from QM, because it doesn't.

No, you talk only of special cases, there is no complete unification. Gravity is unexplained in QM for example.

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.

To see how QM and Relativity are not completely unified, we need not even consider the gravity issue, one only needs to consider a photon. In relativity, the energy of a photon is given by:

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

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

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

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. The second and third equations only apply to massive particles, while the first applies to all particles, even those with zero mass.

Now pc in relativity for a photon would be: $$pc = \gamma m v c = \gamma m c^2$$, the familiar energy equation. However, $\gamma m$ is undefined for a photon because $\gamma$ is 1/0 where the denominator is exactly 0, which makes it undefined. If the denominator was only approximately 0, then it could be argued that γ is infinity for a photon, but that is not the case in current relativity theory.

This is complete BS. The process of equating $pc$ and $\gamma mvc$ for photons is incorrect on its face. There is nothing in the theory of relativity that would even suggest that it should be done.

$\gamma$ is undefined for a photon. So the QM result that pc=hf cannot be explained in relativity for this very reason.

Right, the explanation comes from the unification of special relativity and quantum theory, which has been done, despite the fact that you claim otherwise.

However, if one forgets the definition of p = γ m v, in which γ is undefined for a photon, and plugs pc = hf into the energy equation $$E^2 = (pc)^2 + (mc^2)^2$$, then one gets the correct result that E=hf. But this is an ad-hoc job because pc is undefined for a photon in relativity as I've repeated over and over so that you would understand.

You can repeat until you're blue in the face, but you would still be wrong. pc is not undefined for a photon.

No, let's consider more QM examples. Explain to me how QM explains gravity. I am aware of possible canidates that you will no doubt try to pass off as generally accepted, but I know better - in truth, they are just candidate theories and have problems when trying to unify the two theories.

Why would I need to explain quantum gravity, in order to defend my point?

You forgot to keep going... $F=\frac{dp}{d\tau}=\frac{d(Mv)}{d\tau}=\frac{d(\frac{mv}{sqrt(1-{\frac{v}{c}}^{2})}{d\tau}$. Remember, you need all terms that are going to differentiate with τ to be expanded out.

I didn't forget to do anything. You can, in fact, write force as F=dM/dτ.

I ask again, what was the use of M in the above? I could have just skipped to the last step if I never defined an M...

Obviously, the use of M in that particular equation was to make the relationship more compact. Is that really too difficult to see?

They are all put in, but some are referred to as "non-gravitational energy".

If by a "non-gravitational energy" term you mean a term that describes "energy that does not contribute to gravitation", then kinetic energy is not one of them.

Ho-hum, this disagrees with what you said about all energies contributing to gravitation:

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.

My opinion is that you are wrong, ok?

Unfortunately, you don't have a single good reason for holding that opinion.

Aer, you have been trying the patience of the staff with your insulting tone to others, and we have been watching. But in this post not only have you been patronizing, but you have descended into abject crackpottery. I must insist that you stop doing it.

 

[quantumdude]

You are correct to say that one may use proper mass and ignore relativistic mass forever and for every situation.

That's true.

However, the converse is not true. One using relativistic mass cannot ignore proper mass as it is in the definition of relativistic mass! Furthermore, when doing any detailed analysis, one is required to break relativitistic mass, M into γ and m, as is even apparent in Tom's example of d(Mv)/dt above.

That's also true.

Now for the big question: So what?

This point of yours does nothing whatsoever to show that the definition of relativistic mass is wrong.

One using relativistic mass is not free to not use proper mass in any context!

Sure he is. A particle's proper mass would be its rest mass.

There are not multiple notions of mass, there is only one correct notion of mass and that is proper mass, rest mass, invariant mass (all the same thing).

There are multiple notions of mass that have equal claims to being "correct". Deal with it.

 

[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 [itex]\gamma^2 = 1/(1-v^2/c^2):
$$(pc)^2 = -m^2 c^4 + \gamma^2 m^2 c^4$$
Using the definition of $E=\gamma m c^2$:
$$(pc)^2 = -m^2 c^4 + E^2$$
And viola:
$$E^2 = (pc)^2 + m^2 c^4$$

You were saying?

The second and third equations only applie to massive particles, while the first applies to all particles, even those with zero mass.

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 should be all the results from relativity being described in QM.

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.

Right, the explanation comes from the unification of special relativity and quantum theory, which has been done, despite the fact that you claim otherwise.

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).

Why would I need to explain quantum gravity, in order to defend my point?

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.

I didn't forget to do anything. You can, in fact, write force as F=dM/dτ.

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?

Obviously, the use of M in that particular equation was to make the relationship more compact. Is that really too difficult to see?

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

If by a "non-gravitational energy" term you mean a term that describes "energy that does not contribute to gravitation", then kinetic energy is not one of them.

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?

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.

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

Unfortunately, you don't have a single good reason for holding that opinion.

Name one good reason you have for holding the opinion that relativistic mass is useful. I have one, it is highlighted in red:

In the earlier years of relativity, it was the relativistic mass that was taken to be the "correct" 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.

The accepted usage in the scientific community today (at least in the context of special relativity) considers the invariant mass to be the only "mass", 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.

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

Aer, you have been trying the patience of the staff with your insulting tone to others, and we have been watching.

I know that you have been watching and that you have been called here.

But in this post not only have you been patronizing, but you have descended into abject crackpottery.

Name one thing I'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?

I must insist that you stop doing it.

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

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 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.

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 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