[PmbPhy (OP)]

Question: Who here believes that relativistic mass is merely another name for energy, and why?

According to lightarrow at https://www.physicsforums.com/threads/relativistic-mass.642188/page-2 he falls in to that category but I don't know why.

I'd also like to ask folks here what E = mc² means. Do you also believe that anybody knows why E = mc², i.e. what is the mechanism(s) for this to be true? Do you believe that anybody knows the answer to this question?

Thank you.

Edit: I took an example out so as not to divert attention to it.

[lightarrow]

Can I vote for myself or it was already taken for granted?  []

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lightarrow

[PmbPhy (OP)]

Can I vote for myself or it was already taken for granted?  []

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lightarrow

Sure.

[jeffreyH]

e=mc^2 is just energy. Relativistic mass is energy with momentum. It is also affected by gravity as you showed above. e=mc^2 cannot be used to determine the mass of a photon as it has zero rest mass.

[yor_on]

Wonder if not the key point to people arguing with you Pete is this "While relativistic mass is useful in the context of special relativity, it is rest mass that appears most often in the modern language of relativity, which centres on "invariant quantities" to build a geometrical description of relativity. " What is relativistic mass?

"Einstein preferred to think of his theory in terms of the coordinates of space and time: x, y, z and t. The essential ideas of the theory were conveyed by the algebraic properties of these quantities, treated as variables in equations. Its basic equations are the Lorentz transformation, which, in Einstein's hands, is a rule for changing the variables used to describe the physical system at hand.

The laws of physics are written as symbolic formulae that include these coordinate variables. The principle of relativity of relativity then became for Einstein an assertion about the algebraic properties of these formulae; that is, the formulae stay the same whenever we carry out the symbolic manipulation of change of variables of the Lorentz transformation. The emphasis in Einstein's algebraic approach is on variables, not spacetime coordinates, and formulae written using those variable, not geometrical figures in spacetime.

For many purposes, it makes no difference which approach one uses, geometric or algebraic. Sometimes one is more useful or simpler than the other. Very often, both approaches lead us to make exactly the same calculations. We just talk a little differently about them. However there can be a big difference if we disagree over which approach is more fundamental. We now tend to think of the geometric conception as the more fundamental one and that Einstein's algebraic formulae are merely convenient instruments for getting to the geometrical properties. There is some evidence that Einstein saw things the other way round. He understood the geometric conception, but took the algebraic formulation to be more fundamental. A simple example illustrates how this difference can matter a lot." How Did Einstein Think? /


Einstein did not use geometry to describe it, not as I've understood it at least. It's a later and very useful approach for making relativity come alive in a intuitive way. But the point there is that he did not use it geometrically at all, he used Algebra. And there's a definite difference there.  Considering the site you linked, the attitude shown by those commenting on you wasn't too impressive to me. (htt_p://sci.tech-archive.net/ that is)
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As for you asking what  E = mc2 means
You pick the difficult ones, don't you?

what does it mean?   
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Btw: I'm less and less sure Einsteins approach is the 'worse one'. A geometrical approach goes out from an assumption of a unifying geometrical universe, a 'common container' of us all. Treating it algebraically makes no such assumptions, even though they may linger when you ask the one creating the algebra. Einsteins intuition is still famous, and worth listening too.

[alancalverd]

Nothing to do with belief. I'm an experimental physicst, and when my photon beams in air or tissue exceed 1.022 MeV we get pair production, signalled by the appearance of two 511 keV photons, exactly as predicted by E = mc² and the known mass of the electron (another experimental value).

Whether you believe it or not, it happens every damn time, which is how we diagnose tumors on the one hand, and calibrate small accelerators on the other.

[jeffreyH]

Nothing to do with belief. I'm an experimental physicst, and when my photon beams in air or tissue exceed 1.022 MeV we get pair production, signalled by the appearance of two 511 keV photons, exactly as predicted by E = mc² and the known mass of the electron (another experimental value).

Whether you believe it or not, it happens every damn time, which is how we diagnose tumors on the one hand, and calibrate small accelerators on the other.

Well I think you should know. Thanks for another informative post.

[lightarrow]

Nothing to do with belief. I'm an experimental physicst, and when my photon beams in air or tissue exceed 1.022 MeV we get pair production, signalled by the appearance of two 511 keV photons, exactly as predicted by E = mc² and the known mass of the electron (another experimental value).

Whether you believe it or not, it happens every damn time, which is how we diagnose tumors on the one hand, and calibrate small accelerators on the other.

Photons alone can never generate a couple e⁺ e^-: simultaneous conservation of system momentum and energy would be violated. You have to collide the light beam with another massive particle (an atom's nucleus for ex.) in order to do that.
E = mc², if E is the system total energy and m is the system's mass (that is, invariant mass) is valid only in a frame of reference in which the system's momentum p is zero.
The correct equation in SR is:

E² = (cp)² + (mc²)².

For the OP: I know almost nothing about GR so I can't say if relativistic mass can have a meaning there; according to Pervect in the Physics forum thread you linked (post 18), other concepts of mass are used:

"Relativistic and invariant mass are just the tip of the iceberg, and wind up having little to do with gravity in the end.
Concepts such as Komar mass, ADM mass, Bondi mass, and quasi-local mass wind up as being more directly related to gravity than either relativistic or invariant mass."

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lightarrow

[PmbPhy (OP)]

e=mc^2 is just energy.

To be very clear, it's not energy per se. It's what I call inertial energy, since it's depending only on inertial mass. If the object is a particle and it's not in something like an electric field then there's no potential energy (such as electric potential energy). However if the field is an electric field then the total energy of the particle must include the electric potential energy.

Relativistic mass is energy with momentum.

I don't understand why you say that it's energy with momentum. Can you please elaborate as to why?

e=mc^2 cannot be used to determine the mass of a photon as it has zero rest mass.

Actually, you're wrong. From Relativity: Special, General and Cosmological by Wolfgang Rindler, Oxford Univ., Press, (2001), page 120

According to Einstein, a photon with frequency n has energy hf /c², and thus (as he only came to realize several years later) a finite mass and a finite momentum hf/c.

[yor_on]

Maybe you would like this one Lightarrow?
Quasi-Local Mass in General Relativity.   

Found it while trying to see what those 'quasi-local masses' you mentioned referred too. It's amazingly readable, considering its subject, and mathematics
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Maybe I should have found this one first? The Hawking mass for ellipsoidal 2-surfaces in  Minkowski and Schwarzschild spacetimes. 

"In general relativity, the nature of mass is non-local. However, an appropriate definition of mass at a quasi-local level could give a more detailed characterization of the gravitational field around massive bodies. Several attempts have been made to find such a definition. One of the candidates is the Hawking mass."

And "In the light of modern quantum field theoretical investigations it has become clear that all physical observables should be associated with extended but finite spacetime domains. Thus observables are always associated with open subsets of spacetime whose closure is compact, i.e. they are quasi-local. Quantities associated with spacetime points or with the whole spacetime are not observable in this sense."

Still struggling with this concept, but it fits nicely with Pete's definitions of what 'mass' is, as I gathered from his writing before.  "Imagine a system of two massive bodies at rest relative to each other. If they are far apart, then there will be a gravitational potential energy contribution that makes the total energy of the system greater than if they are close to each other. There is a difference in total energy, despite that integrating the energy densities yields the same result in both scenarios. That energy difference is the energy attributed to the gravitational field. Since the gravitational field has energy, and therefore mass, it is a source of gravity, hence it is coupled to itself. Mathematically, this is possible because the field equation is non-linear."

So, what it discuss is gravity, as potential energy, as mass, between two points of proper mass (as planets). Trying to isolate 'patches' of the vacuum between, giving a 'patch' a 'quasi-local mass' mathematically (gravity->energy->mass), that should fit all expressions and descriptions of a SpaceTime? Remembering that there is no static representation of that gravity in/at any given point, as it change with distance, motion and time, observer dependently too? What about Lorentz contractions? Also that it will be transformed away locally in any geodesic (free falling). Seems a most difficult thing to define, if I now got it right?.  As well as for a black hole, of any type. Or is it just black holes that's interesting here?

[alancalverd]

Photons alone can never generate a couple e⁺ e^-: simultaneous conservation of system momentum and energy would be violated. You have to collide the light beam with another massive particle (an atom's nucleus for ex.) in order to do that.

Which is why the "evidence" I cited was the annihilation photons, not the initial interaction with air or tissue. I might get my hands dirty doing physics instead of talking about it, but dumb I ain't.

[lightarrow]

Photons alone can never generate a couple e⁺ e^-: simultaneous conservation of system momentum and energy would be violated. You have to collide the light beam with another massive particle (an atom's nucleus for ex.) in order to do that.

Which is why the "evidence" I cited was the annihilation photons, not the initial interaction with air or tissue. I might get my hands dirty doing physics instead of talking about it, but dumb I ain't.

Ok, but I haven't understood how you interpret the equation
E = mc².
What is that m for you? Invariant or relativistic mass? When the equation is valid, for you? Always; only in SR; only in SR *and* if the system's momentum is zero; else?

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lightarrow

[lightarrow]

Maybe you would like this one Lightarrow?
Quasi-Local Mass in General Relativity.   
Found it while trying to see what those 'quasi-local masses' you mentioned referred too. It's amazingly readable, considering its subject, and mathematics

My compliments to you, I have understood nothing of it!  []

[Ethos_]

Question: Who here believes that relativistic mass is merely another name for energy, and why?

I'm no expert but here is how I understand the answer to this question.

Relativistic mass is the increase in mass that an object acquires from the energy of acceleration. The energy of acceleration is thus applied to the invariant mass of the original object. Invariant mass remains the same whether in motion or not. So yes, relativistic mass is just energy transferred thru acceleration to the original invariant mass.

[JohnDuffield]

Photons alone can never generate a couple e⁺ e^-: simultaneous conservation of system momentum and energy would be violated. You have to collide the light beam with another massive particle (an atom's nucleus for ex.) in order to do that.

That isn't right actually, there's such a thing as gamma-gamma physics. Two photons can interact to create an electron and a positron. It's the reverse of electron-positron annihilation.

For the OP: I know almost nothing about GR so I can't say if relativistic mass can have a meaning there; according to Pervect in the Physics forum thread you linked (post 18), other concepts of mass are used:

"Relativistic and invariant mass are just the tip of the iceberg, and wind up having little to do with gravity in the end. Concepts such as Komar mass, ADM mass, Bondi mass, and quasi-local mass wind up as being more directly related to gravity than either relativistic or invariant mass."

It's all rather ambiguous. For example invariant mass varies when a body falls down, hence the mass deficit. But conservation of energy applies. If you're up in space and you drop a 1kg brick onto the Earth, then provided the kinetic energy is retained rather than radiated away into space, the mass of the Earth increases by 1kg. And at all points the rest-mass of the falling brick plus its kinetic energy or relativistic mass, which is said to be a measure of energy, add up to a mass-equivalence of 1kg.

[PmbPhy (OP)]

Photons alone can never generate a couple e⁺ e^-: simultaneous conservation of system momentum and energy would be violated. You have to collide the light beam with another massive particle (an atom's nucleus for ex.) in order to do that.

This can happen with any nucleus. The nucleus merely acts as a catalyst. It isn't used up by the interaction meaning that it's there before and after and is unchanged  by the process just like any catalyst.

For the OP: I know almost nothing about GR so I can't say if relativistic mass can have a meaning there; according to Pervect in the Physics forum thread you linked (post 18), other concepts of mass are used:..

Sorry. I have no interest in what he thinks. Only those who post here. He doesn't have a good grasp of the subject. That nonsense about ADM and Komar mass demonstrates that fact.

[PmbPhy (OP)]

Nothing to do with belief. I'm an experimental physicst, and when my photon beams in air or tissue exceed 1.022 MeV we get pair production, signalled by the appearance of two 511 keV photons, exactly as predicted by E = mc² and the known mass of the electron (another experimental value).

Whether you believe it or not, it happens every damn time, which is how we diagnose tumors on the one hand, and calibrate small accelerators on the other.

Dear Alan,

What does that have to do with relativistic mass?

[PmbPhy (OP)]

Question: Who here believes that relativistic mass is merely another name for energy, and why?

I'm no expert but here is how I understand the answer to this question.

Relativistic mass is the increase in mass that an object acquires from the energy of acceleration. The energy of acceleration is thus applied to the invariant mass of the original object. Invariant mass remains the same whether in motion or not. So yes, relativistic mass is just energy transferred thru acceleration to the original invariant mass.

No. Mass and energy are NOT the same thing. Mendel Sachs wrote a paper on E = mc² and clarified this point very clearly. He explained that mass is related to inertial and energy is (loosely) related to the ability to do work. They are therefore not the same thing and they're not even closely to being related in that way. In general E doesn't even always equal mc² anyway. In cases of a closed system, such as when a rod is subjected to stress, then they aren't related in that way.

Also, there are different ways that relativistic mass can increase. You merely mentioned one of them. First of all the relativistic mass of a photon is not zero so it can't be accelerated. It merely has that mass when it's created, same as all elementary particles in particle accelerators. Another way to see an increase in relativistic mass is to change from one frame of reference to another one in which the speed is greater.

There is also a lot more to do with invariant mass than you've mentioned and that most people are aware of. See "An Incorrect Application of Invariant Mass " in the webpage:
http://home.comcast.net/~peter.m.brown/sr/invariant_mass.htm

[PmbPhy (OP)]

Which is why the "evidence" I cited was the annihilation photons, not the initial interaction with air or tissue. I might get my hands dirty doing physics instead of talking about it, but dumb I ain't.

That's an excellent point, Alan. Well stated. Just because we leave something out or don't express something as others might, it doesn't mean it's wrong. This being a perfect example. In fact when you wrote

...and when my photon beams in air or tissue exceed 1.022 MeV we get pair production..

When you wrote this you made it precisely clear that something else was needed and that made it clear that the photons were not alone. In that case lightarrow was wrong in attempting to "correct" you. We all know that air and tissue contain nuclei.

[yor_on]

heh "My compliments to you, I have understood nothing of it!" As mysterious to me too Lightarrow. But I've seen this type of reasoning, as well as Komar mass, in physics forum before, and I want to know why and how they reason in it. This idea with quasi local mass seems to cover it all. The point there is that the idea of using a defined patch to then give it a mass to me collides with Einsteins concept of gravity, in where you transform it away locally. If we call it mass then that mass disappear locally, same with 'energy' which I think describe it (as in doing experiments inside a 'black box') even better.
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Or expressed another way, to argue that there is a mass locally, although not experimentally provable, is to define one observer dependency as primary, the other secondary, to a universe. Alternatively I will relate it to a concept of a universal container, in where it all have to even out. The last one sounds as if it can explain it, but it depends on how you define that 'container' to me. Locally defined, or, as some idea of a premade universe in where it all should 'even out'. As I use only the local definition, a 'premade' universe doesn't exist, it's observer defined.