# Einstein's:Mass increase resulting from Acceleration increase

#### pmb_phy

pervect said:

The example on pg 141 of MTW does not convince me that MTW embraces the concept of relativistic mass. You will note that the term "relativistic mass" does not appear anywhere in the equation you wrote.
I never held that MTW use the term "relativitic mass." When they mean rest mass they say rest mass. I hold that in the examples I gave that mass does not refer to proper mass. You will note that on page 141 that they assign "energy density = mass density." This usage of mass means what you've referred to as relativistic mass due to the relation "energy density = mass density."

If we proceed to the preceding pages for some context, on pg 140, we see

Thus when MTW says on the very following page

$T^{0j}$ = (energy flux) = (energy density) * (mean velocity of energy flow) = (mass density)*(mean velocity of mass flow)

We should interpret their remarks on pg 141 in light of the previous definitions on pg 140.
That would be a bad mistake.

The moral of the story in my opinion is that the term "mass" by itself is ambiguous. By taking a short section of MTW out of context, you make it appear that MTW embraces the concept of relativistic mass, where nothing could be further from the truth.
That's very wrong. I have always held that in some instances they use "mass" to refer to relativistic mass" and any assumptions otherwise is a gross misinterpretation of my point.
[quoted]
The safest thing to do is undoubtedly to write down "invariant mass" or "relativistic mass" every single time the phrase is used.
Thorne and blanchard to this in their new text. This could become quite tedious, so I have no objection to an author writing the term mass(invariant mass) or mass (relativistic mass) to define what sort of mass he or she is talking about, with the understanding that further usages of the term will be consistent with the definition originally offered.
I do not expect the layman or new person on the forums to ask their questions so carefully and precisely, BTW.
Many times the questions arise as to what mass means given the often used relation E = mc2 and they get confused as to why photons have no mass yet it has energy which confounds them.

Pete

ps - I'm had an MRI this morning for which I need to take medication to get through it (I'm claustrophobic why I get squeezed into that darn "coffin." So if I appear to be lax in response its due to the meds.

#### pmb_phy

robphy said:
Concerning the redefinition of "mass".
• I do not think that "mass" should mean "relativistic mass"...As suggested above, I would prefer "apparent-mass" over "relativistic-mass", again emphasizing the observer-dependence.
• Do you also prefer that energy should be referred to as "apparent energy" since it too observer dependant????

Pete

#### robphy

Homework Helper
Gold Member
pmb_phy said:
Do you also prefer that energy should be referred to as "apparent energy" since it too observer dependant????

Pete
For consistency, I suppose the answer has to be "yes"
... and for any other quantity which is obtained using an observer's 4-velocity (e.g. apparent-Electric-Field, apparent-length-of-this-object, apparent-wavelength-of-light, apparent-velocity-of-observer-B). A longer and probably more descriptive phrase would be the "energy measured by this observer".

Certainly, when talking among "friends", it would be hoped that everyone knows the context so that tedious words and phrases could be eventually dropped. However, an important statement (and one which might be quoted without its surrounding context) should be unambiguous.

When discussing non-Newtonian physics (like SR/GR and QM), we have to be clear since our everyday intuition and language is Newtonian. Someday (but apparently not someday soon) we may work to redefine the language to reflect these now-distinct concepts (e.g., proper-time and apparent-time) of the non-Newtonian world.

My \$0.02.

#### pmb_phy

robphy said:
For consistency, I suppose the answer has to be "yes"
... and for any other quantity which is obtained using an observer's 4-velocity (e.g. apparent-Electric-Field, apparent-length-of-this-object, apparent-wavelength-of-light, apparent-velocity-of-observer-B). A longer and probably more descriptive phrase would be the "energy measured by this observer".
The adjective is redundant sinced "energy measured by observer" can have only one meaning.

Pete

#### robphy

Homework Helper
Gold Member
pmb_phy said:
robphy said:
For consistency, I suppose the answer has to be "yes"
... and for any other quantity which is obtained using an observer's 4-velocity (e.g. apparent-Electric-Field, apparent-length-of-this-object, apparent-wavelength-of-light, apparent-velocity-of-observer-B). A longer and probably more descriptive phrase would be the "energy measured by this observer".
The adjective is redundant sinced "energy measured by observer" can have only one meaning.

Pete
I don't know where your quoted phrase, "energy measured by observer", comes from.

Just to clarify my post,
in order to emphasize the observer-dependence, the lone word "energy" should be replaced by either
• "apparent energy" (implicit observer-dependence)
• "energy measured by this observer" (explicit observer-dependence... possibly used as "energy measured by Alice" and "energy measured by Bob", etc...)

If you are implying that "apparent energy measured by this observer" is redundant, yes, I agree.... that is why I did not use such a phrase.

#### pmb_phy

robphy said:
If you are implying that "apparent energy measured by this observer" is redundant, yes, I agree.... that is why I did not use such a phrase.
If one is speaking of flat spacetime an inertial frames then it depends on usage. If there is no field present then its bet to refer to the sum of mass-energy and rest energy as "inertial energy." If there is a field present then the potential energy must be added and then one refers to the sum as the "energy" or "total energy." The time component of the 4-momentum will be the inertial energy. The time component of the canonical 4-momentum will be the the total energy.

Pete

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