Einstein's letter to Lincoln Barnett

[pmb_phy]

In a letter Einstein wrote to Lincoln Barnett in he wrote in (1948) he wrote

It is not good to introduce the concept of the mass

m = \frac{M}{\sqrt{1-v^2/c^2}}

of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the rest mass, m. Instead of introducing m₀ it is better to mention the expression for the
momentum and energy of a body in motion.

Question: Why do you think Einstein said no clear definition can be given?

Thanks

Pete

 

[Gamish]

Perhaps he was referring too the definition of mass. I don't really know, but that sounds logical.

 

[Chronos]

I think he was attempting to emphasize the concept of mass is only meaningful within its own reference frame, as is time and distance. To do otherwise would imply a preferred reference frame - a notion Einstein was trying to dispel.

 

[pmb_phy]

I think he was attempting to emphasize the concept of mass is only meaningful within its own reference frame, as is time and distance. To do otherwise would imply a preferred reference frame - a notion Einstein was trying to dispel.

The idea of relativity is that one should be able to make measurements from any frame of reference. Thus any observer can measure the time interval between two spatially separated events and each observer may measure a different value.

Why do you think that time and distance are only meaningful in "its own reference frame" and what do you mean by "its own reference frame"?

Thanks

Pete

 

[pmb_phy]

Perhaps he was referring too the definition of mass. I don't really know, but that sounds logical.

I believe so too but Einstein himself often used the definition of mass which leads to that expression elsewhere in his work, both before and after he wrote that letter. Seems to be its a well defined quantity to me.

Pete

 

[Chronos]

The idea of relativity is that one should be able to make measurements from any frame of reference. Thus any observer can measure the time interval between two spatially separated events and each observer may measure a different value.

Why do you think that time and distance are only meaningful in "its own reference frame" and what do you mean by "its own reference frame"?

Thanks

Pete

Upon reflection, I too find my original statement.. unsatisfying. Even the term 'meaningful' is not very meaningful. 'Invariant' would have been better. Regressing back to Einstein's remark, I think Einstein was pointing out relativisic mass is not a useful mathematical definition. He instead advocates using energy-momentum four vector description, where mass is Lorentz invariant, hence has the same value in all reference frames. This is logical given that rest mass is the magnitude of the four vector, whereas relativistic mass is the time component of the four vector. Relativistic mass is also misleading in the sense the increase in energy is not a property of the mass being accelerated, it is a property of spacetime geometry.

 

[jcsd]

I guess that it's that you can't have a definition of mass that is exactly the same as the definition in Newtonain mechanics (as you know, the relatvistic mass isn't always the inertial mass), so by introducing any concpet of mass into relativity you must also introduce a new definition of mass.

 

[pmb_phy]

Relativistic mass is also misleading in the sense the increase in energy is not a property of the mass being accelerated, it is a property of spacetime geometry.

mass, like length. is not supposed to be a property of a body so it can't be misleading. Proper mass and proper length are intrinsic properties as they are in Newtonian mechanics. However, in modern termsm, mass in Newtonian mechanics is not an intrinsic property of a particle by definition. It is something that can be derived from the definition and from the properties of the Galilean transformation.

(relativistic) mass is not defined as energy. They are propoprtional under special circumstances. It is not always true that E/c^2 = p/v. Here is an example of when that relation fails to hold true.

http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

This is a fact you can learn by reading Rindler's Intro to SR text. Read the relativitiy of continuos media section.

For an example where P = m_0 dx/d\tau fails to work please see

http://www.geocities.com/physics_world/sr/invariant_mass.htm

Especially the following sections

"Invariant Mass of a System of Particles - Non-Closed System"
"An Incorrect Application of Invariant Mass"

Pete

 

[Chronos]

Pete, I don't think there is any disagreement aside from semantics. I would, however, say it is easy and no special circumstances are needed to define mass [rest or relativistic] as energy using SR transformations. Relativistic mass, for example is the sum of the mass-energy component and the momentum-energy component as given by the expression E^2 = m^2c^4 +p^2c^2. As illustrated by the examples you gave, it is necessary to find the four vector solution to obtain correct results. Relativistic mass is only defined in the reference frame in which it is measured. Rest mass is the same in all reference frames. I'm not familiar with Rindlers textbook. I grew up on Taylor & Wheeler:

Spacetime Physics, 2nd Ed.
The concept of 'relativistic mass' is subject to misunderstanding. That's why we don't use it. First, it applies the name mass - belonging to the magnitude of a 4-vector - to a very different concept, the time component of a 4-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of space-time itself.

 

[pmb_phy]

Pete, I don't think there is any disagreement aside from semantics.

I wish I could have asked Einstein himself what he meant by that since I'm still not sure why he said it. This post was only to see what others think of why he said that. So I'm not looking for agreement/disagreement. I'm looking for your thoughts. I may post my thoughts too of course.

I would, however, say it is easy and no special circumstances are needed to define mass [rest or relativistic] as energy using SR transformations.

I would never defined mass in terms of energy. In my opionion that would be a serious mistake

Relativistic mass, for example is the sum of the mass-energy component and the momentum-energy component as given by the expression E^2 = m^2c^4 +p^2c^2.

I'm not sure what you mean by this. The "relativisitc mass" of a particle is proportional to the time component of 4-momentum, i.e. it is the "m" in P = (mc,p). Or defined in terms of a particular observer U it is m = P*U/c².

When you use the term "sum" a warning flag goes up in my mind. One has to be very careful when speaking about sums of things using 4-vectors. They can't always be added and give a physically meaningful quantity. Several authors I know of have made this point, e.g. Tolman and Ohanian.

Relativistic mass is only defined in the reference frame in which it is measured.

Yes. It is a relative quantity just like the lifetime of a free neutron. Or the length of a moving rod etc.

Rest mass is the same in all reference frames. I'm not familiar with Rindlers textbook. I grew up on Taylor & Wheeler:

For a single particle (or that which can be treated as a particle) that is true. But it ios not generally true. When you make that statement you are saying that in any frame of reference you can determine the rest mass of a particle by finding E and p and calculating m. This process is not always meaningful in the most general of cases.

See this post for an example
https://www.physicsforums.com/showthread.php?p=435649#post435649

I gave other examples in the links above.

I want you to think of this and give me an answer if you don't mind? - How would you measure E and p of the particle?

I have Taylor and Wheeler too. There is one thing they never define in that text - and that's the mass of a non-closed system. They steared clear of that in that text.

Thanks

Pete

 

[Kit Cox]

OK, I'm late on this for sure. Was browsing something about Lincoln Barnett and came across this thread, which seems to have both evolved, and quickly gone extinct, some time back in the Burgess Shale.

Pete said, "I would never defined mass in terms of energy. In my opionion that would be a serious mistake"

Sooo, m=E/c² is a 'serious' mistake? Are there unknown particles that would make this obsolete, or at least require modification? Or do we have a philosophical problem?

And as for the absolute mass of anything, doesn't it have to be referenced to something else that is absolutely stationary, hence all the discussion about 'reference frames' since there is nothing that is at absolute rest as far as is known? A bowling bowl sitting stationary on my table is moving in precession, nutation, rotation, solar orbital, orbital drift outward, inter galactical solar drift, galactic drift, galactic rotation, inter local cluster drift, super cluster drift, et al trajectories at once. OK, I left a few out. The only trajectory I can be absolutely sure it IS NOT moving in at any given time in any 'frame' is the one that gives me a strike.

That may be what Einstein was talking about to Barnett after the '47 edition of "The Universe and Dr. Einstein".

Chris "Kit" Cox

 

[Meir Achuz]

AE might have meant that "no clear definition can be given" because the velocity dependence of mass can have different forms in different applications.
If you try to extend F=ma, using relativistic mass, you need 'longitudinal mass' and
'transverse mass'.

 

[MManuel Abad]

I really recommend you all to read this paper. It's very interesting and readable (easily) and explains all about rest mass and the wrong concept of "relativistic mass" which, If I understood correctly, Einstein disproved:

http://arxiv.org/abs/hepph/0602037

 

[PhilDSP]

If a physical parameter cannot be reduced to a dependence on either longitudinal length (with respect to the source of the radiation) or time then it should be invariant in any frame of reference under the Lorentz transformation or in any form preserving operation on the Lorentz group, shouldn't it? Such a parameter should not be affected by symmetry aspects of spacetime in different inertial frames.

Mass is its own dimension with no defined dependence on time or length. But momentum is dependent on both time and length.

We might take note that the magnetic field variable is also not reducible (as far as we know) to dimensions of time or length, along with the electric and magnetic flux parameters used in integral equations. This seems to be a conundrum. But maybe it's not so perplexing because to evaluate or measure those values you first need to determine the spatial area you are considering.

 

[harrylin]

OK, I'm late on this for sure. Was browsing something about Lincoln Barnett and came across this thread, which seems to have both evolved, and quickly gone extinct, some time back in the Burgess Shale.

Pete said, "I would never defined mass in terms of energy. In my opionion that would be a serious mistake"

Sooo, m=E/c² is a 'serious' mistake?

Similarly, I would never define force in terms of acceleration: those are different concepts and a law isn't the same thing as a definition either. Will you now also ask me if F=d(mv)/dt is a mistake?

 

[harrylin]

AE might have meant that "no clear definition can be given" because the velocity dependence of mass can have different forms in different applications.
If you try to extend F=ma, using relativistic mass, you need 'longitudinal mass' and
'transverse mass'.

How can it have different forms in different applications? The weird thing is that Einstein presents an equation that looks like a definition but next states that "no clear definition can be given". Feynman gave even later an experimental definition that corresponds to that equation. So it's also a riddle to me!

Note that you don't need those other mass terms either and you are not likely to find those terms in a textbook that uses it.