Einstein's letter to Lincoln Barnett

~~pmb_phy~~ · Jan18-05, 11:22 AM

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

$LaTeX Code: m = \\frac{M}{\\sqrt{1-v^2/c^2}}$

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~~ · Jan18-05, 11:53 AM

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

**Chronos** · Jan18-05, 12:50 PM

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~~ · Jan18-05, 06:09 PM

Originally Posted by 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.

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 seperated 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~~ · Jan18-05, 06:13 PM

Originally Posted by Gamish

Perhaps he was refering 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** · Jan19-05, 02:59 PM

Originally Posted by pmb_phy

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 seperated 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** · Jan19-05, 03:26 PM

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 relativty you must also introduce a new definition of mass.

~~pmb_phy~~ · Jan19-05, 06:29 PM

Originally Posted by Chronos

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_wor...gy_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 $LaTeX Code: P = m_0 dx/d\\tau$ fails to work please see

http://www.geocities.com/physics_wor...riant_mass.htm

Especially the following sections

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

Pete

**Chronos** · Jan20-05, 04:06 PM

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

. 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~~ · Jan20-05, 05:18 PM

Originally Posted by Chronos

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 .

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
http://www.physicsforums.com/showthr...649#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