Do Einstein's Theories of Relativity Contradict Each Other?

[Garth]

Was Einstein inconsistent between his theories of Special and General Relativity?

In the theory of Special Relativity we learn that energy and mass are interchangeable E = mc^2.

In the theory of General Relativity we learn that because of Einstein's equivalence principle (EEP) the mass of a particle is invariant. When a uranium atom undergoes fission, the energy released is only the energy of the system, bound up in the atom, that is being re-allocated; the masses of all the constituent particles making up the atom remain invariant.

Are these two theories therefore mutually contradictory?

 

[DW]

No. Mass is invariant in both theories, not just general relativity.

 

[pmb_phy]

Was Einstein inconsistent between his theories of Special and General Relativity?

No.

In the theory of Special Relativity we learn that energy and mass are interchangeable E = mc^2.

True.

In the theory of General Relativity we learn that because of Einstein's equivalence principle (EEP) the mass of a particle is invariant.

The proper mass (aka rest mass) is invariant. That is not a result of relativity. Its a fact of nature which relativity never changed.

When a uranium atom undergoes fission, the energy released is only the energy of the system, bound up in the atom, that is being re-allocated; the masses of all the constituent particles making up the atom remain invariant.

The energy released is not the only energy of the system. The energy released is the Q of the system and the Q of the system is only part of the energy of the system. See
http://www.geocities.com/physics_world/sr/nuclear_energy.htm

Are these two theories therefore mutually contradictory?

Not that I've seen.

Pete

 

[DW]

No.

True.

The proper mass (aka rest mass) is invariant. That is not a result of relativity. Its a fact of nature which relativity never changed.

The energy released is not the only energy of the system. The energy released is the Q of the system and the Q of the system is only part of the energy of the system. See
http://www.geocities.com/physics_world/sr/nuclear_energy.htm

Not that I've seen.

Pete

Your own personal sight is not an independent reference. As always you are spamming for Planck's outdated concept of mass. You are wrong.

 

[quantumdude]

Your own personal sight is not an independent reference. As always you are spamming for Planck's outdated concept of mass. You are wrong.

So what if it's outdated? That doesn't mean it's wrong.

Incidentally, it's not outdated. That concept of mass is still alive and well among those who work in nuclear power.

 

[Garth]

Mass is invariant in both theories, not just general relativity.

The mass of a body as measured by an observer depends on the velocity of the the body in the observer's frame of reference.

 

[quantumdude]

The mass of a body as measured by an observer depends on the velocity of the the body in the observer's frame of reference.

That is just one convention. We aren't obligated to adopt it, and indeed most physicists don't. The convention adopted by most physicists is that there is only one mass: the invariant mass. That quantity is the norm of the 4-momentum. But as I said before, the concept of mass that says m=γm₀ isn't wrong, it's just out of style.

 

[pmb_phy]

That is just one convention. We aren't obligated to adopt it, and indeed most physicists don't.

That is misleading. The majority of particle physicists don't use it. The majority of GRists and cosmologists do use it.

But the way, what are you basing that assumption on?

Pete

 

[quantumdude]

That is misleading. The majority of particle physicists don't use it.

Misleading? Correct me if I'm wrong, but I think that the community of particle physicists is the majority of physicists who use relativity. Factor in those solid state physicists who use relativisitc quantum mechanics or QED, and it's no contest.

The majority of GRists and cosmologists do use it.

Really? Every textbook I have teaches the concept of mass as the invariant norm of the 4-momentum, and they are written by relativists (Taylor and Wheeler, Ohanian and Ruffini, et al). What books do use it? And are there publications in the arxiv that use it?

But the way, what are you basing that assumption on?

All my undergraduate and graduate coursework.

 

[pmb_phy]

Hi Tom

For my response to be logical it turned out to be too long for a post so I started a new thread. See the new thread Those who use relativistic mass and why

Pete

 

[DW]

So what if it's outdated? That doesn't mean it's wrong.

Incidentally, it's not outdated. That concept of mass is still alive and well among those who work in nuclear power.

It is outdated whether it is being used or not and it is wrong. It was a guess that just happened to put $$\gamma$$ in the place that it needed to be in a momentum equation to yield dynamics consistent with special relativity, but the mass term in that equation is NOT where it comes from. It comes from time dilation in the time differential in the velocity term. This missassociation of the factor with the mass is why it is wrong and the modern understanding of where the term comes from in terms of the four vector law is why it is outdated.

 

[DW]

The mass of a body as measured by an observer depends on the velocity of the the body in the observer's frame of reference.

No. Mass is invariant.

 

[Garth]

What we have here is a conflict of conventions of definition of terms.

The question of whether or not the mass of a particle can vary or not ought to be a matter of observation not definition. If we define mass to be invariant then we are blinding ourselves to the fact that it might be otherwise.

In the “classical interpretation” of the Einstein’s equivalence principle (EEP) mass is invariant. Therefore we have masses on the one hand and energies on the other, and although energy has a mass equivalent, they cannot transform one into the other. Yet at a fundamental level a particle seems to be a string, or whatever, of vibrating energy, and sufficiently energetic photons can transform into a particle and its anti-particle and vice versa.

My original question was to question this convention, is it not inconsistent with the precept of SR? Incidentally SR says nothing about the invariance of mass, that has been read in later.

In my theory of self creation I choose to define mass to be able to include potential energy and it leads to some very interesting observational consequences; one of which is a heterodox prediction for geodetic precession, which is about to be measured by the Gravity Probe B satellite.

 

[pmb_phy]

What we have here is a conflict of conventions of definition of terms.

If dw posted what I think he did then I agree 100%.

The question of whether or not the mass of a particle can vary or not ought to be a matter of observation not definition. If we define mass to be invariant then we are blinding ourselves to the fact that it might be otherwise.

There are two definitions in common use.

Let v = 3-velocity. Then when m is defined such that mv is conserved then this is an implicit definition of m and is commonly referred to as inertial mass (aka relativistic mass).

Let U = 4-velocity. Then when m₀ is defined such that m₀U is conserved then this is an implicit definition of m₀ and is commonly referred to as proper mass (aka rest mass).

When people use the term mass, some of them are referring to m while others are referring to m₀.

And that's the whole story on the concept of mass as it pertains to definition.

In the “classical interpretation” of the Einstein’s equivalence principle (EEP) mass is invariant.

Please provide a definition of classical interpretation.

Thanks

Pete

 

[quantumdude]

It was a guess that just happened to put $$\gamma$$ in the place that it needed to be in a momentum equation to yield dynamics consistent with special relativity, but the mass term in that equation is NOT where it comes from.

So what?

In p=γmv, is γ multiplied by m? Answer: Yes.

Does the law of associativity under multiplication still hold? Answer: Yes.

Can I associate (γm) together and call it something else? Answer: Yes.

Does the quantity have the dimensions of mass? Answer: Yes.

Is there anything wrong with giving that mass a name? Answer: No.

 

[DW]

So what?


Can I associate (γm) together and call it something else? Answer: Yes.

Is there anything wrong with giving that mass a name? Answer: No.

Concerning the first question here you are not calling that just "something" else. You are calling it something that it does not mean. Your last question here has a wrong hidden statement. You state that the something you want to name is mass. That is what is wrong.

 

[quantumdude]

Concerning the first question here you are not calling that just "something" else. You are calling it something that it does not mean.

It means "relativistic mass" if I define it to mean that. That is the nature of a definition.

 

[DW]

It means "relativistic mass" if I define it to mean that. That is the nature of a definition.

A missnomer is a better word for it.

 

[quantumdude]

A missnomer is a better word for it.

You do realize that this is just your personal opinion, right?

 

[Garth]

Classical interpretation of mass: "rest mass", i.e. the mass of an object measured in a co-moving frame of reference in which the object is at rest, is equal to the norm of the 4-momentum vector and is invariant. It is a direct consequence of the EEP (see for example Weinberg) and therefore GR.

 

[pmb_phy]

Classical interpretation of mass: "rest mass", i.e. the mass of an object measured in a co-moving frame of reference in which the object is at rest, is equal to the norm of the 4-momentum vector and is invariant. It is a direct consequence of the EEP (see for example Weinberg) and therefore GR.

Why do you use the term "classical" here as a qaulifier for "interpretation"? What is it supposed to refer to? Classical in what sense of the word?.

Where in Weignberg's text do you see Weignberg say "It is a direct consequence of the EEP ... and therefore GR."?

Thanks

Pete

 

[Garth]

"Classical": just my term for "normal convention", there are others.
The conservation of the norm of the 4-momentum vector is true under Lorentz transformations in the absence of gravitation; by the EEP it is also true in the presence of gravitation, see Weinberg's development in "Gravitation and Cosmology" pg. 44, and the definition of the EEP which states that "at every space-time point in an arbitrary gravitational field it is possible to choose a "locally inertial coordinate system" such that, within a sufficiently small region of the point in question, the laws of nature take the form as in unaccelerated Cartesian coordinate systems in the absence of gravitation" .(Weinberg pg. 68)

 

[pmb_phy]

"Classical": just my term for "normal convention",..

You have the privilege of being the first person to use that term in that way in this forum.

The conservation of the norm of the 4-momentum vector is true under Lorentz transformations in the absence of gravitation;

You have to be very careful how you say that. The magnitude of the 4-momentum is not always a conserved quantity. That is only true for closed systems. E.g. if you have a particle which emits radiation then the magnitude of the 4-momentum of that particle changes and is therefore not a conserved quanity. In general it is a function of the proper time of the particle. For details please see Invariant vs. Time Independent at
http://www.geocities.com/physics_world/sr/invariant_mass.htm

You really have to be careful when you add 4-momenta too. Its only meaningful to add them when the particles interact only through contact forces.

...by the EEP it is also true in the presence of gravitation, see Weinberg's development in "Gravitation and Cosmology" pg. 44, and the definition of the EEP which states that "at every space-time point in an arbitrary gravitational field it is possible to choose a "locally inertial coordinate system" such that, within a sufficiently small region of the point in question, the laws of nature take the form as in unaccelerated Cartesian coordinate systems in the absence of gravitation" .(Weinberg pg. 68)

You didn't answer my question. I asked you where in Weinberg hge said that rest mass = mag of 4-momentum is a It is a direct consequence of the EEP (see for example Weinberg) and therefore GR. He does not say that in those pages. Yes, its true what he says on those pages but that rest mass = mag of 4-momentum is not a direct result of EEP. As I explained to you before, rest mass was constant before SR and GR and they (SR/GR) didn't change it or prove it. Just because its true in SR/GR it doesn't imply that the EEP proved it.

Pete

 

[Garth]

There are two uses of the word "invariant" - invariant under coordinate transformation and invariant under particle and/or force interaction. I was using the first meaning of that term.

We do not know whether (rest) mass is/was constant unless it can be measured or compared with something other than rest mass! I suggest that when the energy of a photon, cosmologically a photon taken from the peak intensity of the MBR, is compared to rest masses those masses will be seen to be secularly increasing. To do so however would be to violate the EEP.

 

[pmb_phy]

There are two uses of the word "invariant" - invariant under coordinate transformation and invariant under particle and/or force interaction. I was using the first meaning of that term.

Why do you mention this? I was commenting on your comment "The conservation of the norm of the 4-momentum vector is true under Lorentz transformations in the absence of gravitation". I believe that you used the term "conservation" when you mean "invariance". Did you not?

 

[Garth]

If an observer in one inertial frame observes a particle in another, which is accelerating relative to the observer's frame because of gravitational forces , the four-momentum of the particle is observed to be constant over time, and also equal to its value in the particle's rest frame. It is therefore invariant and conserved. Of course any energetic interactions will change its value but that is an added complication not addressed in my post above.

 

[mijoon]

You do realize that this is just your personal opinion, right?

I believe that this was also the personal opinion of a certain Albert Einstein .

 

[DW]

Classical interpretation of mass: "rest mass", i.e. the mass of an object measured in a co-moving frame of reference in which the object is at rest, is equal to the norm of the 4-momentum vector and is invariant. It is a direct consequence of the EEP (see for example Weinberg) and therefore GR.

Mass is not just equal to the norm of the 4-momentum, it is equivalent to it. As such mass does not depend on frame and as such need not be measured specifically from rest frame coordinates and as such is improper to qualify with the word rest.

 

[Garth]

Mass is not only something to be defined, it is something to be measured. In specifying how it is measured one cannot be too careful.

 

[pmb_phy]

Mass is not only something to be defined, it is something to be measured. In specifying how it is measured one cannot be too careful.

Yup. I quite agree Garth.

Pete