Re: Is the mass of a free falling body increasing?
From: Harry (harald.vanlintel_at_epfl.ch)
Date: 11/29/04
- Next message: Bilge: "Re: Download a new book on quantum mechanics and relativity."
- Previous message: Moonshadao: "Re: Question about God=G_uv"
- In reply to: Rafael Valls Hidalgo-Gato: "Re: Is the mass of a free falling body increasing?"
- Next in thread: Harry: "Re: Is the mass of a free falling body increasing?"
- Reply: Harry: "Re: Is the mass of a free falling body increasing?"
- Messages sorted by: [ date ] [ thread ]
Date: Mon, 29 Nov 2004 13:06:15 +0100
Sorry for the delay, I'm very busy and I had to think about your ideas. I
had similar thoughts as you, but I doubt that it's correct. See below.
"Rafael Valls Hidalgo-Gato" <valls@icmf.inf.cu> wrote in message
news:33d06fe2.0411231409.185018a@posting.google.com...
> "Harry" <harald.vanlintel@epfl.ch> wrote in message
news:<419a0062$1@epflnews.epfl.ch>...
> > "Rafael Valls Hidalgo-Gato" <valls@icmf.inf.cu> wrote in message
> > news:33d06fe2.0411151307.58f1dcb9@posting.google.com...
> > > harald.vanlintel@epfl.ch (Harry) wrote in message
> > news:<3bff5641.0411090750.7be97c8a@posting.google.com>...
> > SNIP
> > > > > > Of course not, that's why I wrote relativistic effects of
> > gravitation -
> > > > > > which only came later with GRT.
> >
> > > > > The thing if not yet completely clear for me. Are you saying that
> > > > > relativistic effects of gravitation appears only with GR? If that
were
> > > > > the case, how it is then possible that you can address a
gravitation
> > > > > free fall using only SR? My question refer precisely to an SR
> > > > > gravitation effect.
> > > >
> > > > Simple, SRT is about the speed v, which changes in free fall.
> > > SRT is about all Physics laws being the same in all inertial frames
> > > (PoR). In any inertial frame a body can have a velocity, but also an
> > > acceleration (a time varying velocity). A body can be at rest in some
> > > instant (v=0), having at the same time a non-zero acceleration. This
> > > is precisely the case we are addressing, the body at rest in some
> > > instant where the free falling starts.
> >
> > SRT: m=gamma*mo
> You consider Mo constant?
I consider Mo constant as long as no radiation or mass is absorbed or
emitted; until now I assumed Mo to correspond to internal energy, thus a
kind of stored kinetic energy.
> Being Mo a mass it must measure an energy, a
> potential one.
Potential field energy is in principle external energy of the field I think.
But that's all part of a puzzle to be solved.
A free falling body is not in a constant potential
> condition. But the formula remains valid! See how the velocity goes to
> c as Mo goes to zero (with a constant M in this case), obtaining a
> photon with zero rest mass (pure kinetic energy with only dynamic
> mass).
Do you mean (roughly speaking and speculating) that a rock transforms into a
photon when it falls into a black hole?
SNIP
> > > > > We know that this is a today common accepted fact,
> > > > > that the rest mass Mo of a body (or particle) is supposed to be a
> > > > > constant intrinsic attribute that does not change with the
position in
> > > > > any field. But don't forget that we are now fixed in 1905!
> > > > > Let's go to the September 27 Einstein's 1905 paper, the first one
> > > > > where the mass-energy relativistic relationship was showed. As I
said
> > > > > before, I didn't find in it (or in the previous June 30 one) any
> > > > > reference about exclusion of gravity or any other kind of field.
> > > >
> > > > OK I had not noticed the month of 1905, thought you'd only want to
> > > > take upto SRT into account. But we include E=mc^2 (which is strictly
> > > > speaking not relativity).
> > > >
> > > I am very surprised with your "E=mc^2 is strictly speaking not
> > > relativity" assertion. I am considering it just one of the principal
> > > achievements of relativity!
> >
> > Certainly not. But I don't blame you, misinformation is widespread. It
was
> > almost derived (and roughly known) before relativity. Einstein even used
a
> > low speed approximation, and I remember that afterwards it was also
derived
> > without relativity and without approximation.
> >
> I have no knowledge about the mass-energy relationship before Einstein
> or after him without Relativity. I will appreciate a lot any
> information that you can bring me about this topic.
I didn't have time to look for it, but I'm sure you can find some in the
archives of this group. As Ives pointed out in his paper in the JOSA of Aug.
1952, p.540, there were for example in 1904 Hasenohrl who concluded that
radiation pressure implied an added apparent mass of 4/3 E/c^2, and Poincare
who determined that the momentum of radiation is S/c^2, with S=E*c. And I
know that some time earlier there was also a book written in which the right
order of energy content was indicated. All this without using "relativity".
By the way, Ives was mistaken about his main point in that paper, as others
later pointed out, but they were mistaken too!. So, to put the "point on the
i" I may still write something about it, but it's not exciting stuff and now
I don't want to waste my time on it. But it has to do with the constant c
that you mention below, although I forgot it too much to be able to tell if
it affects your interpretation.
> I suppose your reference to a "low speed approximation" in Einstein
> work is related to the approximate formula K0-K1=(1/2)(L/c^2)v^2 that
> appears in the Sep27 paper. Few lines before you can see the formula
> K0-K1=L{(1/sqrt(1-v^2/c^2)) - 1} which is the exact one from where the
> quoted approximate one is derived. With the usual developing in series
> you can confirm that the L/c^2 result obtained by Einstein is the
> exact one, not an approximated one. He immediately wrote: "If a body
> gives off the energy L in the form of radiation, its mass diminishes
> by L/c^2". This applies to any value for L. Choosing L=E0 (all the
> energy of the body in the frame it is at rest), we obtain E0=Moc^2 and
> also H0=Mc^2 (all the energy of the body in the other frame where it
> is moving).
Right - and as at near-zero speed classical physics leads to identical
results, "relativity" is irrelevant for determining the rest mass. He did
show that with relativity also moving mass is a measure of the particle's
energy.
> Einstein obtained a universal mass-energy relationship E=Mc^2, valid
> for all inertial frames and for all kind of energies.
The "all kinds of" is the question.
SNIP
> > > > > In the frame the body is at rest (where its kinetic energy K is
zero),
> > > > > its rest mass Mo must measure its total energy E that is also
equal to
> > > > > its potential energy U (I use the E=U+K knowledge valid in 1905,
that
> > > > > was used also by Einstein in his paper).
I am sure that for Einstein it wasn't very clear either. It's easy to
confuse things like internal energy and potential energy.
> > > > That is a weak point: in an electric field the total system energy
> > > > remains constant but the total energy of accelerated ions increases.
> > > > Thus to support that reasoning, you should demonstrate that a
> > > > gravitational field does not give energy to a falling particle.
> > > >
> > > Why do you refer to particular fields? For me one of the most
> > > important points in Einstein's paper is that he discovered a
> > > completely universal mass-energy relationship.
> >
> > I don't refer to that but to your reasoning. Einstein didn't even
mention
> > any fields, but you apply it in a certain way on gravitational fields
> That Einstein didn't even mention any fields?
Not in his E=mc^2 discussion.
> That demands a detailed answer using Einstein's own words.
> The first thing that I put clear here is that the PoR does not exclude
> any kind of field. ALL Physics laws must be the same in all inertial
> frames. You accepted that (take a look at the beginning of our
> talking).
> No, I am not applying it "in a certain way" on gravitational fields. I
> am directly applying it on gravitational fields with the 1905 PoR as
> support.
> But if you have some doubt about this yet, consider the following
> references to the Einstein's paper:
> "Let there be a stationary body in the system (x,y,z), and lets its
> energy -referred to the system (x,y,z)- be E0. Let the energy of the
> body relative to the system (x',y',z') moving as above with the
> velocity v, be H0".
> For me is completely clear that Einstein is referring to a body that
> is at rest in some inertial frame and moving in another inertial one.
> This generality is the crucial point here! I can take per example a
> body at rest over some (non-rotating, but orbiting the Sun) planet
> surface at some height that will start a free falling. The inertial
> frames would be the ones associated to the center of mass of the
> planet and the Solar system.
That generality may have been assumed, or it may not - I doubt that he
implied to include gravitation at that point, as it was also not included in
relativity - he made a similar general statement about clocks that turned
out to be technically wrong because he didn't consider it / mentioned that
it should be excluded. Gravitation was included later.
> "The principle of energy must apply to this process and in fact (by
> the principle of relativity) with respect to both systems of
> co-ordinates".
> By the context it is for me completely clear that Einstein is
> referring to the conservation of energy principle, that in 1905 had
> the form E=U+K, being E:total energy, U:potential energy, K:kinetic
> energy, valid for any closed to energy system (or sub-system).
Maybe; but U of a system can also be field energy.
> Directly from the Einstein's paper we can obtain E=Mc^2, U=Moc2 and
> M/Mo=gamma.
> To support what I am saying read this other quote from the paper:
> "Thus it is clear that the difference H-E can differ from the kinetic
> energy K of the body, with respect to the other system (x',y',z'),
> only by an additive constant C, which depends on the choice of the
> arbitrary additive constants of the energies H and E".
> For me this is definitive.
My analysis showed a mess, complete confusion. But sorry I'm both too busy
to look into it now and plan to put it not here but in a publication later .
> I do not know about any other arbitrary
> additive constants different from the potential energies ones in 1905
> (and they play a fundamental role in Einstein's derivation).
I remember having read comments of others about that too. But the arbitrary
constant was irerelevant for the result, and therefore irrelevant for this
discussion - except if here you want to discuss about Einstein and math
derivations instead of about physics.
> After
> this, to consider fields absent is a totally out of epoch idea. By the
> way, Einstein has not any arbitrary additive constants in his result.
> Once rest mass is considering measuring potential energies, a unique
> zero potential energy condition is established, rest mass zero, a
> common zero for all kind of potential energies.
And where is that?
> > Your
> > inference is known to be invalid when applied to electric fields: at
high
> > potential the energy is not added to the particle's mass. Then why do
you
> > think it will be valid for gravitational fields?
> Are you saying that Einstein's paper is proved wrong for electrical
> fields? It could be true. Maybe you think that only kinetic energies
> are related with mass and not the potential ones? Maybe you think that
> the mass-energy relationship does not apply in an inertial frame where
> a body can be at rest?
> > > If you think that
> > > Einstein had some error in his derivation (or with a higher
> > > probability, I in my interpretation), you must state explicitly which
> > > is it and we can analyze the writing using the 1905 context.
> > > Fortunately the derivation is very short. If you have not it, you can
> > > obtain the paper at
> > > http://www.fourmilab.ch
> >
> > I know and I have it in German and English.
> > Beware, Einstein did mess up a little on that point, but it didn't
affect
> > the end result - I have in mind to write a paper on that, maybe I will.
> > Anyway, it doesn't matter for this discussion. And I explained in more
> > detail above.
> I used in my references the copy in the link I gave you. The detailed
> analysis of Einstein's paper in the 1905 context is my principal goal
> here, specially all related with the arbitrary additive constants
> characteristic of all kind of potential energies.
Then you would do good to read also comments of others about it.
> > > In any way, I do not understand which total system energy are you
> > > considering constant in the case of accelerated ions. Ions can gain in
> > > total energy only taking it for some place different from its own
> > > energy (potential or kinetic). You must supply energy from the
> > > exterior to the huge accelerators used today to obtain high
> > > accelerated particles.
> >
> > Exactly, the energy is supplied by the field, and not added to the ion
mass
> > while in rest. Its total energy increases while accelerating in the
electric
> > field. Then why should it be different for gravitation.
> After Einstein, the ion rest mass measures its potential energy.
> Following him, the electron rest mass in a hydrogen atom must be a
> little less (about 13.6 eV, the "binding energy" or ionization
> potential) than its value when placed very far away from the proton
> (where it has its maximal value, the today "intrinsic and constant"
> value. Rest mass must change with position in a field.
If he implied that, I think he was wrong at that point.
> > > If Einstein's derivation is correct, rest mass measures potential
> > > energy (only a particular case of mass measuring energy).
Oh no!
> > As now explained in more detail, we know that it doesn't measure
electrical
> > potential energy; obviously it doesn't contain it.
> >
> No? Consider an electron-positron pair and permit them to free fall
> each in the other. You will see how the potential energy that
> corresponds to the pair when they are separated, measured by their
> rest mass, will appear as the kinetic energy of two photons (rest mass
> zero).(I am bypassing the unknown process of electrical charge
> annihilation).
As far as I know that's not measured by their rest mass, but by their rest
mass + field energy.
> If you are thinking in a process like electron acceleration between
> the plates of an oscilloscope (or TV set), you must take into account
> that energy must be supplied from the exterior to maintain the voltage
> between the plates. This is a completely different case from a set of
> charged electrical particles interacting. You must specify clearly
> which is your closed to energy system in order to apply the energy
> conservation principle.
Right. I have been thinking about that. The best is, to simplify it to an
isolated system with fixed charges, like on Teflon. Then the equations are
identical as with gravitation, right?
Thus you claim that then the inertial resistance against movement will be
higher than without field.
Please confirm.I would be surprised if that hasn't been tested, in principle
that would be possible.
However, I suspect that it doesn't work in theory, because one can put two
such fields in tandem, and then an identical local condition would result in
a different mass, or am I mistaken?
> > > Why do you
> > > speak about the gravitation field not giving energy to the falling
> > > particle?
> >
> > Because according to you no energy is added during falling.
> >
> What you named "energy added" is the process of converting potential
> energy into kinetic one.
Exactly. I meant that according to you no energy is added to the particle.
> As we know now that the potential energy is
> measured by the particle's rest mass (after Einstein),
I think that's what escaped you: No, we don't know it!
> I considered it
> part of the particle's energy and not something that is added from the
> exterior. Owed to the universal equivalence between mass and energy,
> valid for all kind of energies, a conversion from potential to kinetic
> energy maintains constant the total mass (and the total energy). This
> is precisely the case for my falling body (or for any orbital motion
> in any kind of field).
There is another problem, if inertial mass is identical to gravitational
mass: then what mechanism prevents a falling particle to go faster than
light? Gravitational force is external...
> > > The particle potential energy and its field energy are one
> > > and the same thing, measured by the particle rest mass. For a free
> > > falling particle only its potential energy (its field energy) is
> > > converting to kinetic energy.
That would be true for a closed system, such as with particle decay.
> > Exactly, that's what you stated. Then no energy is added during falling,
> > in contrast to electrical acceleration.
> >
> Consider an electric pendulum. You will see how the total energy is
> maintained constant even if the charged pendulum is accelerated during
> its cycle. The increase in dynamic mass (kinetic energy) is balanced
> by a decrease in rest mass (potential energy), total relativistic mass
> remaining constant. Completely similar with a gravitational pendulum
> (or even with a pendulum with the two kind of fields present at the
> same time!).
The same can be done with a constant rest mass assumption.
> > > > > As you see, a direct derivation from the paper is that the rest
> > > > > mass Mo measures the potential energy U.
You repeated that erroneous conclusion twice.
> But U changes with position in
any
> > > > > field! My conclusion is then that a constant Mo corresponds only
to A
> > > > > CONSTANT POTENTIAL CONDITION.
> > > >
> > > > In an electric field the potential energy is supposed to be stored
in
> > > > the field loose from the ions, not? That is in agreement with
> > > > measurements, the initial mass is Mo.
> > > >
> > > In ANY field, the potential and field energies are one and the same
> > > thing, measured by the rest mass of the interacting particles. If a
> > > system changes from a higher to lower total potential energy state,
> > > its total rest mass diminishes always following the E=Mc^2 proportion.
> > > This is in total agreement with the measurements (defect mass effect).
> >
> > Certainly not. Slow moving ions behave according to their rest mass when
> > at high electrical potential.
> Stop the external supply of energy and try to add kinetic energy to an
> ion without changing its rest mass. To maintain a voltage between two
> plates you need a continue supply of external energy if you are
> accelerating ions with constant rest mass.
See above. It's true that at first sight the electrical field reduces, while
the gravitational field doesn't.
Now that would be interesting to work out.
Do you know a theoretical discussion about it in a book or on the web? It
may be proposed that the electrical field is somehow shielded, and not
converted into something else. Anyway IMO, energy is not converted into
mass, but mass is a manifestation of energy.
> > > > > For a free falling body, only a change from potential to kinetic
> > > > > energy is taking place (as it is very well known), remaining the
total
> > > > > energy E constant. Using the universal E=Mc^2 relationship
discovered
> > > > > by Einstein, the result is a CONSTANT M for a free falling body.
> > > >
> > > > That may be so, but IMO not obviously so. However, again measurement
> > > > results may help. As we discussed last time: if a mechanical atom
> > > > model such as that of Bohr is consistent with your hypothesis, that
> > > > would be a support, and inversely.
> >
> > > Well, Bohr model correspond to 1913, out from our 1905 context.
> >
> > You can take whatever model you like, as long as it's compatible with
> > the laws of nature. For example a spring watch.
> >
> You can obtain a satisfactory explanation of the Pound and Rebka
> experiment applying only 1905 Relativity. The tiny change in rest mass
> for the electrons in the gravitational field result in the tiny
> emitted frequency changes with the height. But this is out of the 1905
> restricted context.
I first thought so too. But now I doubt that that's the correct solution as
to the cause of the frequency change, as I explained above. As the Planck
constant is not dimensionless, it now makes more sense to me that that
changes with gravitational potential: E=h*f.
> > > Yes, I
> > > remember our previous discussions, but for the benefit of readers in
> > > this thread I think it is better to maintain that out for the moment
> > > (including here your last comment).
> > > What do you consider my hypothesis? We are talking about Einstein's
> > > work! I added no thing to the PoR or to the mass-energy universal
> > > equivalence E=Mc^2.
> >
> > I hope you now realise that you did...
> >
> Not yet. You must specify what do you consider I am supposing
> different from Einstein in the 1905 context.
You now made it plausible that he at that moment thought what you think he
thought.
> > > That "mass measures energy" is a conclusion that
> > > belongs only to Einstein. I am only interpreting him in his original
> > > 1905 context.
The question is if all energy that is around affects the inertia ("mass") of
a particle.
Harald
- Next message: Bilge: "Re: Download a new book on quantum mechanics and relativity."
- Previous message: Moonshadao: "Re: Question about God=G_uv"
- In reply to: Rafael Valls Hidalgo-Gato: "Re: Is the mass of a free falling body increasing?"
- Next in thread: Harry: "Re: Is the mass of a free falling body increasing?"
- Reply: Harry: "Re: Is the mass of a free falling body increasing?"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
