| VLADIMIR: Considering the motion of accelerated body from
two IRFs, we revealed much interesting; in that number the following. The essence of trick
which relativists show to the world to consider the uniform accelerated motion is that the
acceleration is allowed to have the constant value only in some mythic ‘accompanying
frame’. Acceleration of the same body considered from the starting stationary IRF
becomes time-variable. But this means that relativists reject the possibility of uniformly
accelerated motion in IRFs! Neither more nor less. Their formula (d1.23) says it. I caught
it only from your service.
But what an ‘accompanying frame’ is it? Strictly
speaking, we cannot call a reference frame what relativists try to impose us under the
term ‘accompanying frame’, at least because we can ‘refer’ to nothing
in it. This is some imaginary, absolutely abstract entity that we can think to be whatever
but not ‘reference frame’. And namely it is absoluted. What is the crux? We have
to sort this out.
SERGEY: If you agree, I would put the question some
softer. By all its properties, the accompanying frame is a usual frame whose speed at the
moment is same as the speed of studied body and its origin – with the body (or its
centre of inertia). And nothing strange or exceeding the classical either relativistic
formalism that along the body’s trajectory we can draw many such IRFs. But how are
these properties used in such or other theory – this is another matter. Though the
accompanying frame is artificial in classical formalism in the meaning in which it is
used, but the Galilean transforms free of premise about space and time contraction allow
to measure the speed and acceleration of a body relative to this frame at some little
interval of time. With it the body’s speed and acceleration measured in this frame
are as if local values, while these values are indefinite out of introduced locality. But
again, if the space-time transformation is absent.
VLADIMIR: I think, the compromise is inappropriate here.
Galilean, the more Lorentz transforms disable us to ‘measure’ something in this
frame, because, even to measure speed, we need at least two readings in the same frame,
and readings separated by a time interval. Just what we have not and basically cannot
have. Thereupon, we not only may not rely on this concept and conclusions from it –
we basically may not consider it otherwise than some mental exercise lame in two legs.
SERGEY: And you are right again, dear Vladimir. The fact
that this entity is artificial is seen already because in classical formalism the concept
of some inertial frame accompanying the accelerated body at the moment is actually
excessive.
VLADIMIR: My opinion is, when they introduced the concept
‘accompanying frame’, it was a desperate and doomed attempt to salvage the
situation, putting things ‘from legs onto a head’.
SERGEY: This is why so-called actual frame appears when
relativists need to consider accelerated motions and affection of forces in IRFs. See, how
Einstein describes the dynamics of accelerated electron in the citation that explains
(d1.11). He translates just to the actual frame which has to be new at each next moment of
time and as if yields that a magnetic field arises. Well, magnetic field is revealed in
labs without permanent change of frames. Moreover, magnetic field shows itself in the
uniform, in average, motion of charge, and Rouland and then Eichenwald showed it.
Induction, not the field as such shows itself when the pattern of charge’s motion
changes. Thus, magnetic field to arise, the electron needs not to be accelerated, it will
be enough if it simply moved. But Einstein needed just the acceleration without which he
could not write (d1.11) that describes, how the force affects an electron as a trial body.
And at the same time Einstein could not pass to the accelerated frame without violation of
SRT postulates. So he goes to subterfuges, presenting the non-conservation of uniformly
accelerated motion in IRFs as the initiation of magnetic forces and other relativistic
effects. Although, even if we consider Einstein’s expressions as the description of
external field’s affection onto electron as a trial body, the force affection far
from always can be found just through the acceleration, more often it is found through
deformation either change of location, when the trial body passes to a new stable state of
equilibrium. Notice, dear Vladimir, just so, finding the charge of trial bodies, we never
find their mass. We need not this parameter, as we find the affection of force statically.
While Einstein had to specify the trial body, introducing its mass and calling it
electron. And again, the actual frame is excessive here. Excessive from the point of
classical physics. But in classical physics we can without great difficulties introduce
this actual frame, as it will change nothing if we take some IRF shifting step-by-step. We
will find the acceleration the same as in the initial frame, as both spatial and temporal
measures don’t change in classical formalism. We simply need not to complicate the
problem, introducing new and new frames.
In Relativity we already may not behave so, as in
frame-to-frame translation the measures of both time and space change. So, when
relativists write the acceleration u’ for accompanying frame in premise
that at least in two sequential neighbouring moments of time this frame remains, – in
this way they admit, they find the uniform acceleration of motion for IRF – just what
I showed you above.
But on one hand relativists, as if step-by-step passing
from one IRF to another, make the body resting in the given frame when they want. See how
Einstein defines the ponderomotive force: “… the strength
of electric either magnetic field as such does not exist (! – Sergey), since it depends on the choice of coordinate system, whether in this
place (or rather, in the space-time vicinity of point event (just the actual frame!
– Sergey)) the electric (! – Sergey) either magnetic field exists. Further we can see that ‘ponderomotive
forces’ introduced up to now and affecting the electric charges moving in the
magnetic field are nothing else than electric forces, if we introduce the frame stationary
relative to the considered charge. So the questions of localisation of these forces (for
example, in unipolar machines) become senseless; namely, the answer will be different
dependently on the state of motion of frame” [A. Einstein. On the principle of
relativity and its corollaries, vol. 1, p. 82].
In the same way Sedov substituted this
‘quantification of inertia’: “With use of actual
frame and actual time we deal in our sensations. The actual time is invariant
characteristic of ageing and all possible inner processes and inner interactions” [L.I.
Sedov. Mechanics of continua, vol. 1, p. 323]. While it could seem, ageing occurs in the
frame which permanently accompanies us.
VLADIMIR: Naturally, in the normal statement of problem
the body’s trajectory is described in the chosen frame by the set (continuum) of
points that belong to this frame.
SERGEY: You said an exact word – in the normal
statement of problem. While here we see a full absurd. “Obviously,
actual coordinate systems do not coincide with the accompanying coordinate system in which
speeds of all particles are always zero; the actual frame is inertial, and accompanying
frame is not inertial at all, of course” [L.I. Sedov. Mechanics of continua,
vol. 1, p. 324]. Namely this is reflected in Einstein’s definition of ponderomotive
forces. Nothing to say that in the frame where the charged body rests, still no one
succeeded to reveal the affection of magnetic force. I don’t say that electric force
to affect, it does not need the charge to move in the field, and Coulomb laws well work in
static. But the very Einstein’s statement that in the accompanying frame the body
rests, while the body’s speed and acceleration are defined in Relativity through the
body’s displacement in this frame, makes absurd the question of actual frame.
VLADIMIR: Just because in ‘abnormal’ statement
through the ‘accompanying’ frames, the body’s trajectory artificially and
without grounds is dropped into the continuum of parts each of which belongs to different
frames, i.e. factually disappears.
SERGEY: With it the sequence of these
‘disappearing’ IRFs describes the non-linearity, which as such speaks of the
absence of these IRFs.
VLADIMIR: Anyway, at best the matter reduces to the
following. The uniformly accelerated motion is represented as a step-by-step-accelerated
with a requirement to consider only the segments of uniform rectilinear motion; this is
nothing else as emasculation of the very concept of acceleration.
SERGEY: And even not step-by-step: when we pass in
classical formalism from one IRF to the next, we can change only the speed of body, not
accelerations, true?
VLADIMIR: Then, of which ‘acceleration’ in the
‘accompanying’ frame can we speak at all? Is not it a forgery?
SERGEY: Forgery of course, in order to hide the
discrepancies of relativistic theory in dynamics and the fact that in Loretnz IRF-to-IRF
transforms the uniformly accelerated motion does not conserve. Because it directly follows
from these discrepancies that the laws of dynamics don’t work in Relativity, even in
IRF-to-IRF translation. Just what we analysed in our dialogue. In turn, from this it
follows that relativists illegally introduced the principle of equivalence, while this
principle is true in classical physics and even, as we saw, not only in IRFs but in some
cases of uniformly accelerated frames. It is clear that relativists may not state same, as
the logic of formal proof of equivalence has been formulated in the classical conception
for Galilean, not Lorentz transforms. Relativists should not drive the way built by
classical physics but if they have developed their own formalism based on postulates, they
would have to develop their own new dynamics, not to take it from classical physics,
basing on obvious equivalence of laws that is seen in many experimental proofs and in
formal substantiation in classical, not relativistic conception. Each has to drive the
road within his own conception, hasn’t he, dear Vladimir?
VLADIMIR: In a larger scale you are right of course, dear
Sergey. But there is in physics such principle introduced apparently by Bohr, it is called
‘the principle of correspondence’; according to it, a new theory has to cover
the old in some limiting case. So your thought “Each has to drive the road within his
own conception” should be corrected in the meaning that there has to be some
succession. It seems, in this case it would be more correct to accuse SRT just that in it
they may not ‘drive the road’ built by classical physics for low speeds. Though
relativists state that in some meaning it works, nevertheless, and are very proud of it.
But in a deeper consideration, the grounds for pride melt.
SERGEY: I agree, should the succession was kept, we could
think so. But relativistic mechanics so insistently rejects classical formalism, even
having booked classical physics to the underground, that such driving with whooping of
rejection becomes nothing than a gibe. In this way Relativity has set itself against
classical physics, going on driving the road built by classical physics and using the
formalism incompatible with that classical.
VLADIMIR: But to state so surely, we have to make our
position clear, how much logical is it – to accuse SRT of awfully written laws of
dynamics. If they think SRT a particular kinematic theory, it would be senseless to expect
from it that it will correctly express the laws of dynamics. If, on the contrary, they
think SRT a covering theory of space-time, the exact and adequate description of
accelerations, forces, conservation laws, rotation etc. is a strong requirement. Without
it, ‘the space-time theory’ is an invalid, not a theory.
SERGEY: And Einstein answers your question in the very
first his work, joining its kinematic part with the accelerated motion of electron in the
field. Let us look at it with the same principle of equivalence, and look with an example
which we showed in our paper and which raised your objection in the beginning of this
discussion.
As you remember, we considered the impulse conservation
law on the example of this law’s transformation in frame-to-frame translation. We saw
that in classical physics all parameters that characterise this translation mutually
contracted and the law gained in new variables an appearance independent of frame-to-frame
translation. This is basically important: should in the translated expressions at least
one translation parameter remained, the conservation law would fully lose its generality,
being dependent on this translation.
Let us see now, whether we can do it in Relativity.
Suppose, in some frame the impulse conservation law is
true. We can substantiate this premise without touching large speeds, in supposition that
some closed model which we consider has a little speed for which the Newtonian formalism
is true. Finally we will come to the relativistic formalism through the supposition that
the moving frame moves relative to the resting with the sub-light speed.
Write the impulse conservation law in the resting 1-D (to
simplify) frame. It will have a trivial appearance, just as in our paper: |
