Datasets:
vnpthack
/
vnpt_data

Dataset card Data Studio Files
xet
 Community
1
text
stringlengths
0
6.73k
are made to the physicist by the prineiple of relativity, we could describe some of
them as follows. The first discovery is, essentially, that even those ideas which
have been held for a very long time and which have been very accurately veriflled
might be wrong. Ït was a shocking discovery, of course, that NÑewton”s laws are
wrong, after all the years in which they seemed to be accurate. Of course iW is
clear, not that the experiments were wrong, but that they were done over only a
limited range of velocities, so smaill that the relativistic efects would not have
been evident. But nevertheless, we now have a mụch more humble point of view
of our physical laws——everything can be wrongl
Secondly, if we have a set of “strange” ideas, such as that time goes sÌower
when one moves, and so forth, whether we /Zke them or do nöø# like them is an
Irrelevant question. 'The only relevant question is whether the ideas are consistent
with what is found experimentally. In other words, the “strange ideas” need only
agree with ezperimemt, and the only reason that we have to discuss the behavior
of clocks and so forth is to demonstrate that although the notion of the time
dilation is strange, 1È is conszs‡ten£ with the way we measure time.
Finally, there is a third suggestion which is a little more technical but which
has turned out to be of enormous utility in our study of other physical laws,
and that is to look at the sụmmetru oƒ the la+s or, more specifcally, to look for
the ways in which the laws can be transformed and leave their form the same.
When we discussed the theory of vectors, we noted that the fundamental laws
of motion are not changed when we rotate the coordinate system, and now we
learn that they are not changed when we change the space and time variables In
a particular way, given by the Lorentz transformation. 5o this idea of studying
the patterns or operations under which the fundamental laws are not changed
has proved to be a very useful one.
16-2 The twin paradox
To continue our discussion of the Lorentz transformation and relativistic
efects, we consider a famous so-called “paradox” of Peter and Paul, who are
supposed to be twins, born at the same time. When they are old enough to
drive a space ship, Paul flies away at very hiph speed. Because Peter, who is left
on the ground, sees Paul goïing so fast, all of Paul”s clocks appear to go sÌower,
his heart beats go slower, his thoughts go slower, everything goes sÌlower, from
--- Trang 307 ---
Peter”s point of view. Of course, Paul notices nothing unusual, but if he travels
around and about for a while and then comes back, he will be younger than Peter,
the man on the groundl “That is actually right; it is one of the consequences
of the theory of relativity which has been clearly demonstrated. đJust as the
mmu-mesons last longer when they are moving, so also wiïll Paul last longer when
he is moving. 'This is called a “paradox” only by the people who believe that the
principle of relativity means that aÏl motion 1s relative; they say, “Heh, heh, heh,
from the point of view of Paul, can't we say that Pe‡er was moving and should
therefore appear to age more slowly? By symmetry, the only possible result is
that both should be the same age when they meet.” But in order for them to
come back together and make the comparison, Paul must either stop at the end
of the trip and make a comparison of clocks or, more simply, he has to come
back, and the one who comes back must be the man who was moving, and he
knows this, because he had to turn around. When he turned around, all kinds of
unusual things happened in his space ship—the rockets went of, things Jjammed
up against one wall, and so on—while Peter felt nothing.
So the way to state the rule is to say that the man tpho has [elt the accelerations,
who has seen things fall against the walls, and so on, is the one who would be
the younger; that ¡is the diference between them in an “absolute” sense, and 1t
1s certainly correct. When we discussed the fact that moving mu-mesons live
longer, we used as an example their straight-line motion in the atmosphere. But
we can also make mu-mesons in a laboratory and cause them to go in a curve
with a magnet, and even under this accelerated motion, they last exactly as much
longer as they do when they are moving in a straight line. Although no one has
arranged an experiment explicitly so that we can get rid of the paradox, one
could compare a mu-meson which ¡s left standing with one that had gone around
a complete circle, and it would surely be found that the one that went around
the cirele lasted longer. Although we have not actually carried out an experiment
using a complete circle, it is really not necessary, of course, because everything
ñts together all right. This may not satisfy those who insist that every single fact
be demonstrated directly, but we confidently predict the result of the experiment
in which Paul goes in a complete cirele.
16-3 Transformation of velocities
The main diference bebween the relativity of Einstein and the relativity of
Newton is that the laws of transformation connecting the coordinates and times
--- Trang 308 ---
between relatively moving systems are diferent. The correct transformation law,
that of Lorentz, is
„h= % — tu
v1 u2/c2'
Ụ =1,
16.1
m (16.1)
rằ t— u#/c2
v1—*2/c2
These equations correspond to the relatively simple case in which the relative
motion of the two observers 1s along their common z-axes. Of course other
directions of motion are possible, but the most general Lorentz transformation is
rather complicated, with all four quantities mixed up together. We shall continue
to use this simpler form, since it contains all the essential features of relativity.
Let us now discuss more of the consequences of this transformation. First, it
1s Interesting to solve these equations in reverse. hat is, here is a set of linear
equations, four equations with four unknowns, and they can be solved in reverse,
for #, , z, in terms of #”,3/,z”,f. The result is very interesting, since it tells us
how a system of coordinates “at rest” looks from the point of view of one that is
“moving.” ÔÝ course, since the motions are relative and of uniform velocity, the
man who is “moving” can say, if he wishes, that it is really the other fellow who
is moving and he himself who is at rest. And since he is moving in the opposite
direction, he should get the same transformation, but with the opposite sign of
velocity. Thhat is precisely what we ñnd by manipulation, so that is consistent. lÝ
it địd not come out that way, we would have real cause to worryl
+ + uf!
#=——————p,
v1—2/c2
, (16.2)
". Ứ + tua! /c2