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Geometrical appearance at relativistic speeds
Volume 35A, number 4
98
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I
PHYSICS LETTERS
I
I
I
~
I H ~
1
14 June 1971
purity interactions on theSuch exchange scattering the tunneling electrons. interactions ap- of
-
parently interfere with the spin-flip processes, quenching the 3rd-order contribution to the scat-
b 16 C 32
tering more rapidly than that due to 2nd-order. 96
b
-
Complete magnetic ordering at even larger thicknesses of Fe is presumed to eliminate the effect completely. We also call attention in fig. 2 to the fact for V ~ 1 mV the conductance in applied field rises above that for zero field, an example of the “overshoot” due to the predicted [3] splitting of 3) term in a magnetic field. Its existence the G( r~:anim,ortant qualitative verification
f 80
c-f b a
~ 94
-
92
-
d
-6
-4
-2
-
0
I
I
I
2
4
6
Complete details of this mvestigation will be presented in a future publication.
-
BIAS (my)
Fig. 2. Conducatnce versus voltage at 1. 12°Kin magnetic fields from 0 to 8OkOe for a junction doped with
iron to an equivalent thickness of 2.4 A.
[1] F. Mezei, Phys. Letters 25A (1967) 534. [2] D.J.Lythall and A. F. G. Wyatt, Phys. Rev. Letters 20 (1968) 1361. (3] J. Appelbaum, Phys.Rev. 154 (1967) 633.
•
being independent of N. We interpret our resuits as evidence of the effect of impurity-im-
GEOMETRICAL
References
APPEARANCES
AT RELATIVISTIC
SPEEDS
A~GAMBA Istituto di Fisica deli’ Universitlz, Genova, Italy
Received 7 May 1971
It is not true, as one might think by a naive application of the principle of relativity, that a moving camera sees a standing exactly like a standing camera sees a moving object.
A great number of papers in the last decade have been devoted to the problem of the visual appearance of objects moving at relativistic speeds, since Terrell [1] and Penrose [2] first pointed out that the so-called Lorentz contraction is invisible under most experimental conditions: the role of the light path differences from the object to the observer having not been properly taken into account in the older discussions of the subject. However, even now, the question seems far from settled, since most authors do not seem to realize the essential difference between a moving observer and a standing object and a standing observer and a moving object. Apparently the
question seems to be dismissed on the very basis of the principle of relativity, but we will see that there is a difference in the two cases, since more than two reference systems are involved. A similar case has already been discussed by Eisner [3] in connection with a paradox in the theory of aberration. To make the discussion more specific let us take a recent paper of Scott and van Driel [4], who present computer made drawings of the appearance of objects moving at relativistic speeds. Taken at their face values, their drawings could be constructed by a not-too-sophisticated reader as Implying that one could in principle perform the following experiments. 227
Volume 35A, number 4
PHYSICS LETTERS
Imagine a camera moving back and forth at relativistic speed. The camera is operated only when passing within a small region, say New York city, at constant speed i3. With such a camera you could than photograph from New York: (a) The Southern Cross. (b) The back of the moon (or Australia: the Earth too is a spherical object!). Now the photons leaving the above objects simply do not arrive in New York, and there is no way of capturing a missing photon, not even with a relativistic camera. The reason why those photons do not arrive in New York, however, is not quite the same in the two cases and a few comments are in order. (a) The photons coming from the Southern Cross are intercepted by the Earth. Barring this fact, a relativistic space traveller could indeed see the Southern Cross by looking towards the north celestial pole, because such photons are floating around this place. They are missed by a standing camera, but are swept by a moving camera. Essentially - apart from using relativity instead of classical mechanics - it is the same effect as the classical one illustrated in fig. 1. Thus with a moving camera one can indeed see the Southern Cross (barring intercep-
-
~J
t4 June 197~
tion of photons by the Earth) because the field of vision has been enlarged by the motion (thus allowing one to capture the floating photons), but ii one stands still and it is the Southern Cross to move, there is no way to see the Southern Cross except by. . turning to one’s back. (b) A similar discussion shows that one can see the back of the moon, only if the moon gets out of the path of the photons (fig. 2). Only then will the photons reach the observer in A, and it is then irrelevant whether the camera is standing or moving. If one camera in A sees the back of the moon, all moving cameras in the same place at the same time (i.e. located in the same absolute space-time point [5]) see the same things, apart from angle disortion due to aberration. No camera can see by “the effect of rotation” a part that is hidden to another camera in the same space-time point. Since for a camera at rest with respect to the moon, the back appears only when the cainera is looking directly at those points, the whole question of the “apparent rotations” amounts to say that.,, all the cameras on the back of the moon, rio matter how they move, see the back of the moon. A far from paradoxial result. The point that has been overlooked, or not sufficiently emphasized in most discussions of this topic, is the asymmetry between “a moving moon and~a standing camera” and “a standing moon and a moving camera”. The emitted photon is asymmetric with respect to the two reference systems. For a further discussion of this point see ref. [3].
~
Reterences
B Fig. I. A machine-gun shooting from B will not hit you, if you stay inside box A et rest with respect to B. You can be hit, however, when the box is moving forward (direction of the arrow) sweeping the floating bullets (indicated by small circles) If you keep box A at rest, moving instead the gun in B. . . according to relativity. you still get through unscathed. *~*
228
[1] J. Terrell, Phys. Rev• 116 (1959) 1041. [2] R. Penrose, Proc. Cambridge Phil. Soc. 55 (1959) 137. [3] F. Eisner. Am. J. of Phys. 35 (1967) 817. [4] G. D. Scott and H. J. van Driel, Am. J. of Phys. 38 (1970) 971. [5J A. Gamba, Am. J. of Phys, 35 (1967) 83. **
98
-
I
PHYSICS LETTERS
I
I
I
~
I H ~
1
14 June 1971
purity interactions on theSuch exchange scattering the tunneling electrons. interactions ap- of
-
parently interfere with the spin-flip processes, quenching the 3rd-order contribution to the scat-
b 16 C 32
tering more rapidly than that due to 2nd-order. 96
b
-
Complete magnetic ordering at even larger thicknesses of Fe is presumed to eliminate the effect completely. We also call attention in fig. 2 to the fact for V ~ 1 mV the conductance in applied field rises above that for zero field, an example of the “overshoot” due to the predicted [3] splitting of 3) term in a magnetic field. Its existence the G( r~:anim,ortant qualitative verification
f 80
c-f b a
~ 94
-
92
-
d
-6
-4
-2
-
0
I
I
I
2
4
6
Complete details of this mvestigation will be presented in a future publication.
-
BIAS (my)
Fig. 2. Conducatnce versus voltage at 1. 12°Kin magnetic fields from 0 to 8OkOe for a junction doped with
iron to an equivalent thickness of 2.4 A.
[1] F. Mezei, Phys. Letters 25A (1967) 534. [2] D.J.Lythall and A. F. G. Wyatt, Phys. Rev. Letters 20 (1968) 1361. (3] J. Appelbaum, Phys.Rev. 154 (1967) 633.
•
being independent of N. We interpret our resuits as evidence of the effect of impurity-im-
GEOMETRICAL
References
APPEARANCES
AT RELATIVISTIC
SPEEDS
A~GAMBA Istituto di Fisica deli’ Universitlz, Genova, Italy
Received 7 May 1971
It is not true, as one might think by a naive application of the principle of relativity, that a moving camera sees a standing exactly like a standing camera sees a moving object.
A great number of papers in the last decade have been devoted to the problem of the visual appearance of objects moving at relativistic speeds, since Terrell [1] and Penrose [2] first pointed out that the so-called Lorentz contraction is invisible under most experimental conditions: the role of the light path differences from the object to the observer having not been properly taken into account in the older discussions of the subject. However, even now, the question seems far from settled, since most authors do not seem to realize the essential difference between a moving observer and a standing object and a standing observer and a moving object. Apparently the
question seems to be dismissed on the very basis of the principle of relativity, but we will see that there is a difference in the two cases, since more than two reference systems are involved. A similar case has already been discussed by Eisner [3] in connection with a paradox in the theory of aberration. To make the discussion more specific let us take a recent paper of Scott and van Driel [4], who present computer made drawings of the appearance of objects moving at relativistic speeds. Taken at their face values, their drawings could be constructed by a not-too-sophisticated reader as Implying that one could in principle perform the following experiments. 227
Volume 35A, number 4
PHYSICS LETTERS
Imagine a camera moving back and forth at relativistic speed. The camera is operated only when passing within a small region, say New York city, at constant speed i3. With such a camera you could than photograph from New York: (a) The Southern Cross. (b) The back of the moon (or Australia: the Earth too is a spherical object!). Now the photons leaving the above objects simply do not arrive in New York, and there is no way of capturing a missing photon, not even with a relativistic camera. The reason why those photons do not arrive in New York, however, is not quite the same in the two cases and a few comments are in order. (a) The photons coming from the Southern Cross are intercepted by the Earth. Barring this fact, a relativistic space traveller could indeed see the Southern Cross by looking towards the north celestial pole, because such photons are floating around this place. They are missed by a standing camera, but are swept by a moving camera. Essentially - apart from using relativity instead of classical mechanics - it is the same effect as the classical one illustrated in fig. 1. Thus with a moving camera one can indeed see the Southern Cross (barring intercep-
-
~J
t4 June 197~
tion of photons by the Earth) because the field of vision has been enlarged by the motion (thus allowing one to capture the floating photons), but ii one stands still and it is the Southern Cross to move, there is no way to see the Southern Cross except by. . turning to one’s back. (b) A similar discussion shows that one can see the back of the moon, only if the moon gets out of the path of the photons (fig. 2). Only then will the photons reach the observer in A, and it is then irrelevant whether the camera is standing or moving. If one camera in A sees the back of the moon, all moving cameras in the same place at the same time (i.e. located in the same absolute space-time point [5]) see the same things, apart from angle disortion due to aberration. No camera can see by “the effect of rotation” a part that is hidden to another camera in the same space-time point. Since for a camera at rest with respect to the moon, the back appears only when the cainera is looking directly at those points, the whole question of the “apparent rotations” amounts to say that.,, all the cameras on the back of the moon, rio matter how they move, see the back of the moon. A far from paradoxial result. The point that has been overlooked, or not sufficiently emphasized in most discussions of this topic, is the asymmetry between “a moving moon and~a standing camera” and “a standing moon and a moving camera”. The emitted photon is asymmetric with respect to the two reference systems. For a further discussion of this point see ref. [3].
~
Reterences
B Fig. I. A machine-gun shooting from B will not hit you, if you stay inside box A et rest with respect to B. You can be hit, however, when the box is moving forward (direction of the arrow) sweeping the floating bullets (indicated by small circles) If you keep box A at rest, moving instead the gun in B. . . according to relativity. you still get through unscathed. *~*
228
[1] J. Terrell, Phys. Rev• 116 (1959) 1041. [2] R. Penrose, Proc. Cambridge Phil. Soc. 55 (1959) 137. [3] F. Eisner. Am. J. of Phys. 35 (1967) 817. [4] G. D. Scott and H. J. van Driel, Am. J. of Phys. 38 (1970) 971. [5J A. Gamba, Am. J. of Phys, 35 (1967) 83. **