Here is this age old thought experiment being told by a professor on Sixty Symbols: https://youtu.be/Cxqjyl74iu4
This explanation using the light clock is extremely frustrating. How can one use a hypothetical example which is physically impossible and then say the "result" explains SR? The photon would never hit the top mirror directly above its source b/c light does not take on the velocity of its source. Instead, the instant it leaves its source it goes straight up while the rocket moves forward, and would strike the back of the rocket (or the top somewhere to the left of the mirror). If the photon struck the mirror it would not move forward with the rocket, but again would go straight down while the rocket moves forward, b/c for the photon to move forward it woud have to feel the friction of the mirror pushing it forward, which is again impossible. The reason a wave such as sound would have the trajectory shown in this example is that the medium inside the rocket, air, is moving at the speed of the rocket and the sound wave would take on that velocity as it left its source. Light does not use a medium to move. The reason a physical object such as a ball would have the trajectory shown is that particles take on the velocity of the souce that is accelerating them. Again, light does not take that velocity on, but instead it instantly has its standard speed (c) as it leaves its source. So, the photon does the exact same thing leaving a moving source as it would a stationary source, it moves at the speed of light in the direction it's facing, hence no length is added to its trajectory as stated in the example, and thus does not prove the time dilation of SR. Anybody else hearing me here? Thoughts?
- 45
- 3
-
That the momentum of light can't change because its velocity can't change is simply false. For photons we have $p=h\nu/c$, i.e. momentum is proportional to the frequency. – CuriousOne Jan 11 '16 at 19:22
-
You say "the photon" as if there was only one. Imagine instead, a spherical wave emanating from a point source (the emitter) and reflecting off the mirror. Some part of the reflected wave eventually interacts with the point-like detector. – Solomon Slow Jan 11 '16 at 19:59
2 Answers
How can one use a hypothetical example which is physically impossible and then say the "result" explains SR?
It isn't impossible, you're just missing the trick, which is that directions get "skewed" a little. Have a look at this question which featured a light beam and a ship's mast. Imagine you're holding the parallel-mirror thing and you're moving thataway → quite fast. If the light didn't reflect up and down, you'd claim it wasn't aimed straight up. Only when you claim it is, and I'm sitting here motionless watching you zoom by, I claim it isn't.
The photon would never hit the top mirror directly above it's source b/c light does not take on the momentum of it's source. instead, the instant it leaves it's source it goes straight up
Your straight up isn't the same as my straight up.
The reason a wave such as sound would have the trajectory shown in this example is that the medium inside the rocket, air, is moving at the speed of the rocket and the sound wave would take on that velocity as it left it's source. Light does not use a medium to move.
It does. Have a look at Nobel Laureate Robert B Laughlin here: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed".
So, the photon does the exact same thing leaving a moving source as it would a stationary source, it moves at the speed of light in the direction it's facing, hence no length is added to it's trajectory as stated in the example, and thus does not prove the time dilation of SR.
The light-path length is longer. Have a look at the Simple inference of time dilation due to relative velocity on Wikipedia. Gamma is derived very simply from Pythagoras's theorem. The hypotenuse is the light path, the base represents your speed as a fraction of c, and the height represents the Lorentz factor.
Anybody else feeling me here? Thoughts?
Cross my heart and hope to die, this stuff is simpler than you think. Michael Merrifield's explanation is right. Have a look at the aberration of light for another example of directions appearing to change.
- 11,097
You may want to consider that a photon is not just a particle, it is also a wave. At any given moment it propagates at speed c in a direction $\vec{k}$ perpendicular to its wave front. But the direction of the wave front differs in different frames.
The clock's frame observes the photon having a wave front parallel to the mirrors, and propagating perpendicular to it and to the mirrors.
But the other frame observes a wave front tilted in the direction of motion at a slope $-\gamma\beta$, and therefore a photon propagating along a direction tilted at a slope $\frac{1}{\gamma\beta}$. The detailed reason has to do with relativity of simultaneity. This answer offers a detailed calculation of how this happens. It is not a first principles one, since it relies on the Lorentz transformations, but it clarifies why everything is self-consistent. See the other answers to the same question for first principles arguments.
In addition there is a neat simulation of the effect here, as a Java applet.
