# Is the explanation of special relativity in Stephen Hawking's "The Grand Design" flawed?

To explain special relativity (in chapter 5 titled "the theory of everything"), Hawking starts with an example involving a flying jet, its passenger (being an observer) and an observer on the earth.

He considers the experiment in which a pulse of light travels from the tail of the plane to its nose. In this case, according to the observer on earth, the light has traveled a longer distance than the distance perceived by the jet's passenger. Now, to the jet's passenger, the light has traveled at a normal speed, while to the observer on the ground, if it weren't for the magic of special relativity, the light would have propagated at a faster than normal rate. Specifically, it is argued that special relativity solves the issue by getting the pulse to seem (to the on-earth observer) to have reached the nose of the jet after a longer period of time than what was perceived by the jet's passenger. Thus, for the people on earth, time on the jet seems to be slower.

The obvious question that the book fails to ask, however, is what happens if we consider a pulse of light moving in the opposite direction i.e. from the nose of the jet to its tail. In this case, based on the reasoning above, to the observer on earth, time on the jet has to be perceived as running faster (instead of slower) than normal, resulting in a logical conflict.

Am I missing something here, or is the explanation flawed?

• See physics.stackexchange.com/questions/143576/… for an explanation. Here we discuss sending light through a hollow tube rather than from end to end of a jet, and we also examine light being sent in either direction. The details of the outcome in each case is discussed. To the stationary observer, the light takes 3.73 sec to pass through the tube in the forward direction, and 0.268 sec in the reverse direction, while in both cases to the observer within the tube, it takes 1 sec.
– Sean
Nov 7, 2014 at 11:45

I haven't read the original passage, but if it is as you describe it, you are correct, sending a pulse in one direction is not enough to show time dilation. There are two classical and very easy to understand examples for both, time dilation and the non-simultaneity of measurements in two reference frames. In the example of the airplane, the subject stays at the center and sends two signals, one to the front and one to the back. To him, both signals will reach the extremes of the airplane at the same time. But for an observer on Earth, the signal will reach the back first, and the front later. So both observers disagree on what is simultaneous. For time dilation, the typical example involves a signal perpendicular to the motion of the observer. In this case it is best to draw a figure, so I'll send you to Wikipedia: http://en.wikipedia.org/wiki/Time_dilation and go straight to the section "Simple inference of time dilation due to relative velocity"

• A longitudinal light clock (one whose signals are parallel to the motion) can also be used to simply demonstrate time dilation. The important thing is that the two events (the sending and the receiving of the light signal in this case) happen at the same place. This is because simultaneous events that happen in the same place are simultaneous in every reference frame, so they allow us to calculate time dilation without any interference from relative simultaneity. You seem so realize this; I'm just clarifying it. Feb 17, 2022 at 10:00

Pouria, unfortunately, Hawking missed one thing. There is no difference in the observation of light speed in his thought problem, and there is no problem with time in your other thought experiment. And there can never be any.

Two persons (especially if they are located in two different frames of reference) cannot see the same photon, or a ray of light. It is physically impossible to see light that is not coming directly to your eye (or measure light that is not coming to your measuring device).

Light is always a local phenomenon. Always.

EDIT

OP noticed that:

... the observers do not necessarily need to "see" the pulse of light it-self moving about, but rather be informed of its reaching its destination (i.e. the nose of the plane in this case) via a light sensor. Upon sensing the pulse of light, this light detector will then simply broadcast by, say, turning on a red light, so that everyone (including earthlings) can be made aware of the pulse of light having reached its destination.

Absolutely correct. But then, there is absolutely no problem with time and simultaneity in this case. Light will travel within the plane only locally, and it will obviously reach both ends of the plane at the same time, so the red signals will be sent off to the ground at exactly the same moment. Therefore, if the person on the ground is located centrally with regard to the plane, s/he will receive both red signals at exactly the same moment again.

To sum up: Light cannot propagate faster (than $c$) for the person on the ground for the simple reason that the person on the ground cannot see it. This observer can only be informed what the passenger on the plane has seen. There are no independent observations/measurement to be compared, as the observer on the ground has no independent data.

• There are a lot of commonly understood tools in special relativity that have to be sorted: Filling space with clocks at $t=-\infty$ and collecting all the data at $t=+\infty$. So you can talk about "the location at time $t$ in frame $X$" and make perfect sense of it. So saying "two persons can't see the same ray of light" is a bit off.
– user12029
Nov 9, 2014 at 8:19
• @NeuroFuzzy: Could you provide a link to an experiment where "all the have been collected at infinity"? Would be interesting. Nov 9, 2014 at 8:26
• @bright.magus it's shorthand for $t$ arbitrarily larger than the duration of the experiment.
– user12029
Nov 9, 2014 at 8:30
• @NeuroFuzzy: OK, I'm not interested in playing games, and deciphering your "shorthands". Should you have a link to an actual experiment where people located in two different frames of reference saw the same photon and compared the speeds and times recorded, I will be much obliged. (Mathematical) speculations do not qualify. I am talking physics. Nov 9, 2014 at 8:39
• @brightmagus I'm guessing that in the case of this question, the observers do not necessarily need to "see" the pulse of light it-self moving about, but rather be informed of its reaching its destination (i.e. the nose of the plane in this case) via a light sensor. Upon sensing the pulse of light, this light detector will then simply broadcast by, say, turning on a red light, so that everyone (including earthlings) can be made aware of the pulse of light having reached its destination. Nov 10, 2014 at 9:35