Understanding Einstein’s special theory of relativity

In imagining a Sci-Fi scenario, I found a simple way of describing, if not explaining, Einstein’s special theory of relativity.

Imagine if a flight to the moon was no different to flying half way round the world in a contemporary airliner. In my scenario, the ‘shuttle’ would use an anti-gravity drive that allows high accelerations without killing its occupants with inertial forces. In other words, it would accelerate at hyper-speeds without anyone feeling it. I even imagined this when I was in high school, believe it or not.

The craft would still not be able to break the speed of light but it would travel fast enough that relativistic effects would be observable, both by the occupants and anyone remaining on the Earth or at its destination, the Moon.

So what are those relativistic effects? There is a very simple equation for velocity, and this is the only equation I will use to supplement my description.

v = s/t

Where v is the velocity, s is the distance travelled and t is the time or duration it takes. You can’t get much simpler than that. Note that s and t have an inverse relationship: if s gets larger, v increases, but if t gets larger, v decreases.

But it also means that for v to remain constant, if s gets smaller then so must t.

For the occupants of the shuttle, getting to the moon in such a short time means that, for them, the distance has shrunk. It normally takes about 3 days to get to the Moon (using current technology), so let’s say we manage it in 10 hrs instead. I haven’t done the calculations, because it depends on what speeds are attained and I’m trying to provide a qualitative, even intuitive, explanation rather than a technical one. The point is that if the occupants measured the distance using some sort of range finder, they’d find it was measurably less than if they did it using a range finder on Earth or on the Moon. It also means that whatever clocks they were carrying (including their own heartbeats) they would show that the duration was less, completely consistent with the equation above.

For the people on the Moon awaiting their arrival, or those on Earth left behind, the duration would be consistent with the distance they would measure independently of the craft, which means the distance would be whatever it was all of the time (allowing for small variances created by any elliptic eccentricity in its orbit). That means they would expect the occupants’ clocks to be the same as theirs. So when they see the discrepancy in the clocks it can only mean that time elapsed slower for the shuttle occupants compared to the moon’s inhabitants.

Now, many of you reading this will see a conundrum if not a flaw in my description. Einstein’s special theory of relativity infers that for the occupants of the shuttle, the clocks of the Moon and Earth occupants should also have slowed down, but when they disembark, they notice that they haven’t. That’s because there is an asymmetry inherent in this scenario. The shuttle occupants had to accelerate and decelerate to make the journey, whereas the so-called stationary observers didn’t. This is the same for the famous twin paradox.

Note that from the shuttle occupants’ perspective, the distance is shorter than the moon and Earth inhabitants’ measurements; therefore so is the time. But from the perspective of the moon and Earth inhabitants, the distance is unchanged but the time duration has shortened for the shuttle occupants compared to their own timekeeping. And that is special relativity theory in a nutshell.


Footnote: If you watch videos explaining the twin paradox, they emphasise that it’s not the acceleration that makes the difference (because it’s not part of the Lorentz transformation). But the acceleration and deceleration is what creates the asymmetry that one ‘moved’ respect to another that was ‘stationary’. In the scenario above, the entire solar system doesn’t accelerate and decelerate with respect to the shuttle, which would be absurd. This is my exposition on the twin paradox.

Addendum 1: Here is an attempted explanation of Einstein’s general theory of relativity, which is slightly more esoteric.

Addendum 2: I’ve done a rough calculation and the differences would be negligible, but if I changed the destination to Mars, the difference in distances would be in the order of 70,000 kilometres, but the time difference would be only in the order of 10 seconds. You could, of course, make the journey closer to lightspeed so the effects are more obvious.

Addendum 3: I’ve read the chapter on the twin paradox in Jim Al-Khalili’s book, Paradox: The Nine Greatest Enigmas in Physics. He points out that during the Apollo missions to the moon, the astronauts actually aged more (by nanoseconds) because the time increase by leaving Earth’s gravity was greater than any special relativistic effects experienced over the week-long return trip. Al-Khalili also explains that the twin who makes the journey, endures less time because the distance is shorter for them (as I expounded above). But, contrary to the YouTube lectures (that I viewed) he claims that it’s the acceleration and deceleration creating general relativistic effects that creates the asymmetry.