Space and time are entangled
Physics Narrative for 14-16
Where are you, and when are you there?
We've introduced the idea that looking out in space is looking back in time on several occasions throughout the SPT materials (for example, in the SPT: Motion topic, in the SPT: Earth in space topic and in the SPT: Radiations and radiating topic). This is dramatically obvious when the distances are huge and it takes the radiations an appreciable time to travel the huge distances (one light year is 9,460,800,000,000,000 metre).
Alice, based on Earth, doesn't see the Sun as it is now, but as it was 8 minutes ago – that's how long the information from the event happening there
now takes to reach Alice. Reflected light from the Moon travels to the Earth in about 1 second. So, again, Alice only notices what's happening on the Moon one second after Bob (the astronaut on the moon) notices the event.
But we've also emphasised that the same (universal) connection between space and time applies locally:
Closer to home light travels about 30 centimetre in one thousand millionth of a second – a foot per nanosecond – so even on the scale of a room, you only know about the past.
This has real consequences for Alice and Bob, who need to find ways to agree on the measurements for a particular process, even when they're not right next to it. Sitting them both beside the event (or even equal distances from it), and so having them co-moving with the event (it appears stationary to them), is one way of enforcing agreement. But if Alice and Bob are not travelling at the same velocity, they cannot both be at the start event of the process and at the end event of the process.
For many practical purposes this lack of being right there does not make much difference, as the time differences in the durations they record are tiny. But the greater the difference in the velocities of Bob and Alice, the greater the difference in displacements from the events, and so the greater the differences in the measurements. The distance from the event and the time at which you record it are necessarily linked by the universal speed (3 × 108 metre inverse second).
The universal speed, which converts differences in distance to differences in time, at which all electromagnetic radiations (including light) travel, ensures that space and time will be entangled in this way. Measurements of space and time are not as distinct as we think. There is a measure that Bob and Alice will agree on, but it has spatial and temporal components.
It turns out that there is no universal clock, that all must agree on. Or, as Einstein reported his own thinking:
It came to me that time was suspect.
So began an intellectual journey that ended with the special theory of relativity, all arising from some very careful thinking about velocity, and how people taking different points of view might record clock times and positions.