Question: How does time slow down when you go faster or have more gravity?

Time slowing down when you move fast – here’s one way of thinking about it – how do you know what time it is anyway – one way is you stand in front of a clock and the hands of the clock emit photons (light particles) that strike your retina and your brain interprets these signals into the position of the hands on the face of the clock and into a time. Imagine the clock strikes 12 and you are stationary in front of the clock and you get hit by the photons and your brain registers the time as 12 o’clock – then you immediately start running away from the clock but at a very quick speed (say 99% the speed of light). The clock then emits more photons 60 seconds later (corresponding to the time 12:01) – if you were stationary these would hit your retina 60 seconds after the ones emitted at 12 and you’d go OK 60 seconds have elapsed the time is 12:01…. however when you are running away from the clock then the photons (travelling at the speed of light) have to catch you up (you are travelling away at 99% the speed of light) – this takes some time – so by the time the 12:01 photons hit your retina you’ve gone a long way and your brain registers 12:01 “late” – it’s as if time has been slowed. If you ran away at the speed of light (only possible if you had no mass !) from the clock just before it sent the 12:01 photons then these 12:01 photons would NEVER reach your retina since you are travelling at the same speed as the photons and you set off before them – so the last time your brain registered a time it was 12:00 and your brain/eye never gets the information that it is 12:01 – so time has frozen at 12:00 and in effect time is passing infinitely slowly. [A sideline hear on “frames of reference” – the person moving away from the clock can also be interpreted as a clock moving away from the stationary person – time inferred from this moving clock is running “slow”, in the “reference frame” of the person time as defined by say their heart-beat is still going at the “normal rate” since the heart-clock is stationary (apart from the beating) with respect to the person whereas the clock emitting light isn’t – that’s enough relativity ed.]

Anyway this is exactly what is happening to cosmic ray muons – they have a lifetime of 2 micro seconds – without this relativity effect then none would reach the earth e.g if they were travelling at the UK speed-limit (70mph) it would mean they’d only travel about 0.02 mm (!) before decaying which means not many would reach the earth from the upper atmosphere which is about 15 km. They are however on average travelling very close to the speed of light (about 99.97%) ie at 1080 million km/h and so then travel about 0.66km – but the RELATIVITY effect means that time for them is ticking slower about a 1/40th of the normal rate so in effect they can travel 40 times further before they decay – this means 40 times 0.66 km ie about 26km – thus explaining the observation that most cosmic ray muons (particularly those of the higher energies) reach the surface of the earth and go through our body. Luckily they are travelling so fast that as they travel through our body they do little damage (interactions causing damage proceed at a higher rate at lower speeds) – if this weren’t the case then we’d get radiation poisoning/cancer. This is true to a point – if the rate of cosmic rays hitting the earth was much higher than we would suffer some damage but nearly all the cosmic rays incident on the earth (many of which are spewed out by the sun) are deflected away from the earth by the earth’s magnetic field. Without this magnetic field we would be bombarded by radiation and die quite quickly. Somewhat worryingly we don’t understand the earth’s magnetic field particularly well (the belief is it’s due to the molten iron slopping around in the earth’s core) and the direction of the field flips every few hundred thousand years – it has probably flipped around 10,000 times in the lifetime of the earth (but not while we’ve been alive) and we don’t know quite what happens. If during THE FLIP the magnetic field is interrupted then our protection from the cosmic radiation could be diminished and human life would get precarious – forget volcanic ash – worry about the magnetosphere and THE FLIP ! Sorry a large digression.

Gravity is more tricky this is the General Theory of Relativity – but the idea here is that gravity bends light and given what I said above that we can infer how time has passed by the interval between photons hitting our eyes then if the photons travel through a strong gravitational field (produced by a massive body) then they travel not on a straight path but a curved path (space-time is bent by gravitational fields) this then means that time is altered…

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