Blog of Veikko M.O.T. Nyfors, Hybrid Quantum ICT consultant

Quantum Mechanics demystified, a try

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What is time? A mystery it is. In various ways.

Measuring time in the past

Still couple of thousands of years ago humans took the time as hours between sunrise and sunset. Hours were counted starting from the sunrise. There was twelve hours to sunset.
E.g. in the bible third and ninth hour are mentioned, among others. Third hour was at about 09:00 and ninth at 15:00 in our impression.

In Israel the day is about 4 hours longer in June than in December. Hour is longer in the summer than in the winter. High noon was experienced at sixth hour sharp, though.
Gets even worse in locations more towards north and south. Sun doesn’t get up at all in winter north from polar circle and south from arctic circle. Not a good interpretation of time at all.

Also, this approach was giving a different time to different latitudal places. Villages tended to have their own private times on their clock towers. If it had been the second hour exact in Helsinki, in Stockholm it would had been a quarter past 1st hour only. Stockholm is 400 kilometers west from Helsinki, you see.

Then the world became smaller. It wasn’t very handy to have each and every railway station with their own time. Who would have printed all the timetables?
Timezones were invented to ease that issue. One global time over the world would had of course been pretty straightforward, but people were so accustomed to their local time scene they wouldn’t just have accepted that. It would had been too odd to have the sun in zenith at five o’clock in the morning, wouldn’t it?
So we nowadays have 24 time zones.

Time is relative Time Dilation

In the end, having local times for each village wasn’t that amiss after all.

You see, General relativity says time is dependent on Gravity. The more gravity, the slower time runs. One living at a valley remains younger than one on the mountains. With current precision clocks it can even be verified time is running faster on the table than on the floor.
Each spot in space has it’s own flow of time. Depending on the gravitational force in effect at that spot.

With special relativity it gets even worse. It says time also runs slower if clock is moving when compared to a stationary clock. This also can be nowadays verified with precision clocks in airplanes. Einstein visioned this without precision clocks available though, based on Maxwell equations on electromagnetism.
So each object in spacetime also has it’s own timeflow depending on it’s relative speed towards other objects.

Also simultaneity is relative, as described in article besides.

Time dilation between moving objects

Consider jetplanes A and B start a flight round the world over the poles, same base field but to opposite directions, speed 800 km/h. After 5 rounds they land on starting field.
What will the cloks show?

Trip round the world with speed 800km/h takes about 50 hours i.e. 180000 seconds.
5 rounds takes 900000 seconds.

From A’s point of view, B is moving with speed 1600km/h i.e. 500m/s relative to stationary A.

Per special relativity time dilation formula, while A’s clock ticks those 900000 seconds, B’s clock appears, as experienced by A, to tick a little less (\(t_0\)):

$900000=\frac{t_0}{\sqrt {1-\frac{v^{2}}{c^{2}}}}$

\[\Rightarrow t_0=\sqrt {1-\frac{v^{2}}{c^{2}}}*900000= \sqrt {1-\frac{(500)^2}{(3*10^8)^{2}}}*900000=899999.9999987483\]

Thus B’s clock should show 0.0000012517 seconds less than A’s clock when they compare clocks at return to base.
But wait, we can do exactly the same calculation from B’s frame of reference. Thus A’s clock should show less with the same amount.


Per my understanding, comparing time between moving objects A and B makes sense only if objects have been stationary with each other at some point of time, with their clocks running in sync then.
Using frame of reference for that occasion to compare relative time between A and B later on makes better sense.
Ultimate frame of reference being that of the Big Bang.

Here A and B were stationary to start with. Then they both accelerated to 800km/h to opposite directions. Clocks, for both of them, started to run slow if compared to the clock on base field. When compared after return, A’s and B’s clocks have both been running slow to the ground clock with the same amount, fourth of the above given 0.0000012517 i.e. 0.0000006258 seconds. You could calculate it ;-)

Of course one can delve into this from other frames of references also, it’s not wrong. But to use time dilation formula as such doesn’t work then.
It is wrong, in my opinion, to say a clock in move runs slower with obeying special relativity time dilation formula in general. Two clocks can be in relative motion to each other and still have the clocks ticking at the very same speed.
Eventually it is a question of forces applied to accelerate objects, which cause clocks tick differently.
Clock experiencing bigger forces and accelerations starts running slower when compared to a clock with less forces and acceleration.
To compare two clocks, how they tick, requires them to have been in a common frame of reference at some point of time. At Big Bang, if no later common frame exists. The one having experienced more forces and acceleration will have the clock ticking slower.

It is all due to the force

The same with force goes on with gravity as well. Bigger force closer to the mass is causing the clock slow down more than smaller force further away.
Once the guy from the valley moves up to the mountain, clocks become in sync, but valley guy’s clock is somewhat behind due to all slowing down at the valley.

A mystery even so

Imagine having yet two more objects C and D, with clocks. They are initially stationary to each other, with clocks in sync. D accelerates to a speed of 100km/h with clock slowing down towards C’s clock.
Imagine there is yet another clock E, which is running steady with clock D now. When clock D then deaccelerates by 100km/h, associated force causes clock D to run slower towards clock E. Thus D’s time must be running even slower after this. What’s the time dilation between C and D now? Their clocks really should be in sync now, shouldn’t they?
Actually what seems to happen here is that D is changing frame of reference back to that of C, as they are stationary to each other now. Thus C and D clocks are now in sync.
Eventually it is not a question of whose clock gets running faster or slower, but in which frame of reference the clock is in. E.g. in here D didn’t slow down even more while deaccelerating from E, E’s clock started to run faster instead if compared to D’s one.


What about the final readings of clocks C and D then?
D has cumulated some time less than C. All the time it was running slow while speeding is not lost while returning back to original frame.
D traveled some distance away from C. How can it be? Shouldn’t it have consumed some time instead to travel the distance?
This might come back to the fact that distance will get shorter as speed increases.

Direction of time

We humans are convinced there is past, present and future. And that time flows from past through present towards future.

Based on the above speculation, present is probably not exactly as we think of it, a global thing. Instead there seems to be countless present times for different spots and momentums. If not infinite. Scale of the time difference between these are such tiny ones, that we just don’t realize this. Instead we think present is at the same time everywhere. Being close to black hole or traveling near to the speed of light would already make a difference, if we ever would be able to make those.

Flow of time is problematic as well. Or the direction of the flow to be more precise.

Entropy is often regarded as being related to time flow. Overall entropy has been higher in the past than what it will be in future. If we had two timely different instances of a closed system, we could deduce which one is older by measuring and comparing their entropies. The one having greater entropy is older.
Just before the big bang, entropy was lowest. Everything was plain energy. From thereon overall entropy has grown.

Time in Quantum and Galactic scale

We humans see a blurred, fuzzy time in our scale and with our limited perception.
A bit like how Neitvuori shows up like green fabric when seen from lake Luonteri. Or the clouds on the valley looking like mattress of bombull when looked from the crest of mountain. When we get closer to Neitvuori or the valley, we realize the the fabric and the matress forming up of tiny leaves of the trees and spray of water molecules in the air.

Similarly, peculiar things seem to happen with time in other scales than our ordinary one.

In Planck scale Quantum Electrodynamics particles seem to be able to travel backwards in time.
Gravity doesn’t exist for a photon as it is massless, thus shouldn’t time pass all at once from it’s perspective. Could it be no time exists for a photon, it’s past and future is the same moment as it’s presence, is it? Moving at light speed might make a difference here also.

On the other end of scales, time does not pass at all in black hole, as gravity being infinite.