Why time is a separate physical quantity

[Studiot]

This is not really an answer to your question, which floats on the boundaries between science, mathematics and philosophy, it is some things for you to think about.

When we talk about a physical property or quantity we look for a mathematical model. We want the mathematical rules to reflect the physical ones (and vice versa) as far as practicable. I don't say as far a possible because there is rarely if ever a total match.

Often we use the real numbers.

So what interesting properties do the real numbers come with?

Well, apart from the obvious arithmetic ones they are well ordered. This is a mathematical statement of the fact that we can place them one after another in order. This affords us the concept of greater than or less than. It also implies that every number has its place and cannot be placed somewhere else on the number line.

Next comes the property of completedness. This is a mathematical way of saying that there are no gaps or numbers not included between the numbers on the number line.

Is this always a good correspondence to physics theory in the light of quantum mechanics? Is time quantised?

Then the reals posess a distance function. This guarantees us that the difference (distance) between say 5 and 7 is the same as the distance between say 5000 and 5002.

This feature can be very useful but does it fit with more complicated (relativistic) theories of space-time? It does however provide the ruler you guys were talking about and suggests that 1 metre or 1 second on Mars the the same as 1 metre or 1 second on Alpha Centauri.

Some physical properties obey rules not reflected in the reals so we introduce imaginary numbers - at the cost of the well ordering principle as complex numbers are not well ordered and cannot be put in greater than less than order.

 

[ErikD]

You might want to watch the BBC documentary http://www.bbc.co.uk/programmes/b00fyl5z" I found it very useful in simply describing the history and our current understanding of time.

 

[ehpc]

Studiot, I think I see your point. So it is not very proper to discuss the essence of spacetime using incomplete language.

ErikD, thank you I'll definitely find this film.

 

[Dale]

Ok, I have read through this forum posts about 'time'. And have another stupid question, this time about clock.

Apparently we measure time with clock. The clock has arrows in it just like in any other measuring device. So we can talk about time changing by looking at indications of that arrows. If they move, we know the time has changed. But I don't get what exactly does this clock measure..

For comparison if we use voltmeter. It is a measuring device too. And it measures electrical potential difference through magnet. So there is an electrical force iteracting with magnet and that's why the arrow moves. So there is an observable participation of some force.
But what with the clock? What drives arrows in the clock? The tension of the spring for example. Or quartz crystal. Or whatever. But not the thing we are measuring. So the time does not actually move the arrows? Or if the time is interconnected with space, than any motion carries a time within itself? So that's why we are talking about time on clock, because when arrow moves, that means there is a movement in time? But then I have a question. Does voltmeter shows time too? It's arrows are moving too, so it should show time shouldn't it?

All measuring devices are essentially the same in principle. We have some unknown physical quantity and a device which operates according to some physical theory to produce a human-readable result which depends on the physical quantity of interest. Usually the device must be calibrated to some reference standard.

In the case of the voltmeter the unknown physical quantity is the voltage and the device operates according to the theory of Maxwell's equations to deflect a needle to some position along a dial which has been properly calibrated to correspond to the number of volts. In the case of an atomic clock the unknown physical quantity is the time and the device operates according to the theory of quantum mechanics to produce a repeating EM wave which can be counted and calibrated to correspond to the number of seconds.