Time dilation

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And apparently I cannot spell it, either.

The problem is that in order to an object to exhibit a visible degree of blueshift (or redshift), it must be moving at a significant fraction of the speed of light relative to the observer - and such an object would not long survive friction from the atmosphere itself, here on Earth. That's why we look at stars and galaxies for redshift; they're far enough away that they can get up to such velocities relative to us without actually hitting us and being destroyed. That's why we have to use the Doppler shift of soundwaves when we want to talk about things on Earth - the speed of sound is low enough that even a car can move at a significant fraction of Mach 1.

Oh. I see. (Sort of).



Back to time dilation: I've remembered a simple formula, one of the few ones I do actually know.

v=d/t

so

t =d/v

Is the "time" element in this equation the same sort of time being talked about in time dilation, or are they two different things?

I can see how t would be lessoned in the above equation if v were greater, so that is what is being talked about in the complex formula I don't understand?

It's a "commonsense" formula for time, but not relativistic time. Your formula doesn't take the speed of the person observing something into account; it claims that time works the same at a million miles per hour as it does at ten. The "complicated" equation says that time passes in a different way when you are going very fast

I'll try go through the formula once more; you seem to understand why increasing v would make t smaller above, and the time dilation equation works in exactly the same way.



I'm going to use bogus numbers, to make the result less confusing.

Examples

if we let delta t be equal to one second, and c^2 = 25 (it's much larger than that in real life), we can see how the time dilation changes as v gets bigger (or the moving observer gets faster).



in the top example, both observers were standing still, so they both experience time passing at the same rate. there is no dialation. Notice how the "0/25" is equal to zero? This means the bottom is equal to one, cause the square root of 1 - 0 is equal to one.

In the second example, the velocity squared (the speed of the moving observer, squared) is "9/25"/ This makes the bottom part smaller. 1/0.8 is equal to 1.25.
This means, for ever second that a guy standing still counts, the moving guy counts 1 and a quarter. So we have time dilation!

I hope that helped, but I doubt it; usually people get blinded by math

I get the gist of it, but I'm fumbling for my white stick anyway.
* whistles for guide dog *

Come back, ruveyn's lecture on the applications of differential geometry in general relativity is next!!

Ok. I'd better stock up on Ibuprofen too.

things go much easier if you scale the speed of light c to be = 1. Then your velocity v is that fraction of the speed of light at which the body travels in the frame of reference. For most every day speeds v is practically zero which is why time dilation and space contraction is so hard to observe.

ruveyn

I would have used that in the above examples, but I wanted to avoid large strings of decimals, or scientific notation. Integers are easier, they clutter the equations less.

I can't believe I forgot to mention that time dilation isn't detectable at low speeds, due to the fact v^2 is usually << than c^2

It all went right over the top of my head.

I never did any advanced algebra, so I don't know what all those symbols mean, and I'm none the wiser. The only kind of algebra I did was dividing both sides of things like 2x-9 = 3x+8 in order to find x.

Surely there must be a way to explain it in words rather than as a mathematical equation.

Isn't there?

Ignore the bit on the top, the example on the bottom is in numbers.

The jist is that when you get close to lightspeed, the bottom bit gets small, and time dilates.

I'm at Year 6 Math only, I have never done Algebra.

They've also tested it by flying an atomic clock around in a jet.

And more recently they tested it by having one clock be just 12 inches above the other:

http://www.dailymail.co.uk/sciencetech/ ... itude.html

You can get it from either speed (generating mass) or proximity to mass (the earth).

It can't be expressed in words very clearly - English isn't well suited to Einsteinian physics; no human language is, really. The best we can do are approximations and analogies, which haven't been that clear for you so far.

It's like trying to discuss quantum mechanics in plain English. A lot of things that happen in that realm don't seem to make the least bit of sense when you try to put them into language...

Yep so when you think if it all in a really,really macro scale... the universe contains all the mass there is and it seems to be expanding at the speed of light.


So.. the universe, from its own frame of reference... doesn't experience time passing.


weird aint it?


(yes, wild leap of logic. im that bored )

It's not too hard to test; satelitte's have to be programmed to take relativity into account, otherwise they go out of sync with "earth-time" rapidly, and give us stupid coordinates for GPS.