It seems to me, in my short time on these boards there is much confusion about what time really is. So Ill go ahead and make a post about it using some simple mathematical examples to improve understanding. As a disclaimer.. I will treat time and its behavior as in the case of special relativity, Those of you more endowed in quantum physics maybe be inclined to argue, but this is a simplistic sakes kind of thread. Maybe should have started a new topic but well see. Ill try and keep it simple and to the point, as most people are not as enthused as me about math and physics.

First lets start by defining what we mean by time. Time is a human idea, it is a scalar quantity we use to measure things or keep track of things. Much like labeling drawers on your tool chest. What time is not is a place. The past or the future do not exist in any real sense, only awareness of them because we perceive time as universal and linear. So looking at stars is not actually looking in the past, what you see when look at a star is light that may have taken millions of years to get, but I assure you the light is in the present, as is the star in question. Because you can not see the star over the vast distance does not mean it is in the past. Say I get a letter from China that took 6 days to reach me, the letter like the light is in the present, it just took "time" to get to me. Furthermore China is not existing in the past because I can not see it.

Now we keep track of time with seconds, the time standard in science. Surprising that most don't know what a second is. Keeping with the whole simple definition thing a second is...

*It is the amount of time it takes a cesium-133 atom to transition between two ground states. Which corresponds to 9,192,631,770 periods of radiation for transition between states to occur.*Now on space-time and space travel.

Space is big, Sitting here in our homes and modern lifestyles we often forget that, if even realize it all. For instance the milky way is approximately 90,000 light years in diameter, our local group is is around 10 million light years diameter. Im sure many of you have heard of a light year, but lets go ahead and define it for everyone. A light year is...

The amount of time it takes light to travel in 1 year or 31 556 926 seconds. Now since we know how fast light travels in a vacuum (299 792 458 meters per second, well call it

*c* from now on) and how many seconds are in the average year, we can calculate how far light goes in a year

*c**(seconds in a year) and we see light goes 9.46 × 10^15 meters (quick break for notation the ^ symbol means raised too) or roughly 5.88 × 10^12 miles.

So that means, that traveling at

*c* it would take approximately 90 000 years to cross the milky way or roughly 10 million years to cross our local group. The fastest man made object was the satellite Helios which traveled at approximately 150 000 miles per hour or 67 056 meters/second or .02% the speed of

*c*. Electromagnetic radiation such as radio waves also travel

*c* in a vacuum. I made an earlier post with a mathematical example which I am going to copy here, baring no one has a problem with that

.

QUOTE(me)

The first radio broadcasts sent into space were in 1958 by President Eisenhower. Thats 49 years ago. Now radio waves are electromagnetic waves and travel at c in a vacuum. How far have those radio waves gone in 49 years?

Lets calculate it, 49 years x 5.86x10^12 miles per year is 2.87x10^14 miles, thats far that number again is 287 000 000 000 000, thats 287 trillion miles, I know unimaginable. But how far is that really? Well the Milky way for instance (our own galaxy) is roughly 90,000 light years in diameter (calculations range from 80k to 100k). In other words the Milky way (for our calculations) is 5.27x10^17 miles across (90 000x 5.86x10^12). That means in 49 years, traveling at light speed, those radio waves have made it a whooping .054% (distance traveled/diameter of the milky way). It only gets smaller from there. Our local group (The milky way and the surrounding galaxies) is around 10 million light years diameter, and that is close on a cosmic scale. So in 49 years, our light speed radio waves have traveled..... .00049% of the diameter of our local group.

Now it has also been stated in other threads that time, is relative to the observer, there is no universal time, but what does that mean? It turns out that speed effects time. Lets use a simple math example to show this.

We need a formula for this, we will use

. This is how time is treated in special relativity and we get this from Lorentz Transformations, which I will spare you all the math of how we arrive at this equation, just know its correct.

Lets say we have two friends bob and tom, tom wants to travel to a planet 20 light years away. In his spaceship we tom's clock, while bob remains behind on earth with his clock.

For simplicities lets define our variables.

we'll call dt and it is the time as seen by bob.

we'll call dt' and it is the time relative to the traveler in our reference frame.(Tom)

v is the velocity relative to Tom, the traveler.

c is the speed of light

and the square root ill write as (equation)^.5

I know, dont get discouraged yet it will make more sense in a minute.

Which we know is 1.89 x 10^17 meters away (get that by light year*20 light years). Now lets say we invent a new type of engine that allows us to travel at 80% the speed of light, or .8

*c*. We then set off for our new planet and wonder how long it will take us to get there.

Well I am sure most of us have seen this equation before from a high school physics or math class

velocity equals distance divided by time. Since we know our velocity, .8

*c* (units in meters per second) and we know our distance 1.89 x10^17 meters we can calculate roughly the time it takes us to get to this planet. So plug in the knows, use some simple algebra and we get 7.9 x10^8 seconds or roughly 25 years. This what here on earth we would guess and indeed it is what bob measures. But what about tom's clock?

Time to use that scary looking equation we saw earlier.

We are looking for dt', the time as seen by tom's clock. so we have dt=7.9 x10^8 seconds, v=.8

*c*, we plug these numbers in and rearrange our equation.

dt'=(dt)(1-(v^2/

*c*^2))^.5 and we get tom's clock shows 15 years have gone by.

So if at the start of our endeavor, Bob and Tom are twins and 30 years old. When tom arrives at this new star, he will seem to be 45 while bob will seem to be 55.

Now to you quantum physics buffs you may want say, we need to add to this! but again its just a simplified example to show that time is relative to the observer, not a universal constant.

edit: forgot I found this nifty little applet to help visualize it.

Time dilation appletWell it appears theres no embed functionality so will have to just clicky the link.

**Edited by camlax, 09 July 2007 - 04:32 AM.**