<p><BR/>Replying to:<BR/><DIV CLASS='Discussion_PostQuote'> If we weren't here to observe, the question is whether that relationship would change or not. Ah yes, but then the question comes up of whether or not the entire universe would exist if we weren't here to observe it! Of course, that idea has come up in conversation about a billion times on this board! Let me know if you like this analogy, Speedfreek: Imagine that you are traveling in your car on a freeway that travels due east, at 65mph. You take an exit ramp that will connect you with another freeway that will take you due north. As you're on the ramp, more of your speed is transfered to the north direction from the east direction. Once you're on the northbound freeway, you will be traveling 65mph north and 0mph east. Isn't this the same idea with time dilation? The faster you travel, the closer you are to the speed of light, meaning your mass is continually increasing. As your mass increases, more energy is required. So, wouldn't this mean that as you travel closer to the speed of light, more of your velocity is transfered from your direction in time to your direction in space? Since it requires an infinite amount of energy to reach the speed of light? <br /> Posted by weeman</DIV></p><p> </p><p><font size="2">Excellent point Weeman. Let me take it a little further. One of the ways the relationship between time and space is expressed is by the Lorentz Transformation which is sqrt(1 - v^2/c^2). This formula is nothing more than the pythagorean formula in disguise. </font></p><p><font size="2">If you have a right triangle with sides A,B, and C with C being the hypotenuse and you know the lengths of sides A and C, how do you find the length of side B? You simply rearrange the formula into B = sqrt(C^2 - A^2). In the Lorentz transformation if we let c = 1, v must then be expressed as a fraction of c. The 1 in the formula is really c^2/c^2 so the formula becomes sqrt(c^2/c^2 - v^2/c^2) and since c = 1, it equals sqrt(c^2 - v^2). Look familiar? In fact a much easier way of finding the amount of time dilation is </font><font size="2">sin(arccos(v))</font><font size="2"> where v is espressed as a fraction of c.</font></p><p><font size="2">We can visualize this by putting v on the x axis, the rate at which time passes which I call t' or time prime on the y axis and connecting them with a hypotenuse equal to 1 or the speed of light</font></p><p><font size="2">So yes, time exists in the same sense that space exists and time passes for a body at rest at the rate of about 299,792,458 meters per second.</font> </p>