Speed and Gravity Vs. Time and Space, respectively

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falkor

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After weeman's superb explanation of why time slows down when you near the speed of light, I'm now seeking similar comprehensive explanations of why time slows down near a massive source of gravity, and why massive objects cause space to curve so as to attract other matter.<br /><br /><b>Speed Vs. Time</b> <br />Result: faster speed = slower time<br />Reason: time is proportional to space. The faster an object travels through space the slower it can travel through time. Time is like a fourth dimension of 3D space.<br /><br /><b>Speed Vs. Space</b><br />Result: ?<br />Reason: ?<br /><br /><b>Mass/Gravity Vs. Time</b><br />Result: more mass/gravity = slower time<br />Reason: ?<br /><br /><b>Mass/Gravity Vs. Space</b><br />Result: more mass/gravity = sharper curved space to attract matter "more powerfully"*.<br />Reason: ?<br />*Is there a better way of describing this?<br /><br />As before, my topic is structured in the form of "fill in the missing gaps"; would be grateful for any help! <img src="/images/icons/smile.gif" />
 
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jgreimer

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*Is there a better way of describing this?<br /><br />I'll try and hope to show a connection between Einstein and the ancient Greek mathematician Pythagoras. As you mentioned the faster you travel the more time slows down. Einstein used the formula created by Hendrik Lorentz to describe the rate of dilation which is t = sqrt(1 - v^2/c^2). If we change v^2/c^2 to (v/c)^2. All we're saying is that we're going to express v as a fraction of c so doing that we can just use v^2. Now we have sqrt(1 - v^2). Remember the pythogoran theorem h = sqrt(a^2 + b^2) but if we already know h and one side how do we find the other side? b = sqrt(h - a^2) right? In the case above h = 1 and a = v as a fraction of c. So what is b? b is the dilation of time. At v=0, t=c, yes time is equal to the speed of light. The whole Lorentz formula can be reduced to t = sin(acos(v)).<br /><br />As you mentioned both velocity and gravity slow time. But what strength of gravity slows time the same amount as what velocity? The effect of gravity on time is the same as a velocity equal to the escape velocity of the gravitational object. In other words the effect of the Earth's gravity on time is the same as the Earth's escape velocity of about 8.7 km/sec.
 
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weeman

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Hah! Well, I wouldn't call it superb, I'm no astrophysicist <img src="/images/icons/tongue.gif" /> <br /><br /> <div class="Discussion_UserSignature"> <p> </p><p><strong><font color="#ff0000">Techies: We do it in the dark. </font></strong></p><p><font color="#0000ff"><strong>"Put your hand on a stove for a minute and it seems like an hour. Sit with that special girl for an hour and it seems like a minute. That's relativity.</strong><strong>" -Albert Einstein </strong></font></p> </div>
 
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