Time Dilation: Understanding the Formula

lewis1440
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I do not fully understand the time dilation formula, if the answer is nearer to 1 does that mean time itself under perspection has slowed or increased?
 
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I would recommend not using the time dilation formula. It is too easy to misuse. Instead, you should always use the Lorentz transform.
 
DaleSpam said:
I would recommend not using the time dilation formula. It is too easy to misuse. Instead, you should always use the Lorentz transform.

ok, thankyou.
 
lewis1440 said:
I do not fully understand the time dilation formula, if the answer is nearer to 1 does that mean time itself under perspection has slowed or increased?
While it's safer to use the full Lorentz transform, IMO the time dilation formula can give better physical intuition if you're trying to picture how things are behaving in a given frame. It's always true that a clock which is moving in a given inertial frame is running slower in that frame, so for example if gamma=1.25, that means in the frame of the observer who sees the clock in motion, it takes 1.25 seconds for the clock to tick forward by 1 second. So the larger the value of gamma, the slower the clock is ticking in the observer's frame. If gamma=1, then that means the clock is at rest relative to the observer, and it's ticking at 1 second per second of time in the observer's frame (no relativistic time dilation).
 
OK, so this has bugged me for a while about the equivalence principle and the black hole information paradox. If black holes "evaporate" via Hawking radiation, then they cannot exist forever. So, from my external perspective, watching the person fall in, they slow down, freeze, and redshift to "nothing," but never cross the event horizon. Does the equivalence principle say my perspective is valid? If it does, is it possible that that person really never crossed the event horizon? The...
ASSUMPTIONS 1. Two identical clocks A and B in the same inertial frame are stationary relative to each other a fixed distance L apart. Time passes at the same rate for both. 2. Both clocks are able to send/receive light signals and to write/read the send/receive times into signals. 3. The speed of light is anisotropic. METHOD 1. At time t[A1] and time t[B1], clock A sends a light signal to clock B. The clock B time is unknown to A. 2. Clock B receives the signal from A at time t[B2] and...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...

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