# What is time dilation?

#### penguinraider

I'd be very happy if you'd answer this, and I'm looking more for the effect of gravity on time, rather than speed.

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#### ZapperZ

Staff Emeritus
2018 Award
penguinraider said:
I'd be very happy if you'd answer this, and I'm looking more for the effect of gravity on time, rather than speed.
I suggest you ask this in the Special Relativity/General Relativity section, since this has nothing to do with QM.

Zz.

#### eNathan

ye, this thread should really get moved to SR/GR. But this is how gravity effects time (in simple terms).

when you are in the presence of a gravitational felid, time will slow down. If you wich to calculate it, you can use the Lorenz Transformation and replace "v" with the "escape velocity" of the earth. For instance...

The escape velocity of the earth is 11265.4 meters per second. This means that you will have to travel 11265.408 to escape the gravity of the earth. But this number does not take into consideration air friction and resistance.

So if I am on eath for 1 day, it only took me 0.999999999. You can see that there is not much of an effect on time in even what seems to be a large gravitational field such as that on earth.

Perhaps somebody can explaine in further than what I did.

#### trosten

time dilation is the slowing of time. Ofcourse as seen by someone else, you can never notice that ur time is running slow !? however you can compare its pace with other observers by monitoring something that should run at the same pace. You can quite easily understand why gravity must slow time by considering two oberservers Alice and Bob. If Alice sits at the bottom of the eifeltower and she send photons/light at a certain frequency f straight up to Bob whos sitting at the top of the eifeltower. Since Bob has higher potential energy then Alice the light must "climb" up to Bob and thus looses some energy to the potential, now from QM we have that the energy of a photon is E=hf, where f is the number of oscillications per second. Since energy is conserved Bob will recieve a photon with approx. energy E=hf-mgh=hf´ now f´ must be a smaller number then f if Bob is to be above Alice and thus Bob is experiencing "less" gravity then Alice. If Alice claims she sends light with frequency 1, that is one oscillation per second then Bob will recieve less then one oscillation per second. Thus Bob will have to conclude that either Alice is lying or her time is running slower then his. Ofcourse he can make other conclusions, such as Alice watch is crazy etc.

#### O Great One

If Alice claims she sends light with frequency 1, that is one oscillation per second then Bob will recieve less then one oscillation per second.
Wouldn't Bob still receive the light at one oscillation per second?

#### Mortimer

Expression for time dilation in a gravity field:

$$\frac{\Delta t_r}{\Delta t_{\infty}}=\sqrt{1-\frac{2GM}{rc^2}$$

The equation calculates the ratio between a time interval at radius r and a time interval at infinity. G is the gravity constant, M the mass.
The Schwarzschild radius is at $$r=2GM/c^2$$

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