Time on 1st & 2nd Floors: Gravity & Light Measurement

[NewToThis]

From my understanding time appears to go slower on the first floor because gravity is stronger there which makes everything move slower, from particles to clock hands. But if light has no mass and can't bee slowed down by gravity then that means time is traveling at the same time on the first and second floor, but to measure light on both floors you would have to use a clock, but clocks are affected by gravity, so clocks on both floors will measure the same time a beam of light has taken to cross the rooms on both floors, is that correct? so if the rooms on both floors are 3 metres across then the time to cross them will be the same, but how can that be if the clock on the second floor is moving faster?

And I don't understand how you can get an accurate measure of light because any measuring device is affected by gravity.

I hoe this makes sense.

 

[russ_watters]

Welcome to PF!

What you describe is not what time dilation is. It's not a matter of gravity pulling on the hands of clocks to slow them down or otherwise applying forces to particles to impede their motion, it is literally that time itself passes at different rates under different gravitational potentials.

And since light's speed isn't affected by gravity, if transit times measured are different, that means the distance traveled must have been different too (that's length contraction).

 

[Ibix]

Drop a brick and an antimatter brick out of the window. Combine them at the bottom, and redirect all the photons straight up. At the top, convert the photons back to matter-antimatter pairs, and drop the brick and antibrick again.

At the bottom, though, the bricks were moving. As well as their mass-energy ($E=mc^2$) they have some kinetic energy. So I can make more photons at the bottom than I need at the top to re-build the bricks. Free energy!

But free energy production isn't possible. The light must somehow lose energy as it climbs back up, and the only way it can do that is to be red-shifted. Pound and Rebka were the first to detect this frequency shift experimentally.

So light is red-shifted as it climbs from the first to the second floor. Let’s set up identical lasers on the first floor pointing up and on the second floor pointing down. Let’s also set up counters that count the light waves as they go out, and as they are received on the other floor. We normally call devices that count cyclical processes "clocks", so we've built identical clocks on the first and second floor. But remember the red-shift. The second floor must measure the first floor clock running slowly - otherwise it would get ahead of the red-shifted light reaching the second floor, and vice versa. So, gravitational time dilation.

Of course, none of this applies if we are shining light around horizontally. We can, therefore, make measurements of light speed etc with horizontally mounted apparatus. That's what we do.

Does that make sense?

 

[Janus]

To expand on what Ibix has said: Imagine the first floor/second floor clock scenario with no difference in gravity strength between the floors. (we have a hypothetical uniform gravity field). Light would still red-shifted going from the first to second floor (and blue-shifted going from second to first) and you would still have gravitational time dilation between the clocks. In fact, if we assume that in both scenarios(gravity weakening with altitude and gravity remaining constant) that gravity has the same strength on the first floor of the buildings, then in the case where there is no difference in gravity between the floors you will have the most difference in the time rates of the clocks.