SCIENCE (said in a deep, meaningfully spooky voice)

[Polito45]

I was ignoring that bit because I don't get it either.

[RB]

That's why we don't get to stand on top of mountains looking wistfully at the sky while women get all foamy over us.

[Tinlad]

What I don't get is how the light can curve inside the falling lab regardless of observer viewpoint unless gravity is affecting the photons differently to how it is affecting the walls.

I roughly get relativity in broad terms. I get that if you are in a car and throw a ball backwards at the same speed as the car is travelling forward then to you the ball flies away from you but to someone stood by the road the ball drops straight down but this falling lab one seems wrong in my mind unless the light falls faster than the lab is falling.

OK, let's alter your example slightly: instead of throwing the ball, just let it drop. If you're inside the car, it appears to travel in a straight line. If you're anywhere else, you can see that the ball is following a curved path. But all observers agree what point the ball hits in the car, they just disagree about the path it took to get there.

This is exactly the same as the experiment I described, but rotated by 90 degrees: the car is providing the 'free-fall' effect, and the falling ball is in place of the laser beam.

The light is curving inside the falling lab, but because the lab is falling at exactly the same rate (because gravity affects matter and photons in the same way), it appears to be travelling in a straight line to an observer inside the lab.

Diagrams!
Inside the lab. The laser beam is seen to travel in a straight line across the opposite wall.

Outside the lab. Bob can see that the laser beam is actually bending downwards as it travels.

If the photons didn't fall at exactly the same rate as the lab, Alice would see the beam deflected either upwards or downwards - which would break the equivalence principle. So she has to see the beam travelling in a straight line, and Bob has to see the beam falling at the same rate as the lab - and thus following a curved path.

[RB]

So Bob doesn't see the beam hit at a lower part of the wall. He sees it hit the same bit of wall but at a closer distance to the earth. Whereas Alice has no perception of the rapidly approaching planet and is blissfully unaware that the light, the lab, its walls and her are curving towards an unplanned experiment in momentum.

I think I get it.

[Tinlad]

Exactly. The experiment is both highly informative and highly deadly (for Alice) at the same time. Physics is fun!

[Polito45]

Ok, that's fairly straight forward.

Now, Alice has cloned herself. She's sitting at one end of a table in the BoxLab facing her clone at the other end.
There's a lamp on the table between them. The Boxlab instead of falling vertically is moving at a constant speed horizontally.
Alice flicks a switch and the lamp comes on. The light from the lamp hits Alice's face and her clone's face at exactly the same time.
Is this what Bob sees?

[RB]

Bob sees an opportunity for an awesome threesome.

[Polito45]

I agree, but he has to figure out why he thinks the light hit Alice's face first... first.

[Tinlad]

Ok, that's fairly straight forward.

Now, Alice has cloned herself. She's sitting at one end of a table in the BoxLab facing her clone at the other end.
There's a lamp on the table between them. The Boxlab instead of falling vertically is moving at a constant speed horizontally.
Alice flicks a switch and the lamp comes on. The light from the lamp hits Alice's face and her clone's face at exactly the same time.
Is this what Bob sees?

I think you're testing me.

This problem is called the relativity of simultaneity. To cut a long story short: no, Bob doesn't see the light hit their faces simultaneously. In fact, there is no such thing as events happening simultaneously - it all depends on your frame of reference!

[Tinlad]

Part IIIa: Gravitational redshift
So, we know that light must lose energy as it move upwards in a gravitational field.

New experiment. We fire a blue laser beam straight upwards from the surface of the Earth. As the beam goes upwards, it loses energy because of the gravitational field. If it were an object like a ball, this would result in the ball slowing down. But this is a laser beam: light always travels at c!

The energy of light is directly proportional to its frequency (E = hf). So as it loses energy, its frequency decreases too. So as the laser beam moves upwards, its colour changes, tending towards the red end of the spectrum. This is gravitational redshift.

In general relatively, redshift and time dilation are both sides of the same coin: you can interpret the effect as either, depending on your frame of reference (where you stand your observer). The final step is to make the slightly tricky leap to reinterpret the above scenario as time dilation.

It'll be totally worth it, I promise.

[Polito45]

I trust you.

There are many tangents I could try to lead you off on here like, if a light beam streaking towards the earth from the sun
has high energy and so is shifted towards the blue end of the spectrum until it hits a medium that saps it's energy, like the earth's atmosphere
which would lower its frequency, shouldn't then the sky be red? Actually, I think I know I'm taking through my backside on this one.

How about this? - Alice and her clone agree that the light hits both of their faces at the same time because they know they are equidistant from
the source of the light and light as you say always travels at a fixed 67 million miles per hour.

Bob sees both the light that's going to Alice's face and the light that's going to her clone's face as traveling at the same 67 million miles per hour
BUT from his perspective, Alice (given that her back is towards the direction of the motion of the Boxlab)is moving away from the original
source of the light and her clone is moving towards it, so from his perspective the light hits the clone's face first.

Both Alice and her clone, and Bob are right. Is this correct?

[Tinlad]

Correct!

Wikipedia has a neat animation to show this:


This is what's called a spacetime diagram. The x-axis is a spatial dimension, and the y-axis is the time dimension. A, B and C are events. Let's ignore B, and say that A is the light hitting Alice's face, and C is the light hitting her clone's face.

If you're in the BoxLab, your velocity relative to the Alices is 0: v = 0. We can see that A and C happen simultaneously.

If you're outside the BoxLab, moving towards or away from it (as Bob is), we can see that this is no longer the case. A is before C, or C is before A, depending on whether you're moving towards or away from the BoxLab.

[Tinlad]

Part IIIb: Gravitational time dilation
Why does gravitational redshift imply time dilation?

Let us construct a clock (of any type: mechanical or digital) that is linked to a light source. Link them such that the light source produces light with a frequency equal to that of the ticking of the clock. Therefore, by measuring the frequency of the light source, you are basically reading the speed of the clock.

For the sake of the experiment, let's say that the clock ticks a thousand times a second. So the light source is emitting light with a frequency of 1000 Hz.

Actually, let's make two of them. One stays with Bob on the ground, one goes with Alice to space.

Bob is on the surface of the Earth. He measures the frequency of the light from his clock, and gets 1000 Hz.
Alice is in space. She measures the frequency of the light from her clock, and gets 1000 Hz.

Alice gets a telescope and looks down at Bob's clock (careful how you read that), and measures the frequency. The photons from the light source lose energy as they climb through the Earth's gravitational field, and thus are red-shifted to a lower frequency. So Alice sees that Bob's clock is running at less than 1000 Hz, and therefore time is running slower for Bob.

Bob gets a telescope and looks up at Alice's clock, and measures the frequency. The photons from the light source gain energy as they fall through the Earth's gravitational field, and thus are blue-shifted to a higher frequency. So Bob sees that Alice's clock is running at greater than 1000 Hz, and therefore time is running faster for Alice.

The light source is completely unnecessary: that just makes it easier to explain. If you had a normal, mechanical clock that you were reading the face of with a telescope, the same effect would be observed.

So a clock that is in a stronger gravitational field runs slower than one in a weaker field and vice versa. Gravitational time dilation! This has been experimentally verified using atomic clocks. In fact, the accuracy of GPS would be rubbish if the effects weren't taken into account.

[RB]

Is that just a relative perception thing or if by some voodoo you 'beamed' Bob's clock next to Alice's instantaneously would they actually differ if they started at the same time and were exactly as accurate as each other before Alice's blastoff.

Is there a universal constant involved or is time universally variable.

[Tinlad]

Time is actually variable. If you synchronise two atomic clocks on the Earth, take one up to space and bring it back again, it will read that more time has elapsed for it.

However...

When you go up into orbit, there is also relative velocity time dilation effects that come into play (special relativity). This is because something in orbit has a high velocity relative to something sitting on the surface of the Earth. It acts in the opposite way to the gravitational effect: time slows down for the high velocity clock. For astronauts going to/from the ISS, this effect is actually bigger than the gravitational time dilation effect, so the net effect is that they come back younger than if they'd stayed on Earth.