You'll have to excuse me if this subject has been brought up before. I'm new to this board so I don't know everything that has been going on On another astronomy board we have been discussing Einsteins equivolancy theory. It was brought up that a person, in a box, would not be able to tell if they were being attracted to the floor due to gravity or due to acceleration. I agreed that all by themselves, with nothing else in the box that you would not be able to tell. But I disagreed that it would be totally impossible to differenciate between gravity and acceleration if you had instuments to measure doppler shifts of light. From the other board :
Now, on a planet, not moving,not obiting, just sitting still in space, with gravity and a very tall box. The light is at the top and you are measuring at the bottom. The light is coming at a constant speed, (for the sake of arguing 186,000 MPS miles per second) If the box is 1 mile high, then it should take 1/186,000 of a second to travel that distance. Reverse the situation and it should still take 1/186,000 of a second. Gravity should not have an effect unless it is because of a massive planet. But since Nigel said that one of us was in it, we would have to assume that it would be an Earth size planet, otherwise we would notice the difference right away. If there is a difference, it would be very small because light has very little mass for our planets gravity to act upon. Ok, now the planet is moving, orbiting around a star. Planets generally orbit at a more or less constant rate of speed. Now when we do the same test, there is a slight difference in times. This is because at the instant the light leaves the bulb, you are at one spot in space. As the light is going toward you, you are moving toward the light, so that when the light reaches you the distance has decreased and therefore the time required for the light to travel is less. Reverse the situation and now when the light leaves the bulb, you are moving away from it so the distance increases and the length of time also increases. It is slight but should be measurable. As the planet revolves, you will find that your tests will reverse themselves. Picture a globe with a box on it, in your hands with the box away from you. As you walk forward, picture a small person in that box, they would be moving toward the light. Now spin the globe so that the box is in closest to you. Now the person in the box would be going away from the light. Now, you are in a constanly accelerating box. When the light leaves the bulb, you are accelerating toward the light, decreasing the distance and time. If you repeat the test, since your speed has increased due to acceleration, the distance changes become more dramatic and you get greater and greater differences in the time it takes for the light to tavel toward you and away from you.
Then it was brought to my attention that when you accelerate that time would change. As you accelerate toward the light, time for you would slow down so that your measurements would be the same. Conversely, as you accelerate away from the light, time would slow down. so I wrote back:
Let's pretend that the speed of light is 60 mph. ( Just to make the math easier ) And the box is 60 miles high. A flash bulb is at the top and you are at the bottom. The bulb flashes. Now the light is traveling toward you at 60 mph. It will take 1 hour for the light to reach you. Now reverse positions. It will still take 1 hour to reach you. Even allowing the gravity, and assuming it's an Earthly strength gravity to have some affect would only be a fraction of a second at best. But just to be generous, I'll give it a minute. So, with the light coming down and gravity helping, it only takes 59 minutes to reach you. Conversly, it will take 61 minutes going the other way. But, no matter how many times you measure it, the results will be the same. And that's the key. Now pretend the box is moving at 10 miles per hour. With the light at the top and you at the bottom. When the bulb goes off it is coming at you at 60 mph. But you are going toward it at 10 mph. Now, as I remember basic high school algebra. The combined speed is 70 mph, going 60 miles will take approximately 51 minutes and 42 seconds. Switch positions and you now have a combined speed of 50 mph going 60 miles whic will take 72 minutes. Or think of it this way. With you at the top of the 10 mph box when the bulb goes off it will take 1 hour to get to where you were when it went off. But in the hour it took the light to get there you have moved 10 miles further.( You're going 10 mph, remember? ) So, at 1 mile per minute, it will take another 10 minutes for the light to get to that point, But in those 10 minutes you have moved some more, so that it evetually takes 12 minutes longer in total for the light to finally reach you. But, you are in a constantly accelerating situation. When you make another measurement. Now you are going 20 mph. With you at the bottom now it only takes 45 minutes for the light to reach you, but with you at the top, it takes an hour and a half, or 90 minutes. But you are still accelerating so the next time you measure, the box is going 30 mph. This time, it takes 40 minutes with you at the bottom and a whopping 2 hours with you at the top
To this I was still told that time would change due to my speed and that the measurements would still be equall to each other. To which I replied :
Ok, so let me understand this. With no motion it will take 60 minutes for the light to travel no matter which way I test it. I agree with that. Now, in motion, you're saying that when I test the light at the top of the box, time for me is sped up, so that at 10 mph it still takes 60 minutes instead of 51 minutes and 41 seconds. Conversely, testing the other way, time has slowed down so that instead of taking 72 minutes, it still takes 60 minutes for the light to reach me. At 30 mph time has sped up more so that instead of taking only 40 minutes, it still takes 60. And conversely, instead of taking 2 hours, time has slowed down so that it only has taken 60 minutes. So, if the box was 120 miles long and I was in the middle, with bulbs flashing at both ends, going 30 mph, time would simutaneously be speeding up to make up the 20 minute difference one way while slowing down 60 minutes the other way. If I had atomic clocks in all three places, how would the clock in the middle handle going faster by 20 minutes and slower by 60 minutes at the same time? Also keep in mind that the faster you accelerate, the greater the difference  10mph 51:42 & 72, 20mph 45 & 90, 30mph 40 & 120. Also as you were saying, the light would be blue shifted, would the light also be blue shifted motionless? If not, then isn't that all the proof you need to tell whether or not you are in a gravity enviroment or being accelerated? That was the original question.
So, even in a small box, with a light bulb at the top and a devise to measure it at the bottom, would there be a blue ( or red ) shifting of light in gravity? Would there be more of a shift when moving? And wouldn't there be a constantly changing, for the greater, shift when accelerating, and wouldn't this be all the proof you would need to tell you whether you were being held down by gravity or by acceleration??
