A Gravitational Redshift in Newtonian Equivalence Principle?

[FallenApple]

So I was reading that the equivalence principle of Newton doesn't work because of a thought experiment. They said that an experimenter shoots bullets( 1 per second) from the bottom of the elevator to the top. This happens in outerspace where the elevator moves up with accleration g. And this happens on Earth as well except there the elevator is stationary realtive to the earth.

They said that the in the upwards acclerating case, Newtons laws show that the bullets will not strike every second whereas on Earth it will. That there is a red shift in the frequency that the bullets hits the ceiling in the accelerating elevator.

This doesn't make sense to me. I know that in the accelerating elevator, the top will accelerate away from the constant speed bullets that try to catch up to it. But the same thing happens on earth. It's just that the bullets deccellerate instead of the ceiling moving away. Mathematically both are equivalent. So I'm not sure where the difference comes from.

We can also infer from Newtonian theory that if an elevator car is stationary on the Earth’s surface, each bullet will take an equal amount of time to travel from the bottom to the top of the car, so again the frequency of arrival at the top will equal the frequency of firing at the bottom. In this case the bullets will be spatially closer together when they reach the top, and moving more slowly, but the frequency will be unchanged. Thus Newton’s theory does not predict any gravitational “redshift” for ballistic particles, whether the car is floating freely in empty space, in freefall near a gravitating body, or stationary near a gravitating body. (For a detailed proof of this, see below.)

Then it says

However, if an elevator car in empty space, far from any gravitating body, is subjected to upward acceleration, equal to the acceleration of gravity on the earth’s surface, it’s easy to see that each successive bullet must travel a greater distance, and Newton’s theory of mechanics predicts a redshift in the frequency of arrival of the bullets at the top of the car. Since Newton’s theory predicts no redshift for the frequency of bullets fired from the bottom to the top of a car that is stationary in a gravitational field, we see that Newton’s theory does not satisfy EEP, even though it does satisfy GEP and NEP.

I don't get how it is "easy to see"

 

[Ibix]

Where did you read this? It's always helpful to provide a reference rather than a quote that might be out of context.

That said, on the basis of what's written, I agree with you. If the gun fires one round per second but the impacts come at a lower rate then we must be building up an increasing number of bullets in flight. This is nonsense, and easy to prove wrong with high school kinematics.

The red shift in an accelerating rocket in relativity comes from clock synchronisation issues which you don't get in Newtonian physics.

 

[stevendaryl]

I found the original essay here: http://www.mathpages.com/home/kmath722/kmath722.htm

It seems to me that the author is making a very elementary mistake. He says that in the case of an elevator accelerating upward (in Newtonian physics), bullets fired from the bottom toward the top will arrive later and later, since each bullet has farther to travel. It's true that each bullet has farther to travel, but it is also true that each bullet travels faster than the last, because the gun is accelerating upward, also, and the speed of a bullet is relative to the gun.

 

[Ibix]

Thanks, Steven. I think I need to read that article carefully. It clearly makes the elementary mistake you describe but, at least at first glance, I agree with its claim that Newtonian gravity does not imply a redshift. Despite that it claims to be opposed in that by Schutz.