# How did Niels Bohr obtain ΔT •ΔE > h?

1. Sep 10, 2011

### Bomicro

I mean when I deduct the Einstein’s box Bohr designed , I can not obtain the ΔT •ΔE > h like Bohr.

1) After balancing, the position of the spring-balance in weighing the box at the time 0 (T0) is Q0, and the weight of the box is M0. Because the experiment did not restrict the measuring accuracy of spring-balance position, so we suggested ΔQ≈0.

2) After rebalancing and the position of the spring-balance localized at Q2, we open the launch window at the time 1 (T1), and close it at he time 2 (T2). The total time (T) for photon to launch is equal to T2-T1; the distance the box moves in the direction of gravity is q; based on the general theory of relativity, the error of T2 we measured and the T (= T2-T1) we calculated is ΔT, and ΔT/ T = (1/c2) • g•Δq. Please pay attention, q≠ΔQ here.

3) The position of spring-balance in the second weighing of the box at time 3 (T3) is Q1, and the weight of the box is M1, the reduction weight of the box measured in the experiment, m, is equal to M0-M1.

4) At time 4 (T4), after rebalancing, the position of the spring-balance is Q2, and the actual decrease weight of the box M is equal to M1-M2.

The experiment can not proved that T3-T3﹥T4 T2, which means that the second reading Q is performed after photon emission and spring-balance rebalancing. Thus we can not concluded from the experiment that Q0-Q1=Q0-Q2, that is ΔM=M-m，ΔE=ΔMc2.

So how can Bohr calculate to obtain ΔT •ΔE > h?

2. Sep 11, 2011

### sweet springs

Hi, Bomicro.

I have drawn the old book of mine from my bookshelf to review original Bohr's writings on the debate with Einstein. Two formula are essential.

Δp = h / Δq < T g Δm
where Δ express delta, Δp is width in measurement of vertical momentum of the box, h is Plack constant, Δq is width in measurement of measurement of vertical position of the box, T is time interval required to re-balance the box, g is acceleration by gravity of the Earth and Δm is change of weight or mass of the box by radiation.
This formula means that RHS T g　Δm, which is impulse caused by emission of radiation from the box, must be larger than LHS the uncertainty of momentum of the box so that the energy or mass change can be measured.

ΔT/T = 1/c^2 g Δq
where ΔT is uncertainty of clock time caused by difference of gravity effect due to uncertainty of vertical position Δq　during during re-balancing time interval T.

Combining two formulas we get ΔT > h/ c^2 Δm or　ΔT　ΔE > h.

I hope the above would be helpful to you in someway.

Regards.

Last edited: Sep 11, 2011
3. Sep 11, 2011

### Bomicro

Hi, sweet springs，
Thanks for the answer. However, I still have no idea about how Bohr perform the experiment to obtained this equation.
For example, what’s the reason that caused the vertical momentum of the box, that is p≠0 (if p=0, and will Δp =0?) Did it bring by the first reading of the position of the spring-balance in weighing the box at the time 0 (T0)? If the answer is yes, then we can read it after balancing, at this time, p is equal to 0, and Δp will equal to 0 too, and Δp = h / Δq < T g Δm will false. In addition, I think the experiment did not measure the vertical momentum of the box, so why Bohr introduce Δp = h / Δq?
If Δq (in ΔT/T = 1/c^2 g Δq) is the width in measurement of vertical position of the box (or uncertainty of vertical position), in the experiment, Δq will be a irrelevant constant, which is in contradiction with Δp = h / Δq < T g Δm.

Regards

4. Sep 11, 2011

### sweet springs

5. Sep 11, 2011

### Bomicro

Hi, I had read some details of the Einstein’s box below. There is only the apparatus and simple explanation. I want to know how to weighting the reduction of the box after photon emission using this apparatus by Bohr. For example, what time does it began to weight, how to weight, how many times he weight, and the measuring accuracy.

http://www.informationphilosopher.com/solutions/scientists/bohr/discussions_with_einstein.html

Regards

6. Sep 12, 2011

### sweet springs

Hi. Bomicro.

May I remind you that this is thought experiment which was thought out and investigated in debate between Bohr and Einstein, thus details of practical performance do not matter.　You should focus your question on theoretical and principal points if you have.

Regards

Last edited: Sep 12, 2011
7. Sep 12, 2011

### Bomicro

It is not a good suggestion.
The details of practical performance are important in my opinion.
Because Bohr revised the details of Einstein’s box Einstein proposed firstly, and he believed the box must be placed on the spring-balance in the gravitational force.

8. Sep 15, 2011

### Bomicro

Hi, can anyone tell me the derivation of the formula "Δp = h / Δq < T g Δm" in detail?
Thank you very much!