Harvard, Jefferson Tower

Photons were moving in a tower 74’ high.• If quantum was emitted from

the top, blue shift was observed on the bottom • If quantum was emitted from

bottom, on a top a red shift was observed

The basis elementsThe carefully prepared source and absorber of photons (-rays with energy 14.4keV) were nuclei of isotope 57Fe.57 57* 57Co Fe Fe

318

15

14.4 103.48 10 [ ]

4.136 10

EHz

h

What are we waiting to observe for?We expect the ray detector at the top of the tower to measure a lower frequency and vice versa.

Let’s estimate expectation value for frequency shift!

The magnitude of the expected shift can be obtained from the conservation of energy and the relativistic mass-energy equivalence.

2

Em

c

2

EE mg h g h

c

Effect estimation

2

1128

14.4[ ] 9.8[ / sec ] 22.5[ ]3.53 10 [ ]

2.998 10 [ / sec]

keV m mE eV

m

It seems plausible to assume that for shift detection, E should have the same order of magnitude as the natural absorption line width .

This accuracy could be achieved owing to the Mössbauer effect, due to which photons lines are extremely narrow…

Nevertheless, the absorption line is not narrow enough for direct measurement of red shift effect.

152.46 10E

E

57810 [ ]

FeeV

Pound & Rebka used a known experimental method to solve this problem…

For 57Fe we have a line width at half-height point :

Effect estimation

Resolution improving:

technique

• The modulation technique is based on the Doppler effect• Essential element of this technique is a

mechanical motion with precisely controlled velocity

Combining data from two periods having Doppler shift of equal magnitude, but opposite sign, allowed measurement of both sensitivity and relative frequency shift

Resolution improving :

technique (cont.)

2 2

0

1

1g

0 0

1 1

2 2

Г

4

0

1.69 10sec

mV c

The absorber power spectrum line had a Lorenzian shape:

Width at half-height point:

Resolution improving:

the speed of modulation estimation

Substitution of the numbers gives an oscillating source motion speed of:

Furthermore, the mentioned modulation technique allowed Pound & Rebka to observe the hyperfine structure of 57Fe

Resolution improving:

error estimation

The gravitational shift could then in principle be deduced from the difference in the two counting rates.

It is advantageous however to provide an additional superposed constant velocity motion chosen so as to just compensate for the red shift, thus allowing us to make a null measurement.

The required velocity was:

Null measurement

60.735 10secconst

gh mV

c

The second order Doppler shift resulting from lattice vibrations required that the temperature difference between the source and absorber be controlled and monitored.

Temperature error estimation

2

22

2

ˆ1 ˆ

1 12

1source abs abs

V rV r Vc

c cVc

A difference of 0.6 0C would produce a shift as large as the whole effect observed.

2

22

V

c

Temperature error estimation

The difference of the shift seen with rays rising and that with rays falling should be the result of gravity.

The average for the two directions of travel measured an effective shift, resulting due to other reason, which is about four times larger than the shift caused by gravity!

What is the cause of mean shift?

By additional experiment Pound and Rebka confirmed their assumption that this shift was an inherent property of the particular combination of source and absorber. They measured the inherent shift for each absorber unit when it was six inches from source and explained it by different Debye temperatures.

2

22

V

c

2

22

11

D D

A TV

A block diagram of the experimental arrangement

15experim

15

theor

5.13 101.05 0.10

4.92 10

Where the plus sign indicates that the frequency increases in falling

Acknowledgments:

Yulia Preezant is like to thank

Mr. Yevgeni Preezant (Technion) for his helpful advice and translation oral presentation in Hebrew.

References:

1. R.V.Pound and G.A.Rebka,Jr., Phys.Rev.Letters 4,337(1960)

2. Gunther Wertheim, Mössbauer Effect: principles and applications, Academic press, New York ,1964

3. R.L. Mössbauer, Nobel Lecture,December11,1961

4. R.V.Pound and G.A.Rebka,Jr., Phys.Rev.Letters 3,554 (1959)

5. R.V.Pound and G.A.Rebka,Jr., Phys.Rev.Letters 3,439 (1959)

6. L.B. Okun’, K.G. Selivanov, V.L. Telegdi, Usp.Fiz. Nauk 42,1045 (1999)