limitation on the photons energy and wave length
TRANSCRIPT
Yoav Weinstein – [email protected] ; Eran Sinbar – [email protected]
Limitation on the Photons Energy
29 June 2015
Images from the Internet - http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/fraungeo.html#c2
Single slit diffraction pattern of light The narrower the slit, the wider the diffraction pattern
This single slit experiment is an optical way to prove the Heisenberg’s uncertainty principle The more you define the exact location of the photon by narrowing the slit ,the less defined is the momentum. This causes a wider diffraction pattern. If the slit is in the size of Planck’s length (ℎ∗=1.62 ∗ 10−35) and assuming that the wave length of the photon is much smaller Compared to Planck Length ( λ≪ ℎ∗) ,than there is practically no diffraction pattern . That means that both location and momentum are well defined within the Planck length. That is a violation of the Heisenberg’s uncertainty principle.
Since that is impossible, we can conclude that there is a limit to λ and a limit to the Photons energy.
𝐸 𝑃ℎ𝑜𝑡𝑜𝑛𝑠 𝑒𝑛𝑒𝑟𝑔𝑦 = ℎ ∗𝑐
λ , Where c is the speed of light and h is Planck constant.
We showed that 𝝀 can not be much smaller than Planck’s length in order not to violate Heisenberg’s uncertainty principle. Assuming that the 4D space time is quantized. • The quantum of space is in the size of Planck’s length (ℎ∗)in each of its 3 dimensions.
• The quantum of time is in the size of ℎ∗
c
Than 𝝀 is limited to its smallest size , 𝒉∗ (Planck’s length). 𝝀 = 𝒉∗
E (Photons energy) is limited to : ℎ[𝐽𝑜𝑢𝑙𝑒 ∗ 𝑠𝑒𝑐𝑜𝑛𝑑] ∗ 𝑐[𝑚𝑒𝑡𝑒𝑟
𝑠𝑒𝑐𝑜𝑛𝑑]/ℎ∗[meter] = 6.62 ∗ 10−34 ∗ 3 ∗ 108/(1.62*10−35)
E Photon [Joule] ≤ 𝟏𝟐𝟐. 𝟔 ∗ 𝟏𝟎𝟖 [Joule]
Summary
The shortest Photon wave length can not be much smaller than Planck’s length without violating Heisenberg’s uncertainty principle. The conclusion is that both Photons energy and wave length are limited by Planck’s length. Assuming a quantized space and time universe as detailed in the slides above , E Photon is limited to 122.6 ∗ 108 [Joule] If space-time are quantized than we assume that there are extra dimensions that divide space-time to these quantum 4D cells (the “grid” extra dimensions).
For more details regarding quantized space and time and the grid extra dimensions, Please review : http://www.slideshare.net/eransinbar1/heuristic-approach-for-quantized-space-time