Photon that "fits" into its schwarzschild radius

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Discussion Overview

The discussion revolves around the relationship between the wavelength of photons and their corresponding Schwarzschild radius, particularly when considering high-energy photons. Participants explore the implications of this relationship and question the appropriateness of applying the Schwarzschild solution to light.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant proposes that as photon wavelengths decrease, their energy increases, leading to a corresponding increase in Schwarzschild radius, and questions the significance of this relationship.
  • Another participant challenges the notion that photons have a size defined by their wavelength, emphasizing that photons are massless and that their properties can vary depending on the frame of reference.
  • A third participant questions the appropriateness of using the Schwarzschild solution for light, suggesting that the conditions assumed in that solution may not apply to photons.
  • Further, a participant argues that classifying a high-energy photon as a black hole is meaningless without another object to interact with, introducing the idea of a photon-electron system potentially forming a black hole.
  • The original poster clarifies that they did not intend to imply that photons have a size or that the Schwarzschild solution is appropriate for light, but rather were curious about the simplicity of the formulas derived.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the relationship between photon wavelength and Schwarzschild radius, with no consensus reached on the appropriateness of applying the Schwarzschild solution to photons or the significance of the derived formulas.

Contextual Notes

There are unresolved questions regarding the definitions of size in relation to massless particles, the applicability of the Schwarzschild solution to light, and the conditions under which photons might interact with other particles to form a black hole.

birulami
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Photons with smaller and smaller wave lengths have a higher and higher energy and these engeries have an increasing Schwarzschild radius [itex]r_s[/itex]. Consequently i can ask when half the wave length [itex]\lambda/2[/itex] is equal to [itex]r_s[/itex], such that one wave length fits into the sphere of the Schwarzschild radius.

I did the calculation and came out with [tex]\lambda/2 = r_s = \sqrt{Gh/c^3} =\sqrt{2\pi}l_p[/tex] where [itex]l_p[/itex] is the Planck length. Incidently the mass of this photon is [itex]\sqrt{2\pi}\,m_p[/itex] with [itex]m_p[/itex] being the Planck mass.

Now I wonder. Should I be at least a bit surprised about such extremely simple formulas or not. To put another way, is this as trivial as transforming [itex]ab=1[/itex] into [itex]a=1/b[/itex], or is there at least one physical statement needed between the Schwarzschild radius and this specific photon wave length? (Hmm, I hope someone can understand what I mean here. :confused:)
 
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Photons are massless and their size is not a very well defined concept - and it is definitely not equal to the wavelength. Furthermore your statement is frame dependent as I can find an inertial frame of reference where your photon has a wavelength in the radio wave band.
 
Before getting all wrapped up with photons and therefore quantum mechanics, why do you think the Swarzchild solution (boundary conditions being static and spherical) is an appropriate one for light?
 
Last edited:
Orodruin said:
Photons are massless and their size is not a very well defined concept - and it is definitely not equal to the wavelength. Furthermore your statement is frame dependent as I can find an inertial frame of reference where your photon has a wavelength in the radio wave band.

Since a photon has no inertial reference frame and is only a single object, it makes no sense to say that an extremely high energy photon is or is not a black hole. Making that classification is meaningless in the absence of some other object with which to interact. Now add an electron to the system.
It is certainly possible that the photon + electron system will have enough energy in a small enough space to form a black hole. This scenario would have meaningful and observable consequences since neither particle would continue to exist after the intersection.
 
Thanks for your answers, except I don't get it where you all are heading. I did not mention the term "black hole", I did not say that the photon has a certain size and I did not pronounce any appropriateness of the Schwarzschild solution for light. All i did was toy with some physical formulas out of curiosity and got an, at least for me, surprisingly simple result. My question is basically whether this is at least mildly surprising or completely trivial.
 

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