# Deriving speed of light from QED

• robcon
In summary, the conversation discusses the relationship between quantum electrodynamics (QED), special relativity, and Maxwell's equations in determining the speed of light. It is stated that QED assigns a mass of zero to photons, and therefore, by assuming special relativity, it can be concluded that photons must travel at the speed of light in vacuum. This leads to a circular contradiction, as QED presupposes special relativity while also replacing Maxwell's equations. However, it is explained that QED is a quantum theory living in Minkowski space, making the speed of light constant. It is also mentioned that gauge symmetry is the essence of both QED and Maxwell's equations, and that photons do not interact with
robcon
Is it possible to derive the speed of light from quantum electrodynamics (like it can be done from Maxwell's equations) or is the fact that the speed of light in vacuum is constant and has a certain value an assumption in the theory?
My understanding is that QED assign a mass zero to photons and so, by assuming that special relativity describes space and time, photons must travel at the speed of light in vacuum.
Based on this understanding don't we run into a circular contradiction? Special relativity was inspired by the constant speed of light that is predicted from Maxwell's equations. QED presupposes that special relativity is true but, at the same time, it replaces Maxwell's equations, therefore pulling the ground off special relativity.

Well QED as you said supposes Special Relativity is true, or rather it is a quantum theory living in Minkowski space (the model of spacetime in special relativity), so the speed of light, or any massless particle, is automatically constant. That's it really, it doesn't matter that Einstein used Maxwell's equations to figure out Special Relativity.

QED is the quantized Maxwell theory. It's a specially relativistic field theory, so that c is postulated finite and how the quanta's momentum and energy are linked through c (the same c as in Maxwell's theory) can be proven.

bhobba
@DarMM - Isn't there a loss in explanation power, though? Maxwell's equation can determine the speed of light without assuming that special relativity holds. QED is an extension of Maxwell's equations but requires special relativity to make the same prediction. How can a more approximate theory make such an important deduction using fewer assumptions?
In addition, we also know that special relativity is an approximation of general relativity (GR) and that general relativity and quantum theories don't coexist well at the quantum level in their current formulations. This means that we can't really use GR to help QED derive the speed of light. Again, we have an important and correct deduction of a weaker theory that disappears in an extension of that theory.

Obviously you can since Maxwell's equations are the classical limit of QED.

In fact a mathematical analysis shows gauge symmetry is the real essence of both QED and Maxwell,s equations, and inevitability leads to EM waves traveling at the invariant speed that appears in SR.

It's simply that the speed is frame independent which immediately implies its the invariant speed of SR. That's the case in QED or classical EM.

In Maxwell's equations its wave solutions are frame independent. In QED I think its tied up with the propagator - its the propagator of a massless particle - but don't hold me to that because my understanding of QED is not as good as I would like. If its massless - it must travel at the speed of light.

There is something in the back of my mind that all gauge bosons are massless - hence, since the photon is a gauge boson, it must be massless. Gauge bosons however can gain mass by interaction with the Higgs field. So the rock bottom essence of why QED predicts the speed of light is photons do not interact with the Higgs.

Thanks
Bill

Last edited:
robcon said:
@DarMM - Isn't there a loss in explanation power, though? Maxwell's equation can determine the speed of light without assuming that special relativity holds. QED is an extension of Maxwell's equations but requires special relativity to make the same prediction. How can a more approximate theory make such an important deduction using fewer assumptions?
In addition, we also know that special relativity is an approximation of general relativity (GR) and that general relativity and quantum theories don't coexist well at the quantum level in their current formulations. This means that we can't really use GR to help QED derive the speed of light. Again, we have an important and correct deduction of a weaker theory that disappears in an extension of that theory.

I am not understanding your question very well. But...
Maxwell equation determines the speed of the electromagnetic wave [light]. The massless particles in SR or QED are not the electromagnetic waves, but the photons. The velocity eg in Maxwell's EM equations can change if you change matterial, the velocity of the photons however doesn't [it's always c because they are massless].
The "massless particles run at speed of light" statement of SR doesn't only refer to the photons, but any massless particle. So it's not that Maxwell equations contain any "large" information about this fact. I hope I made my point clear.

There is no reason to use GR in a QFT as long as the gravitational interactions can be neglected.

robcon said:
@DarMM - Isn't there a loss in explanation power, though? Maxwell's equation can determine the speed of light without assuming that special relativity holds.
Not really, if you have Maxwell's equations and still keep Galilean transformations, then the speed of light is not constant and varies between frames, even Maxwell's equations require Special Relativity for light to have a constant speed in all reference frames.

bhobba
DarMM said:
Not really, if you have Maxwell's equations and still keep Galilean transformations, then the speed of light is not constant and varies between frames, even Maxwell's equations require Special Relativity for light to have a constant speed in all reference frames.

Yep - true.

You have to invoke the POR for the speed of light to be the same in all frames.

Thanks
Bill

Thank you all

## 1. How is the speed of light derived from QED?

The speed of light can be derived from QED (Quantum Electrodynamics) by using the equation c = 1/√(ε0μ0), where c is the speed of light, ε0 is the permittivity of free space, and μ0 is the permeability of free space. This equation is derived from the fundamental principles of QED, which describe the behavior of light and its interactions with matter.

## 2. What is QED and how does it relate to the speed of light?

QED is a quantum field theory that describes the interaction between electrically charged particles and electromagnetic fields. It is used to explain the behavior of light and other electromagnetic radiation. QED is closely related to the speed of light because it is based on the fundamental principles of electromagnetism, which determine the speed of light in a vacuum.

## 3. Can the speed of light be derived from other theories besides QED?

Yes, the speed of light can also be derived from other theories such as special relativity and general relativity. However, QED is the most accurate and precise theory for explaining the behavior of light and its interactions with matter. Therefore, it is often used to derive the speed of light in scientific research and experiments.

## 4. How accurate is the speed of light derived from QED?

The speed of light derived from QED is extremely accurate and has been experimentally confirmed to be 299,792,458 meters per second. This value is considered to be one of the most accurately measured physical constants in the universe.

## 5. Why is it important to derive the speed of light from QED?

Deriving the speed of light from QED is important because it helps us understand the fundamental principles of electromagnetism and the behavior of light. It also allows us to make precise calculations and predictions in various fields of science, such as quantum physics and cosmology. Additionally, the speed of light is a crucial constant in many equations and theories, making its accurate derivation essential for further scientific advancements.

Replies
14
Views
3K
Replies
8
Views
2K
Replies
4
Views
1K
Replies
2
Views
1K
Replies
7
Views
2K
Replies
34
Views
2K
Replies
45
Views
4K
Replies
3
Views
1K
Replies
33
Views
3K
Replies
2
Views
1K