Uncertainty and the Speed of Light

In summary: Sagan once famously said, "We are all star-stuff." Indeed, the universe is full of things that we can only describe in terms of energy and momentum. In this summary, we'll be discussing the uncertainty principle, which is a fundamental principle in quantum mechanics that states that the momentum and energy of particles cannot be known with certainty. This principle is often used to explain the weird behavior of particles, like photons, on a macroscopic level. However, photons do not always behave according to the uncertainty principle--for example, photons can have a certain momentum, but their energy is also uncertain. This uncertainty in energy and momentum becomes the same thing, on a small scale, as the uncertainty in momentum and energy.
  • #1
εllipse
197
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Does the uncertainty principle apply to the speed of light? Do photons merely average the speed of light on large scales, but fluctuate on small scales? Or if you know the exact speed of a photon, does it mean that you can't ever know its position?

It seems to me that if a photon did, for an instant, travel at slower than the speed of light, then it would need a mass, but then again I guess there would also be uncertainty in the mass of a photon within a certain time range? Could a photon, for an instant, travel faster than light? Would it then have negative mass?
 
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  • #2
in QM, speed has nothing to do with momentum. [tex]\Delta{\rho}\Delta{x}\geq\frac{\hbar}{2}[/tex] says nothing about speed
 
  • #3
Doh! Ok gotcha, so since [tex]\rho=\frac{E}{c}[/tex] then it's merely uncertainty in the energy of the photon that causes the uncertainty in the momentum? That's pretty cool I guess, since uncertainty in energy and momentum become the same thing with light.
 
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  • #4
i would have used [tex]\rho=\frac{\hbar}{\lambda}[/tex] to get the uncertainty to be one half the wavelength of the particle in question.
 
  • #5


εllipse said:
Does the uncertainty principle apply to the speed of light?

Good question--I'll toss out my understanding of the answer, and hopefully someone can correct me if I'm wrong!
:smile:

The momentum-position uncertainty principle doesn't affect the speed of light since the momentum of light is independent of the speed. [tex]p = \frac{h}{\lambda}[/tex].

I guess the next natural question is then why is there no uncertainty principle for the speed of light? This, I believe, is because photons are massless (as you said). Thus, they travel on null trajectories in space-time. I suppose one could try to phrase this quantum mechanically, and ask why every observable eigenstate is also an eigenstate of the [observable] velocity of light, with eigenvalue [tex]c[/tex]. I'm not sure if this is a well posed question nor how to answer it.

Perhaps it might also be helpful to think about this from a field theory perspective. Observable particles/fields are always on-shell, that is to say that they satisfy the energy-momentum relation [tex]p^2 = m^2[/tex]. However, "internal" processes in a Feynman diagram which are *not* observed do not have to satisfy this condition. When I was introduced to Feynman diagrams before taking QFT, this was explained roughly via some energy-time Heisenberg relation; we can violate energy conservation, but only for a short time (and a little longer if we violate it a little less). In some sense perhaps we could explain that internal photons that needn't be on-shell can have a different "speed" (perhaps more transparent if we interpret the Feynman diagram in position space and we can note that positions off-shell are giving nontrivial contributions to the integral) from [tex]c[/tex].

I hope that was somewhat helpful--mamybe someone can clear up my own foggy ideas and misconceptions? :blushing:
 
  • #6
In quantum field theory, the speed at which photons travel (which is what I guess you mean by "speed of light"), is subject to variation, at least for virtual photons (which is what the context of your question imlies). Despite this, there is no violation of causality, as is discussed in pretty much every QFT textbook.

Here's a link to an explanation:
http://encyclopedia.laborlawtalk.com/propagator [Broken]

Carl
 
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1. How is the speed of light related to uncertainty?

The speed of light is a fundamental constant in the universe and is considered to be the maximum speed at which any object or information can travel. According to the Heisenberg uncertainty principle, there is a fundamental limit to how precisely we can measure both the position and momentum of a particle. This means that the more accurately we measure the position of a particle, the less accurately we can measure its momentum, and vice versa. Since the speed of light is related to the momentum of a photon, this uncertainty in measurement can affect the speed of light.

2. How is uncertainty calculated in the speed of light?

Uncertainty in the speed of light can be calculated using the formula Δc = (1/c) * Δv, where Δc is the uncertainty in the speed of light, c is the speed of light, and Δv is the uncertainty in the velocity of the particle. This formula takes into account the Heisenberg uncertainty principle and shows that the uncertainty in the speed of light is inversely proportional to the speed of light itself.

3. Does uncertainty in the speed of light affect our measurements?

Yes, uncertainty in the speed of light can affect our measurements. This is because the speed of light is used as the basis for many measurements in physics and other fields. If there is uncertainty in the speed of light, it can lead to errors in our measurements and calculations. Therefore, it is important to consider and account for this uncertainty in any experiments or studies involving the speed of light.

4. Can we ever have a completely precise measurement of the speed of light?

No, due to the Heisenberg uncertainty principle, it is impossible to have a completely precise measurement of the speed of light. This is because as we try to measure the speed of light more accurately, the uncertainty in our measurement of its momentum increases. Therefore, there will always be some level of uncertainty in our measurement of the speed of light.

5. How does the uncertainty principle affect our understanding of the speed of light?

The uncertainty principle challenges our traditional understanding of the speed of light as a constant and unchanging value. It shows that there is inherent uncertainty in our measurements and understanding of the speed of light due to the fundamental nature of particles and their behavior. It also highlights the interconnectedness of different physical quantities and the limitations of our ability to measure them precisely.

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