The speed of light and the uncertainty principle

In summary, the Heisenberg uncertainty principle states that there is a fundamental limit to how precisely we can measure certain pairs of physical properties, such as energy and time. This is represented by the inequality h-bar/2 <= dE * dt. The principle also applies to light, but its energy is dependent on its frequency rather than its velocity. This has been discussed in previous threads and can be further explained by the relation between time and energy defined as \Delta t = \Delta A/(|d\langle A\rangle/dt|\Delta E) \ge \hbar/2.
  • #1
JoAuSc
198
1
The Heisenberg uncertainty principle says that

h-bar/2 <= dE * dt.

Let's say we have this device that emitted very low energy radio waves. Does that mean there'd be a significant probability of these photons traveling faster than light?
 
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  • #3
JoAuSc said:
The Heisenberg uncertainty principle says that

h-bar/2 <= dE * dt.

It's more subtle than that. We can show from general principles that

[tex]\frac{\Delta A}{|d\langle A\rangle/dt|}\Delta E \ge \hbar/2[/tex]

If we now define the bit on the left as [itex]\Delta t,[/itex] we get the oft-quoted uncertainty relation between time and energy.

The justification for making that identification is that it's the average time taken for the expectation of the operator A to change by its standard deviation, so it's roughly the time scale to measure a change in A.
 

1. What is the speed of light?

The speed of light is a fundamental physical constant, denoted by the symbol c, and is defined as the speed at which electromagnetic radiation travels in a vacuum. Its value is approximately 299,792,458 meters per second.

2. Why is the speed of light important?

The speed of light is important because it is the fastest speed at which all matter and energy in the universe can travel. It also plays a crucial role in many areas of science, including relativity, quantum mechanics, and cosmology.

3. What is the uncertainty principle?

The uncertainty principle, also known as Heisenberg's uncertainty principle, is a fundamental principle in quantum mechanics that states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

4. How does the uncertainty principle relate to the speed of light?

The uncertainty principle is closely related to the speed of light because it places a limit on the precision with which we can measure both the position and momentum of a particle. This limit is based on the fact that the speed of light is the maximum speed at which information can travel in the universe.

5. Can anything travel faster than the speed of light?

According to the theory of relativity, nothing can travel faster than the speed of light. This is because as an object approaches the speed of light, its mass and energy increase infinitely, making it impossible for anything with mass to reach or exceed the speed of light.

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