# Phase velocity faster than light?

• shanepitts
In summary, phase velocity is the theoretical speed at which a single-frequency component of an electromagnetic wave would travel in a medium, and can exceed the speed of light in some materials. However, this does not contradict the special theory of relativity as it does not actually convey any information. It is important to focus on the correct theory of quantum mechanics rather than getting too caught up in historical theories.
shanepitts
I am currently taking an undergrads course in atomic physics, and I have just grazed the concepts of matter wave functions, group waves, group velocity, and phase velocity. For the latter, it has been stated that phase velocity can exceed the speed of light. I don't fathom this. Could anyone please help me with this concept?

Does this help?

Per wiki: http://en.wikipedia.org/wiki/Faster-than-light#Phase_velocities_above_c

The phase velocity of an electromagnetic wave, when traveling through a medium, can routinely exceed c, the vacuum velocity of light. For example, this occurs in most glasses at X-ray frequencies.[11] However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information.[12] Thus a phase velocity above c does not imply the propagation of signals with a velocity above c.[13]

Thanks

shanepitts said:
I am currently taking an undergrads course in atomic physics, and I have just grazed the concepts of matter wave functions, group waves, group velocity, and phase velocity. For the latter, it has been stated that phase velocity can exceed the speed of light. I don't fathom this. Could anyone please help me with this concept?

Its purely a mathematical artefact - nothing is really traveling FTL.

Also matter waves was simply an interim theory on the way to full blown Quantum Mechanics that appeared when Dirac published his transformation theory.

Don't spend too long on what is just really of historical interest. Try, as soon as possible, to come to grips with the correct theory. So you understand its REAL basis check out:
http://www.scottaaronson.com/democritus/lec9.html

Your course may not get to this for a while, or indeed at all, depending on its depth, but just keep in the back of your mind this is what QM is REALLY about - the rest is basically historical background.

Thanks
Bill

Last edited:
1oldman2

I can understand your confusion about the concept of phase velocity exceeding the speed of light. This idea goes against our understanding of the fundamental laws of physics, such as the theory of relativity which states that nothing can travel faster than the speed of light.

However, in the context of matter waves and quantum mechanics, the concept of phase velocity exceeding the speed of light is not violating any physical laws. This is because the phase velocity refers to the velocity at which the phase of a wave moves, while the speed of light refers to the velocity at which information can be transmitted.

In matter waves, the phase velocity can exceed the speed of light because it is not carrying any information, but rather represents the probability amplitude of the wave function. This means that even though the phase velocity may be faster than light, it does not violate the fundamental laws of physics.

It is important to note that this concept is still being studied and researched, and there is ongoing debate and discussion among scientists about the implications of phase velocity exceeding the speed of light. So while it may seem counterintuitive, it is a valid concept in the field of quantum mechanics.

I would recommend continuing to explore and learn about matter waves and their properties, and keeping an open mind to new and potentially groundbreaking discoveries in the field of atomic physics.

## 1. How is it possible for phase velocity to be faster than the speed of light?

The concept of phase velocity being faster than the speed of light is based on the properties of certain materials, known as metamaterials, which have unique electromagnetic properties that allow for this phenomenon to occur. These materials are engineered to have a negative refractive index, meaning that light travels through them in a way that is opposite to how it travels in normal materials.

## 2. Does this mean that information can be transmitted faster than the speed of light?

No, even though the phase velocity may be faster than the speed of light, the actual speed at which information can be transmitted is still limited by the speed of light. This is because the phase velocity only refers to the speed at which the overall shape of a wave propagates, not the speed at which individual particles or packets of information move.

## 3. What are some potential applications of this phenomenon?

One potential application of phase velocity being faster than light is in the development of new types of lenses and imaging devices. These materials can be used to create superlenses that are capable of resolving objects smaller than the wavelength of light. This could have applications in fields such as microscopy and medical imaging.

## 4. Are there any limitations to this phenomenon?

Yes, there are limitations to this phenomenon. One major limitation is that it only occurs at certain frequencies and angles, and is heavily dependent on the design and composition of the metamaterial. Additionally, these materials are currently only able to operate at very low temperatures, making their practical applications limited.

## 5. Is there still ongoing research and development in this area?

Yes, there is still ongoing research and development in this area. Scientists are constantly exploring new types of metamaterials and techniques to achieve phase velocities faster than light. There is also ongoing research into potential applications and ways to overcome the limitations of these materials.

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