# How matter waves travel faster than light?

I read this in my physics textbook. It says that matter waves travel faster than light. Why is it so?

Also are matter waves G-Waves?

• @ShubhamWagh Based on the excerpt you posted, your book is very bad. Try buying one of the standard books used in an American physics class instead. Jan 1, 2017 at 9:09
• @knzhou Umm ok thanks BTW its given by our state board council in India, no wonders now! Jan 1, 2017 at 9:12
• @ShubhamWagh Yeah, I'm sorry. We get a lot of questions from Indians who use their state-approved books, and it's always a problem with the book, not the student. Jan 1, 2017 at 9:13
• @Qmechanic HSC textbook standard 12th Maharashtra page no 302 Jan 1, 2017 at 13:32
• Thumbs Up - Light is bent by Gravity, surely the medium light travels is the same Gravity propagates, viscosity of the medium may vary, but Light is subdued by Gravity we know to be true! Light Speed is a constant for Light, not for Gravity, Black holes absorb Light, a -Negative Mass where Light can not escape, a fundamental flaw, the postulate that is mostly true... most of the time, time is another problem in itself. May 14, 2018 at 21:16

I read this thing in my physics textbook.They said matter waves travel faster than light, why is it so?

Matter waves is a confusing terminology coming from the de Broglie quantum mechanical description of particles, which is what matter is at the quantum mechanical level.

Here lamda is the wavelength of the probability distribution that gives the probable location of the particle in space , when it is measured. It is not the particle that is waving, i.e. changing sinusoidaly in space and time, but the probability of finding it at that (x,y,z,t).

Special relativity imposes the limit of the velocity of light on any motion of particles, in all frameworks, classical and quantum mechanical.

Thus there is no way the statement as you have written is correct, unless there is some reference to the phase velocity which can be different for light (classical framework) in a medium. For a particle it would again refer to the probability distribution and will be a non measurable quantity, just a mathematical description.

Also matter waves Are G-Waves?

No , they are probability waves of particles in the quantum mechanical framework, the underlying framework of nature. G waves are gravitational waves. There also exist gravity waves, but that is another story.

Just saw your edit. The statement "matter waves travel faster than light" as written in the book is wrong. Period.

• Well, the statement of the de Broglie wavelength in the book is correct in the low-velocity regime. Since this book looks to be covering non-relativsitic QM only, I don't see a problem with this approximation. So the statement is not "wrong. Period"; rather, it's an approximation that is widely used in introductory texts. Jan 1, 2017 at 5:59
• @probably_someone I am talking about the "faster than light" which was the question. edited in the wrong statement Jan 1, 2017 at 6:57
• @probably_someone (which is also a wrong statement, cool but pure nonsense), Anna is totally right. Lambda = h/p is right, and p can be infinite (i.e., has no limit in physics), but p is not mv in special relativity, and v cannot be faster than c. No exceptions. As Anna said, the book is wrong. Special relativity and QM live together quite consistently. Saying that something can go faster than light is not excusable by saying it's an approximation. You'd say probably but it's more like certainly. And the answer by JMLCarter is also wrong, certainly Jan 1, 2017 at 8:18
• Not related to this question but for my own info: what about galaxies at the out edges of the observable universe? It was stated on this site that they were receding from us at well over the speed of light. Just curious how this is viewed. Jul 3, 2017 at 17:13
• What happens when there are answers totally opposite from each other like here? I often review answers to better understand certain issues. This is one such case. These competing answers only serve to confuse me even more! lol.. And I was pretty confused to begin with.. Jul 3, 2017 at 17:48

In the original non-relativistic formulation of wave mechanics by Schrödinger, his waves did indeed travel faster than light, and in fact their velocity was infinite. The propagator which showed the influence of one space time point on another clearly allowed superliminal influences.

His theory had other problems as well: his waves were unstable under the motion of the observer. Even at a slow walk, a zero-momentum wave (flat) suddenly morphed into a real wave. These problems were probably among the reasons he initially decided not to publish the theory.

the book presents de broglie λ=h/p in classical form. in classical mechanics there is no limit for speed. once you insert the relativistic energy: E=mc^2+(p^2 c^2)^2 you see that matter waves can not travel faster than light.

No massive particle known exceeds the speed of light. Matter waves (water waves, sound waves) and gravity waves are different, as are Electromagnetic waves.

Oh, de Broglie, this will give the wavelength of light (which has no mass keeping the problem easier). For massive particles we are getting into quantum mechanics (as stated in book) in which every particle is described by a wave function. Now it's true that there has indeed been evidence of "quantum teleportation" that exceeds the speed of light. I didn't come across it described in this way before. The mass of the particle itself is not in evidence travelling at the speed of light, it is wave-function collapse - a multi-state distributed wave-particle somehow resolving to a single state local interaction instantaineously when observed. Problem is it could be observed anywhere within it's distribution - (QM is weird, I can't hope to cover it here). Quantum-relativity hasn't been resolved as far as I'm aware, so work is ongoing. (I'm wondering what comes after the word "actually", tbh, we should probably not take the para out of context - perhaps the author is just trying to bring in QM step by step.) I might call it a wave-particle probably not a matter wave.

• " Quantum-relativity hasn't been resolved ", what are you talking about? Special relativity is the mainstream quantum physics, within the mathematics of quantum mechanics. And de Broglie is about particles behaving as probability waves, not light. Jan 1, 2017 at 7:02
• Quantum gravity Jan 1, 2017 at 16:01
• I think the satement that "matter waves travel faster than light" is misleading at best. Matter = some energy. And, as you note - there remains the question of gravity. Jan 1, 2017 at 16:09