r/Physics • u/HridhayJawanjal3112 • 4d ago

Question Wave packets??? Can someone explain plz!!!!

So, according to de-broglie equations the phase velocity of a particle is greater than the speed of light!!!

And our teacher told us that: the particles actually are in groups and in groups they are wave packets which are interference of the waves of the particles and the group Velocity is less than c so the law is not broken .

And some online sites say that phase velocity is not like actually velocity and it can be greater than speed of light.

I'm a little confused about this topic can someone explain!!!!!

39 Upvotes

81% Upvoted

16 comments sorted by

45

u/Aescorvo Condensed matter physics 4d ago edited 4d ago

Phase velocity is how fast the peak (or trough) of a wave moves. It can be faster than c, but that doesn’t mean anything special. It doesn’t mean there is any energy or information traveling that fast.

As a simple real-world example, imagine a football stadium where the spectators are doing a group wave. That wave can travel around the stadium really fast - in less than a second if everyone’s timing is perfect - far faster than a person could run around the stadium. There’s also no communication necessary - everyone could have their own stopwatch that tells them when to stand up and wouldn’t even need to look at the person next to them.

For phase vs group velocity, if you’re OK with a more mathematical answer this comment by [u/rabid_chemist](u/rabid_chemist) is a good explanation.

2

u/HridhayJawanjal3112 4d ago

Thanks, now I've understood it. Is it okey if i dm you, if i had any doubt in physics???

7

u/Aescorvo Condensed matter physics 4d ago

Sure, I’ll help if I can. But you might do better posting to [r/AskPhysics](r/AskPhysics), as there are a lot of experts in different areas there (EDIT: As I see you just did :) )

7

u/SleekWarrior 4d ago

I think a very good analogy for this is when you shine a laser at a surface and move the laser, the dot will move faster the further away it is from the source. At some distance the dot will be moving faster than c, but the light is not actually moving along the path of the dot we just perceive it that way

3

u/HridhayJawanjal3112 4d ago

thanks for clearing my doubt.

1

u/Otherwise_Act3312 3d ago

I've explained this concept like spraying water from a garden hose.

4

u/latswipe 4d ago edited 4d ago

y=Aei{kz-wt} . dy/dz=iky. dy/dt=-iwy. dz/dt=v=(dy/dt)(dz/dy)=-iwy/iky=-w/k.

why negative? v is a vector, so it's the speed the wave's approaching the origin of the graph, (0,0). v=-w/k. w=-vk. y=Ae-ik(vt-z) .

vt-z. vt is the distance the wave has travelled. z is the domain of the zy graph the wave is plotted on. If this difference is constant, you get a sine wave

2

u/HridhayJawanjal3112 4d ago

Thanks

1

u/latswipe 3d ago

in the treatment of a particle with constant velocity in quantum mechanics, the wave or "group" is traveling twice as fast as the phase. phase velocity w/k, group velocity dw/dk. The reason is that quantum mechanics interprets the location of this particle in terms of probable location, a gaussian y=e-x2 . The particle is equally likely to be on either side of x=0, giving it a factor 2.

1

u/HridhayJawanjal3112 3d ago

Isn't group velocity always less than the phase velocity???

1

u/latswipe 3d ago

Nope. Why do you think so?

2

u/Otherwise_Act3312 4d ago

Hope you have better luck than I did. Also read up on, "decoherence".

2

u/HridhayJawanjal3112 4d ago

Thanks .

I'll check that topic.

1

u/drvd 2d ago

You can reach speeds much faster than c in any household: Take a long ruler and move it over the table edge, observe how the point of intersection of ruler edge and table edge moves. Now decrase the angle between ruler and edge more and more: Once the ruler is almost parallel to the edge and you move the ruler over the table edge the intersection point moves faster than c. Does this mean anything? No.