User talk:Sbyrnes321/Archives/2015

The page on Group Velocity

Hi,

I made the edit on the page on Group Velocity yesterday. . Thank you for cleaning up what I wrote! I do have one thing to say, which is that the modulus of the wave packet remaining constant doesn't really mean anything, does it? The actual wave is the real part of the exponential, and at a given space time point, the vibration of the system has a value which is somewhere intermediate between that on the wave packet envelope, because of the vibration within it. That vibration is given by the vibration moving at the phase velocity within the wave packet, in the first order approximation. Thanks,

Aritrop (talk) 18:39, 18 February 2015 (UTC)

Oh, you're right. It's obvious to me how to interpret the absolute value, but it would not be obvious to readers. I just edited to rephrase. Is it better now? I'm sorry that I reverted that aspect of your edit, I didn't realize what the problem was. :-D --Steve (talk) 18:58, 18 February 2015 (UTC)

Hi,

Now it seems exactly how I had wanted to put it. You wrote it much better than how I tried conveying the same thing. Thanks a lot!

And how would you interpret the absolute value?

The way you put it now just seems the easiest way to understand group velocity, to me.

Aritrop (talk) 19:25, 18 February 2015 (UTC)

Thank you!!

Normally when you have waves represented as complex numbers, the absolute value squared of the wave is related to its power. (That is a bit vague; the details depend on the type of wave I think.) Also, I was just imagining File:Wave_packet.svg with the absolute value being "obviously" (in my head) equal to the envelope. :-P --Steve (talk) 19:49, 18 February 2015 (UTC)

Hi Steve,

So you meant the energy travels at the group velocity and so the power of the wave is constant in time? I don't really recall how the power propagates for a general system, but I'm sure what you said makes sense, and it can be shown that the energy is transmitted at the group velocity, assuming of course that there is no distortion. Anyway, i feel it is best the way it's written now, for the understanding of how the group velocity emerges in conjunction with the phase velocity.

Aritrop (talk) 20:03, 18 February 2015 (UTC)

For example, in a wave on a string / spring, there is potential energy and kinetic energy, and energy converts back and forth between them as the wave oscillates. So the wave "passes through zero", but the energy is still there. You don't need to do a time-average in that example.

Energy usually travels at the group velocity, but not always ... after all, there are examples where group velocity is faster than the speed of light :-P --Steve (talk) 20:19, 18 February 2015 (UTC)

Hi,

Sorry I made an edit just now in the previous comment. I think it is an interesting exercise to check that the power actually gets transmitted at the group velocity for normal systems, and I have not done that exercise yet. Aritrop (talk) 20:22, 18 February 2015 (UTC)

If (1) the energy is around the location where the wavepacket is, (2) The wavepacket moves at the group velocity, then therefore (3) The energy must travel at the group velocity.

I think the weird examples that I just mentioned where group velocity is faster than light involve very lossy waves, so the wave is rapidly shrinking everywhere and it's hard to guess how the energy is flowing. --Steve (talk) 20:38, 18 February 2015 (UTC)

Thanks for letting me know. Does it seem like I exhibit nascent traits of a quack? Aritrop (talk) 00:47, 21 February 2015 (UTC)

I don't know what you mean by "quack". I think the group velocity article has definitely improved as a result of your efforts, so thanks again for that. --Steve (talk) 01:45, 21 February 2015 (UTC)

Well, I was looking through the criteria that Warren Siegel gives for identifying quacks, and I was curious if the grandiose way in which I made my first edit did portray some of those characteristics. I'm assuming you're fairly familiar with the conspiracy theory mongering paranoid delusional section of mankind that says and does crazy things. If this sounds crazy and irritating, don't bother to reply, because it's probably all that. Aritrop (talk) 03:22, 21 February 2015 (UTC)

Don't worry, see WP:BOLD. --Steve (talk) 15:59, 21 February 2015 (UTC)

total energy of the universe

That's rigth [1], "According to present understanding" is implicit in every statement of every science article, but I still disagree with the example. I have many friends who are professional physics, and cosmology, to most of them (I guess all!), is just mystics. Every statement of every science article can be (at least in principle) verified by anyone, but we do not even know how to compute exactly the total energy of the universe, perhaps we do not even know the exact meaning of that expression. So why do not say something like "Conservation of energy in the Milky Way is conserved, but this statement does not immediately rule out the possibility that energy could disappear from the Sun while simultaneously appearing in another distant star"? Of course it is not completely clear how to evaluate exactly the total energy of the Milky Way, but the statement is not that problematic. By the way, I do not know whether there is a continuity equation in quantum electrodynamics; entanglement and Einstein-Podolski-Rose paradox surely create problems - maybe they can be solved some way or another, I do not know... I feel that the right idea is that quantities are conserved under their respective appropriate conditions. Everything works just only under appropriate conditions. Cheers. 78.15.165.142 (talk) 01:15, 1 August 2015 (UTC)

OK, I think I see what you mean. I just changed the example to within Earth, and avoided the phrase "total energy of the universe" - [2] - do you think it's OK now? --Steve (talk) 12:25, 1 August 2015 (UTC)

Yes, I think it is much clearer now, thank you!78.15.165.142 (talk) 13:00, 1 August 2015 (UTC)