martillo

So returning to the initial discussion about the phase velocity of the "matter wave" of massive particles... I arrived to the two approaches that could give the phase velocity vp in terms of the linear velocity v of the particles: Relativistic approach: vp = c2/v Non-relativistic approach: vp = v/2 (vg = v) Independently of which one would be better in whatever case, if v is measurable then vp is measurable. The phase itself is not observable and not measurable but its velocity is measurable. The phase velocity is related to the energy and the momentum of the wave/particle: p = E/vp.

Wouldn't the image be a graphic of scanning electron tunneling microscopy on the molecules? Not a x-ray crystallography...

No, forget it, I'm not ready to discuss my hypothesis in the forum at the moment. I tried in the past to discuss for instance the equation of force F = dp/dt in the forum and gave me too much troubles, discussing with several ones at the same time, several days without sleeping appropriately... Do you remember? We discussed a lot in that thread: I'm not ready to have another discussion like that for now. May be in the future something could surge. I will take a look.

So you have been interested about some "offshoots"... May be someday you could be interested in taking a look at my rather radical alternative try... May be not. Too radical, forget it.

No, the text refers to a "light quanta". The text also talks about an associated mass: "...they must have an extremely small mass...". Here the parts of the text @studiot posted for you to check: The text talks about a model for a "light quanta" reconciling the Electromagnetic Wave Theory and Relativity Theory. I think as some mass was associated to the quanta, a velocity "slightly different from c" is needed because in the case of a c velocity the mass would be infinite according to Relativity. I think the small mass comes into place to give a physical reason for the "light quanta" to have momentum and explain the "radiation pressure" @studiot mentions. May be also because the equations E = hf, λ = h/mv and λf = c would give E = mc2 for a quanta (photon) with some mass. Interesting but wrong tentative for a photon with mass I think. For a photon with mass unavoidably Relativity Theory must be neglected...

Yes, that statement called my attention. Do you mean that De Broglie was considering a "light quanta" with a velocity "slightly different" from c? That is really astonishing for me. Let me say going through a very wrong way I think...

I don't understand what you are asking me to explain. Please just say it in a more specific way...

Right. I'm getting a little confused, give me some time...

Well, if you have that crazy theory accepted as a valid one by the mainstream you can make the claim, yes. Not sure about the frequency. Wouldn't it be deduced from the wavelength and the velocity?

Well, to measure and verify the wavelength of electrons you have the Davisson-Germer experiment...

Through the formulas we were discussing about! vp would be equal to c2/v or v/2 just depending on our approach. We just need to have the velocity v of the particle.

Ok, it is not directly observable but it is indirectly measurable. That is what I was thinking...

I did. I apologize. I was editing the post when you posted. So the phase velocity would be an observable afterall...

Seems right... So it would be observable afterall...

But the relativistic approach matches with the non-relativistic approach at very small velocities v << c. The problem in the discussion here in this thread is that the phase velocity of the De Broglie "matter wave" does not verify this. At very small velocities the relativistic and the non relativistic values for vp should be the same and is not the case.

No, λf = vg the group velocity not vp the phase velocity.

De Broglie formula is λ = h/p. According to both the Electromagnetic Theory of light and Relativity Theory photons do not have mass and so De Broglie theory would in principle not apply but they have moment p and so the equation λ = h/p would be valid for photons. With p = E/c you can derive λ = hc/E and with λf = c it can be derived E = hf. Also, for photons the phase and group velocities are vp = vg = c and there's no problem with them. This way De Broglie relation appear straightforward for photons. I agree that for massive particles the De Broglie relation becomes something much more complicated... In which way I would be misrepresenting what you said? At the end, the two different expressions for vp are compatible for you or not?

Yes the phase velocity is totally non observable, not directly nor indirectly by any related physical effect. There's no physical effect related to it. It can't be experimentally verified anyway. But being non observable is not a justification for the different incompatible values that different approaches give to it. If we find incompatible different values something is wrong somewhere. I would not know precisely what is wrong at this time. For @joigus the different values are not incompatible but for me they are so different as to be able to consider them theoretically incompatible: The relativistic approach: vp = c2/vg = c2/v The non relativistic approach: vp = vg/2 = v/2 Considering small velocities v << c for both, do you consider them compatible results?

You know, current theories are full of "non observable" things like this we are talking about in the "matter waves" and "undetectable" things like the "virtual particles" or the "dark matter". So "undetectable" that let me wonder if at the end they would actually exist at all. I'm looking for a theory without any of such kind of things. Something that would look hopeless for you, I know, but not for me. I'm considering some possibilities on some things but I can't discuss them in the forum because of the lack of some theoretical and experimental demonstrations at this time. They just look as possible for me now and I will continue working on them as I could. May be I could come here with something really demonstrable in the future, not sure, just may be... Meanwhile, is important for me to discuss some things in the forum and I appreciate your time dedicated in our discussions. Thanks a lot.

Well, your reasoning is a bit complicated to follow for me... You arrive to two expressions for the phase velocity and say one is the exact one while the other an approximation. The "exact" one: vp = c2/vg = c2/v The "approximated" one: vp = vg/2 = v/2 I can understand now how you justify the difference. I will only say that for me there is a too big difference. The same big difference as to consider E = mc2 + mv2/2 or to consider just E = mv2/2 what is the original cause of the difference. So big difference as for me to consider them incompatible results. But you can say is just my perception. Fine, I will not try to convince you. As for me I just will continue thinking about a better theory that could be able to solve such kind of differences between current theories. Please, just don't try to convince me to not do it. I will not give up anyway.

I agree in the validity of that formula. E can also be expressed as E = γmc2 = mc2 + KE where γ is the relativistic factor (1-v2/c2)-1/2 and so: KE = (γ -1)mc2 Expanding γ in the Taylor series as you did and for v << c then KE = (γ -1)mc2 approximates to mv2/2. But I guess you would have a reason to consider the relation E = (p2c2 + m2c4)1/2 so go ahead. Yes, I have discussed with @studiot in this step by step way other times. It takes its time but could be good to find the key point of agreement or disagreement.

Well, you cut the Taylor series staying with the first two non zero terms. It becomes an approximation of the relativistic energy E valid for small values of the variable v2/c2 only. It is then an approximation of the relativistic energy E for v << c. It is an approximation of the relativistic energy E in the non-relativistic range. Fine, go on.

Something seems to not work for me. The non-relativistic KE verifies KE = p2/(2m) but seems to me is not valid for the relativistic KE. You are adding the constant relativistic term mc2 to the non-relativistic KE. It would be a strange energy, half relativistic and half non-relativistic. I don't know where you can go this way.

Watching the animation but I don't get how it can help in the discussion. Note that for matter waves we have: with the relativistic formula vp = c2/vg and so vp > vg always. with the non-relativistic formula vp = vg/2 so vp < vg always.

Yes. I have no problem that in RT is defined the total energy as E = mc2 + KE for m being the "rest mass".