Unbelievable velocity mass variation!

[OnlyMe]

Right.


The point here is that at relativistic velocities accordingly to Relativity Theory the momentum is P=gamma.m.v with the Lorentz's factor gamma=1/root(1-v2/c2) present and which introduces the relativistic effect in the De Broglie formula.
przyk said on this: "This equation isn't fundamental in quantum physics and is only true in a certain sense on average and with some restrictions." So the question that arises, in agreement with the purpose of the proposed experiment, is if in relativistic conditions the De Broglie relation actually must include the Lorentz's factor or not. Relativity Theory says yes and following przyk this could be questionable in Quantum Physics (note that this would introduce a too important difference with Relativity). What I claim is that the proposed experiment solves this point with testable results which would be very important in Physics.


Well here a problem appears. With the classical De Broglie wavelength formula an unreachable lower limit for an electron would be lambda=h/mc because it actually can never reach the c velocity but if the relativistic Lorentz's factor is included in the formula (accordingly to Relativity) then lambda=h/(gamma.m.v) and this gamma approaches to zero while v approaches to c so now the variation of the De Broglie wavelength is different and even approaches to infinite while v approaches to c.

So you see it is very important to verify experimentally the De Broglie relation at relativistic speeds. I mean to run the old Davisson-Germer experiment but at some higher velocities enough to detect the relativistic effect (in the original experiment the velocities were about 0.2% of c accelerated by just about 50 volts: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html#c1). I proposed a modification to the original apparatus adding a velocity selector to directly determine the velocities of the electrons and not derive them from the voltage measured in the accelerator's plates. I think there would be problems with this.

martillo, except for the first answer, I would call the rest of your above post non responsive. I was not looking for a restatement of the issues, as you see them. I was looking for a more direct answer to the questions.

I repeat the questions below

pryzk and martillo,

I am having some difficulty understanding the point of the original question and a few of what appears to be associated issues.

It seems that martillo has been asking for an experiment where the de Broglie wavelength of an electron (seems to me it could be any subatomic particle) is measured and confirmed to be consistent with theory at relativistic velocities.

Do I have that much right?

Answer, YES.

The second question, is from my limited offsite exploration, and I do mean limited. The de Broglie wavelength of any particle with mass varies with its momentum, or velocity since its mass is constant, both the particle's kinetic and at rest energy contributing to the calculations.

Is this also, though obviously over simplified, at least a simplistic description of things?

Answer ?

Thirdly, as the momentum of a particle with mass increases, its de Broglie wavelength decreases and it frequency increases.

Is this also at least generally accurate?

Answer ?

NOTE: For my purposes understanding this much is likely best before I delve any deeper into the issue and its implications.

 

[martillo]

I can't do it better. May be przyk can help you more.

 

[przyk]

And very interesting and important would be to perform the proposed experiment because what if, just for the case, the relation that would actually work "in practice" does not include the Lorentz's factor

Since the relation follows from the relativistic relation $$E^{2} \,=\, p^{2} c^{2} \,+\, m^{2} c^{4}$$ (as I showed in my previous post), that would require the relativistic relation between energy and momentum to be wrong. If that were the case I would have expected someone at CERN to have noticed something by now.

It's not just a matter of some numbers being a bit different. The relativistic relation predicts qualitatively different behaviour. For example the non-relativistic relation between energy and momentum, $$E = \frac{p^{2}}{2m}$$, is always quadratic. But for $$p \,>>\, mc$$, the relativistic relation between energy and momentum simplifies to $$E \approx p c$$, which is linear and doesn't involve the mass. The result is that, kinematically, high energy particles start to look a lot like massless particles like the photon. This is a feature of relativity that experimenters at the large accelerators are familiar with that has no non-relativistic analogue.

and this factor actually belongs for instance to the Electric and Magnetic Fields?

Can you show that all results observed in accelerators in the last several decades could be accounted for by modifying the electric and magnetic fields in some way? (Hint: many of the interactions investigated in high energy physics are not electromagnetic in nature. For example, muon decay is a weak interaction.) I doubt this, since it means showing that you can recover the predictions of mainstream quantum field theories, which obviously requires you to know the theories.

At the end the real "nexus" between Relativity and Quantum Physics could be unveiled and isn't this what many ones are looking for? I mean how to "match" Relativity and Quantum Physics?

No, you're thinking of another problem: we don't yet have a consistent quantum theory of gravity.

We've had relativistic quantum theories since at least the 1940s and 1950s. Mainstream quantum field theories such as the Standard Model are quantum theories and they're relativistic. Quantum electrodynamics, which is a part of the Standard Model, is a quantum theory, is relativistic, and is famous for being basically the most precisely verified theory in the history of physics.

 

[przyk]

The second question, is from my limited offsite exploration, and I do mean limited. The de Broglie wavelength of any particle with mass varies with its momentum, or velocity since its mass is constant, both the particle's kinetic and at rest energy contributing to the calculations. Is this also, though obviously over simplified, at least a simplistic description of things?

Roughly. It's a bit more complicated than that because quantum particles are generally described by wavepackets that have a distribution in space and frequency. So a particle typically doesn't have a unique momentum but a certain momentum spectrum, and that means it really has a spectrum of wavelengths.

Similarly a wavepacket, being something that's distributed over space, typically doesn't have a unique velocity associated with it. The best you can do there is identify an average position $$\langle X \rangle$$ associated with the wavepacket, and then you can define an average velocity depending on how the average position moves about by $$\frac{\mathrm{d}}{\mathrm{d}t} \langle X \rangle$$. That's why I made the comment earlier about an equation involving velocity not being fundamental in quantum physics. The average velocity is just something you can define once you already know how the wavepacket is evolving, which is governed by the Schrödinger equation. Momentum and the Schrödinger equation are really more fundamental in quantum physics than velocity is.

Thirdly, as the momentum of a particle with mass increases, its de Broglie wavelength decreases and it frequency increases. Is this also at least generally accurate?

Yes (it's also true for massless particles).

 

[Robittybob1]

Is there a connection between these findings and the way an electron operates?

 

[przyk]

What I think is important now from your presentation of the invariant De Broglie law is that you included the relativistic Lorentz's factor in the formula and it was just because of this that the relation is invariant under a change of relativistic frames of reference. I mean invariant under a Lorentz Transform. The relation would be not invariant without the Lorentz's factor in it.
So Relativity Theory demands the Lorentz's factor in the formula.
Now you bring a formulation that seems come from Quantum Physics and say that the Lorentz's factor is not essential in it.

First of all it's worth keeping in mind that back in 2007 I knew relativity, but I didn't know quantum physics. So I could mathematically investigate whether an equation was relativistic but I couldn't tell you whether it made much physical sense beyond that.

The short answer here is that the equation $$\lambda = \frac{h}{\gamma m v}$$ is consistent with relativity in a mathematical sense, but physically isn't very important or fundamental in quantum physics, mainly because the velocity has no fundamental role in quantum physics (see my explanation to OnlyMe above). Also I'd have to think about this, but I think Heisenberg uncertainty would also mean you couldn't really test the relation directly. The problem is that to see clear interference fringes etc. you need particles to have very precisely defined wavelengths, which requires precisely defined momentum. Conversely, the velocity is only well defined if the position is well defined at least in two different places at two different times. If you try to measure the velocity too precisely you'll probably destroy the very effect you're looking for.

 

[martillo]

“And very interesting and important would be to perform the proposed experiment because what if, just for the case, the relation that would actually work "in practice" does not include the Lorentz's factor ”

Since the relation follows from the relativistic relation (as I showed in my previous post), that would require the relativistic relation between energy and momentum to be wrong. If that were the case I would have expected someone at CERN to have noticed something by now.

It's not just a matter of some numbers being a bit different. The relativistic relation predicts qualitatively different behaviour. For example the non-relativistic relation between energy and momentum, , is always quadratic. But for , the relativistic relation between energy and momentum simplifies to , which is linear and doesn't involve the mass. The result is that, kinematically, high energy particles start to look a lot like massless particles like the photon. This is a feature of relativity that experimenters at the large accelerators are familiar with that has no non-relativistic analogue.


“ and this factor actually belongs for instance to the Electric and Magnetic Fields? ”

Can you show that all results observed in accelerators in the last several decades could be accounted for by modifying the electric and magnetic fields in some way? (Hint: many of the interactions investigated in high energy physics are not electromagnetic in nature. For example, muon decay is a weak interaction.) I doubt this, since it means showing that you can recover the predictions of mainstream quantum field theories, which obviously requires you to know the theories.

Of course what I'm talking about in this thread does not include subatomic interactions but in relation to the equations you mention and the experimental results of the relation between energy and momentum at relativistic velocities I can say that yes they can be explained by the Lorentz's factor be present in the electric and magnetic fields since the particles are always accelerated by electric and/or magnetic fields. I have analyzed the experiment being done by students in the "Relativistic Dynamics" experiment at the MIT Junior Lab (http://web.mit.edu/8.13/www/09.shtml) where precisely those equations appears and the relation between energy and momentum are verified experimentally at some relativistic velocities. The experiment is well described in the guide of the experiment (http://web.mit.edu/8.13/www/09.shtml). In the experiment the energy of the accelerated electrons is measured directly with PIN diodes detectors and the guide says for example:
"A plot of energy against B reveals the deviation of the energy-momentum relation from the nonrelativistic quadratic form E = p2=(2m) toward the linear form E = pc valid for a particle moving with a velocity close to c."
I have studied the guide and done some calculations and they perfectly show that the same result can be obtained with the classical definition of the Kinetic Energy and the Lorentz's factor present in the electric and magnetic fields.
I can't analyze the experiments at CERN but I think they follow a similar reasoning and the particles are also accelerated by electric or magnetic fields so I think the same results can in principle be obtained.

 

[martillo]

The short answer here is that the equation is consistent with relativity in a mathematical sense, but physically isn't very important or fundamental in quantum physics, mainly because the velocity has no fundamental role in quantum physics

May be not at some high energy physics experiments as you said but of course is important in the Davisson-Germer experiment which also belongs to Quantum Physics. De Broglie "matter wave" proposition is the most basic postulate of Quantum Physics (among Planck's energy relation E=hf of course).

but I think Heisenberg uncertainty would also mean you couldn't really test the relation directly. The problem is that to see clear interference fringes etc. you need particles to have very precisely defined wavelengths, which requires precisely defined momentum. Conversely, the velocity is only well defined if the position is well defined at least in two different places at two different times. If you try to measure the velocity too precisely you'll probably destroy the very effect you're looking for.

Come on, the 100 years old original Davisoon-Germmer experiement did this very well and I'm talking about to just make quite the same experiment just with the electrons accelerated a little more for example to pass from the original velocities of about 0.2% of c (accelerated by just about 50 volts) to 10% or 20% of c. That would be enough to test the De Broglie formula at some relativistic velocities.

 

[OnlyMe]

Roughly. It's a bit more complicated than that because quantum particles are generally described by wavepackets that have a distribution in space and frequency. So a particle typically doesn't have a unique momentum but a certain momentum spectrum, and that means it really has a spectrum of wavelengths.

Yes (it's also true for massless particles).

Thank you for the clarifications. This is generally what I thought, though I was obviously as I said, over simplifying...

I do understand the difficulty in defining a velocity, when dealing with quantum scales, the main issue I was trying to get at is that velocity as the variable aspect of momentum, when dealing with massive particles, affects the de Broglie wavelength.

I separated massive particles in the question, as it seemed clear that photons having a constant velocity, have a more clearly, or perhaps more narrowly defined wavelength/momentum relationship.

Though I had understood that massive particles have wave characteristics, I had not previously considered, that the associated wavelength and frequency of a specific particle mass, varied in the way described here.

Just so you know where my interest was comming from and not to begin another discussion....

These questions have really been completely aside from your general discussion here. I have been trying to understand some of the attempts in the last decade to describe inertia as emergent from the interaction between the motion of matter through the ZPF... A subject I may never fully understand but find interesting and thought provoking.

It just struck me that if a massive particle's wavelength varies with its momentum, that could be an issue I was missing...

Anyway, thanks again for the clarification... Sorry for the interruption of the primary discussion here.

 

[przyk]

Of course what I'm talking about in this thread does not include subatomic interactions

You realise that just there puts you way behind mainstream physics, right?

but in relation to the equations you mention and the experimental results of the relation between energy and momentum at relativistic velocities I can say that yes they can be explained by the Lorentz's factor be present in the electric and magnetic fields since the particles are always accelerated by electric and/or magnetic fields. I have analyzed the experiment being done by students in the "Relativistic Dynamics" experiment at the MIT Junior Lab (http://web.mit.edu/8.13/www/09.shtml) where precisely those equations appears and the relation between energy and momentum are verified experimentally at some relativistic velocities.

Maybe, but you just picked one simple experiment intended for students. It's hardly representative of the last several decades of experimental physics. All you have is one simple experiment and a blind hope that the same explanation will work everywhere else.

I can't analyze the experiments at CERN but I think they follow a similar reasoning and the particles are also accelerated by electric or magnetic fields so I think the same results can in principle be obtained.

The experiments being done at the LHC are much more sophisticated than the student experiment you just cited. In particular the people at CERN have various ways of knowing both the energies and the velocities of the particles involved. If particles at the LHC weren't obeying the relativistic energy formula, they'd quickly know about it.

 

[przyk]

May be not at some high energy physics experiments as you said but of course is important in the Davisson-Germer experiment which also belongs to Quantum Physics. De Broglie "matter wave" proposition is the most basic postulate of Quantum Physics (among Planck's energy relation E=hf of course).

This doesn't negate what I said: velocity doesn't have the fundamental role in quantum physics that it does in classical physics, as I explained a few posts above.

Come on, the 100 years old original Davisoon-Germmer experiement did this very well

As far as I know they weren't particularly interested in the electrons' velocities, which is specifically what I was talking about.

 

[martillo]

Maybe, but you just picked one simple experiment intended for students. It's hardly representative of the last several decades of experimental physics. All you have is one simple experiment and a blind hope that the same explanation will work everywhere else.

It's a strong evidence and it explains exactly the equations and relationships you asked to be explained with a related experimental support.
Of course there are lot of possibilities that the same reasoning would apply other experiments that at the end are based in the same principles, reltionships and equations.
It's you that take it too lightly because you just don't believe it could work not considering it properly.
Is well justified I know. I know is not easy to believe in it in a first look and decide to dedicate time and effort to it.

The experiments being done at the LHC are much more sophisticated than the student experiment you just cited. In particular the people at CERN have various ways of knowing both the energies and the velocities of the particles involved. If particles at the LHC weren't obeying the relativistic energy formula, they'd quickly know about it.

This kind of comments don't have any kind of mathematical or physical validity. It's just a lazy justification to not analyze de situation properly. But is comprehensible.

 

[przyk]

This kind of comments don't have any kind of validity. It's just a lazy justification to not analyze de situation properly. But is comprehensible.

This attitude is so hypocritical it's mind boggling. High energy physics is something you have never bothered to learn anything about, and yet you expect everyone to take you seriously when you brush it off like this:

I can't analyze the experiments at CERN but I think they follow a similar reasoning and the particles are also accelerated by electric or magnetic fields so I think the same results can in principle be obtained.

You are not "analyzing the situation properly". You are taking an experimental domain you know nothing about and believing whatever you want to believe about it.

 

[martillo]

You are not "analyzing the situation properly". You are taking an experimental domain you know nothing about and believing whatever you want to believe about it.

I didn't take that "experimental domain". You throwed it to me. I just gave some reflections about and you got disturbed. The discussion turned away from rational presentation of mathematical or physical argumentations what you used to do very well othertimes, not now. The discussion doesn't worth now.

 

[OnlyMe]

I didn't take that "experimental domain". You throwed it to me. I just gave some reflections about and you got disturbed. The discussion turned away from rational presentation of mathematical or physical argumentations what you used to do very well othertimes, not now. The discussion doesn't worth now.

Martillo, am I missing something important here? Remember my three questions and your answer to the first one? Quoted below as a refresher.

It seems that martillo has been asking for an experiment where the de Broglie wavelength of an electron (seems to me it could be any subatomic particle) is measured and confirmed to be consistent with theory at relativistic velocities.

Do I have that much right?

Answer, YES.

As far as I know the only places we can do relativistic experiments is in accelerators ether like the LHC or a linear accelerator. And then there is the bit where electrons or other subatomic particles are involved.

That puts the whole question and experiment within the preview of particle physics. Does it not?

Is there a de Broglie wavelength of whole arom's and molecules or "objects"? And if there is, even theoretically, how would we manage to accelerate a complex object to relativistic velocities?

The LHC manages what Lead and Gold nuclei, but those have been stripped of their electrons either before or in the process, so they aren't even atoms any longer.

Przyk, did not drag you into a particle physics discussion, it seems to me the whole issue your raised is one of particle physics.

 

[martillo]

As far as I know the only places we can do relativistic experiments is in accelerators ether like the LHC or a linear accelerator. And then there is the bit where electrons or other subatomic particles are involved.

No. Large amount of relativistic experiments have been done in the Physics history and at much more lower scale and they are very valid. The MIT Junior Lab experiment is just one I have analyzed. You can find my brief analisis on two old otherones at: http://www.geocities.ws/anewlightinphysics/sections/Section2-3_New_interpretations_for_old_experiments.htm.

That puts the whole question and experiment within the preview of particle physics. Does it not?

If by Particle Physics you mean subatomic particles the answer in no. Davisson-Germer experiment is about diffraction of electrons and I'm talking about some modification of it.

Is there a de Broglie wavelength of whole arom's and molecules or "objects"? And if there is, even theoretically, how would we manage to accelerate a complex object to relativistic velocities?

I have heard that some diffraction patterns have been observed for some atoms and molecules but actually I know nothing about. If they were electrically charged ones in principle electric and magnetic fields could do that but if you are considering neutral ones I have no idea.

Przyk, did not drag you into a particle physics discussion, it seems to me the whole issue your raised is one of particle physics.

As I said above if you mean subatomic particles the answer is no. I'm just talking about a slightly modification of the old Davisson-Germer experiment. CERN and LHC have nothing to do with this.

 

[OnlyMe]

Electrons are subatomic particles.

And yes there were early experiments and applications including television that used electron beams.

While we do most certainly base a number of practical applications on the transfer of electrons in one way or another, they remain subatomic particles and as such seem to be best described by quantum mechanics and the standard model of particle physics. And our best tools in that area are linear accelerators and cyclotrons. Electrons favor the linear accelerators.

That is why I said he did not drag you into a discussion of particle physics, electrons are part of that area of science.

 

[Robittybob1]

Electrons are subatomic particles.

And yes there were early experiments and applications including television that used electron beams.

While we do most certainly base a number of practical applications on the transfer of electrons in one way or another, they remain subatomic particles and as such seem to be best described by quantum mechanics and the standard model of particle physics. And our best tools in that area are linear accelerators and cyclotrons. Electrons favor the linear accelerators.

That is why I said he did not drag you into a discussion of particle physics, electrons are part of that area of science.

the Free Dictionary
did define electrons as subatomic particles.

subatomic particle (sb-tmk)
Any of various particles of matter that are smaller than a hydrogen atom. Protons, neutrons, and electrons are subatomic particles, as are all hadrons and leptons. See also composite particle elementary particle

 

[martillo]

I didn't express it well. You referred to Particle Physics what is more associated to the Standard Model features derived from the study of particles' collisions (what CERN and LHC are devoted to) and that's what I intended to refer while writing "subatomic particles".

But please remain on topic. I'm talking about a direct experimental verification of De Broglie law at some relativistic speeds something that seems to haven't been done or nothing have been published since is not mentioned specifically anywhere in the web. I think is something interesting and important thing to do in Physics.

 

[przyk]

I didn't take that "experimental domain". You throwed it to me.

What kind of a retort is that? I am throwing an experimental domain at you that is highly relevant to your claim that relativity can all be washed away just by messing with the electric and magnetic fields a bit. Who's fault is it that you're ignorant of all of it?

You are simply not doing science when you say stuff like this:

I can't analyze the experiments at CERN but I think they follow a similar reasoning and the particles are also accelerated by electric or magnetic fields so I think the same results can in principle be obtained.

I actually know people working on one of the LHC experiments. I think they'd quite rightly feel insulted by what you wrote. There's a bit more to high energy physics than "they use electric and magnetic fields" you know.

I just gave some reflections about and you got disturbed. The discussion turned away from rational presentation of mathematical or physical argumentations what you used to do very well othertimes, not now. The discussion doesn't worth now.

This discussion stopped being rational when you decided it was OK to assume whatever you liked about physics you were too lazy to actually look up.

You said you thought you could restore the nonrelativistic energy formula $$E = \frac{1}{2} m v^{2}$$ to one experiment you looked at, and that you thought the same approach would work everywhere else. At the energies at the LHC this would meen the protons were actually moving at over 80 times the speed of light! At LEP it would have meant the electrons were moving at over four hundred times the speed of light. I told you that at these kinds of accelerator sites the people working there had various ways of knowing both the energies and the velocities of the particles there. Do you think I'm just making this up?