QuantumBrick

Just a side note: A PhD student should not be thinking about publishing papers without discussing with their advisors first. If you don't feel like talking to your advisor about your paper, then you have a bad relationship. Period. Solve your business or change advisors. If you end up switching, then talk to your new advisor about what you are planing on publishing.

Check also what was said by Fermi:

If you do want madly to perform all integrations using proper objects, please check Rohrlich's last section on deformed ellipsoids. If not, than please think about the definition of electromagnetic mass as simply U/c^2. This is the correct object to be associated with momentum, since no factors arise, only 4-vectors are dealt with, and no paradox emerges. The 4/3 problem exists only because a wrong definition of electromagnetic mass is chosen.

The correct procedure, relavistically speaking, is to use the stress-energy tensor to perform all integrations. This is what Rohrlich does. The point is that this is not needed, because with a very simple argument I have showed that the definition of electromagnetic mass provided by 28.4 and used in 28.7 is not correct in SR.

You can ask this, but it's trivial: to arrive at 28.7 Feynman started from 28.3, and later used the transformation law $\vec{p}' = \gamma \vec{p}$ to start from initial momentum $m_e \vec{v}$ and map it to $\gamma m_e \vec{v}$. Equation 28.7 is clearly not relativistically correct, since the $2/3$ factor in front of it prevents the associated 4-momentum to transform as a 4-vector. Thus, equation 28.7 uses the right transformation law for the wrong momentum, obtained from a relativistically wrong equation. The correct one is obtained from $\vec{p} = m_e' \vec{v}$.

I will let you do the exercises I proposed. Then, please, find the error in: for $\vec{p}=0$, $m_e' = U_{elec}/c^2 \Rightarrow \vec{p}' = \gamma U_{elec} \vec{v}/c^2 = \gamma m_e' \vec{v}$. This calculation was done by Schwinger, Fermi, Rohrlich, and dozens of others. Without understanding my answer properly or reading the references I provided, there is no point to continue this discussion.

Exercise 1: Arrive at formula 28.7 without starting from an initial momentum equal to $m_e \vec{v}$. Hint: it's impossible. Exercise 2: define the mass using $m_e' = U_{elec}/c^2$, then redo the calculations I displayed and arrive at the correct momentum in the small velocity regime $m_e' \vec{v}$.

I'll reinforce what I said before: The proper mass that pops up when using the correct relativistic momentum is $m_e'$, not $m_e$. This is explicitly done in my calculations. Feynman's formula 28.7 is wrong.

Check closely: Feynman defines the electromagnetic mass $m_e$ in 28.4, with the 2/3 factor in front of it. Then he later uses it in 28.7 to define relativistic momentum. However, this is not right, and Feynman is only working out the consequences of a poor choice. The proper, correct mass comes from SR and has no 2/3 factor in front of it, since it is given by $m_e' = U_{elec}/c^2$. This mass, then, is later used to obtain the relativistically correct momentum $\vec{p}' = \gamma m_e' \vec{v}$. The mass in 28.4 is wrong, since it comes from an expression that is not correct in SR.

First, Feynman's formula 28.7 is for the relativistic change of the wrong mass, $m_e$, which does not arise in SR: The correct term is $m_e'$. Second, fully accounting for electron deformation involves not neglecting an integral that is only null inside a bare electron. I urge you to check Rohrlich's paper, where everything is extremely well presented, especially the last section where he solves for the stress-energy tensor on the inside and outside of an ellipsoidal electron.

@imsodin I tried both of them and they do work, but tying the knot above the breaking device is much better in my opinion.

@imsodin the knot you provided is standard and works. The difference between them is the fact that when tying your knot you pass a bight inside the biner and when you pull it up, if stops feeding the device. This created a free bight to tie a mule-hitch. That's a great knot. I just don't think it's possible to take a bight without running the rope through the biner, because it would be under tension. I might have to create a video to show what I'm talking about.

@Liam it is. Think about it: if it were not tensioned, it would run through the breaking device. There's no way to create slack below the device without feeding it.

Fact is: in the middle of a rappel you won't be able to hold the rope with one hand and tie this knot with the other and the rope tensioned (the rope below is also tensioned). This technique seems impossible to apply.

@imsodin Don't get me wrong. I like any kind of climbing... Even the ones where death doesn't look you in the eye.

@imsodin "-35 to 50 sounds like a statement by a lawyer, exactly because there is no norm." I want to give a +100 to this comment.

I think this matter is serious enough to send an email to Petzl or something, asking for clarification.

in any fu!@#!@# norm.

@imsodin You're right to question what I said. I didn't express myself very well, but I still this that the the drastic decrease in Young's modulus in the pictures I attached to the OP should provide significant changes in rope properties. One other thing that is bothering me greatly is that some ropes do have some info about the temperature range they should be used at (normally from -35ºC to 50ºC), but no one freakin' says how the fu#! they arrive at these results, because they're not present

If it's a factor > 1 fall it might easily kill you.

It seems to be worse because the rope will never break. That I can assure you. It won't break unless you're climbing on Venus. But taking a fall on a stiff rope can, and most of the time will, break you up.

My guess is, as I commented, that the elastic properties of the rope make it become stiffer with cold and looser with heat. Both are dangerous, but cold seems to be worse.

because elasticity is derived from a derivative of entropy.

@imsodin I liked your answer. It does provide links to info I've never heard of, so I'm pretty happy with it on a side. On the other side, you're quite right to say that the webbing doesn't change with temperature, but I ask you to think about what elasticity is: it is a property of atomic movements inside a chain. If temperatures are low enough, the chain almost doesn't unfold, which means there's almost no entropy change, which by itself means there's almost no elasticity to provide,

@imsodin Yep. Just got here.

As an on-topic response, I've read a lot about Buddhadasa Bikkhu and Maha Nikaya. It is definitely the branch of Buddhism that makes more sense to me: everything is taken with a grain of salt and considered non-literally. Branches like the Thai Forest Tradition are the ones that most drastically oppose my views. I'm glad to say there is a worked, finished, established school that doesn't hurt my scientific preferences. =)

@ChrisW In fact, both the electron and the photon are waves in scattering (the even that knocks the electron off an atom due to radiation). For that you have scattering amplitudes, calculated via quantum mechanics. The thing is that quantum mechanics is not a relativistic theory - that is, it can only describe quantum particles with speeds much smaller than light's "c"... So we needed to change the theory in order to accommodate it within special relativity, and the result is what we call...

That's the precise definition*

Just a side note: photons are actually excitations of an underlying quantum field of symmetry group U(1). That's the previous use definition ;)

But something that crossed my mind was to check which school Buddhadasa Bikkhu belonged to, and it happens to be Maha Nikaya. Perhaps his view is widespread within this branch.

Thanks @ChrisW. You have been extremely helpful since the beginning. I will read the references you've sent and let you know what comes to my mind. Thank you again!

The point is that, IMO, SB goes too far in saying that the Buddhist conception that "the world is suffering and illumination is the way out of it" is non-literal. This didn't please me at all. Striping off vague scientific assertions is one thing, but denying the main premise is a totally different story. Actually, I had a hard time understanding why, in the first place, SB is Buddhism... It just looks like dogmatic nihilism. They keep the eightfold path and deny the four noble truths.

@ChrisW It appears to me Secular Buddhism (SB) is basically atheism of someone who though Buddha had a good idea going on. I like the idea of removing all magic from Buddhism, e.g, I truly appreciate the fact that SB talks about the five aggregates as merely a an idea that would occur to someone who lived before the discovery of neuroscience and biology. I also like to see how, in the light of non-literal rebirth, basically all fundamental aspects of Buddhism remain untouched and valid even though you striped off all scientifically vague terms.

@Dhammadhatu indeed, even the Dalai Lama, by saying he will not reincarnate in Tibet anymore if China doesn't leave it alone, is using literal rebirth as a tool for a (rather childish) protest. I don't know Mahayana very well, but it seems literal rebirth there is the rule. Is this view of rebirth you've shown me common in Theravada? Or which school? Is it well accepted?

@Dhammadhatu I've read all your references. I genuinely thank you for them. The vision that rebirth is happening at every second, and that all these notions that most people push forward as being literal are actually talking about instances of the same existence has changed my view completely. Everything started making sense, now. Even the dozens of worlds, and rebirth, and kamma. Everything. To be safe in assuming this position, definitely, I'd like to know how usual is this point of view within Buddhism, because it seems everyone really talks about literal rebirth.

@ChrisW thanks. I'll talk to Dhammadhatu directly, then.

@ChrisW What is the etiquette about answering your own question? After reading a lot on the subject I've established an understanding (mostly due to Dhammadhatu's references) but I'd also like to know if it's correct. Maybe it's a better idea to create a new question. What do you think?

I'd like to say this line of moderation is very beneficial, in general - specially to a community that allows a certain level of openness in dialogue (physics is very strict, because most questions make no sense). Open moderation is consistent with stackoverflow's line, which is theoretically expected to be very efficient.

@ChrisW Thank you. Since this is my first post in this community, I'm not fully aware of the etiquette here. I'm an active member of [Physics, Mathematics and Mathematica].SE and must admit the etiquettes in those three communities are very different. I'll take a tour on the Buddhism's FAQ and be sure to adequate my behaviour as much as possible to the community's expected line of acting.

@Dhammadhatu Your comments are being of great help. Thank you very much!

Schizophrenic people are absolutely certain they can hear God's voice commanding them to kill their whole families. I can only say, that if you don't have a mind capable of questioning your own experiences, you are not ready for any knowledge - specially what you define as "high".

@RavindranathAkila The main reference for this subject is the classic nature.com/nrn/journal/v15/n3/abs/nrn3667.html. Nature is a generally easy read for scientists of all areas.

@Bhumishu米殊 A truth that cannot be argued is not a truth. It's not a fact. It's pretty much nothing.

@RavindranathAkila References are my stronghold. See livescience.com/32798-how-are-memories-stored-in-the-brain.h‌​tml. Apart from that all I have are RMN articles.

Your understanding of some scientific aspects is wrong. We do have a pretty clear idea of how the brain storages memory (we've even brought it to the molecular level and to neuron spin structure). Another quite common mistake is to say that the observer changes its surroundings and that the Schrödinger's cat is an example... That is simply not true. Quantum Mechanics proves and explains why observation changes a quantum state, but first you must understand what "observation" means. It is not a vague term: it means interaction with a classical quantity (i.e, non-quantized), not with a person.

Find an experiment which shows QM quantities might depend on referencials and that provides a dichotomy between standard interpretations and RQM. After you do it, you will win the Nobel prize and I ask you to come back here and explain it to me. Until then, have a closed (not an open) mind: reality is what we measure.