What if the electron don't have a speed inside the atom ? Is there any experimental prouve of its mouvement on the orbits ? I feel that this is just a theoretical assumption.

You can say that, since nobody has ever watched an electron. However, it is the only solution that fits what we do observe: We can observe that electrons posess various levels of energy inside the atom, and we can observe that the only way electrons can posess energy is by motion. Also, the negative electrons should be attracted by the positive nucleus, and the only sensible explanation why they don't crash into the nucleus is that they are orbiting it. In magnetic materials, we can even detect their direction.

All that said, the traditional notion of electrons as small dots whizzing around is somewhat naive. The modern model goes more in the direction of an "electron mist" surounding the nucleus. Remeber, the electron can be understood both as a particle and a wave.

Hans

For a free electron, outside the atom, there are many experiments that demonstrates it's speed, direction and so on.
What fascinates me is that the whole theory of the atom is based on a classic and very old assumption that states that the atraction of the atom must be balanced by the cinetic force.

bound electrons inside the atom can move down imparting their kinetic energy as photon with certain energy or move up the discrete energy levels by obsrobing discrete quanta of kinetic energies. possessing kinetic energy does not suggest electrons are stationary particles inside the atom. rather, they could be described as standing 3D probability wave function or electron cloud that does not fix the position of the electron.

For a free electron, outside the atom, there are many experiments that demonstrates it's speed, direction and so on.
What fascinates me is that the whole theory of the atom is based on a classic and very old assumption that states that the atraction of the atom must be balanced by the cinetic force.Sorry, but you're waaaay behind the times. The "electrons orbit a nucleus like planets around the sun" model, in which they are kept from falling into the nucleus by their angular velocity, hasn't been used by physics for many decades.

comisaru:

What fascinates me is that the whole theory of the atom is based on a classic and very old assumption that states that the atraction of the atom must be balanced by the cinetic force.

I'm almost afraid to ask, but do you have an alternative theory?

I should I have. But I'm not a professional, just curious. And not yet satisfied with some explanations - but not blaim anyone for this. Also there is to much math (and of course I'm a little lazy).
When I posted the first, I hoped that meanwhile were done new experiments that prouved somehow that mouvement.
For a new theory I could only suggest an anomaly: it could be extracted an electron on higher temperature, but the superconductibility it occurs at very low temperature. I'll think about this and I'll came with some formulas.
Thank you for your coments.

What if the electron don't have a speed inside the atom ? Is there any experimental prouve of its mouvement on the orbits ? I feel that this is just a theoretical assumption.
Comisaru,
You might look at the probelm by considering the electron has vibration motion for sure, linear motion is another problem and most difficult to determine. However, magnetic effects (angular momentum etc) are implied using "orbiting" electrons which I find hard to concepualize given the discrete nature of the electron energy levels.
Geistkiesel :cool:

Also, the negative electrons should be attracted by the positive nucleus, and the only sensible explanation why they don't crash into the nucleus is that they are orbiting it. In magnetic materials, we can even detect their direction.No, on the contrary. The classical (sensible?) notion of orbiting electrons insists that a charged particle in orbit loses energy and therby does crash into the nucleus.
Bohr had a better idea, hence early quantum physics was born.


All that said, the traditional notion of electrons as small dots whizzing around is somewhat naive. The modern model goes more in the direction of an "electron mist" surounding the nucleus.

Hans
Not sure what you mean by a "mist". I would rather think in terms of a probability density.

The electron cannot "crash" into the nucleus for a very good reason. The inherent uncertainty of position and speed (or momentum) at the quantum level. If the electron were to settle onto the nucleus, we would know exactly where it was, and what it's velocity was (zero). This is not allowed. The electron can only be visualized as a "cloud" of probability with varying density and shape based on its energy level within the atom.

This is the same mechanism that causes matter to resist compression beyond an absolute limit. Degeneracy "pressure" is due to the fact that if particles are forced into smaller volumes, their position becomes more defined, so the uncertainty in their momentum increases. You cant smash probability patterns beyomd a certain point.

Comments? Corrections? Anger at a universe with such perverse behavior?

Comments? Corrections? Anger at a universe with such perverse behavior?
You are absolutely correct - an electron is not a sphere-like particle so to speak which a lot of people tend to think of as an electron.

This is the same mechanism that causes matter to resist compression beyond an absolute limit. Degeneracy "pressure" is due to the fact that if particles are forced into smaller volumes, their position becomes more defined, so the uncertainty in their momentum increases.

Hum,
Yeah, excluding weird fermonic condensate states (aka Bose-Einstein condensates) i assume.

The electron cannot "crash" into the nucleus for a very good reason. The inherent uncertainty of position and speed (or momentum) at the quantum level. If the electron were to settle onto the nucleus, we would know exactly where it was, and what it's velocity was (zero). This is not allowed. Hmm...this is sort of cart-before-horse. It is because the electron doen't crash ito the nucleus (by observation) Bohr realised the classical view had to be modified, hence qunatum physics. The electron can only be visualized as a "cloud" of probability with varying density and shape based on its energy level within the atom. Only if you first assert the wave-like properties of the electron, and then declare that the square of the wave function is a probablilty density plot.

de Broglie has a cute (and highly intuitive) proof of the quantum nature of the electron, based on its wave properties. (In fact I think one could go from there to something resembling the Schroedinger ψ-function.)

QuarkHead,

I was not attempting to describe the historical observational evolution of our understanding of the electron (obviously you are right from that perspective). The answer to why an electron dosen't "crash" into the nucleus, for those still thinking of it as a little billiard ball orbiting the nucleus, is because we now understand that electrons (and all particles at the quantum scale) are a new kind of thing - a wave/particle entity that obeys the uncertainty principle. Yes?

QuarkHead,

I was not attempting to describe the historical observational evolution of our understanding of the electron (obviously you are right from that perspective). Well, I wasn't really being historical. By "first" I meant "it is a prior requirement to..." The answer to why an electron dosen't "crash" into the nucleus, for those still thinking of it as a little billiard ball orbiting the nucleus, is because we now understand that electrons (and all particles at the quantum scale) are a new kind of thing - a wave/particle entity that obeys the uncertainty principle. Yes?OK, though I don't like the word "obeys" here. (Am I being pedantic?). It is, rather, an unfortunate fact forced upon us by the (correct) interpretataion of the square of the wavefunction as a probabilty density.

OK, let's do it, it's not hard. First - you will often see the uncertaintity principle explained from what has become known as the "realist" perspective. Namely, that if you want to look at an electron, say, then you have to bombard it with a photon, which changes its energy, posistion, etc. That's fine as an illustration, but that's all it is.

So, the wavefunction is a measure of the electron's energy - different energy, different wavefunction. It therefore follows if you know the energy, you know the wavefunction, and if you know that then, by taking the square, you have a probality plot. But that's all you have! You don't know where it is.

Let's now say you know where it is. What does your probalibity plot look like now? It's a flat line with only a single p = 1 peak, the location. The only way we know of to get a plot like that from a sinewave is to take a whole lot of different waves, each representing different energies, such that "peaks and troughs" destructively interfere except in one place, where the interference is constructive, generating the single peak.

But then you don't know which wave, which energy, "belongs" to the electron. So the uncertainty principle doesn't say "we can't find out experimentally", it says these two properties - speed and location - cannot as a matter of principle both be known

The answer to why an electron dosen't "crash" into the nucleus, for those still thinking of it as a little billiard ball orbiting the nucleus, is because we now understand that electrons (and all particles at the quantum scale) are a new kind of thing - a wave/particle entity that obeys the uncertainty principle. Yes?

superluminal, would you say that this wave/particle entity is fundamentally a bundled form of energy that we call matter? (i.e. e=mc²) I only ask this question because I want to move further into how exactly this energy interacts, but need to establish common ground between us first.

QuarkHead,

I am in complete agreement with you. Nice explanation of the "in principle" inability to pinpoint both position and speed. I've tried to explain that to people before.

And yes, you were being a bit pedantic. :)

Aer,

superluminal, would you say that this wave/particle entity is fundamentally a bundled form of energy that we call matter? (i.e. e=mc2) I only ask this question because I want to move further into how exactly this energy interacts, but need to establish common ground between us first.

Well, umm, yes. I see no problem with that description. Any particle that is completely converted to energy (by antiparticle anihilation?) will yield energy according to E = mc².

superluminal, would you say that this wave/particle entity is fundamentally a bundled form of energy that we call matter? (i.e. e=mc²) .Wave particle duality means just that - energy equations for both wave and particle apply, i.e.

E = mc² = hν (h is Planck, ν is frequency)

Follow your nose from there, and some interesting things happen!

Well, umm, yes. I see no problem with that description. Any particle that is completely converted to energy (by antiparticle anihilation?) will yield energy according to E = mc².
Can we assume that this energy is non-rotational? I don't think it has been proven as such, but I know I've read that opinion from various physicists. Maybe I should do some investigating, but first I'll seek your opinion on the rotation issue.

Not sure I understand. Rotational in what way?

Not sure I understand. Rotational in what way?
Well if the energy is considered contained, it must be contained in some way. Imagine our electron wave/particle balloon'ed up to the size of your monitor. Now it is impossible for us to say what we'd see for sure, but we can make guesses and rule other things out. I am trying to rule out that the energy is rotating round and round - although we may not be able to make this ruling for sure.

Ok. For the simplest atom in its ground state (hydrogen) I would say there is no reason to apply "rotation" to this object. The best visualization I can think of is as a ball of translucent "fuzz" around the nucleus (which is also "fuzzy"). This "fuzz" is the probability density plot of the electron around the nucleus. I can't imagine there being any "thing" to rotate.

This is also not the intrinsic "spin" we talk about. Spin is a characteristic of a particle that represents angular momentum (spin angular momentum) but there is nothing "spinning" in the way we think of. That's my take on it.

Ok. For the simplest atom in its ground state (hydrogen) I would say there is no reason to apply "rotation" to this object. The best visualization I can think of is as a ball of translucent "fuzz" around the nucleus (which is also "fuzzy"). This "fuzz" is the probability density plot of the electron around the nucleus. Unfortunately, this "fuzz" isn't very descriptive. I am willing to go out on a limb and say that we aren't going to get past this "fuzz" phase with any agreement in this discussion.


This is also not the intrinsic "spin" we talk about. Spin is a characteristic of a particle that represents angular momentum (spin angular momentum) but there is nothing "spinning" in the way we think of. That's my take on it. Yes, I am aware that "spin" has nothing to do with rotation, unfortunately this misnomer tends to make one think of rotation however (probably the etymology of the name in all actuality).

How about considering the contained energy a vibration or standing wave type of phenomenom. Can this be ruled out?

Sorry to be rude, but - what are you two talking about? I may be able to help a little, but so far you seem to be content with talking in riddles. I can't even begin to think what either of you is getting at. Again, apologies for my brusqueness.

Sorry to be rude, but - what are you two talking about? I may be able to help a little, but so far you seem to be content with talking in riddles. I can't even begin to think what either of you is getting at. Again, apologies for my brusqueness. All in time :D What I am seeking to do here, is gather exactly everything we can say about an electron - starting first with it's contained energy.

Then "starting first", tell us what you mean by contained energy.

Then "starting first", tell us what you mean by contained energy. The rest energy, e=mc²

The rest energy, e=mc²OK (rest energy isn't the term I would use, but let it go). The energy equation you wrote refers only to the electron viewed as a particle. Let's leave it there (there's a lot more to consider) but you clearly want to work up from the beginning.
Right. You have a particulate electron, with energy mc². What next?

OK (rest energy isn't the term I would use, but let it go). The energy equation you wrote refers only to the electron viewed as a particle. OK - first of all, let's get all semantics out of the way early. What are we going to agree to call, e, in the equation e=mc²? Would it be better if I posed the equation in the form: e=mc² + K, where K is the kinetic energy?

Would it be better if I posed the equation in the form: e=mc² + K, where K is the kinetic energy?
Absolutely not! No way! You're tempting me to show you how E = mc² is derived - let's not go there.

Absolutely not! No way! You're tempting me to show you how E = mc² is derived - let's not go there. OK - I am sorry but we can't even get started on agreement of the simpliest of things, that being e=mc²! My physics notes may be a little old, but they are not that old and in them is the equation: e=mc² + K. Was my physics professor wrong?

I am going to guess that you assume m = relativistic mass in the equation e=mc².

QuarkHead,

Sorry to be rude, but - what are you two talking about? I may be able to help a little, but so far you seem to be content with talking in riddles. I can't even begin to think what either of you is getting at. Again, apologies for my brusqueness.

Well, Aer is asking is series of questions that may sound riddle-like in an attempt to get to some point. You clearly know particle physics, and your input is definitely wanted. If we make stupid statements or assumptions, we need to know about it. But the surest way to piss people off is to anally attack every term usage just because it's not the way you would say it. If we're essentially correct, leave it at that and we'll refine it and get it right before we're done, hopefully with your help.

Aer. As a particle, the electron has energy of mc² in it's rest frame. It's that simple.

QuarkHead, what's the problem?

Aer. As a particle, the electron has energy of mc² in it's rest frame. It's that simple.

That's what I thought. Thank you.

electron mass = 9.10938188 × 10^-31 kilograms

The energy represented by this mass is

9.10938188 × 10^-34 g * (300e8 cm/s)² ~ 2.732 x 10^-23 g cm²/s² (ergs)

electron mass = 9.10938188 × 10^-31 kilograms

The energy represented by this mass is

9.10938188 × 10^-34 g * (300e8 cm/s)² ~ 2.732 x 10^-23 g cm²/s² (ergs) Numbers are nice and all - but what does this have to do with our discussion?

Anyway, I am curious as to your position on relativistic mass. What is it? What is it used for? I did battle over this topic on physicsforums some time ago - unfortunately those proclaiming relativistic mass had very little knowledge in relativity and I found myself explaining very simple relativistic concepts to them.

Numbers are nice and all - but what does this have to do with our discussion?

Not a damn thing.

I am certain of one thing. Physicists do not use relativistic or effective mass. They use the proper or rest mass. As Albert said:

"It is not good to introduce the concept of the mass of a moving body

for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

So, do we need to even talk about "relativistic" mass?

So, do we need to even talk about "relativistic" mass?
Nope, just wanted to make sure this view was expressed by both of us.

e=mc² + K. Was my physics professor wrong?Well, I've just been called names for being too precise! The nearest and least precise way I can put it is that 1/2mv² = mc<sup<2</sup> + Constant. It's not completely right, but it's as close as I can get without being called anal.
Maybe when your prof wrote K he meant a constant?

I am going to guess that you assume m = relativistic mass in the equation e=mc².This is better (although solved for m would be even better). However, nobody now uses the term "relativistic mass". They say "energy"

But the surest way to piss people off is to anally attack every term usage just because it's not the way you would say it.OK. Duly reprimanded. But my experience of this site (leaving aside my background) is that, if people use terms in different or ambiguous ways, then confusion, argument and hostility follow as a matter of course.
Want to cal a rose a poppy? Fine, but we would first have to establish definitions etc. Far easier, I think, to go with the herd, and use terms as they are usualy used.

Maybe when your prof wrote K he meant a constant?
He clearly defined K as kinetic energy I do believe - I don't have my notes with me, so I cannot look them up to check.

QuarkHead,

Why not just write the complete equation for the mass-energy relationship for a particle and we move on?

This is better (although solved for m would be even better). However, nobody now uses the term "relativistic mass". They say "energy"

I already pointed that out. And quit saying "thus and such would be even better...". If it's wrong, tell us. Don't play games. And no one called you names.

Aer. As a particle, the electron has energy of mc² in it's rest frame. It's that simple.

QuarkHead, what's the problem?My problem is, why bring up "rest frames" when talking about sub-atomic phenomena. This ain't your beloved "SR", frames don't come into it, at all.

Don't play games. And no one called you names.Look, it's no game to me, as an engineer you should know that precision is all we have to guide us. I have a very long fuse, but it's not infinite, so leave off the hostility.

Deleted for being pointless drivel.

SL

Fine. Correct us as necessary. Let us start on a clean footing.

My problem is, why bring up "rest frames" when talking about sub-atomic phenomena. This ain't your beloved "SR", frames don't come into it, at all. Regardless of what your particular specialty is, we are considering the energy of an electron in all aspects. If we want to consider an electron moving with a large relativistic velocity - we are free to do so. Does this mean we'll be able to utilize the wave function and whatnot as it is defined? Probably not. But a general view is our (at least mine, remember, I brought up this particular discussion) goal here.

Aer, SuperLuminal: Forgive me, I'm a bit stressed. I have to step out for a while. I'll get back if I can (can't guarantee total sobriety)

Why not just write the complete equation for the mass-energy relationship for a particle and we move on?



OK, you asked for it!
Given the usual assumptions about the equivalence of all inertial frames, constancy of light velocity, then time and length in one frame when viewed from another are related by the Lorentz transformation factor

1/&radic;(1 - v²/c²). Let's call this &gamma; for now;

but note the rather simple fact that v²/c² follows in a straightforward way from the Pythagorean principle

Now consider a body which, for certain fixed time, emits a beam of light L. The body has thereby lost an amount of energy E. It should be clear that the amount of energy lost is proportional to the time of the light emission

If this body happens to be moving wrt to me, then the factor &gamma; applies to our respective times, so I now consider the amount of light emitted to be

&gamma;L. Let's call the energy lost thereby E'

so now E = L, and E' = &gamma;L

and the difference between E and E' is

E' - E = &gamma;L - L = L(&gamma; - 1).

Remember &gamma; can be written as (1 - v²/c²)^-1/2. This is known as a binominial, and there are standard ways of expanding such things using the Binomial thereom (approximate) or the Taylor series (exact)

For example (1 - x)^-1/2 can be written as a converging series

1 + 1/2x + 1/8x² + 1/16x³....

where x = v²/c², as here, then terms represented by x² etc can be ignored, because they yield v⁴/c⁴ etc

so we can write E' - E = &Delta;E = L(1 + 1/2v²/c² - 1)

&Delta;E = L1/2(v²/c²) = 1/2(L/c²)v²

But as we are here dealing with energy of a moving body, &Delta;E can differ from the kinetic energy only by a constant C which can be ignored because it is unchanged by the emission process.

As KE = 1/2mv², this implies

1/2mv² = 1/2(L/c²)v²

and L/c² = m

as L = E, then m = E/c²

i.e E = mc²

OK, you asked for it!
Given the usual assumptions (...) What is the name of this derivation you provided?

What is the name of this derivation you provided?Er...irrefutable? Rather cool? Jolly splendid?

Not sure what you mean.

Not sure what you mean.
I just wanted to look it up for definitions. Did you make this up - is that what you are saying?

I wanted clarification on exactly what L is and how it is measured - I didn't know if that was too much to ask of you or not, so I'd prefer to just look it up myself.

For instance, lets assume (probably incorrectly) that an electron can emit all of its energy as photons and cease to exist. How is this "beam of light" (not really a beam, but beams of photons) measured in terms of L?

For instance, lets assume (probably incorrectly) that an electron can emit all of its energy as photons and cease to exist. How is this "beam of light" (not really a beam, but beams of photons) measured in terms of L?

OK, I guess L is the length of time of light emission. The amount of energy released would also be a function of the intensity of the emission, no?

Also, just like measuring mass, the only proper way to measure energy is in the rest frame of the object losing/gaining energy - I am pretty certain.

I just wanted to look it up for definitions. Did you make this up - is that what you are saying? Yes and no - I adapted it from Einstein.

I wanted clarification on exactly what L is and how it is measured L is a "quantity" of light energy, in our story temporarily (but not finally!) undefined. I hope I showed that L could be identified with &Delta;EFor instance, lets assume (probably incorrectly) that an electron can emit all of its energy as photons and cease to exist. How is this "beam of light" (not really a beam, but beams of photons) measured in terms of L?Hmm. Sorry, but slight confusion here.

The classical picture of the electron as a body in orbit requires it to loose a fixed amount of energy per orbit, finally spiralling into the nucleus. We know this doesn't happen, ergo the classical view, in this case is wrong. Hence quantum physics.

But the sqiggles I offered you were in respone to superluminal's request to show the mass-energy relation, which I interpreted to mean in a general sense.
I don't know how else to do it, frankly, do you?

Posts crossing, nearing midnight here (UK). Bedtime.

I have a few questions. The last time I saw the derivation was probably 10 years ago, but it was definitely different.

Now consider a body which, for certain fixed time, emits a beam of light L. The body has thereby lost an amount of energy E. It should be clear that the amount of energy lost is proportional to the time of the light emission

Yes, and the proportionality factor is the frequency of the light times Planck's constant, right? E=hf?

If this body happens to be moving wrt to me, then the factor &gamma; applies to our respective times, so I now consider the amount of light emitted to be

&gamma;L. Let's call the energy lost thereby E'

Hold on. The frequency of light will not be the same for me.

If you're coming towards me, the light will be blueshifted. If you're moving away, the light will be redshifted.

[Edit: Bad argument (ignoring intensity) removed.]

[Edit: I see that L is neither time nor length. In that case you certainly haven't justified why there's relativistic dilation of it.]

so now E = L, and E' = &gamma;L

As stated above, I disagree that the relationship is this simple. But assuming that...

and the difference between E and E' is

E' - E = &gamma;L - L = L(&gamma; - 1).

Remember &gamma; can be written as (1 - v²/c²)^-1/2. This is known as a binominial, and there are standard ways of expanding such things using the Binomial thereom (approximate) or the Taylor series (exact)

For example (1 - x)^-1/2 can be written as a converging series

1 + 1/2x + 1/8x² + 1/16x³....

where x = v²/c², as here, then terms represented by x² etc can be ignored, because they yield v⁴/c⁴ etc

Why? As v approaches c, ever more of those terms will be significant. If we're at speeds where &gamma; is significant, this is a very bad approximation.

so we can write E' - E = &Delta;E = L(1 + 1/2v²/c² - 1)

&Delta;E = L(1/2v²/c²) = 1/2L(v²/c²) = 1/2(L/c²)v²

But as we are here dealing with energy of a moving body, &Delta;E can differ from the kinetic energy only by a constant C which can be ignored because it is unchanged by the emission process.

&Delta;E is supposedly the difference between the energy lost as seen by the object and you, right? How can you then relate &Delta;E with kinetic energy?

As KE = 1/2mv², this implies

1/2mv² = 1/2(L/c²)v²

and L/c² = m

as L = &Delta;E,

That's not what you wrote above. There you had

&Delta;E = L(1/2v²/c²)

then m = &Delta;E/c²

i.e &Delta;E = mc²
I don't think I can agree...

Woah.

Isn't the total energy of a mass moving wrt me:

E = γ * mc²

?

I don't think I can agree... I agree with that statement. That is - I don't agree.

Woah.

Isn't the total energy of a mass moving wrt me:

E = gamma * mc²

?
That's what I thought, too. &Delta;E is certainly not what I remember...

Woah.

Isn't the total energy of a mass moving wrt me:

E = γ * mc²

?

Yes, E = mc² + K = γ * mc²

I wish I had the derivation on me, but I am sure it is online somewhere too.

I agree with that statement. That is - I don't agree.
But if all Cretans are liars...

;)

Ok, so are we stuck on this for some reason?

(BTW: This statement is false...)

Ok, so are we stuck on this for some reason?

(BTW: This statement is false...) I contend that. First of all, you stated a question, not a statement. Second, how can a question be false? :m:

OK, what statement are you refering to?

Yes, E = mc² + K = γ * mc²

I wish I had the derivation on me, but I am sure it is online somewhere too.
I think E = mc² + K (K being kinetic energy, I presume), is only valid a low speeds, because it's an approximation of &gamma; using only the first two elements of the series QuarkHead showed.

I think. It's late here as well...

[Edit: Yes, that's it. It pops out perfectly. However, the expansion is wrong.]

:D

Post whoring on sciforums! Who would have thunk it...

Aer, it was a joke. Forget it.

I think E = mc² + K (K being kinetic energy, I presume), is only valid a low speeds, because it's an approximation of &gamma; using only the first two elements of the series QuarkHead showed.

This may be true, like I said - the equation came from vague memory.

Aer, it was a joke. Forget it. I figured as much - just nevermind :D :m:

Well this went absolutely no where I wanted it to, ahh well. At least we all figured out what E is I think.

I completely agree.

mc² + K is a low speed approximation while

γmc² is the rigorous solution.

I don't think I understand what this thread is about. Anyway...

The total energy of a particle such as an electron is:

E = gmc²

where g is the Lorentz factor, m is the particle's rest mass and c is the speed of light.

We can also write:

E = K + E₀

where K is the particle's kinetic energy and E₀ is the particle's rest energy. That is:

E₀ = mc²

The relativistic kinetic energy is then easily seen to be:

K = (g - 1)mc²

which for g close to 1 (v &lt;&lt; c) reduces to approximately

K = (1/2)mv²,

the usual Newtonian expression for kinetic energy.

Hope this helps.

I have a few questions. The last time I saw the derivation was probably 10 years ago, but it was definitely different.

Yes, and the proportionality factor is the frequency of the light times Planck's constant, right? E=hf?In this particular context, frequency doesn't enter into it.

As v approaches c, ever more of those terms [i.e.fourth and higher order] will be significant. If we're at speeds where &gamma; is significant, this is a very bad approximation.The argument is one of principle, in such cases it is usual to drop higher order terms.

That's not what you wrote above. There you had

&Delta;E = L(1/2v²/c²)Ooops, you are right, I fluffed. It should have been
The ending should be "E = L......E = mc²". Sorry, I'll amend, if we can now agree.

Woah.

Isn't the total energy of a mass moving wrt me:

E = γ * mc²

?
But I wasn't asked about the total energy. You specifically asked me to show the derivation of the mass-energy relation, which is what I tried to do. You are now answering a different question, and this is true of all posts which follow.

In this particular context, frequency doesn't enter into it.

Then you're going to have to be more precise about what L is, and precisely why it is relativistically dilated.

The argument is one of principle, in such cases it is usual to drop higher order terms.

No. In this case, you're not justified in dropping the higher order terms, because you're not at speeds where the approximation is good. Try plugging in some different values for v, and you'll see what I mean.

Ooops, you are right, I fluffed. It should have been
The ending should be "E = L......E = mc²". Sorry, I'll amend, if we can now agree.
Now I'm totally confused. Is L supposed to embody all the energy of the moving object?

But I wasn't asked about the total energy. You specifically asked me to show the derivation of the mass-energy relation, which is what I tried to do. You are now answering a different question, and this is true of all posts which follow.
But the mass-energy relation is about total energy...

E = &gamma;m₀c²

Expand &gamma; with your Taylor series, approximate to the two first term, i.e. assume v << c, and you get

E &cong; m₀c² + ½m₀v²

[Edit: That Taylor series is wrong. See below. The above still stands, though.]

Then you're going to have to be more precise about what L is, and precisely why it is relativistically dilated.L is defined inter alia as the energy of the emitted light. Before emission, the body has energy, say, E_i and after emission has energy E_f. So E_i - E_f = &Delta;E = L

No. In this case, you're not justified in dropping the higher order terms, because you're not at speeds where the approximation is good. Try plugging in some different values for v, and you'll see what I mean.We are not working with any particular velocity. And even with v = c, the fourth and higher order terms make a negligible contribution.

Now I'm totally confused. Is L supposed to embody all the energy of the moving object?No, it's the energy withdrawn from the body in the form of light. Let me quote Einstein, from his second relativity paper (1905) which I have open in front of me:

"If a body gives off the energy L in the form of radiation, then its mass diminishes by L/c². The fact that the energy withdrawn from a body becomes energy of radiation evidently makes no difference, so we are led to the more general conclusion that:
the mass of a body is a measure of its energy-content"

QuarkHead,

Not to put too fine a point on it but you said:


Quarkhead:

You specifically asked me to show the derivation of the mass-energy relation
And I said:


Me:

Why not just write the complete equation for the mass-energy relationship for a particle and we move on?
Note the words "complete equation".

But I wasn't asked about the total energy

Yes, you were.

Nowhere did I ask for derivations of anything but you seemed desperate to give one. I think this thread was about something more interesting than deriving a relationship we all already understood. Hence my obvious frustration, and Aer's.

L is defined inter alia as the energy of the emitted light. Before emission, the body has energy, say, E_i and after emission has energy E_f. So E_i - E_f = &Delta;E = L

Ok. But then, by relativistically dilating L, you are simply assuming this equation

E = &gamma;m₀c²

and there's no need for the complicated setup.

We are not working with any particular velocity. And even with v = c, the fourth and higher order terms make a negligible contribution.

No.

First of all, you're ignoring from the third term and onwards.

Second, &gamma; goes to infinity as v goes to c. That means that the convergence radius of the expansion must be less than or equal to 1, and it must diverge at x=1. Looking at the series you presented, with v=c (i.e. x=1) the series converges with sum 2, so your expansion is wrong.

Look at the Taylor expansion (http://en.wikipedia.org/wiki/Taylor_series) of the binomial theorem (http://en.wikipedia.org/wiki/Binomial_theorem):

(1 + x)^&alpha; = 1 + &alpha;x + (&alpha;(&alpha;-1)/2!)x² + (&alpha;(&alpha;-1)(&alpha;-2)/3!)x³ + ...

With x = -v²/c², and &alpha;=-½ we get

&gamma; = 1 + ½ v²/c² + 3/8 v⁴/c⁴ + 5/16 v⁶/c⁶ + ...

So, when v is close to c, the third and following terms are very significant, so, yes, taking only the first two terms is the same as assuming v is very small.

Example: Taking v=0.9c the third, fourth and fifth term alone (i.e. their sum) contribute more to the final sum, than the second term. Clearly, ignoring them is a very bad approximation at high speeds.

No, it's the energy withdrawn from the body in the form of light. Let me quote Einstein, from his second relativity paper (1905) which I have open in front of me:

"If a body gives off the energy L in the form of radiation, then its mass diminishes by L/c². The fact that the energy withdrawn from a body becomes energy of radiation evidently makes no difference, so we are led to the more general conclusion that:
the mass of a body is a measure of its energy-content"
Ah, I see what you mean, and why you wrote &Delta;E. But then the mass in your final equation is not the rest mass of either object, but the rest mass which the object has lost by emitting the light, no?

The relativistic kinetic energy is then easily seen to be:

K = (g - 1)mc²

which for g close to 1 (v &lt;&lt; c) reduces to approximately

K = (1/2)mv²,

the usual Newtonian expression for kinetic energy.

Hope this helps. Yes James, this is exactly what I meant for the kinetic energy, I just didn't have the equations on hand to prove my point.

Nowhere did I ask for derivations of anything but you seemed desperate to give one. Then I misinterpreted your question. Remember, though, that when I jumped in, the discussion was distinctly non-technical, and I thought, obviously in a way you found patronising, that I would show the mass-energy relation that everybody knows.

I don't know why you think I was "desperate to give one". I was trying to help.

Remember, though, that when I jumped in, the discussion was distinctly non-technical,
We were discussing the rest energy of an electron. Then you go and say that "rest energy" is the wrong term and proceed to show some derivation:

and I thought, obviously in a way you found patronising, that I would show the mass-energy relation that everybody knows.

About some "mass-energy" relation that only you understand, (what is L again?) which has been widely accepted as erroneous amongst the other members of this forum.

I'm sorry, but I really don't care if you believe your derivation is correct or not - I don't accept it. If you think I am wronging you by stating as such, just keep in mind that it was you who jumped into the conversion between superluminal and I - not the other way around.

Ok. But then, by relativistically dilating L, you are simply assuming this equation

E = &gamma;m₀c²

and there's no need for the complicated setup. Then we are definitely at cross-purpose. I was showing, which was apparently unwelcome' how E = mc² is derived. Not assuming it, as you are.
And L itself is not relativistically dilated, except throught the agency of time dilation.


First of all, you're ignoring from the third term and onwards [in the binomial theorem]. Read what I wrote! I said terms of fourth and higher order, I didn't mention the sequence of terms in the solution (which is arbitrary)

Second, &gamma; goes to infinity as v goes to c. That means that the convergence radius of the expansion must be less than or equal to 1, and it must diverge at x=1. Looking at the series you presented, with v=c (i.e. x=1) the series converges with sum 2, so your expansion is wrong.Yes I agree, I overstated my case in my last to you.


With x = -v²/c², and &alpha;=-½ we get

&gamma; = 1 + ½ v²/c² + 3/8 v⁴/c⁴ + 5/16 v⁶/c⁶ + ...Mmm...for my third and fourth terms I got the coefficients to be, respectively 1/8 and 1/16. I expect you're right, I'll re-check.


Ah, I see what you mean, and why you wrote &Delta;E. But then the mass in your final equation is not the rest mass of either object, but the rest mass which the object has lost by emitting the light, no?Sort of, yes. Although I wasn't trying to draw a distinction between rest mass and "relavistic mass".

Look, apologies all round. I obviously mistook what I was being asked, and at what level I should pitch my obviously inappropriate and unwelcome attempt to help.

And L itself is not relativistically dilated, except throught the agency of time dilation.

But that's the same thing! Assume the object gives of all it's energy as L. Then you are a priori assuming relativistic dilation, when you state that from the embankment frame L appears as &gamma;L. You've not explained why L is relativistically dilated through time dilation, merely stated it was so.

This is fine, because the relativistic definition of the energy of a body with rest mass m₀ is &gamma;m₀c². But since you're implicitly using that, there's no need for the thought experiment; simply set v=0 and the beloved mass-energy relation pops out.

Read what I wrote! I said terms of fourth and higher order, I didn't mention the sequence of terms in the solution (which is arbitrary)

Okay, I was thinking degree of x, you were thinking degree of v and c. Fair enough.

Look, apologies all round. I obviously mistook what I was being asked, and at what level I should pitch my obviously inappropriate and unwelcome attempt to help.
There's no need to apologize. There was a confusion about what the mass-energy relation states, you disagreed, and I for one appreciate the fact that you actually have a derivation for what you mean it states, even if I think you're wrong.

I've been trying to get MacM to show a bit of maths for one of his claims for a week now, and I don't think I'm anywhere near seeing a single equation, and you stepped up willingly when challenged about your interpretation. I respect that, and I would hate for you to stop this practice because we disagree. Everything is so much easier with math...

QuarkHead,

As I said, let's start on a clean footing. I'm in agreement with funkstar here.

There's no need to apologize. There was a confusion about what the mass-energy relation states, you disagreed, and I for one appreciate the fact that you actually have a derivation for what you mean it states, even if I think you're wrong.

I've been trying to get MacM to show a bit of maths for one of his claims for a week now, and I don't think I'm anywhere near seeing a single equation, and you stepped up willingly when challenged about your interpretation. I respect that, and I would hate for you to stop this practice because we disagree. Everything is so much easier with math...

So my main question is, what the hell is this thread about? :confused:

I'm sorry, but I really don't care if you believe your derivation is correct or not - I don't accept it. If you think I am wronging you by stating as such, just keep in mind that it was you who jumped into the conversion between superluminal and I - not the other way around.Right, I'll leave you and Superluminal to it. Good luck!

I've been trying to get MacM to show a bit of maths for one of his claims for a week now, and I don't think I'm anywhere near seeing a single equation, and you stepped up willingly when challenged about your interpretation. I respect that, and I would hate for you to stop this practice because we disagree. Everything is so much easier with math...Ha! Next time you bracket me with MacM, I'll find out where you live and..and..pee in your pond.

Why can't I get this across? The derivation I gave for E = thingy, wasn't my own, it was adapted from Einstein. Is it current thinking? Of course not. Does it take account of quantum realities? No!
But, because I butted in (as I how now been told, rather uninvited) to a slightly less that technical discussion, I thought I would start at the beginning, using an equation that everybody knows.

Oh well.

EDIT: In fact, the more I brood on this, the crosser I get. If any of you can get E = mc² from first principles in any other way - and I do mean first principles- show us how. I know of none.

EDIT: In fact, the more I brood on this, the crosser I get. If any of you can get E = mc² from first principles in any other way - and I do mean first principles- show us how. I know of none.
OK, define first principles - then I'll give it a go.

I for one blindly accept E = mc². Some guy did a lot of hard work to get that and had it comfirmed by a bunch of other hard working guys. I'm told they were fairly smart. (appeal to authority noted, forthrightly and without embarassment re Albert and Co.)

QH:

Ha! Next time you bracket me with MacM, I'll find out where you live and..and..pee in your pond.

Ha! funkstar did that to me too!

Ha! Next time you bracket me with MacM, I'll find out where you live and..and..pee in your pond.

Oh, noes! Don't worry, that wasn't my intention. I simply liked seeing math, for once. 'Tis a bit too rare.

Oh, and superluminal, you did sound an awful lot like you-know-who with that velocity history thingy :p But it was of course, an unwarrented call, because you're actually susceptible to reason, something that seems incompatible with the slightest hint MacM-ism.

Fine, I retract both MacM references. But I'm watching you lot - one cranky post and *BAM*, the MacM label comes rushing! Or it might not... You'll never know. MUWAHahahhaahhhahhh!

*erm* I'll clear off, now.

Fine, I retract both MacM references. But I'm watching you lot - one cranky post and *BAM*, the MacM label comes rushing! Or it might not... You'll never know. MUWAHahahhaahhhahhh!

Now wait a minute - to be a crank, someone has to have a non-mainstream theory all their own and believe it as if God himself wrote it. I don't think you can ever put superluminal under this category - although Quark is close with his little derivation. ;)

So, you still don't like my "velocity history" thingy? I think it dovetails nicely with my notion of referencing the crystal sphere (you know, where the stars are embedded) as a universal reference for the motion of the sun and planets around the earth. Couple that with my bowtie pasta noodle theory of spacetime curvature and you have the makings of a complete TOE. IMHO.

So, you still don't like my "velocity history" thingy? I think it dovetails nicely with my notion of referencing the crystal sphere (you know, where the stars are embedded) as a universal reference for the motion of the sun and planets around the earth. Couple that with my bowtie pasta noodle theory of spacetime curvature and you have the makings of a complete TOE. IMHO. You almost have me convinced - let's see the math. :D :m:

The math? Ha! It's my own system of matrix-convolution and contour integral metric space manipulation in 14 dimensions. It's clearly beyond all of you mere mortals. Ha! Hahahaha!

I don't think I understand what this thread is about. Anyway...

The total energy of a particle such as an electron is:

E = gmc² (...)
James, I hope you don't mind I copied your very good lesson over to physicsforums (http://www.physicsforums.com/showpost.php?p=700194&postcount=27)

There are a lot of very confused individuals over there.

Cross forum pollination! Unholy hybrids! Mutations! Ahhh the horror!

Cross forum pollination! Unholy hybrids! Mutations! Ahhh the horror! As dense as you may think some of the people are here (not going to name names - but a few come to mind), over there is 10x worse! That is why I stopped visiting that forum, but did you ever have this problem where you just forget?

Well I forgot.

Actually, most of the physicists at physicsforums know what they're talking about.

Actually, most of the physicists at physicsforums know what they're talking about. But there are a lot of lurkers that do not! They are who I am refering to.

Most actual physicists seem to stay clear of the relativity forum which is where I was.

Now wait a minute - to be a crank, someone has to have a non-mainstream theory all their own and believe it as if God himself wrote it. I don't think you can ever put superluminal under this category - although Quark is close with his little derivation. ;)
Then I'm afraid you don't know what you are talking about. My "little derivation" was, barring a couple of typos, pretty much that given by Einstein. OK, I answered the wrong question and suffered a lot of abuse thereby. Why? Because people like you haven't read the original literature. Try it, it's a lot easier than you think, and usually goes a lot more slowly than most the the stuff you get by googling, which seems to be your major educational tool.

Oh and by first principles I meant nothing more (or less) than the two postulates of the special theory. We await your solution

Cross forum pollination!
That had me laughing...
Then I'm afraid you don't know what you are talking about. My "little derivation" was, barring a couple of typos, pretty much that given by Einstein. OK, I answered the wrong question and suffered a lot of abuse thereby. Why? Because people like you haven't read the original literature. Try it, it's a lot easier than you think, and usually goes a lot more slowly than most the the stuff you get by googling, which seems to be your major educational tool.

QuarkHead, I actually looked up the 1905 paper, yesterday, and there were several things that are clear in his paper, that are not so in your version (even though his still require thinking). For instance, it wasn't very clear how you link the difference the observed energy loss to kinetic energy, and that constant thingy confused the hell out of me. Also, when the math was wrong, I kinda assumed you were wrong about the idea, since you got the right result. Mea culpa.

Oh and by first principles I meant nothing more (or less) than the two postulates of the special theory. We await your solution
I'm looking forward to this as well.

Problems with language ?

"When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images.
It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature. (Niels Bohr, 1885-1962, on Quantum Theory)"

The problems of language here are really serious. We wish to speak in some way about the structure of the atoms… But we cannot speak about atoms in ordinary language. (Heisenberg, Physics and Philosophy, 1963)

In science one tries to tell people, in such a way as to be understood by everyone, something that no one ever knew before. But in poetry, it's the exact opposite. (Paul Dirac)

What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it. ... That is because I don't understand it. Nobody does.
(Feynman, Richard P. Nobel Lecture, 1966, 1918-1988, QED, The Strange Theory of Light and Matter)

I was thinking that the theory was established till 50’, based on rudimentary experiments, and after that time, the major steps were done especially on math’s and experiments meant to confirm those theories.
Look at the Nobel prize list (http://reference.allrefer.com/encyclopedia/N/NoblPrzTABLE.html ) and you’ll see that after Pauli (’45) and Born (’54), hardly you can see some one in the usual physics books.

Then I'm afraid you don't know what you are talking about. My "little derivation" was, barring a couple of typos, pretty much that given by Einstein.
No it is not. Please show where Einstein gave any such derivation in Einstein's paper (http://www.fourmilab.ch/etexts/einstein/specrel/www/)

Oh and by first principles I meant nothing more (or less) than the two postulates of the special theory. We await your solution
If you think your attempt was using just the first principles of special relativity, then you are terribly mistaken.

Do you at least agree that the total energy is described by:

E = &gamma;mc²?

I'm looking forward to this as well.
It'll be a cold day in hell before I ever try to show any energy derivation based on the postulates of SR! How absurd.

No it is not. Please show where Einstein gave any such derivation in Einstein's paper (http://www.fourmilab.ch/etexts/einstein/specrel/www/)Section 8 was the starting point for a subsequent paper Ann. Phys. 18:632 (1905)


If you think your attempt was using just the first principles of special relativity, then you are terribly mistaken.Right.

Do you at least agree that the total energy is described by:

E = &gamma;mc²?Derive it for us, then I'll tell you if I agree. Unlike you, I don't just spout stuff I read on some web page, I want proof. You provide it.

QH:

Derive it for us, then I'll tell you if I agree. Unlike you, I don't just spout stuff I read on some web page, I want proof. You provide it.

Holy crap, I hope we don't have to derive every well known, fundamental relationship in physics in order to post here. I'm doomed then. I usually find at least three corroborating documents from reputable sources (phys. rev./letters, university websites, Bart Simpsons Guide to Physics, etc.) before accepting something.

Section 8 was the starting point for a subsequent paper Ann. Phys. 18:632 (1905)
That was the section I figured you were refering to.
So what is similar in that section to the derivation you provided?


Derive it for us, then I'll tell you if I agree. Unlike you, I don't just spout stuff I read on some web page, I want proof. You provide it. The very idea of deriving e=mc² from the postulates of relativity is absurd - I am not going to do something absurd!

Your defintion of proof is lacking. Mathematical proofs are not the same as Physics proofs.

All we have to go by is experimental evidence. Not whatever fancy equation we can derive based on a set number of assumptions! If we can prove all our assumptions to be correct by experiment and that there are no missing assumptions needed to get the correct actual physical description of the universe - then we'll be set. Unfortunately it's not possible to prove the negative that they are no missing assumptions. So questions will always linger.

That was the section I figured you were refering to.
So what is similar in that section to the derivation you provided? You don't see it? Let me help you,

E' = &gamma;E(1 - cos&theta;/c)


The very idea of deriving e=mc² from the postulates of relativity is absurd - I am not going to do something absurd! Then derive it from another set of equally reasonable postulates.


All we have to go by is experimental evidence. Not whatever fancy equation we can derive based on a set number of assumptions! If we can prove all our assumptions to be correct by experiment and that there are no missing assumptions needed to get the correct actual physical description of the universe - then we'll be set. Today being the 60th anniversary of the A-bomb on Hiroshima, that comment has something of the flat-earther about it.

You don't see it? Let me help you,

E' = &gamma;E(1 - cos&theta;/c)
You are saying 1 equation is similar to the entire derivation you provided - I don't think so! Two completely different derivations can derive the same thing - that doesn't mean they are both correct! One could be filled with all kinds of holes/errrors.



Then derive it from another set of equally reasonable postulates. my postulate: mass is another form of energy, proof:


Today being the 60th anniversary of the A-bomb on Hiroshima, that comment has something of the flat-earther about it.

There, done.

My point here is, we already know mass is a form of energy - whatever derivation you are wanting doesn't even make sense.

And the flat earth is an assumption proved wrong! A long long time ago as a matter of fact. For whatever reason you brought up that reference is stupid.

my postulate: mass is another form of energy, proof:[Hiroshima]There, done. My point here is, we already know mass is a form of energy - whatever derivation you are wanting doesn't even make sense.



And that's your idea of the scientific method? Then let me say this:
Like everybody else, there are gaps in my understanding, and I make mistakes in my reasoning - everybody does.

But don't you dare presume to be the one to point them out to me.

But don't you dare presume to be the one to point them out to me.
I see, only "other" people can point out your misunderstanding. What is the point of holding a scientific conversation with you if you dare to presume that your knowledge is superior to mine. You fucking putz!

The very idea of deriving e=mc2 from the postulates of relativity is absurd - I am not going to do something absurd!

Why is it absurd? How else do you propose to derive that equation?

Holy crap, I hope we don't have to derive every well known, fundamental relationship in physics in order to post here. I'm doomed then. You see, this is what puzzles me about you google guys. How do you know what you read is true, if you're not interested in the proof? I just don't get it. It's no good saying "reputable sites" if you are not willing to test their judgement.
Nobody expects you to do it yourself, but when somebody tries to do it for you, I'm not sure abuse is the correct response (maybe it's cultural)

You see, this is what puzzles me about you google guys. How do you know what you read is true, if you're not interested in the proof? I just don't get it. It's no good saying "reputable sites" if you are not willing to test their judgement.
Nobody expects you to do it yourself, but when somebody tries to do it for you, I'm not sure abuse is the correct response (maybe it's cultural) Go back and look at my responses, I accepted your derivation as a plausible attempt. But upon trying to verify it, I couldn't accept the steps you took as scientifically sound - maybe I didn't understand something which is why I tried to inquire on definitions. All I got in response was your refusal to regard the derivation as anything but the derivation of Einstein himself - which it is not.

Why is it absurd? How else do you propose to derive that equation? OK James, let's see you give it a go. Derive e=mc² on the principle of relativity and the invariance of c. That is: (1) Every physical theory should look the same mathematically to every inertial observer and (2) The speed of light in vacuum, commonly denoted c, is the same to all inertial observers, is the same in all directions, and does not depend on the velocity of the object emitting the light.

Aer:You then:I'm sorry, but I really don't care if you believe your derivation is correct or not - I don't accept it. And you now: I accepted your derivation as a plausible attempt. But upon trying to verify it, I couldn't accept the steps you took as scientifically sound .See any similarilty? I must be dim, because I see none.

QuarkHead:

You see, this is what puzzles me about you google guys. How do you know what you read is true, if you're not interested in the proof? I just don't get it. It's no good saying "reputable sites" if you are not willing to test their judgement.
Nobody expects you to do it yourself, but when somebody tries to do it for you, I'm not sure abuse is the correct response (maybe it's cultural)

I didn't abuse you for that at all. You can derive fundamental results all you want. You're a better man than me. However, I somehow thought this thread was about more than showing the derivations of known expressions. I suspect that it is completely derailed by this. If I abused you it was for that only.

And us "google" guys have good reasons to do what we do. As you know, I have an engineering education. I am not a professional physicist, but I've been exposed to many aspects of physics.

Are you a physicist? As a professional physicist, how do you intend to get anything done if you disregard peer reviewed results and have to derive every result from scratch? Is this not why we have the peer review system? Are you going to reproduce every experiment that has historical bearing on your recearch? Good luck.

So in my case, if I don't already know something (how did I learn it in the first place???) I look up a number of "reputable" references and make a judgement. The more fundamental it is, the more likely I am to trust it.

E = mc^2 is outside my desire, and probably my ability, to derive. And unless it's an exercise in your math ability, what bearing does it have on this thread?

You then:
I'm sorry, but I really don't care if you believe your derivation is correct or not - I don't accept it.
And you now:
I accepted your derivation as a plausible attempt. But upon trying to verify it, I couldn't accept the steps you took as scientifically sound .

More like:

What is the name of this derivation you provided?

I just wanted to look it up for definitions. Did you make this up - is that what you are saying?

I wanted clarification on exactly what L is and how it is measured - I didn't know if that was too much to ask of you or not, so I'd prefer to just look it up myself.

OK, I guess L is the length of time of light emission. The amount of energy released would also be a function of the intensity of the emission, no?

Also, just like measuring mass, the only proper way to measure energy is in the rest frame of the object losing/gaining energy - I am pretty certain.

I don't think I can agree...
I agree with that statement. That is - I don't agree.

Well this went absolutely no where I wanted it to, ahh well. At least we all figured out what E is I think.


AHH - Here we go, this is where I said that:


We were discussing the rest energy of an electron. Then you go and say that "rest energy" is the wrong term and proceed to show some derivation:

About some "mass-energy" relation that only you understand, (what is L again?) which has been widely accepted as erroneous amongst the other members of this forum.

I'm sorry, but I really don't care if you believe your derivation is correct or not - I don't accept it. If you think I am wronging you by stating as such, just keep in mind that it was you who jumped into the conversion between superluminal and I - not the other way around.



See any similarilty? I see a misrepresentation of myself!


I must be dim
Agreed.

You are absolutely correct - an electron is not a sphere-like particle so to speak which a lot of people tend to think of as an electron.
However, when an electron undergoes two hole diffraction it is detected as a point particle on the scintilation screen.

The wave-particle duality nature of the electron was constructed to explain how the electron can pass through two holes at the same time and thereby produce the well known diffraction pattern. However this is an ad hoc description that does not flow directly from QM mathematics.

Absent in most discussions of this nature is the necessity of including nonloocal force centers in the model describing the motion of the electron, or other QM particles. Absent the inclusion specifically in the electron model, the model is definitely incomplete. See JS Bell 'speakable and unspeakable in quantuim mechanics'. Included in the nonlocal force cenetrs is the phenomenon of "spin"


Geistkiesel :cool:

However, when an electron undergoes two hole diffraction it is detected as a point particle on the scintilation screen. The screen detects the release of a photon, the photon is released at a point.

Aer:

Why is it absurd? How else do you propose to derive that equation?

OK James, let's see you give it a go.

I asked you first.

Why is it absurd? How else do you propose to derive that equation?

OK James, let's see you give it a go.

I asked you first.

HORSESHIT. You asked me to do no such thing. QuarkHead asked me to. I told him, that what he was asking me was absurd. SEE ABOVE. Then I asked you to do it since you seem to believe it is not absurd.

AGAIN, let's see your derivation.

Special Relativity has limited application, that is in flat spacetime. The energy-mass relation is more abstract than that - that is all I am trying to say.