User talk:Edgerck

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Reliance on Information

How trustworthy is the information in WP?

I believe this question is important for all WP users. I am currently conducting an experiment to help answer this question. I hope the answer will be helpful to improve WP and its use.

Since information in WP is dynamic, this question cannot be answered by simply sampling at specific times. Instead, I decided to measure the lifetime of correct information (defined following WP policy), that I seeded in WP edits of selected articles. As an important side benefit, the editing work should provide a concrete editing benefit to WP.

Read more on the Reliance on Information Experiment >>

Comments

Please submit experiment comments on the experiment talk page

Mass and energy in special relativity

How to know that you are being swindled: if the book, course you are taking, or article you are reading differs from the answers given here — complain! These areas (barring any new physics discovery!) are not controversial today.

Read the answers: Mass and energy in special relativity

Truth and trust

Truth is subjective. Wait. No! Subjective truth is a pleonasm.

Why?

Because, subjectively, we usually think that we are right. And what someone calls "truth" is what that person considers to be right. So, this is a full pleonasm.

What? You do not agree? That is not what you think is true? Well, it does not matter! This is the truth.

read more >>

Mass of composite systems

Point 11:

"...or write the energy-momentum relation m² = E² - p² and infer that, in a closed system, mass must be conserved because the energy momentum 4-vector is conserved."

Yes, but we are still allowed to consider the mass of the closed system, which is not the same as the sum of the masses that are in the system. If you let an atomic bomb go off inside an infinitely strong container, then the mass of the container is the same as it was before the explosion. Even if there is no container, one can still define the invariant mass of the system after the explosion, which is not the same as the sum of the invariant masses of the particles after the explosion. That sum will have become less, of course. Count Iblis 18:13, 28 May 2007 (UTC)

If you let an atomic bomb go off inside an infinitely strong container, then the mass of the container is NOT the same as it was before the explosion. See answer #6: Contrary to classical physics, an isolated (free) system can reduce or increase its mass by internal mass energy conversion. For example, mass is not conserved when an isolated body (in a system considered large enough to be closed) emits a photon, or undergoes nuclear fission or fusion (see references in article). Thanks. Edgerck 19:52, 28 May 2007 (UTC)

We are considering a closed system that does not interact with the outside environment. This means that the walls are insulated and cannot radiate any energy away to the outside environment. One can argue that such boundary conditions are not under all cirumstances physically realizable (neutrinos can easily escape and how does one pevent tiny amounts of gravitational waves from leaving the system), but that's a different issue.

If nothing can leave the system, then the total momentum and enrgy of the system remains the same. The mass of the system (considered as a big thing in itself) is the same. This mass is not the sum of the (rest) masses of the particles in the system. If I want to know how much force is needed to accelerate th system as a whole then I need the mass defined in this way.

Just like if you need to know the exact mass of the atom you need to take into account the internal energy of th atom and can't just add the rest masses of the electron to the rest mass of the proton. Although this internal energy is called "binding energy" it has a potential and a kinetic part. The Hamiltonian contains a kinetic term and a potential energy term and in the ground state both terms contribute to the total energy.

If we replace the atom by an "electron in a small box" filled with radiation, then we can talk about the mass of the box, which will remain the same, provided nothing (not even radiation) leaves the box.

The atomic bomb example is just a pedagogical example where we made this box absurdly large... Count Iblis 21:10, 28 May 2007 (UTC)

Even if nothing can leave or enter the system, the mass of the system may change. This is what answer #6, quoted above, says. This is mainstream knowledge today. Edgerck 21:18, 28 May 2007 (UTC)

That's not true, unless you are misinterpeting what the cited article says (in particular the "small print", e.g. nothing leaves but what about radiation?). Also, when considering some reaction involving particles, then the "default" meaning of total mass will usually be the sum of the rest masses of the individual particles and not the invariant mass of the system considered as a whole.

You do understand that a box filled with radiation has a larger mass than the same but empty box? Count Iblis 22:03, 28 May 2007 (UTC)

When physicists say "a system considered large enough to be closed" then nothing enters or leaves, radiation or not. What you call "default" meaning above does not exist -- the total mass of the helium nucleus is not the sum of the rest masses of it nucleons. Your last question is undefined. Nonetheless, in SR, a photon has no mass. So, if an atom emits a photon, the system atom+photon has less mass, even though it has the same energy. Hope this is useful. Edgerck 22:36, 28 May 2007 (UTC)

No, you are completely mistaken here. This is why you should read and understand the physics, and not just use quotes from articles and books as authoritative texts (I'm not saying that the articles you cite are incorrect, just your reading of them). A box filled with thermal black body radiation at some temperature T has a well defined internal energy and therefore it has a well defined mass. This mass has a well defined experimental interpretation as it gives you the inertia of the box.

"the system atom+photon has less mass". You are adding up the invariant masses of the atom in its ground state to the invariant mass of the photon. But this does not give you the invariant mass of the composite system. Now, I fully agree that in practice we are usually interested in the mass of the atom after it has emitted the photon, which is, of course, less than the atom in the excited state. The atom+photon" system's mass is perhaps of academic or pedagogical interest only. But in theory you can imagine capturing the atom plus photon in some system with perfectly reflecting mirrors and measuring the inertia of this system. If we place the excited atom in the box and wait until it has decayed then the the mass of the box will not change.

Have yo forgotten your own your text in which you wrote that the invariant mass of two photons, each with an energy of E can vary from 2E/c^2 (when the total momentum is zero) to 0 (when the total momentum is 2E/c)? Clearly, if you heat a box so that its interior is filled with radiation then, because the total momentum of the radiation plus the walls of the box remains zero, the total energy divided by c^2 will give you the invariant mass. This thus increases by E/c^2 were E is the total energy of the radiation. Count Iblis 23:13, 28 May 2007 (UTC)

I could probably cite hundreds or even thousands of books and articles of authoritative authors in Physics that agree with most of what you say above, including Einstein's 1906 paper on E=mc² when he included the mass of the emitted photon in the mass of the box. Today, however, we know that this is not correct because the photon is massless.

Regarding you conclusion above, it does not follow from my text on the mass of a two photon system (which I quoted from Wheeler, referenced). If you disagree, please try to publish it in a peer-reviewed physics journal and you will see what other physicists have to say about it. Thanks. Edgerck 23:47, 28 May 2007 (UTC)

Yes, quoted and referenced, but not understood correctly. I think this is perhaps an unexpected result of your wikipedia experiment. There is no substitute for discussing things from first principles. You can quote things as much as you like, but if you don't understand it, then the quotations aren't worth all that much.

Have you not noticed that if the mass of the two photon system is 2E/c^2 the total momentum of the two photon system is zero? Doesn't this ring any bells? If you start with para-positronium (bound state of electron and positron, total angular momentum is zero) then after it decays into two photons, the photons move in opposite directions (momentum is conserved). Count Iblis 00:04, 29 May 2007 (UTC)

Of course you know you're right. But unless you (one day) agree on what I wrote above:

Nonetheless, in SR, a photon has no mass. So, if an atom emits a photon, the system atom+photon has less mass, even though it has the same energy.

the best we can do right now is stop. This thread exemplifies what I observed before, that WP editing rules are nonsensical. People get angry over an impossible proposition. Truth is subjective. An editor cannot write what he does not agree on. But anyone can edit.

So, I find that WP's rules are putting us both at odds, and that is not what I personally want. It is not my truth. Thank you. Edgerck 00:17, 29 May 2007 (UTC)

Ok, but three final points. First of all I'm not angry (I'm used o discussing with people who I strongly disagree with). Anger has, i.m.o. no place in open and frank discussions. Second, I agree that the wiki rules all by themselves won't get you very far. A procedural discussion like X says P but Y says Q is not as insightful as discussing P and Q directly from first priciples while leaving persons X and Y outside the discussion (but they can be cited in the article).

Third, back to the physics, if the system is a hydrogen atom you agree that the mass is not the sum of the masses of the electron and the proton, but if the system is an atom plus photon you are using this rule, which, you yourself acknowledge, does not hold in general. The mass of the combined system is always the energy of the energy in the zero momentum frame. The value of that energy is, of course, due to the energies of the contituent parts, the binding energies etc. etc.

Perhaps your reasoning is that the difference in mass between proton plus electron and the sum of the two parts is due to binding energy bt the photon is not bound in the system atom plus photon.

However, you then forget that the binding energy of the electron in the hydrogen atom is part kinetic and part potential. The expectation value of the kinetic energy "<psi|p^2/2m|psi|>" is not zero. Without this, the binding energy would be even larger (i.e. ground state energy would be even less).

Anyway, i.m.o. you should take rules of physics more seriously than the wikipedia rules. Why one rule for one closed system (atom plus photon in a box, total momentum = 0) and another for another closed system (electron plus proton in a box)? Count Iblis 00:42, 29 May 2007 (UTC)

Thanks for the WP comment. I do not want to convince you about anything. I value free-thinkers. I think a starting point would be if you agree with those phrases. It's OK if you don't; I value you as a human being just the same. A lot of people don't even know the question and yet have perfectly nice and rewarding lives. Thanks. Edgerck 00:55, 29 May 2007 (UTC)

--

I wanted to point out the following from Taylor & Wheeler, "Spacetime Physics" in the section "Use and abuse of the concepts of mass", pg 247.

Q: Does the explosion in space of a 20 meaton hydrogen bomb convert .93 kilogram of mass into energy....

A Yes and no! The question needs to be stated more carefully. Mass of the system of expanding gasses, fragments and radiation has the same value immediately after explosion as before; mass M of the system has not changed.

This directly contradicts some of your points, which also seem to lack internal consistency.

i.e you write earlier in the thread

If you let an atomic bomb go off inside an infinitely strong container, then the mass of the container is NOT the same as it was before the explosion.

This is directly inconsistent with the above quote from Taylor & Wheeler (which you yourself quote from) - it is also inconsistent with your correct statements about the energy-momentum 4-vector of the system (in this case, the bomb) being both conserved and invariant.

If you write the energy-momentum 4-vector of the bomb before the explosion, and after the explosion, how can you possibly believe that energy is conserved (the same before and after the explosion), that momentum is conserved (the same before and after the explosion), but the invariant mass (E^2 - |p|^2 in geometric units) somehow changes?

Several other posters have pointed this out to you already, but I thought I would do so along with some references. Pervect 07:24, 31 May 2007 (UTC)

TALK page question on mass

...apologize if I misunderstood you, but I read you think that mass is conserved in SR. You seem to link it to the invariance and conservation of 4-momentum. Can you please clarify? Otherwise, we agree that mass of the system is defined to be the magnitude of the energy-momentum 4-vector and is thus an invariant. Thanks. Edgerck 23:10, 28 May 2007 (UTC) Retrieved from "http://en.wikipedia.org/wiki/User_talk:Sbharris"

Answer: Yes, invariant and also independently conserved. I link mass to invariance and conservation of 4-momentum, since the best definition of mass (particle and system mass) in SR is the norm of the summed 4-momenta of the system. Invariance and conservation are different things, of course, but 4-momenta has both properties. Energy and momenta are not frame-invariant due to depending on frame for definition, but both are conserved over time, if you stay in the same inertial frame. 4-momentum is BOTH conserved AND invariant, and so avoids this problem. What you weigh on a scale is actually the norm of 4-momentum of the system you weigh. Fly past at high V and E/c^2 changes, but the scale shows the same weight. You need weight (and therefore also mass) to be an invariant, and not just total energy/c^2. It is actually 4-momentum which is closely connected with what we normally call "mass" in GR. The stress-energy tensor is just 4-momentum plus 3 4-momentum fluxes at a point, and although the stress-energy is not Lorentz invariant, it is also only mass-energy concentration at a point, and needs integrating over a volume to give you a classical mass. When you do that, you find the result IS Lorentz invariant, so long as you integrate out to flat space so there's no question of having taken care of the warpage of the G field that results from shifting frames. Mass charge is rather like electric charge-- the field is compressed in different frames but a version of Gauss' theorem keeps the source constant. But the same cannot be said of total energy of a system (which just gets bigger and bigger the faster you fly by it) and so that's another reason that E/c^2 is a bad definition for mass. Obviously total energy has nothing to do with gravity, if you sum up gravity in all directions over a decent volume. 4-momentum is a better candidate for the conserved quantity which is connected to the G field, and which is invariant with proper integration techniques. SBHarris 00:09, 29 May 2007 (UTC)

Let's stay within SR and start with the 4-momentum, if that is OK for you. To me, if a quantity is invariant, then it will have the same measured value in any inertial reference frame; if a quantity is conserved, then its value, as measured in a particular inertial reference frame, does not change over time. Please just let me know if you agree, yes or no, before I continue. Thanks. Edgerck 00:44, 29 May 2007 (UTC)

Yep. Agree. 4-momentum for systems is both conserved and invariant. Energy and momentum for any closed system are conserved over time and over interaction, but (due to frame-dependence for their very definition) are NOT invariant. Moreover, since proper mass (also called invariant mass) of a system is the norm of its total 4-momentum, this quantity is also (like 4-momentum) both conserved and invariant. SBHarris 01:03, 29 May 2007 (UTC)

Mass is an invariant but is not conserved in SR. Mass can be converted to massless energy (photon), even 100% (mass annihilation). Thanks. Edgerck 05:28, 29 May 2007 (UTC)