Talk:Special relativity/Archive 17

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Archive 15

1905?

The special theory of relativity was proposed in 1905 by Albert Einstein in his article "On the Electrodynamics of Moving Bodies".

Please note that Einstein did not, in fact, live or was conceived in 1905.

Zeroxy 04:26, 17 May 2007 (UTC)

Actually, Einstein was born in 1879 and was 26 years old in 1905 when relativity theory was published.

This introduction is misleading and technically incorrect for a purist. The 1905 paper is not special relativity in the sense we know it but a larger theory which introduced the special relativity theory as an introductory kinematical theory prepatory to the electrodynamics theory. The term "Theory of Relativity" is first used by Einstein only in his 1911 paper in which it is made clear that this term applies to the kinematical part of his 1905 theory. So what we call special relativity is really a subset of the entire theory. But common usage has come to apply this term to the kinematical and the electrodynamical parts of Einstein's theory.

Many people fail to realise that Einstein's theory is not contained in the 1905 paper alone, and thus fail to read his other papers of 1907 (this is really the most important one of all, more so than the 1905 paper), and the papers of 1910 and 1911, which discuss the relationship of the theory to the problem of the ether in greater detail. All of them should be read as well as the 1912 unpublished version which has only recently been published. The reader is urged to consult Einstein's Papers, a set of books which contains these papers as well as those on general relativity and other interesting bits of information. 72.84.67.164 15:13, 9 July 2007 (UTC)

Confusion. Help needed

I am confused a bit by relativity so I have a question. It stems from a lot of things, most noteably a film I saw on YouTube, of all places! It explains Special Relativity by giving an example of a moving train, which from the stationary observer's point of view was hit by lightning simultaneously and from the observer in the train the train was struck first of all by the one in the front and then the one on the back - but isn't that merely an optical illusion? I shall explain my reasoning. The stationary observer will have seen the truth of the matter as the light at the front would have less distance to travel by the pace the train was travelling at would fool the moving observer.fleebfleeb

Hello confused. ask yourself how can you tell which observer is moving and which one isn`t. if you can`t answer that question, your reasoning falls apart.Dauto 02:48, 23 May 2007 (UTC).

This talk page is for discussions about the content and the format of the article. It is not for helping you understand the subject of the article. Your question stands a good chance of getting properly and adequately answered on Usenet group sci.physics.relativity. Good luck. DVdm 21:02, 20 May 2007 (UTC)

Mass-energy equivalence bullet

New text, improving on the apple example to show that mass is indeed convertible to energy:

Equivalence of mass and energy, E = mc² — mass can be converted to energy. In particular, the mass of two apples together is less than the mass of each isolated (free) apple, the mass difference being the energy that is released when the apples are brought together, divided by the speed of light squared.

Edgerck 01:35, 22 May 2007 (UTC)

You need to mention the gravitational potential energy for clarity. I think you mean "mechanical energy" by "Newtonian energy". However, when we do calculations in relativity we use the appropriate relativistic definition of energy. Count Iblis 02:12, 22 May 2007 (UTC)

Also "Mass to energy conversion is NOT necessarily a violation of classical (Newtonian) energy conservation". Just take two systems of hard spheres one with total energy E1 and the other with total energy E2. Let them exchange energy by exchanging spheres. If the total number of spheres in each system doesn't change but the total energy in each system does change, then the mass of each system does change. Count Iblis 02:38, 22 May 2007 (UTC)

Count Iblis is essentially correct. If anyone is out of the mainstream of physics here, he is Edgerck. The momentum four-vector (including energy) is proportional to the velocity four-vector. Mass is just the proportionality "constant". If we eliminate the constant from the equations, we get

{\vec {p}}c^{2}=E{\vec {v}}.

Energy should be defined in such a way that it is conserved. This requires that it include the energy due to rest mass as well as kinetic energy. JRSpriggs 04:21, 22 May 2007 (UTC)

"Conservation of energy implies that in any reaction a decrease of the sum of the masses of particles must be accompanied by an increase in kinetic and potential energies of the particles after the reaction." was introduced by Ems57fcva and is in direct contradiction to "the mass of two apples together is less than the mass of each isolated (free) apple, the mass difference being the energy that is released when the apples are brought together, divided by the speed of light squared." -- which is correct. The last phrase after this one, inserted by the same user, is also not correct. Editor Ems57fcva should revert or declare a dispute since this item was already in discussion here.

If the apple example above does not appeal to some editor's appetite, I suggest replacing it by: "The mass of a helium nucleus (that has two protons and two neutrons) is somewhat less than two times the proton mass plus two times the mass of a neutron." This phrase, which also contradicts the current version, is supported in mainstream literature, including Kenneth R. Lang, Astrophysical Formulae, Springer (1999), ISBN 3540296921

I hope this is useful. Edgerck 09:58, 22 May 2007 (UTC)

I don't see a contradiction. The reason that the mass of a helium nucleus is less than that of the individual particles is because, after you bring two protons and two neutrons together, they emit energy (I guess in the form of gamma radiation). See Binding energy#Mass defect.

The sentence "Ems57fcva should revert or declare a dispute" implies a rule which I have never seen here, so that rule probably does not exist. -- Jitse Niesen (talk) 10:24, 22 May 2007 (UTC)

Hmmm, I have to admit that I'm no longer very sure about it. But I think the energy balance is as follows. When bringing the separate neucleons together in a bound nucleus, we get a decrease in potential energy and a decrease in mass; these are balanced by an energy increase carried away by the gamma radiation. -- Jitse Niesen (talk) 10:42, 22 May 2007 (UTC)

Jitse: The rule is that the person doing the reversal #3 (CI in this case) should NOT, and the reversal #3 should be reverted. Ems57fcva knows this rule, and mistakenly (in good faith, I believe) warned me about the reversal #3, and then changed himself to what he wanted without discussion here.

The contradiction is that the "decrease of the sum of the masses of particles" is NOT "accompanied by an increase in kinetic and potential energies of the particles after the reaction." After the reaction, the energy corresponding to the mass defect was released as radiation and is not present in the kinetic and potential energies of the particles.

Hope this is useful. Edgerck 10:50, 22 May 2007 (UTC)

But the usual way of writing down such reactions is by including the photons (if there are any). An kinetic energy is, by definition, the energy minus the rest mass (times c^2, but I always use units such that c = 1). So, there is nothing wrong even if "the energy is carried away by radiation". Also, the energy doesn't need to be carried away by radiation at all. Consider e.g. a collision between two protons yielding three protons and an anti-proton. Sum of rest masses are not equal on both sides. Kinetic energy is (partially) converted to "rest mass energy", total energy is conserved. Count Iblis 14:21, 22 May 2007 (UTC)

CI: Please think why you are insisting on energy conservation in a bullet point about E=Mc^2. You are mixing things. On my edit listed at the head of this item, I would delete the apple example on second thought (as I see it is a bit long graphically) -- but, at least, it is not wrong and even longer, as what is currently there. Hope this is useful. Edgerck 19:03, 22 May 2007 (UTC)

Can you explain what is wrong with the current formulation (I mean the physics, not the length of the text)? Please no references, just explain it from first principles. You, me and most other regular editors are all experts in physics. Special relativity is almost a high school level topic. Count Iblis 20:19, 22 May 2007 (UTC)

CI: if you so kindly ask, I offer three contributions. First, please read my edits from the archives, as they stand by themselves and include verifiable references, as I would probably not explain them otherwise. Second, you could follow my additional comments above (all supported by their references as well). Third, please take a look at #9 (and others) in my read-only repository of current themes in special relativity, all with references, at Mass and energy in special relativity. Hope this is useful.Edgerck 20:56, 22 May 2007 (UTC)

Edgerck, unfortunately, this is not helpful. I'm an expert in special relativity and I don't need to study this subject. You are the one who has poblems with the text and you give me a few references?? What am I supposed to do with that?

You write that a system of two photons each with an energy of E can have an invariant energy ranging from 2E to zero. True, but then in the system's zero momentum (a.k.a. "rest") frame, the invariant energy is equal to the total energy. So, the relevance of all this plus the refs to Okun etc. etc. are all irrelevant unless you can point out the relevance. Since relativity is a very simple topic it can all be explained from first principles. Most likely you are using some nonstandard definitions.... Count Iblis 21:39, 22 May 2007 (UTC)

CI: You are the one who changed my edit to something incorrect, so you are the one who needs to tell me why you did so -- because I do contest your reversal. Reversal without justification, when requested as I did to you, is vandalism. I hope I don't have to call a dispute. Further, I did not write that "a system of two photons each with an energy of E can have an invariant energy ranging from 2E to zero." Maybe you are just not communicating what you think. I am going to let you take some time to read on. If you don't have the references at hand, you can find some of them in books.google. You can write to those authors as well. Hope this is useful. Edgerck 21:58, 22 May 2007 (UTC)

No, I'm not going to do that. You are the one who is claiming that energy is not conserved and invoking non standard notions such as "Newtonian Energy". We don't need references for such an elementary topic as this. It only complicates matters as different authors may use different conventions. And some nonstandard definition used by you is the source of the problems anyway. This can be most easily cleared up by you by explaining things without using any references.

Avoiding refences forces you to get to the hearth of the matter. In fact, I recently had a dispute with some editor about the asymptotic expansion of the Barnes G-function that was entirely caused by the other editor geting confused by a reference that uses different conventions.

Also, note that I did not keep on reverting you. Your last version was reverted by EMS, who agreed that my version as better than yours... Count Iblis 22:39, 22 May 2007 (UTC)

CI: I kindly remark that I did not claim that energy is not conserved. Please recall that you reversed my edit 3x in less than 24h, in violation of the 3RR. I am formally asking you to please explain your reversal. Thanks! Edgerck 22:52, 22 May 2007 (UTC)

Reverting 3 times is the limit. Reverting 4 times is a violation of the rules. And note that I did not revert your last edit. That would have been a violation of the 3RR rule. But I wasn't exactly counting the number of reversions I was making. The reason why I let your last edit stand was because I thought it was a bit better than the previous versions of your edits. Also, it is a good thing to let others have a look and let them make changes. EMS reverted your edits later...

The reason I changed the text was because it suggested that the total energy can change. I therefore explained that E = M c^2 simply means that the energy content of a mass in its rest frame is Mc^2. This is ultimately the meaning of this equation. The fact that a change in M can lead to energy being released as radiation etc. is a consequence of this. Count Iblis 23:34, 22 May 2007 (UTC)

I kindly remark that the text did not suggest that the total energy can change. In fact, this is the article bullet text that you reversed (btw, I think you reversed my texts more than 3x in 24h, but who is counting?)

Equivalence of mass and energy, E = mc² — mass can be converted to energy. In particular, the mass of two apples together is less than the mass of each isolated (free) apple, the mass difference being the energy that is released when the apples are brought together, divided by the speed of light squared.

I see no reason to change it. The text uses E=mc²and specifically talks about the mass difference and its energy equivalence to keep total energy constant, to wit: (mass before - mass after)c² = energy released. The text also does not needlessly repeat the formula in words (what's the point?). Please (you or EMS, it's just the same for me), revert to the text that I had worked on before. Thanks! Edgerck 23:58, 22 May 2007 (UTC)

Edgerck, I just looked at the history of the page and I noticed that you made changes that were reverted by some others (all of whom are experts in this topic) over the last few days. So, I think you should just discuss why the changes you want are necessary.

About the apples, you need to mention the gravitational potential energy for clarity. But this two apple system, for which the mass is indeed less than the sum of the masses of the individual apples, is a bad example. The effect is so small that it is swamped by other effects. E.g. a tiny charge on the apples would undo this effect. You can't put the apples on top of each other, because then the elastic deformation energy of the bottom apple is much larger than the mutual gravitational energy.... Count Iblis 01:40, 23 May 2007 (UTC)

Edgerck - The point of the repetition is to drum the idea into people's heads. I will let the fact that others are not reverting my edit (but are reverting back to it after vandalism) speak for itself. As for the apple business: The issue is its utility and not its correctness. Part of what Count Iblis is trying to tell you is that this example says too much and too little at the same time. You are bringing up the issue of gravitatinal potential and then assuming that the reader will make the connection without further elabotarion. To make matters worse, the needed elaboration will turn the bullet point into a full paragraph, and this is just of proper inthis article. --EMS | Talk 05:45, 23 May 2007 (UTC)

CI and EMS: I already discussed all clarifications on my edit. I stand by it: it's way better than the current text, which is incorrect, off-topic, and even longer. But, for right now, I just want to leave the matter in your hands and in the hands of the community. I'll be much happier if you revert your edits yourselves. I hope this is useful.Edgerck 07:19, 23 May 2007 (UTC)

Section on 'comoving'

In the sentence Since there is no absolute reference frame in relativity theory, a concept of 'moving' doesn't strictly exist, as everything is always moving with respect to some other reference frame., should concept of 'moving' be concept of 'stationary'? I'm no expert in this field but it felt like it read incorrectly. I say this because you then introduce the concept of 'comoving' which seems to replace 'stationary' with a more accurate term, rather than 'moving'. 194.203.31.210 09:09, 23 May 2007 (UTC)

I do not see any section named special relativity#comoving. Could you be more specific about where it is? JRSpriggs 11:12, 23 May 2007 (UTC)

"potential energy is included in mass"

What was meant is the mutual potential energy of unbound particles or potential energy of the particles in an external field. The mutual potential energy of two particles contributes to the (invariant)mass of the two particle system, not to the mass of the individual particles.

No. According to NPOV refs. and the energy-momentum equation (E² = m² + p²), the sentence "The mutual potential energy of two particles contributes to the (invariant)mass of the two particle system" is better left unsaid. Edgerck 17:01, 6 June 2007 (UTC)

In that case, I suggest we dump these so-called "NPOV refs" as they cannot be used to let someone gain an understanding of special relativity. Count Iblis 18:29, 6 June 2007 (UTC)

But anyway, I do think that omitting "potential energy" improves the sentence because of confusion. Usually it is used to mean the potential energy of a bound state, but then that bound state is considered as a particle with some mass... Count Iblis 13:05, 3 June 2007 (UTC)

Ed Gerck is testing reliance on information in WP

See here. Count Iblis 17:19, 3 June 2007 (UTC)

This sounds like a violation of Wikipedia:Don't create hoaxes which, among other things, says "Please do not attempt to put misinformation into Wikipedia to test our ability to detect and remove it.". JRSpriggs 06:03, 4 June 2007 (UTC)

This is not a hoax, was announced widely in the proper WP lists while it started, and there was NO incorrect information inserted in my edits. My experiment rules make this absolutely clear.

Regarding WP purpose's, I edited exactly those articles that were NOT neutral. All my edits are documented and explained.

All my edits represented an honest attempt to improve verifiability and neutrality of the articles, which were biased to use outdated information. If, because I am not perfect and the volume of my edits was very large, any of my edits contain material that is found to be incorrect, that can be taken into account as I explain in my experiment's conditions for impartiality.

Further, I did not take an anonymous identity exactly so people would understand that this is an honest attempt to 1) improve some WP's "eye-sore" articles; and 2) see how long that improvement would last, be improved more, or just disappear. Thank you. Edgerck 17:46, 4 June 2007 (UTC)

Edgerck kept adding back "any mass can be converted to energy" after it was correctly removed (I just wish that I had removed it myself). This is the addition of misinformation. Energy is not something distinct from mass. Rather mass is a subclass of energy. Energy can change form, but the amount of it does not change (within a fixed inertial frame in special relativity). Mass is the energy in the rest frame of the object. And thus it is the total energy minus the kinetic energy (of the object as a whole, i.e. not including motions of parts relative to each other) in any inertial frame. JRSpriggs 04:36, 5 June 2007 (UTC)

I am beginning to see this whole episode as a violation of WP:POINT. Ed Gerck - It is not a fair test of information retention on Wikipedia for the information to be at all controversial either in its content or placement. It also does not help that you have not done much to generate a consensus regarding the matter of mass/energy. My overall view is the Wikipedia is fairly good at retaining information, but very lousy at retaining opinions. IMO, it is your opinion regarding the mass/energy relationship that was removed, and not necessarily the information behind that opinion. --EMS | Talk 15:53, 5 June 2007 (UTC)

I`ll have to come in edgerck`s defense here. he`s got a point when he says that rest mass is an invariant (AKA 4-space scalar) while Energy is the time-like component of a 4-vector. these are two different kinds of objects. But some authors choose to use the word mass to mean the relativistic mass, and that mass is not an invariant. It can be obtained from the energy by use of the famous formula: E=mc^2. So, at the end, it all comes to a matter of semantics. What do we mean by mass? do we mean the rest mass? if so, then edgerck is right. do we mean the relativistic mass? if so, then he is wrong. The real question here then is: what do we choose to mean by th word mass? I vote on edgerck`s side just because it seems wastefull to me to reserve the word mass to mean something as redundant as the relativistic mass (After all that`s just the energy times a constant that I usually set to 1 anyways...)

You miss the point. Ed claims that since an atom loses mass after emitting a massless photon, that mass is not conserved in SR. Thus, he's wrong no matter WHAT definition of mass is used. In fact, system mass is conserved for any given single observer (single frame) during such a reaction in a closed system, whether the system "mass" spoken of, is the relativistic or invariant sort. The difference is that the system mass is an additive property of the individual system component masses if we use relativistic mass (even the photon has a mass, there), but it isn't, if we use invariant mass (the closest we get is that in one special frame, the COM frame, system mass is the root-of-sum-of-squares of individual masses). But that's a sort of geometric sum, not an ordinary algebraic sum.

In any case, most physicists prefer to give up mass additivity in systems when they already have energy and momentum additivity, in order to define system "mass" as something which is not only conserved in closed systems for single frames (like energy and momentum) but also is Lorentz invariant for systems and across reactions (unlike energy and momentum), and thus is the same in any frame.S B H arris 02:10, 6 June 2007 (UTC)

Perhaps we are focusing too much on the meaning of "mass" here. I think the real disagreement is over "converted". Since I and (I think) most readers will understand "converted" to mean something like — breaking a table into its component pieces of wood and building two chairs with them is converting a table into two chairs. Mass is definitely not converted to energy in that sense regardless of how you define mass. However, one could say, for example, that the energy of rest mass is converted to the energy of radiation in certain reactions. JRSpriggs 05:34, 6 June 2007 (UTC)

Convert: change the nature, purpose, or function of something; "convert lead into gold"; "convert hotels into jails"; "convert slaves to laborers". So, "convert mass to energy" is fitting to the definition, and is also widely used in physics in the same use (see refs. given), even though crank websites that I cited elsewhere insist otherwise. Mass and energy are not two forms of the same thing (notwithstanding what WP says today), which also makes "convert" the correct word to use.

Mass is defined in terms of energy (i.e. the total energy of the system in the zero momentum frame)and it is therefore just energy. The fact that mass is an independent property for a particle than it's total energy is just an artefact of the way we defined it. Count Iblis 18:43, 6 June 2007 (UTC)

We all know the NPOV refs. deny that mass is "just energy". For example: to every mass there's a corresponding energy but there's not a corresponding mass to every energy; mass is a scalar while energy is the time component of a 4-vector. Mass and energy are apples and speedboats. Edgerck 03:22, 7 June 2007 (UTC)

I know that Okun is a proponent of the idea that mass is something completely diferent from energy. He uses arguments like you gave. But ultimately this is a metaphysical discussion. You can't prove it one way or the other way. I mean, ultimately apples and speedboats all consist of atoms. Similarly, in physics if you put h-bar = c = G = 1, everything becomes dimensonless and if there were physical quantities that are fundamentally different from each other, that difference becomes irrelevant as far as the physics is concerned.

Of course, you could argue that there quantities that are fundamentaly different but that we can pretend otherwise. See a discussion with Okun, Duff and Veneziano on this matter here.

Regarding loss of mass by an atom upon emission of a photon, this is stated very clearly and verbatim in the literature cited (Okun and others).

Agreed. Count Iblis 18:43, 6 June 2007 (UTC)

Regarding the mass of an atom+photon system being less than the mass of the atom before the photon is emitted, in other words, that the mass out is different from the mass in, this is not a privilege of the atom+photon system and can be found cited in many texts, that I ref'd as well.

The above two points are not relevant to the bullet point edit that I introduced. The first one is. Thank you. Edgerck 16:56, 6 June 2007 (UTC)

Nonsense. Give me one reference that explicitely states that a closed, isolated system that has no interactions with the outside environment (e.g. it cannot therefore radiate heat) can change its invariant mass. I think I can find a few refences stating this but they consider extra dimensions into which particles can vanish... Count Iblis 18:43, 6 June 2007 (UTC)

"There is no separate principle of mass conservation. Rather, the energies and momenta of such particles are given in terms of their masses and velocities, by well−known formulas, and we constrain the motion by imposing conservation of energy and momentum. In general, it is simply not true that the sum of the masses of what goes in is the same as the sum of the masses of what goes out. "

"To illustrate the problem concretely and numerically, consider the reaction 2H + 3H → 4He + n, which is central for attempts to achieve controlled fusion. The total mass of the deuterium plus tritium exceeds that of the alpha plus neutron by 17.6 MeV. Suppose that the deuterium and tritium are initially at rest. Then the alpha emerges at .04 c; the neutron at .17 c. In the (D,T) reaction, mass is not accurately conserved, and (nonrelativistic) kinetic energy has been produced from scratch, even though no particle is moving at a speed very close to the speed of light. Relativistic energy is conserved, of course, but there is no useful way to divide it up into two pieces that are separately conserved. In thought experiments, by adjusting the masses, we could make this problem appear in situations where the motion is arbitrarily slow. Another way to keep the motion slow is to allow the liberated mass−energy to be shared among many bodies."

by Frank Wilczek (Physics Nobel Prize winner), in Physics Today, 57N12 10-11 (2004).Edgerck 03:22, 7 June 2007 (UTC)

This is about the sum of the rest masses not being conserved. It doesn't say that invariant mass of 2H + 3H is not the same as that of 4He + n. It does say that there is no conserved notion of mass that you can divide up into pieces that are indivudualy conserved. This does not contradict the factthat invariant mass is cnserved as that quantity cannot be divided up either.

If you are argueing that in the aricle we should mention that the sum of rest masses rather than invariant mass is sometimes the quantity of interest, then you do have a point. The invariant mass for composite systems is always a useful theoretical concept to do calculations. But in some cases the system consists of unbound particles that are not contained in a box. The mass of such a hypothetical box is of no interest to us, neither are we interested in the contribution to the gravitational field of the system. Count Iblis 13:42, 7 June 2007 (UTC)

When physicists talk about mass, they mean invariant mass. What part of "There is no separate principle of mass conservation." would have to be changed so that it is easier to understand? Hope this is useful. Edgerck 16:03, 7 June 2007 (UTC)

The sentence: "There is no separate principle of mass conservation" means that conservation of (invariant) mass is not separate from conservation of energy and momentum. Wilczek writes: "Suppose that the deuterium and tritium are initially at rest" So, we are in the zero momentum frame. He also writes: "Relativistic energy is conserved, of course," And of course momentum is also conserved. That means that the total momentum of the alpha plus neutron is still zero and that thebtotal energy of that system is the same as it was before. So, the invariant mass is the same. However, it is the case that "The total mass of the deuterium plus tritium exceeds that of the alpha plus neutron by 17.6 MeV".

And although invariant mass is conserved, this quantity does not have an additative property like momentum, energy or total mass (i.e. the sum of the rest masses which isn't conserved in special relativity). Wilczek writes: "Relativistic energy is conserved, of course, but there is no useful way to divide it up into two pieces that are separately conserved." Count Iblis 17:29, 7 June 2007 (UTC)

You seem to stumble in the simplest of phrases. Just read that paragraph and you will read the sentence "In general, it is simply not true that the sum of the masses of what goes in is the same as the sum of the masses of what goes out." This is the classical declaration of non-conservation: what goes in is not what goes out. Mass is not conserved in SR. Mass and invariant mass are synonymous. That's all according to WP:NPOV and WP:Verifiability, but not according to WP articles today. Let's see what happens tomorrow. Edgerck 22:58, 7 June 2007 (UTC)

Mass in the meaning Wilczek is contemplating is definitely not invariant mass of system of particles. The sentence "sum of the masses" he uses makes that very clear. You say that "Mass and invariant mass are synonymous". That's indeed the case, but you do have to define for which system you take the invariant mass. Wilczek consideres the single particle invariant masses. He takes the total mass to be the sum of the invariant masses of the individual particles. Now that quantity is not conserved. But the invariant mass of the entire system is conserved, however that may not be a quantity of interest. You cannot split this quantity up and assign each particle part of this quantity so that the invariant mass of the total system becomes the sum of these quantities.

Do you understand that if particle one has a (invariant) mass of m1 and particle two has a mass of m2 then the system consisting of particle one plus particle two, does not necesarily have mass m1 + m2? Count Iblis 02:50, 8 June 2007 (UTC)

Correct. Nobody claimed that invariant masses are additive in systems to give a system total invariant mass. System m is not equal to m1+m2, and yet there is a well defined m. Moreover, when m1 and m2 change in a reaction, so long as the system is closed, the system mass calculated by vector sums (not simple arithmetic sums) is still m, which is same as the old system m. That's the magic. Invariance is not equal to subcomponent additivity. These are vectors. As I keep trying to tell Ed, to get the length of two added vectors you can't just add the lengths of the vectors, since they may not be pointed in the same direction. To add them, you have to add their components, THEN calculate the length of the total final vector. This is what is invariant, this length. Nobody ever claimed it was made of the lengths of the vectors which compose it.

And I have to add that I think Wilczek is wrong that "There is no separate principle of mass conservation." There certainly is if you define mass as invariant mass. But he's right (and nobody ever argued otherwise) that system mass is not generally the simple direct sum of masses of subcomponents, if you define system mass (and subcomponent mass) in this way. S B H arris 02:59, 8 June 2007 (UTC)

To Count Iblis: You said "The invariant mass for composite systems is always a useful theoretical concept to do calculations. But in some cases the system consists of unbound particles that are not contained in a box.". I have a little quibble with this. I think that it is not useful to define the mass of an unbound system.
To Edgerck: Please do not split the comments of other writers by inserting your own comments in the middle. That is confusing and impolite. JRSpriggs 06:57, 8 June 2007 (UTC)

JRSpriggs: if you have a comment about a user's style, it is better to clarify the issue in the user's page. It will also be more polite. Regarding indented comments, this is common in electronic communication and here. I find it especially useful when I am misquoted in a long posting, where it would be worse to let the reader be misled rather than just interrupted. Hope this is useful. Edgerck 18:02, 12 June 2007 (UTC)

Ok, for unbound particles, what I meant by "useful theoretical concept" is simply manipulations using inner products of four-momenta in computations when considering collisions/decay of particles.

The mass squared is the square of the sum of the four-momenta and that quantity can sometimes play a useful role in simplifying the calculations. Count Iblis 13:24, 8 June 2007 (UTC)

In a closed system, "what goes in" is the initial state and "what goes out" is the final state.

That's a loose and bad way of putting it. A closed system has a boundary that nothing from the environment crosses, either before, during, or after the reaction. If you're talking about "what goes in" to the reaction, and "what goes out" of the reaction, that's fine so long as none of it interacts with the environment or crosses the imaginary boundary line (which we can draw anywhere we like, so long as we don't change it) then that's fine.S B H arris 18:19, 12 June 2007 (UTC)

In between, the system evolves without any interaction (in or out) with the environment. Of course, this is an abstraction (as no system is truly isolated), but is useful in theoretical and even experimental (negligible influence) considerations. So, the statement in Physics Today that "In general, it is simply not true that the sum of the masses of what goes in is the same as the sum of the masses of what goes out." shows that the opposite statement found in WP today (that mass is conserved in SR) is simply not supported by WP:NPOV and WP:Verifiability references. Edgerck 18:02, 12 June 2007 (UTC)

No. Ed, can't you understand that the total system mass is NOT the "sum of the masses?" The total system mass is what is conserved. However, the sum of the masses is NOT conserved in reactions (in general, though it may be in a few particular cases). Nobody here, ever said it was. Nor is the sum of system masses equal to the total system mass, usually. Nobody here said it was. None of this changes the fact that TOTAL system mass is invariant and conserved. This can happen even though system mass has nothing to do with sum of sub-masses. S B H arris 18:19, 12 June 2007 (UTC)

Editing others' comments

There has been some discussion here about whether it is ok to break up one editor's comments by interspersing them with responses. My reading of WP:TALK#Others.27_comments indicates that such action counts as editing another users comments and that it should generally be avoided (see the policy on Interruptions). Timb66 23:12, 12 June 2007 (UTC)

A question of relevance: E²=m²c⁴+p²c²

This is a long question which I'm going to put forward as a hypothesis.

When calculating the total energy of a moving object, physicists use the equation E²=m²c⁴+p²c².

E is the total energy m is the rest mass p is the relativistic momentum c is the speed of light.

This equation suggests that an object will gain energy as its relative speed increases.

p is defined as γmv where γ is the relativistic element called the Lorentz factor, defined to be 1/the square root of 1-v²/c², v is the relative velocity to the observer. This means that as v approaches the value of c, γ will approach infinity. This takes the total energy towards infinity.

The implication of this equation is that if a massive object is near a relative speed of c, an impact with an object in the same inertial frame as the observer could potentially release nearly an infinite amount of energy. Equally, to accelerate an object to c would take an infinite amount of energy.

This is an argument as to why this may not be the case.

An object moving relative to the observer will be observed to have slower processes in accordance with the special theory of relativity. Time, and thus an objects ability to express energy, appears to slow down within any moving object. This means that if we accelerate an object at a steady rate (according to the observer), the acceleration within the observed object will be experienced as a steadily increasing rate of acceleration.

For example, if the steady acceleration is 9.8 m/s² to the outside observer, once time appears to be running at 1 second inside the observed object for every 100 seconds for the observer, those within the observed object will experience the acceleration at 980 m/s². As the observer attempts to accelerate the object to a relative speed of c, the acceleration experienced inside the observed object will be nearly instantaneous.

This is why circular particle accelerators take so much power. As objects approach very high relative speeds, any acceleration is going to take more energy because we are effectively increasing the acceleration. However, I must wonder whether the view that an object is increasing its mass is the most accurate way of viewing this event.

So what about the first law of thermodynamics? Regardless of what is going on within the observed object (the normality within) we, the observers, are pouring in enormous amounts of energy to accelerate even the tiniest particles to a large fraction of c. What work is possibly being accomplished? Where is the energy going?

My suggestion is the work being done is changing the inertial frame. The power necessary to actually change the rate of all the internal process of every single particle of a massive object is enormous. But this is exactly what the general theory of relativity suggests we are doing every time we change the inertial frame of any massive object.

It is not unlike raising an object within a gravity field (putting something on a hill). It is an act of turning kinetic energy into potential energy.

For example, if an atomic bomb was detonated while passing an observer at near the speed of light, its internal processes would be experienced at a very different rate to that of the observer. (Note to physicists: I realise that only a fraction of the bomb’s mass is converted to energy (Per the physicist’s comment on my blog entry (http://emergenceofus.blogspot.com/2007/07/relative-energy-limits-when-appearances.html), though I don’t understand why this is necessary to stress.) Most likely, the observer will experience a mild increase in heat, no dangerous levels radioactivity and certainly no shock waves (from the explosion). This reason for this is time has slowed down so much that the maximum rate of energy release will be drastically slowed.

This is not unlike hibernation in complex animals: the energy expenditure is minimised through the slowing of internal processes.

At the extreme, an object travelling at a relative speed of c can release no energy from within because no processes can be observed within an object travelling at c. This is not unlike the concept of cryogenic freezing: no energy or change is expressed or experienced.

But what happens if we were to decelerate the detonating bomb into the same inertial frame as the observer?

As the bomb approaches the same inertial frame as the observer, the more quickly the internal process will appear to cycle. Energy can be released at a much greater rate. As such the explosion becomes more “noticeable”.

Note that the full extent of the proper energy, E=mc², can only be fully experienced by the observer when the bomb and the observer are within the same inertial frame.

So, what happens if our detonating atomic bomb is accelerated from c into the same inertial frame as an observer?

The act of accelerating the bomb into the inertial frame of the observer will bring into play the principles of the general theory of relativity. Acceleration of any sort slows “time”, or the internal processes. This means that the internal processes of our bomb are once again slowed relative to the observer and the full power of E= mc² is diminished. On the other hand, the potential energy from decelerating the object into our inertial frame can be realised as kinetic energy.

At rest, a massive object has a maximum energy potential of mc². But as soon as mass is in motion relative to an observer, the energy derived from this part of the equation must be decreased even as the potential energy from the change in inertial frame adds to the total energy.

According the equation E²=m²c⁴+p²c², as an object approaches the speed of light, the energy contained within will approach infinity. So even if the rest mass energy is effectively reduced to zero, as an object approaches c the energy potential of the momentum (p²c²) will approach infinity. If v ever equals c, the denominator goes to zero. The quotient dictates infinite energy.

But the problem is that the slower internal process of any massive object will also affect what is now considered momentum energy, especially as the rest mass m is once again included in this part of the equation. (p²c² where p=γmv)

None of this is reflected in the current equation.

This energy can only be experienced by capturing the relative speed and converting it into energy. Once again, general relativity tells us that any massive object experiencing the forces of acceleration will slow the internal processes. Therefore, the maximum amount of potential energy contained within the momentum of any mass is reduced.

One physicist (see comments on previous blog entry) felt the need to distinguish the kinetic state of an object verse the actual energy that can be experienced in reality by an observer. I cautiously suggest that a theoretical energy state that cannot be experienced in reality is not really part of reality. It is possible that the faultless math is taking us to something similar to the ultra violet catastrophe.

In reality, we lose energy in the very act of trying to access it. The only question is: will the energy loss exceed the gain predicted by an equation that suggests infinite energy?

The most violent collision possible for anyone to observe within our universe is two objects colliding head-on at just under the speed of light. For the purposes of examining the extremes, let’s just assume the two objects are both travelling at exactly c relative to an observer.

It will seem to the observer that no time is passing within either moving object. As such, there is no rest mass energy available. Even infinite mass will yield no energy because no processes can be expressed. However, the moment we begin the deceleration process, not only do we gain some energy from the mass, we can begin to access the enormous energy contained in the inertial frames. But the more we access the potential energy, the more we the forces of acceleration act upon the internal processes of the object, robbing it of its full proper energy potential (E= mc²). The general theory of relativity tells us that the processes needed to express the energy are being slowed which reduces the amount of energy that can be expressed at any given moment.

A collision between two equally massive objects will bring both of them into the inertial frame of the observer nearly instantly. There would be so much going on within such a collision that the math would be incredibly convoluted.

However, consider the extreme: if both colliding objects were converted totally into energy by the collision, what would the result be? I would suggest that the maximum amount of energy released in such an collision would be E=(m_object1+m_object2)c².

My suggestion is that mc² is the maximum amount of energy that can be expressed in our universe by any massive object regardless of its inertial frame.

Thus:

Postulate 1: Energy must be inside the same inertial frame as the observer before it becomes relevant. Postulate 2: E=mc² is a universal energy maximum for any given amount of mass, regardless of its inertial frame of reference and its associated momentum. Thus

m_restc² – m_motionc² = p (easily testable with the right equipment)

I would want to change p to the potential energy stored in the new inertial frame (or perhaps this is the same as momentum).

It could be that the act of creating relative movement is simply an act of translating proper energy into a potential energy in the form of a different inertial frame. The system as a whole neither gains nor loses energy. The energy expended to create acceleration is spent by doing the work of slowing the processes down within the system. That is why the special theory of relativity is only relevant to observed objects. Regardless of how an object may appear to an observer (nearly infinite mass, no time, no length) the experience within that object is one of normality.

So, my question is: why do you think I'm wrong?

Thank you very much for looking at this.

Cheers, --Tgooding 11:09, 31 July 2007 (UTC)

The solution to your problem is fairly simple, but this is not the proper place to deal with it. You might consider taking this to a place where people can really help you. If you can stand the heat, I recommend the Usenet physics groups sci.physics.relativity and sci.physics.

Cheers, DVdm 11:55, 31 July 2007 (UTC)

Thanks, I will put on a flame suit and post. Cheers, --Tgooding 12:54, 31 July 2007 (UTC)

Violation?

Count Ibis wrote: "If you read the actual paper they put on the arXiv, then you see that what they have measured is an predicted effect. In no way does this violate causality" I'm sure you are right, but surely such an announcment is noteworthy and a mention could be included in the article? Timb66 04:49, 17 August 2007 (UTC)

I googled for the statement by Dr. Nimtz: "For the time being, this is the only violation of special relativity that I know of" and found that it was reported in 298 different sources. Superluminality doesn't violate causality. Properly understood, superluminality only violates the principle of relativity. --e.Shubee 11:15, 17 August 2007 (UTC)

Interesting. I think this is worth mentioning in the article, since most people will think that something new has been discovered. Timb66 12:59, 17 August 2007 (UTC)

I understand why one would want to include it. I see a few problems though, which have to do with how wikipedia is supposed to work. In case of this and other "latest news" reported in the media, we know that newspapers are not so reliable sources.

In case of this news item I read some news stories that are completely wrong. We can deal with that by citing the preprint, see here. However, if you read this preprint, you'll see that what they've measured is not generally considered to be a violation of special relativity. If we want to include this properly in wikipedia, we would have to violate slightly the rules for original research.

This is why many wiki editors from wikiproject physics do not like to include "the latest news" in wikipedia by citing such preprints. Now, I'm far more liberal than most other editors from wikiproject physics. I don't really mind including it, but then we should focus on the actual physics that is reported in the preprint. We can justify doing this and violating slightly the wiki rules for original research, because many editors here are experts in physics.

As long as we don't say that: "we can't analyze this paper because that would be original research" and then just include the information from newspapers even if that contradicts what's been reported in the preprint, I'm fine. Count Iblis 13:58, 17 August 2007 (UTC)

This is the conventional point of view. And we see here that Nimtz has been involved in similar research before :) Count Iblis 14:10, 17 August 2007 (UTC)

I very much agree with Count Iblis on this issue. With breaking news, the best thing to do is to give the dust a chance to clear and to allow some time to gain some perspective on the matter. New findings are often hyped by their discoverers to gain attention and funding for more research. Furthermore, news sources will often pile on with the hype into order to sell more product. "Special relativity violated" is a much more grabbing headine than "Odd QM effect reported that may violate special relativity". So my advice is to take this with a grain of salt and see if it even makes it into a decent journal and also what it says if and when it is published in a serious journal. --EMS | Talk 19:03, 17 August 2007 (UTC)

Erroneous, misinterpreted, or otherwise misleading experimental results are not unusual. So as a general principle, I think that we should wait until an unexpected result has been replicated by other scientists before we mention it in a mainstream article like this one. JRSpriggs 00:36, 18 August 2007 (UTC)

The preprint is odd. For example, the title bar of my pdf reader has "Macroscopic experiments with virtual photons" but the title on the first page reads "Macroscopic violation of special relativity". Further, in the abstract, there is: "The evanescent modes (i.e. tunneling) lie outside the bounds of the special theory of relativity. [we] show that evanescent modes are well described by virtual photons as predicted by former QED calculations." It occurs to me that the original title is a much more accurate description than the 'sensational' title that it was apparently changed to. Alfred Centauri 00:47, 18 August 2007 (UTC)

Postulates

The introduction gives a false impression of the postulates of SR. They are in fact that the laws of physics are independent of your reference frame and that the speed of light is independent of the motion of the source, whereas the first paragraph suggests that awld albert postulated the invariance of c for different reference frames. This is a result derived from the actual postulates, not a postulate itself. —Preceding unsigned comment added by JealousCamel (talk • contribs) 11:50, August 29, 2007 (UTC)

Mass energy equivalence

This means that a mass of m contains an amount of energy of m c^2. Mass is never converted to energy as that would imply a violation of conservation of energy. Although one can say that energy in one form is converted to energy of another form. Also note that there exist no such thing as "Newtonian energy". How is that defined? Can you do an experiment that distinguishes "Newtonian Energy" from anothr type of energy? Of course not! Count Iblis 17:56, 21 May 2007 (UTC)

CI: You want to change a simple entry for mass-energy equivalence to a long statement including : any mass contains an amount of internal energy equal to $mc^{2}$ . Conservation of energy implies that in any reaction a decrease of the sum of the masses of particles must be accompanied by an increase in kinetic and potential energies of the particles after the reaction. This second part of this statement is not only off topic for the entry, but is false. Two different isolated systems, with the same energy, can have different inertial masses -- this is mainstream physics. See, for example, Edwin Floriman Taylor, John Archibald Wheeler, Spacetime Physics: introduction to special relativity, W.H.Freeman & Co Ltd (1992), ISBN 0716723271.

This is the statement that should be used instead: any mass can be converted to energy. This statement is in accordance with mainstream physics.

BTW, I know that [Fallacies and the Non-Conversion of Mass to Energy] and other crank sites disagree, but any mass can be converted to energy (the reverse is not always true).

I changed the page back to the correct, and short, statement. I have no intent in going into an edit war. Please read the reference and write to John Wheeler (and other authors) if you disagree with the page as it stands. Hope this is helpful. Edgerck 18:43, 21 May 2007 (UTC)

Edgerck, your comments are irrelevant as we are talking about the "rest" mass here. Your version of the article suggest that energy is not conserved. The total energy of an isolated system in it's own rest frame is, by definition equal to it's mass. That's how mass (a.k.a. rest mass or invariant mass) is defined. Count Iblis 23:26, 21 May 2007 (UTC)

CI: This means that you want to make that extensive change just because you think that the statement 'any mass can be converted to energy' should have "rest mass" instead of "mass"?

On another topic, the HTML mark up comment that I added to the text is just visible to editors, to prevent editors falling into common traps. Do you have a question about the mark up? Thanks. Edgerck 00:24, 22 May 2007 (UTC)

The other items in the list also have clarifications, so why not this one? Many people don't understand the meaning of E = m c^2, they think that it says that mass can be converted into energy where "conversion" is meant in the literal sense, i.e. they wrongly think that you have a decrease in mass and an increase in energy. We need to emphasize that total energy is conserved. This can be done by giving an example of a reaction involving particles in which the sum of the masses of the particles changes.

Not sure about the mark up, I'll take a look... Count Iblis 00:40, 22 May 2007 (UTC)

CI: My reply has three parts:

1. This item is just a bullet list. The interested reader can follow the link to the mass-energy equivalence item in the formula E=Mc^2. There is no point into copying by value when it's copied by reference already.

2. Contrary to what you say above, it's simply true (see the references I gave above!) that mass can be converted into energy where "conversion" is meant in the literal sense, i.e. physicists correctly think that you can have a decrease in mass and an increase in energy. One example is an atom emitting a photon. This is basic stuff.

3. Please do not revert the edit anymore on this, as your opinion is shown to be incompatible with basic, referenced stuff. Crank notions in [Fallacies and the Non-Conversion of Mass to Energy] should not find room in WP.

Thanks. Hope this is helpful.Edgerck 01:22, 22 May 2007 (UTC)

2 That's just nonsense. Conservation of energy is rigorously true in physics. Do you have a reference that says that energy is not conserved? I don't think so! You are simply misinterpreting what Okun is saying. I also note that Okun has a certain number of views that are not held by most other physicists, in particular about a fundamental distinction between mass and energy, and between length and time. Count Iblis 02:00, 22 May 2007 (UTC)

If you do calculations like finding the recoil energy of the atom after the photon is emitted you write down conservation of four-momentum. Have you ever done such calculations (you must have since you have studied physics)? So, what you mean by mass being converted to energy is simply the fact that the atom after the photon is emitted has a lower rest mass that can be related to the energy of the photon. But the total energy of atom plus photon is exactly the same as the energy of the excited atom (because binding energies are not the same).

3 Irrelevant nonsense. Yes, that may be crack stuff, but conservation of energy is NOT a cranck notion.

Count Iblis 02:00, 22 May 2007 (UTC)

I'm trying to figure out what is going on here. E=mc² most certainly indicates that mass and energy are related and interchangable quantities. There is nothing that keeps any mass from being converted into energy under the proper circumstances or vice-versa. For example, under normal conditions an electron stays an electron, but if it should encounter a positron you end up with two gamma-rays: That is pure mass-energy conversion. Similarly, and energetic enough photon can be turned into an electron-positron pair!

Also, I find this focus on apples to be most counter-productive, and that goes double for claiming that two apples together weight less than they do apart. That may be true due to a loss of gravitational potential energy, but most people are not going to notice that and it makes the article look silly. A better example is the helium-4 nucleus, which weighs noticibly less than two free protons and two free neutrons do due to the loss of nuclear binding energy. However, that is also better talked about in the article on mass-energy equivalence instead of in a bullet point. --EMS | Talk 02:55, 22 May 2007 (UTC)

EMS(ems57fcva): I'll be brief. This so heavily discussed bullet point is NOT about energy conservation. A short explanation of E=Mc^2 (without spelling out the formula, what's the use?) and a motivating example should suffice. Your reversal of my edit (which had correct information), well-intentioned as it might have been, introduced incorrect information (see item below) and is not helpful to someone trying to grasp this subject. On second thought, I would delete the apple example -- but, at least, is not wrong. Hope this is useful. Edgerck 18:58, 22 May 2007 (UTC)

The E=mc² equation actually appeared in an extension to Einstein's 1905 paper that came out a few months later. If you study the derivation, you will realize that Einstein has taken a classical derivation of E=mc² that involves Maxwell's equation for radiation pressure, and he has then mixed it all up with his relativity stuff. E=mc² has got nothing whatsoever to do with Einstein's theories of relativity. Gilbert Lewis demonstrated the pure classical/radiation pressure derivation in 1908. (Herbert Dingle 18:49, 5 October 2007 (UTC))

Perfectly rigid and very long rod

So, if I had an extremely rigid and long rod, and I pushed on one end of it, would the other end not move simultaneously (or nearly simultaneously once any internal slack was taken up). At any rate, would this transmission of information not beat a beam of light to the other end? —Preceding unsigned comment added by 207.161.41.71 (talk) 15:41, 10 October 2007 (UTC)

This is not really the place to explain this (Usenet is ideal) ... but the push goes to other end at the speed of sound for the material. The more rigid, the higher the speed. Note that the material is made from atoms, and the speed of sound ultimately depends on the electromagnetic interaction between these. The speed of interaction between two atoms is limited to the speed of light, so the net sound/push signal speed between two parts of a macroscopic rod will be less than the speed of light. DVdm 18:04, 10 October 2007 (UTC)

Energy requirement to move a small mass (a ship) faster than speed of light

ok , there is this problem i had with mathematical formulas used in physics , most of all infinite concept for example Zeno's paradox : An arrow cannot reach its target ever , because it has to pass through an infinity of points in space , which would take an infinite time, clearly an mathematical truth brought to absurdity by applying in to physics.

if one would consider same principle of mathematical abstraction one could see same effect applies to moving a small object through space at a speed bigger than that of light. Sorry i don't have the formula with me (!) , but the universe didn't need it when actually breaking special relativity and expanding in early moments of Big Bang much faster than speed of light , carrying with it all the atoms he could find ... well i can't say for sure what this means ... either speed of light was much faster then ... or he didn't need exactly an infinite amount of energy just a very big amount . Using my assumption it would be possible to estimate the numbers of atoms in the universe moved by the Big Bang , divide them by the numbers of atoms you need to move(a ship-medium size) and you could find a rough estimate of the energy needed to move it faster than light or rather say , same speed of Big Bang expansion. —Preceding unsigned comment added by Pef333 (talk • contribs) 00:34, 21 October 2007 (UTC)

If you keep accelerating in one direction, you will approach the speed of light, but time dilation will prevent you from reaching it in any finite time (provided the proper acceleration remains bounded, as it must). So much for Zeno's paradoxes.

Understanding the inflation of the universe in the early stages of the Big Bang requires a knowledge of general relativity, not just special relativity. Put crudely, the particles in the universe do not ever exceed the local speed of light, rather space itself expands — the distance between things increases even if they do not move. JRSpriggs 17:15, 22 October 2007 (UTC)

intro. to article

Although the article does state what Special relativity is in the first paragraph, it doesn't exactly do so very quickly (should be first sentence ?) - cf. General relativity. I'd like to fix this. However, as I'm not a regular editor of this article, and before I start potentially messing things up and arguing with people, has this point been discussed before ? Thanks. MP ^{(talk•contribs)} 22:24, 2 November 2007 (UTC)

I agree, the intro states when SP was proposed, but not what it is, although it is obvious. It needs to state that it is a theory of physics first. Beast of traal T C _ 17:28, 4 November 2007 (UTC)Beast of traal

What is not currently made clear is that relativity, like quantum mechanics and thermodynamics, is not an ordinary physical theory which merely describes a particular phenomenon, e.g. bulk modulus. Rather they are second-order theories which constrain all acceptable physical theories. JRSpriggs 04:30, 5 November 2007 (UTC)

Are causal loops paradoxical?

The article says that if effects can propagate faster than light, then "faster than light signals can be sent back into one's own past. A causal paradox can then be constructed by sending the signal if and only if no signal was received previously.". While this is the conventional wisdom, I feel that it is speculative. I have read (unfortunately, I do not remember where) that someone showed that in classical (non-quantum) physics such a loop would simply result in a kind of Fixed point (mathematics). That is, the signal would take on a value that resulted in the same signal being sent back. Even if you tried to apply an amplifier and limiter to convert analog to digital, there will be a value in the middle which cannot be pinned to the upper or lower limit. JRSpriggs (talk) 05:50, 13 December 2007 (UTC)

I've read similar things. Both in case of tachyons and in case of wormholes, any attempt to "change the past" won't work due to details of the physics. Of course, if you start with a constent mathematical description that allows for closed timelike loops, then you won't get a paradox; what happens in the loop is always self consistent.

So, we could say that physics must somehow resolve this so-called "Tolman's Paradox", see also here. The obvious way would be to disallow faster than light signals, but if it allowed, there must be nontrivial effects which would prevent the signal from being used to set up the paradox. Count Iblis (talk) 14:44, 13 December 2007 (UTC)