Challenge Questions

I agree with Jim. By splitting atoms the nett result will be a slightly lighter weight and some energy converted from the bomb. Even if the box does not conduct electro mechanical rays and it bounces forever inside the box the box should still weigh less than before the explosion.

Why does the "heat" have to leave the box? If the box (and contents) is only lighter after the heat has left: what about any other exothermic reaction which might take place in the hypothetical box; would the the box gradually decrease in weight as it returned to ambient?

Dear friends,

None of indestructible box can prevent the ultrasonic waves and the X ray radiation completely. Whatever negligible they might weigh, the box will be lighter after explosion.

R S Sahni

Although the challenge question is hypothetical, there is a real world counter part in a black hole.

Black holes are essentially "indestructible" when it comes to electromagnetic radiation which is what makes them black. However, from the change in the rate of precession we can reasonably infer that they are losing mass, even though neither mass nor energy are visibly escaping.

If both of the above conclusions are correct then the only possible explanations are that the mass/energy of the black hole is being converted into heat energy or gravimetric energy which are then radiating away causing the mass/energy reduction we believe we are observing.

Sincerely,

Mr. Gee

I would give this one to Jim....

Hi, Mr Gee!

"If both of the above conclusions are correct then the only possible explanations are that the mass/energy of the black hole is being converted into heat energy or gravimetric energy"

I think you mean that the only possible explanation is that it is being converted into some kind of energy. After all, energy is energy is energy, and by any other name would act in a different manner to achieve the same ends. In addition to heat energy and gravimetric energy able to exist in a black holw, you might also consider kinetic energy (translational), chemical energy, electromagnetic energy, and potential energy or all kinds, especially of eventual release of some original chemical properties of the black hole's resident mass in case of premature reversal (mini bigbang).

But anyway, if the A-bomb goes off in the black hole, and its mass is eventually lost through radiation, does it remain contained in the box that the black hole acts as?

Mark

Depends on how indestructible the box is. Will plasma, quarks or neutrinos pass through? If so it will be lighter.

As the others have said, as the atomic bomb converts mass into energy and that energy can be conducted or radiated through the box, the weight would be less.

The box would weigh more absorbing the matter from the bomb. Not all will be converted to energy. That by the box being indestructible the matter of the box does not become part of the explosion. And we are just talking about the weight of the box and not the combined weight of box and bomb. If box and bomb it would be less.

Once again we have a challenge question that is ambiguous.

Is the question JUST asking about the box weight or the combined total weight??

The definition of "Indestructable box" may not be the same as "Leak proof"

You could call a seive for flower an indestructable seive, as the material is permitted to pass through the seive, but the seive is still the same after using it for its application (ok there is an amount of wear caused by the material to be seived and the parts of the seive that come in to contact with the moving material, but its quite small)

Maybe.

Like many said before, if radiation and heat can escape then less.

If the indestructible box is a 100% barrier than the same

If the indestructible box reflects the energy inward then a tiny singularity?

Mass is the same as before the explosion, provided the box does not leak. The question says the box is indestructable, not that the seams cannot open.

This was done around the late fortys early fiftys. The container was 16 inch armor steel. the explosion was contained. I'm sure that the parameters included weighing before and after.

The simple answer is there is not enough detail in the question to know a definitive answer, is the box being "weighed" on Earth to start, then moved to Mars for instance. The reason this seemingly stupid scenario question is asked is because I believe the questioner really meant to use the term "Mass more or less than ..." . In other words the question is full of assumptive details or missing information, etc. Is the former of this query wanting to know only info about the box itself or it's relationship to it's contents before and after? Way too many variables to question here.

It is a test to see which engineer the answerer is, an engineer that does nothing waiting for information or the engineer who tries to formulate a solution with the information at hand.

You put an atomic bomb inside an indestructible box. You blow up the bomb. After the explosion, does the box weight more or less than before the explosion?

Well if the box is only indestructable it will weight less as the mass converted into energy will leak by readiation, heat, sound & etc but if the hypothetical box is also leak proof then it will weigh the same

The box weighs the same.

If it were not indestructable, but merely able to hold its shape against the bomb, the energized particles from the bomb would have combined with the box's atomic matrix, adding to its weight.

If the box were completely destructable, but able to be gathered up in-toto to determine whether it had gained or lost weight, the same result would apply. More atomic structure = more weight.

If the box were to be composed of fissionable material, and fissioned along with the bomb, it would have weighed less.

But as the box was indestructable, nothing about its weight would have changed.

Mark

Hi, Guest!

Relax. The only reason you haven't ever read so much nonsense in response to one of these questions is because you have'nt been around long enough to have participated in very many.

Just stick around. You ain't seen nothin' yet! So far, all you've seen is the junior stuff.

We haven't even got started!

Mark

Is that true "It is quite clear what the author meant - the weight of the box with contents". Then his use of a nuclear bomb is incidental? Because any bomb in the box after exploding it would make the combined weight weigh less.

Why is the auther not clarifying the question inspite of all the comments he/she may have read?

Hi Guest. You state that "An atomic explosion converts some mass to heat and light, which have no mass". This is not true. Gravity effects all energy (including light) as has been proven in practicall experiments (bending of light around massive objects in space due to their gravity, etc). If all of the mass of the bomb inside the box was converted to electromagnetic energy, ie, heat and light, and none leaked out then its mass would still remain the same. So it is very relevant whether heat and light gets out.

"I've never read so much nonsense in response to one of these questions."

Do you know where the heat from a nuclear bomb comes from?
It's the result of converting some of the mass of uranium and plutonium nuclei into to heat (possibly also of deuterium and other nuclei, depending on the type of bomb). So the rest mass of the atoms and particles that exist after the nuclear reaction is lower than what was there before. While the heat energy remains inside the box, you can characterise it as the sum of the velocity of the particles that make up the contents of the box plus photons within it. Photons have mass according to their energy (for a photon, the famous E=m.c² clearly leads to m=E/c²), and moving particles weigh more than stationary particles [m=m₀/√(1-v²/c²)]. So, if the heat escapes, either there are fewer photons, or the particles slow down. Either way the total mass is reduced.

Finally - it would be good to have you on board as a "registered" contributor; but be aware that paper qualifications mean nothing here - we are (quite rightly) judged only on the combination of our knowledge and understanding, together with our ability to communicate them.

So You are saying that Energy is created!! Wonderful!

Less.

When the bomb explodes, the mass will be converted to some form of mass and energy. Majority will be converted to radiant energy. This radiant energy toghther weth the heat generated as the product of reaction will heat up the walls of the container and will dessipate in the form of heat energy to the atmosphere. So the container together with the contents will weigh less than what was before.

Hi, zodiac!

You might have a good point there, if the OP meant that the weight for the bomb plus box were being considered for a change. The question only says "does the box weight more or less...".

I might be inclined to agree with you, though, because (see my own response somewhere above) otherwise, it might be a trick question centering around the term "indestructable".

Certainly, if the question means to include some worthwhile physics re the bomb itself, you have made a good point re acceleration/conversion of mass & presence/dissipation of photon particles.

If, by "indestructable", however, the OP also means the box is impervious to heat or cold or particle bombardment, then the heat of the air inside would have nowhere to dissipate, and conservation says the box would weigh the same regardless of light emissions during the explosion.

Mark

Matter can neither be created or destroyed, only changed. Therefore if the box is truly indestructible in that it can contain the effects of the nuclear explosion, no matter will be lost. Hence, the box will weigh the same. You cannot convert matter into energy.

E=mc^2

The fact that mass (matter) can be converted to energy by splitting an atom is the whole point of the question. You would be correct if the bomb were TNT - no matter would be converted to energy, but in a nuclear explosion matter is converted to energy.

You cannot convert matter into energy.

Unless, of course, Einstein was right with his e=mc² thing. But if he were right, then we could have atomic bombs, which could release huge amounts of energy. If Einstein was right, then the box and its contents will weigh less after the explosion, and whether or not the energy "gets out" would make no difference.

It seems likely that, assuming the original bomb was a fission bomb, the bang would be followed by a fusion reaction.

Hi Ken,

Your reply, which seems to have had a hint of sarcasm, touched on an interesting point. If you think of the bomb detonation as a "little big bang" inside the box, then because the particles and energy are trapped they will bounce around and interact. In effect, a little universe would be created inside the box...

Sorry guys, I have to stick to my guns on this one. You'll see.

Hi Ken, while I agree with the first part of your response I disagree with your statement that "If Einstein was right, then the box and its contents will weigh less after the explosion, and whether or not the energy "gets out" would make no difference". Einstein proved the equivalence of mass and energy and that regardless of what form it is in (as long as the energy is the same) it will be affected by gravity in the same way, ie, the box plus bomb will weigh the same after the explosion if none of the energy gets out.

I find it hard to disagree with the Wikipedia quote given in post 43, which supports silvCrow's contention in post 42, that energy is massless.

Einstein's mass-energy equivalence does not mean that mass and energy are equivalent in the way they are effected by gravity, it only means the mass can be converted to energy according to m=e/c². We know that the sun's mass continually reduces because of the conversion of mass into energy. The light travels away from the sun, and is not pulled back into the sun by its gravity. If light acted like mass, then it would be decelerated by gravity. Photons have zero rest mass.

So I am still firmly in the camp that says that the box will be lighter after the explosion, and that its mass will be the same when it is very hot and after it has cooled.

Hi Bob,

A good response, but I remain unconvinced -- not because I truly believe you are fundamentally wrong, but because we are at about the edge of what is, for me, observable, objective science, vs a belief system.

There comes a point in thought experiments where I say "does not compute" due to the level of abstraction. A box containing light but nothing else is at that point. If such a box could exist, then we should be able to turn of the lights in a photographic darkroom, and watch the light slowly decay as the walls convert light to heat. I think we know that even if all the walls are highly reflective mirrors, still the "light" is no longer "there" as soon as the light emitter is turned off. So let's allow a light emitter to be in the box. Let's say a lamp controlled by a timer. The lamp can go on and off instantly.

I'd postulate that the mass of the box would be exactly the same with the light turned on or with it turned off. If the light had a dimmer, the box would have the same mass regardless of the dimmer setting. I'd also postulate that the analogy for massy particles falls apart here: I think we agree that the light, as recorded by an infinitely fast video camera (also timer controlled) would "go out" in an amount of time equal to the [distance from lamp to box wall]/c rather than an amount of time that allows for photons bouncing around as if they were bb's, gradually being absorbed where there are imperfection in our reflective surface.

If photons had mass, then I'd accept your argument. But as far as I know they do not. My understanding of photon mass is more or less as outlined in this link.

I've read a Brief History of Time. This discussion has made me think I should also read A Briefer History of Time, because regarding relativity, I can really only mouth the words -- I have no real, concrete understanding. Try as I may, I have been unable to grab a photon to take a good look at one. I have a hard time even with the massy particles -- the last neutrino I tried to catch went right through me... just like coffee.

Hi Ken,

I agree that unless you fundamentally understand something your belief in whether it is right or wrong is based on trust, ie, do you trust what the scientists are telling us, even if it goes against common sense? I cannot claim to fundamentally understand relativity so I am also working from a belief system based on what I have seen/heard/learned. I think the main problem here is that common sense tells us that mass is a single fixed property of an object that results in certain things like the downward force it exerts when it is stationary in a gravitational field (rest mass), momentum and having its motion affected by gravity. It is therefore hard to conceive that an object with zero rest mass can have other "mass like" properties. Despite this it is experimentally verified that light has momentum (can exert a force on an object) and is affected by gravity. The only "mass like" property it doesn't have is rest mass since it cannot be stationary and if it did have rest mass it could not travel at the speed of light. I am not sure what you are getting at when you say that "I think we know that even if all the walls are highly reflective mirrors, still the "light" is no longer "there" as soon as the light emitter is turned off". This knowledge sounds like a belief based on visual observation rather than any objective scientific experiment. Are you trying to imply that light cannot reflect off a surface (surely not) or that there is some fundamental limit to the number of times that it can be reflected? In any case the light is present while it is still bouncing around the room which due to its speed makes it seem to disapear immediately. You then postulate that if you put a lamp in a box (presumably a box that doesn't allow any energy/light to escape) then the box + lamp would weigh the same before as after you switched it on. The answer depends on whether the energy source for the lamp is inside or outside the box. If it is inside then I agree the weight remains the same, if it is outside then the weight increases by amount of energy that enters the box. Your link talks about the "rest mass" of photons which I agree is zero. Here is a web reference to a book which discusses the topic of energy adding mass:

http://books.google.com.au/books?id=bU4xUMuJlukC&pg=PA22&lpg=PA22&dq=if+light+energy+could+be+contained+in+box+would+its+weight+increase&source=bl&ots=GZUFGVcTwI&sig=msEKPtVtO5dZXt5-xkmHLbTfIp0&hl=en&ei=Pii3Sfv4Epim6wPMmP2oCQ&sa=X&oi=book_result&resnum=2&ct=result#PPP1,M1

Thanks BobD,

Suddenly the "light" came on.

You are right; my contention that when the light is turned, off the room goes instantly dark (ignoring filament cool down time, etc) is based on observation without thinking about how one would really measure if that, in fact, happens. What really happens in an ordinary room (I suppose) is zillions of partial reflections in an extremely short time, with some energy converted to heat in the walls with each partial reflection. I suppose that in a perfectly reflective room, one could turn off the light source, and light would bounce around the room endlessly (ignoring re-absorption and possible re-emission by that light source of something other than visible light.) (I suppose one practical concern here would be in making the observation.)

I suppose the difficulty in conceptualizing this is that the amount of mass is so small for a very large amount of energy. Therefore we "know," (we think) that as things cool down their mass does not change, because in our ordinary experience with small temperature changes (hundreds to a couple thousand degrees) the energy change when represented as mass is very hard to measure with a scale. C² is , after all, a very large number.

I'll have to ponder this more when I have time, but appreciate your taking the time straighten out my thinking.

Hi Ken,

Glad you saw the light. It is a difficult concept to grasp as it seems to go against common sense and practical experience which says that mass is a fixed quantity associated with matter and as long as the quantity of matter doesn't chage either does its mass. It is hard to imagine that by adding energy to a spring by winding it up, and/or heating it, you are also increasing its mass but this is exactly what happens (even though the increase is so small it cannot be measured). Unfortunately these concepts are normally buried in so much maths that most people don't have the time or inclination to delve into them.

Hi Ken

So you don't believe in radiation pressure? (Sorry, that was just to get your attention). Just to add further insult, the following all demand the "special relativity" theories of which this is a special case:
atom bombs
satellite ballistics
red shift (though GR comes into that too)

Regarding photon acceleration by gravity, the earliest demonstration was due to Eddington. His writings on the subject remain as good as anyone's; however, they range from popular articles* to quite abstruse papers. His textbook "Mathematical theory of relativity" remains a classic, even though some of the stuff it covers uses the notation of the time, which makes it (possibly unnecessarily) difficult.
*In contrast to some cosmological "best-sellers", these were actually read and enjoyed rather than merely bought

I doubt that on it's own the following will help a great deal - but I'm hopeful that it will spur you to continue your enquiries**.

I think we can take it as agreed that the rest mass (m₀) of a photon would be zero. But it is moving at the speed of light. So it's effective mass is m₀/(1-v2/c2) which you will quickly see means that its effective value is 0/0, which means that it can take any value. In fact, according to Einstein's theories, the effective mass of a photon is dependent only on its energy - and a zero-mass particle is in fact the only one where we currently have the ability to convert all the E of E=mc² into thermal motion.

**N.B. I find it hard to think of a worse place to start than "a brief history of time". That book is an attempt to convey some peculiarly specialised topics of current discussion to a more general public. To those involved in the field it's either an amusing side-dish or a source of irritation; for the rest of us it may or may not give some insight - I admit to falling into the camp of those who gained precious little from it. The various bits of Wikipedia are actually as good an introduction to special relativity as any textbook I've found (others who disagree can make better suggestions) - but whatever you do you have to be prepared to wade through at least some of the equations (special relativity isn't all that difficult provided you confine your attention to a single spatial dimension, and that's more than enough to get through this stuff).

regards

Fyz

Ken, BobD - apologies - but this is weird. When I posted my answer, I had gone through all the postings that were visible. But following your kudos link I went straight to ones (obviously posted well in advance of mine) that I had not seen.

Hi Fyz,

Sure... rub my nose in my dimwittedness.

The root of my misunderstanding is (was?) mainly in linguistics, I think. Because of the name, I associate "photon" with light, and when I think of light, I think mainly of the visible spectrum but fairly often think about UV and IR. We know other animals (bees, for instance) might argue with me about what is "visible," and we know that eels can "see" via electrical fields and that bats can "see" with sound. We know that light is just one part of the EM spectrum, and can reasonably assume that photons move around to produce wave actions outside of the light frequencies. The terminology can make this stuff fairly muddy to me, but that is probably because I have not studied it enough.

I have long accepted the reality of e=mc², but not in a perfectly literal sense. The wave-particle duality has been a stumbling block for permitting a literal interpretation (and intellectual laziness, or more charitably, "lack of enough hours in the day", makes gaining a better understanding difficult). So I have been willing to say that photons act as if they have mass when they travel and act as if they have no mass at rest. That is quite different than saying that photons have mass when moving, and have no mass at rest.

I suppose my early fascination with physics had to do with its ability not just to explain the unseen, but to, with some time effectively make the unseen seen. In Newtonian physics, (and by extension other branches of science largely based upon [or explainable by] Newtonian physics -- such as chemistry, aerodynamics, combustion, electronics -- all things with which I have direct hands-on experience) the unseen can at least be observed by its effects on test instruments we can hold in our hands (and by driving cars, flying airplanes, sailing boats, etc). We can kluge something together to make many measurements in Newtonian physics, and by making those measurements, the unseen becomes "seeable" and concrete. You can electrolyze some water, measure the energy that goes into that process, and measure the energy that comes out of burning the resulting gases, and see that the first is greater than the second... and you can see how that will always be the case. Today, most of the stuff that can be adequately explained in Newtonian terms has become, in effect for many people, perfectly tangible: even if you cannot see the H2O bonds breaking, the process is just as tangible as separating sand into two piles.

The situation is different, for me, with modern physics. While I can calculate that the mass value of an entire month of my electrical energy consumption is 22 micrograms, I would have a very difficult time making the measurement*. Thus, in comes the belief system -- I trust scientists who have the means to measure this stuff. But still, (given my intellectual laziness) am I not sure whether photons really have mass at certain times or simply act as if they have mass.

* Although it could be argued that every time I hold a tangible GPS in my hand I have hard, tangible, proof of a set of theories that, taken together, also say that my house really should weight 22 micrograms more at the end of the month than at the beginning (assuming all the impossible practicalities of keeping the energy inside are satisfied.)

*In contrast to some cosmological "best-sellers", these were actually read and enjoyed rather than merely bought

I always enjoy your dry sense of humor. I "liked" Hawking's book but otherwise agree with you regarding it. My son, in 7th grade, had to a "Notables" project, in which you pick a famous person to write about, make an onstage presentation about that person, participate in a "news conference" as if you are that person, etc. He was painfully shy, but had read Hawking's book and liked it, so he decided to "be" Stephen Hawking. He used text-to-speech capability in this laptop to give his presentation (and his good friend played Issac Newton, pushing his wheel chair), so he never had to speak a word.. and the time required to answer each question also meant that he didn't have to answer a lot of questions. The audience loved it.

Dim=incapable => N/A in this case. (There would have been no point in writing).

BTW, I find general relativity more than a little challenging.
Beyond that point, I would say I have little understanding of "modern physical theories". By which I mean the modernism that started some time in the early 1970s. Assuming that I am still around, I will be willing to give it serious attention whenever it comes up with unique new predictions - even if these are not immediately testable (on the basis that once we establish a basis for predictions we can at least search for other ones that may be testable).

Hi, Blink!

When light hits the event horizon of a black hole, it cannot escape the gravitational pull and is at first bent, and then trapped from leaving until the black hole may self-destruct.

Given that, there is no black hole inside the box, so the light energy could escape except that the box is indestructible, which probably means that it can't...no big deal since light is easy enough to block anyway. So is heat energy, for the most part at ambient temps at least...maybe not at atomic explosion temps...but for the purpose of the question, we have to assume it is. Both are means of excitation of molecular structures through the transfer of energy, and in the case of the explosion, also of sub-atomic structures, causing heat and light manifestations (if we were in the box to witness them) during & after the explosion.

I think that in spite of the changes of state with the accompanying changes in mass of each state of the bomb's transformation, the total weight of the box's contents (assuming no escape) must remain the same. Nothing in, and nothing out.

Mark

Given that the question author did not supply any other definition, then I think we must use the common definition of indestructible, meaning "impossible to destroy". Presumably this could mean that the box could be deformed by the blast, but we can assume that if the box burst a seam, then its function as a box (a container) would be violated, and that therefore the box has been "destroyed".

An indestructible container was constructed for "Gadget," but was not used, so I don't know that we have experimental evidence one way or the other. But certainly, there is some size and thickness of glass box that will contain a nuclear blast. Such a box would let out a large portion of the light, and given time, also a large portion of the heat*, and a lot of the other things we think of as waves or particles (both massy and massless). There is nothing in the concept of "indestructible" that suggests a perfect insulator or perfect opacity to visible light or other EM phenomena.

I am fairly sure that most of us agree that if a conventional bomb were in our box, there would be no change in the box+contents mass. Many of us (but not all) agree that as such a box heats up and cools down during and after the explosion that its mass does not change, even though we know that energy is leaving the system (the box) in the cooling down. Several of us believe that energy is massless, and we would use E=MC² as evidence of that: it is not, after all E=X(M)+ MC².

Although I am in the last group, I'll defer to anyone willing to do the experiment to show that we are wrong.

* Here, I am using heat to mean: A form of energy associated with the motion of atoms or molecules and capable of being transmitted through solid and fluid media by conduction, through fluid media by convection, and through empty space by radiation.

Ken,

Your comments are generally useful and good, however on this one I am not so sure when you say this:

So I am still firmly in the camp that says that the box will be lighter after the explosion, and that its mass will be the same when it is very hot and after it has cooled.

If I understand you right, you say that the box will be lighter but its mass is the same, regardless if hot or cold.

Measuring in the same frame of reference, mass and weight would have the same relationship, or not?

Not quite, no one is making any great distinction here between weight and mass. The sensible answers are divided among those who agree with guest at post #18 and those who agree with BobD at post #70. If you agree with guest then it doesn't matter (no pun intended) if the box is allowed to "leak" the energy, where if you agree with BobD then the box will initially be the same weight (or mass) but will gradually get lighter if it "leaks" energy.

Measuring in the same frame of reference, mass and weight would have the same relationship, or not?

Yes, they'd have the same relationship. I was being unclear. I was attempting to say that the box (including contents) will have less mass after the explosion, and also that the mass (of the box and contents) will not change as the box and contents cool down after the explosion.

This question is similar to the weight of birds in a sealed box. Is the box combined weight when the birds are perched more than when the birds are flying.

To answer the bomb question; assuming a totally sealed box when nothing escapes; then I guess the weight will be the same. If heat escapes, then the box will weigh less because the heat came form the conversion of mass to energy. If the box was 100% insulated against everything and exactly the same size and shape before and after - how can we tell the bomb had gone off.

As a matter of interest, can somebody do some sums on an example to show what the temperature and pressure in the box might be.

I read or skimmed all the responses (to this point) & did not see any references to our own 'big bang' scenario. Supposing our universe is a closed system- it must be or energy would continually dissapate & mass & heat (energy) would never have the oportunity blow up! So which is it: an 'open' or 'closed' universe? Which brings to mind that mass has the property of attracting more mass to it(self) & create its own closed (like) scenario. So the box (I agree with most) will weigh less. However that energy went somewhere. Where is it? It's all relative. But to a point. Imagine this parallel(?). Stick a songbird into a sealed indestructible box. If it begins to sing do those sound waves dissapate bird energy & weight? How about if the box is sound proof? This ? is more toward our own circumstance. Carlos

"The choices you make might be mistakes but it's never too late to turn around." Johnny Lang- musician

There is nothing in the question to burn your brain so much.
This is already proved by Einstein by his theory and is clear from his statement.
- The mass of a system cannot change, so long as energy is not permitted to enter or leave the system.

The explanation can be simplified as below.
By Einstein's theory we have E = Mc2.
Which says : M = E/c2.

As it is a closed system the Energy is not permitted to leave or enter the system (The BOX).
Thus the Energy before and after when the bomb is blown remains same, supporting theory - law of conservation of energy which says 'Energy is neither created nor destroyed'.

Thus Energy - E in the Equation above will always remain a constant.
The equation E/c2 will always result a constant.

So the mass inside the BOX will remain always the same.

Are you therefore saying we have mass because energy are moving at light speed or that you can convert energy to mass by moving it at light speed? Then photons must have mass or all electro magnetic waves are bogus as they get converted to mass because they move at light speed. Wow now I must stop as I can smell the shit I am talking.

I asked a similar question here once, about a "perfect" material that couldn't be compressed. Everyone qualified their answers with the fact that it couldn't exist. That's not the point.

The box is perfect.

It has no seams and is impermeiable to anything - radiation, neutrinos, quantum tunnelling, angry spirits, etc.

The explosion occurs - you don't see or hear anything; no thump, no flash of light or warmth, no glow

The box is still sitting there - it hasn't moved; you can't tell that the explosion has occured but it has

Does the box weigh more, less or the same?

I'm just sleepy enough to comment.

The OP stated, "You blow up the bomb". This could be construed to conclude that You must have some form of attachment to the bomb.

So if "you" can physically cause the bomb to explode then the box must not have a lid and the weight of the bomb + the box would Definitely be lighter after the bomb explodes, (although you wouldn't be around to do any measuring). The box itself would weigh the same if it is so totally indestructable that it can't lose any of its own mass or absorb any energy or mass from the bomb at detonation.

Or, if "you" cause the bomb to explode by means of some type of signalling device then the box, although indestructable, cannot be impervious to radio or some other form of signal. So, that would conclude that the weight of the box + the bomb would be lighter after the bomb explodes because the box would allow matter to escape in the form(s) of energy. The box itself, however, may be heavier if it absorbs more matter/energy than it allows to escape. (another discussion....)

Now, if "you" can cause the bomb to explode using a particle entanglement detonater and the box is completely indestructable to the point of not allowing any matter/energy transfer Out of the box then box + bomb would weigh the same after detonation. Else, box + bomb would weigh less if matter/energy can escape.

HS!!..The ramblings of a Mad Man!!..LOL I'm going to bed now....

Again with the nitpicking.

Perhaps "The Clapper" was used. It's what all nuclear-armed nations should use to detonate their warheads.

Before you "close" the 'Box' (after all you must put the bomb in it) you put a timer in with it that triggers the atomic explosion.

No need to have an outside connection to the inside to set it off through which "things" could escape.

Hi, Floram!

I just used my transporter to place the box around the bomb.

Mark

Are you forgetting some thing? The Bomb can be detinated by a timer.

The question does not state that the box is sealed up or even has a lid on it. The weight of the bomb is not mentioned. Therefore, if the box is indestructable, there would be no change in the weight of the box once the bomb has been detonated and is no longer in the box.

I'm no rocket scientist (He--, I'm not even sure if I'm anything anymore!), but I learned in physics class back in ought forty two that matter can neither be created nor lost under controlled conditions.

However, with the advent of nuclear reactions and the resulting creation of new elements therein, I'd say my high school science teacher was wrong.

But, I'm sticking with it and saying the weight stays the same.

Conclusion: Nothing can escape nor enter the box.

Besides, I'm too old a dog to learn new trix.

Ken

It will way less because mass would turn to light from the explosion.

If the occurrence is nuclear fission and the result is a heavy atom into lighter atoms of hydrogen or helium..... probably helium, then the "weight" of the box is lighter.

The sum of the mass may be the same due to the box.

I think a few of you don't truly understand e=mc^2.

When the bomb goes off some mass is changed into energy. This energy has no mass so it has no weight. This former weight is now a lot of heat/light. Heat and light don't have measurable mass. Period. The box will weigh less than before the bomb went off. It will be really hot inside but lighter. It does not matter if any heat or light escapes-- it has already lost mass in the conversion to energy in the atomic explosion.

When you heat up a chunk of metal does it weigh more?

I sure don't want to be the poor sucker that opens the box.

Awwww..... that is too easy of an answer silvCrow. There has to be a trick to it to make it fun.

Wiki:

In a nuclear reaction, the total (relativistic) energy is conserved. The "missing" rest mass must therefore reappear as kinetic energy released in the reaction; its source is the nuclear binding energy. Using Einstein's mass-energy equivalence formula E = mc², the amount of energy released can be determined. We first need the energy equivalent of one atomic mass unit:

1 u c² = (1.66054 × 10^-27 kg) × (2.99792 × 10⁸ m/s)²

= 1.49242 × 10^-10 kg (m/s)² = 1.49242 × 10^-10 J (Joule)

× (1 MeV/ 1.60218 × 10^-13 J)

= 931.49 MeV,

so 1 u c² = 931.49 MeV.

Hence, the energy released is 0.0238 × 931 MeV = 22.4 MeV.

Expressed differently: the mass is reduced by 0.3 %, corresponding to 0.3 % of 90 PJ/kg is 300 TJ/kg.

You forgot to factor in the effects of some of us who are three bulbs short of a chandelier. May the eyes of Heisenberg be upon you.

Hi silvCrow. I think you may be one of those that don't understand the equivalence of energy and matter. You state that heat and light don't have measurable mass. In a sense you are correct because you can never isolate a stationary photon and measure its mass, however, it is still affected by gravity as is all energy whether it be composed of matter or energy. If you don't believe me look up gravitational redshift and blueshift on the net. Even if all of the matter of the bomb was converted to light energy the weight would be the same because the frequency of the light hitting the top of the box would be red shifted relative to the frequency hitting the bottom due to gravity. This would result in a net downward pressure which would be interpreted as weight. So the box plus bomb would weigh the same before and after the explosion as long as none of the energy leaked out and it very much matters whether any heat or light escapes.

It is kind of funny to see that so many of us (myself included) are being thrown off by one of the simplest trick questions in Physics 101. What is the difference between mass and weight?

The OP asked us about weight - not mass, so what needs to be considered is what happens to an object's weight after an explosion?

Particles escaping from a nuclear explosion become so excited that some are blasted away at velocity sufficient to leave the earth's atmosphere. If the box will not let any particles or energy escape then remaining matter inside the box would be left bouncing around in a very hot gaseous state which I suppose would never cool. The weight of a heated gas due to the effect of Gravity is reduced and goes negative if there is enough heat, so the total weight of the box and its contents would definitely be less even if you don't consider the change in mass. In fact, if the box is light enough, then the total weight could be so small that the box would float like a hot air balloon.

We could do a vector analysis to determine if the box will float, but I'm too lazy I would need to know a quantitative value for the buoyant force which would require information about the particles inside the box, and we would need to know where the box is (what planet, etc.). (The box must be close to another object since it has weight.)

Hi, EElectrician!

While the weight of a heated gas is less than that of a cold gas, this gas is contained in a box while it is cold, and then while it is heated up as well. The amount of gas does not change, and therefore neither does its weight, hot or cold.

You may be thinking of a hot air balloon, where the heated gas is fed in, and being lighter than the cold gas around it due to the rapid movement of its uncontained molecular structure, occupies a greater expanse than the cold air. In that case, the amount of air within the balloon is less than the outside equivalent. But the air was heated before being placed into the balloon.

One might make the same argument (although it would be a very strange one, completedly dependent upon this amazing impervious box) that the amount of potential light energy present in the bomb, either exploded or waiting, was also the same before and after release, albeit occupying a larger space inside the box than when it was just in the bomb as photons, particle waves, or what-have-you when the atomic bond holding the nuclei of the bomb's structure together was ruptured by the blast.

In this case, it may not just be a matter of e=mC², but also the first law of thermodynamics that offers the insight as to whether the box plus contents changes in weight, and reverting after that back to e=mC², to determine that while the form of energy has changed, the sum of the energy remains the same, and thus so does the weight.

Mark

That's a good point, but my point is that weight is not a constant property for any object - not even on earth. If I want to feel good about myself I step on a bathroom scale inside a 747 at 30000 ft; I should way about 2 - 3 lbs less because the effect of gravity on my body is lessened at higher elevation.

In the case of the box all of the heat will produce an upward buoyant force (thermodynamics) which will act opposite the direction of gravitational pull.

Besides, the fission reaction will create hydrogen gas when the fuel atoms are split. The released H2 will try to rise creating an upward force which will be negative compared to gravity, so the resultant weight will be less.

Here's another thought:

Since the excited particles are trapped inside the box they will continue to bounce around. If we assume that no energy can escape, then the bouncing particles will be moving at speeds close to the speed of light, and the energy of the particles would have no where to dissipate. This would result in infinite near light speed atomic and subatomic collisions. So, a couple of things must happen over and over again until the end of time:

Every time a Hydrogen atom (released in the initial fission reaction) with enough kinetic energy collides with the nucleus of a larger atom then the hydrogen proton fuses with the larger nucleus in a fusion reaction which releases energy.

Every time a neutron (released to trigger the initial fission reaction) with enough kinetic energy collides with the nucleus of an atom, another fission reaction would occur that will release another proton and more energy.

The result of all of this chaos would be that eventually there will be a lot more energy inside the box then matter, so the box will eventually have so much energy in it that gravity could no longer hold it in place, so the box would have no weight at all. (It would still have mass, but no weight.)

Perhaps at some point we would end up with a mini-black hole because of runaway fusion like a collapsing star?

depends if any of the radiation or energy escapes. If it does then it would weigh less.AKA (E=MC^2)

I think you have it all wrong. When the explosion detonated, in a sealed, impervious, indestructible box, matter is converted into energy.(heat, x-rays, and light, etc.) Eventually, as the radiations impact and are absorbed by the remaining materials within the box, they will be converted all to heat. Heat, as most of us can relate to in the "dog days of summer", is very heavy. (Shoot, I cannot even move some days.) Therefore the box will be heavier, not lighter.

DUH!

*Disclamer* - The views expressed here are a test of the "what is wrong with people!?!" system. They are an exadgeration of this engineer's interpretation of 90% of the comments on this thread. Had this been an actual posting it would have been fact based, and made much more sense.

Jim 35848, I gave you GA as you satisfactorily and correctly answered both interpretations of the question. Box or box and content.

In my experience there is no such thing as an indestructible box. The emitted pressure from the radiated blast vs. the constructed density of the box is in true relevance to the question. The bomb, assuming it is the same type and class as the one dropped on Hiroshima or Nagasaki placed in a cube; say 8'x8'x8' is going to be obliterated no matter what its made of.

Therefore going back to what one of the respondents said earlier I have to work with the information I have at hand which is nothing but a bomb and a box with no other details. How big is the box? What is the box made of? How big is the bomb? are the questions to be asked before the conclusion can be given.

Although Albert Einstein was correct in the fact that E=Mc2 that has largely been the theory since the invention of the hydrogen and the atom bomb, However given the harsh economic times we live in today and with new technology emerging every second of every hour we have resorted to the old fashioned method of seeking new renewable energy sources with the equation Mc2=E. It has been done.

I have to disagree.

The question as posed states that the box is indestructable.

That given, nothing can get in and nothing can get out, period.

Energy (radiation) is contained by the very premises given - an "indestructable" box.

Until Einstein's Theory can disprove me, I stand by my original conclusion.

Ken

Just a short word in your favor: Theories don't prove anything.

Indistructable means it will survive the the blast unharmed, it doesnt mean that radiation cannot pas through it, for all we know it is ACME rubber metal that will expand with the blast.

Is it a Quantum physics question? like shrödingers cat, or is there only a blast when we look at it or like heisenberg we can only know the position of the blast not it's weight? (ok i am stretching it)

it think it would weigh MORE because a bomb has chemicals like calcium. like filling a tractor tire. weighs more after inflated.

Hi, icjr!

Welcome to CR4! Hope you continue to enjoy yourself in here. It's a great bunch of folks.

When you fill a tractor tire, you import --as it were-- air into the tire from the outside. Because the box is sealed, there is no way to import anything into it from the outside, so whatever's inside when you start is all you'll ever get in there.

Mark

I would think the atomic bomb might be too rusty(the atomic era has long gone and been forgotten) to explode but it does start to leak radiation. The radiation can leak outside the box and cause damage to the environment. Hence, no changes to the box but big changes to our well being.

Time to give the box and these rusty atomic bombs to the Martian.

Assuming the whole experiment went bottoms up and the box did not survive, Can you still re-cycle the radiation for your solar radiation energy saving system ? I think yes you can.

I go back to my original statement that not enough information is present. Many placed various unmentioned characteristics on this box that were not part of the given question. For instance: an indestructible box does not mean it completely enclosed the bomb, only that it is indestructible. We do not know if it can expand with the explosion or if it is so large (size of the universe for instance) that any atomic explosion inside would be meaningless. We do not know that impervious means nothing can be "radiated" through it such as energy. How did someone seal in the box a bomb if the box is indestructible and as such there is no way to change it's characteristics to close it up (Welded?). Do we really know the bomb goes off? All one can really do is state various concepts about things we do know about physics, or assume we know, anyway, until another Einstein comes along and rocks our world a little. By the way has anyone read about the real world research into invisibility cloaks? Shall we go off on another tangent? ...............

A new line of thought (but no answer)

The box is nondustructible

a) It is not impervious to mass - The mass of the box+contents will obviously decrease dus to escaping alpha rays (and may be the exploding small particles)

b) It is impervious to mass but not energy

c) It is impervious to mass and energy

When a radio-active decay (or explosion) takes place -

The radio isotopes are highly unstable- a lot of energy (binding) is used up in keeping it all together. Mostly this is the energy that is released in the decay(slowly) / explosion (quickly) -

In fact the mass of the particles added up together (forget about the mass conversion to energy) as I learnt ages back (may be wrong) is more than the actual atomic mass. And the difference is more as the nucleus becomes larger and also the unstable nuclii.

This difference by E=mc² is used as the binding energy. and a part of this is released as the energy of the explosion.

The energy released will remein energy, heating up the box, escaping etc will not matter, since the energy anyway is currently mass less.

But the results of explosion will now need less energy to keep their nuclii together, hence added up atomic mass will be more.

(Can some body add up α + β + Final Element mass - Initial Element mass? even for one atom ? )

U²³⁵ = Pa²³¹+ α + β

Focusing on the weight of the box (not box and bomb).

The mass of the box will increase as it will "pick up" the particles released in the reaction. It will then weight more.

"The total rest masses of the fission products from a single reaction is less than the mass of the original fuel nucleus. The excess mass is the invariant mass of the energy that is released as photons (gamma rays) and kinetic energy of the fission fragments, according to the mass-energy equivalence formula E = mc²."

I wonder if the answer is pressure related. I've read some theories on pressure and particle mass variation. Can't find it though.

Note: I said I read it..... didn't say I agree/disagree.

I pondered this question as I lay in bed waiting for Morpheus to overtake me last night, and it struck me what I had been missing and what others must have missed also.

THE BOX.

Does "the box" weigh more or less, is the stated question. Nothing is said about the contents of that box. Whether the contents change or not has no bearing on the weight of THE BOX.

Therefore, the box, being indestructible, is the same weight and remains unchanged.

Ken - no rocket scientist he...

Let's look at this again.

These are the accepted definitions according to Wiki:

In the physical sciences, weight is a measurement of the gravitational force acting on an object.

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force.

In common usage, matter is anything that has both mass and volume (takes up space). A more rigorous definition is used in science: matter is what atoms and molecules are made of. Matter is commonly said to exist in four states (or phases): solid, liquid, gas and plasma; other phases, such as Bose–Einstein condensates, also exist.

So. let's not confuse the issue. The question states an indestructible box. My interpretation of that is that nothing can get in or out of the box. The questions also states that the bomb explodes. And finally, the question asks if the WEIGHT of the box changes after the explosion.

Real simply now... the detonation will cause the matter to break apart into protons, neutrons, and electrons. Because of the indestructible box, not one single particle can escape. Some of them will reconfigure themselves into other atoms and some may just randomly bounce around. But, none of the particles can escape the box. Now, the mass inside the box may change, but the total weight will not, because no matter got in or out of the box.

What do you think?

The question states an indestructible box. My interpretation of that is that nothing can get in or out of the box.

Your interpretation would then not be in line with the common definitions of indestructible: impossible to destroy. The container built for Gadget could be considered indestructible. For our purposes, if the box was not destroyed entirely, but was damaged enough to lose some of its function, (such as a seem splitting),then we could reasonably say it had been destroyed for its function. But to suggest that the box cannot be heated by the explosion (and therefore could subsequently radiate this heat outward) seems like a very large stretch on the word indestructible. We can easily imagine an indestructible box: a fire cracker will have no effect on a 500 mm cube made of steel with 10mm thickness, other than warming it -- just scale up and you have you indestructible box for a nuclear explosion. (The container for Gadget was 240 tons, I think).

Otherwise, what you write would apply for Newtonian physics, but not, as far as I know, to modern physics. See, for example, post #18.

We know that after the explosion, we will have a very hot box. We know (and almost all agree) that some of the mass of the bomb has converted to heat energy. The mass of that box will not change as it cools. I think that most of us agree that heat does not have mass. If you propose that it does change in mass as it cools, then by what mechanism? If some of the mass has converted to heat energy and if heat energy has no mass, then the box and contents must be lighter after the explosion.