# Thought experiment



## TheTomG (Sep 18, 2011)

Ok, so don't know how many of us are scientifically inclined, but here is a thought experiment that has been bugging me.

We'll pretend our universe is very limited, in order to simplify things. There's me, a pole that is one light year long, and a machine on the other end that can detect any movement at all in the end of the pole no matter how tiny.

So, I push the pole at my end - of course the pole is very massive being so long, and I of course drift away from it thanks to the opposite and equal reaction and not being grounded on anything, but I have applied a force to the pole and so it must move.

How long does it take the other end of the pole to move?

It can't be instantaneous, because then the movement has happened faster than the speed of light. It must take at least a year. So what happens in the meantime?

Now I'm thinking that actually what happens with real matter is that the other end doesn't move at all and instead the atoms and molecules in the pole really just compress and this compression wave fades out due to friction and other forces between the molecules using it up.

Of course what I'm kind of interested in is that means all movement would in fact be a compression wave of molecules pushing against each other, so when I push a ruler across a table, there's actually a time delay between me pushing one end, and the other end moving.

Would that be right? Would all materials and objects work that way (there's no perfect material where the atoms / molecules are so heavily and tightly locked in place that they can't compress, e.g. like diamond?) Does all movement work like that, and if so do those compression waves move at different speeds through different materials? At what length for any given material does the movement "die out" and not reach the other end? Does the material decompress again and the end of the object move back?

The absurdity and impossibility of the thought experiment with the light year long pole leaves me to wonder just what really is happening with real materials, because it can't be that the objects actually move, the whole structure moving at once, it must be that something more weird is really going on, just the scales on which we operate don't let those effects show up.

Anyone got some thoughts or even information for me on what really goes on in terms of movement on the macro level arising from movement on the micro level etc?

Thanks!
    Tom


----------



## PTeppic (Sep 18, 2011)

Why can't the other end of the pole move instantaneously? Since it's physically connected, this is how it would move...


----------



## J Riff (Sep 18, 2011)

A lightyear-long guitar string.... would take a year for the note to be heard at the far end? Or longer? Beats me.


----------



## TheTomG (Sep 18, 2011)

That's the fun in the thought experiment, and why it bugs me 

If its instantaneous, then an event at point A can have consequences at point B faster than the speed of light, which I am thinking is not allowed. What if our detector at the other end triggers a bomb - then I can cause cataclysmic events to occur, transmitting a message (or consequence, or effects, or actions) faster than light, and the consequences will have happened long before the light from the originating event gets there.

I could have a theoretical matter transmitter, sending information faster than light that causes an object to be reconstructed at the other end faster than even light can physically travel the distance.

I believe (but I'm not that much of an expert) that is not allowed and could give rise to paradoxes. I may well be wrong   I believe if something becomes true "in theory" then it becomes only a matter of time before it is made true in practice, so I think this must be untrue even in theory.

If it is untrue in theory (and I am happy to see a debate on that), then I think the truth is that our concept of a solid object is in fact in error. If I run into one end of a train, it takes a while for the other end to move, even though it is "one train." The carriages of course have gaps and have to jostle into each other to push the next one along, and that has to happen all the way along the length of the train before the other end moves.

I am thinking this concept may go down to the molecular / atomic level, that our "one object" actually moves by its atoms jostling into each other, and as such the information takes time to transmit.

Again, I may be wrong! All inputs and thoughts welcomed. Is the speed of consequence allowed to be faster than the speed of light?


----------



## Abernovo (Sep 18, 2011)

I would have thought it would take slightly more than a year, although the difference would be so slight as to make no difference to an observer without a chronometer capable of recording the most miniscule particles of time.

Now bear in mind I trained as a biological scientist, not as a physicist but here goes, according to my understanding (which could be completely wrong):

Subject TheTomG presses the rod, which appears solid, but is made up of molecules of rod matter, setting up what could be seen as a compression wave, but I figure might also resemble, as you described, a slow moving train with the engine at the rear, where each carriage suddenly jolts into motion as the couplings compress. Far end of the rod eventually moves approximately one year later.

However, a few caveats that I can think of in relation to exact time taken.
1)The gravitational mass of and interactions between the subject pushing the rod, the rod itself and the recording machine at the other end. They might be small, but they would, according to my understanding (not great) of Relativity, have an effect.
2)Our outer space is not a perfect vacuum, but a near vacuum. Are there any external factors on the movement? Even something such as dust from your spacesuit, presuming you're not an alien form capable of living without what we would comprehend as breathing
3)Where I really come unstuck, molecular, atomic and subatomic interactions. I know that they do not always move uniformly, which I suspect would further slow the consequential movement, but past that, erm??

Of course, what really happens is one year and three nanoseconds later, the rod smacks the measuring machine in its robotic eye, the experiment fails and we have to start all over again.

Thank you. I like this question. It made me think. I'd love to know a definitive answer. The more I learn the more I realise how little I know.


----------



## Huttman (Sep 18, 2011)

Wiki has some interesting, if not heavy, points on the subject. This link might also have some info:
http://www.rebelscience.org/Crackpots/nasty.htm
I remember hearing something about instantaneous changes in polarity  between molecules, which would be FTL. I think for the physical universe to work, matter cannot move quicker than 186,000 miles per second, but it does not mean there are not loop holes or other physical phenomenon that would prohibit shortcuts through 'normal' space. (wormholes/folding space?) 
As for this pole question, certain parameters would have to be assumed, such as it's rigidity. A pole that long would certainly bend and then 'catch up' to it's original form, and that would not travel FTL. For the sake of argument if the pole were completely rigid  as I assume this thought experiment is saying, perhaps effect can travel FTL, not actual atoms. The pole never travels FTL, just the effect of movement does.
Thanks for the thought playing! It has been enjoyable. I'm not a scientist in any way, but I do enjoy the subject and am glad I can 'keep up' while watching a program on television about it, while others in my house are kind of, huh? (And then I read the Wiki article, and I'm like, huh?)


----------



## RJM Corbet (Sep 18, 2011)

Ok, I think if you hit the head of a nail a light-year long with a hammer, the whole nail will move with a speed proportional to the force with which you hit it, so the point of the nail will move downward, but never faster than the speed of light.

The wood will slow it down, and the nail will be compressed along its length. It will either become a shorter nail, or if it's made of good steel, will spring back to its original length by various molecular forces, and the friction will be transformed to heat, by conservation of energy and momentum.

If you hit it and cause just one electron to move down the length of the nail, from the head to the point (ie: the nail itself does not move) then the electron still cannot exceed the speed of light. That will be the same as just shooting an electron through steel. The steel will slow it down at some proportional rate, depending on what sort of steel it's made of, etc.

It's like hitting a tennis ball, the whole ball moves, but it flattens, then springs back to shape, is slowed by air resistance, heats up with the compression, etc. A whole mix of forces, down to atomic level. But never faster than the speed of light.

Something like that ..?


----------



## TheTomG (Sep 19, 2011)

Thanks for the input all, and glad others find this kind of thing fun too! Not a lengthy reply yet due to this having been a truly awful day and I'm just passing through briefly before collapsing into a vodka-aided sleep  But I will get back to everyone on these great and interesting ideas.

I have no story in mind with this, just like playing these sort of games with problems that vex and intrigue, though who knows what inspiration such discussions and thoughts might create!


----------



## chrispenycate (Sep 19, 2011)

The impulse will move down the pole at the speed of sound in the material the pole is made of. This can be a lot faster than the speed of sound in air (depending on the rigidity of the material), but, even with diamond (at 12,000 m/s) will be a lot slower than the speed of light (300,000,000 M/s).

So you'll have died of old age before the far end moves.


----------



## RJM Corbet (Sep 19, 2011)

chrispenycate said:


> The impulse will move down the pole at the speed of sound in the material the pole is made of. This can be a lot faster than the speed of sound in air (depending on the rigidity of the material), but, even with diamond (at 12,000 m/s) will be a lot slower than the speed of light (300,000,000 M/s).
> 
> So you'll have died of old age before the far end moves.



Yes, so whatever wave or pulse or particle you send along that pole, will travel at some speed depending on what it is, and what the pole's made of, but can never travel faster than light, and if you shift the whole pole, it cannot travel faster than light either ..?


EDIT: _Huttman_ that _rebel science_ link, to me, is not scientific at all, at all.

If there are two bodies and one _appears_ to be moving away from the other, like galaxies, which one is actually moving? 

If I walk away from you, it's obviously me in motion. But relativity only applies to large distances and high speeds. Or very small distances and high speeds, at atomic level. At quantum level it's impossible to determine both position and velocity. It's one or the other, it's not a maths trick but a fact and a riddle of nature. Newtonian physics is adequate for everyday distances and speeds.

So I don't know where this 'rebel scientist' comes with his physics, but he really doesn't seem to have thought it thru?


----------



## Huttman (Sep 20, 2011)

Wow, someone posting something on the internet that was not right? I'm aghast! Actually, thank you for clearing that up, RJM. I glanced at it only but did not read through it thoroughly like I should have. Even with my novice understanding of science I should have seen that as well.

P.S. I think everything is in motion, constantly. Everything.


----------



## J Riff (Sep 20, 2011)

Waitaminit...we have a teeter-totter a light year long. One end starts down... and the other end waits for physics to say it's OK to move up>?


----------



## PTeppic (Sep 20, 2011)

The question seems to be changing here. Is it a pole that we're pushing in the direction of its length or a teeter-totter/see-saw?


----------



## RJM Corbet (Sep 20, 2011)

J Riff said:


> Waitaminit...we have a teeter-totter a light year long. One end starts down... and the other end waits for physics to say it's OK to move up>?





PTeppic said:


> The question seems to be changing here. Is it a pole that we're pushing in the direction of its length or a teeter-totter/see-saw?



If one end is moving up and the other down, around a central fulcrum point, you're going to end up with the same effect as if two equally spaced points were revolving around a central point, like spokes on a wheel ...?


----------



## Ursa major (Sep 20, 2011)

RJM Corbet said:


> If one end is moving up and the other down, around a central fulcrum point, you're going to end up with the same effect as if two equally spaced points were revolving around a central point, like spokes on a wheel ...?


Given the slow speed of propagation, only limited movement at one end (a few thousand kilometers, perhaps) and a reasonably "fast" movement**, wouldn't the movement at one end of the pole have stopped long before the other end has started moving?

If the fulcrum were to be replaced by an axle, they could (eventually) be moving at the same time, but the pole would not look like a spoke as it would be curved. (I'll leave someone else to work out the curvature of the pole given, say, a one light year length and a speed of propagation through it of 12000 m/s. Choose your own figure for cycles per light year and time, if any, to accelerate to this. )



** - This is a thought experiment. If we allow for an apparently (relatively ) static fulcrum have a light year away, we can allow for some serious force to be applied to one end of the pole.


----------



## RJM Corbet (Sep 20, 2011)

So how high will a pole-vaulter be able to clear with a light-year pole?

Bets paid out when he lands ...


----------



## PTeppic (Sep 20, 2011)

The material of the pole seems to be vital.

If my dodgy maths is right, if a 1km pole of graphene (1cm2 in area) were pushed with 1N force, the pole would compress by 10um. Which for a light-year length bar, seems to be around 95,000km. Wow.


----------



## Ursa major (Sep 20, 2011)

Impressive....


----------



## Metryq (Sep 20, 2011)

The universe will turn out to be much smaller than previously expected. Thanks to an Asteroids-like "round space" effect, the person pushing the pole will merely poke himself in the back of the head.


----------



## TheTomG (Sep 30, 2011)

So, amusing that not long after this discussion started up, where the question of going faster than the speed of light is raised, there is a suggestion that neutrinos are perhaps doing this already:

http://sanfrancisco.ibtimes.com/articles/222081/20110929/faster-than-light-neutrinos-would-not-necessarily-prove-einstein-wrong-cern-theory-e-mc2-special-the.htm

So, now we can modify our thought experiment and say if we have a light year long pole made out of neutrinos....

Ouch I just poked myself in the back of my head


----------



## Vertigo (Sep 30, 2011)

A little off topic but never mind; during some research into relativity equations recently I came across this:



> So the idea that the rocket's ceiling ages faster than its floor (and that includes the ageing of any bugs sitting on these) transfers to gravity: the ceiling of the room in which you now sit is ageing faster than its floor; and your head is ageing faster than your feet.  Earth's rotation complicates this effect, but doesn't alter it completely.
> This difference in ageings on Earth has been verified experimentally.  In fact, it was absolutely necessary to take into account when the GPS satellite system was assembled.


 
I always knew there had to be a reason why I have such a youthful body with such a wise old head


----------



## Ursa major (Sep 30, 2011)

It wouldn't be true if you were lying.








(Down, that is.)


----------



## Vertigo (Sep 30, 2011)

You know I figured that would be an opening for you Ursa!


----------



## Metryq (Sep 30, 2011)

Perhaps this explains the FTL neutrinos at CERN—the light-measuring clock at the receiving station is mounted high on the wall, and the neutrino-measuring clock is set in the floor like a bathroom scale.

/sarc


----------



## BookStop (Sep 30, 2011)

I heard that neutrinos move FTL, but I thought the difference was so little that it wouldn't necessairly make a measurable difference to someone pushing the pole.

Do we know how neutrinos move through seemingly solid objects?


----------



## Ursa major (Sep 30, 2011)

From Wiki:


> Neutrinos do not carry electric charge, which means that they are not affected by the electromagnetic forces that act on electrons. Neutrinos are affected only by the weak sub-atomic force, of much shorter range than electromagnetism, and are therefore able to travel great distances through matter without being affected by it. Neutrinos also interact gravitationally with other particles.


 

The question I have is: if neutrinos, which do have mass, are exceeding _c_, how has this affected their mass?


----------



## Vertigo (Sep 30, 2011)

Ah now Ursa that is exactly the question that I suspect has all the scientists in a tizzy right now as, if all the measurements are correct, then it should be *greater* than infinity  (since mass goes infinite at the speed of light).

Bookstop: all apparently solid matter is mostly (by a long long long way) empty space; vacuum. Much like the universe in fact; if you threw a planet through the densest part of a galaxy the chances of it hitting anything significant are microscopically small. Matter only appears solid due to the elctromagnetic forces that prevent other matter from "slipping between the spaces". However as neutrinos are very very small and have no charge they are not constrained in the same way, so flying through solid matter for them is just like the planet flying through the galaxy. This is why they are so hard to detect. Occasionally (very occasionally) a neutrino will strike something giving a measurable event.


----------



## BookStop (Sep 30, 2011)

So would that leave one to assume that neutrinos, which travel through our space slight faster than light, then they would travel through a seemily solid (mostly empty space) object even faster than light could. That is to say, would like be more likely to strike objects?


----------



## Vertigo (Sep 30, 2011)

That all depends it is by no means certain they do travel faster than light. The scientists that ran the experiment think it more likely that there is a flaw in the experiment than that neutrinos move faster than light. Also the way they and light interact with matter is very different.


----------



## Nik (Oct 2, 2011)

IMHO, the original 'pole' problem comes down to the 'speed of sound' in the material, per CPK's reply. Whether you thump the end or the side, the displacement wave must propagate through the material...

Sounds like a wave-guide, where the 'source' doesn't 'know' the other end is open or terminated until twice the single transit time...

( IIRC, this is also related to how seismometry can establish how Earth has a solid core surrounded by liquid outer core, then the liquid mantle: shear waves can't pass through liquid... ;- )

FWIW, there's nothing to prevent particles travelling FTL. Those hypothetical whatsits are termed tachyons. You just can't have particles with finite rest-mass travelling *at* speed of light...

I'd hope there's new science here, but the odd result may be as simple as miscalculating the mascon effect of the Alps...


----------



## Ursa major (Oct 3, 2011)

Wouldn't a particle, of whatever rest mass, accelerating from zero to FTL at some 'point' be travelling at _c_?


----------



## Metryq (Oct 3, 2011)

Ursa major said:


> Wouldn't a particle, of whatever rest mass, accelerating from zero to FTL at some 'point' be travelling at _c_?



The hypothetical tachyon is assumed to reign at all speeds above the speed of light. So the neutrino could not be a tachyon—unless someone wants to start fudging up all the definitions and math to gloss over this "problem" at CERN.


----------



## Moonbat (Oct 3, 2011)

With the 'pole' experiment, would the distance it is pushed have any effect. 
I can imagine that if the end were hit with a hammer then the 'wave' would propogate through it at whatever speed is determined by its makeup, but what if it was ever so slowly nudged, even just the distance of 1 plank length (or the width of an atom - whichever atom it is made from) would the slow gentle push allow it to move without causing the 'wave' effect as the force is transmitted through the pole?

Because, according to the rules of the thought experiment, the pole is 1 light year long and the question relates to how anything can move faster than light, and in this case it isn't the pole that moves faster than light, but the information that the moving of the 'pole' represents.

Did we ever agree upon a rigidity of the pole?


----------



## Metryq (Oct 3, 2011)

Moonbat said:


> Did we ever agree upon a rigidity of the pole?



A thought experiment can completely ignore all laws of physics, but what would be the point? In reality a pole a lightyear long would not be possible. If it were, then the pole would have too much inertial mass for anyone to move it, and any induced wave would probably dissipate below the noise threshold before passing the orbit of the Moon. Et cetera.


----------



## Vertigo (Oct 3, 2011)

I think you will find that, no matter how gentle the push, a wave will still propagate along its length. In fact it doesn't need to be that long for it to happen. All bodies that have mass have inertia and for the movement to act instantaneously at both ends would require either zero inertia (impossible) or perfect rigidity (possible in the centre of a neutron star maybe?).

The bottom line of course is that, even ignoring the initial impossibility of a light year long pole, you will still not achieve instant movement at both ends. In fact even if your pole was only 1 metre long it still will not move instantaneously at both ends.


----------



## Forgotten Realms (Dec 4, 2011)

Well, to me universe is unlimited if you see it as a whole. When our "universe" ends, the next one begins. It's infinite. Boundaries are set by people themselves because it's difficult for some coping with extension beyond their grasp. But universe is not unchangeable neither fate. Everybody of us is there in the link to make a change, to make us ourselves and the world tick.

Concerning solid matter I'm far away from any standardized ideas as - here I agree with you, Tom - solid matter only seems to appear solid. There are a lot of particles, molecules and atoms, that are gathered in such a density that they make matter look solid. When the particles are disturbed or drift apart, so-called solid matter will crumple into nothing. That is why such solid buildings like concrete buildings or even more solid looking things are fading away. Nothing of solid matter is of constant duration. 

Seeing it this way, I come to the following conclusion: When atoms are blown away, they will gather at another place, founding another solid structure, could be the same form, but even could be another one - could be the same particles, could be the same mixed with other ones. Could even be the same time, but also could be another one. I always considered this as a reasonable (reasonable for me!) explanation for the Philadelphia experiment. So, time travel and teleportation seems quite possible to me.

Concerning your pole theory, I think the atoms are shifting to another place and gathering at a new one. Time plays no role, could be in one year, could be at once - depends on what makes the solid pole to move and when ;-)


----------



## Metryq (Dec 5, 2011)

*Forgotten Realms* wrote:

• Well, to me universe is unlimited if you see it as a whole.

Ah! Logic at last. </sarc>

• But universe is not unchangeable neither fate.

By definition, fate is unchangeable. The opposite is free will. Both concepts belong to the world of philosophy, not physics.

• I always considered this as a reasonable (reasonable for me!) explanation for the Philadelphia experiment.

I thought the movie had nice atmosphere, but I knew nothing of the conspiracy theory when I saw the movie. I thought the ship's name, _Eldridge_, was a play on the word eldritch ("weird and sinister or ghostly"). Then I learned of the wild stories and had a good laugh.

Science is constrained by what can be empirically tested. It's a bummer, I know. But if you can come up with documentation of these evaporating/teleporting particles, we'll start getting that pole built.


----------



## Forgotten Realms (Dec 5, 2011)

Thanks, Metryq, but in first line I'm some kind of a philosopher. Perhaps I was mislead by the title "Thought"-experiment, which does not automatically qualify that things have to be proved according to the range of physics. I interpreted it more like "What would you think?".

Well, I really do not know what "it's a bummer" means, but it does not sound very positive. Whatever it means, I won't take it an insult and it's o.k.

I have something to come up with, but I don't know if I would have enough post counts to post two links - well, but would be one about "D-branes" and the other one about "Superstringtheory".

http://en.wikipedia.org/wiki/D-brane

http://en.wikipedia.org/wiki/String_theory

It best describes my way of thinking at last.


----------



## Metryq (Dec 5, 2011)

> The theory has yet to make novel experimental predictions at accessible energy scales, leading some scientists to claim that it cannot be considered a part of science.
> 
> ...
> 
> As the theory makes no predictions, it cannot be falsified. Others such Peter Woit state that string theory isn’t even science as it makes no predictions, not even wrong ones, and thus cannot be falsified.



You _did_ read the articles you linked, yes? And just because something is a "thought" experiment doesn't mean it is complete and utter fantasy—unless we're talking about strings and branes. 



> Inductive reasoning moves from specific details and observations (typically of nature) to the more general underlying principles or process that explains them (e.g., Newton's Law of Gravity). It is open-ended and exploratory, especially at the beginning. The premises of an inductive argument are believed to support the conclusion, but do not ensure it. Thus, the conclusion of an induction is regarded as a hypothesis. In the Inductive method, also called the scientific method, observation of nature is the authority.


----------



## TheTomG (Dec 6, 2011)

Just for fun, here is today's interesting mathematical proof of unusual things about our universe:
http://io9.com/5864946/a-mathematical-bug-shows-us-why-the-3d-universe-leads-to-murphys-law

Yep, by thought experiment, it was meant in the way that Einstein would mean it - we can't actually perform the experiment, but we are meant to use mathematics, logic, and scientific principles to try to figure out "What would happen if...."

"It's a bummer" just means it is a piece of bad news, something depressing. "It is depressing that the nature of science is such that it is constrained by the need to empirically test something."

Even thought experiments start with what we know from empirical testing, and try to picture what would happen in extremes that we can't (or not yet) actually test. Basically, empirical testing leads to theories, we then imagine some extremes and see what happens to those theories, if odd conclusions arise, or even inconsistencies.

Ultimately, it would be awesome to actually go ahead and do empirical testing on those extremes, and that somethings becomes possible. With faster speeds and space travel, atomic clocks can test if velocity and time are inter-related as proposed. With bigger and badder particle accelerators, we can generate more extreme events and see what comes out the other end of the collisions.

So the comment was (as I read it) that it's a shame we can't just imagine things, and they become real


----------



## Metryq (Dec 6, 2011)

TheTomG said:


> Just for fun, here is today's interesting mathematical proof of unusual things about our universe:
> http://io9.com/5864946/a-mathematical-bug-shows-us-why-the-3d-universe-leads-to-murphys-law



Thanks, TheTomG, that was fun. I guess it was a good deed when Keiichi Morisato collapsed the wave function of the Schrödinger's Whales.


----------



## odangutan (Dec 6, 2011)

Vertigo said:


> The bottom line of course is that, even ignoring the initial impossibility of a light year long pole, you will still not achieve instant movement at both ends. In fact even if your pole was only 1 metre long it still will not move instantaneously at both ends.


Yes. The standard answer to this experiment assumes that:

1) There is no such thing as a perfectly rigid pole (hyuk hyuk)
2) A non-rigid pole behaves like a series of linked, deformable quanta (think of a train being actually made of carriages and linkages between carriages...what happens when an engine shunts into that train?).

So, yeah, a pressure wave will propagate along the pole at a speed which would very likely be less than light speed, C.


----------



## TheTomG (Dec 6, 2011)

Which is interesting I think, odangutan, because it means when I push a pencil across a table, the other end of the pencil actually takes an amount of time to move. Imperceptible to us, but most likely a measurable amount of time.

Of course that would apply to any sort of movement of any sort of object, things that appear instantaneous and happening as a uniform singular event (the whole pencil moving at the same time) are in fact not so.

That was one of the odd conclusions I was wondering if it were true.


----------



## odangutan (Dec 7, 2011)

Yes, of course.

Imagine that the pencil is made of jelly/jello*. If you pushed one ened then you'd expect there to be some deformation of the pencil, you might even see it. A wooden pencil is more rigid than jelly/jello but it is not _perfectly rigid_; there would be less deformation but there would still be some.

You have to remember that, despite what we might think on our human scale, there is no such thing as a 'negligible amount' of anything as far as the Universe is concerned.

*delete as applicable.


----------



## TheTomG (Dec 7, 2011)

It's a wild and weird world we live in! I was also thinking the other day about the "irresistible force meets and immovable object" and it occurred to me, just like you say here, that EVERY force is irresistible. Doesn't matter how small the force is, there has to be some consequence when it acts on an object - like you say, there's no negligible amount.


----------



## Metryq (Dec 7, 2011)

TheTomG said:


> I was also thinking the other day about the "irresistible force meets and immovable object"



That's a logical paradox, of course. "Solutions" can be as weird as a writer wishes, such as Oscar forcing Igli to eat himself in Heinlein's _Glory Road_. But in the real universe, a "negligible" amount of force would result in the object applying it to the given "immovable object" to rebound. Cosmologies that posit an infinity in all "directions" will show some measure of "give" or compression if one uses the right scale. Outside of that, it is a quantum threshold—how much force before the "immovable object" finally gives way?

By definition, one of the terms is wrong. Paper, scissors, rock.


----------

