I can’t quite explain why, but the thought occurred to me that if there were no universal speed limit then there could be no identity. Everything could be everywhere else simultaneously. Even actually be everything else simultaneously. Does this make any sense? Would it be possible for anything in the universe to have an identity - as an atom, a photon, a Buick, whatever - if there weren’t an upper cap on speed?
Warp 10.
aka - chronosyncratically infindibulated.
I can’t remember in which book I read it, but there’s a possibility that every atom is the same one. Logically, I think I’m misremembering that, 'cos it would make more sense if it were every electron was the same one, and proton, and neutron.
Ahem, that’s Chronosynclasticly Infundibulated there, Stoney.
<<sigh>>
Must be from Schenectady.
There are a few logical problems with the OP.
Even if there were no upper bound on speed, it would still take infinite energy to move a particle at an infinite speed. Even massless particles require energy to move, so they wouldn’t be exempt. Since infinite energy is impossible*, then all particles would still move at finite speeds. As long as all speeds are finite then nothing could be everywhere simultaneously.
There might be some very odd effects in such a universe, but I don’t think that simultaneity would be one of them.
*in our universe. I don’t think a universe with infinite stores of available energy is possible in any universe though. That would make the equations very top heavy. 
Sorry, QtM I’m going to have to disagree with you there.
I believe the correct term is chronosyncratically. For one’s self being everywhere and nowhere at the same time.
You may be right about the spelling of infundibulated, though.
Why assume that our equations are valid in another universe?
I don’t think you need to invoke infinite speed. Travel at light speed would mean that no time is passing. Hence, “one particle” could be everywhere simultaneously (it takes no time for it to go from here to there to wherever).
Perhaps I’m misunderstanding, but it seems like the OP assumes that two things can’t occupy the same point in space and time without actually being the same thing. I’m not convinced, though.
Are you sure?
Chronosyncratic: From Chrono or time, plus Syncratic, or brought about by fusion of forms of belief/practice.
Chronosynclastic: From Chrono or time, plus Synclastic or curved towards the same side in all directions.
To me, the “synclastic” element is what brings in the “everywhere/nowhere” element.
If there were not a speed limit, logically liight and possibly gravity would travel with infinite speed. This presents a few difficulties.
Well, I was making a joke, hence the smiley. However, if you want to defend the physical existence of infinite energy available to move particles at infinite speeds in any universe you’re free to do so. Please show equations.
Travel at light speed means that no time passes inside the reference frame of a massless particle. Those massed observers outside the reference see that time passes for that particle.
A universe of massless particles moving at light speed may be possible, but along with being contrary to the what the OP asked about, I don’t see how they could be everywhere simultaneously. Massless particles would get created (how, I don’t know) and move in a straight line forever (there would be no gravity in that universe, I don’t think) until they intersect another one. What happens then depends on what the massless particles are. However, definitely no everywhere involved.
Could you try defending this by giving an example of two things that could occupy the same point in same and time without actually being the same thing?
And don’t forget the Pauli Exclusion Principle:
chronosynclastic infundibulum:
Hmm. That almost gave my spellchecker a migraine.
Regarding Einsteinian reference frames:
If you replace the speed of light with instant speed, the Lorenz Transformation becomes the Gallilean Transformation.
Regarding only one electron/proton/neutron in the universe:
Richard Feynman realized that an anti-particle moving forward in time behaves exactly like a normal particle moving backward in time (as plotted on a Feynman Diagram). Someone postulated that a single electron or whatevermaybe bouncing back and forth between the Big Bang and Big Crunch, thus filling the cosmos with all the matter we see throughout time.
Aren’t you describing the bare bones basics of String Theory? Ok, maybe not.
I think String Theory makes everything, everywhere and everywhen connected. I could be wrong, I’m afraid my head will explode if I think about it too much.
Carry on…
But if the particles were travelling at infinite speed, the collisions would happen at the same time that the particles were created. And since given enough time, every particle would collide with every other one, they are all hitting each other at the same time. In fact, I don’t think time could be said to exist in such a universe at all. And without time, could the universe be said to exist?
I need a lie down.
Is anyone going to Aldebaran 7 this week? Could you give me a ride?
Was that you sleeping in the back seat? We got back from Aldebaran yesterday, it was a great trip! Customs was a pain, though. We’re not leaving until tomorrow tonight, and my memory is a little hazy (FTL travel and alcohol can do strange things to your brain), so maybe some other Dopers came along too.
Actually, I had the Pauli exclusion principle in mind when I said it . . . as your quote states, it only applies to fermions (e.g., protons, neutrons, electrons, quarks, etc.). There is a whole other class of particle to which it doesn’t apply, namely bosons (e.g., photons, gravitons, W and Z bosons, mesons, etc.) So far as I know there is no rule against to bosons occupying the same point in space-time. (Although I should mention that it would be impossible to say definitively that they were at the exact same point, because of the uncertainty principle. But I think you could at least say that it’s possible for both particles to have non-zero probability density at a point.) Moreover, the Pauli principle is only a restriction on identical particles (meaning two electrons couldn’t be in the same state, but an electron and a proton could be, because they’re different particles.) And since it’s just a restriction on two particles having the same state, that means even two electrons could occupy the same point in space time so long as they differed in some other way (such as their spin orientation – and since every Fermion has at least two possible spin states, that means you could have at least two of every fermion at a given point.) Although, again, with quantum mechanical particles the best you can really do is talk about whether they both have non-zero probability density at a given point.
At any rate, the exclusion principle would prevent two identical particles (including identical spin states, etc.) from occupying the same point in space time even if they were traveling at infinite speed – it isn’t the speed limit that prevents it, it’s a separate law. As an analogy, think of an infinitely fast particle contained in an impenetrable box. Because of the particle’s infinite speed, it can occupy all points in the box at once (although it doesn’t have to occupy them all, as it could just bounce back and forth on a single line). But it still can’t get outside the box, as those points are off limits due to a separate restriction, namely the impenetrability of the box. It’s not being too slow that was stopping it from getting there in the first place.
I should also mention that simply doing away with the universal speed limit wouldn’t necessarily mean anything could travel infinitely fast, only that there was no cap on speed. Unless something was initially going infinitely fast, or was able to achieve infinite acceleration, it would still take it forever to reach infinite speed.
I’m not convinced. Photons may be able to occupy the same quantum state, and may possess identical properties, as in a laser. But does that in any way imply that more than one distinct photon can occupy the same place at the same time? If two separate photons meet don’t they necesarily interact? If an electron and proton meet as in your example, don’t the other fundamental forces come into play?
Your infinite speed particle in a box must also therefore have infinite energy. Bye bye box. Talk of infinite speeds of particles has no real meaning that I can understand. Nor can physics handle such an object, because it would create a singularity where our current physics doesn’t work.
I’ve already said that raising the upper bound on light speed makes no conceptual difference as long as that speed is still finite, as it must be. The only way to alter that is to make the upper bound infinite and nobody has yet suggested a serious way to handle the infinite energy required.