Time is a dimension, but not like space

How could an effect precede a cause if there were no speed limit to causality?

No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).

Of course, this doesn't fit with a universe described by general relativity, where time can be different for different observers. But you wouldn't have a universe described by general relativity without that constraint in the first place.

How would you compare two infinities? E.g. speed of light inside a moving train vs speed of light outside of it.

An infinite speed implies instantaneous effect. So it wouldn't matter how you were moving. If two people launched something that travelled with infinite speed, one on the train travelling at 100mph, and one on the ground beside it, it would take zero time for both of them to reach their destination.

At least, that's what I surmise. I'm not a physicist.

Here's a great video explaining how, due to relativity, FTL travel can cause grandfather paradoxes: https://youtu.be/an0M-wcHw5A?si=RYFGOmQOlaC2t0bM

Edit: in short, not all reference frames can agree on the order of events, and FTL events propogate "backwards" between some reference frames.

> How could an effect precede a cause if there were no speed limit to causality?

> No matter how fast an effect propogates, it is always after the cause (with an infinite speed, I guess effects happen instantaneously, but not before).

If everything happens instantaneously then there is no real cause and effect, and the universe would be over before it really got started.

No speed limit does not mean that everything goes infinitely fast.

If the speed limit is infinite, what else would you expect to happen?

Light traveling at infinite speeds, atoms and such not.

If effects were instantaneous then atoms would not exist.

There can be many types of effects in a hypothetical universe.

Imagine a universe like Conway's way of life, where only neighboring cells can be affected in one timestep. Now add to it a rule that all blocks have a color, and the color of all blocks are changed when one block changes color. Now you have a universe with both immediate and non-immediate effects.

Agreed, an infinite speed was just the most extreme edge case of having no limit.

Nice video, thanks for posting.

But what is “One time step” in that universe? We have the idea of a light clock - light bouncing between two perfect mirrors in a vacuum - as an ultimate clock.

The distance between the mirrors is a number of meters. A meter is based on how far light travels in a second. How long it takes light to go between them is based on the speed of light. Speed, distance and time are connected.

If we untether the speed of light and it’s unlimited, then in some sense there is no way to say how long it takes light to bounce between the mirrors - it doesn’t take any time. And there is no way to say how far apart the mirrors are, if light passes between them instantly that implies there must be no gap to cross. If light crosses no distance in no time then it also bounces back covering no distance in no time, ahh does lots of bounces in no time. There goes the concept of a time step and any concept of “non immediate effects”.

If you try and add time as a separate thing, then you have some kind of Conway’s game simulation - but that gives you a way to track where light is (which simulation cell it’s in) and therefore a kind of distance (how far the mirrors are apart in simulation cells) and then you lock down how light moves in “simulation cells travelled per timestep” which brings you back to a fixed speed of light again.

That doesn't mean that light (causality) couldn't be faster, right? You could increase the speed of light (causality) as much as you want and wouldn't run into any paradox.

A ‘one level of cells in one timestep’ is a speed limit, and a very slow one actually.

old grannies driving at 30mph on the freeway, me at infinity.

on edit: not everything travels at the speed limit, if the speed limit right now is the speed of light - then why doesn't everything travel at the speed of light?

People say if the speed limit was infinite that everything would happen instantaneously - but they still need to explain why everything should go at the speed limit in this other universe, when not everything goes at the speed limit in ours.

Almost everything (electrical fields, atomic radius, even speed of sound in materials) seems to derive in some way from the speed of light and related effects.

What does it mean to increase the speed of causality? This seems like asserting that we can add as many tick marks to the axis as we like, since the only universal unit of measurement is a velocity's percentage of C.

If we imagine something going faster than the speed of causality, we're simply misconcieving the properties of space.

Right. The speed limit itself is arbitrary.

I'm having trouble with this assertion. Light travels slower in water than in air, by your assertion that light is the limit of causality; then surely we can create a paradox with ftl right in a pool.

perhaps this is an effect of having a speed limit in a universe, if a universe does not have any set speed limit (which is somewhat different than the phrasing speed limit is infinite) perhaps the discussed derivation of other speeds would not exist in the way it does in our universe.

>Light travels slower in water than in air, by your assertion that light is the limit of causality

The limit of causality is the light speed limit in vacuum, not "whatever happens to be the max speed of light in some medium".

Light (as in visible light) is also irrelevant to this, it's just an example of something moving at that speed.

Mainly in the sense that you can create an amp that goes to 11.

With respect to what, though? One light-second would still be one light-second. The sizes of atoms and elementary particles probably also are a function of that. (We don’t know that, but it seems plausible.)

what assumptions have to be true for such a universe to exist? did it just appear fully formed with N number of cells and defaulting to a color?

a hypothetical universe is mostly worth discussing seriously if there's a physics that is coherent, not just a mathematical landscape. At least it isn't that interesting in the discussion of universes, but might be in discussing mathematical ideas, but those do not necessarily mean there's a universe represented by it.

Yes. You can pretty easily think of an experiment where a waterborne person throws a switch that changes some distant object, only to see that object change "before" they threw the switch because the experiment actually communicated the switch change via an airborne method unavailable to the waterborne observer.

I don’t think that actually works. In this case you’re talking about a round trip, with the switch’s outbound signal traveling fast (airborne/vacuum light speed) and the return signal of the object visually changing traveling slower (water light speed). The total round-trip where you see the effect of flipping the switch would take longer if either leg involved water, but it wouldn’t cause the perception of it to happen ahead of the act of flipping the switch.

I fail to see how a vacuum permits violations of casualty. Care to explain?

Observer A and observer B are mermaids. A throws a switch that turns on a light on a light house. Relative to each observer, the can see the cause and effect. B invents a periscope that allows them to see faster than light. Now B will be able to see the light turn on before the switch is flipped.

Replace periscope with “wormhole” and you get a more traditional experiment. The question of can we use this to violate casualty is non-sensical, because we can’t violate casualty (even with faster than light travel). In the traditional experiment, if I see the light turn on, the cause has already happened; sending a message “back in time” won’t change that.

However, this is only because all frames of reference stay the same. If you could actually travel back in time, who knows what would happen. That’s largely why this whole conversation makes no sense. You can’t violate casualty with FTL, only with time machines and FTL isn’t a Time Machine.

Causality does not depend on the speed of light. Rather, light travelling in a vacuum happens to travel at the maximum speed of causality.

If light is slower in other mediums, that has no effect on how quickly causation can happen.

The vacuum has nothing to do with causality.

It's just that light (if there is nothing in its way, so in a vacuum) will travel at the max speed of causality.

Causality violation can happen in general relativity when something moves faster than the max speed of causality (which is the same speed as light in a vacuum).

In general relativity, FTL can be used as a time machine.

Light moves with `c` speed regardless of medium. Whenever we say light moves slower in a medium, we simply mean it is measured to be slower, it is macroscopically slower, it's as if having a hypothetical vehicle that, when it moves, it always moves with a constant speed, but you measure it by taking the time of departure in place A, time of arrival in place B, measure the distance |AB| on a map, and from that calculate the speed of the vehicle. Your measurement will be affected by exact path shape (which isn't a straight line), as well as the number of times the driver decided to take a break to sleep in a motel, eat something, go to a toilet on a gas station etc.

Then you should be able violate casualty with simple water, otherwise FTL cannot be a Time Machine because it is quite simple to go FTL.

You're saying that an atom's decay rate is a function of the speed of light? What proof do we have of this? Does Newton's law of momentum also erroneously leave out the c component?

FTL is shorthand for "Faster than Light" but here it really means "Faster than Light in a Vacuum".

Light actually has nothing to do with it; it just happens to travel at the max speed allowed by the universe when there's nothing that impedes it's motion (i.e. in a vacuum).

So the acronym should really be "FTLIAV"!

This example seems… bad to me. Are you simply saying that light moves slower from A to B through a medium like water because it takes a path that is less direct to navigate the medium?

The speed limit being infinitely large does not intuitively imply that anything should be able to go at infinite speed.

I agree, that answer is misleading. The way I've always understood it: light is an EM wave, and it interacts with medium that it travels through. When traveling through a vacuum, the "beam" source is the origin, but when traveling through a medium the "beam" is a propagation of emissions from the matter absorbing, oscillating, and re-emitting a photon. These interactions take (an extremely small, but nonzero) amount of time, but the light being absorbed and emitted always travels at c.

This is the experience of a photon.

Faster than light in a vacuum. Not faster than light in other mediums. See the many other explanations on this thread.

There are many things that can go faster than light, most of which we don't know about yet. But one thing is for sure, quantum entanglement can be undone faster-than-light. It's just that nobody has yet figured out how to send information through that medium, and it may even be impossible. But clearly, causality isn't being violated here and it goes faster than light in a vacuum.

Absence of a speed limit doesn't mean all speeds are infinite. It's just the picture everyone assumed before relativity.

You'd be able to use an FTL laser to shoot your own grandfather as a baby. Plus you'd be able to receive an FTL broadcast of what's going to happen tomorrow.

If decay rate is related to the elements composition (seems to be true), and the forces holding elements together include Electromagnetism and the Lorentz Force which also seems to be true, then yes. [https://en.m.wikipedia.org/wiki/Classical_electromagnetism_a....]

See also [https://en.m.wikipedia.org/wiki/Electromagnetic_four-potenti...]

Notably, light is a form of electromagnetism, so this shouldn’t be as surprising as it is. c is an explicit part of many formulas, interestingly. And electromagnetism was the first thing tackled in special relativity.

> How could an effect precede a cause

I can't think of anything purely in the physical plane, though there's this:

https://en.m.wikipedia.org/wiki/Retrocausality

But if one includes metaphysics, one example (there are others) is an individual's anticipation of another individual doing something in the future could cause them to act in the present.

This is quite the stretch on its own, but if you include this (which exists, as much as people don't like to admit it depending on the context):

https://en.m.wikipedia.org/wiki/Consensus_reality

...it is possible, in that it comes down to the question of is it true that the effect proceeded the cause, and if enough people believe something is true, it is true. And if you disagree, observe human behavior for a while and see for yourself - people will tell you it is true with absolute sincerity, and they often will act in the physical plane based upon that "truth". Wars are started over "not true" "truths", perhaps even all of them.

And if that's not enough, another route is perhaps people really can see the future. People with absolute sincerity tell me they can constantly. Perhaps they are hallucinating (they swear to me they are not), but perhaps they are not, maybe it is yet another thing that science has yet to discover, or cannot discover due to non-determinism, non-falsifiability, consensus reality (a theory cannot be(!) true unless there is consensus agreement that it is true), etc.

Please don't shoot the messenger.

Anything is possible if anything is possible.

In this universe, fundamental forces like electromagnetism directly contain things like c, so if c is infinite, everything is going to work very differently.

It's literally the same thing. The medium doesn't matter, see Einstein's equations. It all boils down to "relative to what". Light moves slower around a black hole, and that is in a vacuum. None of the arguments make any actual sense.

There is a maximum speed, "c" that anything can move relative to something else in this universe.

If light happens to move slower than c under some conditions, that is irrelevant. It isn't the speed of light we care about, it is c.

Essentially, when we say FTL, it means "faster than c", not "faster than light".

No. It actually goes slower. https://youtu.be/uo3ds0FVpXs?si=b7sDxNuQkTuwAkcP gives a pretty good overview.

Edit: wrong one https://youtu.be/yP1kKN3ghOU?si=hsBj0RpzOb3JZWdS the one above is the "why."

Maybe we should have started with c. Could have avoided this whole discussion.

Wolfram would disagree.

No. It propagates slower.

https://youtu.be/KTzGBJPuJwM?si=Pab2F0EFsB4oGhUo

But that case can be explicitly ruled. There being no highest speed doesn't mean that there is infinite speed. No edge, no edge case.

> Wolfram would disagree.

many people believed in, and advocated for, string theory. Don't make it real.

> But one thing is for sure, quantum entanglement can be undone faster-than-light. It's just that nobody has yet figured out how to send information through that medium, and it may even be impossible. But clearly, causality isn't being violated here and it goes faster than light in a vacuum.

In quantum entanglement, two particles can be entangled in such a way that measuring one particle instantly determines the state of the other, even if they are light-years apart. This "instantaneous" connection seems faster than light, but it cannot be used to transmit usable information in a meaningful way.

The phenomenon does not violate relativity because no classical information can travel between the particles faster than light. Entanglement is a correlation, not a means of communication and hence NOT a means of causation.