How Faster than Light Speed Breaks CAUSALITY and creates Paradoxes

0:00 - FTL is possible!
2:43 - Why is there a speed limit?
4:37 - Einstein's postulates
6:22 - What if speed of light was infinite?
8:29 - What if we could send instantaneous subspace signals?
13:22 - No warp drives?
14:12 - Special offer from Wondrium

Further reading:

Summary:
If you point a powerful laser at the moon, and spin it 100 times per second, the dot on the moon will move 3X the speed of light. This is ok. The maximum speed limit is not a limit with which things can move, but is a limit on the speed of causality. A cause cannot have an effect anywhere in the universe faster than the speed of light.

What are the implications of having a speed limit on causality? Why is there a limit in the first place? And how would causality be broken if information could travel faster than light.

Only a force can cause something. The speed of information is the speed of a force field. You can’t send information faster than the force field can change. This sets an upper limit on its speed. Light in a vacuum travels at c, the maximum speed because photons are massless. Without mass there is no restriction on its velocity.

Einstein’s theory of special relativity is based on two postulates. Neither of the postulates state that FTL is impossible. Postulate 1: The laws of physics are the same in every reference frame. Postulate 2: The speed of light in a vacuum is constant, and independent of the motion of the source of that light.

But what if this maximum speed was infinite, implying that the speed of light is infinite? For one thing using the equation E=MC^2, it would require an infinite amount of energy to accumulate any mass in the universe. So no massive particles could form.

The other problem is that we would not have light at all. In Maxwell’s equations. c equals one over the square root of the permittivity and permeability of free space. Permittivity is the resistance of free space to the formation of electric fields, and permeability is the formation of a magnetic field by an electric current. But if you set c equal to infinity, it would mean that these interactions of electricity and magnetism would not happen. There would be no waves, and thus, no light.
#fasterthanlight
#causality
What if we kept special relativity, but we allowed faster than light communication, for example like instant subspace communication like in Star Trek? The problem is that in special relativity, it is not clear what instantaneous means. What’s happening “right now” depends on how fast, and in which direction you’re moving. There is no absolute now. The now depends on the reference frame.

For example, imagine Alice on earth, and Bob in a rocket traveling 0.87c towards Proxima Centauri, our nearest neighboring star.

The world line for Alice will be straight up, because she will not be moving in her frame of reference, but she will be moving forward in time. Her clock on her world line will tick normally for her. Bob's clock will be moving at half the rate of Alice's due to Bob's speed relative to Alice

But from Bob’s perspective, he is not moving, and the earth is moving away from him at 0.87c. So from Bob's perspective his clock is running normally. And it is Alice’s clock that is running at ½ the speed of Bob’s clock.

Here's how this would break causality: Alice sends a message to Bob using an instantaneous signal to Bob at her 4 seconds. It would arrive to Bob when his clock reads 2 seconds. But from Bob’s perspective, Bob receives the signal at 2 seconds, when Alice’s clock was at 4 seconds. But her clock is running slower than Bob’s from Bob’s perspective. This means that the signal from Alice would have to travel back in time to reach Bob.

Because Bob receives the signal at 2 seconds, he could read the signal and reply at his 4 seconds using the same instantaneous "subspace" signal. That means Alice would receive the reply at her 2 seconds. She would receive the reply BEFORE she sent the message at 4 seconds.

If this was permissible, Alice could use Bob to send messages to herself in the past. She could send a message to herself at 2 seconds, to not the send the message to BOB at 4 seconds. In that case, how did she receive a reply to a message that she never sent?

Anything that allows information to travel to the past causes paradoxes like this and the grandfather paradox, among others. So such a thing is not permissible, and does not happen according to physics as we understand it. There is no absolute time. And there is no absolute now.

[PublicVoidFoo]

I used instant communication to ask you a question but you gave me the answer before I asked so no need to ask. Thanks Arvin!

[nikolaospavlakos]

The matter of why FTL breaks casuality in special relativity was never explained better than in this video! Kudos!

[WhompingWalrus]

Man, I would say the typical "I wish I had teachers like Arvin when I was in school", but nah - I'm glad Arvin's precisely where he is right now. He reaches way more people this way, and his miraculous ability to put complex topics into plain English as well as these mad useful graphics couldn't exist so completely in any other medium. The fact that anyone can access it, for free, at any time, from any place, and pause/fast-forward/rewind or watch at 2x speed or 1/2 speed - this - everything right here - it's just perfect.

If you're reading this, thank you Arvin (:

[CthulhuTheory]

The problem here lies in time dilation. If the message is sent at 2 seconds and gets to the target at 2 seconds, that's true instantaneous.Same if the response is sent at 3 seconds and gets back at 3 seconds. Causality and paradoxes occur because what's described here is a message traveling back in time itself in the first place. But that's an issue of perspective with time dilation taken into account. If the message travels instantaneously between two points that are not experiencing time dilation, then there is no paradox.

So the answer to this paradox is that even though the transmission to bob was instantaneous and bob appears to have received it in the past according to his clock (but only his clock) the response still comes back instantaneously at 4 seconds and is received at 4 seconds by Alice.

Remember, we're not talking about actual time travel, just perceived time. The universe itself isn't changing, only the way the people involved experience it.

[betaneptune]

This is the clearest explanation of how FTL communication can cause causality problems that I have ever seen. No arbitrary line is drawn that the narrator just states is FTL. Every line of the "subspace" message is explained. Good job, sir! Thank you, sir. BTW, in Star Trek TOS episode "The Enterprise Incident, " Tal says, "The subspace message will take three weeks to reach Starfleet." I don't know where the instantaneous bit comes from. Maybe from one of the later series. No matter. Your explanation is superb! Thanks again. -- Recall that what's instantaneous for Alice is not, in general, instantaneous for Bob, and vice versa. And that's part of the answer.

[jameshughes]

I never intuitively understood what light was or how it propagated until I saw this. I've known logically for ages, but never really 'got' it. For some reason this description really clicked with me, thank you so much for this video.

[alphasalsa]

I’ve heard of the back in time paradox before, but not this well explained, thanks!

[josephcrotty]

This channel is probably one of my most favorite. A gem in a sea of garbage. Never stop making these.

[Dismythed]

If Alice on earth were considered moving away from Bob at the same rate Bob is moving from earth, there would be no dilation. Time dilation is due to Bob's velocity. Without a difference in velocity, there is no dilation. That is why an object in orbit experiences slower time even though it remains stationary over the same spot on earth. It is experiencing greater velocity.

If there is no difference in velocity, then instantaneous communication does not break causality. If one is moving faster than the other, instantaneous communication still has not broken causality because both are still aging forward in time, but at different rates.

If Alice communicates from earth's 4 to Bob's 2, it is because Bob has aged slower. It is NOT because Bob is further back in time. If he slows down in relation to Alice, then he shares the same frame as Alice, but he remains to have aged slower because he accelerated for a time.

Instantaneous communication is EXACTLY THE SAME as if Bob stopped accelerating in that instant. So this explanation of instantaneous communication breaking causality is flat out wrong.

If Bob is moving so that he is experiencing time at half the rate of Alice, then Alice's instantaneous communication will appear to be going 2x speed as he is talking to her, while Bob's instantaneous communication would appear to half the dilation as she observes it. They would be experiencing time dilation in real time from their vantage point. There would be no time travel, no breaking of causality, whatsoever.

So the first diagram is correct because it represents Bob's acceleration, but the second diagram is wrong because it represents a backwards timeframe, which is NOT what is happening.

the second diagram inverts their position while maintaining their time differences. This is an asymmetric inversion of the table, therefore it is wrong. This would represent if the first person were to move into the future though stationary, then they would certainly break causality if they communicated with the person backward in time. This is a time flow diagram, not an velocity difference diagram.

Instantaneous communication is therefore possible without breaking causality because both people have moved forward to the same point in time, just with different experiences of time. Imagine if one person literally experienced time at half the rate as everyone else. It would not break causality for them to communicate with everyone around them. That person is not stuck in the past. He is just not as quick as everyone else. Is a fly 1 day in the future because it experiences time faster than us?

Also, physicists always complicate the matter by directly relating two observers to each other. But it is not their relationship to each other that causes dilation, but it is due only to their differences in velocity, that is, their frame of reference in time. Slowing back down to their starting speed, or returning to their staring position, does not erase the loss of time because time only ever moves forward, NEVER backward.

But slowing down below the speed of those in the starting frame does allow their frame to return to be potentially equal with the one who left. For instance, if a person orbits the sun in the earth's path of transit at twice the velocity that the earth orbits the sun, then all that person needs to do is remain in place at the original starting point and move in a circle equal to the diameter of the earth's surface as at the same latitude for a year, or at least move out and back to match the same distance and velocity until the earth reaches that point again to undo the time variance. But this requires no moving backward in time. It is merely the tortoise and the hare switching places.

[gizmoknow-how]

I saw cool world's YT video on this topic and it was a great video, but I had hard time understanding the causality breakage. Your video almost made me understood the issue of causality breakage.

Right on man, keep it up.

[bensimmons]

Arvin Ash is the most underrated youtube channel in existence. Keep up the beautifully simple explanations to the equally beautiful complex ideas

[roswellautopsia]

This was really well done and explained with great clarity. I had not found this channel before but im sure to keep watching

[crome]

Fantastic explanation, but now I'm more confused about time dilation. In your example about Bob and Alice and how each of them has a "normal" clock according to their own reference frame, and perceive time to be slower for the other - well then, how will their ages have changed when Bob finishes the trip? Isn't he supposed to age slower since he's traveling so fast?

[jamesmitchell]

The problem with the example of Bob and Alice is that in special relativity Bob's perception of time is irrelevant to the way Alice is aware of her relative time space

[BloodJunkie]

Moving lazer across the moon from earth does not break the speed of light. It's like when you move a garden hose too fast and the stream breaks into chunks of streams and no longer stays a constant stream. Same is true for shadows.

[michaelblacktree]

Thumbs up for the Zefram Cochrane reference.

[oldtimerf]

And God said "let there be a speed limit to information transmission, that there may be light" and there WAS light.

[gizmoknow-how]

Einstein's idea of space and time not being absolute, but the speed of light being absolute is nothing short of groundbreaking.

This simple yet complex idea has opened so many doors to the answers to the nature of the universe.

[photoniccannon]

You are excellent at delving into very deep topics and explaining them in ways that people can understand. Always great content as usual

[SahilSharma-jciv]

Firstly I would like to take refrence from an older video, Delayed choice quantam eraser. In the simplified experiment shown, I am taking at face value that the beam splitter were placed in such a way that there is absolutely 50% chance of the photon going downward or through the splitter(since I ain't a pro on the topic or the way actual experiment is conducted). Maybe there are some unknown variables/decoherence which is causing the photon to go through a certain path. And its just the past/present causing the future which is perceived vice versa.

Now about this video, firstly I would like to say that the timeline graph example was one of the best to understand the concept as shown in graph form. But, assuming from this video if there is an AbsoluteTime which is represented in vertical axis, the whole process needs to be done from one reference point. ( I am talking about absolute time coz Earth is also moving, so is the solar system and the galaxy and so forth the universe is also expanding hence all are having some speed hence we may perceive time differently than the absolute time.) The reference point should not be changed mid process. It could be either the absolute time, Alice's time or BOB's time. So the graph shouldn't move after Bob receives message from Alice. If taken from absolute time reference, say Alice sent message at X seconds which is 4 seconds for Alice and 2 seconds for Bob, who even if replies instantaneously the absolute time would still be X which is 2 seconds for Bob and 4 seconds for Alice so how does the message travel back in time? I hope I am not mixed up in the term 'Special relativity'.
But still assuming that somehow the message/information traveled back in time, doesn't it support the Idea of Determinism. The future effecting the past, A loop created which is caused by itself.

I don't know if I am thinking in the right direction but still I loved the video cause it made me think all this. Thanks for the ignition of the thought process and would love to be enlightened/steered more.

P.S. what I actually wrote is so different than what I thought I was going to write when I started. It is the thought process of writing which eventually made this so lengthy and the way it is. I don't know if that too is determinism. :-)