SR #X5: Still No FTL Radio?

Back in 2015, to celebrate Albert Einstein’s birthday, I wrote a month-long series of posts about Special Relativity. I still regard it as one of my better efforts here. The series oriented on explaining to novices why faster-than-light travel (FTL) is not possible (short answer: it breaks reality).

So no warp drive. No wormholes or ansibles, either, because any FTL communication opens a path to the past. When I wrote the series, I speculated an ansible might work within an inertial frame. A smarter person set me straight; nope, it breaks reality. (See: Sorry, No FTL Radio)

Then Dr Sabine Hossenfelder seemed to suggest it was possible.

We went round (and round and round; apologies for the heinous length). At one point I thought we were saying the same thing in different ways, but it seems not.

I think it’s still true that, at least effectively, there is no FTL radio.

Dr Hossenfelder’s proposition is that FTL is fine, except where it violates “time’s arrow.” This opposes the idea that FTL necessarily always does, so FTL isn’t fine.

[Experts: Movement along a space-like interval requires imaginary time — time values require the square root of -1. This also suggests FTL isn’t fine.]

So the issue is whether FTL signaling is ever allowed under any circumstance. I’m including this as a footnote for the SR tutorial, since it applies to the “no FTL” theme. Maybe the question isn’t as closed as I thought.

That said, I’m not convinced. The discussion continues on her post, but I’ve dropped out. We seemed to be talking past each other…

§ §

My first comment wasn’t accepted — likely because I linked to the post I wrote. I wanted to know which part of it fails.

Second try without link:

I share the confusion of many of your readers. My question is: if instantaneous communication (an “ansible”) were possible, what would happen if communication was attempted with a distant point where relative motion places the distant point’s past in the volume of simultaneity?

Could instantaneous communication work between distant points that were not in relative motion?

What would happen instead?

Reply:

The same thing that always happens if you try to communicate with your past self.

She’s a busy women with a career, papers, presentations, a blog, and a YouTube channel. Her posts get lots of comments, many not as thoughtful as others. I can understand short replies.

Digging deeper:

But I don’t have an ansible, so that’s not an experiment I can try.

Is FTL communication between distant points *not* in relative motion possible?

Reply:

Is FTL communication between distant points *not* in relative motion possible?

Possible in the sense that you can buy a device that will do it for you? No, at least not right now. Possible in the sense that nothing prevents it. Yes, see video.

“But I don’t have an ansible, so that’s not an experiment I can try.”

The impossibility to send messages into the past has nothing to do with the speed of the signal. It’s impossible because we have an arrow of time.

FTL always opens a (potential) path to the past, which implies the “arrow of time” is always violated (as it turns out “potential” is the key here).

I offered the scenario from the post I’d written:

If you accept the SR scenario where, because of foreshortening, a too-long train fits entirely inside a too-short tunnel (such that doors at the tunnel’s entrance and exit could briefly close), AND if FTL signaling is possible, then there seems a causality issue WITHOUT violating time’s arrow.

Imagine Alice at the tunnel’s entrance, Bob at the tunnel’s exit. The tunnel is very long, but Alice and Bob can signal each other with an FTL device capable of 20x (or whatever) speed of light. Importantly, it does take *some* time; it respects time’s arrow.

Meanwhile, on an even longer train, Carol is at the rear, Dave is at the front. They also have an FTL device that allows them to communicate.

Call t0 the moment Dave and the front of the train, having passed through the tunnel, reaches Bob. The train continues, Dave passes Bob, and — ON THE TRAIN — at some later time t2, Carol and the train’s end reach Alice at the tunnel mouth.

But according to Alice and Bob, at t0, Carol’s clock on the train reads t2 while Alice’s reads t0, just like Bob’s.

Why can’t Carol, at her t2 report to Alice (at her t0) an incident that occurred at Carol’s t1, which Alice can then tell Bob, who can tell Dave, all of whom agree it’s t0, such that Dave can then signal Carol at her t0 about what happens at her (their) t1?

No one is violating time’s arrow, but with FTL signaling there seems a causal loop. Is the scenario wrong somehow?

“Dr A.M. Castaldo” stepped in, but it turned out the doctor wasn’t clear on the scenario. (Dr Hossenfelder didn’t participate. The thread ended.)

On another thread, in reply to another comment, I wrote:

I [wish] Dr. Hossenfelder would tell me exactly why the scenario I presented fails. Time’s arrow flows forward in each part of the scenario, but the combination [of] information between frames, plus FTL signaling within a frame, seems to create causality violations.

It’s a situation commonly presented in a variety of texts, and if it fails, I’m really curious what the proposed failure mechanism is.

My understanding at this point remains that FTL is ruled out because causality and SR are both true.

[I typed that directly in the comment box on the blog page, which is why words got left out. That blog platform doesn’t have a good commenting system.]

The reply put me back at square one:

Wyrd,

I have already said this dozens of times. If you seem to create causality violations then you did not have a consistent arrow of time, hence your scenario is not possible. What I am saying is that faster than light signalling does not lead to causality violations as long as you keep in mind that an arrow of time exists.

I wasn’t responding to the conditional aspect of what she was saying. But she wasn’t responding to our questions, either.

The confusion comes from whether the potential violation is sufficient, or if there must be an explicit means for violation. She seems to argue the latter. Either way, FTL isn’t possible in that situation.

I kept trying:

Sabine, I understand what you’re asserting. I’m asking how the scenario I presented doesn’t respect the arrow of time. It proceeds normally in both frames.

If FTL signaling is allowed from Alice to Bob, why can’t Alice give Dave (through Bob) information she learned from Carol?

You say this can’t work. What part fails due to time’s arrow?

Reply:

The part that fails is the part in which you try to send information against the arrow of time. It’s not a question that can be answered in more detail without you writing down the foliation that defines the arrow of time. But if have a loop, then at least one of the legs must go against the foliation regardless of what the foliation is.

The scenario I presented is well-known and is plenty for her to give a specific answer.

Once more unto the breach:

Well, I don’t know what a foliation is, and the Wiki page for it only mentions GR (once) which isn’t helpful, and the Wiki SR page doesn’t mention foliation at all, so I can’t respond to it.

You’ve agreed Alice can FTL signal Bob, so that’s okay. In the Alice-Bob frame, Carol coincides with Alice, and Dave coincides with Bob, so normal communication between those pairs should be okay. The pair coincidences are simultaneous in the Alice-Bob frame. What part of this fails or is incorrect?

*I* think it’s the allowance of FTL signaling.

Now, as they say, the plot thickens:

Wyrd,

“You’ve agreed Alice can FTL signal Bob”

I have not agreed on any such thing. I have said over and over again that signalling is possible only if it’s not in conflict with the arrow of time. A foliation is slicing of space-time in space and time. Loosely speaking it assigns a direction of time to each point of space at any moment of time. It’s also known as a 3+1 split.

I objected:

Wyrd: “You’ve agreed Alice can FTL signal Bob”
Sabine: “I have not agreed on any such thing.”

But above I asked: “Is FTL communication between distant points *not* in relative motion possible?”
You answered: “Possible in the sense that nothing prevents it. Yes, see video.”

(Seeing the video is where this all started.) So I got the impression you agreed that Alice can FTL signal Bob since they are both in the same frame (at opposite ends of the tunnel). And note that the FTL signaling does take time in their frame. Some very brief period elapses while the FTL message goes from Alice to Bob.

Allowing FTL in one frame seems to allow a causal loop if you also agree Carol can send a message to Alice (which Alice passes to Bob) and that Bob can send a message to Dave. In both cases normally because one party passes, and coincided with, the other.

This is scenario that goes back the Einstein. I ask you to please take a close look at the scenario I described and explain exactly where and how it fails if FTL signaling is allowed.

I hear what you’re saying about time’s arrow (and I do believe time is fundamental and “flows”), but I don’t see how or where it breaks this scenario. That’s the question I’m asking.

She replied:

Wyrd,

Oh, I see, my bad. When I said that FTL communication is possible between distant points, I merely meant that there can be such points, not that it is possible between any such points.

As I have said, if you can produce a causal loop, at least one signal must have gone against the arrow of time. This is why you arrive at a supposed paradox. It is not the faster than light signalling that creates the paradox, it is ignoring the existence of an arrow of time.

So FTL signaling isn’t possible after all? (I’m still assuming the potential violation is sufficient.)

I replied asking if we agree. The reply wasn’t passed. The P.S. comment I submitted was, though:

“…if you can produce a causal loop, at least one signal must have gone against the arrow of time.”

FWIW, I’m not convinced the scenario I presented violates time’s arrow in any particular event. The *combination* of events results in a causal loop, but each event (other than the FTL signaling), as far as I can tell, fully respects known physics and time’s arrow.

The message from Carol to Alice, and from Bob to Dave, certainly respects time. The different slicing of what the two frames consider “simultaneous” is plain SR from Einstein’s own example. Even the FTL signal from Alice to Bob takes a brief time. Every separate event respects time’s arrow.

But the FTL signal introduces a causal loop. I don’t see how time’s arrow has anything to do with it, but I do see that FTL signaling breaks causality. Since I believe in SR and causality, I don’t need time’s arrow to rule out FTL.

Reply:

Wyrd,

“But the FTL signal introduces a causal loop. I don’t see how time’s arrow has anything to do with it”

It’s in conflict with the existence of an arrow of time. Hence, if you know that an arrow of time exists, which we do know, then you know that this cannot happen. Ie, as long as you keep in mind that an arrow of time exists, faster than light communication does not lead to paradoxa. What causes the paradoxa is forgetting that we do have an arrow of time.

Still hasn’t quite sunk on me. To the extent it has, I’m not sure I buy it.

I thought this would be my final comment:

We can at least agree FTL signaling is *not* possible, and I think we’re saying the same thing in why, because “breaks causality” is really just another way of saying “violates time’s arrow.”

I’ll leave it with this: “Time flies like an arrow. Fruit flies like a banana.”

I thought I’d at least get a laugh and that we could end on agreement.

If only:

Wyrd,

“We can at least agree FTL signaling is *not* possible”

No, this is wrong and certainly not something I will agree on. It is not possible to violate the arrow of time. Faster than light signalling is possible as long as it does not violate the arrow of time. Your conclusion that faster than light signalling is impossible because you have made the false assumption that it the arrow of time can be violated is logically wrong.

Drat!

But maybe zeroing in on her view, at least:

“Faster than light signalling is possible as long as it does not violate the arrow of time.”

The problem is that FTL signaling does violate, as you say, the arrow of time.

I walk away confused. First you said FTL signaling is possible. Then you said is isn’t. Now you’re back to saying it is.

Can you show me a scenario where FTL signaling works?

Reply:

Wyrd,

“The problem is that FTL signaling does violate, as you say, the arrow of time.”

No, faster than light signaling does not necessarily violate the arrow of time and I certainly did not say it does. In fact, I have said the very opposite, see blogpost.

“I walk away confused. First you said FTL signaling is possible. Then you said is isn’t. Now you’re back to saying it is.”

What I have said over and over again is that faster than light signaling is not possible if it violates the arrow of time.

“Can you show me a scenario where FTL signaling works?”

Do I have a faster than light signalling machine? Unfortunately not.

She still insists it’s possible. But its starting to sink in what she means.

I asked:

So,… sometimes it works and sometimes it doesn’t?

She replied:

Basically, yes.

Physics sometimes works and sometimes doesn’t? This troubles me.

Pushing the point:

Are you saying Alice and Bob can use their FTL radio just fine unless Carol and Dave zip past in their train? Then it stops working? What is the physical failure mode that prevents it from working?

Does it continue to work if Alice doesn’t get Carol’s message?

If it’s a machine, there has to be a reason it breaks.

Reply:

They can use it as long as that is compatible with the arrow of time.

We’re creating a fine horse puree here.

But this may be the crux:

The point Amos and I keep making is that FTL is never compatible with the arrow of time. There is always some frame of reference where a space-like interval appears to go backwards in time.

One more reply:

“The point Amos and I keep making is that FTL is never compatible with the arrow of time. There is always some frame of reference where a space-like interval appears to go backwards in time.”

This is wrong. There is always a reference frame where a space-like interval appears to to backward in time *IN THE COORDINATES OF THIS FRAME*. As I have said a gadzillion of times, this is totally irrelevant because you can choose whatever coordinates you want. The only thing that matters is that it is compatible with the arrow of time.

She acknowledges the interval that “appears to go backward.”

The question is what happens in different scenarios:

I get that you’re saying Alice can FTL signal Bob, so long as Carol and Dave don’t come zipping past to take advantage of the simultaneity differences.

My problem is this suggests the FTL “radio” works only in the right conditions, so my question is: What is the failure mechanism of the FTL radio when Carol and Dave are present?

If it’s a physical machine, something must account for it working sometimes and not other times.

Reply:

Wyrd,

“What is the failure mechanism of the FTL radio when Carol and Dave are present?”

The arrow of time doesn’t depend on what Carol and Dave or Alice and Bob or Peter and Mary do. You can’t signal against the arrow of time for the same reason as always, it would require decreasing entropy, so it requires extremely finetuned initial condition. As I said, it’s like unmixing dough. It’s not going to happen.

Unless we engage on specifics, this just goes round and round.

I gave up. (Another reader posed a question to me; I answered, but my reply hasn’t posted yet.)

§ §

Dr. Hossenfelder seems to believe FTL radio works, at least in some circumstances. But without specifics, without an example, I’m not sure.

I’m not the only one. The “Amos” mentioned above argues the point in terms of movement along a space-like interval. That debate continues.

Stay slower-than-light, my friends!

∇