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I would also add point 3.5 which explains that there has been a historic transition (Electroweak Symmetry Breaking) where particles which were massless and travelling at the speed of light before, slowed down and attained mass due to the Higgs field condensing. As the energy that was released back then due to this transition had to be finite, the Lorentz factor argument about infinite energy can't be entirely accurate: if the transition works in one way without involving infinite energy, it should surely work in the other way too (otherwise energy conservation would be violated).

No, the second argument was "there exists a reference frame such that the paradox is resolved" not " this is the only situation in which the paradox is resolved. "

She just wanted a counter example to the claim "faster than light travel produces a paradox no matter what" by showing " well, not in _this_ case" so there might be other cases. Or even all cases, who knows.

Thank you, agreed.

However, the existence of the privileged frame by itself won't allow the paradoxes to be resolved. It would also require some kind of a "time police" as well, some kind of a process that would force the event ordering to be causally consistent.

I'm trying to visualize this, and it would look like a cone that would block any FTL messages in the direction of the receiver. As the time passes, the cone will get slimmer, until it disappears once the causality catches up.

> It would also require some kind of a "time police" as well, some kind of a process that would force the event ordering to be causally consistent.

If I understood the video correctly, there does not exist a time police at all, let alone one that forces things to be out of order (i.e., causality loop), vs in order or visa-versa. If it's ambiguous, then it's not fair to assume that it would cause a paradox any more than it's fair to assume it wouldn't -- and the argument goes that is not evidence for a paradox at all. Again, hammering down on the argument that "here is a just-as-plausible situation in which there would be no paradox -- however specific it might be, therefore we cannot assume there is a paradox necessarily".

I can't tell if I'm misreading point 1, barely rephrasing:

Special relativity disallows faster than light travel because it requires moving faster than light.

I can't gain a lot of insight from that point.

D'oh. Nope, it's just me typing too fast.

It should be: "Special relativity disallows faster than light travel because you need to cross the lightspeed barrier".

No, that kinda is right - under special relativity, as your apparent velocity from a fixed reference frame increases, it takes more and more energy to accelerate closer to light speed, so _moving_ faster than light is disallowed.

Another way of putting this is: we know because of special relativity that you can't just strap a lot of rocket boosters on a spaceship and expect to go faster than light. That won't work; if you want to _travel_ faster than light, you have to do it another way.

For a particle travelling faster than light (a tachyon) it takes more and more energy to decelerate the closer to light speed you are, and at zero energy velocity would be infinite. At least via a naïve look at what SR says.

> 3. However, from the past experience with physics, we know that mathematical infinities or singularities are often just an evidence of the theory breaking down. So perhaps it's the case here, and a more complete theory will allow to work around the infinity somehow.

Then it won't take infinite amount of energy, just (infinity minus one). Also, how do you stop? need another near-infinite energy?

But also also, due to time dilation and length contraction, wouldn't you end up in a 2d universe where time doesn't pass for you?

> 5. However, if there exists a privileged reference frame, then this can be worked around.

Don't know if she mentioned it, but there is at least a unique reference frame, which is the CMBR rest frame.

She absolutely mentions it. It's basically her entire point.

I was waiting and waiting for her to make her point and explain why FTL would not violate causality. Then she hand waves about the comoving frame in two sentences, insinuating that it might be a preferred frame of SR, and that's it.

It's not like this is some huge oversight that she found there. After all, we define the age of the universe to be in the CMBR rest frame, because it will be less in any other frame. So the CMBR rest frame is unique, yes, but it is not fundamental in the framework of SR. See this, for instance: https://www.astro.ubc.ca/people/scott/faq_basic.html

She also pointed out that causality is weird in quantum mechanics, so it could break at the big scale too!

Why a privileged rest frame avoids paradoxes: It's pretty simple really, I laid it out in my blog post here: https://forwardscattering.org/post/36

So, in the abstract an absolute reference frame eliminates paradoxes, sure, but isn't it the case that in the real universe, every version of the experiment in your blog that has been carried out has found no evidence of such a frame? Because if we're making claims about the real universe as Hossenfelder is doing, that means you can't actually lean on an absolute reference frame. The CMBR might kind of look like one if you squint, but the CMBR comes from matter that is in the end subject to the same relativity we are. Unless some version of the Mach principle turns out be real, with teeth.

Which experiment are you referring to?

Anyway, no experiment to-date has detected an absolute reference frame. But that is not to say that one doesn't exist.

It’s also laid out quite well in the post video.

It's really not. I have no idea from the video what the actual consequences of privileging the co-moving frame are on an attempt at creating a paradox except "maybe not a paradox! :)"

> It would require some pretty un-physical behavior, like not being able to move in certain directions if you receive an FTL message.

I don't think that is necessary, what do you have in mind?

They mistook a diagram in the video showing flow of time for velocity. You can go there and back again in space at faster than light, but your local time bubble runs forward in each case. No traveling back in time. An external observer sees you traveling back in time the way we see gravitational lensing but your personal frame of time marches forward.

>Which is impossible, because you'd need an infinite amount of energy to do that.

To date I’ve never seen any experimental evidence that the energy required for

A -> B = DV1

X -> Y = DV2

Where X >>> A and DV1 == DV2, was any different. I’ve read countless people claiming it is so under existing theory, but again I’ve seen no concrete experimental evidence.

Imagine two people standing on the “nose” of two mostly identical but different asteroids in vacuum, where one is traveling at 1000mph relative to galactic center and another at 95% the speed of light.

If both jump with equal force I believe they’d accelerate the same, though one should in theory require far more energy to do so if acceleration towards C requires exponentially increasing energy.

I’m aware of the existing theory hack around “reference frames” and that the rate of time is different in each location due to the dV but I don’t actually believe that any of that occurs for macroscopic masses.

There’s better evidence velocity messes with our clocks than velocity messes with time.

force = mass * acceleration.

At relativistic speeds, the mass goes up (significantly).

So the same amount of force results in lower acceleration.

>At relativistic speeds, the mass goes up (significantly).

What evidence is there of this actually occurring with any human-scale masses?

I'd guess none for human-scale masses, but lots of evidence from particle accelerators of electrons having huge mass/energies.

Good luck witnessing a human sized thing moving at that sort of speed.

There's this, however: https://www.scientificamerican.com/article/stars-that-race-t...

> but I don’t actually believe that any of that occurs for macroscopic masses.

How could it not if it does for smaller masses? What is the theory for the difference?