# "Measured" velocities?

1. Aug 31, 2014

### ViolentCorpse

I was reading Isaac Asimov's introductory physics text "Understanding Physics". In the chapter on Relativity, he mentions in a footnote:

I'm not sure what he means by this. Could anyone elaborate a little on this? I'll really appreciate it!

2. Aug 31, 2014

### m4r35n357

That's rubbish; if the impossible were suddenly possible, and something were to approach us at such a ludicrous speed we would just see it after it had passed us, like we do with the sound of supersonic objects.

3. Aug 31, 2014

### Staff: Mentor

I'm not sure what he means either; it's been a *long* time since I read this book. But I *think* he may have been referring to the fact that it's not really possible to construct a theory of interacting tachyons (objects that move faster than light), and if you can't interact with them, you can't measure them. I can't be sure, though.

4. Aug 31, 2014

### Staff: Mentor

This is true provided the object can emit light (or at least something that we can detect). But that may not be possible; see my post in response to the OP.

5. Aug 31, 2014

### Orodruin

Staff Emeritus
I would hope that he is referring to that the distance between objects can grow faster than the speed of light (i.e., expanding universe). But as it stands I would say this is impossible to tell.

6. Aug 31, 2014

### m4r35n357

Yeah, there's no way to follow the logic, he's postulating something that is not detectable, so it ain't physics.

7. Aug 31, 2014

### D H

Staff Emeritus
It's a bit hard to tell what Asimov was writing about with what is perhaps a quote out of context. That said, what Asimov wrote is wrong, but not for the reasons cited above. What's wrong is that we can and do see objects moving faster than the speed of light. Extremely distant objects have a recession velocity greater than the speed of light. And yet we do see them.

8. Aug 31, 2014

### Staff: Mentor

Hm, yes, it's possible Asimov was referring to this. I don't know if I still have my copy of the book to check the context.

9. Aug 31, 2014

### Matterwave

A recessional velocity is not a real velocity in the sense of the word "velocity" I would argue though...and nowhere do we measure their velocities either, we just measure their redshifts, and it happens to be z>1, which, if we naively plug into the non-relativistic Doppler shift formula gives us a v>c.

@OP: objects which do not interact at all are hidden to us since by definition we can never observe them. Such objects are beyond the realm of physics.

But if they DO have some interactions (perhaps even just gravitationally, like the dark matter for example) then we might be able to start talking about physics.

10. Sep 1, 2014

### ViolentCorpse

Just in case anybody wants to see it in full context for themselves, you can find it on Page#104, Volume 2 of the book. (a pdf version of the book is easily available on the internet). I remember a few pages back another instance where he puts emphasis on the word "measured velocity" for some reason.

Last edited: Sep 1, 2014
11. Sep 1, 2014

### ViolentCorpse

That's the first thing that came to my mind too. But yeah, can't say for sure. It's too vague.

12. Sep 1, 2014

### Staff: Mentor

Hold on, Asimov is a science fiction writer. Did he also write a textbook? That is odd. Without context the comment sounds like a misunderstanding that may have been a plot element so he believes it is true.

13. Sep 1, 2014

### ViolentCorpse

Asimov wrote a lot of material on factual science too and he was a PhD in biochemistry. This textbook I'm talking about should have anyone believe he were a PhD in Physics, though. Yeah, it's introductory with minimal math, but he delivers it with such clarity that it's not difficult to see that it's coming from a man of deep understanding.

I would say he was the most scientifically well-read sci-fi writer. So if it's coming from him, I'd take it seriously. That's not to say he can't be wrong, though.

Last edited: Sep 1, 2014
14. Sep 1, 2014

### Staff: Mentor

I always liked his science fiction.

I read the thing in context and I think he is simply wrong. The context is the velocity addition formula, and superluminal particles are certainly consistent with the formula. If it were in a context like showing why charge is only compatible with a massive particle, then that might have been valid.

15. Sep 1, 2014

### Staff: Mentor

Asimov was extremely prolific. We're talking hundreds of books, including several popular science classics. Some of his stuff was excellent.

16. Sep 1, 2014

### PAllen

But a recession velocity is NOT a relative velocity. It is a growth of proper distance in a given foliation, which makes it unambiguously a separation speed - which can trivially exceed c. As I am sure you agree, relative velocity at a distance is undefined (or, at least, fundamentally ambiguous) in GR. [But if you define it via comparing vectors after parallel transport, it is always < c for timelike vectors].

17. Sep 1, 2014

### mal4mac

It's, largely, Feynman's Lectures on Physics, simplified for high school students (and almost as old!) Asimov does reference Feynman, at least. Not a bad thing, by the way, I remember being entranced by it when I encountered it in my Public Library at the age of 14. Just be careful though, he was a chemist, so he may not get all the physics right. Actually, is there anything else that does as good a job for 14 year olds? I certainly haven't seen anything. It's about time a physics professor had a go at doing something like this. It's a bit embarrassing to be outdone by a chemist?

18. Sep 1, 2014

### m4r35n357

On the subject of causality, and just to point out I'm not knocking the guy, many years ago I enjoyed his "paper" on "resublimated thiotimoline", http://en.wikipedia.org/wiki/Thiotimoline ;)
I don't think his teachers saw the funny side, though.

19. Sep 1, 2014

### Staff: Mentor

Understanding Physics isn't quite a textbook; it's more like a book for the serious lay person, who isn't going to get a degree in physics but wants to understand it at a level beyond the usual "pop science" presentation. Asimov wrote *lots* of books and articles about science along these same lines; for example, I first learned about biochemistry and the Krebs cycle from his book Life and Energy. So yes, he was a science fiction writer, but he wasn't *just* a science fiction writer.

20. Sep 1, 2014

### Staff: Mentor

Is the context anywhere online?

Yes, that's true; but I still wonder if he had some (quite possibly mistaken) idea about tachyons in the back of his mind. The paper by Bilianuk and Sudarshan about the possibility of faster than light particles was published in 1962, four years before this book (although the term "tachyon" wasn't coined until 1967, according to Wikipedia).

21. Sep 1, 2014

### Staff: Mentor

22. Sep 1, 2014

### Staff: Mentor

Thanks! On reading this, I no longer think he had tachyons in the back of his mind (I also don't think he was referring to recession velocities of distant galaxies). I think he was just making a logical error. The passage in the main text that ends with the footnote referenced in the OP is:

But this is not actually a valid deduction. Mathematically, you can deduce the following from the relativistic velocity addition formula:

(1a) If both velocities being added are less than $c$, then their sum is less than $c$.

(1b) If both velocities being added are *greater* than $c$, then their sum is less than $c$.

(2) If one of the velocities being added is equal to $c$, then the sum is $c$, regardless of whether the other is less than, equal to, or greater than $c$.

(3) If one of the velocities being added is greater than $c$, and the other is less than $c$, then their sum is greater than $c$.

Asimov only considers cases 1a and 2 above, and his "deduction" really only allows for case 1a. But logically, all of the cases given above are possible, and considering them all, Asimov's statement is not correct.

23. Sep 3, 2014

### ViolentCorpse

I agree! I wish there were more books like this and Feynam's on all subjects of natural science (and perhaps even maths).

Hahaha. That's great. Thanks for that!

And thanks everyone for clearing the confusion. I guess I must remain on my toes when reading Asimov now.

24. Sep 3, 2014

### D H

Staff Emeritus
I disagree with you here. Now that we have the context, it appears to me that Asimov was indeed writing about tachyons and your case 3 in that footnote.

Rather than saying that the observed velocity would be greater than c in this case, that footnote dismisses your case 3 as non-observable. From a popularization of science perspective, I think that that noting this in a little footnote is a better approach than getting mired in overly technical and an off-topic discussion of what was viewed at that time as conceivably possible but also unobservable. (And perhaps even the footnote was unnecessary from a popularization of science perspective.)

There's no reason to consider your case 1b; Asimov was writing about relative velocities as observed by a subliminal observer.

25. Sep 3, 2014

### Staff: Mentor

I see that this is a possible reading, yes. But if so, he's still making a logical error, because the velocity addition formula he's using is perfectly valid mathematically if one or both of the velocities is greater than $c$. There's nothing in the formula, or in the derivation of it, that restricts "measured" velocities to be equal to or less than $c$. So it is *not* possible to deduce, just from the assumption of constant $c$, that only velocities less than or equal to $c$ can be measured. One would need to add that as an extra assumption.

I agree that that was the case he implicitly had in mind; but that doesn't mean it's the only case that has to be considered, logically speaking.

Last edited: Sep 3, 2014