# If Julian Barbour is Correct, is the Speed of Light Special?

According to this article in Discover Magazine, Albert Einstein's Theory of Relativity is wrong, because it didn't fully live up to the ideas of Einstein's idol, Ernst Mach. Mach proposed a truly relative theory of relativity, where nothing in the universe has an exact position, only a relative one based on the positions of other objects. Barbour thought Einstein's relativity created relative positions, but only by linking them with time. He has been trying to make a new theory in which both space & time are completely relative. At least, that's what I can gather from the article.

Another "absolute" in Einstein's relativity, which the article did not go over too much, is light. Einstein thought light is the "speed limit" of the universe. The way I understand it, any 2 people, no matter how far apart they are or how fast they are going, see an event at a 3rd location as happening at the same time, relative to their locations.

Therefore, whenever you move, you travel through not just space, but also time (called time dilation), because others must see you at each different place at the same time as each other. Therefore, we can not travel at the speed of light, because then others would see us at all places at once. I believe that if we go faster than the speed of light, we travel backwards in time because others see us going backwards. If any of this is wrong or confusing (I'm sure it is), please feel free to ask for clarification or just edit if you have enough rep.

Has Barbour theorized publicly about the special place in Einstein's theory for the speed of light? In Barbour's theories, is the speed of light some mystical breakpoint in the laws of physics, where you travel forward in time by going slower, then backwards in time by going faster, and who knows what happens when you go exactly that speed? We have done tests that seem to confirm time dilation, but I'm not aware of any tests that measure time dilation relative to the speed of light. In short, Is the speed of light special in Julian Barbour's theories of relativity like it is in Einstein's?

• Relevant: en.wikipedia.org/wiki/Shape_dynamics – Brandon Enright Nov 14 '14 at 4:17
• Interesting. The Wikipedia article mentions Weyl, just like the Discover article. You don't usually get to see how connected everyone's theories are to each other unless you really study this stuff. – trysis Nov 14 '14 at 4:44
• Practically half the mathematics of physics is based on the amazing work of Hermann Weyl. – Brandon Enright Nov 14 '14 at 5:06
• Then it's strange that Einstein liked Weyl's theory potentially disproving his own, but threw it out because it was "mathematically messy". Sour grapes, perhaps? – trysis Nov 14 '14 at 5:10
• I think your characterization that shape dynamics disproves general relativity is not correct. I don't know what most physicists think about shape dynamics however shape dynamics isn't trying to disprove general relativity, it's trying to be even more general than general relativity. – Brandon Enright Nov 14 '14 at 6:01

You are pushing very hard on the limits of this site, trysis. This site focuses on established physics. Julian Barbour is far removed from established physics, so far removed that he can't get a job as a physicist.

That said, you are very much misreading that pop sci article. Barbour's complaint is that general relativity is not fully Machian. He has no complaint with regard to the speed of light being special.

If space-time constitutes a differentiable space then there are two possible answers regarding a speed that all observers will say is the same locally. One possibility is that this universally agreed upon speed is infinite. This results in Newtonian mechanics. The other possibility is that this universally agreed upon speed is finite. This results in relativistic mechanics. The third choice, that spacetime is not a differentiable space goes far, far beyond established science. Even Barbour doesn't go that far (but some theoretical physicists do).

All experimental evidence is consistent with

• That space-time is a differentiable space,
• That the universally agreed upon speed is finite, and
• That this universally agreed upon speed is the speed of light.

Barbour, along with some others, want a universe that is fully Machian. General relativity, while motivated by Mach's principle, is not fully Machian. For example, one can meaningfully ask in the context of general relativity whether or not the universe is rotating. From a Machian perspective, this question makes no sense. It's a downright stupid question from a Machian perspective.

• I apologize. I was just so taken by that article & I almost want to see him succeed. That said, I agree he is way out there with his theories. – trysis Nov 14 '14 at 14:38
• Julian Barbour is far removed from established physics, so far removed that he can't get a job as a physicist. He publishes in refereed journals, e.g., arxiv.org/abs/gr-qc/0407104 . I don't see what the problem is. – Ben Crowell Nov 14 '14 at 15:44
• @BenCrowell, I don't know the guy and his work, but if you look at your link you'll see he's one of five authors and he has no affiliation. Again, I have no opinion on him but I write this in the interest of understanding how metadata of publications work. – Helen Apr 19 '17 at 17:14
• @Helen--Julian Barbour is one of the world's greatest mathematicians, who's best known as having solved an extremely well-known conundrum known as the "three-body problem". But math isn't physics, and the physicist Godel's Incompleteness Theorem has, since the 1940's, left its influence on physics a little reduced. Barbour's cosmological theory, worked out in collaboration with the physicists Koslowski and Mercatti, will be described in a popular science book titled "The Janus Point" that Random House is planning to release on Aug. 29, 2019. – Edouard Jul 10 at 15:16

Light can only travel at one speed (in a vacuum), approximately 300,000 km/s. It doesn't matter what frame of reference it is created in, it never goes faster or slower than this speed, and it doesn't matter what frame of reference you are measuring it from, you will always measure it to be the same speed.

This is given by Maxwell's equations, Einstein's Theory of Relativity and backed up by all experiments we have done to test this. I don't think anything contradicts this including Julian Barbour's theory.

So in this sense the speed of light is special. In another sense the speed of light has to be something so whatever figure it is is not remarkable in itself, it is simply another constant of physics.

From what I can gauge from that article, Julian Barbour's theories are essentially the same as Einsteins theory of relativity in that they predict the same things. Where they differ seems to be in the separation of time from space-time and in the definition of a theory of gravity which is not based on space-time. In Julian Barbour's theory time is emergent (not tided to space) but otherwise roughly the same (e.g. time dilation still occurs). This had some repercussions for gravity at larger distances (due to the different interpretation of time) that may effect our understanding of dark matter and dark energy. But nothing conclusive so far.

Another "absolute" in Einstein's relativity, which the article did not go over too much, is light. Einstein thought light is the "speed limit" of the universe. The way I understand it, any 2 people, no matter how far apart they are or how fast they are going, see an event at a 3rd location as happening at the same time, relative to their locations.

Your understanding is incorrect. You cannot compare clocks in different frames of reference, nor agree on an event in a third frame of reference as having occurred at the same time in those two frames of reference. You are correct that the speed of light seems to be the 'speed limit' of the universe. All experiments we have done bear this out (nothing has ever been measured going faster than the speed of light) and it seems likely that nothing can be. I couldn't see anywhere that Barbour's theory differed from or contradicted this.

Therefore, whenever you move, you travel through not just space, but also time (called time dilation), because others must see you at each different place at the same time as each other.

We are always travelling through time (time always travels forwards) and essentially Earth is moving through space so we are always moving. I don't think this the right way to look at things. Its better to think of time dilation as occurring as speeds approach the speed of light. Time dilation simply means that time slows down for that frame of reference (relative to a stationary one). Both frames are still there and can measure things, its just that their clocks may differ in the times they record for events outside their frame of reference.

Therefore, we can not travel at the speed of light, because then others would see us at all places at once.

No this is wrong. We can't travel at the speed of light as it requires increasingly more energy to accelerate us to that speed (infinitely so) so we can never reach it. But extrapolating (thought experiment only) then if we see someone in a spaceship travelling past us at the speed of light, we see time frozen for them (e.g. no movement whatsoever in the space ship, including no aging of the pilot, no electrical signals, no movement of air particles, etc). The spaceship is entirely frozen relative to itself, but relative to us it is flying by at the speed of light. It's not everywhere, its still a single entity moving past.

I believe that if we go faster than the speed of light, we travel backwards in time because others see us going backwards. If any of this is wrong or confusing (I'm sure it is), please feel free to ask for clarification or just edit if you have enough rep.

People have postulated this but currently it is just extrapolating the laws of physics past their known limits. As far as we know you can't go faster than the speed of light so this can't occur.

Is the speed of light special in Julian Barbour's theories of relativity like it is in Einstein's?

I'm just going by what I read in the link to the article you provided but from what I understand Barbour's theory doesn't treat the speed of light any differently from Einstein's theory of relativity. E.g. its still the speed limit for all matter and nothing can go past it. His theory does separate time from space, but I don't think this leads to any new behaviors of time (e.g. travelling backwards in time) or for time dilation at relativistic speeds (e.g. it would still behave like Einsteins models predict).

When an observer starts moving towards a sound source, the wavefronts start hitting him more frequently, which is obviously caused by the increase in the speed of the waves relative to the observer:

http://faculty.washington.edu/wilkes/116/slides/Physics116_L08-interference.pdf "Sound waves have speed c, and f and L are related by c=Lf. For an observer moving relative to medium with speed u, apparent propagation speed c' will be different: c'=c±u. Wavelength cannot change - it's a constant length in the medium, and same length in moving coordinate system (motion does not change lengths). Observed frequency has to change, to match apparent speed and fixed wavelength: f'=c'/L."

When an observer starts moving towards a LIGHT source (with small speed u), again, the wavefronts start hitting him more frequently, and the frequency shift obeys exactly the same equation as in the case of sound: f'=(c+u)/L. It is quite reasonable to conclude that, for light as for sound, the frequency shift is caused by the increase in the speed of the waves relative to the observer, in violation of Einstein's relativity:

http://www.youtube.com/watch?v=bg7O4rtlwEE "Doppler effect - when an observer moves towards a stationary source. ...the velocity of the wave relative to the observer is faster than that when it is still."

It is not difficult to see that Einstein's relativity can only be saved if the observer can somehow change the wavelength of the incoming light. That is, as a result of the motion of the observer, the wavelength of the incoming light must shift (at least the observer should somehow see it shifting) from L to L'=cL/(c+u).

Unless Einsteinians find a way to justify the real or apparent shift from L to L'=cL/(c+u) caused by the motion of the observer, Einstein's relativity is doomed.