Exceeding the Speed-Of-Light Explained Simply (and the Quantum riddle solved at no extra cost)

It has recently been in the news that some particle may have exceeded the legal speed limit for all things : 299,792,458 metres per second.

Of course, this will probably turn out to be a bad sum somewhere or perhaps waves ganging up, but the whole hubbub has raised my hackles, and here’s why.

Because Albert Einstein at no time said what they say he said (see here for example). They misunderstand relativity! Things can move at any speed we want, and I will try to explain the fuss now.

So let’s get to it!


First, we have to consider the way space warps when we move.

The problems started when people realised that light always seems to have the same speed, regardless of the speed you were moving when you saw it. This seems to be a contradiction, because surely if you fly into the light ever faster, it will pass you ever faster?

Well the tests were pretty clear, this does not happen. The speed is always c.

For several years, people were unsure why – until they were told by Einstein in 1905. In the meantime, another ponderer of the problem (Lorentz) decided to write down the maths that are required to square the circle.

The so-called Lorentz equations show, unequivocally, that space and/or time need to warp in order for relative speeds of c not to be exceeded, even when two items are going very close to c in opposite directions to one another.

So something needed to give, and it was space and time!

So, newsflash! it was not Einstein that first published on space and time warping. His contribution (along with Henri Poincaré and a few others) was to explain how and why. His special theory showed that because there is no ‘preferred’ frame of reference, a speed limit on light was inevitable. The term ‘relativity’ come from this – basically he said, if everything is relative, nothing can be fixed.


Ok, so we have some nice observations that nothing seems to go faster than the speed of light  – and we have a nice maths model that allows it. So why do I persist in saying things can go faster than the speed of light?

Let me show you…

There is a critical difference between ‘going’ faster than light and being ‘seen to be going’ faster than the speed of light, and that is where I am going with this.

So lets take this apart by asking how we actually define speed.

If a particle leaves point a and then gets to point b, we can divide the distance by the time taken and get the mean speed (or velocity to be pedantic).

The issue with relativistic speeds are that the clock cannot be in both point a and point b. So we need to do some fancy footwork with the maths to use one or other of the clocks. So far so good. This method will indeed never get a result > c.

The nature of space forbids it – if the Lorentz transformations that work so well are to be taken at face value, then for something to exceed c by this method of measurement, is much the same as a number exceeding infinity.

So all is still well. Until you ask, what about if the clock is the thing that travelled from a to b?

In this case, the transformations cancel! The faster the movement, the slower time goes for the clock, and you will see its ticks slow down, thus allowing its speed to exceed c.

The clock will cover the distance and appear to have tavelled at c on your own (stationary) clock, but the travelling clock will have ticked fewer times!

If you divide the distance by the time on the travelling clock, you see a speed that perfectly matches what you would expect should no limit apply. Indeed, the energy required to create the movement matches that expected from simple Newtonian mechanics.

The key point here is that while the clock travelled, the reader of the clock did not. If you do choose to travel with the clock, you will see it tick at normal speed, and see the limit apply – but see the rest of the universe magically shrink to make it so.

Some have argued that I am not comparing apples with apples, and that by using an observer in a different frame to the clock I am invalidating the logic.

To those who say that, I have to admit this is not done lightly. I have grown more confident that this inference is valid by considering questions such as the twin paradox over and over.

The twin paradox describes how one twin who travels somewhere at high speed and then returns will age less than his (or her) stationary twin.

Now if we consider a  trip to Proxima Centauri (our nearest neighbour) the transformations clearly show that if humans could bear the acceleration required (we can’t) and if we had the means to get to, say, 0.99c for most of the trip, that yes, the round-trip would take over 8 years and no laws would be broken. However the travellers themselves will experience time 7 times slower (7.089 to be precise). Thus they will have aged less than 8 years. So, once they get home and back-calculate their actual personal speed, it will exceed all the live measurements.

This has bothered me endlessly. Although taken for granted in some sci-fi books (the Enders Game saga for example) this clear ‘breakage of the c-limit’ is not discussed openly anywhere.

Still uncertain why people were ignoring this, I read a lot (fun tomes like this one) learned more maths (Riemann rules!) and also started to look at the wider implications of the assertion.

On the one hand, the implications are not dramatic, because instant interstellar communication is still clearly excluded, but that whole issue of needing a 4 years flight to get to Proxima Centauri is just wrong. If we can get closer to c we can indeed go very far into the universe, although our life stories will be strangely punctuated, just as in the Ender books.

But what about the implications for the other big festering boil on the body of theories that is physics today – quantum theory?

Well, if one is bold enough to assert that it is only measurement that is kept below c and not ‘local reality’, then one can allow for infinite speed.

In this scenario, we are saying measurement is simply mapping reality through a sort of hyperbolic lense such that infinity resembles a limit. Modelling space with hyperbolic geometry is really not as unreasonable as all that, I don’t know why we are so hung up on Euclid.

With infinite speed at our disposal, things get really interesting.

We get things like photons arriving at their destination the same tme they leave their source. Crazy of course… but is it?

Have we not heard physicists ask – how is it the photon ‘knows’ which slit is blocked in the famous double slit experiment? It knows because it was  spread out in space all the way from it’s source to it’s final point of absorption.

If you hate infinities and want to stick with Lorentz, you can equally argue that, for the photon, going exactly at c, time would stand still. Either way, the photon feels like it is everywhere en route at once.

If the photon is indeed smeared out, it probably can interfere with itself. Furthermore, it is fitting that what we see is a ‘wave’ when we try to ‘measure’ this thing.

A wave pattern is the sort of thing I would expect to see when cross sectioning something spread in time and space.

Please tell me I’m wrong so I can get back to worrying about something useful. No, don’t tell me – show me – please! 😉

7 thoughts on “Exceeding the Speed-Of-Light Explained Simply (and the Quantum riddle solved at no extra cost)


”the travelling clock will have ticked fewer times” than the stationary clock because the minute hand of the travelling clock needs to not only move across a small part of the clock’s face, but also across the distance travelled by said moving clock & against any air resistance ~ even though every part of the clock (casing, face, hands, springs etc) is travelling at the same speed, the hand has to reach a point on the clock’s face that keeps moving away from it, so that hand would need to move faster than usual to keep a proper account of time… 
It’s surprising that the hand ever reaches the next point on the face of the travelling clock ~ i guess its success depends on how fast the clock is travelling.
Ultimately it is the hand of the travelling clock which has slowed down, not time itself; we need to use a g-force proof clock to check if / how travel affects time itself.

(love your double-slit theory by the way ;)

    1. RE my above response to your time slows down theory:

      when i saw a demonstration of a clock tickiing slower because it was travelling, the clock was facing me / the observer, and the clock’s minute hand was moving in the same direction as the train carring that clock ~ they were passing infront of me, from my left to my right ~
so that was the image i had in my head when i read your related article & when i responded to it.
I then realized that, if the clock had faced any other direction, most [if not all] of my post would make no sense at all…hence this explanation / apology.

      I do still think it’s the timing device, not time itself, that slows down, but then i’ve never crossed the galaxy in a rocket and returned to find that i’m the only one who isn’t old …nor have i found a plausible and easy to understand explanation of why that might be possible.

      Am still looking though, so please do share any new related insights!

  2. Hi Jackie. Thinking about moving clocks is (for me anyway) one of the delights of life.
    Whether ‘things’ slows down, or time itself, is perhaps a moot point, what is time other than the meter of the progress of things?
    I have written a bunch of posts on this: http://theprovincialscientist.com/?tag=time

    I for one am pretty sure that ‘time’ itself distorts, and that it is continuous, but that’s just my instinct, I can’t prove it.
    It is based on my understanding of fields and how we know mass distorts space-time – if light curves becuase it is going straight through curved space-time, can we not be sure that time has ‘field-like’ properties? Like an elastic sheet rather than just a sequence of events (interactions of ‘things’ like clock hands…)

    I am officially rambling!

    PS I enjoy your comments, very thought provoking, and the poem too!

  3. The more i think about these things the trickier they are to put down on paper, but i think the following makes sense (it might go off on a tangent or two, but hopefully those will help).

    Like you, i accept that gravity affects space-time, and that its effects can be found all the way around an object (not just ‘under’ the object as some depictions of ‘the weight of a world’ imply).
    And i am one of those people who you’d say would argue that space isn’t curved / that “space and time simply vary in density in different locations”, but i’m not sure that we’d agree on how they vary, especially as you (like most people) believe that time moves slower in high gravity areas.

    Maybe you think time is condensed (/ ‘thicker’) in such areas, and that’s what makes it go slower (?), but i think only the most desolate parts of our universe might allow time to go really slow.

    I think that in non-desolate areas space and time get displaced by large clumps of matter in the same way that water does on Earth, yet at the same time they are both found everywhere [even inside those clumps of matter] …because they’re each more fluid than water and more pervasive than air.

    I think their environment determines their consistency and density.
For example, where space-time interacts with a large amount of matter/gravity (or vice versa), time might become thinner (sort of like how air can become thinner), and if more matter arrived / if the amount of gravity increased, then that area of time would get even thinner.
    So, near the event horizon of a black hole, time would be very thin, and over that horizon it would be extremely thin.

    But such thinning might make it possible for time to flow faster than usual…

    Take dark energy: 

    as it fills the gaps created by matter’s gravitational pull on other matter, it widens the gap between those clumps / it seems to get stronger ~ its parts could be said to thrive as they spread …become ‘more effective’ when they dis-integrate.

    Time might also become ‘more efficient’ as it thins.
We might even find a way to use it to reach distant places that we wouldn’t otherwise live long enough to reach…

    Imagine that two people [of the same age] are given identicle pieces of time to traverse (/ are given the same place in time to arrive at), and the same starting point, BUT one has a stash of gravity in their tardis-style pocket and uses it to make their piece of time thinner
…their journey would [to a stationary observer] look much longer and therefore slower than the other person’s, BUT their thinned-out time might be flowing so fast that they arrive at the stated destination before the other person.

    And at a younger age than the other person.

    Not that those two people would know it (right away, if ever) because they’re not in the same place and time to see it ~ the first to arrive could sit and wait for the other to turn up, but then they’d lose the time they saved
    (maybe i’ve been reading too much dodgy sci fi 😉

    The point is, how something looks [to someone outside of an experience] isn’t necessarily how it is.

    People know that already, from hearing various witness accounts of a single event, and from studying eg photons… And because they know that time is an illusion.

    Rather like a clock’s ability to tell time.

    Clocks are not designed to cope with or measure gravity’s affect on space-time, so observing a clock’s inability to function properly under extreme conditions isn’t going to tell us much.

    And even when they’re working properly they’re only ‘measuring’ the man-made divisions of the Earth’s circumference between one sunrise and the next ~ although the distance between ticks was decided by science-cum-nature, clocks can’t actually register anything.

    The mercury in a thermometer can tell which days are hotter, but a clock can’t tell which days are longer, or even if it’s dark outside.

    Even an atomic clock (with a ‘bouncing’ isotope inside it instead of ticking machinary) can’t help us measure gravity’s affect on time, because not only is it confined to a very controlled environment, but it’s also being used to measure time as a linear phenomenon.

    I don’t think time is two dimensional ~ people who believe in a holographic multiverse might say that it must at least have some two-dimensional aspects, but even the flimsiest strip of film, or the thinnest string, has 3+ dimensions.

    Trying to determine the flow rates of ‘stretched’ time by observing astronauts as they try to out-fly various strengths of gravity (or eg trying to figure out how to manipulate time by studying a racing car driver’s gear control), might be interesting / fun, but it’s probably not going to teach us anything about space-time’s properties.

    We’re like that isotope, stuck in an environment that influences everthing we do whether we want it to or not …so even if nature was obliging enough to let us see one of its actions from every possible angle, we’d probably mis-interpret it.

    But, then again, some people have figured out some stuff, so i guess they just had the knack.

    1. RE ‘dark energy fills the gaps between clumps of matter’

      ~ i should have said that the ‘clumps’ in this instance are huge / galaxy sized, & i maybe should’ve ex plained that an expanding universe needs to do more than simply displace space-time [when eg galaxy clusters move further apart] if it wants to avoid a ‘big rip’

      …so maybe that’s why dark energy is one of the ingredients of a ‘growing’ universe…

      I think that as huge amounts of matter/gravity (or vice versa) accumulate they emit certain ‘substances’, like dark matter [which sticks around and adds weight to their mix] ~ i think it’s possible that gravity and / or space-time produced dark energy so they too would hold together (as more black holes emerged, and more eg galaxy clusters came together, the amount of dark energy produced, either as a by-product of that activity or as a gradual reaction to it, would have increased also).

      I think its spread might [like the ‘stretch’ of time near stong gravity] be capable of reversing itself …which means if / when dark energy has no give left, it could spring back to its unstretched state…
Failing that, if / when it meets the outer edges of our universe it could be repelled by them and reflexively turn back on itself…

      But then again, maybe that’s where it came from in the first place ~ maybe as our universe grew and pressed its edges against other dimensions that energy leaked in, and then, as our black holes and galaxies came together / as our universe reduced that outward pressure, that energy stopped seeping in BUT the dark energy already here then got stirred up by the motion of eg galaxies being attracted to eachother, and started pushing back [again, but this time outwards not inwards].

      Either way something is likely to give, rebound, or push back, so whether or not this particular universe started off with the ingredients of an oscillating universe it could very well be one.

  4. A lot to take in! I can’t dispute what you say – and I guess that’s the issue with it – people like us need to put rigour behind ‘talk’ by putting some maths into the mix to give it steucture and consistency. It is too easy for words to sound good and too hard to check them for contradictions – that’s why maths is so important in this field… and that is what I am working on lately (hence fewer ‘wordy’ blog posts in the last year or two)!

  5. I’m terrible at remembering equations [& what they represent] so, although i can do “find the value of x” type sums, my maths isn’t that good,

    & as you can tell from at least one of my moving clock related messages, i can get so caught up with one aspect of a topic that i forget to consider other aspects and end up going in a direction that doesn’t make sense even to me

    & i wouldn’t have a clue how to present a ‘new’ idea in math ~ surely i’d need to get my hands on some thinned time or eg dark energy [& some lab equipment] first anyway…

    So am happy to leave those things to people who are (if not now then hopefully in the future) able to do them.

    But thanks heaps for sharing your knowledge and ideas & for giving gist-minded people like me a chance to get involved ~ even though i didn’t understand some parts of some articles (eg how certain info led to certain conclusions about
Relatavistic speeds, & using a Hyperbolic lense to map reality) you explained some things more clearly than anyone else has, & you gave me lots of things to google, so i’ve learnt some new things and been reminded of things i learned at school, all of which was enjoyable :-)

    Good luck with your mathematical experiments!

Leave a Reply

Your email address will not be published. Required fields are marked *