Category Archives: Time

Another way to think about Space-Time: A fresh start…

I have been kept away from writing on this for a few years, due to life – three kids, crazy job, lot’s of travel, yada yada. But that was true before so that’s a bullshit excuse.

The real reason I kept away because I was discouraged.

I had got stuck in my progress of understanding space-time.

But today I got a wake-up call…

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I read a book excerpt (on Gizmodo) of ‘Spooky Action at a Distance’ bu George Musser just published last week.

And right there, in plain English, it was: “If you agree that the fundamental level of physics is not local, everything is natural, because these two particles which are far apart from each other explore the same fundamental nonlocal level. For them, time and space don’t matter.” A quote of Micheal Heller.

Damn. People thinking about quantum entanglement decided that if we accept distant entanglement was indeed ‘real’, as we accepted the speed limit on light is ‘real’, that space itself would adapt to avoid a paradox.

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So what?

Well, in my own work I had decided that exactly the same assumption could be used to explain away the weird interference in the double-slit experiment.

My approach was this:

If we take the Lorentz Transformation to calculate the geometry of the double slit, we see that from the perspective of the single photon, the whole journey is compressed into a single spot. And under such conditions, interference between the ‘possible paths’ is no longer a contradiction.

It also hints tantalizingly that the wave nature of light is a sort of artifact of trying to cross section what is essentially a point event.

I am therefore very grateful to George Musser, because he will allow me to pick up this thread and see where it leads.

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I like to start by imagining I am a photon, leaving from, say, my nose, and heading away from earth across the galaxy, eventually terminating somewhere, let’s say on a far-off star – being absorbed as an electron there leaps up to a higher orbital.

From the photon’s own perspective, if that’s a possible perspective to have, time has not progressed – this means it leaves, travels and arrives at once. This means that even as the photon is waiting to leave an atom on my nose, there is a sort of connection with another atom, far away across the galaxy, which is waiting to accept the photon, and then click, all of that distance disappears, it’s all a single point in space, and the photon relocates, somehow without even having to move. My nose and the stars are somehow momentarily at one. Spooky…

This started as a fancy, but I can’t seem to break it!

For example – the approach also seems to have something to say about energy quantisation…

The issue there is that electrons should fall to the atomic nucleus, but don’t – this is because they can’t find an outlet for ‘that particular quantity’ of energy.

Now, with the idea that space and distance are illusory, we can look at every photon emission as paired with an ‘acceptance’ somewhere else. So far we’ve assumed these are unrelated events, but now we see they must be the same event – so it seems natural that these events require some degree of serendipity to occur. Not just any atom can absorb just any photon…

It strikes me we could test this thinking, how can we do it?

Can we send photons that really have no inevitable target? Seems like we could, but the maths is telling me no…

Help!

PS See my first public post about this subject from 2011 here.

The speed of evolution – revisited…

I have been keeping my eye on the evidence that ‘life experience’ can be passed on in your genes.DNA

It has been proposed many times as a mechanism of evolution, and indeed was considered likely before the concept of ‘selection’ was understood. It’s attractive because saying that ‘survival’ is the one and only way to adding value to the genes seems, well, wasteful.

Surely, you’d think that a fear of snakes based purely on the idea that people who were not afraid of snakes were ‘taken out’ of the gene pool by snakes, is less efficient than a mechanism that captures experience – that snake killed my dog, I should avoid snakes, and so should my kids…

However, once DNA was understood and shown to be dense with what seemed to be all information that could ever be needed, dissent waned to an all time low. The mechanisms of DNA were pretty clear – your DNA was set at birth and while it might mutate a little randomly, had no way to ‘learn’ from your life before being combined with a partner’s to create offspring. The case seemed pretty settled.

There remained niggles though. I worried about the speed of evolution as we have so very much to learn and so little time to evolve! So I looked for ways evolution could amp up its power. It seemed to me that nature, so darn clever at self-optimisation would make improvements to our design based on non-fatal experience, or indeed passive observation.

Others similarly concerned continued, often in the face of deep scepticism, to study what is called epigenetics, the science of heritance not coded by DNA – and thus having the potential to be edited during our lives.

I first heard about it around 10 years ago when media reported that the actual DNA sequence was not the only way info could be stored in cells – in theory the histones present can affect how the DNA ‘works’ (how genes are ‘expressed’) and their presence could thus change the characteristics of any lifeform coded therein. The type and number of histones may be few (relative to the number of base pairs in DNA) however, the many locations and orientations they can take create a fair number of possible combinations and permutations.

When I heard about this theory, I was put into a state of high curiosity. On the one hand, it was a little blasphemous, but on the other hand tantalising. If nature could find a way to combine the power of selection with the potential benefits of life experience, we could get much faster and more effective evolution.

My curiosity was soon rewarded with another possible mechanism for smuggling info to the next generation. DNA methylation – the idea is that DNA can host little ‘attachments’ in certain places. These may be temporary, and reversible, but they have now been clearly shown to alter how the DNA expresses itself.

On the face of it, the evidence that DNA expression is environment dependent is rather strong, but the idea that the environment around the DNA coil actually contains consistent and persistent intelligence picked up during our lives is much harder to prove.

And so teams have been beavering away trying to get to the bottom of this, and this week one such group has fresh news for us. A Nature Neuroscience paper has tested the theory in a rather clever way.

lab miceThey started by teaching some mice a new fact (that a certain smell would be associated with trauma) and then later, tested their kids. Lo and behold the kids whose parents had been taught fared significantly better in the test than untrained, unrelated mice.

This may sound a little trivial, but you must remember that the current ‘popular’ understanding of genes is that they only gain intelligence by surviving – or more precisely they shed stupidity by dying. However, here we are seeing information pass between generations without the need for anyone to die.

Furthermore, because of the carefully selected lesson taught to these mice, the researchers were actually able to see that a specific part of the DNA, while not different in design was nevertheless more active.

Now, I do not know enough about DNA to double-check this claim, but you can rest assured others will – because that’s what journals are for – and in this case the implications are huge.

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Like what, you ask?

Well, off the top of my head, it means that much of what we do between birth and reproduction will affect all our descendents – this undermines the idea that one’s body is one’s own to do with as one pleases.

It also indicates that there is potential for us to deliberately control the expression of our DNA, allowing us to do some genetic engineering without actually changing the DNA sequence.

More importantly, and more controversially, it would mean natural selection would not need to explain all the marvellous diversity we see around us on its own.

It remains to be seen what proportion of our ‘design’ is coded for outside the DNA, or indeed how much this mechanism can improve or speed up evolution, however I for one hope it works out to be right and that mother nature has indeed figured out how to seriously boost the power of selection.

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!

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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.

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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! 😉

Fun Physics Questions: Does time flow in baby steps?

Question: is it possible time flows in little steps?

At some small scale, could it be, that time is simply a ‘symptom’ of a sequence of events, or states, that there is no actual time passage ‘between’ those states?

This scenario has interesting implications – it suggests life is a bit like a movie – a series of pictures on a strip of celluloid, or pages in a book, and like a book, while the story may unfold to you at whatever speed you read it, it does not matter how fast you read the story itself still has its own pace.

This doesn’t mean the book has to be pre-written, it can still unfold with utter unpredictability, the book is unfinished if you like – the important point is that we are stuck experiencing the passage of time at a rate determined internally – by the rate of chemical reactions in our brains. The drum beat of those reactions would feel the same no matter how fast or slow they seems to an outside observer. They could even be paused for a few minutes – we could not tell!

Now physicists studying energy balances of sub-atomic particles have seen that energy often seems to come in little chunks (the ‘quanta in’ quantum), and that can imply that time may also be chunky (maybe Planck time?); alas, time chunking has contradictory implications – contradictory to common sense anyway- like infinite energy flux, not to mention infinite speeds, but hey if you can just get your head around some of the workarounds physicists have dreamed up (quantum tunnelling for example) everything’s all right again. I am personally highly suspicious of workarounds, and that is what I think they are!

Anyway, even if you try to get away from quantum weirdness, you get sucked back in – take for example this geometrical example. Consider the relative positions of three point objects (small particles?) moving freely in space: they could, for an instant, line up perfectly, but if your measurement were infinitely accurate, this could only occur for an infinitely small duration so long as the particles are moving. If you try to explain this by saying space is divided up into chunks (like ‘snap to grid’ in MS Powerpoint) you get into geometrical issues that three points cannot always be integer increments apart  (nor even rational increments apart) without breaking the most basic number axioms.

So even if space isn’t chunked, it turns out you can appeal to the uncertainty principle, which handily says you can only measure the position of anything infinitely accurately if you allow its momentum to be anything at all, including infinite – and infinite momentum is exactly what you (temporarily) need if you are bold enough to let time ‘leap’.

So none of these issues with time chunking turn out as solid proofs against the possibility, they just make things more slippery!

Aside: rather than a book, I like to think of our universe as being a bit like a computer program  – I like to think about Pac-man when it plays itself in ‘demo mode’ – in demo mode, used to allure people at the arcade, the computer controls both the ghosts and pac-man. In the computer, a sequence of commands is run in the CPU and the speed of the computer (like the reader of the book) controls the rate at which we ‘see’ the ghost-chase on the screen, but this speed is invisible to pac-man himself – yes the ghosts chase faster across the screen, but he can run faster too.

[youtube=http://www.youtube.com/watch?v=htl_vwkZWHw&NR=1]

Question: Does a time-increment universe allow time travel?

Well I don’t think we can ‘skip’ events out (we have to experience them all), but if we can go somewhere where events are more or less ‘dense’, maybe we can. We will not feel the difference, we will not get any extra life-span, our cells will age just the same – but if a friend had gone to another place is space-time, where events have bigger gaps, he may have aged at a different rate, and when you meet your friend again one of you will have time travelled forward and the other backward relative to one another.

Is this really possible? Well, yes, I think so – this model ties in very well with relativistic time travel: if you assume events are more spaced out (less dense, with bigger ‘leaps’ between them) in areas with more mass nearby. or when moving vary fast, it maps perfectly.

Conclusion

That’s it for now! Of course, maybe time does not leap, I don’t know, but its something I love to think about! Please let me know your thoughts…

Hysteresis Explained

Hysteresis (hiss-ter-ee-sis). Lovely word. But what on earth does it mean?

Hysteresis is one of those typically jargonny words used by scientists that instantly renders the entire sentence if not lecture lost on its audience. Sure, you can look it up on wikipedia, but you may die of boredom before you get to the point, so I am going to explain it here.

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Hysteresis on the way to school

Let’s go for a walk. Let’s say we are ten years old and we are walking to school. The route is simple. The school is a few hundred yards down the hill on the other side of the road. Now consider the question: at what stage do we cross the road? Immediately? Or do we walk all the way to opposite the school before crossing – or somewhere between?

Assuming there are no ‘official’ crossing points, I bet you cross immediately, then walk down the far side of the road.

How can I make this prediction? Well, I assume that crossing the road requires there to be no traffic, so if there is no traffic as you start the journey, it is a good time to cross. If there is traffic, you just start walking down the road until a gap appears, then you cross. This strategy allows you to cross without losing any time. If your strategy had been to cross at the school there is a real risk you will need to wait, thus losing time. So it turns out the best strategy to avoid any waiting is to cross as soon as you can.

So now picture your walk home. Again, it makes sense to cross early on. The result is that the best route to school is not the same as the best route from school. This is an example of hysteresis – or a ‘path dependent phenomena’.

Hysteresis  everywhere

The dictionary will drone on about magnetism and capacitance and imaginary numbers. A much nicer example is melting and freezing of materials – some substances actually melt and freeze at different temperatures. This shows that the answer to the question: “is X a solid at temperature Y?” actually depends – on the path taken to that temperature. Just like what side of the road you are halfway between home and school will depend on whether you are coming or going.

It seems to me that falling asleep and waking up also bear some of the hallmarks of hysteresis; although they could be considered a simple state change in opposite directions, they feel very different to me – I  seem to drift to sleep, but tend to wake to alertness rather suddenly.

Now think of a golf club in mid swing. As the golfer swings, the head of the club lags behind the shaft. If the golfer where to swing in reverse, the club head would lag in the other direction – thus, you can  tell the direction of movement from a still photograph. We can therefore say the shape of a golf club exhibits hysteresis – and again you see see why it is so-called “path dependent”.

This logic can be taken further still – wetting is not the opposite of drying and likewise heating is rarely the inverse of of cooling. Let’s imagine for example that you want to make a chicken pie warm on the inside and cool on the outside. This is best done by warming the whole pie and then letting it cool a little. The temperature ‘profile’ inside your pie thus depends not only on the recent temperature but has a complex relationship with its more distant temperature history. This particular point is somewhat salient at the moment as we ask the question: is the earth heating up? 

So what?

Good question. I’m not a fan of jargon, and hysteresis is not a word I hope to need to use in my smalltalk. However, you can see that it encapsulates a rather specific and increasingly important concept that is pretty hard to replace with two or three simpler words; thus it passes my test of “words a scientist should understand that most don’t”. Please let me know your own additions to such a list!

 

 

How to prove that space is curved…

Question: if you lived in flatland (a 2-d world), how could you tell if the land was curved in the third dimension?

Answer: geometry!

It turns out many of the mathematical rules we learned at school ‘fall apart’ if the working surface is curved. For example, can you draw a square on the surface of a sphere? No!

So can we use this insight to tell if our 3-d world is curved in a mysterious fourth dimension? Yes!

If we set off from earth, went in straight line for, say 1 light-year, then turned 90º, went 1 light-year, turned 90º again, and then did this yet again, you should have traced a perfect square, and be back exactly where you started. If you aren’t, something is amiss!

 

Now it turns out that it we do this, we will indeed discover an error; but why? And how do we know this?

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Newton told us that a massive object in motion will continue to travel in a straight line, unless acted upon by external forces. Some people think that Einstein overturned this insight, but he didn’t; indeed he extended it: he said that the force of gravity is not actually a force, and thus objects falling under gravity are actually going in straight lines! Indeed this makes sense, as anyone ‘falling’ does indeed not sense any acceleration, but rather feels ‘weightless’. Thus they are not actually accelerating, they are going straight – in curved space.

Now anyone who has thrown a ball can see this is absurd on the face of it, but Einstein was serious, and he is right, from a certain perspective. The ball is not going in a straight line through ‘regular’ space, but is going on a straight path in a 4-d construct called ‘space-time’. Likewise, he would argue that the planets are tracing straight lines around the sun; and indeed the ‘parabola’ of a baseball is actually not a parabola, but a very small part of the enormous ellipse that would be traced in the baseball could fall though the earth and go into ‘orbit’ §.

Anyway, Einstein’s model says that light travels in straight lines, but we have seen that light bends when it passes near to the sun (this can most easily be tested during an eclipse) – so… if one of the sides of your ‘perfect square’ were to pass near the sun, it would also be bent and if you followed the above rule to draw the square, you would not end up where you started.

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Physicists have grown used to Einstein’s model, and better tests for the flatness of space have been developed. For example, if you drew a circle on the surface of a sphere, the area would not equal Πr2, but would be less. Likewise, in 3-D space, we could plot a sphere and then measure the volume and if it did not equal 4/3Πr3, we would know something was amiss.

So physicists have looked at how light bends, and how the planets move, and found out, amazingly (but predicted by Einstein) that the error in this spherical volume calculation is directly proportional to the mass of matter within the sphere – proving that the warpage in space is proportional to (and thus caused by) ‘mass’.  Thus mass warps space.

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MC Escher: 'Grid'

But is space really warped in some ‘extra’ dimension?

Well, this is a good question. Maybe it is some extra ‘spacial type’ dimension, but you could also look at time as a fourth dimension, and argue that this space is not ‘curved’ at all, but rather that space and time simply vary in density in different locations. I personally like this way of looking at it, it eliminates the need for some vague ‘extra dimension’, and therefore swiftly removes the possibility that space could be ‘closed’ or fold back on itself in this extra spacial dimension. Occam’s razor thus prefers the ‘density’ model!

Footnotes:

§. In Wikipedia, they state that balls bounce in perfect parabolas, but note they also mention a ‘uniform’ gravitation field, and it is well to remember that the earth gravitational field is not uniform, but radial. Thus I stand by my assertion that missiles follow elliptical paths just like planets and comets. Of course, an ellipse is a close relative of both the parabola and the hyperbola, so this is not really that dramatic.

Open question about relativity

A quick open question for physicists:

If you accelerate off in one direction, and keep accelerating until you are travelling fast (a relativistic speed), special relativity supposedly says the universe contracts in the direction of your travel. Fine, I can see how that makes some sense.

Now consider a massive body, such as the sun – it warps space time in its vicinity, presumably roughly equally in all directions, creating a symmetrical ‘dent’ in the fabric of space-time (if you like the trampoline analogy).

But if you fly past at a relativistic speed, and space is contracted in the direction of your travel, will the sun’s sphere of influence also be contracted, turning it from a “sphere of influence” into an ‘oblate spheroid of influence’?

Or will its shape be maintained for some beautiful reason (which is what I suspect)?

Thx.