A Barrier to Understanding

Most people have heard of Chuck Yeager.

This guy was the test pilot for the Bell X1-A and he was the first person to "break the sound barrier".

What that actually means is that his craft went faster than the speed of sound in air.

A lot of people who do not understand much physics ask the same question about light.

"Is there not a light barrier to break also?" they cry.

The answer is no, for the reasons specified below.

Sound travels in air, and is a vibration of air molecules.

Light travels in a vacuum.

There is no reason why an aircraft can surpass the speed of sound in air, as the effect largely is governed by the doppler effect, which is the same effect that police sirens seem to sound differently when they pass you.

But Einstein produced equations that clearly showed that anything travelling at the speed of light (except photons, which are massless) will end up with infinite mass. try pushing an infinite mass beyond the speed of light and I think it will be found that it is quite difficult.

The thing about space speed is that because mass increases the faster you go, it gets ever harder to push it. The technical way to say this is that the energy from the push goes to increase the mass, not the speed.

The more you push, the more of your push goes into the mass increase.

Oh, and another thing, if your craft gets very near the speed of light, time stops for it.

Are you Positive?

Let's make a quantum jump ("quantum" jump these days means to most people "a specific" jump) to what Paul Dirac did.

In those days, the early thirties, quantum mechanics was still in it's infancy, as was special relativity.

What Paul Dirac did was to try to marry quantum mechanics with relativity for the electron, the simplest particle.

His results were astonishing.

He wrestled with the maths involved, turned the mathematical handle, and out came the washing.....But there were TWO results, not just the one.

The one he was after, the electron, was quite clear. What was NOT clear, however, was the other answer. The maths had produced something no experimentalist had ever done!

Paul Dirac simply shrugged off the shock and said "There must be another particle out there, with the same mass as the electron, but oppositely charged".

Outrageous!

In 1932, Carl Andersson found it in his cloud chamber. The path it took had the look of an electron, but curved the opposite way. It was henceforth named the "positron".

Paul Dirac and Carl Andersson had just revealed anti-matter!

Outrageous!

Travelling Families - Solution

The problem is a paradox, or a seeming paradox. How can a twin possibly be older then her twin brother?

Moreover, why is it the guy the one who ages faster? After all, it's relativity, is it not?

Relativity says there is no difference in the points of view of either twin, since Chere can always say that is her brother who is moving very fast away from her.

So who is right?

It was just this kind of thing that led Einstein to realise that having Inertial Frames was not enough. An Inertial Frame is a point of view that conforms to all laws of physics in a consistent manner. Einstein said that all these are equivalent.

It is like saying that you cannot detect absolute motion

This is true, except when there are accelerations or gravity are present (they are equivalent). This so hard, it took Einstein 11 years to formulate it. He called it General Relativity.

This is how we resolve the paradox. If we realise that for Special Relativity, accelerations are not invloved, so the twins Inertial Frame (points of view) are NOT equivalent

Why? Because in order to return, Chere has to slow down, stop, turn around and speed up again.
That means we can actually TELL who is moving, and it is Chere, so she stays younger.

More details can be found here....

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html#sr_vs_gr

Travelling famillies - a lesson for all would-be relativists

There now follows a demonstration of what Special Relativity (SR) can get up to given it's wicked way. In particular, the misunderstanding of the term "Inertial Frame".

Suppose we had a brother and sister on earth, in fact identical twins. We will call the brother "Mahal", and the sister "Chere".

Chere, the rocket scientist, invents a powerful rocket capable of near light speeds, and plans a trip to Proxima Centuri , the nearest star. Mahal, however, does not like flying, so decides to stay at home.

On their 25th Birthdays, Chere blasts off attaining a speed of 86.6% the speed of light. As the distance to promima Centuri is 4.2 light years, it takes her 4.86 years to get there. She stops, turns around, and blasts back, taking another 4.86 years to get to earth, making the trip time about 9.72 years. The equation used can be seen in the following LINK (equation 1)

The point is, because Chere has been travalling much faster them Mahal, her time has slowed down a bit, and when she gets back, here own "twin" is much older than she is! There is a better example of this HERE

All things being equal. this has been exprimentally proved, and that this is what happens. However, if relativity is right, we could just as well say that from Chere's point of view, it is Mahal who rushes away from her at 0.866c, so it would be him who is the younger when the trip ends? So who is right? They can't both be!

It is exactly this type of question that stumps those who tell us "Oh, I know all about Relativity".

Is anyone able to tell how to figure it out ( you would need a thorough understanding of the subject to be correct!)? I have left a clue - the second sentence.

This is a subject very dear to me, hence the character names. "Mahal" is "dear" in Tagalog (chosen because the twin who stays is (M)ale), "Chere" is "dear" in French (chosen because "Chere" is the French feminine adjective).

What is the difference between Special Relativity, and General Relativity?

Here is the first part of General Relativity. However......

Do NOT be put off! Please read further!

Not a lot of people know this, but Einstein only published 3 papers. One on the explanation of Brownian motion (movement of atoms in a gas), another on the explanation of the photoelectric effect (what happens when a light is shone onto a metal), the latter of which was established from the then new quantum theory, and his triumph, “On the electrodynamics of Moving Bodies”.

The third became known as “Special Relativity”, published in 1905. (hereafter, referred to as “SR”). It dealt with objects travelling very fast, but not being accelerated.

What has this to do with the gobbledegook you see here?

Well, Einstein was not happy with his SR theory, as it assumed constant velocity.

He wanted to encompass it into a theory of relativity that took into account acceleration as well, and his idea led to THAT gobbledegook up there, of which this is only the first few lines.

It took a long time ( I think it is obvious why!), but in 1916 he came up with General Relativity (hereafter referred to as “GR”). In it, he incorporated acceleration, but at a cost. He had to introduce a fourth dimension, along with the other three we know and love (the straight lines of – “here-there”, “up-down”, “right-left”). The other dimension we also knew and loved was simply “time”. He called his new ‘creation’ , “Spacetime”, and it meant not one of the four could exist without the other three.

He even borrowed a branch of abstract math from some guy named Riemann that had hitherto no foreseen practical applications. Einstein needed equations in 4, not 3, dimensions. Ok, we math people who already know linear algebra, are aware that math can be carried out in any number of dimensions (some call it Matrix Algebra), but Einstein was the first to make use of it beyond three dimensions, and what is more, he was able to show that it could be proved practically, a fact not physically proved until 1919 with Eddington.

It is called ‘Tensor theory’. The “theory” bit, describing the mathematical, not the physical aspects. Einstein made tensor algebra real.

So how did this make physics better?

One BIG thing it altered, was the physical perception of ‘gravity’. It was now longer a 'force' (take note , Luke), but a physical , geometric effect.

Essentially what had happened was this: this guy Riemann, much earlier, had ‘culled’ a branch of math from nowhere called ‘Riemannian Geometry’, which dealt with the scenario that space need not be ‘flat’, as we know it , Jim.

Einstein simply applied it to the geometry of his Spacetime, PLUS, there was one complication…..mass. In the words of John Wheeler….”Matter tells space how to curve, and space tells matter how to move”. There was a lot of math, and I MEAN a lot, and the example, given is just a taster.

What you see there is just ONE component of the math needed to describe GR in just two dimensions. Yes, I did say only TWO dimensions. This is what you see there. The other components occupy another two pages, and for four dimensions, correspondingly more.

Before you ask, yes, I do understand the components individually, that is, the spatial functions which descibe space itelf, the second order partial differentals which descibe it's curvature, and the trigonometric functions, which are an inevitable consquence of curves. This is calculus with a vengeance!

Anyway, the difference between SR and GR is that owing to the Principle of relativity (all physics laws remain the same no matter where or who or when you are), SR explains extreme velocities (speeds), GR explains extreme accelerations (changes in speeds). It is interesting to note that because of the Principle of relativity, accelerations are treated the same way as the state of being in a gravitational field.

The Principle of relativity is explained in a recent post.

BUT what most people do not realise , is that like SR, GR has also been venerated many times with practical demonstrations.

If Einstein is really 'wrong', he is only 'wrong' in the sense that Newton was.

Both scientists have been proven to be right.

Oh Woe to you people who 'believe' Einstein was 'wrong', as, in effect, you will have to 'prove' Newton 'wrong' too.

...and who can argue with that?

Eintstein WAS wrong!

Was Einstein wrong about the speed of light? Can it be broken? Some physicists claim to have done in the following experiment....

The experiment in question has a particle that travels from an emitter to a detector. During the time it takes to get from end to the other, it passes through some sort of substance. When the particle is timed, the travel time through the substance in the way, is LESS than the travel time that light would have taken for the same distance.

So the particle appears to be travelling faster than light.

Actually, it appears to be travelling faster than light in that medium, which we all know is perfectly possible.

However, certain questions raise their heads over this result.

The theory of Relativity actually says that no information can travel faster than light, in fact if you look further down my blog to the post on "Phase Velocity" and "Group Velocity" (June 25, 2005) you will find another, apparently similar, conflict there.

Having studied quantum mechanics, the concepts of Group Velocity and Phase Velocity are well known to me, as is the Tunnel Effect.

The "Tunnel Effect" is a quantum mechanical effect only. It's main use is in Josephson Junctions, transistors that use the effect. The effect is this: Under certain circumstances, particles that bounce against a wall, the particles sometimes go right through the wall, and the time it takes to do this seems to be immeasurable.

The present conflict arose because the particles these scientists used appeared to be travelling faster than light, because the particles were using the "Tunnelling Effect" to get through the suff that is in the way. What the particle is doing before and after the tunnelling is completely described by a wave equation known as 'Shrodinger's Equation'. BUT, during the tunnelling, the particle is described by a different wave function (in fact, it is an exponential curve) and therefore we can tell virtually nothing about it (as usually, the particle is in the middle of a solid piece of material), other than the fact the probability amplitude (the information needed to tell us where it IS) decreases exponentially.

Most physicists already agree it is a paradox, but the fact is that the particles are travelling in a medium (compare glass) whose speed of light there is LOWER than the speed of light in a vacuum, perhaps there is no paradox at all. Particles have, after all, been seen to travel faster than the light in that particular medium, giving rise to "Cerenkov Radiation". This effect is striking when one glimpses the water bath of a nuclear reactor, which appears to 'shine' blue. No, it is not a dye, but the electrons emitted by the core are travelling faster than the speed of light in the water, and the blue is the Cerenkov radiation emitted by them.

But the equations in this case, the equations of special relativity, tell us exactly WHY nothing can go faster than light in a vacuum. Is the particle in this particular experiment violating this? NO, because it is NOT travelling faster than light in a vacuum.

However, the experiment given is only a consequence of quantum mechanics, as an exhibition such as depicted , can only be demonstrated by the tunnelling effect, which is an effect that is only valid for particles in the atomic realm.

There are no implications here whatsoever that the same effect can be , nor ever will be, applied to material, macroscopic particles like a car, a dog, or tennis ball. ALL must conform to the equation that says that, for them, light speed (as in the speed of light in a vacuum) is, in fact, impossible.

Here's the proof - the simple consideration that the speed of light is the same, the following three equations simply came through from the math, where v = speed, T = Time, L=Length, m=mass. c, of course, is the speed of light in a vacuum. The "0" means each of these as measured when v = 0.

Please don't worry about the math, because the most important thing here is in equation 3, the last one.........


.......in the last equation, it is clear the mass increases the faster you go, because that thing in the "[]" is always increasing, and look what happens when v=c >>>>> m(v) becomes infinite!

Obviously this cannot happen, so particles can never travel at the speed of light in a vacuum.

Anyone who "thinks" this is untrue is invited to 'disprove' these equations, which were first studied by Fitzgerald and Lorentz, just before Einstein actually used them in his Special Relativity paper ", On the Electrodynamics of Moving Bodies", in 1905.

If all this appears difficult, it is childsplay compared to the General Theory of Relativity (1915).

I think the reason why Physics is so dependent upon math is PATENTly obvious here.

Einstein WAS right....

....Einstein was probably one of them!

(Close Encounters of the Third Kind)

In my last post on relativity, I intimated that the speed of light IS constant. By constant, this means the same for all observers.

Those smart-asses who say 'but the speed of light in glass and water is different, so it can't be constant' have entirely missed the point. "Constant" refers to all observers travelling in the same medium that light is travelling through at the time, be it water, air, or a vacuum.

Indeed a vacuum is always chosen because in all measurements of the speed of light, none is ever bigger than that measured in free space.

NOW we start. I doubt many people do not know where all this came from, but it is quite simple, and is called "The Principle of Relativity".

To make you realise what it is, perhaps a few questions would suffice.

How fast are you going right now? Most of you will say you are sitting, and are therefore not moving. A few will say " At about 100kph, I am on a train". The question really is, how fast you travelling relative to the Earth. The first group has answer 0 kph, and second group 100 kph, relative to the Earth.

But how fast is the Earth moving? Well, relative to the Sun, about 30,000 kph, as the Earth goes around it.

How fast is the sun moving? Well, relative to the galactic center, about another 250,000 kph.

We don't notice this because of a blanket surrounding us called "The Atmosphere" which travels along with the Earth, so we are only aware of travel on the Earth.

So, how fast are we really travelling? 100kph? 30,000 kph? 250,000 kph?, or their sum, 260,100 kph?

Yes, but what is the Galaxy moving relative to? The answer is the Local Group, and the point is, the process can go on for a long time to calculate real speeds.

So, how fast you are going actually means "How fast are you travelling past object X".

Simple mechanics with a little thought.

However, Einstein went further. His question was this:

" If in free space, with no 'object X's' to measure with, how fast are you travelling past that there other spacecraft? With a little more thought, you can see that the answer is not clearly cut, for you could be stationary, and the other spacecraft is moving past you. SO, who , in the end, can say which one is moving and which stationary? Indeed, BOTH spacecraft could be moving and you would never know the difference!

Next time you take the kids out for a drive, get in and ask them to hide under a blanket at the back, so they cannot see out. Next, jump up and down in your seat a little, your wife too, and the kids will be convinced you have started!

Point is, if you have nothing by which to tell you if you are moving (a tree, a bump in the road, another spacecraft), it is impossible to tell if you are or not! Ask the pioneers of sea exploration 200-300 years ago, they knew all about it.

Put succinctly, "free motion is impossible to detect" - the Principle of Relativity. This is where the word comes from - you have to be moving relative to something to tell that you ARE moving. THIS is the central tenet of Relativity.

What has the speed of light to do with this? Well, if true , there are certain consequences.

Einstein realised that the speed of light simply cannot be anything else BUT the speed of light, and that it was the same for all travellers, no matter how fast they travel. Otherwise they could work out how fast they were moving. For instance, if you are travelling towards another planet at 30,000 kph, the speed of light would be (speed of light (minus) 30,000 kph). SO you can calculate your speed. BUT the Principle of Relativity forbids this, therefore the speed of light is the same for them, as it is for us, here on Earth.

This principle has explained many things, a good example is a star going round another. Try to think what you would see if the speed of light were slowed down when the rotating star moved away, and what you would see when it was speeded up as it moved towards you. You would see the star in two places at once! This of course, does not happen, and is well explained by the constancy of the speed of light.

Another proof of the Principle of Relativity is in electromagnetism. Sometime back I was writing about the speed of light and electricity, and that it had actually been derived (logically deduced from) electricity and magnetism considerations alone. This also means it does not change.

Contrary to popular belief, light is not a barrier like sound is, it is more like a forcefield that grows stronger the nearer you get to it. Whereas sound barriers can be broken, it is physically impossible to go even as fast as light, let alone go faster.

When I say physically impossible, this is fact, because the harder you push to go faster, the energy you put in goes to increasing the mass (according to E = Mc**2), not to increasing the speed. Ask any particle physicist or nuclear scientist. BUT this is the realm of Special Relativity, and deserves another post, as does General Relativity. Both theories came about because of the simple tenet of the "Principle of Relativity".

From little acorns do mighty oak trees grow.

Ultimate speed limit....?....Nah, Einstein is WRONG.

The speed of light has often been described as "The Ultimate Speed Limit", a 'barrier' because people have always been informed of this.

And, without knowing why, they have been imbibed with the belief that this is the actual scenario, without having been informed as to why this statement has been made public as if it is fact. Conesquently, they have likened it to the 'sound barrier', a totally different thing.

Hence the plethora of people (especially in the physics rooms) who believe that Einstein 'was wrong', because just like sound, they believe that the 'light barrier' can be breached.

Wrong or right, this is what happens: Nothing can travel faster than light, and what is more, there is no way to even approach those speeds.

Whatever people believe or led to believe, be it good-intentioned or not, the truth is that the speed of light is completely unnattainable. But how do I explain this in normal terms?

I deal in this stuff almost every day, so watch this space as to how it can (or cannot be done).

Most of the boffins in the physics rooms are completely unware that sound and light travel in a different way. In fact, light travels in a totally inexplicable way, to them at least, or it would if they had studied rudimentary wave theory.