h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I've only just started studying this. I am only at the Special Relativity Stage. Although I understand a fair amount of the math, I still have many "parsecs" to go. However, two things have struck me so far:

A. The "convenience" of stating that the Speed of Light (c) is constant.

B. The concept of Time.

A. although being conveniently postulated to assist with producing the theory, I get the feeling that it holds us back. Because the speed of light has been, for want of a better word, assumed to be constant. The statement that we can't travel faster than it is based upon that assumption. Therefore, can the result be valid?

B. I think the concept of time should form the basis. If Time is assumed to be the great universal constant, would this produce different results?

Don't ask me! I've only just started out on this quest. But I hope to find the answers. If only to prove to myself that Einstein's Postulates are valid. Other questions exist, such as can inertial frames be separate or are they just subsets of each other.

I can't remember his name, but I heard an eminent scientist on Radio 4 (in the UK) answer a question about the validity of evolution vs creationism by stating (not a quote) that maybe God created the universe, in the form that it is, 10 secs ago. Just to confuse scientists like him. - Is this valid?

Either way, whether he did or didn't I think we should all strive to find out what interests us, with the proviso that it doesn't hurt anyone (it may upset many, but that's their problem).

As to the God thing, well if he did create the universe 10 secs ago, then maybe he is the "mice" searching for the question to his anser, and we are his processors. If so then the above statement stands. If not then the above statement still stands, because then we should just jolly well find out what the *&£@^£&^ is going on out there!!!

Regards

A. The "statement" that we can't travel faster than light is proven by Einstein's theories. As you go faster and faster your mass increases and you need more energy to keep you going, this increases expontentially as you get closer to the speed of light. This results in you having an infinite mass when you reach the speed of light and hence an infinite amount of energy - this, is of course, impossible.

B. Time is not a universal constant, a fact which forms the basis of Einstein's work (and a lot of other smart people since! ). There are experiments that can be done to prove this fact. The most famous being putting an atomic clock in a plane and on the ground, flying it to the other side of the world and then comparing the times (the clock in the plane, since it was travelling faster, will end up being behind the clock that stayed stationary).

Another way to imagine that time is relative to the observer is to take a clock and fly away from it at the speed of light. Since the light from the clock face would never reach your eyes once you started moving, from your point of view the clock would have stopped. Therefore from your point of view (which is the whole idea behind it, it being relative to the observer) time has stopped.

Both the Stephen Hawking books and Brian Greene's "The Elegant Universe" are fantastic "layman" guides to this stuff, all of which is fascinating (and a good way to baffle people at parties ).

I understand the equation E=MC^2, and that gives you the impossibility of travelling at the speed of light. Also I understand that time and lenght are variable. However, all these results have been achieved from Einstein's postulate that the speed of light is constant. This I believe forms the very basis (at least is one of the basics, besides the constancy of physics in different inertial frames et al) of the Theory of Relativity. My point is what if the postulate is not true.

For instance, Euclidean Geometry is base upon the fact (again amongst others) that the shortest distance between two points is a straight line. However, this is not necessarily the case, as shown in the Theory of Relativity.

So, if the speed of light is not fixed, but time is then would the results in Relativity change? I don't know this yet and maybe I am being incredibly naive in asking the question. However, I am really looking forward to finding out in my studies. But please continue...

As far as the impossibility of reaching higher velocities than c (light) is concerned, this "fact" has been proved experimentally:
When emmitting light from a source that is moving with, let's say 2 thirds of c to all directions according to the simple addition of movements THIS light needs to have the speed of 1/3 c backwards and 1,6 c forward, evidently.
Of course the experiment couldn't be done with the source travelling 200,000km a second, but it proved that if it were, the velocity of this light "flying" backwards would be exactly the predicted c-v with v being the speed of the source. In the other direction the speed must have been c+v, that it FASTER THAN LIGHT.
(which MUSTN'T be possible according to Einstein)
Well, somehow Einstein seemed to be right
The light emitted into the direction of movement of the source STILL HAD ONLY THE VELOCITY C !
That seemed to prove the theory with the most scientific phrase: THAT'S THE WAY IT IS, full stop.

Still, such evidence really sounds cool (anything just refuses to be faster than light), but that needn't mean much.
To come back to geometry, GAUSS wanted to check which geometry (the one of Euklid, of Riemann or Lobatschewski) reflected reality and simply measured the angles of the triangle formed by 3 mountain peaks. (That's a really cool experiment 'cause every1 can try it for themselves, unlike quantum phisics ;o)
In the end Euklid was the winner, the sum of the 3 angles always formed MOST accurate 180°.
That would be a prove like the one above - but does it really work?
Of course it doesn't. (why would I mention it here? ;o)
It's postulate is that light always travels straight (the shortest connection between 2 points), and Einstein proved that even light had a weakness for gravity.
On the other hand, it is extremely fascinating that one can explain the universe WITHOUT modifying the laws of optics (that's: light travels ALWAYS straight) and WITHOUT space curvature (which also contradicted a lot of theory in the beginning but is accepted by now) - simply by a non-Euklidean geometry!
So in fact a lot of things in physics end up like in philosophy - both theories go, just chose what you prefer. There is no mistake in any of them. It's just "a different point of view".

However, what I wanted to ask was whether you (or anybody else finding this) could tell me about what you mentioned that Relativity would mean that the shortest distance between 2 points is not the straight line - haven't heard of that yet!
(at least not connected to the Theory of Relativity)

And what I just intended to say was, that when I was 14 years old (or something like that) and heard of all this I also thought nice, but what Theory would come out if you took the contance of time as a postulate? How well would this theory work?
Anyway, I haven't found the time (and the knowledge) to figure this out yet (and no-one ever explained it to me ;o) and as I'm doing my A-levels just now it ain't the right moment again,

still I'd be happy if you'd answer, I'm sure I'll C it very soon

huh! I just realized how LONG this got!

As far as the impossibility of reaching higher velocities than c (light) is concerned, this "fact" has been proved experimentally:
When emmitting light from a source that is moving with, let's say 2 thirds of c to all directions according to the simple addition of movements THIS light needs to have the speed of 1/3 c backwards and 1,6 c forward, evidently.
Of course the experiment couldn't be done with the source travelling 200,000km a second, but it proved that if it were, the velocity of this light "flying" backwards would be exactly the predicted c-v with v being the speed of the source. In the other direction the speed must have been c+v, that it FASTER THAN LIGHT.
(which MUSTN'T be possible according to Einstein)
Well, somehow Einstein seemed to be right
The light emitted into the direction of movement of the source STILL HAD ONLY THE VELOCITY C !
That seemed to prove the theory with the most scientific phrase: THAT'S THE WAY IT IS, full stop.

Still, such evidence really sounds cool (anything just refuses to be faster than light), but that needn't mean much.
To come back to geometry, GAUSS wanted to check which geometry (the one of Euklid, of Riemann or Lobatschewski) reflected reality and simply measured the angles of the triangle formed by 3 mountain peaks. (That's a really cool experiment 'cause every1 can try it for themselves, unlike quantum phisics ;o)
In the end Euklid was the winner, the sum of the 3 angles always formed MOST accurate 180°.
That would be a prove like the one above - but does it really work?
Of course it doesn't. (why would I mention it here? ;o)
It's postulate is that light always travels straight (the shortest connection between 2 points), and Einstein proved that even light had a weakness for gravity.
On the other hand, it is extremely fascinating that one can explain the universe WITHOUT modifying the laws of optics (that's: light travels ALWAYS straight) and WITHOUT space curvature (which also contradicted a lot of theory in the beginning but is accepted by now) - simply by a non-Euklidean geometry!
So in fact a lot of things in physics end up like in philosophy - both theories go, just chose what you prefer. There is no mistake in any of them. It's just "a different point of view".

However, what I wanted to ask was whether you (or anybody else finding this) could tell me about what you mentioned that Relativity would mean that the shortest distance between 2 points is not the straight line - haven't heard of that yet!
(at least not connected to the Theory of Relativity)

And what I just intended to say was, that when I was 14 years old (or something like that) and heard of all this I also thought nice, but what Theory would come out if you took the contance of time as a postulate? How well would this theory work?
Anyway, I haven't found the time (and the knowledge) to figure this out yet (and no-one ever explained it to me ;o) and as I'm doing my A-levels just now it ain't the right moment again,

still I'd be happy if you'd answer, I'm sure I'll C it very soon

huh! I just realized how LONG this got!

sorry, something went wrong so I've the same posting 2 times...

To answer your question about where I saw that the shortest distance between two points is not necessarily a straight line, this I found in Einstein's book "Relativity - The Special and The General Theory". It is, in a sense, a "dumbed down" version written by the great man himself, and translated into English by Robert W. Lawson. I am finding it very enjoyable and, I think, an extremely good starting point for Relativity. (By the way IBSN No : 0-415-09104-7).

Anyway back to the point. He doesn't say that the shortest distance isn't a straight line, but that it is an axiom within Euclidean Geometry. Mainly because proving the "truth" of the axiom is very difficult or impossible. To quote him "... We cannot ask whether it is true that only one straight line goes through two points. ..."

It is a very good book, get it if you interested.

On the rest I'll reply at a later

Thanks for replying

The ideae of a straight line being the shortest distance between 2 points has always been accepted. However, if you think of light, or any other e-m radiation, it may be possible to think of a straight line in space as the shortest TIME between 2 points in space. Light would then curve to make sure that the time taken was a minimum, but to a casual observer, the light would APPEAR to have travelled a longer Distance. Remember one of the most important discoveries of relativity is the fact that TIME is NOT a constant but is indeed a variable. Asssuming c to be constant allows us to think of compressed and stretched time.
I posted a note on the theory of the flat universe which poses some interesting questions on this matter.

Bead

I have always been taught that FTL travel is possible as long as you can jump over c without passing through it. In a sense that is what the FTL laser is doing. It is browing energy from the near future to jump over as a quantum effect. This is why a TOE would allow hyperdrives to be built.

Einstein created a theory for our universe that is brilliant but incomplete. He new this, the unified field theory, the resent consept of an ever expanding universe, were all things that he was aware of and spent years working on but failed to work out in his lifetime.

The belief that we "understand" the universe, or can understand the universe is silly. It's infinite - no mater how much we know it is insignificant. As HHG postulates we can't possibly exist when we are measured against our own scientific methods but we do .

Can we travel faster than light?

Anything is possible, consider quantum mechanics, bits of matter jump from one state of existence to another instantaneously. Consider anti-matter or the anti-gravity concept of the ever expanding universe. What about the bizzare need for matter to join together in specific patterns and how it animates itself with life.

The concept of multiple universe's. The answers are interesting but the depth of the problem is endless. Enjoy the journey.

thx, but I assume I'd rather read the book in German

yes, an axiom is by definition something we cannot prove (though it should be also something "evident" - but of course nothing's evident..) and Euclidean Geometry has this as one axiom. Riemann for example constructed a geometry where parallels meet, or, in other words, it is impossible to draw a line through a point not on a line without making the two lines meet... There is another geometry that "proves" that the number of such "parallels" is infinite...

PROVING means only showing undoubtedly that a thesis is the correct and logical consequence of some axioms - that cannot be proved - or not more that to other axioms. It's the Muenchhausen Trilemma - you've only three insatisfactory choices: defining things in circles, that's including the proved fact in the proof, (the reason for something being is it's being like this); stopping the definitions - with axioms; or regressing endlessly - what of course can't be done.

So the best thing we can have are COHERENT theories, but never CORRECT ones - at least, we can never know!

Interesting points. And a number have come in since my last reply to you. Probably the book would be better read in the original German, which I would love to do. However, having a "typical" insular british upbringing my educators missed the opportunity to make me multi-lingual, as are our continental cousins. A fact which I am, and I know a lot of Brits are, extremely envious of. Didn't mean to sound patronising or anything, I was just so excited about reading the subject straight from the man himself, other than it being diluted by others.

On the point of axioms. It seems to me that provided you set your axioms first, anything is possible. Obviously those axioms need to bear some relation to reality. Obviously by changing them to fanciful ones then you could, I presume, prove anything literally. Therefore, the setting of the axioms and the reasoning behind them needs the most careful study. Otherwise, later when masses amount of work has been done, your whole world may collapse. I believe, but cannot at this time quote an instance, that this has happened in the past. Einstein himself states it in a way about Euclidean Geometry compared to Gaussian, in a round about way.

It seems to me that getting back to, or at least continually referring back to basics is a most important practice for any theorist all along the way. In a form of Ju Jutsu I study many years ago, I had the privilege of meeting our Soke (Grand Master of the form). His greatest measure and skill was to perform the first Kata (form) taught to initiates of the art. Not only to perform it though but also to perfect his technique. It was his measure of his competency. There is a valuable lesson to be learnt here I feel.

Thanks for all the replies, please keep them coming, I am thoroughly enjoying these exchanges.

Cheers
Vaughan

I've been reading some pretty controversial stuff lately...
Basically, it asserts that the speed of light is NOT a true constant,
but a value dependent on the magnetic permeability and electrical
permitivity of free space (analagous other types of wave travelling
in other mediums - as explained by Maxwell) - What is more surprising
is that measurements of C over the past century or so have been
steadily decreasing with time. Furthermore, it has been observed that
red-shifts of distant objects occur in discrete quantized values (not
a smooth curve of values as one might expect) - this may suggest that
the red-shift is not due to an expanding universe as suggested by Hubble,
but some other mechanism may be responsible - possibly related to the
slowing down of light.

Another interesting question... Do you know what the "speed of gravity"
is ? - the answer may surprise you. It's not C. It's not slower than
C. Nor is it infinite. It is (much) faster than light. (I forget the
figures...) But this may suggest one reason why gravity is so hard to
fit into a GUT / TOE / Standard Model of physics...

Want to read more...
http://ldolphin.org/cdkconseq.html

H.Dickins

Having studied Relativity, I still don't get why you can't accelerate up to the speed of light. I have asked several physicists about this, and no one has given me a satisfactory answer so far.

Firstly, if you are inside a spaceship that is accerating, your mass does not increase. You have your normal mass the whole time. Also, time does not slow down for you. So why can't you, in your spaceship, just keep on accerating at a constant rate until you reach the speed of light?

The outside observers would never see you reach the speed of light. But from your point of view, could you reach it?

One aspect of relativity and quantum theory is the abandonment of a conventional linear view of everything from calculations to the concept of time itself.

Instead of seeing the universe as beads on a string, it is perhaps more helpful to look at the abstract notions which are associated with paradigms drawn from the realm of poetry or from music.

In this way the beauty and the elegance of the form is the description itself, rather than the physical realisation as a three dimensional model.

If time is non linear, as it is in novels, etc, then space too could be seen to flow as a river with eddy currents which would allow the observer to experience a complex interaction of time and space and to abandon our conventional view of physics and the universe.

Space and time as non linear features of an abstract universe would permit new dynamic calculations that would create in itself a mathematical paradigm that would take an individual into a virtual world.

The closest I have come to modelling this, is imagining a chess game where the pieces react according to a complex series of moves that permit, say, the bishops to move as knights or to allow the
queens to jump over other pieces.

The role of each player would be to determine which set of rules are in play, and in this way the game would evolve from the basic moves into a complex and dynamic pattern that would transend the three dimensional model to allow a game to be played in many dimensions.

The speed of light is an upper bound that is energy dependent, the nearer you get to the speed of light the more energy is required to go faster. The limit of this exponential growth is infinite at the speed of light. The statement that the speed of light is a constant is really an assumption. Einstein discussed the speed of light boundary as an upper structural constant of the universe, i.e. it is the same for all reference frames.

Particularly recollected by an 'oldie'such as myself,are the several aspects outlined.
An original experiment was several years prior 1972. There is no doubt that a jet went all the way round the world twice to attest some difference. Although an incremental difference was deemed to exist between the two sets of two clocks,it was too hard to say the precise value. It was referenced as 'being of the order of a billionth of a second.'
The other point of interest is complimentary as well,with respect to the speed of light being superceded by photons in an actual lab test. It requires of space that its vacuum density be extremely low. Even so,the photons and wave behavior were held to be'broken'. The conclusion was that the subject cannot be informational at root. Hence the Special Case is a myth of a kind. Also of interest should be that in 1962, H Bondi the mathematician published papers in the Illustrated London News. He did argue the case
for a clock system, transmitting signals up to c,relative to a stationary observer.
The more one reaches back into the last century the more one finds complimentary facts in relation to the previous contribution.

Arguments about creationalism are quite heavy of late. I welcome a lighter approach. This '10 secs to God' implication is certainly capable of confusing. Scientists say that IF a single origin is seriously entertained,then Time itself and hence Laws of Physics,then entered the scheme of things.
This interviewer has rather set up his own problem,alongside the difficulty of proving how old the Universe is.
At the present time there happens to be an emergent mystery of an origin which involved the evolution of quarks;these being held together by a relative force of enormous magnitude. In fact it would seem that the CERN proof in Europe suggests that maybe - with great caution - one could say that the Universe as a single entity is the wrong concept. It is made up of other dimensions of activity. ie the several dimensions higher than the usual 4, are a coincidence related to the regional change we call an 'Origin'. If these overlap by nature ie gravity leaks greater than the Einsteinian predictions,maybe there is a case to refer to this type of answer later on. Like you I 'wait by the seashore'.
The cry goes up 'how long' amongst amateurs like us.

I can take your question on the basis that I was alive in 1962 and read of the full meaning of Relativity as published by H Bondi in London Illustrated News. It covers relative motion over a wide field as you infer.nb H Bondi was a Principal of Kings College C London. You might be able to get old copies from their library.
Now this issue of the shortest distance between two points in time. It is a fact of gravity experience that a jet pilot falling through a catenary curve (maths A level)will experience weightlessness a short while and travel between two points in the atmosphere faster than if he chose to dive along the straight path at a uniform rate. Yet the length of the curve of a catenary between these two points(invoked by your query) is longer. Gravitation does this trick in our own proper time.
Other issues in your write-up are very interesting;you would have to study more to overcome the personal barrier a bit better I reckon.
eg. Light does slow down according to an atomic research project to photograph it(Density of Space theory). Of interest to you will also be the fact of post 1984 graphics in an IEE biased magazine which argued out the history of Lorentz theory. Applied alongside gyroscopic tests. Beyond philosophy these days. The old science library idea should help you. Additionally from late last C.:-a test to show two lasers passing close to each other. They literally twisted along their respective paths.
Your Educational Journey ahead will be full of new surprises I am sure.

This idea of yours inferring that human minds may be hurt' by degrees. The most learned can hurt your pocket over loans ,if thats what you are trying to say. Just a suggestion along social lines,rather than grammatically,one could seek out all the photographic elements of the transitional physics - both macro and micro as a hobby without spending so much. Theoretically,if someone ever noticably turned up to disturb human progress -presumably to supervene the workspaces of everyone else in astrophysics - it would amount to explaining a misconception of the hyperforce in some way.It would not be some private problem anymore about how to pick up the subject ' more interestingly ' as you infer. I personally can't think of anything more devastating than waking up in ten years time to a newspaper report about the moon not being Einsteinian. That is the tests by satellite-Apollo. This being the case by then,not only would the settlement of the moon be wrong but the age of the Universe into the bargain, fella. Why not just wait til then ?
We might be dead from bird flu-chaos well before,anyway.