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Massive Discussion of Space and Time
By Andrew Hodges (P4403) on Wednesday, June 13, 2001 - 09:01 pm:

If you have a matrix with real eigenvalues e1, e2 and e3 and real eigenvectors v1, v2, v3, it has a geometrical interpretation; it respresents a 3-way stretch of factors e1, e2 and e3 in the directions of v1, v2 and v3 respectively. What is the geometrical interpretaion of the situation if the eigenvalues and eigenvectors have imaginary/complex values?

By Arun Iyer on Saturday, June 16, 2001 - 09:13 pm:

if we represent comples numbers according to argand then they are no more than an ordinary point.

so i think that their representation must be the same as it is for real values.

if anyone else has some other ideas i would love to hear that.
love
arun

By Andrew Hodges on Sunday, June 17, 2001 - 02:45 pm:

Hi, i took the matrix for a standard 2d anticlockwise rotation of x degrees about the origin:

cos x -sinx
sin x cos x

The eigenvalues for this matrix were e^(ix) and e^(-ix) with eigenvectors
1
i

and

1
-i

respectively.
This seems to suggest that complex/imaginary eigenvalues and eigenvectors represent a rotation, but i am wondering if this is able to be quantified better, e.g. is it possible to ascertain the axis of rotation/invariant line and any enlargements associated with the rotation from the eigenvalues and eigenvectors?

By Sean Hartnoll on Sunday, June 17, 2001 - 03:19 pm:

Hi, a pure rotation has no enlargements. This is essentially what the problem is telling you when you get complex e-values with unit modulus. My guess would be that when you get a complex e-value, they will always come in pairs, the modulus will give you an enlargement and the phase will give you the angle of rotation. The axis of rotation is a 3D concept: if you extend your matrix to 3D by adding a 1 in the bottom right corener, then you will get an e-vector (0,0,1) which is the axis of rotation, I think in general for a 3D rotation you'll get two pure phases (e^ix, e^-ix) and an axis of rotation given by the e-vector of the third e-value which will be 1.

Sean

By Arun Iyer on Sunday, June 17, 2001 - 08:04 pm:

i do feel sean is correct.
would love some more ideas and responses on this one!!
anybody hearing me out there.

love
arun

By Andrew Hodges on Monday, June 18, 2001 - 09:00 pm:

Hey Arun, i have an idea; you stated above that you would expect the geometrical interpretation of a matrix with complex eigenvalues/vectors to be the same. This isnt true in Real Space, but what about 'Complex space', would matrices with complex e-values/vectors represent 3way stretches here? If so, what would a matrix with real eigenvalues and eigenvectors represent geometrically here?

By Arun Iyer on Tuesday, June 19, 2001 - 09:32 am:

dear andrew,
i am not particularly clear about your idea of complex space.

can you clarify a bit

love
arun

By Andrew Hodges on Tuesday, June 19, 2001 - 05:15 pm:

Im not sure about in 3d, but if you consider 2d, it would be like the Argand plane, as opposed to the standard x-y plane.

By Arun Iyer on Tuesday, June 19, 2001 - 07:05 pm:

This third dimension might be important.It could be dealing with some really advanced mathematics or it is something yet to be discussed about.

(Pardon me if you feel crazy about what i am going to say but i have this feeling this third dimension must have something related with time dimension)

would love your arguments on this please!!!

love arun

By Andrew Hodges on Thursday, June 21, 2001 - 04:27 pm:

This is getting complicated! Could you expand on your feeling about the 3rd dimension being related to the dimension of time? Can only matrices with real eigenvectors be arranged into the form UDU^(-1) ? If not this would be very helpful, as the transformations occurrring would then be more obvious to pick out.

By Arun Iyer on Friday, June 22, 2001 - 11:07 am:

i am quite unable to expand my feeling on this thing.However,i have been wondering,
if we can represent bodies or particles as points in real space then there must be something like anti body and anti particle which are represented in " complex space ".This is just a rash thought i have which i was about to erase but
stephen hawking's string theory is changing my mind.

pardon me for going out of topic but still i feel this is quite fascinating.

for your second question , what is UDU please tell me.

love arun

By Sean Hartnoll on Friday, June 22, 2001 - 05:13 pm:

You might be interested to know that particles such as the electron are represented by things called quantum fields with take _complex_ values, so they live in complex space. Also, when you complex conjugate the field, you get the field of the antiparticle, the positron.

Sean

By Andrew Hodges on Friday, June 22, 2001 - 09:25 pm:

For a real matrix M with real eigenvalues, we can express it in the form UDU^(-1) where U is the matrix of the 3 eigenvectors, D is the diagonal matrix containing the eigenvalues, and U^(-1) is simply the inverse matrix of U. We have

M = UDU^(-1) Expressing a matrix in this form is of great use, as it makes clear what transformation the matrix M does. Ill do an example (im just picking values off the top of my head here)

If a matrix had eigenvalues 1, 2 and 3 with eigenvectors

1 2 3
2 3 1
3 1 2 RESPECTIVELY!!!!!


then M would be

123
231
312

multiplied by

100
020
003

multiplied by inv.of
123
231
312

A simple result, but of great use!

Also it does sound interesting, combining the concepts of complex numbers and antiparticles in the way above! Complex numbers are also of great use in calculating quantum 'probability amplitudes' that is, calculating the chances that particular quantum events will occur. Your feeling about the time dimension being related is interesting too, could the concepts of time and antiparticles be related in some way? Do antiparticles move through time in the same way that particles do?

By David Loeffler on Friday, June 22, 2001 - 11:36 pm:

Didn't Feynman prove that antiparticles were identical to ordinary particles reversed in time?

By Sean Hartnoll on Saturday, June 23, 2001 - 02:17 am:

strictly what this means is that if you complex conjugate all the equations (particles to antiparticles), let t -> -t (time reversal) and let x -> -x (parity change) then you end up with the same physics.

Sean

By Andrew Hodges on Saturday, June 23, 2001 - 04:57 pm:

Thats exactly what i was thinking - i must have read it somewhere, and was not sure if it was actually true!

By Andrew Hodges on Saturday, June 23, 2001 - 04:59 pm:

Does this mean that antiparticles are moving backwards in time?

By Sean Hartnoll on Saturday, June 23, 2001 - 05:10 pm:

No, not really. Strictly speaking it is saying that if a particle moved backwards in time, it would look like an antiparticle. There is some confusion on this point even in standard textbooks though. Mathematically, there is no ambiguity, it is just a symmetry of the system, but the physical interpretation is sometimes confusing. But I should emphasise that things DO NOT travel backwards in time, this would cause all sorts of paradoxes. However, it is sometimes useful (for example, it helped Hawking discover that black holes radiate) to think of antiparticles as though they were particles with time running backwards.

Perhaps a clear way of looking at it is this: Suppose we were to film the universe and then run the film backwards. Would the evolution of the universe going backwards behave like a some kind of universe going forwards in time, or would it be completely different. What the CPT theorem says is that it would look the same AS LONG AS we also change particles to antiparticles (C) and invert the parity (P).

Sean

By Arun Iyer on Saturday, June 23, 2001 - 07:25 pm:

Well Sean you have said all this!!
Here's my own thought,

A person stays at one place for some time he is infact travelling in time.THE FACT is that we all travel in time with a fixed " time velocity ".That's the relative velocity is ZERO.
That's Why we don't feel that anyone is travelling in time.The unique thing here is that this velocity is unidirectional.

If we are able to accelerate this velocity or reverse it we will be able to travel in time.

Your arguments please!!!

love arun

By Arun Iyer on Saturday, June 23, 2001 - 07:29 pm:

ON YOUR QUESTION ANDREW,

Can only matrices with real eigenvectors be arranged into the form UDU^(-1) ?

I think yes,because i cannot think of how a 3x3 matrix with complex eigenvectors/eigenvalues
and be represented as UDU^-1.

Any one with their arguments are welcomed!!

love arun

By Sean Hartnoll on Saturday, June 23, 2001 - 07:34 pm:

Arun, in fact according to special relativity (which is very well supported experimentally) we don't all travel in time with the same velocity. For example, the faster you move, the slower your time goes relative to someone who is moving more slowly (with both the velocities measured with respect to some fixed point). And in fact he velocity isn't unidirectional either because time and space get mixed up in special relativity. However, there is always a well defined sense in which there is a future and a past (have you heard abot light cones - it essentially works because the speed of light is constant) and so there is a well-defined sense in which time reversal does not happen.

Sean

By Andrew Hodges on Saturday, June 23, 2001 - 07:40 pm:

Hang on what about entropy? Entropy always increases or remains the same as time goes by, so if we ran the universe backwards it would appear to decrease, hence the universe could not look the same could it?

Arun, consider space and time together. In fact, everybody's speed through space-time is the same. hence, the faster we move through space, the SLOWER we move through time. You can consider the following quantity as being invariant:

(ct)^2 - x^2 - y^2 - z^2

Wher c is the speed of light, t is the time axis, and x y and z are the spacial axes.

By Sean Hartnoll on Saturday, June 23, 2001 - 08:02 pm:

Okay, regarding entropy. At a microscopic level it is simply true that the equations of the standard model are symmetric under a CPT transformation. Entropy is a macroscopic thermodynamics concept, which like temperature is not necessarily a useful concept (in fact, in general it isn't defined) in considering microscopic dynamics. You need to think about the initial conditions also. So for example, if I started with a gas of particles in the top corner of a room, the law of increase in entropy (which is derived from the microscopic description) says that after some time has passed I will probably find the gas distributed accross the room. Now, suppose I run the film backwards in this case and change the gas to an anti-gas (in practice, this would mean changing the charges of all the particles involved). I would see the particles collect together and end up in the top corner. This does violate the increase of entropy law, but that does not mean it is not a possible evolution of the system. The increase in entropy is only probabilistic. What has happenned in this case is that we start with a very special configuration of particles which is such that when you let them evolve, they all end up in a lower entropy state. But at no point is it inconsistent with the laws of physics. What I'm trying to say, is that at the level we are talking (it may change in the context of quantum gravity) the increase in entropy is law is not a law in itself, but is simply something that is overwhelmingly likely to happen given the microscopic law, but not 100%.

Sean

By Andrew Hodges on Saturday, June 23, 2001 - 08:23 pm:

Yes, the increase in entropy is overwhelmingly likely to happen - but very overwhelmingly so! Say we had loads of universes - even one for every planck time gone by in this universe - i would still bet the likelihood is that entropy increases in every single one of them! What makes our universe so special? Of course there is the argument of the anthropic principle, but even though we live in an area of the universe of exceptionally low entropy, the anthropic principle could not be used to show that overall entropy throughout our universe will not increase. I can see that this problem is looking like one of the 'anomalies' between quantum and classical physics and may not be resolved until a better theory of macroscopic behaviour, such as quantum gravity is developed.

By Sean Hartnoll on Saturday, June 23, 2001 - 08:28 pm:

The main point is that reversing time in our universe would not give as an inconsistent universe, just a very unlikely one.

Sean

By Andrew Hodges on Saturday, June 23, 2001 - 09:10 pm:

Ok, yeah i understand what you are getting at. I just feel that if a physical theory is to be a correct one, it must be one which makes the universe that we are in an average, unexceptional one.

By Sean Hartnoll on Saturday, June 23, 2001 - 09:27 pm:

Yes, this is true. At the moment however, there are two things, the theory and the initial conditions, which need to be put in by hand at the moment.

By Arun Iyer on Monday, June 25, 2001 - 11:34 am:

Well Andrew and Sean,
the point you have said is the exact one which i tend to disagree with special relativity. For me it presents no logic when we mix space and time.

suppose i travel from my home to my aunt's house
and you are travelling from your place to a place in africa with a plane in that same time. Here it doesn't matter how much physical distance you are covering but we have travelled the same
"time distance" that is say 1 hour.

About time distance,
This is where my mind goes for the third dimension of complex space.

Guys these are my own ideas , AS of now i have no proofs for it but i do think they are correct as far as my logic goes.

Would love your suggestions Andrew and Sean.

love arun

By Sean Hartnoll on Monday, June 25, 2001 - 04:17 pm:

Arun, unfortunately, special relativity is not really something you can disagree with! It has passed many, many tests, in particular, people have put a clock in a spaceship, gone around the Earth several times and then compared the clock with a clock that stayed at rest, and it was found that the clock in the spaceship had gone slower exactly as predicted by relativity.

Sean

By Arun Iyer on Tuesday, June 26, 2001 - 06:41 pm:

Thanks for the info,
but i still can't get over it

love
arun

By Andrew Hodges on Tuesday, June 26, 2001 - 07:53 pm:

I think it is the counterintuitive nature of the topic that makes it difficult to comprehend! Ill try again;

Imagine you want to get from A to B, where A and B lie on the same line. The quickest way to get there is to just go straight along the line. Now imagine if A and B were the same horizontal distance apart, but B was further down:

A----------- B (1st case)

A-------------
--------------
-------------B (2nd case)

If you travel at the same speed in each case, which one will take longer to get to?

The second case, obviously. To put it simply, if you travel at an angle, it takes longer to get someplace. Above we are considering two separate SPACIAL dimensions, we know time is a dimension too, and so THE SAME RULE APPLIES. We all move through spacetime at the same constant rate, but the more we move through a spacial dimension in a given time, the bigger the metaphorical 'angle' detracting us from moving through time at the fastest possible rate. Do you see what i am getting at Arun?

By Arun Iyer on Thursday, June 28, 2001 - 06:55 pm:

I can quite understand you andrew.
My question is,
What is the thing which keeps us from going faster in time or is there a mathematical relation between space and time?

love arun

By Andrew Hodges on Friday, June 29, 2001 - 05:18 pm:

Space is time and time is space. Thats all that can be said really, if you think about it, you cannot have one with out the other - it takes time to move from place to place. Time is basically change. Yes there is a mathematical connection between space and time. I wrote it down further up this page(the equation invariant under coordinate transformations).This is just a special relativity equation - it does not take gravity into account - it is taken from a geometry developed by Minskowski early last century.

By Arun Iyer on Friday, June 29, 2001 - 08:16 pm:

I saw that equation and i also saw one thing

"where t is time axis"

can you explain this time axis to me.

love arun

By Andrew Hodges on Sunday, July 01, 2001 - 10:09 am:

OK, normally, in a cartesian plane you have an x-axis and a y-axis. These denote a point in space. If we were to give the axes the units metres, the point (3,2) would represent the point 3 metres to the right and 2 metres up from the origin (0,0). Now, if we keep the x-axis but get rid of the y-axis and put a time, t-axis there instead we can specify points in time. This is very important. If you want to meet up with a friend, you might say 'meet me outside the shop'. This specifies a point in space. But you would also specify a point in time as well; you might say 'at 12:30p.m.' And so by having a time axis, we can describe points completely in space and time. We need an origin (0,0) from which to base measurements. This is a time and a place where an EVENT has occurred. An event could be anything from the start of the universe to when you saw your favourite rock band! But we can say, using the time axis, t seconds after the event, i am stood at a point x metres from where the event occurred. Using the time axis concept we can draw lines showing a particles movement through space over time. e.g. if the units of the x-axis are in metres and the units of the t-axis are seconds, a particle moving in the x-direction only at a speed of 5 m / s would be denoted by the line x = 5t. Such a line denoting the movement of a particle through space and time is called a particles WORLDLINE. If you want the particle to move through all 3 space dimensions as well, just add the y and z axes, creating a 4dimensional movement!! (As you've got your t-axis, as well as your standard x,y and z axes!)

Is that explanation clear enough? I hope i havent patronised you!!

Andrew

By Arun Iyer on Sunday, July 01, 2001 - 07:51 pm:

Andrew,
Will this t-axis have negative direction as well?

If yes,
How would you represent particles and bodies on the negative t-axis , in other words, what would be your interpretation?

Don't worry you haven't patronised me!!
i am just being rationalistic as much as i can.

i have this dream of becoming a physicist.
Even if i don't become one , HEY , it can't stop me from thinking like one.

love arun

By Olof Sisask on Monday, July 02, 2001 - 12:52 am:

What's the difference between thinking like a physicist and being a physicist? :)

You could consider the negative t-axis as being the time before an event occured.
For example, -3600 on the t-axis could represent an hour before time 0, which could for example be the time you ate breakfast.

Regards,
Olof

By Andrew Hodges on Monday, July 02, 2001 - 07:37 pm:

What if t was an imaginary axis? Im not sure, but ive a feeling this has something to do with imaginary time; we may be living in an imaginary universe!

p.s. I would like to be a physicist too, ive got a long way to go yet though, thinking intuitively really helps though, like you did earlier with your concept of everyone moving through time at the same rate:)

By Arun Iyer on Monday, July 02, 2001 - 08:03 pm:

Andrew,
You don't know how happy i am after i have joined the nrich club.

I have found here members who are similar minded with me.

Boy!!I would sure like to meet you and other members of the nrich club.Its been a great companionship.

Long live this tradition!!!

ON MY DOUBT,
it is something we will have to wait to get an answer.

love arun

By Sean Hartnoll on Monday, July 02, 2001 - 08:52 pm:

The introduction of imaginary time is purely, 100%, a mathematical trick that you do in the middle of calculations, it doesn't correspond to anything, and you change back to real time at the end. The point is that if time is imaginary (say it) then the invariant expression is

x^2 + y^2 + z^2 + t^2

which turns out to be more convenient than

x^2 + y^2 + z^2 - t^2.

Sean

By Arun Iyer on Monday, July 02, 2001 - 09:25 pm:

Sorry olof,
I didn't read your message at first.
On your question,
I think it all depends on the position of your reference frame.This gets a bit tricky as everyone will end up with different answer at the end.

Well sean,
Let's Hear Your conclusion!!

love arun

By Sean Hartnoll on Tuesday, July 03, 2001 - 12:12 am:

I'm not sure what the question is! But the point is that everybody always ends up with the same answer for certain things, such as the x^2+y^2+z^2-t^2 expression, and so there is a way in which everything fits together.

Sean

By Arun Iyer on Tuesday, July 03, 2001 - 08:14 pm:

Sean,
Now i am really confused.

As we started with this discussion on complex space,But end up in real space.

Now how does that fit together??
(Pardon me for being so argumentative but that's me the old tubelight)

love arun

By Sean Hartnoll on Wednesday, July 04, 2001 - 12:26 am:

Okay, let me try to sort this out. On the one hand there is the kind of complex space that was initially being discussed. One the other hand there was a discussion about relativity. Andrew suggested that the idea of imaginary time in relativity might have be related to the idea of complex spaces.

Now, what I was trying to say was that there is a concept of imaginary time in relativity, but that it does not mean that we live in a universe with imaginary coordinates.

We live in a universe that (for the sake of this argument) has four real (as in real number) dimensions which we label x,y,z,t. Now, time is a bit different to the other dimensions. And mathematically this shows up in a minus sign in front of terms involving t2 compared to the other terms x2, y2, z2. Now the point is that if we set t' = it, then t'2 appears with the same sign as x,y,z because we have an i2 = -1 term so t2 = -t'2. So if we work with t' instead of t, then all the dimensions look the same and time is not special. It turns out that it is easier to do calculations in this setup. But at the end we change the variables back again to t = -it', so we are back where we started.

I.e. imaginary time appears as a mathematical change of variables int he middle of calculations, not at the start or at the end, and it is the start and end of calculations that have physical meaning.

Sean

By Arun Iyer on Wednesday, July 04, 2001 - 06:55 pm:

sean,
I think i can read you.

you mean,
the initial and final states are in real space though the process of conversion of initial state to final state may go through complex space.

am i right??

love arun

By Andrew Hodges on Wednesday, July 04, 2001 - 07:43 pm:

Does this mean that 'imaginary time' behaves like a dimension of space? And if so, does complex space behave like other time dimensions?

Also with respect to the CPT theorem, if the 'c' stands for charge conjugation does that literally mean conjugate the charges OR swap particles for antiparticles. I am just interested as antiparticles are not simply particles with opposite charges, they have certain other differing properties as well.

Andrew

By Sean Hartnoll on Thursday, July 05, 2001 - 04:03 pm:

Arun - yes, that's pretty much what is happenning.

Andrew - yes, imaginary time is just another spatial direction. And yes, I guess that if you changed spatial dimensions to imaginary you'd get more timelike directions, but this tends to have problems (how do you deal with two times!?).

The opposite charge is the most important property of antiparicles, but yes other properties also get flipped. However, in teh equations of the theory, it just something analogous to taking the complex conjugate.

Sean

By Arun Iyer on Thursday, July 05, 2001 - 07:37 pm:

Well Sean,
(On the question by andrew)

Can we here tend to accept the parallel universe concept?

love arun

By Andrew Hodges on Saturday, July 07, 2001 - 05:02 pm:

Im not sure what you are getting at here Arun:-S
The parallel universe concept is merely an interpretation of quantum mechanics. As far as I know there is no physical evidence to support the concept, the mathematics behind quantum theory merely allows it to be a possibility.

By Arun Iyer on Saturday, July 07, 2001 - 06:39 pm:

Well,
Sean said that handling two times would be a problem.Well,there you are!!!

If we do have a parallel universe then it is possible to have two times right!!

Anyways this is just a suggestion so they are bound to have opposite views and ideas!!

love arun

By Andrew Hodges on Sunday, July 08, 2001 - 11:44 am:

Would the time axis not be the same in many parallel universes? Parallel universes break off from our own all the time, and then behave differently from ours, would they, then have the same concept of time as we do, if some of their history is the same as ours? Wouldn't the space dimensions be the same as ours as well? Perhaps they differ from our universe in some different respect, perhaps they differ by a'fifth dimension' or something.

By Arun Iyer on Sunday, July 08, 2001 - 06:29 pm:

Ha ha ha

andrew,
your questions are something.....er..
Something of which i have no idea whatsoever.

when it is said that it is parallel universe then its properties something like that of line which is parallel to another line.

er.. i think!!!!

love arun

By Sean Hartnoll on Sunday, July 08, 2001 - 10:23 pm:

I don't think the parellel universe idea is considered very seriously by most physicists. It doesn't help explain anythings and lands us with a multitude of unneccessary universes. It is a best unnecessary. But it can make good science fiction though.

If there were two times, they would in some sense be perpendicular to each other, not parallel. The paralel universe idea is different to the two times idea. And like I said the two times idea has problems.

Sean

By Olof Sisask on Monday, July 09, 2001 - 11:43 am:

On a slightly different note - what is space? Is space just the 'nothing', which contains matter? How can 'nothing' have dimensions such as depth, height, width? Was there time before the big bang? Just a couple of things I've been wondering about... :)

Regards,
Olof

By Arun Iyer on Monday, July 09, 2001 - 06:35 pm:

OLOF,
How can space be nothing?

It has you,me,sean,andrew,earth,mars,jupiter..etc.
It is a huge container and we don't know yet what all it contains.

That's what makes it so much interesting.
If you ever get there,you will know why
DENNIS TITO spent so much money to get there.

Its absolutely beautiful!!!(Imagine that)

love arun

By Arun Iyer on Monday, July 09, 2001 - 06:37 pm:

OLOF,
About your second question,
I am sure i would have answered that if i were existing before BIGBANG.

love arun

By Olof Sisask on Monday, July 09, 2001 - 07:36 pm:

It is indeed beautiful Arun! This brings up the question, can nothing contain something? If space is something, then what is there outside space? Nothing..., which would be like space ;-).

I think time must always have existed - how can an event occur if there is no time? Maybe you can consider the Big Bang to be the point 0 on the real number line (or some other analogy) - with infinitely much time extending in both directions. This is of course provided time is linear, which is probably wrong!
Arghhh... !

Regards,
Olof

By Sean Hartnoll on Monday, July 09, 2001 - 07:45 pm:

Firsly, space and time are not separable. There is not a before to the big bang. All the laws of physics break down at that point, including the idea of time.

Spacetime is just a manifold. Think of the surface of a balloon. There is no outside, what would be? It is not a well defined question.

So space certainly is something, with certain properties. The curvature of space is gravity, which certainly is visible, our passage through time makes us grow old.

Sean

By Arun Iyer on Monday, July 09, 2001 - 08:06 pm:

Ya , I get you sean.

Though,It would be quite evident if we were to see the BIGBANG ourselves.

The computer graphics which are developed to explain BIGBANG seem quite inadequate everytime we see it.

Though the main question remains
"where the hell did the heavy mass come from"

Don't you feel so??

love arun

By Andrew Hodges on Monday, July 09, 2001 - 08:34 pm:

Arun, is space a huge container? Thats what Newton thought, but if there was nothing in this container, how would we know one part of it from another, we wouldn't know how fast we were travelling, in what direction we were travelling, whether we were accelerating or not, or even if we were moving at all!! If there is nothing but space, nothing exists.

Arun, on your last post are you asking where mass comes from? If so, i can partly explain. For some reason at the start of the universe, more matter than antimatter must have been created - as if there were equal amounts of each, they would all have collided and annihilated each other. So we got more matter (i dont think why we did has been explained yet though). At present there are a few theories explaining mass. One predicts a force carrying particle, named the higgs boson. As some particles move through space they attract these bosons, though some more than others. Think of it like this: if you had a room full of scientists, and einstein happened to walk through, they would all get excited and run up to him, asking him questions etc., if he were a particle, he would be a massive one, as many scientists (representing the higgs boson) are crowding round him. However, if I walked into the same room, there would be no such reaction - i would not attract mass, and so would represent a massless or nearly massless particle such as a neutrino or a photon.

One question i have on the subject though is: What causes particular particles to attract more of the higgs bosons than others? (obviously it cant be because certain particles are more famous than others!).

Andrew

p.s. is there such a thing as good science fiction?!!

By Andrew Hodges on Monday, July 09, 2001 - 08:42 pm:

Olof - space is something, it is three dimensions! 'Nothing' would be simply 0 dimensions, which our brains cannot handle unfortunately, as they are so used to working in three-dimensions!

By Olof Sisask on Monday, July 09, 2001 - 09:50 pm:

Indeed Andrew! But what was there before the Big Bang (and I know that saying before the Big Bang implies that there was time before it, but otherwise how could an event have occured)? No space-time? Something of 0 dimensions? Then how can something of 4 dimensions come from that? And why 4 dimensions? And when we say that the Big Bang occurred so-and-so many billion years ago, is that relative to something that is perfectly still (and what does that mean)?

Sean - I can't quite see how this manifold idea works. Could you elaborate a bit more please? Cheers,

Olof

By Sean Hartnoll on Tuesday, July 10, 2001 - 02:08 pm:

Andrew - if I understand the question, I think the answer is that different particles hae different charges. It would be completely analogous to say the fact that an electron and a proton would attract each other because they have opposite charge whilst an electron and a neutron do not, because the neutron has no charge. In the case of the Higgs, the "charge" in question is more complicated, but it's the same idea.

Olof - it is a valid question why the big bang occured, and I don't think it has been answered. Some people talk about quantum fluctuations (i.e. something out of nothing) but this still wouldn't explain where quantum mecahnics came from. So the big bang certianly doesn't solve all the philosophical questions you might want, it just explains a range of things like the expansion of the universe, the cosmic microwave background etc.

You can think of the universe exactly like a baloon that is being blown up (a manifold is just an n-dimensional surface in essence). When we say the universe is x billon years old, it is with respect to someone who is staying still as the universe expands (so they are in fact moving away form everything as thy stay still!).

So the at the big band, there is no space, it is 0-dimensional if you like, but the most important thing is that there is a singularity, everything just blows up, so the physics you are using to describe it simply are not valid.

Sean

By Olof Sisask on Tuesday, July 10, 2001 - 03:07 pm:

I see, thanks a lot Sean. I still can't quite get my head around how a point can be still in space, however. Would it be 'the point' 'where' the Big Bang singularity popped up? Again, it's a flawed question, but I hope you can see what I mean.

Olof

By Arun Iyer on Tuesday, July 10, 2001 - 08:09 pm:

Andrew,

When did i say space had nothing in it infact it has this entire universe.

I think this propped up the idea of lumineferous
ether in minds of huygen.

love arun

By Arun Iyer on Tuesday, July 10, 2001 - 08:11 pm:

andrew you said " for some reason ... higgs boson..." do you know what is this reason.

love arun

By Arun Iyer on Tuesday, July 10, 2001 - 08:14 pm:

Sean how can you say that all physics breaks down at bigbang,
isn't it the start of the generalisation of physics?
love arun

By Sean Hartnoll on Tuesday, July 10, 2001 - 11:24 pm:

Olof - I see what you mean, but there is no reason for the big bang to pop up anywhere. At t=0 we don't know what happenned and for t>0 you have spacetime, and there is no need for spacetime to be inside something else.

Arun - an anology: in the theory of fluid dynamics (i.e. of how water moves, for example) if you don't take into account friction, you find that at some point it predicts that the speed of the water becomes infinite. Now this infinity just means that your model is not correct. And in fact what happens at these points is called turbulance (random motion, more or less). But you cannot describe turbulance within the origin model. It is the same with the big bang. At a certian point everything goes to infinity, and what this is saying is that at this point the model we are using (general realtivity) is not correct.

Sean

By Andrew Hodges on Wednesday, July 11, 2001 - 07:18 pm:

Arun, if you mean why was more matter than antimatter created in the early universe; i dont know!!

Arguments please

Andrew

By Arun Iyer on Thursday, July 12, 2001 - 07:04 pm:

Sean i think i am reading ya....

love arun

By Arun Iyer on Thursday, July 12, 2001 - 07:05 pm:

Andrew
yes that is one of my questions.

Another question is
where did this matter and anti matter come from??

love arun

By Andrew Hodges on Friday, July 13, 2001 - 09:57 am:

do you know einsteins equation E=mc^2? This is where matter and antimatter come from, they have in fact been converted from energy into matter. But where does this energy come from? Well, everywhere in the universe has some energy in it, even a vacuum! If there was absolutely no energy at all in a vacuum, then we would know something about its quantum state with 100% certainty. Heisenbergs uncertainty principle forbids this, so even in a vacuum there must exist a certain amount of energy.

Thats the best answer i can give, if im incorrect in parts, feel free to correct me, im reaching the limits of my knowledge here! And if you want a deeper answer, it would probably be best if you asked a philosopher!

Andrew

By Arun Iyer on Friday, July 13, 2001 - 06:56 pm:

Well Andrew (or anyone reading this message),
I never read about "vacuum with energy".
you know you have just fiddled with my idea on vacuum.

1.How do you define vacuum then?

2.if vacuum has energy,then do you think the space between the planets is filled with energy(some atleast)?

3.How is it we don't see any mass developing between the planets (i.e in space or the vacuum outside the atmosphere)?

4.If vacuum has energy does it obey the principle of energy conservation?

there are actually lotsa questions but i am just asking the one's which i feel are imp.

love arun

By Arun Iyer on Friday, July 13, 2001 - 06:58 pm:

Is there any philosopher out there?

love arun

By Brad Rodgers on Friday, July 13, 2001 - 11:59 pm:

Just to add a little, as Sean has said, there's no reason to assume that there is a cause for the universe, as the concept of causation is solely based on what we have observed in the universe. Assuming that there is a cause for the universe is like assuming that gravity exists outside of the universe (Yet, since philosphy has been ask for, there is no reason to assume that cause and effect or gravity do not exist outside of the universe).

Just to contradict everything I have just said, here are some possible ideas as to what was before and what caused the big bang:

a) nothing: there was a lack of cause and effect

b) another universe: This universe had a big crunch like our universe has (or is it had) a possibility of. After "crunching", it consequently expanded once again.

c) a black hole: Stephen Hawking has proposed that the ill understood laws of quantum gravity allow for a black hole to radiate mass and eventually explode and form a "baby universe". I think he used quantum field theory to back this up.

A new theory that tells us how the laws of gravity operate in very small areas could rule out two of these, or predict that one of these must've been the way the universe formed. And, just to confuse things more if there is a lack of causualty outside of the universe, wouldn't that mean that if one thing is formed, then everything possible of being formed must've been formed. So an object, say an X, has been formed, as well as universe in which an X has never been formed, even outside of the universe. Is that contradictory? Is the concept of cause outside the universe contradictory? Is the sky falling? My personal opinion is that the mind, having only experienced what is in this universe, cannot possibly decide what is outside the universe, and it is futile to try to do so.

Brad

By Andrew Hodges on Saturday, July 14, 2001 - 06:41 pm:

Arun

1) A vacuum is a space devoid of any particles such as those in air etc. Classically it is totally empty, although electromagnetic radiation can pass through it.

2) Yes, the space between planets is filled with this 'vacuum energy', for instance it is believed (although it has not been confirmed) that if two bodies exert a gravitational field on each other, they are constantly exchanging force carrying particles called gravitons.

3) Remember mass is different to energy, just because we have energy, it does not mean that we have mass as well out there, all einsteins E=mc^2 equation says is that energy can be converted into matter and vice versa.

4) No, for small periods of time, quantum theory permits the law of energy conservation to be broken (particles can be created out of nothing)! These short term violations average out over space and time, so that in general (globally) the law of conservation of energy is obeyed.

On the subject of philosophy, one interpretation of quantum theory has an interesting consequence. Think about youngs two slit experiment, but with electrons instead of light. Quantum theory shows that if we leave this system alone, interference effects occur, i.e., if we fire the elctrons one at a time, they seem to go through both slits at once, behaving like a classical wave instead of a particle! If we try and observe this though, say by firing photons at the system, this interference pattern is destroyed. (You cannot observe something without disturbing ('touching') it in some way). So by trying to observe something, quantum theory says we change the outcome of what is happening. This means that our conscious brains are affecting the quantum system, and so physical experiments are affected by consciousness!! This suggests that reality is in fact subjective (i.e. it doesnt exist if a conscious being is not there observing it)!

By Arun Iyer on Saturday, July 14, 2001 - 06:55 pm:

Well andrew,

Now where does vacuum store energy?
I mean like do you know its mechanism of storage of energy?

love arun

By Arun Iyer on Saturday, July 14, 2001 - 06:58 pm:

andrew,
talking about the expt. you described.

is it true that matter to wave conversion is true.

I mean like i still cannot believe de broglie's equations l=h/p

love arun

By Arun Iyer on Saturday, July 14, 2001 - 07:06 pm:

I truly do agree with you BRAD.
But you know one thing as far as i have observed in my 17 years and odd age is that nature has always followed some generality.

It is us who are not given the vision to see through these generalities.(For some yes,but not all)i do mean we can assume various many things just by understanding things around us.

So,what do we need is some powerful tool to see this world.I do believe maths would serve us this purpose.

Well, you just go through this discussion page and you will see what i mean.

love arun

By Andrew Hodges on Sunday, July 15, 2001 - 10:54 am:

Heres an interesting argument Arun. Every day you wake up and get out of bed and expect the sun to rise. Everyday it rises, it has done for a few billion years! In fact we expect it to,as it has done for every day of our lives. However, we know that one day the world will end and the sun will rise no more. How do we know the same thing isnt true of physical theories? Everytime I let go of my pen it falls out of my hand to the ground; but whats to say that the next time I let go of my pen it will fall to the ground? I just believe it will because its happened every time before and so it seems like an overwhelmingly likely possibility, but there is no law that says it must - arent newtons 'laws' really just observations of what has happened on past trials of particular experiments. In fact the only principle that tells me my pen will probably fall to the floor is the principle of induction!

So this means that there is no such thing as a physical law. All laws are simply observations of nature throughout time.

Do you agree with this statement?

Arguments Please

Andrew

By Andrew Hodges on Sunday, July 15, 2001 - 11:07 am:

Arun (as far as I know) the vacuum doesnt 'store' energy at all, it is just there! Particles and antiparticles just pop in and out of existence all the time. Interestingly though, this energy can be harnessed. Imagine all the photons, for instance moving through the vacuum. They all have different wavelengths associated with them. Now, if we took two metal plates and put them really close together, so that the distance separating them was really tiny (nanometre scale), only photons whose wavelengths are smaller than the distance between the two plates could get between them, as the ones with wavelengths longer thean the distance of separation would not 'fit' in the gap. This means that there would, on average, be more photons outside the plates than between them, so a pressure would be exerted pressing the plates together, as there are more particles outside than in. This means a force has been exerted ( called a casimir force), and so work can be done and so energy can be gotten out of the system!

Arun, on your question regarding the experiment, who knows? Quantum mechanics effectively steals the mathematics behind classical waves to verify experimental results. The actual physical interpretation of it is not as yet known; there are a number of physical interpretations of the theory, such as the parallel universe interpretation, feynmanns try all paths interpretation and the copenhagen interpretation (regarding consciousness) which I explained above.

What cant u believe about debroglies equation?

Can you accept the results E=mc^2 and E=hf? If so, the debroglie equation is merely an algebraic reshuffle of those (remembering that c=f x wavelength, for photons and p=mc).

By Arun Iyer on Sunday, July 15, 2001 - 07:17 pm:

It is an interesting argument Andrew but,
When you say sun rises it doesn't actually rises does it or when you say your pen is falling it is not actually falling isn't it.

That's what i said it, all beholds in the eyes.
It is the perspective through which we see things. You say sun is rising i say earth has now turned towards sun.you say pen is falling,i say pen is being pulled down by earth.

When i say this,I assume that earth always turns and earth always pulls everything down.

how do i assume it?
i assume it because it has maximum probability.
with this probability value i can deduce a function which will answer your question.

it may be right or wrong.after all this is a trial and error method.

are you getting through me andrew??

love arun

By Arun Iyer on Sunday, July 15, 2001 - 07:23 pm:

Andrew,(on your answer)
"Particles and antiparticles just pop in and out of existence all the time"

This (as i presume) is an interesting assumption.Say let me go by it.i have some ques.
1. When do they pop in and pop out?
2. explain to me "energy is just there(vacuum)"

love arun

By Arun Iyer on Sunday, July 15, 2001 - 07:26 pm:

andrew,
i can accept de broglie equation but i cannot in anyway accept that matter-wave conversion is possible as the equation suggests.

(Another example where our vision is restricted)
love arun

By Sean Hartnoll on Sunday, July 15, 2001 - 08:09 pm:

The above few posts are talking about interesting things, but a few clarifications may be helpful:

- Even if quantum mecahnics does end up being related to consciousness, this doesn't make it subjective (subjective is when different people see different things, this doesn't happen).

- The wave-particle duality needs to be understood carefully. The point is that systems at a certain energy have a certain frequency attached to them (de Broglie). When we are not looking at the system it evolves like a wave with the given frequency,at when we do look, there are certain probabilities of seing a particle with various energies. I.e. we always see particles, but they evolve like waves. So it's not that a particle is a wave at the same time, it's just that there are two realms in which we describe its developement: we we look and when we don't. It's a bit wierd I agree, but it is consistent and experimentally tested (similarly to my remark on SR above, quantum mechanics is not really something you can choose to not accept, you just ahve to get to terms with it).

- physics is more than just induction. Given the set of all past experiments, there are infinitely mnay curves that pass through all the data points. The point about science is that (1) it describes things in terms of simple underlying model and (2) it makes predictions.

- the feynman path integral approach isn't a different way of interpreting QM, it's a different mathematical formalism that turns out to be mathematically equivalent to other approaches. It' important to understand that the philosophical baggage isn't actually necessary for calculating things in QM, the various "interpretations" are just re-interpretations of the maths to make us feel better aout somehting that is a bit strange (to put it lightly).

Sean

By Andrew Hodges on Sunday, July 15, 2001 - 08:53 pm:

An objective reality is one which exists even when it is not being perceived. It is independent of consciousness. A subjective reality exists only when it is being perceived. This is what, as I understand it, the copenhagen interpretation holds to be true.

Mustn't any experiment be subjective? Say you are in a room with a table in the middle, with a friend standing beside you. Do you perceive the same table? Yes and No - you perceive certain qualities to be the same, you both see that it has a particular shape, and if you were both to measure it or weigh it, you would both get the same result, but it doesn't look the same, the colour will look different from your viewpoint to your friends, as the light reflects off it differently. Now if you have two independent pieces of equipment recording an experiment, they cannot be in exactly the same place at the same time; they will both observe the experiment differently, subjectively. For instance if they are recording sound from a source several metres away, the sound will, most likely reach the two sources at slightly different times, as they are in slightly different positions. Science explains this difference in terms of the extra distance that the sound waves have to move to reach one recorder as opposed to the other. I believe that science attempts to remove the subjectivity of experiences, and place them in an objective, and experimentally verifiable framework.

By Andrew Hodges on Sunday, July 15, 2001 - 08:56 pm:

Sean, i dont quite understand what you mean when you say there are infinitely many curves which fit through all the data points. Have an infinte number of experiments been carried out? If not, isnt it just an induced result? Im probably misunderstanding your argument.

Andrew

By Michael Doré on Sunday, July 15, 2001 - 09:05 pm:

Andrew; to take a simple example, let's suppose the empirical result F = kx (Hooke's law) has been tested a million times by experimentalists, and every time the relationship was tested it was found to be true. Does that mean that F = kx is the only way of describing the given results? No, of course not. There is also (for example) a one million degree polynomial that passes through all the data points, and there are countless other curves that agree entirely with experiment. However:

1) The one million degree polynomial passing through the data points is much, much more complicated that F = kx.

2) If you do the experiment again, the million degree polynomial will probably fail.

The one million degree polynomial is a relationship proposed with hindsight, whereas F = kx is a prediction, because after about 100 trials the experimentalists would be convinced that F = kx is correct, but no-one in their right mind would think of the one million degree polynomial, since it is totally arbitrary. (Why one million degree? Why are all the coefficients the way they are, when countless other equally complicated polynomials would also fit the first 100 data points?)

By Sean Hartnoll on Sunday, July 15, 2001 - 11:05 pm:

Michael has answered the second question nicely. Regarding subjectivity:

As you say an important assumption science makes is that you can abstract some objective things from experiments that are slightly different (subjective) for each observer.

What I was saying is that quntum mechanics is no more subjective than normal classical mechanics. I.e. once I make a measurement, all other observers will agree. So for example all obervers will agree which slit the electron went through if it is observed as it goes through the slit and also where it landed on the photogrpahic plate if we don't observe it as it goes through the slit.

You are right that the status of observations is different in QM, observations interfer with the world and cause the "collapse of the wavefunction" in the copenhaguen interpretation, but all experimental data comes from once the wavefunction is collapsed, and all observers will agree on what it has collapsed to (so the state of the world is objective).

Sean

By Brad Rodgers on Sunday, July 15, 2001 - 11:40 pm:

On the note of science being subjective, here's a passage by Bertrand Russell from An Inquiry Into Meaning and Truth:

"We all start from 'naive realism,' i.e., the doctrine that things are what they seem. We think that grass is green, that stones are hard, and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones, and the coldness of snow are not the greenness, hardness, and coldness that we know in our own experience, but something very different. The observer, when he seems to himself to be observing a stone, is really, if physics is to be believed, observing that effects of the stone upon himself. Thus science seems to be at war with itself: when it most means to be objective, it finds itself plunged into subjectivity against its will. Naive realism leads to physics, and physics, if true, shows that naive realism is false. Therefore, naive realism if true, is false; therefore is is false."

I'll let you ponder over the consequences of this before posting my own resolution, but the philosopher Hume came up with a resolution to this paradox years before it was even presented! He thought that certain principles of naive realism were engraved in our brains before we were born; principles such as cause and effect, mathematics and perhaps even something like gravity, essentially things considered a priori and neccessarily true. (this next part I don't think is due to Hume, I think it's due to Berkley [see the dialogues between Hylas and Philonius for more]®) As these things were engraved in our brains, the world would be unimaginable without them, and we adapt our perception to suit them. So in that sense, certain aspects of physics are neccessarily true and will stay that way. I don't really agree with this, and as I said, I will post my own resultion in a little while. In the mean time, think of your own resultion...

Hopefully that has been a little enlightening, if not far too long,

Brad

By Sean Hartnoll on Monday, July 16, 2001 - 02:38 pm:

Firstly, Brad I think the argument you attribute to Hume is actually Kant's (the so called transcendental approach whereby cause and effect and space and time etc. are categories within which we are forced to see the external world, the merit of this approach was that it presented a way of unifying what had earlier been contradictory ways of looking at the world: the empiricists (including Hume) had difficulty moving from the experimental data to the ideas of causality, for example, and the rationalists (e.g. Descartes) who had difficulty moving from ideas to the real world. The transcendental approach is quite powerful, and I think it is true that certain aspects of the way we see the world are not something we can escape easily).

Secondly, I don't agree with Russell's argument.
The ingredient missing in my opinion is the idea that physics takes the effects of the world on us (subjective if you like) and produces a model that explains and predicts these subjective effects, and therefore confers to them a certain objectivity. If there was no underlying exterior reality, there would be no reason why simple models would ever work. So the very fact that physics works is an argument for realism.

Another idea that may be useful is that people's sensory biology is more or less the same, so I am able to predict not only what I will experience, but also what someone else will.

Sean

By Arun Iyer on Monday, July 16, 2001 - 07:11 pm:

Well everyone out there,
there are somethings which keep physics to a boundary.

Let me explain it a bit.
We still are finding it hard to develop an android who can cry,laugh when told a joke,has a happy face or any kind of emotions.

We are the most beautiful creation in this world.Yet we are forced to see the world it is today because we are unable to create an artificial human(I hope you see why?)

I am saying this all just to change one little last line in sean's message 2nd para.
Sean,
realism is an argument for the fact that physics works and it is not the vice versa.

love arun

By Andrew Hodges on Monday, July 16, 2001 - 07:55 pm:

Does everybody perceive the world in the same way?
How do we know that one persons perception of the colour green is not the same as another persons perception of the colour red? We learn colours because we are shown and exposed to them from childhood - "look at the red balloon and the red car", parents would say - but what is to say that the child sees the car as his parent does? All that we can infer is that something of a particular colour can be distinguished from something else of a particular colour - most people would agree that two 'red' objects have the same colour, even if in the eyes of the different people the colour red looks different. Can you see what I am getting at? I would be interested to hear arguments on this.

On the subject of physical laws, is there such a thing as a physical law? I think it was David Hume, who observed that when a boat moves threw water, a wake is created. People believe that the movement of the boat causes the wake, but Hume took a sceptical approach and asked if it really did! If you let go of a ball it falls to earth. We say gravity CAUSES it to fall to earth, but is that the case? Are we not making an assumption here? Isnt the concept of gravity a mathematical abstraction in itself, designed to explain why balls fall to earth anyway? What in fact is gravity - we know Newton and Einsteins Law to be incorrect!So here is my big question: Can any physical law be a TRUE law of nature, or is every law simply an approximate and greatly simplified model of nature - will we ever be able to describe nature in terms of what it intrinsically is , or will we only ever be able to make mathematical approximations?

By Arun Iyer on Monday, July 16, 2001 - 08:29 pm:

to your first question andrew,
i would say yes.

the names red,blue are given by humans for our conveniences to identify something (colours in this case).They are not printed on them (colours).

this is what is taught to us.so you would say a colour is red only if you are taught such and such colour is called red.

i think the point you are coming at is the different shades of colour.YES,they are quite different as different as our opinions are.Nothing is wrong or is right unless there are certain rules which would help us in deciding.

love arun

By Arun Iyer on Monday, July 16, 2001 - 08:35 pm:

andrew,
on the second para,

i would say that we could only make mathematical approximations.

I already said that you have to be a creator to know what is happening(in my last message)
or
you should have the vision to see what is hapening around us.(in my previous message)

we don't have either.

i hope you understand.
love arun

By Brad Rodgers on Tuesday, July 17, 2001 - 05:29 am:

Sean, your argument against Russell is very good, and something that I had not thought about. My argument is that in any theory in which results disagree from a previous theory, you do not use results from a previous theory to formulate the new theory. This seems like a simple statement, but it is very important. This is why special relativity needs a "new" axiomatic formulation when we are generalizing it to include non-inertial frames.

On a similar note, here's another 'paradox' by Russell (or at least told by Russell). Suppose that we look at a table. Now, when we look at it, we see that it is brown, that it is 4 feet by 6 feet, and that it is smooth. But then we pull out a microscope, and observe the table under it. We see that instead of being smooth, it is covered with billions of tiny riples made of wood, and upon observing it even closer, we find that those riples are not in fact made of 'wood', but rather molecules and atoms. Now, here's the paradox: if what we see with our own eyes at first is not in fact reality, why should we trust what is observed through a microscope that we still see with our own eyes to be any more accurate?

This time I'll post the resolution, or at least my personal resolution. When we see that table at first, we are indeed seeing reality, but of course only a fraction (say 1/2) of it. The next time we look a bit closer, we see a bit more. As we look closer, we still are not seeing reality in its full, but we are coming closer and closer to it. The first time we see 1/2; the next time 3/4; and the next 7/8. Of course, in reality, this neat and nice pattern would not be followed, we might one minute not be able to see a thing, then a little be closer be able to see all of reality. Anyways, the point is that we probably won't be able to find a final theory, as reality is literally changing as we delve deeper into it, and even if we can find a final ultimate theory that makes all the right predictions, we'll never know that it is a final theory.

Brad