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[Neruz]

What I am trying to get at with the divide by zero is that the universe divides by zero occasionally.

This comment leads me to believe you do not understand what mathematics is.

[dreiche2]

What I am trying to get at with the divide by zero is that the universe divides by zero occasionally.  If we wish to do proper physics, we need a system that allows us to calculate the effects of such cases.

Your mum divides by zero.

So far, handling zero as if it is actually an unknown infinitesimal value has never failed me.  And the multiplicative inverse of such a zero would be a specific but unknown infinite value.  So 1/0 = 1*inf and inf/0 = inf^2 and 5/inf = 5*0.  I would like to know what you think of such a system.

But 5*0 is 0? Period? Unless you break normal multiplication as well in your system.

Before I go on, quick question: I assume +inf and -inf are distinctive in your system?

[Innominate]

The universe never divides by zero for the simple reason that numbers don't actually exist. Numbers are things we use to analyse and explain reality, they are not themselves real.

What is real to the universe? Fields (in the physics sense, not the mathematics one), space and time. Pretty much everything, particle or otherwise is reducible to these three components. Numbers don't factor into it.

[DreamThorn]

What I mean with 'the universe divides by zero' is that a physical thing with a zero-like value is sometimes found in an inverse multiplicative relation to some other physical value.

Some examples.  If your distance from a charge is zero, you have to divide by zero to calculate the potential.  AFAIK at a black hole's event horizon the curvature (or slope?) of space-time is infinite, inverting the roles of time and space.  The rest mass of a photon is zero, but this is multiplied by an infinite mass factor and results in a real number for the perceived mass.

And I propose that one cannot say that 5*0=0, because this causes a loss of information.  If you were to divide 5*0 by 0 you need to get 5 again.

One of the values of -inf would be -1/0.  There would also be -563/0 or -inf/0.  Because of this multiplicity in values you could say the only inf is 1/0 and then express all the others as multiples of this one.  The only true 0 would be 1*0, but you would still have such things as -23*0 or 0^5.

0^0 would then be 1, because 1 is the multiplicative identity.

There could even be absurdly complex zeroes like 23*0^4 + 44*0^2, distinguishable from other zeroes by the results of calculations.

What I need to prove is that there are no cases where exactly the same function with the same inputs would give different answers.

In an old attempt of mine to calculate pi, I discovered that tan(90 deg) * 0 = pi.  This would mean that tan(90 deg) = pi/0.  If I can find another calculation that shows tan(90 deg) to have a different value, I think we will have disproven my hypothesis.

[Neruz]

The rest mass of a photon is zero, but this is multiplied by an infinite mass factor and results in a real number for the perceived mass.

It's really not that simple. Photons do not have mass, but they do have energy (which, by the way, is theoretically impossible.) The reason for this is because Photons cannot be brought to rest, which breaks a number of proven theories unless you give them a rest mass of 0, at which point everything works again.



I'm not sure how to respond to your post DreamThorn, it seems like you're talking complete nonsense to me. And not just regular internets nonsense, we're talking first grade 'wat' nonsense here.

[dreiche2]

What I mean with 'the universe divides by zero' is that a physical thing with a zero-like value is sometimes found in an inverse multiplicative relation to some other physical value.

Some examples.  If your distance from a charge is zero, you have to divide by zero to calculate the potential.  AFAIK at a black hole's event horizon the curvature (or slope?) of space-time is infinite, inverting the roles of time and space.  The rest mass of a photon is zero, but this is multiplied by an infinite mass factor and results in a real number for the perceived mass.

Can you ever be at zero distance to a charge? And the photon calculation just does not happen that way. Thinking about resting photons does not make sense. And in general, thinking about accelerating to and reaching light speed is like asking what happens to a 1m long stick if I shorten it by 2m. Do I get a stick with negative length?

So +inf and -inf are distinctive, right? Then, tell me: What is in your system the value of

sin(1/x) * 1/x

for x = 0?

And I propose that one cannot say that 5*0=0, because this causes a loss of information.  If you were to divide 5*0 by 0 you need to get 5 again.

One cannot say 5*0 = 0... well.

0^0 would then be 1, because 1 is the multiplicative identity.

What has that to do with 1 being the multiplicative identity?

Here, I've got an alternative suggestion for a system:

1/0 = 'spaghetti'
inf/0 = 'tomato'
5/inf = 'meatballs'

Is that system better or worse than yours? Why?

See, I can even compute the mass of a photon: Take a rest mass of 0 and multiply it with just the right version of tomato, and you just get the right value as a result!

ps: Sorry if I'm being sarcastic, don't mean to offend.

[Starver]

AFAIK at a black hole's event horizon the curvature (or slope?) of space-time is infinite, inverting the roles of time and space.  The rest mass of a photon is zero, but this is multiplied by an infinite mass factor and results in a real number for the perceived mass.

Slope as measured by what definition?  I would say that the slope = c (i.e. represents the escape velocity at that point, which something needs to go faster than to escape), and even within the EH, the slope is still finite (just more than 'c').

You'd be on firmer ground suggesting the centre of the black hole is a (mathematical) singularity.  As well as being considered a physical one (because of the mathematics).  But if space is bent so much that the 'depth' of the funnel is infinite then there is no actual point where the asymptotic slope reaches infinite itself and zero is divided (it just becomes a rather impossibly large/small value, depending on which side of the divide-sign you have your slope parameters).

The other zero/infinity/undefined point is in "what's north of the North Pole?"-type situations, but that's arguably a different issue.

[Sean Mirrsen]

Accelerating to and reaching lightspeed is not impossible, nor does it require infinite energy. Simply because we cannot see it happen due to some weird scientific rule, doesn't mean it won't. Even talking within relativity, if you just keep accelerating, you will go faster. Contracting length, extending time, and elusive light don't mean a thing. Within the brilliantly built system, they all cancel out. I don't know what the maths say about it, but accelerating so that you appear to travel at lightspeed to an outside observer may be impossible. But with everything relative, you and your ship will remain relative to yourselves. The planets and stars will move past you faster than light, so they will do everything to appear moving slower than light. Within space as it is, you are still moving faster than light would, and as soon as you decelerate you'll see that you have, indeed, been moving faster than light, as evident from your position. It's a simple bastardization of the principle, but it works. Star Trek warp drives contract and expand space, but it may be that space just warps itself relative to you.

Think about it - if thruster fuel gains mass as the ship speeds up, won't it mean its combustion will produce greater thrust? The ship's hull will increase in mass while keeping its volume, therefore it'll become denser and more resilient. Within logic, if sufficiently warped, it all works out.

[Starver]

Accelerating to and reaching lightspeed is not impossible, nor does it require infinite energy. [..]

I hate to cut and run on this (they're closing the office down early, in anticipation of something called "snow", so I can't spend too much time on this), but I don't think you and I are quite in agreement here.

As the theory has it, you can try to accelerate forever, and to you your own acceleration is continual, but you never catch up with any light that left you because whatever speed you think are going, it appears that light is still departing you at the speed of light.  Should you get to the speed where that light is (from a hypothetical objective observer's POV) retreating from you at snail's pace, your awareness is also progressing at a relative snail's pace so the light is still retreating.  Your self-observed constant acceleration is viewed as an asymptotically slowing acceleration towards but never reaching 'c' from the observer's POV.  (I'm assuming said observer has a stationary vantage point that can keep your everlasting attempt to reach 'c' in view.  And it does not really depend on whether the observer is located at your original starting position[1], somewhere along the track[2] or 'at the end of universe' waiting for your advance-guard photons and then yourself to come steaming past[3], the latter being at near-but-not-actually-'c' speed.)

Anyway, there's this 'snow' stuff, and though I think they're being overcautious at the moment, I am being chucked out of here and I think I've procrastinated long enough.

[1] Which would involve the light from you and the photon[4] spending time to travel back along the race-course
[2] The visible heralding of the start would occur roughly the same time as the photon actually raced past you, and then you have much the same issue as footnote-1 for the rest of the event.
[3] And if there's nothing special about the universe, like a wrap-around geometry, you'd again then spend the rest of eternity watching a retreating (and increasingly delayed) image of the race.  But the point is that wherever you stand, you'll never find a point where you can stand to watch the space-ship overtake, catch-up or even (still astern of the photon) match speeds with its target.  Tantilising close to the latter, yes.  Increasingly close, but it's like a Zeno's Paradox but with the logical flaw made tangibly real.  You can only ever subdivide the remaining difference in speed and aim for a fraction of the way along it, in increasingly small steps that becoming vanishingly small for you but tick themselves off in non-infinitesimal timescales for the universe as a whole.

[4] For the sake of argument, I'm assuming they 'see' the light particle, even though they wouldn't ever see it except by its collision with their eye or some optical instrument, at which point it would no longer be racing across the universe.  And the least said about the chasing spaceship colliding with the observer's eye/instrumentation, at some point in time immediately thereafter, the better.

[dreiche2]

Within space as it is, you are still moving faster than light would, and as soon as you decelerate you'll see that you have, indeed, been moving faster than light, as evident from your position.

I have thought more about that as well (well I think I am thinking about the same thing). Here's the setup:

I'm stationary on earth and about to travel to a distant planet one light year away. I accelerate really fast and reach cruising speed of almost c. Now, everything around me well be moving at almost c as well. However, this is with respect to contracted length measurements. So, wouldn't that mean that what was a light year distance would now be much less? So essentially, I start at zero velocity relative to earth and 1 light year distance to the other planet, I accelerate, and then the distance will be much less than a light year. Which means that in my frame of reference, I would need less than a year to reach it. And then I will decelerate once I'm there.

So that looks like, if I look at my watch before I begin the journey and again after I arrived, less than one year should have passed (for myself at least!), while I traversed a distance of one light year. So haven't I effectively travelled faster than lightspeed?

And actually, you know what: I think that is true. If you take your own proper time, but distance as defined in an outside frame of reference, such as earth here, to calculate your "speed", then you get such a result. It's just that from the outside observer, more time has passed, so from their point of view you didn't travel faster as light (and btw, any apparent symmetry paradoxa about why there is a net time difference are again resolved by considering acceleration).

But I think you're right, if your concern with speed is how far you can travel within your, say, lifetime, then you can effectively travel faster than lightspeed. Am I wrong here?

Apart from that: You seemed surprised when someone called you arrogant, but to appear from nowhere claiming the theories that thousands of smart people have developed over a hundred years are all nonsense, while you will find a better solution as a pastime endeavour, is just not very modest...

I really have to stop discussing these things now and get some work done though...

EDIT: So essentially, travelling at highly relativistic speeds has a net effect like an age preserving cryochamber would, so to say...

[alway]

I don't know what the maths say about it,

I think I found your problem.
Relativity is a theory based on math, and as such it will not really make much sense until you understand the equations and the effects predicted by them. The two unalterable principles of relativity are really the speed of light and the omnipresence of causality. Breaking one will break the other, and neither can be broken. One can not break the speed of light without also inadvertantly creating a time machine.

But as dreiche says, you can travel faster than light according to the frame of reference in which you started's distance compared to your time. However, distance also warps for you causing it to appear as if you never go faster than light when comparing time onboard to distance onboard. This is consistent with the idea of no frame of reference being any more special than another. From the frame of reference of time and mass of an outside observer, mass increases to balance out the time dilation's effect on the energy of the craft. In essence, relativity is a series of counterbalancing asymptotic functions which when combined make for a stable, if unintuitive, theory of space-time.

[dreiche2]

In essence, relativity is a series of counterbalancing asymptotic functions which when combined make for a stable, if unintuitive, theory of space-time.

Actually, just to clarify, because I want to counter the idea that these different effects need to be hacked together to fix the various problems: They are all just different aspects of one underlying type of transformation.

I'll give a pretty relevant analogy: Rotations in normal, three dimensional Euclidean space.

So let's forget about relativity for a second. Assume there is a vector pointing from the origin of your coordinate system to the point (1, 1, 1). If you were to rotate the vector 30 degrees around the z axis, and then afterwards 50 degrees around the x axis, what will the new coordinates be? Or equivalently, when you rotate not the vector but your own coordinate system, your frame of reference, in the corresponding opposite direction?

Well, I have no idea, I would have to calculate the resulting coordinates using rotation matrices. Now, here is a property of rotation matrices: They leave the length of the vector unchanged, like they intuitively should. But what if you didn't know about rotations? What if someone came to you and said, well here are the coordinate transformations you should use, without telling you about rotations? By playing around with them you would find that, as by magic, the change in the three component lengths of your original vector are always such that the total length remains unchanged. Isn't that a big coincidence?

Well, no, because the argument goes the other way around. You know from the start that rotations should leave the length of vectors unchanged, and together with some other properties (for any rotation, there should always an inverse rotation), you can derive the class of matrices you can use for rotations. It is exactly those matrices that leave the length of any vector unchanged.

Now, back to relativity: Here, the world is described not in three dimensional space, but in a peculiar 4 dimensional space that includes time as a fourth dimension. To change in between frames of references, you need to do coordinate transforms, which actually correspond to rotations in this special space. The transformation matrices are the Lorentz transformations. Much as rotation matrices in Euclidean space leave the length of the vector unchanged, i.e. invariant, these Lorentz transformations leave certain other properties invariant (namely the equivalent property to length, which has a physical interpretation).

So the Lorentz transformations describe how to do coordinate changes in this 4D space, warping time and space in the process. Length contraction and time dilation are just special cases of the general transformation, much as you can think of special cases of Euclidean rotations. But you don't have to come up with time dilation, length contraction etc. separately to fix your theory in a patchwork like fashion. You start with a general type of transformation, and these different effects just fall out of it.

And again, much as you could derive the properties of rotation matrices from some underlying principles, you can do the same for Lorentz transformations. If I remember correctly, it goes like this: If the speed of light is constant in any frame of reference; If all frames of reference are equivalent; and if the allowed transformation should be linear (i.e. describable with simple matrix multiplications); then you can derive exactly how the corresponding matrices should look like, and these matrices that fulfil the criteria are exactly the Lorentz transformations. You will then find such weird effects on time and space. But the starting point are these assumptions. See wikipedia.

Basically, if you can accept that time and space are interwoven, then the Lorentz transformation are pretty much the simplest thing you can come up with while staying consistent with your assumptions. If you can accept these assumptions and are ready to face unintuitive consequences, the resulting theory comes about without hacking.

[bjlong]

I wouldn't say that this is FTL travel, in any sense of the word. Rather, this is STL travel with a classical velocity that's much greater than the speed of light. This is entirely possible, but you need to remember the implications of this in the long-term. Ships that do this are effectively lost to the rest of the universe, as in the twin paradox, so that first colony ship? Won't be seeing those people ever again.

Sean, your theory sounds exactly like the ether theory. Down to its objections with experimental results. The only different thing is this idea of energy that can only be tapped into by light.

[Sean Mirrsen]

This ain't no luminoferous(sp?) aether. It encompasses everything, not just light. It also emanates from pretty much everything. It's not aether, it's energy. On a different level, it's probably also inspired by "nature tolerates no void", applied to the very bottom of the universe's structure. Energy fills the void between elementary particles.

[Neruz]

Deciding that there should be no 'voids' is a pretty major leap of faith, do you have any actual evidence to back up what is, quite frankly, a somewhat rediculous idea?