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llanitedave
Humble Megalomaniac

Reged: 09/26/05

Loc: Amargosa Valley, NV, USA
Re: Scary relativity [Re: petrus45]
#6225954 - 11/30/13 09:13 PM

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It's very possible to be infinite but bounded. Think of a ray or plane that begins on a point in space. There is a definite boundary beyond which that shape cannot extend in a particular direction. However, it is infinite in the other direction.

Fractals is another good example. They have strict mathematical boundaries. Yet those boundaries can scale to infinity.

But you seem to be saying the defined part of the geometry is *not* infinite. Rather, "it is infinite in the other direction." This is consistent with my point, which is that defined geometric points, lines and shapes are finite, to the extent they are defined. To the extent a ray, a plane, or a spiral fractal pattern are "infinite" they have no geometry which defines the *end boundary* of the shape - only the beginning or the middle. To the extent there is no end boundary, there is no geometry.

That's one way of looking at it. Note, though, that for any geometric shape, whether plane, ray, line, or fractal such as the Mandelbrot set, there is no point within the geometric coordinate system that is undefined. Every point is explicitly defined to be either within the set or outside of it.

Another cool thing about the Mandelbrot set is that even though it has an infinite perimeter, it has a finite area. So it's both bounded and infinite.

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petrus45
sage

Reged: 01/31/11

Loc: SW Ohio / N Ky.
Re: Scary relativity [Re: llanitedave]
#6236000 - 12/05/13 06:52 PM

Quote:

Another cool thing about the Mandelbrot set is that even though it has an infinite perimeter, it has a finite area. So it's both bounded and infinite.

I am not a mathametician, but my understanding is a mandelbrot set can have a finite upper limit on area, but no finite lower limit. Thus, effectively, it does not have a defined geometric boundary as to how small the pattern can get. To the extent it has a defined upper limit on area, it is not infinite since there is a boundary. Thus it would not be an exception to the propositon that infinity does not have a geometry.

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PeterR280
Pooh-Bah

Reged: 05/27/13

Re: Scary relativity [Re: petrus45]
#6236037 - 12/05/13 07:17 PM

The lack of lower limit of area is what plagues General Relativity.

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petrus45
sage

Reged: 01/31/11

Loc: SW Ohio / N Ky.
Re: Scary relativity [Re: PeterR280]
#6236405 - 12/05/13 11:20 PM

Quote:

The lack of lower limit of area is what plagues General Relativity.

I was reading back through some of the prior entries, namely the following:
- The thought experiment with the speedy moon eclipsing the sun, despite the Lorenz contraction.
- The idea that the concept of infinity is something "strange" in Euclidian geometry.

What I am able to crib together from all of this is the following:
- All of our empirical knowledge about the universe is limited by Euclidian geometry, i.e. the shapes and measurements we can see, hear, touch, etc.
- Euclidian geometry has mainly to do with finite boundaries.
- "Infinity" is a misnomer; for it simply means non-finite. It is a self-definition in the negative, but which actually has no free standing quality. As soon as we reach into "infinity" and measure a piece of it, it enters the realm of "known" and therefore ceases to be "infinite." Infinity is simply the unknown.
- Somewhere beyond where Euclidian geometry reaches its boundary, relativity allows us to "know" certain realities of the universe by mathematical deduction - realities that perhaps would otherwise be termed "infinite" or "unknowable" - realities we will never observe empirically (as in the moon experiment, in which we cannot actually "see" the curvature of spacetime around the moon though it may be there right before us), because the limits of what we can empirically observe is bound by our ability to perceive light, and spacetime is "self correcting" relative to our perception.

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PeterR280
Pooh-Bah

Reged: 05/27/13

Re: Scary relativity [Re: petrus45]
#6237088 - 12/06/13 10:58 AM

Th mathematical models allow you to do "thought" experiments that you could never do in real life. It was called "Gedunken" experiments in Einstein's time to test the theory. You can come up with paradoxical situations which may indicate a problem with the theory and then solve the appearant paradox with the mathematical model to show that it is valid.

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GregLee1
professor emeritus

Reged: 07/21/13

Loc: Waimanalo, HI
Re: Scary relativity [Re: petrus45]
#6237310 - 12/06/13 12:47 PM

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"Infinity" is a misnomer; for it simply means non-finite. It is a self-definition in the negative, but which actually has no free standing quality.

There have been plenty who agree with you:

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Finitism is a philosophy of mathematics which accepts the existence only of finite mathematical objects. The finitist philosophy of mathematics is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects like infinite sets are accepted as legitimate mathematical objects existing in some Platonic universe of mathematics.

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Rick Woods
Postmaster

Reged: 01/27/05

Loc: Inner Solar System
Re: Scary relativity [Re: GregLee1]
#6248192 - 12/12/13 12:36 AM

Did we ever resolve the headlight thing?

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brentwood
Carpal Tunnel

Reged: 11/04/05

Re: Scary relativity [Re: Rick Woods]
#6248433 - 12/12/13 07:48 AM

Not yet! Choran did go on a physics forum and they did confirm what I had been saying and did report as such on here. There was no comment IIRC from our resident 'Brain Trust'!
It appears that when those of us that do not fully understand this stuff ask questions on Relativity, those that do understand think we are challenging it.
Nothing could be farther from the truth. I fully accept that c is always c. The headlight thing is just an anomaly.
If you can measure the speed of a car, in the same reference frame as you, at .9c, and the car puts on its headlights you will measure the speed of the light coming from the headlights as c. As seen by an observer, again in the same reference point as you, but a distance away and the car moving across your view, not away or towards you, it will APPEAR that the light is leaving the car at .10c!
The light is moving across your point of view say from left to right at c, while the car is following behind at .9c.
We were told that this was wrong, but we would eventually understand why it was wrong. Still waiting!

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GregLee1
professor emeritus

Reged: 07/21/13

Loc: Waimanalo, HI
Re: Scary relativity [Re: brentwood]
#6248495 - 12/12/13 08:38 AM

Quote:

If you can measure the speed of a car, in the same reference frame as you, at .9c, and the car puts on its headlights you will measure the speed of the light coming from the headlights as c. As seen by an observer, again in the same reference point as you, but a distance away and the car moving across your view, not away or towards you, it will APPEAR that the light is leaving the car at .10c!
The light is moving across your point of view say from left to right at c, while the car is following behind at .9c.

The conditions are impossible simply because you can only observe light that reaches you. Not light that "is moving across your point of view". You're thinking of yourself as an omniscient observer who can somehow sense the true positions of things in a way that is independent of physical processes. But there are no such relativistic observers.

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brentwood
Carpal Tunnel

Reged: 11/04/05

Re: Scary relativity [Re: GregLee1]
#6248606 - 12/12/13 09:34 AM

A series of sensors along the path of the light that put a flag up when hit by the light. We could see the flags going up one by one and be able to calculate the speed of light from that.
Light activated garden gnomes that do cartwheels when hit by the beam.
And of course I have to add that the sensors & the gnomes are in the same reference frame as ourselves!

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GregLee1
professor emeritus

Reged: 07/21/13

Loc: Waimanalo, HI
Re: Scary relativity [Re: brentwood]
#6248632 - 12/12/13 09:46 AM

Quote:

We could see the flags going up one by one ...

What do you mean "see"?

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GregLee1
professor emeritus

Reged: 07/21/13

Loc: Waimanalo, HI
Re: Scary relativity [Re: Otto Piechowski]
#6248719 - 12/12/13 10:33 AM

Quote:

Infinity refers to a quantity to which if an additional amount were added, the size of the original quantity would not be changed. So, if an infinite length is being considered, that infinite length plus another foot would still be equivalent in size to the original infinite length without the additional foot.

If you add a finite length at the beginning of an infinite ray, I suppose the length of the ray would not be changed, but if you added it at the other end, I think the length would be changed. And if the amount you add is infinite, also, the size may be changed, as when you add the real numbers to the rational numbers, obtaining the reals, since there are more reals than rationals.

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PeterR280
Pooh-Bah

Reged: 05/27/13

Re: Scary relativity [Re: GregLee1]
#6248768 - 12/12/13 10:55 AM

Cantor tried to categorize infinities into sets and came up witha hierarchy of infinities. For example, he showed that there are more irrational numbers than there are whole numbers. For example, if you count all the possible rational and irrational numbers between zero and one, there are more numbers than the entire set of whole number.

If you match 1 with .1 and 2 with .11 and 3 with .111, etc.. You can assign a decimal fraction of just 1s with all the whole numbers and still have many more infinities of decimal fractions between 0 and 1. There is some controversy over his number theories of infinities

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brentwood
Carpal Tunnel

Reged: 11/04/05

Re: Scary relativity [Re: GregLee1]
#6248978 - 12/12/13 12:37 PM

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We could see the flags going up one by one ...

What do you mean "see"?

Well you know how when you 'see' your next door neighbour putting up his flag, well its like that except you are farther away!

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GregLee1
professor emeritus

Reged: 07/21/13

Loc: Waimanalo, HI
Re: Scary relativity [Re: brentwood]
#6249160 - 12/12/13 02:12 PM

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Well you know how when you 'see' your next door neighbour putting up his flag, well its like that except you are farther away!

I don't need to be concerned with relativistic effects when I'm watching my neighbor. What I'm trying to get at is that, in my opinion, you're not playing by the relativity rules when you describe your experiment without giving a physical account of how you make your observations of these flags. I guess light would have to pass from a flag to your eye, and that would take some time to happen?

By the way, did you see the post earlier in the thread from Charlie B giving a reference to this account of superluminal motion? I think this answers the headlight question.

Edited by GregLee1 (12/12/13 02:34 PM)

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brentwood
Carpal Tunnel

Reged: 11/04/05

Re: Scary relativity [Re: GregLee1]
#6249240 - 12/12/13 02:33 PM

Yes I understand that it does take time for the light to reach us, and yes I did assume that this is happening quite some distance away, so far in fact that all the events are happening in the same direction, so there is no shifting of angles of view. I suppose you could have the ship fly through a gas that would change colour when hit by light. You would then 'see' the gas change when the light hit it, but then of course the speed of light is not quite c because it is no longer a vacuum.
So again you 'see' the car travelling at .9c, and you somehow 'see' the light it shines ahead as c, so it 'looks' as though the light is leaving the car at .10c.

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GregLee1
professor emeritus

Reged: 07/21/13

Loc: Waimanalo, HI
Re: Scary relativity [Re: Rick Woods]
#6249369 - 12/12/13 03:41 PM

Quote:

Did we ever resolve the headlight thing?

I thought that Charlie B resolved it with his reference to superluminal motion.

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brentwood
Carpal Tunnel

Reged: 11/04/05

Re: Scary relativity [Re: GregLee1]
#6249489 - 12/12/13 04:56 PM

Quote:

Quote:

Did we ever resolve the headlight thing?

I thought that Charlie B resolved it with his reference to superluminal motion.

No just the opposite. Superluminal motion seems to show light from quasars travelling at >c, where as 'Brentwood's Paradox' seems to show <c.

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Charlie B
scholastic sledgehammer

Reged: 03/22/08

Loc: Sterling, Virginia
Re: Scary relativity [Re: brentwood]
#6249560 - 12/12/13 05:28 PM

Quote:

No just the opposite. Superluminal motion seems to show light from quasars travelling at >c, where as 'Brentwood's Paradox' seems to show <c.

Not what it said. The jet is moving close to c, the light from the jet is moving at c. The apparent motion of the jet is superluminal at the correct angles.

Regards,

Charlie B

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brentwood
Carpal Tunnel

Reged: 11/04/05

Re: Scary relativity [Re: Charlie B]
#6249962 - 12/12/13 09:47 PM

Ok, I'll rephrase it. (phew!) Superluminal motion has to do with STL , Brentwood's Paradox talks very roughly about APPARENT Slower than light.

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