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Search: Posts Made By: Vorpal
Forum: Science, Mathematics, Medicine, and Technology 2nd August 2014, 04:13 PM
Replies: 2,104
Views: 221,008
Posted By Vorpal
Are you perhaps thinking of Cooperstock and Tieu...

Are you perhaps thinking of Cooperstock and Tieu [arXiv:astro-ph/0507619 (http://arxiv.org/abs/astro-ph/0507619)]?
Forum: Science, Mathematics, Medicine, and Technology 27th July 2014, 04:01 PM
Replies: 13
Views: 1,261
Posted By Vorpal
Having definitions of "point" and "line" at all...

Having definitions of "point" and "line" at all is a quaint relic of bygone age. The Euclidean definitions of "point" and "line" aren't really used in modern axiomatizations of geometry, e.g.,...
Forum: Science, Mathematics, Medicine, and Technology 12th July 2014, 07:42 AM
Replies: 84
Views: 4,339
Posted By Vorpal
If you try to "work out what x is", what you'll...

If you try to "work out what x is", what you'll get is x can be anything except 0:
x⁻¹ = 1/x
x·x⁻¹ = x·(1/x)
1 = 1
A slightly more pedantic definition might be:
For any x, x⁻¹ is the element...
Forum: Science, Mathematics, Medicine, and Technology 24th June 2014, 03:15 AM
Replies: 8
Views: 1,069
Posted By Vorpal
Bell's theorem says that a quantum theory can't...

Bell's theorem says that a quantum theory can't have locality, counterfactual-definiteness, and realism all at once. Denying CFD doesn't automatically bring about locality.

MWI says that there's a...
Forum: Science, Mathematics, Medicine, and Technology 23rd June 2014, 08:32 AM
Replies: 8
Views: 1,069
Posted By Vorpal
In classical mechanics, trying to make a...

In classical mechanics, trying to make a superposition of eigenstates gets you something indistinguishable from a mixed state, which you can then interpret as your lack of knowledge about the...
Forum: Science, Mathematics, Medicine, and Technology 27th April 2014, 05:38 PM
Replies: 1,631
Views: 91,465
Posted By Vorpal
You're speaking as if it's not already explained....

You're speaking as if it's not already explained. :confused:

In relativity, a massless particle has to have E/p equal to its speed, which is the characteristic speed of spacetime (commonly labeled...
Forum: Science, Mathematics, Medicine, and Technology 27th April 2014, 05:10 PM
Replies: 1,631
Views: 91,465
Posted By Vorpal
Photons are massless, so relativity requires that...

Photons are massless, so relativity requires that they travel at whatever the characteristic speed is.

If photons were not massless, that would change things quite a bit, but the experimental...
Forum: Science, Mathematics, Medicine, and Technology 27th April 2014, 04:53 PM
Replies: 1,631
Views: 91,465
Posted By Vorpal
It changes nothing physical. It's just a change...

It changes nothing physical. It's just a change of label.

The key feature of special relativity is that is that spacetime has a characteristic speed, a maximum causal speed in an inertial frame,...
Forum: Science, Mathematics, Medicine, and Technology 27th April 2014, 03:06 PM
Replies: 2,104
Views: 221,008
Posted By Vorpal
Just another way Maxwell's equations become...

Just another way Maxwell's equations become prettier with magnetic monopoles than without...

One can do a bit better if one treats the relationship between the EM tensor and its dual as a...
Forum: Science, Mathematics, Medicine, and Technology 26th April 2014, 11:09 AM
Replies: 2,104
Views: 221,008
Posted By Vorpal
The equation W.D.Clinger refers to is (6.108) in...

The equation W.D.Clinger refers to is (6.108) in both the 1975 second edition and the 1999 third edition. In the first edition you've linked (which I've never seen until today), it is (6.82) instead....
Forum: Science, Mathematics, Medicine, and Technology 25th April 2014, 03:59 AM
Replies: 2,104
Views: 221,008
Posted By Vorpal
A somewhat more faithful transcription of...

A somewhat more faithful transcription of Heaviside's paper follows (Ụ should have dot above):

Finally, the appearance of V is to indicate that vector product that follows it is the vector (i.e.,...
Forum: Science, Mathematics, Medicine, and Technology 12th April 2014, 06:49 PM
Replies: 1,631
Views: 91,465
Posted By Vorpal
It's nonsense. The kindest interpretation is that...

It's nonsense. The kindest interpretation is that Gonuguntla is trying to describe the stress vector and just calls it pressure for some reason, so at best this is a confusion of ideas that are...
Forum: Science, Mathematics, Medicine, and Technology 25th March 2014, 07:38 AM
Replies: 2,104
Views: 221,008
Posted By Vorpal
The "right-hand rule" is just an artifact of...

The "right-hand rule" is just an artifact of using pseudovectors in place of bivectors (http://en.wikipedia.org/wiki/Bivector). In three dimensions, standard Hodge duality maps bivectors to vectors...
Forum: Science, Mathematics, Medicine, and Technology 22nd March 2014, 05:16 AM
Replies: 2,104
Views: 221,008
Posted By Vorpal
This is not only of dubious relevance, but...

This is not only of dubious relevance, but manages to the the direct opposite of the facts.

Benko gave up his spot for Fischer because Fischer refused to participate in the 1969 US Championship...
Forum: Science, Mathematics, Medicine, and Technology 2nd March 2014, 11:22 PM
Replies: 45
Views: 3,630
Posted By Vorpal
As long as you don't try to do the same to "no...

As long as you don't try to do the same to "no one", and many do on the interwebs, you will have my support. Some lines should never be crossed.
Forum: Science, Mathematics, Medicine, and Technology 1st March 2014, 01:16 PM
Replies: 2,104
Views: 221,008
Posted By Vorpal
Huh? Vorpal, it's the crux of it. If there's no...

Huh? Vorpal, it's the crux of it. If there's no Riemann curvature you haven't got a gravitational field. Things don't fall down.[/quote]
-- A nonzero tidal tensor implies that there is nonzero...
Forum: Science, Mathematics, Medicine, and Technology 28th February 2014, 02:16 PM
Replies: 2,104
Views: 221,008
Posted By Vorpal
The essence of the Newtonian intuition... ...

The essence of the Newtonian intuition...

carries over into GTR: if you have two geodesics with four-velocity u and a nearby geodesic connected with n connecting points of equal affine...
Forum: Science, Mathematics, Medicine, and Technology 16th February 2014, 03:56 PM
Replies: 159
Views: 9,569
Posted By Vorpal
For an idealized Earth-Sun system, it would be...

For an idealized Earth-Sun system, it would be inside the Sun. But the actual solar system is a bit different, mostly as a fault of Jupiter:...
Forum: Science, Mathematics, Medicine, and Technology 16th February 2014, 03:13 PM
Replies: 159
Views: 9,569
Posted By Vorpal
I'm not sure what "they" refers to here. I'm also...

I'm not sure what "they" refers to here. I'm also not sure where you're going with this, but I think I can guess.

Let's consider just the Earth and the Sun for simplicity. Perhaps you're thinking...
Forum: Science, Mathematics, Medicine, and Technology 15th February 2014, 11:11 PM
Replies: 159
Views: 9,569
Posted By Vorpal
I've never said that gravity moves...

I've never said that gravity moves instantly--actually, I've explicitly said it does not.


I've never said that they didn't decay. I've merely said that they don't decay fast enough to crash into...
Forum: Science, Mathematics, Medicine, and Technology 15th February 2014, 12:19 PM
Replies: 159
Views: 9,569
Posted By Vorpal
At c. I've already explained, with references,...

At c. I've already explained, with references, why that does not mean that orbiting bodies accelerate towards the retarded positions.


They're stable enough to not spiral into the Sun within a...
Forum: Science, Mathematics, Medicine, and Technology 15th February 2014, 11:25 AM
Replies: 159
Views: 9,569
Posted By Vorpal
Nonsense. The only claim I've made about the...

Nonsense. The only claim I've made about the stability of orbits here is that they're stable enough for the Earth not to spiral into the Sun on the timescale of a handful of centuries. This is very...
Forum: Science, Mathematics, Medicine, and Technology 15th February 2014, 05:26 AM
Replies: 159
Views: 9,569
Posted By Vorpal
Because the total effect is brought about by a...

Because the total effect is brought about by a near-cancellation of terms that are individually time-delayed.

Let's take the EM case again. The electric field of a charge moving with uniform...
Forum: Science, Mathematics, Medicine, and Technology 15th February 2014, 01:46 AM
Replies: 159
Views: 9,569
Posted By Vorpal
For the motivating analogy of electromagnetic...

For the motivating analogy of electromagnetic field of a uniformly moving charge, see just about any EM textbook that discusses the Lorentz transformation. The electric field is directed toward its...
Forum: Science, Mathematics, Medicine, and Technology 14th February 2014, 10:51 PM
Replies: 159
Views: 9,569
Posted By Vorpal
It doesn't happen. If it did, orbits would be not...

It doesn't happen. If it did, orbits would be not nearly as stable as they are.

There's a similar issue in ordinary electromagnetism--for example, a charge with constant velocity has a electric...
Forum: Science, Mathematics, Medicine, and Technology 14th February 2014, 09:02 PM
Replies: 159
Views: 9,569
Posted By Vorpal
That doesn't happen. Putting in an eight-minute...

That doesn't happen. Putting in an eight-minute delay puts a force component on Earth that makes it orbit unstable on the order of a few centuries. This is very tough to reconcile with the historical...
Forum: Science, Mathematics, Medicine, and Technology 11th February 2014, 09:59 PM
Replies: 15
Views: 2,960
Posted By Vorpal
His conclusions would be wrong-headed even if...

His conclusions would be wrong-headed even if that claim were true, which can be argued separately*, but in fact it is false. While the claim does the describe the four most famous of black hole...
Forum: Science, Mathematics, Medicine, and Technology 28th January 2014, 12:25 PM
Replies: 18
Views: 885
Posted By Vorpal
It's more than a little ambiguous, come to think...

It's more than a little ambiguous, come to think of it, whether the "non-" in "non-absolutely convergent" modifies the "absolutely" or the "absolutely convergent." In other words, whether mijopaalmc...
Forum: Science, Mathematics, Medicine, and Technology 28th January 2014, 01:07 AM
Replies: 18
Views: 885
Posted By Vorpal
There's an ambiguity here. Does this mean you...

There's an ambiguity here. Does this mean you evaluate both series (by whichever method if not the conventional definition), then subtract? If the value is finite, then yes. Otherwise, undefined.
...
Forum: Science, Mathematics, Medicine, and Technology 26th January 2014, 03:46 AM
Replies: 68
Views: 3,529
Posted By Vorpal
If you ask yourself what justifies the quoted...

If you ask yourself what justifies the quoted step, you'd probably want a principle like "I can rearrange the order of the sequence I'm summing arbitrarily without affecting the sum."

It is true...
Forum: Science, Mathematics, Medicine, and Technology 26th January 2014, 03:04 AM
Replies: 68
Views: 3,529
Posted By Vorpal
That is pretty much correct, yes, but it's not an...

That is pretty much correct, yes, but it's not an essential difference. Because what's conventionally meant by the sum of a sequence, the value of a series, is also a function of a given sequence...
Forum: Science, Mathematics, Medicine, and Technology 22nd January 2014, 11:34 PM
Replies: 584
Views: 17,723
Posted By Vorpal
Yes, my post answers exactly that scenario. ...

Yes, my post answers exactly that scenario.

As for the formula, it's the same thing. Velocity addition is boils down to angle addition in our case. Try this...
Forum: Science, Mathematics, Medicine, and Technology 22nd January 2014, 09:31 PM
Replies: 584
Views: 17,723
Posted By Vorpal
I'm not sure I understand the question--you just...

I'm not sure I understand the question--you just prescribed their their velocities relative to Earth, so those are the velocities in Earth's frame. Velocity is just displacement over time. There's no...
Forum: Science, Mathematics, Medicine, and Technology 22nd January 2014, 10:43 AM
Replies: 584
Views: 17,723
Posted By Vorpal
Number of object doesn't matter. STR is as...

Number of object doesn't matter. STR is as consistent as Euclidean geometry, since Minkowski spacetime is just a sign flip in the metric away from Euclidean space.

This is especially obvious in...
Forum: Science, Mathematics, Medicine, and Technology 21st January 2014, 01:56 AM
Replies: 68
Views: 3,529
Posted By Vorpal
I gave definitions of both explicitly* and...

I gave definitions of both explicitly* and explained some of the motivation for having something other than the common definition of a series sum.

I kept on using explicit names for them because...
Forum: Science, Mathematics, Medicine, and Technology 20th January 2014, 10:01 PM
Replies: 68
Views: 3,529
Posted By Vorpal
That's a definition, as per every calculus books...

That's a definition, as per every calculus books published in the last century, and most probably significantly longer.
Def.: Σn>0 an = limn→∞ Σ0<k≤n ak
The conventional meaning of the sum of an...
Forum: Science, Mathematics, Medicine, and Technology 19th January 2014, 03:08 PM
Replies: 68
Views: 3,529
Posted By Vorpal
That's not what's going on. The meaning of "+" is...

That's not what's going on. The meaning of "+" is completely standard here. Since "+" is a binary operation, the property of associativity also forces a unique meaning of any sum of finitely many...
Forum: Science, Mathematics, Medicine, and Technology 19th January 2014, 06:16 AM
Replies: 68
Views: 3,529
Posted By Vorpal
I'm afraid not. A convergent series will...

I'm afraid not.


A convergent series will have only one limit of partial sums, and phrasing this condition more precisely illustrates exactly where some of the other possibilities lie.

For...
Forum: Science, Mathematics, Medicine, and Technology 18th January 2014, 01:14 PM
Replies: 68
Views: 3,529
Posted By Vorpal
You're mis-diagonising the problem, and as a...

You're mis-diagonising the problem, and as a result missing some interesting mathematics. This is bad, because the point of mathematics (qua mathematics) is to explore interesting abstract structure....
Forum: Science, Mathematics, Medicine, and Technology 18th January 2014, 08:30 AM
Replies: 68
Views: 3,529
Posted By Vorpal
Why would that end discussion? There are many...

Why would that end discussion? There are many ways to assign a value to an infinite series, of which the common meaning is just one. As long as we're careful not to equivocate between them, there's...
Forum: Science, Mathematics, Medicine, and Technology 18th January 2014, 12:31 AM
Replies: 68
Views: 3,529
Posted By Vorpal
What you can do is prove that on Re(s)>1, ζ(s) =...

What you can do is prove that on Re(s)>1, ζ(s) = Sum[ n^{-s} ] satisfies
[6] ζ(s) = Sum[ (-1)^{n-1}/n^s ]/(1-2^{1-s})
by direct series manipulation, which is completely valid there. So far that's...
Forum: Science, Mathematics, Medicine, and Technology 17th January 2014, 11:10 PM
Replies: 68
Views: 3,529
Posted By Vorpal
The sum doesn't exist because the series is...

The sum doesn't exist because the series is divergent, and the sum of the series means the limit of the partial sums.

That doesn't mean we can't have concepts that acts analogously to the sum of...
Forum: Science, Mathematics, Medicine, and Technology 16th January 2014, 02:22 PM
Replies: 12
Views: 1,181
Posted By Vorpal
I think I have to slightly disagree with...

I think I have to slightly disagree with Ziggurat's point. Not about the utility of relativistic mass (it's indeed redundant and pointlessly confusing), or the reasoning that bare facts should be...
Forum: Science, Mathematics, Medicine, and Technology 28th November 2013, 06:25 PM
Replies: 31
Views: 1,043
Posted By Vorpal
This isn't really correct. As a particular...

This isn't really correct. As a particular example, if you have completely Euclidean constant-time slices, as in,
[1] ds² = -(1+2Φ)dt² + (dx²+dy²+dz²)
where Φ is small and time-independent, then to...
Forum: Science, Mathematics, Medicine, and Technology 10th November 2013, 04:45 AM
Replies: 60
Views: 6,330
Posted By Vorpal
That's not the point. In almost all of cases like...

That's not the point. In almost all of cases like this, the theory that triumphs was understood by some bright people, recognized as a genuine contribution, and built upon. Your examples here...
Forum: Science, Mathematics, Medicine, and Technology 10th November 2013, 02:34 AM
Replies: 60
Views: 6,330
Posted By Vorpal
Completely disagree. No, it is both...

Completely disagree.


No, it is both correct and fair. Eddington ca. 1930s and was a crank. Bohr, Fowler, Gamow, Kramers, von Neumann, Rosenfeld, and Wigner all knew it at the time, although they...
Forum: Science, Mathematics, Medicine, and Technology 9th November 2013, 04:52 PM
Replies: 60
Views: 6,330
Posted By Vorpal
I'd call it "confirmation bias" instead, but...

I'd call it "confirmation bias" instead, but otherwise yes.
Eddington's story was itself caused by Eddington inventing reasons to confirm his belief about 136 or 137 being special, so it itself was...
Forum: Science, Mathematics, Medicine, and Technology 9th November 2013, 04:08 PM
Replies: 60
Views: 6,330
Posted By Vorpal
That's just wrong. Well, at best, that's...

That's just wrong. Well, at best, that's extremely misleading.

There never was a time when it looked it might be "exactly 1/137", at least not in the sense of there having ever been an even...
Forum: Science, Mathematics, Medicine, and Technology 8th November 2013, 09:17 AM
Replies: 20
Views: 1,087
Posted By Vorpal
A dimensionally-neutral (indeed, blind to even...

A dimensionally-neutral (indeed, blind to even topology) term is content that generalizes the notion of length/area/volume to an arbitrary field of sets. I've seen this term used instead of...
Forum: Science, Mathematics, Medicine, and Technology 2nd November 2013, 07:26 AM
Replies: 116
Views: 7,327
Posted By Vorpal
That's almost but not strictly speaking true....

That's almost but not strictly speaking true. Intel processors have had the RDRAND instruction since Ivy Bridge, and it generates random numbers non-deterministically, at least in the sense of having...
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