swansont

IIRC — photon scattering a second-order interaction, so it doesn't become important until high energy. But interference is not the same thing, and happens readily at all energies.

Electrons interfere, too. Single photons interfere with themselves. One issue is trying to separate the concept of waves from that of photons. You can't. Light exhibits properties of both. As do electrons.

Ah, but the original proposal was a simple set of rules, before the idea morphed*. I agree that modeling the real universe require knowledge of the laws, but the "simplified universe" of a two-state system is much simpler. Two spin states and an interaction. * and I think that's a source of confusion in this thread, because we have multiple ideas being discussed.

There certainly are discussions on the topic, but since you can't eliminate one or the other to test, is there any way to test this? I think it's more philosophy than science. All you can do is make arguments either way.

But language certainly did not appear on its own. Didn't the development of language require thought? At worst, I think that they co-developed.

Yes indeed. Relativity (and quantum mechanics) are not logical by the standard of everyday experience. That's one of the hurdles to understanding it. It's not intuitive when you start learning about it, and it can be a long row to hoe before any of it even starts to become intuitive. Physics is also not just math or accounting. In accounting you have rules, but you can make up new ones. In physics, we are bound by how nature behaves, and have to deduce the rules empirically. Merged post follows: Consecutive posts merged I like that analogy and can't recall having heard it before. You can use SR on any one tile, but as soon as you start comparing two tiles, GR applies.

Very roughly: Visible often means you can see it with your naked eye; sometimes this also includes the aid of magnification. Observable means it can be detected, though it may require instrumentation. I don't think there are precise definitions that always apply, though.

It's not an illusion. The restriction on being less than c is only for two objects. If I see an object going at at 0.75c to my right, and at 0.75c going to my left, they are separating at 1.5c. To each other, though, they are separating at 0.96c, and none of our clocks are running at the same rate. You'd have to know the acceleration to come up with a numerical answer, and the math gets messier. http://en.wikipedia.org/wiki/Time_dilation#Time_dilation_at_constant_acceleration edit: I can't yet vouch for the veracity, but check out this calculator, and the "long relativistic journey" section http://www.cthreepo.com/cp_html/math1.htm This is definitely not an easy topic to grasp.

Initially I was going to disagree, but then I thought, where did language come from?

I don't know that it's meaningful to say that space doesn't exist at c. As for saying mass can't move at c, I think it's basically equivalent — we can't get into that frame of reference.

Sounds like the Ising model, which came up in another thread recently. And sure, you can model it. http://en.wikipedia.org/wiki/Ising_model I think that if your rules are internally consistent, you'd end up with a completely deterministic system.

That's geographical size, though, and doesn't matter. Land can't vote. It's population that's important.

You have to be able to describe physics in that frame, and the way we (mathematically) get from one to the other is with a Lorentz transformation. This breaks down at v=c, meaning you can't transform into the frame, or more problematically (AFAICT) you can't invert the math and do a transform back to your original frame.

Ran across this: The 20 most gerrymandered congressional districts in the US http://www.slate.com/id/2208216/slideshow/2208554/fs/0//entry/2208555/ Some of these are amazing,with the tenuous connection between parts of the districts. Are there any rules about this? I wonder if some mathematical limitation could be placed on how much surface length/area you have, or some limit to how convex or concave the district could be.

The calculators only apply to local space, where special relativity applies. Once you get into regions of inquiry where General relativity applies, it's a different ballgame.

Objects with mass behave a certain way, and massless objects behave a different way. photons behave the way massless objects behave.

Have you heard of any investigations into this? A quick Google turned up http://www.rexresearch.com/cottell/cottell.htm http://www.halfbakery.com/idea/Ultrasound_20Fuel_20Atomization so at least some people have been thinking about it.

For the same observer, it should be the same.

I've seen this before somewhere. AFAICT the idea here isn't that what we see is literally a hologram, it's that information in the universe may be encoded in a way similar to holograms, i.e. 3-dimensional information being stored in a 2-dimensional space. An example they give is that the information about a black hole might be encoded in the surface defined by the event horizon.

Standard GR disclaimer: My depth of knowledge in GR is limited As with Special Relativity, what different observers see can be explained by different effects, e.g. in SR the stationary observer sees time dilation while the moving one sees length contraction, but they can agree on why their clock reads what it does when the trip is over. In GR, the effect of moving into different frames is also important. If I'm in a gravity-free area, I measure lightspeed to be c. If I'm in a gravitational potential I also measures lightspeed to be c, if I confine the measurement to be made in a locally flat region of spacetime. In case 1 you move between frames, so no clock is going to measure the trip to be 500 seconds. In case 2, an observer might measure light speed to be something other than c, if they were to assume everything is in the same frame of reference. From what I understand of the Shapiro delay (time delay of light passing near a massive object), you can view it either as a time dilation or as due to the extra length of travel due to the curvature of space. However, if one were to be unaware of these effects, it would seem like the light had slowed down. Bending and time delay have both been measured as confirmations of GR. 3. The construct of GR is that it is the geometrical effect, in which mass warps spacetime and gives rise to time dilation. Gravity is a perception of moving or being in that warped spacetime — things fall the way they do because of the curvature. Gravity and curvature are the same thing, rather than one causing the other.

Well, that depends on how you define "complicated" Speeds don't add linearly. Joe will be traveling at ~.99995c relative to earth. If we take a different example and use 0.5c for both the mother ship and Joe (instead of 0.99c), then Joe will be going 0.8c relative to earth. The nonlinearity of velocity addition is much reduced at low speeds, so at speeds we're used to experiencing we don't notice it. The equations are at http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html and there are calculators, too. The case that applies most directly is the third box, with the rocket sending out a projectile

OK, I had a very quick glance, and it's very intriguing. The idea that the paradox relies on the particles annihilating/interacting when (classically) their paths should overlap gives me pause, though — how do we know that the interaction takes place all of the time? I assume that's measured independently and there's a statistically significant deviation from that in the "dark" coincidences. I tried emailing the article to me at home and it doesn't seem to have worked, despite it being relatively small, so I'll have to address that tomorrow, and a more thorough read will have to wait.

I haven't had time to look at it. I was disappointed in the article though — I don't think it explained very much at all. I still don't know what the Hardy paradox is.

I'm not sure what the paradox is here. If you have two observers moving away from each other at 0.99c, both observers will see this to be the case. To see this it doesn't matter who did the accelerating. To increase the separation speed one would have to add energy, and to calculate this use the proper equation, which diverges at c. Using the wrong equation might give you an answer that exceeds c, but that's not a paradox.

Do we really want to know how the sausage is made? I suspect it has to do with longevity, number of posts and reputation.