swansont

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.

This is a long-standing issue of definitions. Using the normally-used definition of mass (the invariant mass or so-called rest mass) this isn't true. It holds if you use a certain definition called the relativistic mass, but that causes other difficulties. What is true with either definition is that the kinetic energy's dependence on mass diverges at c, and then we reach the conclusion of it requiring infinite energy to do so.

I assume Deity status is a rep power of 25?

I think it's more accurate to say that there is a gradient in the frequencies — the rate at which time passes is different depending on your position. I don't know what "bent in time" means or how to interpret it. The time dilation is a kinematic effect. Once you stop spinning, every point on the propeller is in the same inertial frame, and the time dilation effect goes away.

Hydrogen masers, cesium clocks and rubidium clocks all exhibit the same time dilation effects. This would seem to rule that conjecture out.

Is it possible for you to exert a force on an object without it exerting a force on you? If yes, give an example. If no, then you must at least provisionally agree that forces come in pairs. An example of the law, not the law itself. F=ke*Q1*Q2/r^2 describes the force on Q1 and Q2. You cannot have a force on Q1 without having the force on Q2. One charge does not exert or feel a force of there are no other charges around.

That assumes you are right. If the rest of the internet is right, the amount of misconception goes down. Merged post follows: Consecutive posts merged Oh, my. Is ego bosonic?

Indeed. One needs to measure the amount of rotation to see the magnitude of the effect, but since we're all rotating like this it would only come into play for someone with different orbital parameters. Locally, assuming linear motion won't have much effect, and then we can assume we are at rest. The expansion is an effect of General Relativity, and basically means that distant objects are in a different frame of reference than our own, and I think I'm right in saying that these are not simply different inertial frames. The space is expanding, (though calling it an ether can be problematic because of historical reasons) Locally, you have inertial frames and nothing exceeds c. But the remote frame is non-inertial, as viewed by us, and you lose the restriction on c unless you account for the expansion of space. Or perhaps it's better to say that with regard to reference frames, the expansion of space is a non-inertial effect. (If Martin happens along he may find some fault with my generalizations. Much of GR is outside my area of expertise)

emphasis added — I've highlighted the relevant part of the quote. Inertia can be equated to the body's inertial mass. It's not a force. It's the mass. The employee could have said that there are 1000 grams in a kilogram as part of that video. It would be true, and yet not be an explanation of the 3rd law. The third law is decidedly NOT only a consequence of the inverse-square law. You can observe it in e.g. a spring between two masses that are held together and then released (a simple explosion). That force is linear in x. (Edit: I see D H mentions the example of Hooke's law as well)