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Einstein's Other Theory of Everything

nautil.us

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Re: Einstein's Other Theory of Everything

#21

Post by pdonis »

phkahler wrote: post #17

An electron falling (electrostatically) toward a proton will reach the speed of light at some point. This is of course the same distance where inside it would need an escape velocity greater than c. So that's an event horizon due to a different force. Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out…

> An electron falling (electrostatically) toward a proton will reach the speed of light at some point.

No, it won't. A correct relativistic analysis of the relative motion of the electron and proton will show their relative speed never reaching c, let alone exceeding it. You can't just plug numbers into Coulomb's Law for this case, because Coulomb's Law by itself is not relativistically correct. You need to use the full Maxwell's Equations and the relativistic Lorentz force law.

> So that's an event horizon due to a different force.

No, it isn't. No force in the relativistic sense produces an event horizon. In relativity, gravity is not a force, it's spacetime geometry, and so is an event horizon in spacetimes where one is present.

> physicists will usually say something like "oh you have to treat that with quantum mechanics".

They are correct in the sense that once the electron and proton get close enough together, classical relativity and Maxwell's Equations are no longer a good model. But as above, you don't need to do that to realize that your claim about reaching the speed of light is wrong.

Re: Einstein's Other Theory of Everything

#22

Post by cheschire »

phkahler wrote: post #17

An electron falling (electrostatically) toward a proton will reach the speed of light at some point. This is of course the same distance where inside it would need an escape velocity greater than c. So that's an event horizon due to a different force. Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out…

If you make a game that is 4D, you can visualize moving 4-dimensionally via a 3 dimensional shadow. See the book Flatland for more concepts like this if this sounds interesting.

Now you can get quite good at predicting where you will end up after a while, and even be able to remember how to get places. But does that mean you are thinking 4 dimensionally? No, you’re still thinking in 3 dimensional shadows.

I get the feeling that is analogous to what happens when you try to do what you’re describing.

Re: Einstein's Other Theory of Everything

#23

Post by pdonis »

mr_mitm wrote: post #20
phkahler wrote: post #17

An electron falling (electrostatically) toward a proton will reach the speed of light at some point. This is of course the same distance where inside it would need an escape velocity greater than c. So that's an event horizon due to a different force. Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out…

You're trying to solve the two body problem of an electron and a proton classically including relativistic effects. But we know this is not describing reality, because an electron orbiting a proton should radiate energy in form of electromagnetic waves and quickly collapse into the proton. The orbit of an electron in the ground state is well outside the Schwarzschild radius of the proton. Quantum mechanics successful…

An electron-proton pair approaching each other will not necessarily form a hydrogen atom by emitting radiation. They could just scatter off each other, and if the impact parameter is large enough, this process could be modeled reasonably well by an analysis using classical relativity. Or, at high enough energy, other particles could be produced, which would require quantum field theory to model.

Re: Einstein's Other Theory of Everything

#24

Post by the__alchemist »

smusamashah wrote: post #16
dr_dshiv wrote: post #3

An alternative to the “ball on rubber sheet” model of gravity is “twisting a lump out of a sheet of silly putty.” You get the same curvature without relying on gravity to serve as a model of gravity (which always bothered me a bit) For clarity, here’s what I mean: if you flatten out some silly putty (or pizza dough should work) then pinch and twist together some of the sheet into a lump, that pulls along the surround…

Balls on sheet is a wrong model imo. It needs gravity to work and therefore doesn't explain gravity. I like to imagine a sponge. If you could somehow make dense lumps inside the sponge (may be apply heat in its center somewhere using microwaves?) everything around that lump will be feel a tension/attraction towards that lump. That's my mental model.

I think the balls on sheet is an OK compromise. The reason for me is, it's tough (but not impossible as you point out) to visualize functions over 3D space. Your sponge does that and I like it! (You could also use color-coding, vector-gradients etc) The ball and sheet uses a spacial dimension as the function value, and that's the dimension the needs gravity to work acts on. So, if you accept that as a compromise, it's OK; we are saying that dimension is a convenience.

Re: Einstein's Other Theory of Everything

#25

Post by pdonis »

phkahler wrote: post #17

An electron falling (electrostatically) toward a proton will reach the speed of light at some point. This is of course the same distance where inside it would need an escape velocity greater than c. So that's an event horizon due to a different force. Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out…

> Some claim matter falling into a black hole never really does from the point of view of an outside observer.

Such claims are wrong. The correct statement is that the outside observer never sees the matter reaching or falling inside the event horizon. But that's not because it never happens; it's because the spacetime geometry prevents light emitted at or beneath the horizon from getting back out to the outside observer.

Re: Einstein's Other Theory of Everything

#26

Post by tux3 »

phkahler wrote: post #17

An electron falling (electrostatically) toward a proton will reach the speed of light at some point. This is of course the same distance where inside it would need an escape velocity greater than c. So that's an event horizon due to a different force. Some claim matter falling into a black hole never really does from the point of view of an outside observer. I've seen weird sounding descriptions like it "spreads out…

A problem with trying to use concepts like this and asking "what if?" is that it's reasonning and trying to extrapolate from an analogy

It's one thing to use analogies to guide your intuition, but physical theories are written in the language of math, and not the language of analogies!

You don't have to use QM to describe protons and electrons at a fine level, but it is very hard to do otherwise, because whatever new theory you want to invent would also have to agree with QM on all the experiments where we have observed quantum effects. You can make an even bigger theory, but you can't throw away the existing approach without reinventing most of its results.

You're welcome to try, of course. But be aware you'll need cold hard math, not just high-level ideas

Re: Einstein's Other Theory of Everything

#27

Post by jacknews »

dr_dshiv wrote: post #3

An alternative to the “ball on rubber sheet” model of gravity is “twisting a lump out of a sheet of silly putty.” You get the same curvature without relying on gravity to serve as a model of gravity (which always bothered me a bit) For clarity, here’s what I mean: if you flatten out some silly putty (or pizza dough should work) then pinch and twist together some of the sheet into a lump, that pulls along the surround…

Or ripples in a table-cloth - the ripples gather the surrounding cloth, just like mass deforms spacetime.

These models are also an intuitive way to illustrate why the speed of light is a limit.

A ball rolling on a rubber sheet, or a boat on a lake, etc, can travel faster than waves in the rubber or water. So why can't matter travel faster than light? With ball-on-sheet type models, you need to resort to abstract relativity arguments about mass going to infinity, time slowing, causality, etc.

But if particles are actually just waves or knots or whirlpools or whatever, they clearly can't possibly travel faster than the speed of waves in the medium.

Re: Einstein's Other Theory of Everything

#28

Post by cyberax »

raattgift wrote: post #15
dr_dshiv wrote: post #3

An alternative to the “ball on rubber sheet” model of gravity is “twisting a lump out of a sheet of silly putty.” You get the same curvature without relying on gravity to serve as a model of gravity (which always bothered me a bit) For clarity, here’s what I mean: if you flatten out some silly putty (or pizza dough should work) then pinch and twist together some of the sheet into a lump, that pulls along the surround…

The "balls on a rubber sheet" is a pain because nothing is in free-fall: there are dissipative contact forces between the balls and the rubber sheet. Consequently realistic initial [position, velocity] values for the test ball cannot give you a stable circular orbit around the central mass ball. Venus isn't about to fall into the sun. Now try setting up Earth-Moon or the Jovian-Gallilean systems on the rubber sheet.…

> The "balls on a rubber sheet" is a pain because nothing is in free-fall

The balls on a rubber sheet model is actually really great, but not in the way it's typically presented (rolling a ball down the curvature). Instead, just use a pen to draw lines to show the concept of geodesics.

Start like this:

1. Imagine that you can move without friction if you stay at the same vertical level.

2. Draw a line on a flat rubber sheet, that's a line in free space. It's just a straight line that can go on to infinity.

3. Now put a ball onto the rubber sheet, so you get some curvature. Now the lines near the ball that stay on the same level are not straight lines, but circles.

Re: Einstein's Other Theory of Everything

#29

Post by carapace »

dullcrisp wrote: post #13
dr_dshiv wrote: post #3

An alternative to the “ball on rubber sheet” model of gravity is “twisting a lump out of a sheet of silly putty.” You get the same curvature without relying on gravity to serve as a model of gravity (which always bothered me a bit) For clarity, here’s what I mean: if you flatten out some silly putty (or pizza dough should work) then pinch and twist together some of the sheet into a lump, that pulls along the surround…

> without relying on gravity to serve as a model of gravity (which always bothered me a bit) Why though? Would it help if the sheet were in a centrifuge?

> Why though?

It bothers me too, why? because it's circular reasoning: acceleration can't explain acceleration.

> Would it help if the sheet were in a centrifuge?

No, for the same reason. (You're imagining a tube-shaped membrane?)

To make it worse, it's developing a wrong idea that hides the right and deeply strange idea: when an object passes a mass and its path seems to deflect what's really happening is that the object is moving in a straight line the whole time and space itself is curved. (The situation is actually a little stranger than that, but I'm no physicist so I won't try to explain any further.)

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