Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Einstein's Other Theory of Everything

nautil.us

Post reply on HN
Print view View original

31–40 of 138 posts

Re: Einstein's Other Theory of Everything

#31

Post by csomar »

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…

I thought it's impossible for any object with non-zero mass to reach the speed of light?

Re: Einstein's Other Theory of Everything

#32

Post by IAmGraydon »

tux3 wrote: post #26
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…

Well said. I think Einstein himself used the same kind of analogous thinking to guide his intuition, and wouldn’t have been nearly as successful as he was without allowing himself this sort of unbounded thinking. In the end, however, he proved these intuitions true or false with the light of math.

Re: Einstein's Other Theory of Everything

#33

Post by greysphere »

pdonis wrote: post #21
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 f…

> You can't just plug numbers into Coulomb's Law for this case, because Coulomb's Law by itself is not relativistically correct.

Sorry if this is a bit pedantic, but as someone trying to study this at the moment, I don't see this the same way and I'd like to validate my interpretation: You can just plug numbers into Coulomb's law, that part is correct. But then the problem of infinite velocities comes from interpreting the 'F' side of the equation, assuming Newton's law (F=ma), rather than using its relativistic counterpart.

Coulomb's law: F = qq'/r^2

Lorentz force law: F = q(E + mu x B)

For the 2 particle case, both of these say the same thing (substitute into the Lorentz eq E = q'/r^2, B = 0 and you get the same thing).

The promotion from non-relativistic to relativistic mechanics is a change of what 'F' means.

nonrelativistically: F = p' = m v' = m x'' = m a

relativistically: F = p' = \gamma m v' = \gamma m x'' = \gamma m a

where \gamma is the Lorentz factor.

Interpreted this way, infinite velocities are avoided.

But, as r->0 we still have an infinity problem - namely infinite energy! This necessitates a quantum mechanical correction to both the Coloumb and Lorentz laws.

TLDR: relativity is necessary when things start to move 'very fast', qm is necessary when things are 'very small'

Re: Einstein's Other Theory of Everything

#35

Post by XorNot »

pdonis wrote: post #23
mr_mitm wrote: post #20

Earlier quoted context omitted.

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.

You can't just reject evidence like this though: electrons orbiting protons don't emit synchrotron radiation. So whatever else you want to the prize, you have to be able to reproduce this result.

Re: Einstein's Other Theory of Everything

#36

Post by [deleted] »

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…

[deleted]

Re: Einstein's Other Theory of Everything

#37

Post by sigmoid10 »

greysphere wrote: post #33
pdonis wrote: post #21

Earlier quoted context omitted.

> 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 f…

> You can't just plug numbers into Coulomb's Law for this case, because Coulomb's Law by itself is not relativistically correct. Sorry if this is a bit pedantic, but as someone trying to study this at the moment, I don't see this the same way and I'd like to validate my interpretation: You can just plug numbers into Coulomb's law, that part is correct. But then the problem of infinite velocities comes from interpreti…

You can plug arbitrary values in, but you can not expect to gain any valid predictions or reasonable physical insight from Coulomb's law as soon as you are no longer dealing with static point charges. That's because B and E are not independent quantities but actually closely intertwined components of the electromagnetic field strength Tensor F. As soon as you start dealing with motion, these components will mix, preserving only certain quantities like the tensor contraction E^2-B^2. So even if you construct a case where B=0 at time t=0, that will no longer be true once you had any acceleration of your charge carriers.

In the fundamental quantum field theory picture you don't even have forces and particles in the original sense anymore. The dynamics are then described by interaction between the em field and charged fermionic fields. Stuff like Coulomb's law (or any other force potential) only emerges as a macroscopic low energy approximation for specific field configurations.

Re: Einstein's Other Theory of Everything

#38

Post by motohagiography »

naively, i'd wonder if the time properties of black holes could be used to effect local super-massive gravitational effects on entangled particles here.

e.g. they figured out how to entangle the electron and proton of a hydrogen atom with a complementary particle that is being pulled into a black hole, like if there were a way to entangle or entrain a local atom with hawking radiation from a black hole, where as the effect of entanglement, the local atom adopted the dialated time/gravity of its remote counterpart in the black hole. the effect would be that states of matter which only existed on the ephemeral femtosecond scale here would be stabilizied for longer time periods because its "clock" had been slowed down by its adopted clock entanglement via hawking radiation in a kind of black-hole-time.

maybe better for a movie script or fiction, but people who think of these things reason them through logically before doing the math as well.

Re: Einstein's Other Theory of Everything

#39

Post by vlovich123 »

motohagiography wrote: post #38

naively, i'd wonder if the time properties of black holes could be used to effect local super-massive gravitational effects on entangled particles here. e.g. they figured out how to entangle the electron and proton of a hydrogen atom with a complementary particle that is being pulled into a black hole, like if there were a way to entangle or entrain a local atom with hawking radiation from a black hole, where as the…

I don’t believe you can entangle items remotely like that.

Re: Einstein's Other Theory of Everything

#40

Post by [deleted] »

motohagiography wrote: post #38

naively, i'd wonder if the time properties of black holes could be used to effect local super-massive gravitational effects on entangled particles here. e.g. they figured out how to entangle the electron and proton of a hydrogen atom with a complementary particle that is being pulled into a black hole, like if there were a way to entangle or entrain a local atom with hawking radiation from a black hole, where as the…

[deleted]
Post reply on HN