Cosmic Speed Limit

Saipanne

So, I have no physics background, i just cobble together info from various sources.

One thing I frequently come across is that we 'dont know' why there is a limit on the speed you can travel between two points.

I was thinking, because of relativity, as your velocity increases time slows down for the "passenger" relative to an outside observer. Afaik, time stops entirely at C, so isn't the speed limit C just a consequence of time being unable to slow any further? As opposed to C being this magical mystery limit?

Capt'n Midnight

There's been no evidence to contradict the speed of light in a vacuum being the top speed.

Particle accelerators like CERN allow what happens at high speeds to be observed and measured. Simple things like how much energy the particle have. And how radioactive decay slows down at high speeds.


A transformer converts electrical changes into magnetic changes and back again. So electricity and Magnetism are related. But when Maxwell worked out the equations he found that they predicted an electromagnetic radiation with a velocity related to the electrical and magnetic properties of a vacuum.


https://en.wikipedia.org/wiki/Speed_of_light#Propagation_of_light

It turned out to be the same as the speed of light.

Hotblack Desiato

Saipanne wrote: »

I was thinking, because of relativity, as your velocity increases time slows down for the "passenger" relative to an outside observer.

An example of this is muon decay. Muons are particles which at low velocities have a given half-life before they decay, but for muons moving at relativistic velocities their 'lifetime' is stretched.

https://en.wikipedia.org/wiki/Time_dilation_of_moving_particles

The other problem with trying to bust the speed of light, for any massive particle (photons have no mass) is that mass increases exponentially at relativistic velocities and ultimately approaches infinity at c, therefore requiring infinite energy to accelerate to c.

https://en.wikipedia.org/wiki/Special_relativity#Causality_and_prohibition_of_motion_faster_than_light

mickmackey1

Capt'n Midnight wrote: »

A transformer converts electrical changes into magnetic changes and back again. So electricity and Magnetism are related. But when Maxwell worked out the equations he found that they predicted an electromagnetic radiation with a velocity related to the electrical and magnetic properties of a vacuum.

Yeah I don't quite understand why he didn't take the next intuitive step, namely that light speed cannot be exceeded in a vacuum. He would now be as famous as Einstein if he had.

Maximus Alexander

c = sqrt(E/m)

Saipanne

Maximus Alexander wrote: »

c = sqrt(E/m)

What happens when m=0?

Maximus Alexander

Saipanne wrote: »

What happens when m=0?

:pac:

ps200306

mickmackey1 wrote: »

Capt'n Midnight wrote: »

A transformer converts electrical changes into magnetic changes and back again. So electricity and Magnetism are related. But when Maxwell worked out the equations he found that they predicted an electromagnetic radiation with a velocity related to the electrical and magnetic properties of a vacuum.

Yeah I don't quite understand why he didn't take the next intuitive step, namely that light speed cannot be exceeded in a vacuum. He would now be as famous as Einstein if he had.

'Cos he didn't believe in the vacuum! In one sense, Faraday was ahead of Maxwell in that he conceived of the field as an explanation for "ghostly action at a distance", but then he also assumed that any physical effects mediated by the field would propagate instantaneously.

Maxwell was more mathematical than Faraday, but also knew that his waves propagated at a finite speed. The idea of wave propagation without a medium was preposterous, hence the concept of the aether. The Michelson-Morley experiment only took place two years before Maxwell's death, and even then its interpretation was the subject of much controversy. People were still trying to figure out how they might rescue the aether by local frame-dragging. It was nearly two decades more before anyone bit the bullet and proposed that the existence of the aether was surplus to requirements. By that time, Lorentz had handed a lot of the mathematics to Einstein on a plate -- both his famous transformations and the covariant description of electromagnetism.

The only difference with Special Relativity (which was originally called the Lorentz-Einstein theory) was that, whereas Lorentz had effectively said "it almost looks as if the aether doesn't exist, ha ha ha", Einstein's went the whole hog and consigned the aether to the same scientific graveyard as the celestial spheres, phlogiston and the four humors. :pac: :pac: :pac:

Capt'n Midnight

Electromagnetic forces travel at the speed of light (by definition).

The Earth orbits the where the sun appeared to be 8 minutes ago. I'm still a little confused about the speed of gravity. For example if a star goes supernova there will be a lot of mass moving very fast. For observers far away the rough symmetry means the centre of mass won't change much.

But for (soon to be deceased) observers closer in is there any chance they could detect the shift in mass by the distortion in space time before the electromagnetic effects hit them ? Or would the distortion be unobservable because of lack of external reference, in the same way that the speed of light is constant for all observers.

Yes we have observed black holes colliding. And maybe if we had more detectors we could triangulate better and if we had even more we might be able to detect how fast the gravity wave propagates.

ps200306

Capt'n Midnight wrote: »

Electromagnetic forces travel at the speed of light (by definition).

The Earth orbits the where the sun appeared to be 8 minutes ago. I'm still a little confused about the speed of gravity. For example if a star goes supernova there will be a lot of mass moving very fast. For observers far away the rough symmetry means the centre of mass won't change much.

But for (soon to be deceased) observers closer in is there any chance they could detect the shift in mass by the distortion in space time before the electromagnetic effects hit them ? Or would the distortion be unobservable because of lack of external reference, in the same way that the speed of light is constant for all observers.

I don't think a truly symmetric core collapse supernova would produce any gravitational waves. Even in Newtonian gravity, a spherically symmetric mass distribution is indistinguishable from a point object. However, it seems like core collapses are less symmetric than once thought. Neutron stars seem to be born with high initial velocities, assumed to be due to some sort of "kick" at the point of creation. It's thought that gravity waves from core collapses might be detectable in future. In that case we'd expect to see the waves detected at the same time as the neutrino burst, since both of those are relatively unaffected by the stellar envelope whereas the EM radiation could take hours to work its way out through the layers.

Capt'n Midnight wrote: »

Yes we have observed black holes colliding. And maybe if we had more detectors we could triangulate better and if we had even more we might be able to detect how fast the gravity wave propagates.

Hasn't that already been done with the Hanford and Livingston detectors of LIGO? Even within the limits of two detectors I thought they used the time delay between detectors to triangulate the first black hole merger to a particular (large) area of the sky. Or is it that they assume speed-of-light propagation in order to do the sums? Now I'm confused too.

Capt'n Midnight

ps200306 wrote: »

I don't think a truly symmetric core collapse supernova would produce any gravitational waves. Even in Newtonian gravity, a spherically symmetric mass distribution is indistinguishable from a point object. However, it seems like core collapses are less symmetric than once thought.

That's why I suggested a close observer, as the mass closer to them would have more of an effect than that mass exiting the far side of the supernova.

Thinking a little more, any orbiting planets or companion stars would also produce some asymmetry.


But supernovas are impressive.
https://what-if.xkcd.com/73/

Which of the following would be brighter, in terms of the amount of energy delivered to your retina:

A supernova, seen from as far away as the Sun is from the Earth, or

The detonation of a hydrogen bomb pressed against your eyeball?

[Can you hurry up and set it off? This is heavy.]

Applying the physicist rule of thumb suggests that the supernova is brighter. And indeed, it is ... by nine orders of magnitude.

But those black holes colliding released three solar masses worth of energy or about 100 times more than a hypernova. And we all know there are bigger black holes out there.

ps200306

Capt'n Midnight wrote: »

That's why I suggested a close observer, as the mass closer to them would have more of an effect than that mass exiting the far side of the supernova.

Nah, that's the cool thing about it -- as long as it's spherically symmetrical the near and far components have exactly the same effect. The closeness of the near side is compensated for by the fact that more of the force is lateral, whereas the far side is closer to being all in the same direction. Newton himself proved it with a bit of calculus -- the force is all directed toward the centre no matter where you are (as long as your on the outside .... if you're inside a spherical shell you'd be weightless no matter where you are, according to another cool piece of calculus).

ps200306

Capt'n Midnight wrote: »

Thinking a little more, any orbiting planets or companion stars would also produce some asymmetry.

The gravitational wave energy is sobering to calculate though.

Jupiter in nice round figures is one thousandth of a solar mass, and is two million times further from the Sun than the separation between the two black holes (approx 30 solar mass each) in the first LIGO detection just before merger.

The gravitational wave power is:



If we divide the black hole merger power by the Sun-Jupiter power we get a ratio of:




The absolute figures work out at about six kilowatts for the Sun-Jupiter system ... which would presumably not be easy to detect from any distance. The black hole merger peaked at about 4 x 10⁴⁹ W !!!

Capt'n Midnight

ps200306 wrote: »

if you're inside a spherical shell you'd be weightless no matter where you are, according to another cool piece of calculus).

This by the way is a big problem for Dyson Spheres. You can't rely on gravity to keep the sphere centred on the star.

So Dyson Swarms.

ps200306

Capt'n Midnight wrote: »

This by the way is a big problem for Dyson Spheres. You can't rely on gravity to keep the sphere centred on the star.

Never occurred to me. That's cool ! :pac: