Light Speed?

[Person012345]

So far as I'm aware, they're not so much PREDICTED by GR as one possible solution for a part of it. There are other possible mathematical solutions, which are also equally valid (mathematically - which ones are correct physically remain to be seen).

Like what exactly?

[Diche Bach]

Right on all counts.

However, there has to be SOMETHING that's large enough out there to cause the gravitational lensing that has been noted by some telescopes, and to create the enormous gravity well that generates galaxies (without it, there would be no discrete galaxies - stars and other large bodies would be far more evenly distributed across the universe than they are). After all, our sun is in orbit of SOMETHING rather large (putting it mildly) somewhere at the heart of the Milky Way.

Oh that is interesting. I had heard the idea of a BH in the center of Milky Way, but didn't exactly pickup that they are hypothesized to be at the heart of _most_ or all galaxies. Interesting! Yes, it does make sense that it would need to be something quite massive to act as the central body for an entire galaxy of several billion stars to revolve around it.

Here is my one question though. Assuming it is a black hole at the center or Milky Way, presumably it formed either just before or just after the galaxy began to coalesce. Now I can't remember if they think our galaxy is an first or second generation one, but in any event, 6 to 10 billion years old galaxy I would think (at least)?

So why is it that, after that much time for the BH to have cleared the space around it, it hasn't? Instead of a black blank spot with the other side of the galaxy lensing behind it and nothing energetic crashing into it (because it has had plenty of time to clear its surroundings out to extent of its ergosphere I would think?) we got a giant cluster of gass and energetic activity.

[NGTOne]

Oh that is interesting. I had heard the idea of a BH in the center of Milky Way, but didn't exactly pickup that they are hypothesized to be at the heart of _most_ or all galaxies. Interesting! Yes, it does make sense that it would need to be something quite massive to act as the central body for an entire galaxy of several billion stars to revolve around it.

Here is my one question though. Assuming it is a black hole at the center or Milky Way, presumably it formed either just before or just after the galaxy began to coalesce. Now I can't remember if they think our galaxy is an first or second generation one, but in any event, 6 to 10 billion years old galaxy I would think (at least)?

So why is it that, after that much time for the BH to have cleared the space around it, it hasn't? Instead of a black blank spot with the other side of the galaxy lensing behind it and nothing energetic crashing into it (because it has had plenty of time to clear its surroundings out to extent of its ergosphere I would think?) we got a giant cluster of gass and energetic activity.

Because the distances are so unimaginably vast. Consider, for instance, that our sun is, in fact, ORBITING a body that is about 27,000 light years away. Even if the black hole at the center of the galaxy WERE operating for all that time, it likely wouldn't even have made a dent - if it is, in fact, a black hole, I'd bet dollars to doughnuts that the brightness and energy that we observe are an unimaginably vast accretion disk (accretion sphere?), and the energy and gas is all the stuff that the hole is sucking in getting smashed together. And, naturally, as you get closer, the stuff gets packed in tighter and tighter (means more energy the closer you get).

If it's not a black hole at the center, I would imagine that any object that massive would be putting out some pretty damn exotic forms of energy (and loads of it), both on its own and through its interaction with the stuff around it, which might account for the lightshow we see.

Edited August 18, 2013 by NGTOne

[Anton P. Nym]

Uhhh, black holes are not something for which we have 100% empirical confirmation, right?

Perhaps not 100% confirmed, but if Cygnus X-1 isn't a black hole then we know far less about physics than we think we do.

-- Steve

[aNewHope]

If there are no black holes, how would you explain THIS? (Centre of the Milky Way)

[NGTOne]

If there are no black holes, how would you explain THIS? (Centre of the Milky Way)

Those objects appear to be orbiting normally, albeit extremely quickly (to be expected given the scales and forces involved). Such orbits could be caused not only by a black hole, but by ANY sufficiently massive object. Thing is, under the current understanding of our universe, a black hole is the only object that COULD BE massive enough to hold a galaxy together.

[Yourself]

Those objects appear to be orbiting normally, albeit extremely quickly (to be expected given the scales and forces involved). Such orbits could be caused not only by a black hole, but by ANY sufficiently massive object. Thing is, under the current understanding of our universe, a black hole is the only object that COULD BE massive enough to hold a galaxy together.

Not exactly. As it stands black holes are not massive enough to hold together our galaxies (this is where that whole dark matter thing first showed up; there wasn't enough actual mass to account for the orbital velocities of the edges of galaxies).

What makes us relatively certain that there is a black hole there is that it's the only thing that could cram that much mass into such a tiny area. So far its behavior is not inconsistent with our understanding of what black holes are, so there's no reason to postulate that it's anything different.

[NGTOne]

Not exactly. As it stands black holes are not massive enough to hold together our galaxies (this is where that whole dark matter thing first showed up; there wasn't enough actual mass to account for the orbital velocities of the edges of galaxies).

What makes us relatively certain that there is a black hole there is that it's the only thing that could cram that much mass into such a tiny area. So far its behavior is not inconsistent with our understanding of what black holes are, so there's no reason to postulate that it's anything different.

True enough. However, it is a matter of some debate in the astrophysical community as to why no intermediate-sized black holes have been discovered. We have ones that are a few dozen solar masses, and the big ones at the hearts of galaxies that are millions or billions, but nothing in between. This seems to lend credence to the theory that the black holes we see everywhere and the ones that hold together galaxies are two different (though possibly similar) phenomena.

[Diche Bach]

Ah okay. So while the existence of Black Holes in general is not 100% confirmed there are several candidate one could say are 99%.

Given the gravity involved, I don't suppose there is anyway that any sentient being will ever be able to actually directly measure a black hole.

Thus, I'm gonna go with: Black Holes are "God."

[NGTOne]

Given the gravity involved, I don't suppose there is anyway that any sentient being will ever be able to actually directly measure a black hole.

Well, without spacetime warping and adamantium spacecraft, not really, no.

NASA, you hear me? Get to it!

[Astronut25]

If there are no black holes, how would you explain THIS? (Centre of the Milky Way)

[snip]

They're orbiting magik, obviously.

Ah okay. So while the existence of Black Holes in general is not 100% confirmed there are several candidate one could say are 99%.

Given the gravity involved, I don't suppose there is anyway that any sentient being will ever be able to actually directly measure a black hole.

Thus, I'm gonna go with: Black Holes are "God."

No, they're where God divided by zero.

Although seriously, they have been confirmed. The orbital velocity below a certain altitude exceeds c (speed of light). That by definition is a black hole, since nothing can escape it (except through Hawking Radiation IIRC) and no force can hold up to it (it will collapse into a singularity). Although whats going on inside black holes are in question (IIRC), their existence isn't. aNewHope showed one, and here's a Blazar that's created by a Supermassive Black Hole (the orbital velocity of the Accretion disk approaches c).

IIRC, GR doesn't prohibit going faster than c, it just says its impossible to accelerate to c. Although you kinda have to accelerate to c before you can exceed it, which makes it impossible.

Edited August 19, 2013 by Astronut25

[Person012345]

IIRC, GR doesn't prohibit going faster than c, it just says its impossible to accelerate to c. Although you kinda have to accelerate to c before you can exceed it, which makes it impossible.

No, that's wrong. To accelerate past c (even if we could magically somehow skip c) requires more than infinite energy according to GR. The way around it is not to somehow "skip" c, but rather to not accelerate (as in the alcubierre drive for example).

[Person012345]

Think of it this way: Energy and mass are the same thing (E=mc^2). As you gain more energy you also gain more mass. There is a point where you have such huge amounts of inertia that you need to add tremendous amounts of energy just to accelerate by a little bit. Except the weight of the energy you just added makes the return from the energy even lower. It increases in such a way that there is a speed you will never be able to reach because your returns from your energy are so small and diminish with every bit of energy you add. That speed is c. It's true that you can always accelerate, but you will never reach that magic number. Or beyond. To do so would require infinite (or more than infinite respectively) amounts of energy.

This isn't a precise explanation as the real one is mathematical and has to do with spacetime warping, but it's a decent explanation (since mass warps spacetime anyway).

[Astronut25]

[snip]

I remember that from when I studied GR. I heard somewhere a long time ago (before I had studied it) that the formula had an asymptote at c, but had real values when v does not equal c. I had just reviewed the formula right after my initial post, when v = c then you end up dividing by zero, but if v > c then you get an imaginary value for E. Now curiosity is killing me, what does that mean v>c if E is imaginary?

Edited August 19, 2013 by Astronut25

[NGTOne]

I remember that from when I studied GR. I heard somewhere a long time ago (before I had studied it) that the formula had an asymptote at c, but had rational values when v does not equal c. I had just reviewed the formula right after my initial post, when v = c then you end up dividing by zero, but if v > c then you get an imaginary value for E. Now curiosity is killing me, what does that mean v>c if E is imaginary?

Under my understanding of relativity (and physics overall), it's physically meaningless - a mathematical solution, but not one that translates to reality.

If I'm wrong, the implications could be profound - time travel? Infinite energy (or the reverse)? Hell if I know.

[Astronut25]

Here's something that's been bugging me ever since Minutephysics had made a video about the formula E^2 = (mc^2)^2 + pc^2 (

). It is the Pythagorean Theorem for Right Triangles (A^2 = B^2 + C^2), but what if it isn't Right (A^2 = B^2 + C^2 - 2BC cos theta IIRC).

E^2 = (mc^2)^2 + pc^2 - 2mpc^3 cos(what?)

Edited August 19, 2013 by Astronut25
Typo in Formulae

[K^2]

I remember that from when I studied GR. I heard somewhere a long time ago (before I had studied it) that the formula had an asymptote at c, but had real values when v does not equal c. I had just reviewed the formula right after my initial post, when v = c then you end up dividing by zero, but if v > c then you get an imaginary value for E. Now curiosity is killing me, what does that mean v>c if E is imaginary?

Most likely, it means absolutely nothing. A formula like that is only good up to a singularity. In other words, all of the Lorentz boost formulas are only valid for v<c.

But if we assume that these formulas are correct and try to ask what it would mean for particles assuming everything else extends to that region nicely as well, we can look at the Shrodinger Equation for the answer. So long as velocity is high enough, say, v > 10c, we should be able to use non-relativistic wave equations. In that case, the wave vector for a particle satisfies ħ²k²/(2m) = iE for some real value E. That gives us solution, k = (1+i) Sqrt(Em)/ħ. Since this quantity has both imaginary and real parts, the wave itself will be losing amplitude.

In other words, if a state with v>c can exist and follows algebraic extensions of equations we have for sub-light particles, such a state must immediately decay.

But again, it most likely has nothing to do with reality to begin with.

[WestAir]

In other words, a Tachyon, once formed, will immediately flatline? Is it possible the reason is that causality then works in reverse with such a wave, meaning t time is always a negative or opposite value? The Tachyon instantly decays because it reaches its cause and causality dictates it can no longer exist?

[NGTOne]

In other words, a Tachyon, once formed, will immediately flatline? Is it possible the reason is that causality then works in reverse with such a wave, meaning t time is always a negative or opposite value? The Tachyon instantly decays because it reaches its cause and causality dictates it can no longer exist?

No compelling evidence towards the existence of tachyons has ever been found. Moreover, according to the Standard Model of physics (the currently most widely-accepted model), they don't even exist theoretically.

[K^2]

I'd say the more interesting statement of Standard Model is that even if they somehow did exist, none of the known particles could interact with them.

[NGTOne]

I'd say the more interesting statement of Standard Model is that even if they somehow did exist, none of the known particles could interact with them.

The even more interesting bit is that, given our current understanding of causality and the Standard Model, (if we were able to interact with tachyons, naturally) it would be possible to easily create a grandfather paradox using tachyons.

Imagine if party A sends a superluminal message using tachyons. From his frame of reference, they're moving FTL. From party B's frame of reference, they're moving backwards in time. Then, when party B receives the message, he sends out a reply. To him, the reply is moving FTL. To party A, the reply is travelling backwards in time. In short, it's possible for a reply to a message to arrive before the message itself, setting up some interesting experiments in paradoxes and the immutability (or possible lack thereof) of causality.

[Stochasty]

Most likely, it means absolutely nothing. A formula like that is only good up to a singularity. In other words, all of the Lorentz boost formulas are only valid for v<c.

I have seen a couple of papers on the arXiv discussing the mathematics behind Lorentz transformations between time-like and space-like observers. I don't remember the conclusions in detail (I only briefly skimmed the papers), but as I recall nothing in the transformations were ill-defined.

That said, I otherwise agree with you; there are issues involved in defining reference frames for space-like observers which render such results unphysical even if they are mathematically well-defined.

[K^2]

I don't remember the conclusions in detail (I only briefly skimmed the papers), but as I recall nothing in the transformations were ill-defined.

It's not really so much about how well they are defined. It's more about the fact that when you have boundaries in your abilities to probe a model within some parameter space, it's absolutely useless discussing whether the model applies beyond these boundaries. It's one thing if the boundaries are purely due to practical limitations. Then we can expect things to be nice and continuous. But if there is an actual singularity, like the v=c case, there is just absolutely no reason to assume that mathematical continuation of the model beyond that boundary has anything whatsoever to do with reality.

it would be possible to easily create a grandfather paradox using tachyons.

Grandfather paradox is almost trivially resolved in field theory, so it's not a very compelling argument. Me and Stochasty have actually had discussion on possibility of time travel in GR without involving exotic matter. I still need to track down some of these papers, by the way. Point is, time travel might very well be within realms of physical possibility, so even if it remains out of practical reach, we still couldn't discount a possibility simply based on it leading to time travel related paradoxes.

[Morrigi]

I just want to reiterate a few points.

First of all, you cannot accelerate to c by conventional means. This would require infinite thrust applied to an infinite mass.

Second, black holes are a very well-known phenomenon. There is no question that they exist, only what happens inside them.

Third, it is absolutely impossible for anything to pass the event horizon and come out again without breaking the laws of physics as we know them without getting into quantum effects like Hawking radiation.

[Seret]

Point is, time travel might very well be within realms of physical possibility

AIUI forwards is definitely on the cards, backwards is more iffy.