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This didn't mention the expansion of space at all. The universe may be infinite in size but we'll never see the light of stars that exist so far from us that they are beyond the distance at which space expands faster than light can travel. That's why we have a dark sky and it will just get darker as more things we see now eventually expand beyond that barrier. One suggested end to the universe is the Big Rip in which all matter eventually separates in this way such that the distance between all matter is infinite:

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

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Yep. Currently, some galaxies are traveling away from us faster than light.

http://curious.astro.cornell.edu/about-us/104-the-universe/c...

That blew my mind! So now it turns out Einstein was wrong??

We can't get particle to seriously travel faster than light and there is entire galaxy going faster??

I don't think it means Einstein was wrong or that one galaxy is moving "faster than the speed of light". It means in respect to each other two galaxies are moving faster than the speed of light. In other words each of two galaxies is going faster than half the speed of light, one of them being us (in relation to the other observed Galaxy).

That's extremeley not true, and the whole point of Relatively is to explain why.

I've also had a long-time question around this point. I've asked various university physics professors, and they all stutter and disagree (which means either we really don't know or I'm going to all the wrong universities). The underlying question is: When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?

If it's photons emitting from flashlights pointed in opposite directions relative to each other, then are they compressing space as they travel so as not to exceed the speed of light? Or even massive particles accelerated to over half the speed of light at different times around an ellipse so there is a moment when their opposite directions make one traveling at greater than the speed of light relative to the other? (Or even particle accelerators on two different planets already expanding away from each other - does this just mean that space is really twisting and turning all the time to make sure no particle ever exceeds the speed of light relative to any other particle?)

It has been my understanding - and appreciation at Einstein's unbelievable insight and brilliance - that relativity is truly relative because there really isn't any such thing as an arbitrary particle or space that all other motions are measured from. But if this is true, does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?

I'm sure there are great answers to this, but I've always wanted a definitive one. Anyone have any comments on this?

"When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?"

It's a theory postulating that a particle can't travel faster than the speed of light in relationship to a particle that isn't moving. In practice all particles are moving in relation to some other particle thus it's not something you can visibly measure or see. At least that is the way I always viewed it.

does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?

IANAP, but I've never read that space twists to prevent the SOL from being exceeded. I think you're thinking of time and mass. It would require an infinite amount of time or infinite acceleration to for something to accelerate to the speed of light relative to something else.

Space is twisted by the presence of matter, and we call that gravity.

If it's photons emitting from flashlights pointed in opposite directions relative to each other, then are they compressing space as they travel so as not to exceed the speed of light

No. My understanding is that from the point of view of a photon time is completely stopped. Nothing moves relative to it because of this. Since nothing moves relative to it, nothing is exceeding the speed of light relative to it.

> The underlying question is: When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?

It's based on the observation of two points of references moving a different speeds shining light and the light from each traveling at the same speed. So the speed of light is measured relative to other light. The speed of light is constant, and it is so regardless of point of reference. Flashlights pointed in opposite directions has nothing to do with the speed of light. The light is traveling at the same speed in opposite directions.

> When we say in general relativity that particles can't travel faster than light, what is that speed measured relative to?

Relative to a local inertial frame, i.e., relative to an inertial observer (i.e., an observer in free fall, feeling no force) who is at the same spatial location as the particle whose speed is being measured. That is the only context in which the concept of "relative velocity", as it appears in the "can't travel faster than light" condition, has any physical meaning.

All of your suggested examples attempt to compare "relative velocity" between objects that are not at the same spatial location. That has no physical meaning in GR.

It's perhaps not altogether useful to regard c as a speed. Or rather you should redefine your idea of speed. It's a universal constant relating matter to spacetime. Time is a length measurement, and you're already moving at c in that dimension. If you start accelerating then you are trading time velocity for spacial velocity, so as you approach c your movement through time approaches zero.

> does that really mean that space is really so constantly twisting and turning that SOL can't be exceeded?

The speed of light stays the same and both time and space twist and turn around it. It's weird, but having a preferred reference frame would be just as weird. c is a dimensionless constant, and light happens to travel at that speed because it has no rest mass.

Think of it this way: c isn't a speed limit, it's the only speed that anything can travel at. Specifically, time is only one component of four-dimensional spacetime. If you move in x, y, and/or z, the vector length of that spatial movement has to come out of your velocity in t.

So it's not that you can't travel at c meters per second; it's that if you do, you'll zero out your velocity in the "seconds" component.

To cite an example from one of Neal DeGrasse Tyson's lectures, that's one of the funky things about photons from the most distant stars: they don't experience the passage of time at all from their own point of view. They arrive at our eyes/telescopes/radios as soon as they're emitted. Meanwhile, their velocity is limited to c from our point of view. The same thing would presumably happen to you if you could travel at c... but there would be other inconvenient effects in that case, such as an infinite increase in mass.

I found this [1] PBS video useful.

[1] https://www.youtube.com/watch?v=msVuCEs8Ydo

The galaxy isn't traveling faster than c away from us, but space is being created in between. So, nothing is actually accelerating, there is no problem, Einstein is still right.

In fact, space is being created everywhere, including yourself and the computer screen. However the amount is so small that you don't notice and local forces nullify the change anyway. With large distances, this amount accumulates, and overwhelms the force of gravity and starts to create the apparent acceleration of distant galaxies away from us. Further explanation from paulddraper: https://news.ycombinator.com/item?id=11068125

Yes, this makes sense. If this is the case though, then aren't there some obvious problems with how we think of dimensions (at least the first three or four anyway)?

It seems like creating space to fill the "voids" between particles moving at-what-would-be-faster than the speed of light is like a tesseract for whatever matter is in that rapidly created/expanding space. Unless that space is only accessible to the particles creating it by their relative motion (which still gives us problems with our ideas of dimensions)?

This isn't really correct. Expansion of space is not the same thing as accelerated expansion of space. Aaccelerated expansion is indeed due to something "pushing" objects apart--that something is called "dark energy". But expansion itself, apart from the effects of dark energy, does not push on anything; it doesn't exert any force that moves objects apart or works against gravity. So thinking of ordinary expansion (apart from accelerated expansion) as "creating space" in between objects isn't really correct. It's unfortunate that so many pop science treatments use this way of speaking, since it leads to the incorrect inference I've just described.

The space is expanding and its expansion rate is accelerating. Dark energy is not pushing objects apart, it is causing the acceleration of expansion of space.

What you said isn't even pop science, it is blatantly wrong.

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

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

And the money quote:

It is called "dark" because it is not interacting with normal matter, but only with the space time structure.

from http://physics.stackexchange.com/a/206217

> What you said isn't even pop science

What I said was an attempt to explain how the basic model cosmologists use works in layman's terms. It wasn't intended to be "pop science" or even "real science"; that would be building the model, not trying to explain how it works.

The references you give are not "real science" either. Try looking in a cosmology textbook or a peer-reviewed paper. Or, even better, work out the science for yourself instead of arguing from authority.

> The galaxy isn't traveling faster than c away from us, but space is being created in between.

That's an intriguing way of phrasing, never thought of it this way. I'm aware that space is expanding, so space must indeed being created in-between.

I'm guessing this space has to contain no energy at all, so it must be made of absolutely nothing, right?

The galaxies themselves are not moving faster than the speed of light, their relative distances are because of the rate of the expansion of the universe.

> That blew my mind! So now it turns out Einstein was wrong??

No, because the light speed limit only applies to things moving through space, not to space itself, which can and does expand faster than light speed.

> We can't get particle to seriously travel faster than light and there is entire galaxy going faster??

The galaxy isn't traveling through space at faster than light speed, it's being conveyed along with the space that surrounds it at a speed that exceeds light-speed from the perspective of some distant location in space.

The expansion of the universe also leads to red shift of the light from (nearly) all the stars that we'd otherwise expect to see. This means that the frequency of their light is moved away from the range that our eyes can see.

My understanding of the expansion of space is that the expansion doesn't occur locally, but is only noticeable over large distances. is that incorrect?

It occurs everywhere, proportionally. The effect isn't great enough to notice unless you are looking at light-years.

Also, gravity and electromagnetism increase at close proximity, so on less-than-cosmic scales, they overcome the minute amount of spatial expansion.

therefore the statement " all matter eventually separates in this way" , strictly speaking, seems false since gravity and electromagnetism overcome expansion at local levels.

Yeah, both are right in context. It's just like saying "gravity doesn't make objects fall at the same speed". It actually does make them fall at the same speed...but if you include other relevant forces, the overall effect is different.

FYI, gravity might eventually overcome spatial expansion on a cosmic scale. But we don't know. https://en.wikipedia.org/wiki/Big_Crunch

I thought the Big Crunch was disproven because we found that the expansion of the Universe is accelerating. Dark Energy wins over Dark Matter...forever.

More likely than not, the Big Crunch will not happen. From Wikipedia:

"Recent experimental evidence (namely the observation of distant supernovae as standard candles, and the well-resolved mapping of the cosmic microwave background) has led to speculation that the expansion of the universe is not being slowed down by gravity but rather accelerating. However, since the nature of the dark energy that is postulated to drive the acceleration is unknown, it is still possible (though not observationally supported as of today) that it might eventually reverse its developmental path and cause a collapse."

It was my understanding that this is true from our perspective in time right now, but the Big Crunch could still be plausible if the universe turns out to be young enough (which it seems like it is) that not all the fusion fuel has been exhausted. Once it is, we'll have big clouds of nuclear waste interspersed between black holes, and perhaps in this environment the Big Crunch could still occur.

I think another question for the Big Crunch is what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang? For example, the sun compresses hydrogen to produce helium and release massive energy. Black holes are undoubtedly compressing helium enough to make Beryllium, but this doesn't seem to release any energy that can escape the gravity that created the pressure required in the first place. So for the Big Crunch - Big Bang cycle to hold up, what type of matter (and how much of it) has be be compressed (and is gravity the only force that's compressing it) to the point where some type of "fusion" reaction produces enough energy to escape the compression forces?

> perhaps in this environment the Big Crunch could still occur.

No, it couldn't. The nuclear waste will still have the same average energy density, on the scale of the universe as a whole, as the unexhausted fusion fuel does now. We know that energy density is too small now to make the universe recollapse, so the same must be true any time in the future.

> what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang?

The Big Bang was not an exothermic fusion reaction. Our current best model is that the Big Bang was caused by a very large energy density being transferred from the inflaton field (the field that drove inflation in the very early universe) to the various fields in the Standard Model of particle physics (electrons, quarks, photons, etc.). This "reheating" created the hot, dense, rapidly expanding state that we refer to as the Big Bang.

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