The Hubble telescope can see the light from the big bang.My question is if our universe is expanding that would make everything that's in front of our solar system be in the future? And also can Hubble see ahead of our solar system and does the bang big light ends behind our solar system?
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1$\begingroup$ You would do well to do some investigation. Several of your assumptions such as "Hubble can see light from the big bang", are not true. And there is no "in front of our solar system" $\endgroup$– James KCommented Jan 23, 2016 at 12:13
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There are a couple of misunderstandings here. Let's take one at a time:
The Hubble telescope can see the light from the big bang.
The Hubble Space Telescope (HST) doesn't actually see light from the Big Bang. HST has several instruments on board, both for imaging and spectroscopy, but they all operate in the infrared, optical (i.e. "visible to humans"), and ultraviolet wavelength range. When you mention "light from the Bing Bang", I suppose you're thinking of the cosmic microwave background radiation (CMB), which is light emitted 380,000 after Big Bang. This is "the closest" we can get to Big Bang (yet). HST is unable to detect microwaves; instead we have other telescopes for that, the most recently-launched being Planck.
My question is if our universe is expanding that would make everything that's in front of our solar system be in the future?
The expansion of the Universe is one of the most difficult concepts to get one's head around. But firstly, Big Bang wasn't an explosion, hurling matter outwards from a central point in an otherwise empty Universe. Galaxies, on average, don't travel much through space. Rather, they lie relatively still in space, but space itself expands. The distances between galaxies increase all the time, and previously, before galaxies were formed, the distance between atoms and other particles increased. An often-used analogy — which you shouldn't take too far — is a balloon with dots painted on. The dots are fixed on its surface, and when you blow it up, the distances between the dots increase despite the dots still being fixed.
Secondly, your question seems to confuse space and time. Even if the expansion were an explosion, we would travel through space, and yes, you could say that we travel through time as well, but saying that the future is "everything in front of our Solar system" doesn't really make sense (to me, at least). What's in front of you when you travel through space is just more space; you can look at it before you get there, but that doesn't mean you look into the future (in fact you look at the past, since the light you detect with your eyes has spent some time traveling toward you).
And also can Hubble see ahead of our solar system
It depends what you mean by "ahead". It can definitely see things outside the Solar system. The Solar system consists of one star and it satellites (planets, comets, asteroids, etc.) out of the few hundred billions that make up the galaxy we call the Milky Way. Our Galaxy is itself only one out of at least some hundred billion — and quite possibly infinitely many — galaxies that float around in our Universe. And yes, HST can see many of these. But if by "ahead" you mean "into the future", then the answer is no.
and does the bang big light ends behind our solar system?
As mentioned above, the Big Bang light — or the CMB — was emitted shortly after Big Bang. That means that it has been traveling for 13.8 billion years through space. Light travels one lightyear per year, but since the Universe is expanding, the distance that the CMB has traveled is more than 13.8 billion lightyears; in fact it's some 46 billion lighyears. This is the most distant "thing" we can see, way, way beyond the Solar system which for comparion is of the order of one lightyear large.
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$\begingroup$ I am tempted to edit your answer to remove the "— and quite possibly infinitely many —". Your answer is great, but I think that this little excerpt is problematic and should be removed. If we would have infinitely many galaxies out there, then we would need infinite space to accomodate them, and since the space expands at a finite speed since the Big Bang, the space has a finite size and thus a finite number of galaxies. Or perhaps, I just failed to understand what you meant with that. $\endgroup$ Commented Jan 24, 2016 at 20:00
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$\begingroup$ @VictorStafusa: You're right that an infinite number of galaxies would need an infinite space to accomodate them, but nothing disallows an infinite space; in fact observations seem to indicate that our Universe happens to be infinite (since $\Omega_\mathrm{tot}$ seems to be unity). I know this possibility can be hard to accept, but it is nonetheless the case. If indeed the Universe is infinite, then it was "born" infinite. And if it had been born finite, it would stay finite. $\endgroup$– pelaCommented Jan 25, 2016 at 7:34
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$\begingroup$ I fail to see how a theory about an infinite space and an infinite number of galaxies could be compatible with a theory of space expanding at a finite velocity (likely lightspeed) in a finitely distant past out from a singular point. Also, I fail to see how $\Omega_{\text{tot}}$ being a unity is compatible with a Big Bang theory. You could argue that the Big Bang theory could be false, but this would defeat the entire point of your answer. $\endgroup$ Commented Jan 25, 2016 at 7:47
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$\begingroup$ You seem to have an inaccurate, but very common, understanding of Big Bang and the expansion of space. Big Bang wasn't an explosion of matter from a central point. Big Bang was the creation of space, finite or infinite, and the subsequent expansion of this finite or infinite space. This expansion makes the distance between particles increase at rate that is $\sim$proportional to their distance such that, below a certain distance, particles recede from one another at $v<c$, and above this distance $v>c$. $\endgroup$– pelaCommented Jan 25, 2016 at 8:32
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$\begingroup$ Also, $\Omega_\mathrm{tot}=1$ is completely compatible with Big Bang and in fact is the (currently) favored value. As I said, I admit the the notion of a universe that starts out as infinite is difficult to get one's head around. I think one of the reasons is that it is best described mathematically, since physically we tend to picture this for ourselves and create 2D analogies, which are bound to fail. $\endgroup$– pelaCommented Jan 25, 2016 at 8:35