I came up with this line somewhere:  To properly experience $n$ dimensions the retina of the organism should be at least of $n-1$ dimensions. And human eye has $2$ dimensional retina, so we can experience at most 3 dimensions properly.  Now my question is:  Do more than 3 dimensions exist?  What is the proof that 'there exist only 3' or 'more dimensions do exist'?
46252
As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist.  Is there any direct or indirect evidence supporting a fourth dimension?
101936
As a first approximation, I don't see how a wavelength of less than 2  could exist. The question is: Are there any other limits that would come into play before that?   For example:   Would the energy density cause the photon to turn into a black hole or something like that? Would the energy of the photon exceed the total mass+energy of the universe?
118705
I would like to understand how Physicists think of space-time in the context of String Theory. I understand that there are $3$ large space dimensions, a time dimension, and $6$ or $7$ (or $22$) extra dimensions, and all these dimensions need to fit together in a way such that the extra dimensions are compactified (with a Calabi-Yau or $G_2$ structure).   My question, however is not about the possible $10$, $11$ or $26$ dimensional manifolds that may be possible, but about whether string theorists consider space-time as somehow quantized (or discrete), or rather as a continuous manifold, or are both options possible? In other words, can strings move continuously through space, or are there a discrete set of locations where strings can be, and does string theory rule out one of the options?  How about the same question in loop quantum gravity (LQG)? Should I think of the spin networks in LQG as describing a discrete space-time?  Thanks for your insight, or any references you may be able to provide!
123553
If complex numbers are in some sense 2 dimensional numbers, would it be useful or logical to extend the complex number system to a system of 3-dimensional or even n-dimensional numbers? If this does not make sense in general, why does it make sense only to extend from the 1st dimension to the 2nd dimension? What is special about 2-dimensional numbers that they are needed but n-dimensional numbers are not? I know that we have $R^k$, which is in some sense a field of $k$ dimensional numbers, but that is very different from the way in which complex numbers are constructed. So my question is could the complex numbers be extended to a 3rd dimension (or even an nth dimension) in the same way that the real numbers are extended to the complex numbers, in which the properties of complex numbers are preserved as a subset of this higher dimensional space?
48662
I have some questions with string theory:   Why is it that there is exactly 4 large spacetime dimensions while the rest remain small? It is a nonlocal QFT. How could that fit in GR?
65559
I keep hearing that universe expands. Since all is relative, the expansion must be relative to something. And since universe is all there is ... You got my point.  The only points of reference are inside the universe itself. Bonds forming, their length measured in wavelengths, etc. Red shifting of light tells us things fly away. So our point of reference is only light. (am I missing something?)  Here is my question. In a thought experiment, would it be valid to say that properties of light are somehow changing around us if we keep the size of the universe constant? If yes, what are the consequences of this line of thought? Would it give us any additional insight into what's going on?
45471
Is there any scientific experiment that can lead us to conclude we live in 3 spatial dimensions without the premise of the conception of limited dimensions?  Thank you all who helped in the improvement of this question (which was not clear at first).   EDIT:  I know that this can be a little philosophical, but it is also a scientific question.  Let's consider the scenario where the mankind was not ever able to see.  Let's also consider that this limitation could be surpassed thus not limiting us to reach a scientific and technological knowledge "similar" to what we have today.  Would this civilization of blind people reach the conclusion that they are living in a 3D spatial world?  Is the sense of touch enough to reach that conclusion? Is there any scientific experiment that can lead us to that conclusion without the premise of the conception of limited dimensions?  Would it be easier, harder, or just different to reach a conclusion predicted by the M-Theory? (please do not focus only on this last question)
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I answered a question here with a quote with the following quote from Cosmologist George Ellis.     “Similar claims [about a multiverse] have been made since antiquity by many cultures. What is new is the assertion that the   multiverse is a scientific theory, with all that implies about being   mathematically rigorous and experimentally testable. I am skeptical   about this claim. I do not believe the existence of those other   universes has been proved—or ever could be. Proponents of the   multiverse, as well as greatly enlarging our conception of physical   reality, are implicitly redefining what is meant by ‘science.’”—pg 39      “For a cosmologist, the basic problem with all multiverse proposals is the presence of a cosmic visual horizon. The horizon is   the limit to how far away we can see, because signals traveling toward   us at the speed of light (which is finite) have not had time since the   beginning of the universe to reach us from farther out. All the   parallel universes lie outside our horizon and remain beyond our   capacity to see, now or ever, no matter how technology evolves. In   fact, they are to far away to have had any influence on our universe   whatsoever. That is why none of the claims made by multiverse   enthusiasts can be directly substantiated.”—pg 40-41      “A remarkable fact about our universe is that physical constants have just the right values needed to allow for complex structures,   including living things. Steven Weinberg, Martin Rees, Leonard   Susskind and others contend that an exotic multiverse provides a tidy   explanation for this apparent coincidence: if all possible values   occur in a large enough collection of universes, then viable ones for   life will surely be found somewhere. This reasoning has been applied,   in particular, to explanation the density of the dark energy that is   speeding up the expansion of the universe today. I agree that the   multiverse is a possible valid explanation for the value of this   density; arguably, it is the only scientifically based option we have   right now. But we have no hope of testing it observationally.”—pg 42      “All in all, the case for the multiverse is inconclusive. The basic reason is the extreme flexibility of the proposal: it is more a   concept than well-defined theory. Most proposals involve a patchwork   of different ideas rather than a coherent whole. The basic mechanism   for eternal inflation does not itself cause physics to be different in   each domain in a multiverse; for that, it needs to be coupled to   another speculative theory. Although they can be fitted together,   there is nothing inevitable about it. … Nothing is wrong with   scientifically based philosophical speculation, which is what   multiverse proposals are. But we should name it for what it is.”—pg 43   Now with this in mind if these theories cannot be independently verified should their truth not lie in  method outside physics or what is also known as meta physics?
28943
I read that the cross product can't be generalized to $\mathbb R^n$. Then I found that in $n=7$ there is a Cross product:   Why is it not possible to define a cross product for other dimensions $ \ge 4$?
89315
Since the  makes a statement about domains defined in terms of real numbers, it would appear to invalidate statements about nature that we derived by applying real analysis. My reasoning is this:  If you can "duplicate" an abstract 3-dimensional ball defined, in the usual way, using the domain of real numbers, then clearly the domain of real numbers must be unsuited to describing physical objects (for instance The Earth), because duplicating them would double their mass (and thereby energy). But we use real numbers to reason about nature and derive new laws (or basic results) all the time in physics.  In the same way as we could integrate over the earth's volume to determine its mass from its density (for instance), we could apply the Banach-Tarski theorem to show that we could generate as many earths as we liked, right?  Does this mean that the mathematical foundation of physics is flawed? (I hope this question is not too provocative!)
98991
Is it a coincidence that there are four fundamental forces and four spacetime dimensions ? Does a universe with three spacetime dimension contain four fundamental forces? Can magnetism  be realized in three dimensional spacetime?  Edit 1: Thanks alot for the answer. I'm a first year undergrad student so this may seem naive. If there is a symmetry that mixes spacetime symmetries and internal symmetries of the theory (e.g. gauge symmetry) then there might be ways that spacetime geometry have effects on the particle spectrum and interactions of the theory so you can describe things in geometrical manner . The mechanisms that lead to the structure of spacetime may explain why there are four forces.
104318
I am studying how animals (including the human beings) can perceive distances thanks to their eyes and their ears. I am focusing on the fact that they always go in pairs: two eyes, two ears, etc.  About the sight, I think our eyes use the parallax. But is this enough? Is this the only way we can perceive distances with them?  About the sounds, I think it is merely by interferometry, but I am not convinced, because the distances between our ears and the wavelength are not always comparable to one another.  What do you think about it? Thanks in advance,  Isaac
2574
The following image serves to aid the reader in understanding the "privileged character" of $3+1$-spacetime.    The wikipedia article on , and the  "The priveleged character of $3+1$-dimensional spacetime" in particular, made me think a bit about the possibility that we might live in a non-integer amount of spatial and/or time dimensions.   The notion of attaching a non-negative real number to a metric space has at least mathematically already been described by such concepts as "" and "".   This may sound silly/ignorant/absurd to professional practicing theoretical physicists. To me (a layman), however, it doesn't sound much stranger than the idea of wrapping up six extra dimensions (which is, from what I understand, considered to be a serious possibility by those who study $10$-dimensional String Theory) into intricate shapes called "Calabi-Yau Manifolds".   Has any research on $(a +b)$-dimensional spacetime (where $a,b \in \mathbb{R}_{\geq 0} $) ever been done? If so, what where the findings? If not, why not?
84836
Could any one just tell me a sketch of the proof of the followings?  $1$. If $n&gt;1$, does every linear transformation on $\mathbb{R}^n$ have an invariant subspaces of dimension $2$?  $2$ Is there a vector space $V$ and a linear transformation $T$ on $V$ such that it has exactly $3$ invariant subspace?  Thank you!
24412
The question is the well-known      If there are so many/infinite stars, in every direction, why is it dark at night? Where goes all the light we don't see?    Discussing with a friend we found different answers.   The first (my friend's answer) is that given the fact that in a finite amount of time (in this case, the age of the universe), light can travel only a certain, finite, distance, we cannot see, if they actually exist, stars farther than such distance (about 13 billions of years, I guess). Then he states (or better, I got him notice he implicitly does this)  that within this radius there aren't enough stars to fill the night sky, and that's why we have darkness without sun's light.   The second answer (mine, or anyway the one I heard from a minutephysics YouTube video) is that despite of the big size of the observable universe, cosmological expansion red shifts most of the light out of the visible radiation range, so that the majority of light can't be seen by our eyes at night, while if we use, for example, an infrared camera, we should see a brighter sky, and lenghtening more and more the wavelength at which we observe the sky, we come to the uniform background radiation.  So my question is, what is the right answer? Is it one of the above-mentioned or even a third one?  EDIT: I've seen both answer may be acceptable, but what is the main contributing phenomenon?
61577
I don't have any idea of general relativity but intend to learn. Is it a good idea to study general relativity in two dimensions (time and single spatial dimension) in the begining to get good idea on the subject? If it is, then please give some references for such a treatment.
105555
Just watched the 'How Big is the Universe?' TV program and it indicated that the universe is believed to be infinite in size. They used an approach involving measuring the internal angles of triangles. Or something like that anyway.  But hang on, the Universe has a known starting time and size followed by a finite time expanding at a finite speed. So surely, by definition, it cannot be infinite? I can accept it is honking big but by definition it cannot be infinite. Are they misleading me?