question stated in title.
Four that we know of for sure: three spatial and one for time.
It takes four numbers to completely specify a place and a time. For example, "three meters above the earth's surface, at zero degrees longitude and forty-five degrees latitude, at three seconds past midnight"
In our expanding universe, fixed spatial ordinates do not exist. This greatly complicates defining spatial locations. You could choose an arbitrary ordinate, like the center of earth, but, that is merely a local and temporary convenience. You could define an ordinate using more 'durable' objects, like supermassive black holes at the center of galaxies, but, measurement error would be an issue. Extra dimensions do not offer a solution to this dilemma.
In super string theory, there are predicted to be 10 dimensions. In string theory there are predicted to be approximately 26.
Obviously, these are just theories. Do not rely on this answer.
In general when people talk about spacetime, they consider the 4dimensional spacetime (1 time-3 spatial dimensions). Exceptions are stated beforehand. In general things can also work for any number of spatial dimensions, eg you can look for Kaluza-Klein theories which have 1 time and 4 spatial dimensions...
To the statement of Wild about strings and superstrings- some theories are able to predict the number of dimensions in order to be selfconsistent... you can have a 26 dim string theory (bosonic strings) which are actually not physical since they don't have fermions, or you can have 10 or 11 dimensions in superstring theories which consider the existence of fermions and could be more physical.
The next step is the worst... The extra spatial dimensions should be curled up/compactified so that you can't see them in practice (we only see 3 spatial dimensions). Considering I guess only gravity, the estimate is that they should be smaller than some micrometers (I guess less 3μm).
I think it's fair to say we don't know. Some theories suggest there might be more than four but we haven't found evidence they exist yet.
Some theories suggest the extra dimensions are curled up small and experiments have been done to try and put maximum size limits on those extra dimensions. At best we can say if this or that type of extra dimension exists it must be curled up smaller than some limit.
PS: Got to laugh. A google search for "size limit for extra dimensions" brings up lots of hits related to the size limits of airline carry on luggage.
I agree. Although, 3μm is no where near to invisible, especially with the advancement of the photon microscope. So, not only should we be able to observe string entanglements, we should be able to calculate a certain maximum potential of dimentions. This is assuming that it is not much less than 3μm.
@Wild, as I pointed out the limit is in case you consider only gravity to be able to live in those dimensions... For other interactions, it depends on how deep inside we are able to see so far (around less than 10^-18 m)
Thanks for clearing that up.
@Chris Do you prefer LQG or ST?
This question is nonsense ...
First of all, I don't think preferences matter.
Secondly, I don't know much about Strings (except for some basic stuff) and even more about LQG (nothing). They both are nice.
Finally, I prefer closer to "experimental verification" theories of physics, rather than pure mathematical ones (I'm closer to Glashow's idea on that- however I don't degrade the string theory, but see it as a toy... if it or LQG predict fine testable results so be it!). But that's a matter of "IMO".
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