Dear Sofia,

How many dimensions has the Universe? Facetiously I would answer "How many would you like?" Or cynically "Enough". "Dimensions" are not physical entities but are mathematical devices that we invented to organize our interactive experience with our surroundings. We invented "dimensions" and use them to locate "events" in time and space. There are the unlimited dimensions associated with the p's and q's of configuration space in physics and there are the infinite dimensional Hilbert spaces of quantum mechanics. There are as many dimensions as are needed to solve whatever be the problem at hand.

Dear Dwight,

Thanks for your answer. However, it does not seem to me that " "Dimensions" are not physical entities but are mathematical devices that we invented ". The fact that

(1) (ds)2 = (dx0)2 - (dx1)2 - (dx2)2 - (dx3)2 = const.,

shows that dx0, . . . , dx3 , fit a universal law.

We cannot add an additional dimension as you say, " How many would you like? ". An additional dimension, x4, if correct, would render the relation (1) incorrect, i.e. we should have

(2) (ds)2 = (dx0)2 - (dx1)2 - (dx2)2 - (dx3)2 - q(dx4)2 = const.

(where q = either +1 or -1). Also, there should exist transformations from x0, x1, x2, x3, x4, to x0', x1', x2', x3', x4', which would preserve the constant in (2).

As to QM, the bases in the quantum formalism are not in the physical space. In relativity we speak of physical dimensions - i.e. directly and precisely measurable.

I repeat again the essence of my question: it seems to me that for a worm-hole to be possible the physical space should have at least one more dimension, i.e. the 4D space in (1) should in fact be imbedded in at least a 5D space, completely physical.

With kind regards

Dear Sofia,

If, instead of thinking about the surface of the sphere as a 2D structure, we see it as a 3D structure with a constraint (r constant), digging a hole through the sphere would be a change on this constraint.

Thus, we could think of the whormhole as a change of constraint in our 4D space.

Dear Marcos,

I don't understand what you say. For being able to dig a worm-hole through the sphere, the space HAS TO BE 3D, NOT 2D. As long as you are on the sphere, the geodesics are curved. If you want a shorter geodesic - a worm-hole - you need a shorter geodesic. That needs i.e. the sphere has to be imbedded in a higher dimension space, 3D in this case.

So, I don't understand the issue with changing of the the constant. Once you admit that the 2D surface is imbedded in a 3D space, it's obvious that you can get a shorter geodesic. So, what gives the fact that the worm-hole changes the sphere from being perfect, to a sphere with a tunnel through it?

"we could think of the whormhole as a change of constraint in our 4D space"

How so? In the case with the sphere the formula r = const is in the 3D space not in the 2D. For the 4D space, a worm-hole is a change of the constraint imposed in the 5D space not in the 4D.

(Can you tell me at which stage are you with your M.Sc.? Did you choose a topic already? I hope that you'd choose a very interesting one.)

Dear Sofia,

The idea of worn hole is came from Einstein Rosen bridge, well this is true that general relativity only concern with 4 dimensions. Dimensions are the entities which allows us to measure its existence. Going through a worm hole will let you pass the time. So if you will take N dimensions of space and 1 dimension of time, and then you will solve it. It will only converge into 3 dimensions of space and 1 dimension of time because the only relevant factor here is time. Though normalisation of tensors in N dimension is very complex. And why N dimensions of space will decompose into 3 dimensions is because when you will set the boundary conditions for any tensor or vector to move through the worm hole, you will define it with the help of general relativity. Otherwise if you will use quantum field theory, you will end up making N dimensions in M universes.

That's why we use 4D for calculating worm hole problem

Dear Shubham,

it converge in 3 dimensions of space and 1 dimension of time, but does it presuppose that our 4D-spacetime is contained in a "bulk" with more then 4 dimensions ?

Dear Shubham,

" if you will take N dimensions of space and 1 dimension of time, and then you will solve it. It will only converge into 3 dimensions of space and 1 dimension of time because the only relevant factor here is time."

Can you prove this "convergence"?

Moreover, which are those space-dimensions that you take? Please read again my formula (1) in the question:

(1) (ds)2 = (dx0)2 - (dx1)2 - (dx2)2 - (dx3)2 - q(dx4)2 = const.

Any additional dimension that you take, let's name it Q, has to be a physical one. It has to mix up with the other 4 under some 5D Lorentz-type transformation, i.e. time and space should be able to transform into Q.

Which physical quantity do you suggest that may be this Q?

Dear Sofia,

I am going to maintain my point of view that we invent the means to describe the Universe as we perceive it to be. Our point of view approximates the likely much larger entity the constitutes the Universe in its entirety of which we have only partial knowledge which we are trying to piece together using our descriptive and analytic tools. We arrive at many enigmas like the four fundamental forces that we devised to fit our observations. Then there is antimatter, dark matter, dark energy, etc. that befuddle us and to date defy incorporation into our invention of what we initially called "reality" that has become a beast of larger scope than our intellect developed to deal with - survival amongst predators, environment and each other. Our, do I dare say, "primitive" intellect has led us to contemplate a larger picture using the mental tools we had at hand that may be inadequate to the grand task in which we employ them. We introduced dimensions to describe what we perceived in our environment when we moved about in it - forwards, backwards, up, down and sideways. But along came Minkowski and Einstein and their "fictitious" four-dimensional spaces that may be more truth than "invented" fiction. We must be careful not to read too much in our "inventions" as being any kind of "absolute" reality but, on the other hand, accept that what we “invent” conveys a message but not necessarily “truth”.

Dear Dwight,

The equation of constant relativistic interval (ds)2 in 4D is not fictitious, it is confirmed by experiment.

"We must be careful not to read too much in our "inventions" as being any kind of "absolute" reality but, on the other hand, accept that what we “invent” conveys a message but not necessarily “truth”. "

I don't understand you, the electricity you use at home is not real? The GPS you use when traveling, is not real? So, which "message"?

My question was whether space and time may transform into a 5th physical quantity, as would require the formula (1) in my question. (To tell you more explicitly, I see in Internet all sort of reports about queer time-anomalies happening in the presence of very strong electromagnetic fields. It's plenty of such things. Of course, these stories may be cheep fictions for making sensation, but may as well be true facts. It's very late in the night - bed-time - otherwise I would get some more into details.)

There are four known dimensions -- the three dimensions of space, and the spacelike dimension of time, as described by Einstein. There are theories (e.g., string theory) that are trying to solve questions that may have no answers that propose that there are a very large number of dimensions that are so small that we can't notice them, but the mathematicians and cosmologists working on them can't agree what the best number of dimensions to try might be (usually around a dozen, counting the four we know exist, but there is no universal agreement about that).

As to the other part of this question (I am not attempting to answer the entire discussion, despite the reference to it at the start of the thread), wormholes do not and cannot exist. In the earliest days of mathematical theories studying black holes, various assumptions were made to simplify the math, which led to perfectly symmetrical models of black holes. In those perfectly symmetrical models, it was conceivable (though unlikely) that things falling into a black hole might be able to avoid falling into its singularity, and perhaps even exit through the supersymmetrical "other" side of the hole, producing a "white hole" there, and a "wormhole" between the two sides. However, real black holes are not like the super-symmetric objects used in those early theories, and when you get rid of any of the assumptions that produced those super-symmetric theories, the symmetry disappears and anything that falls into a black hole ends up at the singularity and stays there for the rest of eternity. And with that, both white holes and wormholes disappear into the mists of history.

Dear Alexander,

What do you think how many dimensions are required to measure the existence of Cube. The answer is 3, well now think how many dimensions are required for the calculating the gravitational field around the Earth. Well the answer is 4 dimensions. Now think how many dimensions are required for measuring the existence of singularity in the black hole. Well, we don't know yet. It can be zero or can be infinite.

Dear Sofia,

General relativity already converges those dimensions in 3 space dimensions and 1 time dimension.

Your formula (1) does make sense like the sphere has no end or no starting point but worm hole has starting point and endpoint, even though in 3 & 2 dimensions both points appears to be the same. I am not so sure because dark energy does provide the opening through the continuum of black hole if it is spinning. But if your equations is even 20% correct then that Q is the path of other universe through that hole, though it mean there is no wormhole but a passage to other universe.

Dear Shubham,

Thanks for your reply

... and if is the time to have more dimensions, instead of the classical theory that wants it one-dimensional? ... could have more hidden dimensions, including some negative ones in which the past time falls

perhaps journeys back in time are physically impossible because of these negative dimensions (in which the past time falls) that can not be explored by any "object" that has a positive dimension (> = 0)

According to my thesis a universe can only have one time dimension. If it has more dimensions than we wouldn't be able to know if our universe is expanding or not.

I do not know ... I am not a physicist and I can not express a technical opinion about it, but there are many theories that associate a multidimensional nature with time ... for example, Professor Itzhak Bars does research in two-time physics

I know about multiple time dimensions but according to my thesis there can be one dimension in every universe.

Dear Sofia et al

I believe that Einstein himself referred to his four-dimensional space as being "fictitious". The interval ds2 = c2t2 - dx2 - dy2 - dz2 is applicable in the domains of applicability of STR and GTR but is it not possible that these are but approximations to a larger domain just as Newtonian physics is an approximation to the larger domain of STR? Let us not box ourselves in but always try to think outside the box and expand our point of view which is our means of probing "reality" beyond the local environment that our intellect evolved to deal with.

Do we discover or invent our conception of the Universe? A little bit of both. We discover the phenomena but invent the means to describe and represent them, mostly with the mathematical tools available to us. The tools are not reality and ds2 is not reality but it works as a representation of that part of "reality" where it is applicable.

Dear Courtney Seligman

Thanks for your beautiful and illuminating answer. You see, my question stems from the dream of the humankind to reach distant stars.It is hard to accept that it is impossible. As our Sun is growing older, reaching other places to live for the humankind is a necessity, not only matter of curiosity. So, we try all sort of means to make it more feasible. As I see your skills, would you though visit also my other question

https://www.researchgate.net/post/What_happens_with_the_proper_time_in_a_curved_space_How_it_is_influenced_by_presence_of_fields_of_forces

With kind regards,

Sofia

To those that put the problem why time has only one dimension,

my personal answer is that OUR UNIVERSE IS A DYNAMICAL ONE, i.e. changes occur. Time is needed for measuring CHANGE. If one looks at a star and sees it at a position P, looking at the star again one will find it at a position P'. The longer is the distance |P - P'| the longer is the TIME INTERVAL between the two observations. We define TIME as measure of a change. In fact, for being able to compare the rate of change of different processes, we use ONE SINGLE CONCEPT OF TIME for any type of change. This is why time has only one dimension.

Dear Sofia,

You know that water has three phases: steam, liquid and ice. Matter has three phases also: Pre-matter, electromagnetic field and substance. Black Hole is the convertor of phases. Quant of substance - neutrino - is the toroid vortex of field. Quant of field - graviton - is the toroid vortex of Pre-matter. Quant of Prematter is sphere. Collapsed dimensions of string theory are directed deep into matter and not wide.

In general, the bodies of the macrocosm are determined by ten dimensions — four basic and six additional rolled dimensions:

- spatial coordinates and time — 4;

- toroidal neutrinos — 2;

- toroidal gravitons of the electromagnetic field — 2;

- spherical branes of Pre-matter — 2.

Please look at my picture and read "Electromagnetic Gravity. Part 2".

Yours

Valeriy Pakulin

Dear Valeriy,

How do you write the relativistic interval in your 10-dimensional space? In the 4D space we write it as

(1) (ds)2 = (dx0)2 - (dx1)2 - (dx2)2 - (dx3)2,

Note that it contains only 4 terms, and that (ds)2 is a constant under a Lorentz transformation. In your 10 D how would it look like, and under which transformations is it constant?

Best regards,

Sofia

Dear Sofia,

I see that You have not time to look at my book again. The quanta of elctromagnetic field - gravitons - move with light speed. There is Yang-Mills equation in string theory. It discribes the moving quanta Pre-matter with macro view of point. The interval is for BODIES. Field and Pre-matter is our external environment. We only begin to think about it.

Dear Valeriy,

Which chapter in your book speaks about worm-holes? Please notice that my question is about the possibility of worm-holes. I look at a book or any other material, if it addresses my problem

Dear Sofia,

I say You good bye.I will not bother You more.

I do not do fantasies and fairy tales.

Best

VP

Dear Valeriy,

It's not in my nature to let somebody go from me sad and disappointed. Let me explain: my domain of competence in the non-relativistic QM. My knowledge in this domain is very deep - of course you may consider this statement of mine as lack of modesty. But, I don't lie, it is indeed very deep. Unfortunately, it went at the expense of other fascinating domains as QFT and general relativity.

The consequence is that I can't read your book. There are additional people that ask me to read their books and I have to decline, with regret. The reasons are the same. I am on overdraft of time - I see your picture you are young, while I am old. Next, I don't have enough competence for judging a QFT theory or a theory about general relativity, s.t. I stick to the general accepted theories.

Thus, it's not from me that you have to ask your theories be read and discussed. Look in RG for people competent in those domains.

So, you can tell me good-bye, while I have no reason to tell you good-bye. I just explained my limitations. It is TOO LATE for me to try to get into the depths of QFT and general relativity. I don't have tens of years ahead. This is the cruel truth.

With all the best wishes,

Sofia