What Shapes Can We Visualize in the Fourth Dimension?

[theriddler876]

hey, anyone out there care to offer their thoughts on the fourth dimension? as in what would it be, all I have is that a fourth dimensional object would seem like a 3 dimensional object moving down and then disapearing?

 

[selfAdjoint]

I suppose you mean fourth spatial dimension, rather than the Minkowski 3 space, 1 time geometry of relativity. For that, you should inquire on the relativity board.

The best insight into a spatial fourth dimension is to read the delightful classic little book, "Flatland". Almost any library or bookstore should have it. It works on the analogy of an individual who lives in a two dimensional world - his name is "A. Square" - who learns about three dimensions.

Another way to insight would be to look up "tesseract" on a search engine. Aside from hits on Madalyn L'engel's misuse of the term in her children's boooks (avoid her description), you should find many discussions on how to represent simple four dimensional objects in three dimensions, just as we represent three dimensional objects on a flat piece of paper with perspective.

Four dimensions would have two directions that are perpendicular to our three dimensional world. They have been given the names "ana" for four dimensional "up" and "kata" for four dimensional "down" with respect to our space. Of course these are just the Greek words for up and down.

So borrowing a description from Flatland, if a four dimensional sphere were to start anawards of our world and move through it in the kata direction, what we would see, as it intersected our world woild be first a tiny three dimensional sphere (cross section of the four dimensional sphere near its kata pole) which grows in size to a maximum (the "equator" passing through), and then decreases gradually again to its mini size before vanishing, having passed commpletely through our world and out the other side.

 

[Mentat]

You know, I had no idea that the two directions of the fourth spatial dimension had already been named. I once read a science fiction novel called "spaceland", wherein they called the two other directions "vin" and "vout" (for obvious reasons).

 

[selfAdjoint]

Right around the year 1900 there was a little flurry of intellectual interest in "visualizing" the fourth dimension. Books appeared to teach it, or give an illusion of teaching it, and I believe it was they which gave the names ana and kata. At that remote epoch educated people were still expected to know a little classical Greek.

 

[hawaiidude]

as most know, 3 dimensional has an xyz...4 dimension can be a worm hole...a worm hole has a an xyz and time

 

[theriddler876]

all dimensions have time, I dont' think time can be a dimension in itself, and time travel is most likely impossible unless in one direction, and that is forward if we were living in a 2D world we would still have time as a progression, what we did 15 minutes ago it can be plotted in a graph using x and Y coordinates, labeling each graph with a time signature,

 

[John]

You are right. Dimensions must have two directions, which is where the "di-" in di-mension comes from. I think di means, two. People who say time is a dimension, and people who say there are four spatial dimensions are wrong, for the reason you gave, which is that time only moves in one direction.

But string theory says there are ten dimensions. If you are in a 2D world, and you define that world as a group of points, when you lay down the points you must have separation between points. String theory says there is a separation between points: that points are really little strings. So if you take small strings, draw little lines and lay them out on a piece of paper, the most efficient arrangement of three strings is a triangle. If you continue to lay out strings, connecting them all, you continue to make triangles until you construct a space. Now if you travel from point to point, or string to string, you find you can only go in three directions. If we construct a plane out of strings, we can only travel in three directions from the string we are at, to the string next to it. All travel has to be from point to point, or string to string, and that limits travel to only three directions. Each direction back and forth is a dimension in this construction of strings.

If you go from a random point A to a random B, you have to zigzag through the strings. To describe A to B you need an x and y axis. So this 2D space constructed from strings has five dimensions.

In a 3D space constructed from strings, there are ten dimensions.

 

[John]

Here is a diagram. The X's are points that have separation between them. To travel from A to B, it would look like

oooXoooXoooAoooXoooX
oXoooXoooKoooXoooXoo
oooXoooXoooKoooXoooX
oXoooXoooXoooKoooXoo
oooXoooXoooKoooXoooX
oXoooXoooBoooXoooXoo

In the macro world, you would only see travel directly from A to B, but a photon or electron really has to zig zag through an arrangement of strings.

 

[Jeebus]

In 3 dimensions, we all have an intuitive understanding of what length and angle mean, and it is not at all clear how to extend these concepts to higher dimensions.

However, if we introduce coordinates and think about vectors, one can express both length and angle in terms of vector operations, and these operations readily generalize to any number of dimensions.

The formula for the length of a 3-dimensional vector (x,y,z) is also easily obtained: you draw a right-angled triangle whose hypotenuse is the vector (x,y,z) and whose other two sides are (x,y,0) (whose length is x² + y²since it's really just a 2-d vector) and (0,0,z) (whose length is just |z|).


For example, a vector in 4-dimensional space can be given by four coordinates as (x,y,z,w), and its length is defined to be by analogy to the length formula in two and three dimensions.

This, then, gives a definition of what the concept of length means in four and higher dimensions.

The other main geometric concept is that of angle. Again, we have an intuitive understanding of what it means in our 3-dimensional world, and it's not at first clear how to generalize it to higher dimensions.

However, if you apply the law of cosines to the three vectors u, v, and u- v, the angle between u and v satisfies the equation.

 

[John]

What would space be like if it was made of points like a TV screen is made of pixels?

Today, the newest TV cameras form three light rays out of every bright light source, because the light is spilling out along the three lines that the pixels line up in. If you have an old computer screen, not a flat screen, you can look at its pixels and see how they line up in three directions. And of course you can see how, in some places, straight lines are squiggly.

Physical points have to arrange themselves in triangles on a TV screen. I thought, "How can physical points arrange themselves in 3D space?" They would arrange themselves in tetrahedrons. Two tetrahedrons base to base have lines going in seven directions. When you look at a star, you can see rays going in six or seven different directions, just like you see light spilling out in three directions on a TV screen due to the arrangement of pixels. Old cameras had two rays, which is called a lensing effect. New cameras have three rays, which is not due to the lens, but due to the arrangement of pixels. Stars have six or seven rays, which is just what I would expect since I realized the arrangement of points in space line up in seven directions. In 3D space, one ray might be pointing straight at you so you would not see it. If you see a star with five rays, which is rare, the rays are very clearly defined, since two rays are more or less pointing at you, and the other five are very flat and evenly spaced to your line of sight. Sometimes, on big lights you see rays and the lensing effect. And the number of rays changes depending on when you look. Space has an absolute structure, and the Earth is rotating through it. The way to count the rays is to count all the rays on one half of the star or bright light. A bright light in a TV camera has three rays on one half of the light source, and those three rays continue on the other side in the same direction.

I think the rays of a star, and of a light source on a TV screen show us how the multiple dimensions work. They are an arrangement of points that form the minute structure of space. And on a TV screen, certain lines are not straight, but squiggly. From enough distance, they can look straight. Photons have to travel along the points that line up in seven directions, seven lines of dimension. When they go in certain direction, they go very squiggly, which is no problem when you understand that light does not hurtle through space, but is pulled through space from point to point; it can change directions and change back without losing energy; it can be slowed down and regain its speed. So it is pulled along from point to point. They are points arranged in seven directions, seven dimensions since they are the only seven directions that are possible in the smallest structure of space. Photons spill out over those seven dimensions near a bright light source, not due to a lensing effect, but for the same reason there are three rays in a new TV camera from a bright light source. It's a "dimensional effect".

 

[John]

oooRoooXoooXoooXoooXoooRoo
oXoooRoooXoooXoooXoooRoooX
oooXoooRoooXoooXoooRoooXoo
oXoooXoooRoooXoooRoooXoooX
oooXoooXoooRoooRoooXoooXoo
RoooRoooRoooRoooRoooRoooR
oooXoooXoooRoooRoooXoooXoo
oXoooXoooRoooXoooRoooXoooX
oooXoooRoooXoooXoooRoooXoo
oXoooRoooXoooXoooXoooRoooX
oooRoooXoooXoooXoooXoooRoo

Dimensional spillover effect, look for it on a TV screen.

X's are pixels, R's rays

 

[maximus]

according to Flatland (and numerical logic) the fouth spatial dimension would have 16 terminal points and 8 sides.

...just thought i should add...

 

[John]

Logic says something is a straight line, but if the points can have varying degrees of separation, the straight line can curve. If you make a very smooth marble table and call that flat, but look at it through a microscope, it is very rough. The points that make up space are not perfectly orderly, just like nothing else is perfectly orderly.

 

[Rader]

Originally posted by John
The idea that points of space have varying amounts of separation is not contained in logic. Logic says something is a straight line, but if the points can have varying degrees of separation, the straight line can curve. If you make a very smooth marble table and call that flat, but look at it through a microscope, it is very rough. The points that make up space are not perfectly orderly, just like nothing else is perfectly orderly.

If you are looking from the macro to micro or micro to macro there is space between points whether it is logical or not. The atom is a point to us but there is a lot of space between the neuton and its electrons. When the Hubble telescope looks at 1 arc second of the sky where nothing is visisble and thousands of galaxies appear there is most certainly space between the galaxies.
When invisioning dimensions it is geometrically difficult for the human mind to put it togetter. The first second and third are easy to invision because we see them every day. But imagine that there is a limit to small, the plank lenght. From the plank length extends a dimension that leaves each point in 360 degrees outward as a cone to infinity, each time becoming larger. Anywhere on the 360 degree circle is the distance of the plank length or width if you may. Following the plank length to infinity you can observe the universe in all its sizes. I have always called this dimension simply the big small dimension.
Only by reaching the speed of light can you experience this dimension.
From outside the universe an observer would have to view this dimension as an infinite amount of plank length points converting into infinite cones curling back on themselves. It would have to form a solid ball yet from inside the ball there would still have to be space between the plank lenghts. Why is the plank length mathematically the samllest unit possible?

 

[John]

The Bible says, In the beginning, the world (universe) was without form, and the Spirit of God brooded above the waves of the abyss. I did some thinking and realized matter cannot be compressed, but it can easily be pulled apart. I realized by looking at what matter does, the most basic form of matter had to be like water, impossible to compress and easy to pull apart. When I concluded that, I remembered the first line of the Bible, which describes the initial state of the unvierse as a sea. We know this was the universe and not the Earth because, next God created light.

So I had invisioned a sea of matter surrounded by the vacuum. The gods, whose bodies are made of fire, heated up the matter. The "drops" of liquid matter are dispersed throughout space. They are in a perpetual state of expansion with the vacuum pushing inward. The vacuum creates the strong force. Space itself is expanding against the strong force, not gravity. These drops of matter become the points of space. All movement at the particle level can only go from point to point, and the points have to be arranged in a matrix that only allows seven directions. These seven underlying directions are the seven hidden dimensions.

 

[alkaline]

http://tetraspace.alkaline.org

go there for some explanations on the fourth dimension.

 

[John]

The real change comes when you construct a plane or a cubic space with strings. You suddenly realize you can only travel in seven directions in the cubic space, if you only travel along the strings. Since the strings represent points, then you can ONLY travel back and forth in seven directions. These directions become dimensions, but you still have the three classic dimensions. A straight line from point A to point B is not really straight. It has to zigzag through multiple dimensions in the underlying structure.

 

[sol1]

Originally posted by John
You can't come up with any more dimensions than three, in math. Math asumes there are an infinite number of points in any line, plane, or any cubic space. String theory says points are little strings, so a line has a certain number of points.

The real change comes when you construct a plane or a cubic space with strings. You suddenly realize you can only travel in seven directions in the cubic space, if you only travel along the strings. Since the strings represent points, then you can ONLY travel back and forth in seven directions. These directions become dimensions, but you still have the three classic dimensions. A straight line from point A to point B is not really straight. It has to zigzag through multiple dimensions in the underlying structure. When we understand how this structure works, we can manipulate gravity and momentum because they both work due to this underlying structure. Things don't float through space at consistent speeds, but they are pulled along a matrix of underlying dimensions at consistent speeds. My ideas predict that space will be more dense far away from massive bodies. In more dense space things will slow down, because the strings that make space are shorter. When Voyager mysteriously slowed down, after it left the solar system and the vicinity of Saturn, Jupitor, and Uranus or Neptune, I realized my ideas were right, and I started posting on these Internet sites.

I am having dificulty with the zig zagging that you are demonstrating.

http://www.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html

How do you explain your zig zagging here?

Sol

 

[John]

Imagine a small square drawn on a sheet of paper. You are at a point in that box.

Math says there are an infinite number of non-dimensional points in that box. So you can go in an infinite number of directions to a point next to the point you are at. But what if there are only four points in the box?

With only four points in the box, you can only go from the point you are at in three directions. That means the flat box has three dimensions instead of two, because those are the only three directions possible.

Now imagine the universe has a finite number of points. So at the smallest level, just like being in a box with only four points, there are only a limited number of directions. Those limited directions become dimensions.

It is not logical to assume this line ______________ and this line __ both have the same number of points. They are different lengths, yet supposedly, they have the same infinite number of points. If they each have a different number of points, then they each must contain a finite number of points. Lines that we know are two different lengths cannot both contain the same infinite number of points! Therefore, since they must have a finite number of points, in a square or cubic space you can only go in a limited number of directions. The question becomes, how many points can you stack around one point? Draw points on a flat piece of paper. Start from any point and go to a point beside it. Now go from the original point to a different point. Find another point that you can go directly to from the original point. These are three lines of dimension on this plane constructed from points. In cubic space there are seven lines of dimension in a space constructed from points.

 

[Rybo]

Buky Fuller says that the physical Universe is not macro-infinite but micro infinite inas
much-as the rock --.or quark--- potentially is break apartable into infinitly smaller parts.

I think if there can be micro-infinite somthingess then there also must be marco-infinite
somethingess ergo there will exist infinite multi-verses or the infinite bubble-like Universes.

However, i think neither are true in the sense that there is both a micro-quantisizing limit
--i.e. the quantum graviton Planck or sub-planck limit--
and the larger finite macro-physical Universe.

Where does the many varying concepts of geometrical "dimension" and mathematical "powers" fit into these scenarios I've laid out above? I am not sure.

Dicussion of dimension is like 'time' in some ways in that it seem to have so many varying concepts surrounding it as well as some overlap or no overlap that it nearly makes for paradoxes and/or recursive/recycling loops spiraling in or/then out of our ability to make senae of it.

The proof is in the pudding even if the pudding is still only a probaility without causal geomtric visuals to to help explain the deeper nature --i.e triangulated/structr-- of those probalities.

Jabob Bekenstien in his August article "Scieitific American" might argue this by saing thatt our brains percevie a 3-D world which is really only 2-D visual --i.e. screen-like of non-seeable holographic world.

Now that really blows --or compresses-- my mind if his --and Hawkings-- mathamtical black hole studies are correct.

Rybo

 

[John]

I think I have actually come up with a mathematical proof that only infinite is infinite.

This line ____ and this line ___________ are different lengths, but we currently assume they both contain the same infinite number of non dimensional points.

Two lines that we know are different lengths CANNOT contain the same number of points.

String theory says a point is really a small line, for example, I typed four underlines to make the first line, and 11 underlines to make the second. The first contains four small lines, and the second contains 11. The only line that can contain an infinite number of small lines, or strings, is an infinitely long line.

Therefore, if we describe any space that has bondaries, that space must contain a finite number of points. If it contains a finite number of points, then the individual points must be arranged in a pattern within that space. If you have a space with 25 points like the one below, the points have to be arranged in a pattern. If that space were to have 25 million points, they still have to be arranged in a pattern. Then, when you go from one point to any point beside it, you can only go in a limited number of directions.

oooPoooPoooPoooPoooP
oPoooPoooPoooPoooPoo
oooPoooPoooPoooPoooP
oPoooPoooPoooPoooPoo
oooPoooPoooPoooPoooP

If you were to go from the bold P in the center to any point next to it, you can only go back and forth in three directions. If there could be an infinite number of points in this limited space, then you could go in any direction. There has to be a limited number of points in this limited space, and then the points must be arranged in a pattern. You can only go from any point in three directions. Check it out. Try to go in any other direction. You can only go from where you are to any point beside you. All travel is from point to point. You can't go between points, and you can't go around points.

The background on this website, as new screens come up, has many dots in a square pattern. If you are at any dot and you want to go to any dot beside it, you can only go in a limited number of directions (four), even though there are many dots.

The pattern of triangles, not squares, is a more stable pattern and only gives you three directions.

 

[Rybo]

Originally posted by sol1
I am having dificulty with the zig zagging that you are demonstrating.

http://www.vislab.usyd.edu.au/gallery/mathematics/diffeo/diffeo.html

How do you explain your zig zagging here?

Sol

Hello Sol,
Here is quote from the link you gave.

"Aha! It took a full 720 degree rotation to straighten it out again. You may have noticed no strand passed through another strand."

720 is the total number of degrees of the 12 surface angles of a tetrahedron.

Ive attahed an visual of an unusal tetrahedron

Rybo

 

[Rybo]

Originally posted by John
I think I have actually come up with a mathematical proof that only infinite is infinite.

This line ____ and this line ___________ are different lengths, but we currently assume they both contain the same infinite number of non dimensional points.

Two lines that we know are different lengths CANNOT contain the same number of points.

String theory says a point is really a small line, for example, I typed four underlines to make the first line, and 11 underlines to make the second. The first contains four small lines, and the second contains 11. The only line that can contain an infinite number of small lines, or strings, is an infinitely long line.

Therefore, if we describe any space that has bondaries, that space must contain a finite number of points. If it contains a finite number of points, then the individual points must be arranged in a pattern within that space. If you have a space with 25 points like the one below, the points have to be arranged in a pattern. If that space were to have 25 million points, they still have to be arranged in a pattern. Then, when you go from one point to any point beside it, you can only go in a limited number of directions.

oooPoooPoooPoooPoooP
oPoooPoooPoooPoooPoo
oooPoooPoooPoooPoooP
oPoooPoooPoooPoooPoo
oooPoooPoooPoooPoooP

If you were to go from the bold P in the center to any point next to it, you can only go in three directions. If there could be an infinite number of points in this limited space, then you could go in any direction. There has to be a limited number of points in this limited space, and then the points must be arranged in a pattern. You can only go from any point in three directions. Check it out. Try to go in any other direction. You can only go from where you are to any point beside you. All travel is from point to point. You can't go between points, and you can't go around points.

The background on this website, as new screens come up, has many dots in a square pattern. If you are at any dot and you want to go to any dot beside it, you can only go in a limited number of directions (four), even though there are many dots.

The pattern of triangles, not squares, is a more stable pattern and only gives you three directions. In a cubic space the most stable pattern is tetrahedrons. One tetrahedron has lines going in six directions. Two tetrahedrons back to back give you seven directions. An infinite number of tetrahedrons still gives you seven directions. Those are the missing seven dimensions.

Thanks for you viewpoint John,

We assume the two lines have an infinite number of points because we assume there is no space-time micro-quantum llimit. I agree with you that there are a limited number of points for each line.

"Infinitly long line" is like "holy war" they are both an oxymoron(?) i.e. infinity and eternity are not a long length or long time they are beyond size or time ergo beyond limits and words like "long" that imply such. Not to correct you John cause I am sure your very much aware of the terminolgy relationships.

Fuller would say we have minmally 12 options of direction --6 positive and 6 negative-- to travel from any space-time spherical/vertexial/point/moment due to his isotropic vector equilibrium matrix(IVM) of close-packed spheres/spherics which define four hexagonal planes in --60 dgree coordination to each other-- extending from any spherical/vextex/point of space-time.

I need to learn more about these 7 dimensions as related to cubic/XYZ/cartesian space but not include in our conventional cubic 3-Dimensions. Yes i have read Kaku's book "Hyperspace" amd been to some string theory sites but I am still missing the 7-D boat some how.

The 11th dimension --a.k.a. as the fourth-- is time if I am correct ergo 10-26 and 11-27 is the two common hyper dimesional numerical relationships.

Rybo

 

[John]

I had believed pure math doesn't have strings, but has non-dimensional points. The truth may be, even pure math must have strings, not points, because it is impossible to factor something down to infinitely small. So the smallest thing possible has to be a small line or a string. And here is where it gets very different, if you construct space out of strings, you can only travel in seven directions in that space: when you build space out of strings that form equilateral tetrahedrons.

I am making a new assumption that space itself, math itself is made of strings. Each equilateral tetrahedron is constructed from six strings (small lines of equal length). Taking it to its simplest element you have my version of a string, which is this: if you think of a ruler, each number on the ruler is separated by a distance. I call the distance from 1 to 3, a string. If you break the numbers into fractions, and if you continue to make the fractions smaller, the strings get smaller. 1/8 is smaller than 1/2. As you break the ruler down into smaller and smaller segments, you have smaller and smaller strings. We think of the distance between two points on the ruler as eventually disappearing, so we assume the smallest segment is a non-dimensional point. The smallest segment in a line has to be a string. It can’t be a non-dimensional point. If there are no non-dimensional points, and if you build a spatial reality out of strings rather than non-dimensional points, space must be a structure of equilateral tetrahedrons!

If you travel along the lines of the tetrahedrons, you find you can only travel in seven directions. There are only seven directions that you can travel in the most fundamental structure of string space. This conveniently concurs with the seven extra dimensions predicted by string theory.

(We are told a string theory “point” has six dimensions. I say string theory space is made of equilateral tetrahedrons, which have strings going in six directions. There are the mirror image tetrahedrons that make up the space, which are tetrahedrons that have strings going in six directions, but one of the directions doesn’t repeat. The number six is significant, but there are a total of seven directions if space is made of tetrahedrons constructed from strings.)

I think the strings that form space are much bigger than the strings that form particles. They are on the order of an eighth of a millimeter: a distance that we can actually see. We can’t experimentally find the strings that form particles because they are too small, but we can easily find the strings that form space. We can find them in a snowflake, and in the erratic paths of particles after collisions.

 

[John]

I am basing extra dimensions on the limited number of directions you can travel if you arrange a limited number points in a space. I made a mistake in my calculations. I wanted the number of directions to match the number of extra dimensions. We already have three dimensions. String theory says ten dimensions. We need the seven missing spatial dimensions.

In counting the number of directions you can go in a space made of tetrahedrons: if you only travel along the equal-length lines that make the tetrahedrons, which are strings, and you only travel along the strings; you can only go in six directions.

Watching The Elegant Universe last night on PBS, it said a string theory "point" has six dimensions. In a space made of strings that form tetrahedrons, each intersection has lines going in six directions, not seven like I previously counted.

That gives us nine spatial dimensions, using my definition of dimension. Each string theory point would have six dimensions.

I actually took new pencils that were all equal length and put enough of them together to physically count the number of lines at each intersection. I was average at math formulas, but made an A+ when geometry came along.

 

[sol1]

What Dimension Means?

John,

Then how would you explain "continuity," in terms of what geometry can do?

You have consistently held to points, but this cannot happen at supersymmetrical levels because of the energy recognized.

I have created a link for those who wish to expand there minds in terms of dimension (What is dimension?) , and this follows strict lines. If one is to expand to understand how such points become smeared at high energies then you have to undertand how GR and QM come together gives insight into dynamical movements. How would you do that in points in regards to spherical and hyprbolic undertandings, as dynamical movement? Reinmann lead us to spherical considerations, yet there is a negative expression, if we understood the triangle and its degrees of, how would we know which way to measure this value?

The Friedmann equation and curvature help greatly here.

I see your sincerity and drive, and recognize it in myself... yet there is information that we must become aware that might have limited our vision of things. I mean this in a polite and respectful way. I am open to corrections as well.

Sol

 

[John]

The thing that is confusing physicist/mathematicians is that some things, which appear to be a certain way, are really only expressions of what they are. Continuity is the best example.

If you have four “points in space” they can look like this:

Point…………Point……………………….Point………………………………..Point

A particle, like a photon is always going to travel from point to point in the same amount of time. So if we measure distance by time, such as light years, those four points will be seen as having the same distance between them. We would measure a light year in our vicinity of the universe, and assume a light year is the same length everywhere.

Yet, if we measured the photon by physical distance going between those four points, we would know the photon has clearly sped up.

Electrons orbiting a nucleus can speed up on one side of the atom if the points of space are farther apart on that side of the atom. If the electrons are going faster on one side of the atom, their centrifugal force will pull the atom to the side the electrons are orbiting faster.

So if you imagine an orbit where the electron is following points of space, and the points are farther apart on one side due to space being warped by a large mass, the atom will accelerate into the large mass.

This works because there are two mathematical systems interacting. In one system, the points are considered a continuum. We consider there is no distance between the points. In the other system, which is string theory, we consider the distance between points and consider what the particles are actually doing as they travel from point to point.

 

[THE[>U<]DUDE]

Forgive my clear and utter ignorance (newness can often equal naivety), but I was taught that the speed of light is constant.

Or is that constant in different fundamental situations/environments?

Photons are particles traveling at a constant speed - so how can they effectively appear to 'speed up' (gain a velocity) and 'slow' back down at will? According to the basic principles I can recall about General Relativity the alterations in mass alone caused by the added velocity would be astronomical!

I understand the concept about the photons being 'pulled' from one point to another - but that would mean that the greater the apparent 'gap' breached between two points the greater the acting 'pull' - which is the same as saying the greater the force acting upon the photon. Which force is this? Because if this 'force' can increase the speed of light then surely it is one to be reckoned with, even on a fundamental scale!

Please illuminate . . .

 

[selfAdjoint]

You are right. John is mistaken. Seen from any inertial frame of reference, the photon takes twice as long to travel twice the distance. John may be thinking of the fact (also true) that the photon experiences no proper time in doing either trip. These two facts do not contradict each other in relativity.

 

[John]

The speed of light is not completely constant. There is gravitational lensing, which happens due to gravitational warping of space. The amazing thing about gravitational lensing is that light must go faster to bend around the sun. It is impossible to set up a model for gravitational lensing where light does not increase slightly beyond the speed of light.

In regular lensing light slows down, and that makes it bend.

We also now know that we can supercool space and make light nearly stop. Why? Because there must be an energy in space itself that is pulling light along. Supercooling space takes that energy away and brings light nearly to a halt, amazingly, preserving all the wavelengths and characteristics of a particular light so that when you unfreeze it, it returns to its original self!