# Time and space the same?

1. Jun 4, 2006

### Ratzinger

It has certainly been asked here before, but I would like to ask one more time how far time and space differ.

According to relativity sapce and time can be rotated into each other, merged into one spacetime entity and so forth so that so taht some authors say they are things of the same kind. The difference is only a minus sign in the metric.

The difference that we human beings notice is due to that we are sentient beings (or macroscopic systems where thermodynamics matters) goes then the explanation. But basically and fundamentally time and space are the same.

Is that true?

thanks

2. Jun 4, 2006

### Garth

The Minkowski metric is:

$$d\tau^2 = dt^2 - \frac{1}{c^2}[dx^2 + dy^2 + dt^2]$$

This means that although space and time are all dimensions of space-time, time bears the same mathematical relationship to the space dimensions as the imaginary numbers do to the real.

The fact that, although time may be a dimension, it is not exactly the same as space is intuitively obvious, is it not?

Garth

Last edited: Jun 4, 2006
3. Jun 4, 2006

### Mortimer

Garth is right. Time is different in Minkowski geometry. The odd thing, though, is that in Lorentz transformations this difference seems to vanish, since time and space partly transform into each other as a function of relative velocity.

4. Jun 4, 2006

### HallsofIvy

No, realativity does not say "rotated into each other". You can mathematically set up the equation so it looks like a rotation but you would have to use an "imaginary" angle which has no physical significance.

5. Jun 5, 2006

### Ratzinger

Thanks very much so far.

Suppose you would nothing know about space and time, and then I would come and tell you there is a manifold with a Minkowskian metric defined on it, called spacetime, the one coordinate with the plus sign we call time.
What could you tell from that about the nature of space and time?

Or differently asked, does automatically causality and time direction follow from it?

EDIT: And what if the one who knows nothing about space and time says things like that:
- space and time are on equal footing
- things can move through space and time
How does he see the difference between time and space, just from knowing the Minkowskian manifold called spacetime?

Last edited: Jun 5, 2006
6. Jun 5, 2006

### Meir Achuz

I tend to agree with your first post, but time direction is a separate fact.

7. Jun 5, 2006

### Meir Achuz

The only difference is the - sign for x^2 in the metric.
"Rotation" can be generalized for the LT Minkowski space. Thinking in terms of space-like angles or cosh and sinh for the LT just confuses things. \gamma[1,-v;-v, 1] can be considered a 4D Minkowski rotation matrix in space-time.

8. Jun 5, 2006

### robphy

If you instead made reference to "complex- or imaginary-valued angles" and "cos and sin", I'd agree that this may be confusing.

However, the use of rapidity [the real-valued "angle" for which one uses cosh and sinh in the Lorentz transformations] is natural in special relativity because rapidity [unlike velocity] is an additive parameter, which can be seen by finding the eigenvalues and eignvectors of a Lorentz Transformation [restricted to the 1+1 case for simplicity]. If misused rapidity can be confusing... but used appropriately, it will allow one to import many aspects of one's Euclidean geometric intuition.

9. Jun 5, 2006

### robphy

By being able to impose a Minkowski metric on a manifold, it says that your manifold is flat (i.e. has zero Riemannian curvature). However, that fact doesn't tell us whether your manifold is like an [infinite] plane, or spatially-closed (like a cylinder that is infinite in the "time direction"), or temporally-closed (like a cylinder that is infinite in a "space direction"). The latter case allows a causality violation: closed-timelike curves. If your manifold has identified various cuts and removed-points, you can create all sorts of causality violations. So, the topology of your manifold plays a role in its causal structure.

10. Jun 5, 2006

### Meir Achuz

"it will allow one to import many aspects of one's Euclidean geometric intuition"

That helps if you like trigonometry.

11. Jun 5, 2006

### Ratzinger

That’s interesting.

But let’s assume an infinite plane spacetime. Is it right to say that alone the statement spacetime is a Minkowskian manifold does not explain how we humans perceive time and space, and how they both differ. We also need to say time is what clocks and space is what rods measure. The metric and its different signs for space and time do not give the full picture.

12. Jun 5, 2006

### Garth

True. An example would be the Lat-Long coordinate system used to map the Earth's surface. Are the singularities at the North and South poles genuine singularites or just a coordinate breakdown? A smooth continuous transformation into a non singular coordinate system reveals these singularities at the poles to be an artifact of the coordinate system.

In mapping space-time with a metric what do the dx's and dt's refer to? Unless you can specify how the space and time coordinates relate to a system of measures, rulers and clocks, then there is a degeneracy in the statements you make about their geometry and topology.

In GR for example that relationship between coordinates and systems of measure is established by the conservation principle, the Conservation of energy-momentum, which leads to constant atomic 'rest' masses. Thus atomic rulers are defined to be of fixed length and atomic clocks to be regular.

The method of measurement, the conservation principle, together with the metric intrinsically define the geometry. Topology may be imposed extrinsically, IMHO by 'Occam's Razor' I would intuitively tend towards simply connected topologies.

Garth

Last edited: Jun 5, 2006
13. Jun 7, 2006

### Balence

Space and time are just abstract tools created by man to measure the distance or time between two or more objects or events. Is space-time still just a theory, I know in many schools its being taught as fact and questioning it results in failure of tests concerning it. Science is a tool created to better understand the universe by questioning it, however it seems science is turning into a religion. The idea of space-time is full of holes and I'll start with the idea that space and time had a beggining. How can an abstract measurement (time) have beggining if we can say an hour before the beggining, and if space did not exsist until a certain time what space does it occupy? Thats one hole in it. I'll throw some more in as people present proof because Ive seen the majority of the proof out there and it falls short.

14. Jun 7, 2006

### pmb_phy

No. Space and time are not the same thing. Even Einstein acknowledged this fact in an article he wrote in Nature (Feb. 17, 1921, p 783) to this effect.
One cannot physically rotate space into time. That would be like rotating a clock into a rod which makes no sense. Space and time are different things which have seperate and distict definitions but which, to a limited extent, are treated as parts of one thing, i.e. spacetime.

Pete

15. Jun 7, 2006

### masudr

eek, I always thought that to an observer beyond the event horizon (for a Schwarzschild metric, say) my time looked like his space and my space looked like his time; i.e. my clocks measure what his rulers measure and my rulers measure what his clock measures?

I might have gotten mightily confused...

16. Jun 8, 2006

### pmb_phy

I'm not sure what you mean but I think any confusion may be in confusing a "spacelike" spacetime interval with a "spatial interval" and confusing a "timelike" spacetime interval with a "time interval."

There is a comment made my Minnkowski in his his Address at the 80th Assembly if German Natural Scientists and Physicians at Cologne (where he introduced the notion of "spacetime" into physics) where states
Pete

17. Jun 9, 2006

### pmb_phy

I looked this up in the text of Ohanian et al. Gravitation and Spacetime - 2nd Ed.. On pages 439-440 the authors state
This means that values of r measure time. But this value of time is in the spacetime interval from which the sign determines what is spacelike and what is timelike. A differential spatial coordinate dr is still a displacement in space which the spacetime interval measures a timelike spacetime interval.

Pete

18. Jun 9, 2006

### Garth

Or another way of putting it is: "When inside the Schwarzschild radius of a black hole you can no more prevent yourself from approaching the central singularity than we, outside the Schwarzschild radius, can prevent ourselves from going into the future."

Garth

19. Jun 9, 2006

### rbj

doesn't causality, the arrow of time (i haven't heard of an "arrow of space" in general) and the $ic$ scaling factor for the t-dimension pretty much set it apart qualitatively from the x, y, and z dimensions?

there is an important relationship between space and time and the $c$ scaling factor is not merely the speed of light or of E&M, but is the speed of all things instantaneous. but time is still different until the day i can get into my timemobile and put it into R.

Last edited: Jun 9, 2006
20. Nov 14, 2007

### AngryBeaver

Very interesting points, i would like to input my thoughts.
In response to Balence on his questions about the holes in the space time theory: First i will say that science is a wealth of knowledge of the physical world gained by experimentation and observation.

Also in my opinion if you are to believe in space and time being one, you must admit that the universe is infinite, at least in that it has been here forever. But, after saying this you could consider the big bang the "beginning" of time because everything before that point has no effect on the future. So you could say an hour before the big bang something happened, although it has no effect on anything after the big bang.

21. Nov 26, 2007

### Hernik

I just found this passage in Igor D. Novikov's "The River of Time" page 102:

" When the term of postgraduate studies was almost up, I wrote a paper about this 'different' time, and this is still one of my pet papers. The gist of the discovery of mine was that once we switch from the external space to the space inside a black hole, the time coordinate in the formulas is simply replaced by the spatial radial coordinate, and vice versa. In other words, time transforms into the spatial radial distance and this distance is time itself!"

It seems to be related to what you were mentioning, so I thought it could be relevant.

henrik

22. Nov 26, 2007

### Chris Hillman

IMO, this kind of quotation out of context is very misleading; I urge anyone curious to see some of the posts in my current sig (Nov 2007).

Last edited: Nov 26, 2007
23. Nov 26, 2007

### Coin

Hi,

This is a very interesting comparison, I do not think I have ever seen it made before. Do you think you can elaborate on why the Minkowski metric would force time quantities to behave like this?

24. Nov 27, 2007

### Garth

I have been using this description of the relationship between space and time in my lectures for many years.

If we ask, "Why should the sign of the time2 dimension be the negative of the space2 dimensions?", one answer would be to say, "Well, that's the way the world is."

The understanding that time is a dimension as well as 'length, width and height' is obvious from Einstein's argument that: "You cannot measure the position of an event except at a particular time and you cannot measure the time of an event except at a particular place."

Yet as I said in my original post #2 above, the fact that, although time may be a dimension, it is not exactly the same as space is intuitively obvious, is it not?

The 'peculiarities' of SR, and consequently GR, derive from this (+---), or (-+++), signature of the metric.

One temptation that should be avoided is to then try to treat time exactly the same as the space dimensions by using 'ict'. This practice has been discussed before here. As I said then, Misner Thorne & Wheeler do a good article on this subject: "Farewell to ict" in 'Gravitation' Box 2.1, page 51.

The problems with it are:

1. Vectors (contravariant) and one-forms (covariant) are confused.

2. Thus it hides the character of the geometric object being dealt with.

3. The essentially very different rotations in Minkowski and Euclidean space are confused.

4. Thus it hides the nature of the parameter in transformations; is it cyclical or does it asymptotically tend to infinity?

5. It hides the completely different metric structure of (++++) and (-+++) geometry.

In (++++) Euclidean geometry a zero interval between two events implies they are the same event, in (-+++) Minkowskian geometry it implies they both lie on a null geodesic, one event may be a SN Ia explosion at the far side of the universe and the other the observation of that explosion on Earth billions of years later.

6. The causal structure of the universe , limited to all events in the past light cone of a particular event Xa that influence Xa, is broken.

7. Finally, and as a consequence of the above, no-one has been able to discover a way to make an imaginary ict coordinate work in the general curved space-time manifold.

Garth

Last edited: Nov 27, 2007
25. Aug 23, 2010

### eternalspace

I think that space and time are the same. The illusion that space and time are two different things is ridiculous. The whole universe is time...and time uses up emptiness hence time and space are the same.