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Why should time be considered as a 4th dimension?

cheers,

sad

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Why should time be considered as a 4th dimension?

cheers,

sad

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mathman

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In Galilean space-time you could consider time the fourth dimension, but in relativity time isWhy should time be considered as a 4th dimension?

In relativity, the relative measure of time between any two observers is related to their relative orientations in space-time.

The only difference between an Euclidean 4-dimensional Galilean space-time and a Minkowski space-time is that the rotations work differently.

Both the Galilean E

So actually there is not that much of a difference!

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The Lorentz metric is invertible, whereas the Galilean metric is not invertible.In Galilean space-time you could consider time the fourth dimension, but in relativity time isnotthe fourth dimension!

In relativity, the relative measure of time between any two observers is related to their relative orientations in space-time.

The only difference between an Euclidean 4-dimensional Galilean space-time and a Minkowski space-time is that the rotations work differently.

Both the Galilean E^{4}and the Lorentz O(1,3) make a 10-dimensional symmetry group.

So actually there is not that much of a difference!

The Lorentz metric yields three classes of vectors [spacelike, timelike, and null], whereas the Galilean metric yields only two classes...with spacelike and null coinciding.

The Lorentz group and the Galilean group have different sets of eigenvectors.

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[(ct')^2 + (vt)^2]^1/2 where vt is the spatial component and ct' is the temporal component, both of which have units of distance. Rather than thinking of c as local light speed, think of it as the rate of expansion of the Hubble sphere - you like everything else are being effortlessly carried along a distance ct each second

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The above (e.g. a statement like "all objects move at c") would only apply to objects withIf you can think of it metaphorically as all objects always moving at a constant rate equal to c - then you traveled 3 x 10^8 meters in one second w/o even moving from your chair. This becomes a useful tool that leads to the invariance of the interval - all objects move at c, ...

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Garth

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Because the position of an event cannot be described except at a specific time and the time of an event cannot be described except at a specific position. (Albert Einstein)Why should time be considered as a 4th dimension?

Furthermore, using a space-time continuum also resolves certain problems in 19th Century physics, such as the invariance of the speed of light in the Michelson-Morley experiment and it makes Maxwell's equations invariant between different inertial frames of reference.

Garth

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so far none of these answers tackles the fundamental nature of time as compared to that of space. Thats understandable, since time is something we thing with and only perilously about...

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Perhaps i'm misinterpreting this explanation, but it seems to me you are saying: "Time should be treated as a 4th dimension because we treat it as a 4th dimension." That seems a bit circular to my question. I don't see your example as an explanation either, since it leaves room to assume the reason time and space change together in inertial frames could be due to the way they are arranged in an equation, not whats indicated by nature.

thanks,

sad

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what does the sign indicate? You have pointed out how different time is to a spacial dimension, why then should it be treated as a dimension? Perhaps this is a question of semantics, but if it is called a "4th dimension", that implies it is built upon the former 3 dimensions, just as the Y-dimension is only thus in reference to the X- dimension, etc.^{th}dimension. it has a different sign attached to it in that [itex] \eta[/itex] metric. there is also no "arrow of space" that i am aware of (except i guess in black hole).tis not qualitatively identical tox,y, orz, the latter 3 which are qualitatively identical.

I am interested in hearing more about the arrow of time in a black hole.

thanks,

sad

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HallsofIvy

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I would be interested in hearing what you think the word "dimension" **means**.

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Garth

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The question is: "How are events connected up in space and time?"what does the sign indicate? You have pointed out how different time is to a spacial dimension, why then should it be treated as a dimension? Perhaps this is a question of semantics, but if it is called a "4th dimension", that implies it is built upon the former 3 dimensions, just as the Y-dimension is only thus in reference to the X- dimension, etc.

Take an infinitesimal interval ds separating two events:

Now the separation in 2 dimensions is given by Pythagoras' theorem:

now expand it to 3 dimensions:

now expand it to 4 dimensions where the fourth dimension is time; do we get

dx

Unfortunately this isn't correct, there are two things wrong with it.

First there is a question of units, we have added the squares of 'apples' and oranges'! We need a conversion factor to convert time into distance, such a factor has the dimension of velocity, so call it c, we have to multiply dt

Secondly in SR we

In Minkowski space the maximum velocity is c, massive objects can only approach c asymptotically and massless objects such as photons can only travel

We now have:

This is called the Minkowskian metric and accurately describes the behaviour of objects with clocks and rulers moving relatively to each other at high speed.

The result of this construction of a 'space-time' continuum out of space and time is that time is seen to be a dimension like the other three but with a difference. It bears the same mathematical relationship to them that the Imaginary numbers do the the Real. The fact that if time is a dimension then it is not exactly the same as the others is intuitively self-evident.

I hope this helps.

Garth

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maybe time will tell which times are tales

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russ_watters

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That really isn't true, rewebster. To scientists and engineers, this issue is unambiguous.

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Out of curiosityWe now have:

dx.^{2}+ dy^{2}+ dz^{2}- c^{2}dt^{2}= ds^{2}

This is called the Minkowskian metric and accurately describes the behaviour of objects with clocks and rulers moving relatively to each other at high speed.

The result of this construction of a 'space-time' continuum out of space and time is that time is seen to be a dimension like the other three but with a difference. It bears the same mathematical relationship to them that the Imaginary numbers do the the Real. The fact that if time is a dimension then it is not exactly the same as the others is intuitively self-evident.

To me time is measured by the metric,

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Garth

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If there is no motion when moving between the two events thenOut of curiosityGarth. why do you call this fourth dimension time?

To me time is measured by the metric,notby the t coordinate.

in which case if

Using this form of the metric

Garth

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I fully understand what you are saying but I don't look at it that way at all.If there is no motion when moving between the two events thendx, dyanddzare all zero. Then

dsand the space-like interval is i x time. One could write everything in terms of the time-like interval^{2}= -c^{2}dt^{2}d[itex]\tau[/itex]:

dt^{2}- c^{-2}dx^{2}- c^{-2}dy^{2}- c^{-2}dz^{2}= d[itex]\tau[/itex]^{2}

in which case ifdx, dyanddzare all zero thend[itex]\tau[/itex]isdt, the interval is time in the rest frame.

Using this form of the metric[itex]\tau[/itex]is the proper time or time-like space-time interval between the two events.

Garth

To me space-time is a frame

In the case you mention, the proper time vector happens to be pointing in the same direction as the t axis. This is the trivial case.

But clearly, in a more general case, where we have several objects that are in relative motion with each other, we immediate see that not all the directions of the proper time vectors point towards the t axis.

Then if we analyze this situation a bit further we can see that the t axis does not measure time but instead is a means to describe relative angles between the individual proper time vectors.

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Thus, similar to definitions of other fundamental quantities (like space and mass), only the units of time measurement are defined in science, not time itself.

http://en.wikipedia.org/wiki/Time

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But what, really is the significance of this? No one is really claiming that time is a fourth spatial dimension. But it so happens that the math works out quite well if we treat it in a similar way to the spatial dimensions. I think the bottom line is that time is being treated as a fourth dimension only because of the similarity between separate relativistic transformations of space and time.

So even though we treat time and space similarly in the mathematics, they are indeed inherently different quantities.

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Garth

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Although we all have a psychological experience of time and its 'passing', as physicists we can only talk about time as something we measure with a clock.

Thus, similar to definitions of other fundamental quantities (like space and mass), only the units of time measurement are defined in science, not time itself.

http://en.wikipedia.org/wiki/Time

The clock measures units of time defined by some regular physical process such as the vibration of a caesium atom in an atomic clock.

The space-time diagram is drawn in the instantaneous rest frame of the 'first' observer, other observers are on time-like world-lines that are inclined to the 'first' time axis, that is in the rest frame of the first observer's measuring its proper time.

These other moving observers' instantaneous 4-velocities make different angles to each other and the diagram's time axis, however the same situation can be drawn in the rest frame of another observer. In this case the first observer's 4-velocity is now inclined.

Garth

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I presume you are not saying that each object has his own space-time.The space-time diagram is drawn in the instantaneous rest frame of the 'first' observer, other observers are on time-like world-lines that are inclined to the 'first' time axis, that is in the rest frame of the first observer's measuring its proper time.

These other moving observers' instantaneous 4-velocities make different angles to each other and the diagram's time axis, however the same situation can be drawn in the rest frame of another observer. In this case the first observer's 4-velocity is now inclined.

If one has a collection of objects in relative motion in space-time, we readily can see that the t dimension does not represent time. Instead, the metric describes time.

Do you understand my point?

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Anyone that has to use 'time' , 'time as/in measurement' , 'measurement of movement' , and 'measurement using/as time' , or any variation of them HAS to have a concrete 'definition' or standard of those as it applies to the field/theory/experiment they are doing (an applied application, such as a researcher, experimenter, etc.) as it requires them to do so.

From the same wiki 'time' page:

"Time has long been a major subject of science, philosophy, and art. The measurement of time has occupied scientists and technologists, and was a prime motivation in astronomy."

If someone was 'into' a Newton aspect, they'd hopefully use some definition of time that Newton ascribed to; relativity uses 'spacetime'; etc.

When thinking about the fundamental aspects of time (what is time? , Is spacetime the correct 'thinking' about 'time'? and Can anyone come up with a 'definition' for 'time' to work with all theories?), I think is coming in under the idea of the 'The Philosophy of the Physics of Time'.

To me, this is where some discussions run into problems:

Philosophy of the ideas of Physics and the various theories (theorists) vs. the ideas of the 'accepted' principles of the various Physics Theories (applied physics)

It seems to me there's even a subset under the Theorists:

Challenging/questioning a theory (philosophy of the theory) vs. Defending/explaining the theory (knowledge of the theory)

Time to an applied physicist may be accepted as 'the measurement of time'; but, Time (to me) is still something that is still not completely explained/ doesn't have a complete explanation.

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I agree with Stainsor in some ways that whoever first attributed the word 'dimension' with the word 'time', altered the 'definition' of 'time'.

From the same wiki 'time' page:

"Time has long been a major subject of science, philosophy, and art. The measurement of time has occupied scientists and technologists, and was a prime motivation in astronomy."

If someone was 'into' a Newton aspect, they'd hopefully use some definition of time that Newton ascribed to; relativity uses 'spacetime'; etc.

When thinking about the fundamental aspects of time (what is time? , Is spacetime the correct 'thinking' about 'time'? and Can anyone come up with a 'definition' for 'time' to work with all theories?), I think is coming in under the idea of the 'The Philosophy of the Physics of Time'.

To me, this is where some discussions run into problems:

Philosophy of the ideas of Physics and the various theories (theorists) vs. the ideas of the 'accepted' principles of the various Physics Theories (applied physics)

It seems to me there's even a subset under the Theorists:

Challenging/questioning a theory (philosophy of the theory) vs. Defending/explaining the theory (knowledge of the theory)

Time to an applied physicist may be accepted as 'the measurement of time'; but, Time (to me) is still something that is still not completely explained/ doesn't have a complete explanation.

-------------------------------------------------

I agree with Stainsor in some ways that whoever first attributed the word 'dimension' with the word 'time', altered the 'definition' of 'time'.

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