What is the true nature of time?

[cshum00]

this is one of the several MATHEMATICAL definitions of 2-dimensions. This is NOT a scientific definition.

Yes, you are right; that is not a scientific definition. I just wanted to paint a picture of how dimensions can be represented in mathematics. Unless, you are saying that the scientific definition of dimension is not based on the mathematical definition of dimensions. If so, then correct me and define it for me in proper, easy and lame words so that someone with no knowledge can understand it.

This is incorrect and misleading. I'm a scientist. When we say space we simply mean...space. Space is that which has no shape or dimension. An object's shape can be specified or characterized by 3 dimensions; length, width and height, in space. These are parsimonious scientific definitions. Now if mathematicians by whatever convenient convention choose to call this "3-D space", whatever. IMO, the term "spatial dimension" is a misnomer.

Yes, you are right. "Spatial dimension" and "3-Dimensional space" have two different meanings. But a person with no knowledge of science will think of both of them as one and same thing. Depending on the context of the speech, scientists still might refer 3-D space as just "space". And thinking of spatial dimension as the mathematical model is not wrong neither since its representation in mathematics was based on it.

Scientists don't say this. Well...good scientists at least. Treating time as a dimension may not be controversial in the establishment but it's certainly self-contradicting and leads to irrational conclusions.

Sorry, that was my fault. I shouldn't have said "spacial" dimension but just dimension. I just wanted to say that treating time as a dimension is nothing new but rather the way it is used in Special Relativity is non-intuitive.

Which is why using it as a dimension is irrational. And mathematics does this not physics.

No, i didn't say that using dimension is irrational. I am saying that time is mostly visualized as one universal time and mostly as the independent variable. What i meant by "irrational" was non-intuitive. I guess i should have carefully picked the words. What i meant to say in t he last paragraph was that it is non-intuitive to think of time can depend on a spatial dimension; like the way it is used in Special Relativity for time dilation.

 

[ghwellsjr]

Wasn't this covered in my post #11 and #6 as well as many others?

you last post (#11) was:

I agree with you, there shouldn't be a problem, but unfortunately, Mother Nature doesn't agree with us and, so, we lose. It does make a difference which co-ordinate system we use and there is no way for us to determine which one is the correct one, so that is why we use the four-vector interval.

Time is placed orthogonal to the three components of space in the "imaginary" direction and it works and that is why we do it. If you don't like it you need to come up with another scheme that works but you can't stick to the one you have because it doesn't work.

and i replied:

Please explain. I'm confused.

If it works so good why is gravity a problem? Why aren't the SM and GR compatible? Does this have anything to do with the mathematical formulations of these models? Just asking. Thanks.

and i waited ...

My contribution to this thread was to answer Parbat's question, "How can we say 'time' is a dimension?" from post #3 after I asked him to elaborate on his nebulous original question from post #1.

I was pointing out to him and to you that the reason we treat time as an added "dimension" to normal vectors with three components is so that we can arrive at an invariant "distance" between two events which are separated both in space and time. I pointed out that just as the three components of normal vectors are orthogonal to each other, the "time" component in a four-vector is also orthogonal to the three "space" compontents because it is placed in the "imaginary" direction. Since you had previously used the term "orthogonal", I assumed you would know what that meant. Maybe I should have suggested that anyone who might still be confused on this issue should look up "spacetime interval" for a more complete explanation.

I understood your posts to mean that you didn't see any problem with determining distances between events and you said you didn't understand why we combine time and space to get the spacetime interval. I was trying to help you understand that aspect of Special Relativity.

But your follow-on posts revealed that you were not taking in what I was saying and others were also trying to help you see what a four-vector was all about (which is the topic of this thread) and so when you asked me, "Why aren't the SM and GR compatible?", I didn't want you or anyone to know how stupid I was because I have no idea what SM is and I didn't know that it was incompatible with GR, so I just hoped I could let it slide but now you have brought it up again and so I must confess, I'm stupid, I have no idea what you are asking about. Someone else is going to have to answer.

 

[TheAlkemist]

Yes, you are right; that is not a scientific definition. I just wanted to paint a picture of how dimensions can be represented in mathematics. Unless, you are saying that the scientific definition of dimension is not based on the mathematical definition of dimensions. If so, then correct me and define it for me in proper, easy and lame words so that someone with no knowledge can understand it.

I already did but i'll do it again.

A dimension is a concept that attributes shape/structure to a physical object. In scientific convention, the shape/structure of physical objects in space are described by 3 dimensions; length, width and height.

Yes, you are right. "Spatial dimension" and "3-Dimensional space" have two different meanings. But a person with no knowledge of science will think of both of them as one and same thing. Depending on the context of the speech, scientists still might refer 3-D space as just "space". And thinking of spatial dimension as the mathematical model is not wrong neither since its representation in mathematics was based on it.

if "spatial" in "spatial dimension" and "space" in "3-dimensional space" just implies that the object that's being described by the dimensions is in space, I have no issue with that. But i doubt this is what is meant. I think what's meant is that space itself has dimensions, i.e., shape and structure. I just don't agree with this abstraction. Unless, like u said, you're talking about "mathematical objects"... which are just conceptual models. And again, I'm not saying they are wrong or aren't useful, they certainly are.

Sorry, that was my fault. I shouldn't have said "spacial" dimension but just dimension. I just wanted to say that treating time as a dimension is nothing new but rather the way it is used in Special Relativity is non-intuitive.

no need to apologize. and i agree with u, it's non-intuitive. but not only that, it's also ambiguous and very fuzzy.

No, i didn't say that using dimension is irrational. I am saying that time is mostly visualized as one universal time and mostly as the independent variable. What i meant by "irrational" was non-intuitive. I guess i should have carefully picked the words. What i meant to say in t he last paragraph was that it is non-intuitive to think of time can depend on a spatial dimension; like the way it is used in Special Relativity for time dilation.

i didn't say that u did (i don't think u ever did though). I'm the one that's saying it's irrational and also INCONSISTENT. As you have pointed out.

 

[TheAlkemist]

My contribution to this thread was to answer Parbat's question, "How can we say 'time' is a dimension?" from post #3 after I asked him to elaborate on his nebulous original question from post #1.

I was pointing out to him and to you that the reason we treat time as an added "dimension" to normal vectors with three components is so that we can arrive at an invariant "distance" between two events which are separated both in space and time.

I understand whytime is added as an extra-dimension. It's simply to make the mathematics and the theory workable. Adding the property of invariance to the dimensions using time presupposes that time has directionality--forward and backward. Maths uses the "number line" (that can go in both directions, +ve and -ve) and calls it time. And now that time has been endowed with number and line attributes you can do things like dilate, warp and bend, etc. it...much like a physical object.
But i realize that this may make it easy to visualize and the theory makes useful predictions. No problem with that. Only thing is that when u start having concepts (mathematical objects) interacting with physical objects things can get messy and confusing imo. Like here:

What is rather counter-intuitive, is that physics treats time not only as a independent variable but also as a dependent variable. Meaning, that time is no longer universal but the value of it can be changed and influenced by other factors. In the case of special relativity in physics, time can be changed by the 3 other dimensions of distance.

I pointed out that just as the three components of normal vectors are orthogonal to each other, the "time" component in a four-vector is also orthogonal to the three "space" compontents because it is placed in the "imaginary" direction. Since you had previously used the term "orthogonal", I assumed you would know what that meant. Maybe I should have suggested that anyone who might still be confused on this issue should look up "spacetime interval" for a more complete explanation.

I know what orthogonal means. And placing time in an "imaginary" direction is no problem now that it's been morphed into a number line. The concept of spacetime interval embodies basically everything i said above.

I understood your posts to mean that you didn't see any problem with determining distances between events and you said you didn't understand why we combine time and space to get the spacetime interval. I was trying to help you understand that aspect of Special Relativity.

But your follow-on posts revealed that you were not taking in what I was saying and others were also trying to help you see what a four-vector was all about (which is the topic of this thread) and so when you asked me, "Why aren't the SM and GR compatible?", I didn't want you or anyone to know how stupid I was because I have no idea what SM is and I didn't know that it was incompatible with GR, so I just hoped I could let it slide but now you have brought it up again and so I must confess, I'm stupid, I have no idea what you are asking about. Someone else is going to have to answer.

sorry, i shouldn't have abbreviated. SM = Standard Model and GR = General Relativity. Maybe i mean Quantum Mechanics (as described by the SM) and GR.

I guess what I'm getting from the answers to Prabat's question is just explanations of how making time a number line makes the mathematics workable.

 

[ghwellsjr]

I was aware that QM is not compatible with SR because it is not invariant under Lorentz transformation (unless this has been resolved since I learned that) which, I suppose, means that it is also not compatible with GR.

I am very confused on your position and what you are trying to say throughout this thread. I have been trying to help you understand what a four-vector is and how it allows us to define a frame-independent spacetime interval between two distant (in both space and time) events.

Have I been wasting my time because you already understand all this? If yes, could you have explained it all to Parbat?

Do you disagree with the concept of the spacetime interval? If yes, is that because you believe it is unnecessary and the same issue can be addressed some other way?

 

[cshum00]

A dimension is a concept that attributes shape/structure to a physical object. In scientific convention, the shape/structure of physical objects in space are described by 3 dimensions; length, width and height.

I don't think you are defining dimension in general but rather you are defining spacial dimension here. If i am not wrong, the abstraction of dimension in science does not limits the attributes of just "shape/structure" but in additional to those also to more abstract properties like time, mass and so on; in which these attributes and properties does not only describe/define a physical object but the entire physical reality. Where in the case of spatial dimension, it is a set 3 dimensions of lengths each orthogonal to each other; where each dimension has the name of length, width and height.

 

[pervect]

There are a large number of related but different concepts in mathematics relating to dimension, but one of the most primitive concepts (in my opinion, probably the most primitive concept) needed to define dimension is a set of points, and a concept of "neighborhood" or "open balls".

When you can define what points are "near" other points in your set because they are in the same neighborhood or "open ball", you have what mathemeticians call a topological space.

This minimum of structure is the bare minimum of what you need before the concept of dimensoinality makes sense. If you just have a random set of points, and no notion of which points are neighbors, you can't really come up with any meaningful concept of dimension.

The concept of dimension that's mathematically applicable when you do have a topological space is probalby not particularly well known, it's called the "hausdorff covering dimension". It relates to the amount of unavoidable overlap you need to completely cover your entire universal set. For instance, to cover a line with open balls requires a minimum overlap of two, some points will be in two different balls when you make a complete cover. To cover a plane some points would have to be in three different covering sets, and in general your minimum cover will require some points to be in n+1 open balls, where n is the usual notion of the dimensionality of the space.

While you can apply the above definitions to finite sets of points, they really aren't that interesting unless you deal with infinite sets.

 

[Phrak]

I can have 3 dimensions of space, and add one dimension of temperature and add pressure and throw in attitude for a 6 dimensional mathematical space. It's not a very interesting space. Pressure doesn't have a lot to do with distances nor attitude, nor attitude with pressure or temperature.

What makes 3 dimensional space more than three arbitrary things stuck together, is that we can make a distance measure using the Pythagorean theorem no matter how we rotate our chosen X,Y,Z coordinates around.

The same sort of thing is true for spacetime (and yes, there are Lorentz invariant quantum theories). In this case, the distance (called the interval so we don't confuse it with spatial distance) is unchanged when space and time coordinates are rotated about.

Does this solve any issues in the foregoing discussion?

 

[Dale]

this is one of the several MATHEMATICAL definitions of 2-dimensions. This is NOT a scientific definition.

... Now if mathematicians by whatever convenient convention choose to call this "3-D space", whatever. IMO, the term "spatial dimension" is a misnomer.

... Treating time as a dimension may not be controversial in the establishment but it's certainly self-contradicting and leads to irrational conclusions.

Which is why using it as a dimension is irrational. And mathematics does this not physics.

I have seen this sort of anti-math diatribe on occasion, usually by serious crackpots and cranks. It is fundamentally wrong.

As long as a theory uses some mathematical framework to make predictions about experimental results then the fact that some particular element of the theory is also a purely mathematical object does not make it non-scientific. The use of mathematics in science, particularly physics, is important for making sure that the predictions are logically self-consistent. The treatment of time as a dimension is both mathematical (it is one dimension of a pseudo-Euclidean space) and scientific (the mathematical "norm" in this space is equal to the physical duration measured by a clock).

Because the math is used by a theory to make measurable predictions the denigration above is not warranted. When scientists say that time is the fourth dimension they mean that there are physical predictions (which can be experimentally tested) that can be made by constructing a four-dimensional mathematical space and equipping it with a certain "norm". So far, those mathematical predictions have been thoroughly tested and found to be physically correct.

 

[TheAlkemist]

I was aware that QM is not compatible with SR because it is not invariant under Lorentz transformation (unless this has been resolved since I learned that) which, I suppose, means that it is also not compatible with GR.

I am very confused on your position and what you are trying to say throughout this thread. I have been trying to help you understand what a four-vector is and how it allows us to define a frame-independent spacetime interval between two distant (in both space and time) events.

Have I been wasting my time because you already understand all this? If yes, could you have explained it all to Parbat?

I apologize if if I didn't make position clear from the beginning (though I think I did). I simply do not agree with the inconsistent usage of the term "dimension".

Do you disagree with the concept of the spacetime interval? If yes, is that because you believe it is unnecessary and the same issue can be addressed some other way?

Yes and yes.

I don't think you are defining dimension in general but rather you are defining spacial dimension here. If i am not wrong, the abstraction of dimension in science does not limits the attributes of just "shape/structure" but in additional to those also to more abstract properties like time, mass and so on; in which these attributes and properties does not only describe/define a physical object but the entire physical reality. Where in the case of spatial dimension, it is a set 3 dimensions of lengths each orthogonal to each other; where each dimension has the name of length, width and height.

OK, then why u can't have just tag on, say, temperature, and static charge yo x,y,z,t and call it 5D?

 

[TheAlkemist]

While you can apply the above definitions to finite sets of points, they really aren't that interesting unless you deal with infinite sets.

why?

 

[ghwellsjr]

Do you disagree with the concept of the spacetime interval? If yes, is that because you believe it is unnecessary and the same issue can be addressed some other way?

Yes and yes.

I'd like to hear how you determine the "distance" between to widely separated events in space and time that is invariant when observed from different frames of reference. In other words, how do you address the issue that "spacetime interval" addresses?

 

[TheAlkemist]

I can have 3 dimensions of space, and add one dimension of temperature and add pressure and throw in attitude for a 6 dimensional mathematical space. It's not a very interesting space. Pressure doesn't have a lot to do with distances nor attitude, nor attitude with pressure or temperature.

What makes 3 dimensional space more than three arbitrary things stuck together, is that we can make a distance measure using the Pythagorean theorem no matter how we rotate our chosen X,Y,Z coordinates around.

The same sort of thing is true for spacetime (and yes, there are Lorentz invariant quantum theories). In this case, the distance (called the interval so we don't confuse it with spatial distance) is unchanged when space and time coordinates are rotated about.

Does this solve any issues in the foregoing discussion?

Ur right, temperature, pressure and attitude have nothing to do with shape. As for spacetime, this interval u speak of is simply a number-line that's been added as an extra "time dimension". A metric for duration so to speak. The purpose of adding this is to endow the model with Lorentz symmetry right? Is this in anyway related to the concept of T-symmetry? If so, isn't the the physical universe we observe time asymmetric (because of 2nd Law of thermodynamics?).
Hope I'm not way off here...

 

[TheAlkemist]

The use of mathematics in science, particularly physics, is important for making sure that the predictions are logically self-consistent.

But there are several cases where it introduces self-contraction.

What qualifies one as a crack-pot?

The treatment of time as a dimension is both mathematical (it is one dimension of a pseudo-Euclidean space) and scientific (the mathematical "norm" in this space is equal to the physical duration measured by a clock).

physical duration? as opposed to non=physical duration?
How was it measured before clocks were invented?

Because the math is used by a theory to make measurable predictions the denigration above is not warranted. When scientists say that time is the fourth dimension they mean that there are physical predictions (which can be experimentally tested) that can be made by constructing a four-dimensional mathematical space and equipping it with a certain "norm". So far, those mathematical predictions have been thoroughly tested and found to be physically correct.

Denigration? OK. I'll stop because it seems like I'm upsetting some people. Not my intention. Making predictions isn't the only crireria for what makes a theory correct by the way.

 

[Dale]

But there are several cases where it introduces self-contraction.

No. There are several cases where it introduces confusion in beginning students, but not self-contradiction. That is the whole point of establishing a unified mathematical framework for a theory.

Making predictions isn't the only crireria for what makes a theory correct by the way.

Making accurate predictions about the results of experiments is the only scientific criteria. Other criteria amount philosophical or personal preference.

 

[TheAlkemist]

I'd like to hear how you determine the "distance" between to widely separated events in space and time that is invariant when observed from different frames of reference. In other words, how do you address the issue that "spacetime interval" addresses?

u realize that implicit in ur question is the notion of measuring time as a distance? besides, spacetime interval addresses an issue created by the conception of space and time as a single entity. it's like a custom designed solution.
My short answer to ur question is that it's irrational and conceptually impossible to measure space (emptiness) between objects. U measure the physical object in space. But i'll leave it here. I'm not changing any minds in here anyway. and I'm not trying to offend anyone. just commenting.

 

[TheAlkemist]

No. There are several cases where it introduces confusion in beginning students, but not self-contradiction. That is the whole point of establishing a unified mathematical framework for a theory.

Ok.

"The term 4-D means that it takes 3 spatial coordinates and 1 temporal coordinate to specify the position of a point or event.

"An object is said to have as many dimensions as there are axes required to locate its position in space"

Are both definitions above correct?

Making accurate predictions about the results of experiments is the only scientific criteria. Other criteria amount philosophical or personal preference.

Ok. ur right.

 

[ghwellsjr]

u realize that implicit in ur question is the notion of measuring time as a distance?

That's why I put "distance" in quotes, so that you would not take exception to my terminology because I can't tell what terminology you prefer.

besides, spacetime interval addresses an issue created by the conception of space and time as a single entity. it's like a custom designed solution.

Spacetime does not create the issue, nature does, and spacetime interval is a solution.

My short answer to ur question is that it's irrational and conceptually impossible to measure space (emptiness) between objects. U measure the physical object in space. But i'll leave it here. I'm not changing any minds in here anyway. and I'm not trying to offend anyone. just commenting.

But you said you could solve the same problem that "spacetime interval" solves except by another method. Now are you telling me that you don't believe there is any solution?

Let's take, for example, the first half of the twin paradox. The twins (or two identical clocks) start out at the same age (or set to the same time) at the same location. One of them accelerates away and travels at a high speed for awhile and then decelerates and comes to rest with respect to the first twin (or clock) some distance away. This defines two events: the first is when the traveler starts out and the second is when the traveler stops. When this situation is analyzed from different frames of reference, different answers will be determined for the actual physical distance the traveler traversed and for the actual physical time that it took the traveler to make the trip. Do you agree? If yes, then how do you reconcile the different measurements of distance and time? If no, then please explain why.

 

[cshum00]

OK, then why u can't have just tag on, say, temperature, and static charge yo x,y,z,t and call it 5D?

You can as long as it is mathematically useful. Physical "spacial dimension" only has 3 dimensions x,y,z. Time is a dimension but not a spatial dimension. Because Special Relativity uses both spatial dimension and time dimension then we combine them so that it is mathematically useful and we call it "space-time dimension".

I am just saying that you were not defining dimension abstractly enough but you are rather defining spatial dimension in specific instead.

 

[Phrak]

Ur right, temperature, pressure and attitude have nothing to do with shape. As for spacetime, this interval u speak of is simply a number-line that's been added as an extra "time dimension". A metric for duration so to speak. The purpose of adding this is to endow the model with Lorentz symmetry right? Is this in anyway related to the concept of T-symmetry? If so, isn't the the physical universe we observe time asymmetric (because of 2nd Law of thermodynamics?).
Hope I'm not way off here...

As in space alone, there is no preferred direction in spacetime that you can call the time direction. In this regard they are inseparable, unlike space+temperature, say. A Lorentz symmetry is more of a rotational symmetry, similar to rotating spatial vector.

 

[DaveC426913]

As in space alone, there is no preferred direction in spacetime that you can call the time direction. In this regard they are inseparable, unlike space+temperature, say. A Lorentz symmetry is more of a rotational symmetry, similar to rotating spatial vector.

I could be misunderstanding you but the time dimension is different from the other spatial dimensions; it is "timelike", whereas the others are "spacelike". At least one defining distinction between the two is that timelike dimension(s) only permit movement in one direction.

 

[Dale]

"The term 4-D means that it takes 3 spatial coordinates and 1 temporal coordinate to specify the position of a point or event.

"An object is said to have as many dimensions as there are axes required to locate its position in space"

Are both definitions above correct?

The first is basically correct, although I would have been more specific (e.g. "The term 4-D spacetime"). The second is not correct, it seems to be describing the dimensionality of a space and not the dimensionality of an object as it says.

 

[Phrak]

I could be misunderstanding you but the time dimension is different from the other spatial dimensions; it is "timelike", whereas the others are "spacelike".

It was in my opinion that to throw in that sort of detail would cloud the issue at the level of understanding of the question. However I didn't make my case very well, did I?

To try again: <We cannot pick-out anyone direction in spacetime and say "this is the time direction". Observers in relative motion will not agree. In this regard space and time are inseparable.> How's that?

At least one defining distinction between the two is that timelike dimension(s) only permit movement in one direction.

I don't know what the meaning of movement in time is. However, world lines of classical and incoherent particles are confined to the interior of the light cone.

To be really abstract, the difference is that rotations in space have a real valued parameter of rotation, whereas rotations between space and time have an equivalent imaginary parameter. But this doesn't really tell us what class of objects must have their world lines confined to the interior of the light cone... hmm...

 

[ghwellsjr]

My short answer to ur question is that it's irrational and conceptually impossible to measure space (emptiness) between objects. U measure the physical object in space.

I hope you realize that the issue we are talking about isn't confined to distances between objects in empty space, the same issue exists between the shape of a single physical solid object on the surface of good old earth. The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?

 

[Phrak]

The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?

I'm not sure what you are attempting to infer, but the Michelson Morley experiment yielded null results. They measured no difference in dimensions, or anything else.

 

[ghwellsjr]

MMX was the inspiration for Lorentz to explain the null result by saying that the physical dimension of the apparatus was contracted along the direction of the aether wind. Michelson, on the other hand, believed that he could not measure the aether wind because he thought the Earth was dragging the aether along with it.

 

[John232]

I don't think even the best physicst can explain exactly why time is a dimension. The best explanation I have read in any book written by one is that if they where to point out on a map the exact coordinates where you will meet them you would never be able to meet them there without knowing when they will be there. Then the time coordinate allows your meeting.

 

[Dale]

I don't think even the best physicst can explain exactly why time is a dimension. The best explanation I have read in any book written by one is that if they where to point out on a map the exact coordinates where you will meet them you would never be able to meet them there without knowing when they will be there. Then the time coordinate allows your meeting.

Seems like even amateur physicists can explain exactly why time is a dimension.

 

[TheAlkemist]

That's why I put "distance" in quotes, so that you would not take exception to my terminology because I can't tell what terminology you prefer.

Spacetime does not create the issue, nature does, and spacetime interval is a solution.

But you said you could solve the same problem that "spacetime interval" solves except by another method. Now are you telling me that you don't believe there is any solution?

Let's take, for example, the first half of the twin paradox. The twins (or two identical clocks) start out at the same age (or set to the same time) at the same location. One of them accelerates away and travels at a high speed for awhile and then decelerates and comes to rest with respect to the first twin (or clock) some distance away. This defines two events: the first is when the traveler starts out and the second is when the traveler stops. When this situation is analyzed from different frames of reference,different answers will be determined for the actual physical distance the traveler traversed and for the actual physical time that it took the traveler to make the trip. Do you agree? If yes, then how do you reconcile the different measurements of distance and time? If no, then please explain why.

No. I believe there's a fundamental error in the relativist's notion of distance. What's actually being measured as "distance" is actually "distance traveled". hence why "distance" is defined in terms of c. Relativity alludes to the qualitative static distance (between two objects or "events") but explains the theory with respect to dynamic distance traveled. Case in point is the phenomenon of "length contraction".
If I'm standing 20 yards away from a tree (where there's a measuring device) and a muon zips past me at near the speed of light, relativity theory says that the distance between the muon an the tree contracts. Now did the static distance between me and the tree shrink or was it the distance between the muon and the tree? And if the answer is the later, then say there's a rock between me and the tree, did the distance between the rock and tree also shrink?

You can as long as it is mathematically useful. Physical "spacial dimension" only has 3 dimensions x,y,z. Time is a dimension but not a spatial dimension. Because Special Relativity uses both spatial dimension and time dimension then we combine them so that it is mathematically useful and we call it "space-time dimension".

I am just saying that you were not defining dimension abstractly enough but you are rather defining spatial dimension in specific instead.

As far as I'm concerned, time is not a dimension. it's simply a number line. it's then endowed with orthogonality and combined with the 3 "spatial" dimensions. as such mathematicians have simply just created, lie u said, a useful framework for modeling the physics of objects in space.

As in space alone, there is no preferred direction in spacetime that you can call the time direction. In this regard they are inseparable, unlike space+temperature, say. A Lorentz symmetry is more of a rotational symmetry, similar to rotating spatial vector.

So what's the preferred direction of temperature?

I hope you realize that the issue we are talking about isn't confined to distances between objects in empty space, the same issue exists between the shape of a single physical solid object on the surface of good old earth. The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?

I understand it as an indirect inference from a null-experiment.

 

[Mentz114]

No. I believe there's a fundamental error in the relativist's notion of distance. What's actually being measured as "distance" is actually "distance traveled". hence why "distance" is defined in terms of c. Relativity alludes to the qualitative static distance (between two objects or "events") but explains the theory with respect to dynamic distance traveled.

In flat spacetime distance can be defined as coordinate separation in a consistent way. What is a ruler but a stick with coordinates marked off ? In SR each inertial observer has a set of coordinates and a definition of distance. The Lorentz transformation allows us to transform the coordinates between frames.

Case in point is the phenomenon of "length contraction".

Which is what happens when a distance in one frame is expressed in the coordinates of another frame.

It is completely consistent and your assertion

there's a fundamental error in the relativist's notion of distance

is incorrect.

 

[ghwellsjr]

Case in point is the phenomenon of "length contraction".
If I'm standing 20 yards away from a tree (where there's a measuring device) and a muon zips past me at near the speed of light, relativity theory says that the distance between the muon an the tree contracts.

SR says that in your rest frame, the muon itself is contracted but the distance the muon has to travel is not contracted. In the rest frame of the muon, the distance between you and the tree is contracted but not the muon itself. That's why it can survive long enough to make the trip.

Now did the static distance between me and the tree shrink or was it the distance between the muon and the tree? And if the answer is the later, then say there's a rock between me and the tree, did the distance between the rock and tree also shrink?

There are two answers depending on whether you are using your rest frame or the rest frame of the muon. In your rest frame the distance between the rock and the tree does not shrink. In the rest frame of the muon, the distance between the rock and the tree is shrunk.

You can use either rest frame (or any other frame) to analyze the situation and they will all get the same answer, which is even though the half-life of the muon is too small for it to survive traveling "long" distances", from your rest frame, it survives because it's clocks are running slow and from its rest frame, it survives because it doesn't have very far to travel.

 

[ghwellsjr]

I hope you realize that the issue we are talking about isn't confined to distances between objects in empty space, the same issue exists between the shape of a single physical solid object on the surface of good old earth. The Michelson-Morley experiment is what started this whole thing. It was a single very large, very solid, very massive object that seemed to be changing its dimensions simply by being rotated. How do you understand Lorentz contraction when applied to MMX?

I understand it as an indirect inference from a null-experiment.

Yes, that is very true. I'm glad you agree with me and everyone else on this point.

 

[alkadh455]

Wow, what a question. Well, we all know that time is the duration it takes actions to happen. Time is the fourth dimension, as Einstein viewed it. People before Einstein, like Newton, viewed time as a definite quantity. They viewed it as a definite measurement that is the same for everybody. Then came Einstein, and said that time is in fact relative, it is not an equivalent quantity for everyone. First, he said that the ultimate speed of the universe is the speed of light (you can't go faster than the speed of light). He also said that time is a relative measurement, it depends on your speed; the closer you travel to the speed of light, the slower time beats. Also, time beats faster if you are away from gravitational pull (that's why our GPS works the way it does. It has to take General Theory of Relativity into consideration).That is our basic understanding of time.Time travel to the future is very possible, you just have to go on fast speeds and you age less than your twin, you are in some sense a traveler to the future, However, we don't really know for time travel to the past, because you can't change your past. There are also some new theories on time such as wormholes, and string theory's tiny curled up extra dimensions... The subject of time is really a huge subject, and physicists are still investigating on time.

 

[cshum00]

As far as I'm concerned, time is not a dimension. it's simply a number line. it's then endowed with orthogonality and combined with the 3 "spatial" dimensions. as such mathematicians have simply just created, lie u said, a useful framework for modeling the physics of objects in space.

You are getting it all wrong. Time IS a dimension. The problem is that you are mixing between "spacial dimension" and dimension in general!

In math, dimension can be ANYTHING! as long as you can represent it on a number line and have it to be useful for mathematical representations and calculations.

In science, dimension takes a further step and says that it is anything that is a FUNDAMENTAL QUANTITY that that is why we assign a symbol for it's dimension.
http://en.wikipedia.org/wiki/Physical_quantity#Base_quantities.2C_derived_quantities_and_dimensions"

TIME is a FUNDAMENTAL QUANTITY! You don't have to trust the wiki link that i sent you but search and look around books and you will find that TIME IS INDEED A DIMENSION!

Stop being stubborn and saying that when a scientist say dimension they must mean spacial dimension; which IS NOT! Spacial dimension is a subset of dimension!

As for the word space part, mathematicians do use the word space when they could actually mean just dimension. Meaning when mathematicians say space, they don't mean spatial dimension but dimension in general and it occurs! And for scientists who have deep math background do so as well! That is why some people misunderstand that when some scientist say space referring to spatial dimension of space which might not be the case depending on the content of the speech!

 

[Passionflower]

TIME IS INDEED A DIMENSION!

In Galilean spacetime time is surely a dimension, but is that the case in relativity?

I think in relativity time is the length of a path between two events in four dimensions. You think I am wrong?