pmb

I said it was a type of spatial dimension, unto which you have tried to argue its not, but now you seem to be agreeing that it is the fourth dimension of space. Contradictory much?

I can't tell what you know or don't know. However it seems to me that you don't know what a space is in the mathematical sense of the term. You seem to keep confusing it with the familiar meaning of the word as in the set of all spatial locations.

For example:

(1) Let p = pressure and v = volume. The pv diagram used in thermodynamics is a type of space whose points are (p, v) which have nothing to do with the normal meaning of space. But the (p, v) are elements of that space.

(2) We call a set of values x¹, x², ..., x^N a point. The variables x¹, x², ..., x^N are called coordinates. The totality of points corresponding to all values of the coordinates within certain ranges constitute a space of N dimensions. Other words, such as hyperspace, manifold, or variety are also used to avoid confusion with the familiar meaning of the word "space." The space Rⁿ is the usual n-dimensional space of vector algebra.

(3) A vector space is a set V with operations of addition and scalar multiplication. The elements of V are called vectors. The operaion of addition combines two vectors in the vector space to produce another vector which is also in the vector space. The operation of scalar multiplication combines any real number a and any vector v to produce another vector in the space can labeled av. The operators must the following eight axoims

(1) commutative law of addition

(2) associtive law of addition

(3) additive identity law

(4) additive inverse law

(5) distribution law (vecetors)

(6) distribution law (scalars)

(7) associateve law of multiplication

(8) scalar identity law

(4) Hilbert space is a function space (set of functions) which has the following properties

(1) The space is linear

(2) There is an inner produt defined on the space

(3) The space is complete. Every Cauchy sequence of functions in the Hilbert space converges to an element of the Hilbert space

The vectors in an abstract vector space can be matrices. They don't always have to be geometrical vectors. Elements of Hilbert space are quantum states and can be something as simple as a stationary state such as [math]\Psi(x) = A e^{ikx}[/math].

These are what I mean by mathematical spaces. The examples of spaces that I gave are not related to Cartesian 3-space but to something abstract such as a collection of vectors to form a vector space. Spacetime is a kind of space. It too is a mathematical space in that its not a Cartesian 3-space which has only spatial elements in it. Spacetime is the space which consists of 4-positions X which are events in spacetime. As I said earlier an event is the conflation of Cartesian 3-space with time to make something altogether new, i.e. spacetime.

When you've been using the term spatial it appears to be in the sense of pertaining to Cartesian space. Its not. Its about spacetime which is of a different nature than Cartesian space. The metrics in Eucliean space and Minkowski space are even different.

I actually don't even believe time exists. What I know is that time makes up the forth dimension of the metric; ie. it is a type of spatial dimension.

Yes. Time is very much the fourth dimension of spacetime. I explained all of this above.

Spacetime is also known as Minkowski space. But this is a different use of the term "space" than the typical physical meaning. Its a mathematical space. Mathematical spaces don't neccesarily represent space as in the "spatial" kind of space. Minkowski space is a good example of that. Its not the "spatial" kind of space but a mathematical space. And its quite true that time is a dimension in that mathematical space. But you shouldn't be confusing the two kinds of meanings of the term space and it seems likeits what you're doing.

In relativity, time is called ''imaginary space'' and space is called ''imaginary time''.

Not really. One can use an imaginary coordinate but this is exceptionally rare thing to do. Almost nobody uses that concept anymore.

So I'm trying to clarify in my head a better idea of the observer, and how it fits into relativity and quantum mechanics, but I'm not finding the info I need scattered about. Anyone mind just giving me whatever rundown you think fits the question, and/or if there's any equations that directly relate?

The following definition of observer is from A first course in general relativity by Bernard F. Schutz, page 4

It is important to realize that an 'observer' is in fact a huge information-gathering system, not simply one man with binoculars. In fact we shall remove the human element entirely from our definition, and say that an inertial observer is simply a coordinate system for spacetime, which makes an observation simply by recording the location (x, y, z) and time (t) of an event. This coordinate system must satisfy the following three properties to be called inertial:

 

(1) The distance between point P₁ (coordinates x₁, y₁, z₁) and point P₂coordinates x₂, y₂, z₂) is independant of time.

 

(2) The clocks that sit at every point ticking off the time coordinate t are all synchronized and all run at the same rate

 

(3) The geometry of the space at any constant time t is Euclidean.

I don't see that there needs to be an observer in quantum mechanics, just something that can make measurements. But if it is required then the above should work fine.

Of course it is a type of spatial dimension, I've told you more than once now, ..

I know what you believe. Now I want to know why you believe it. What do you think it means to say that time is a dimension in space, i.e. a spatial dimension?

What I don't get is why don't you think that space is a temporal dimension?

Taylor and Wheeler write on page 18 of Spacetime Physics

Today we have learned not to overstate Minkowski's argument. It is right to say that time and space are inseperable parts of a larger unity. It is wrong to say that time is identical in quality with space.

You know what space is, right? Loosely stated, it's the totality of "points." Each point in space is identified by exactly three numbers, i.e. it takes three numbers to specify the position vetor R = (x, y, z). Time is what we read on a clock. A time reading is not used to identify a point in space. An event is the conflation of a clock reading and the position vector and expressed as X = (ct, r). The collection of all events is called spacetime. Nothing about this indicates that time is a spatial dimension. In fact all the literature I've quoted states that time is not physically the same thing as space.

I just find it a bit deceiving saying that time ''isn't a space dimensions'' when clearly this is what it is when you read top texts on the subject.

I disagree. A point in Minkowski space is denoted as follows X = (time, space). This is an element in spacetime. It is not an element in space. Its only mathematically that the temporal variable is in some ways treated like the spatial variables. But in no way can it be called a spatial dimension.

Please eleborate on why you believe that time is a spatial variable. Thanks.

I always thought the concept of an ad hominem fallacy was relatively simple and didn't imagine it needed as much clarification as it has gotten here.

 

a) "Your argument is invalid because of x, y and z. Furthermore, you are an idiot"

b) "You are an idiot, your argument is wrong because of x, y and z."

 

are both not fallacies, but involve a personal attack.

It appears that you might have missed what swansont and I were discussing. The term personal attack is not taken as the word "person" acting on "attack". I.e. personal attack is a term which does not mean attack on a person.

I have a text which defines these terms. On this point it says

Whenever we attack a person instead of his or her argument, we commit a form of the fallacy known as personal attack.

Do you see how this is not the same as attack on a person?

He didn't mention your name, as far as I was aware?

I intentionally left it out so that this wouldn't get persaonal. Had she not said anything, which is what I was hoping, then this wouldn't be dragging anybody into it. It was intended to be abstract and as such I'l say whatever I please, so long as I don't mention particular people. And as I said, I will never read anything of her's again, including posts. And I mentioned that it was a moderator, not that someone told me something in their capacit of moderator. I mentioned it because it would have no meaning withoug it because the subject was about moderators having access to what we rep.

hi - Chill out. You should never have said it was you whom I was talking to in PM. Nothing in those PMs mattered except for the retribution I got for saying how I felt and how I didn't like being observed using the rep system. Nobody knew anything about you until you yourself told them.

All I can suggest to you is actually investigate this for yourself. Try searching for the Minkowski spacetime triangle because nothing I have told you is false.

I believe that you believe exactly what you say. And I've researched this many many years ago. Eintein had something to say about this as does Tolman.

From A Brief Outline of the Developement of the Theory of Relativity, by Albert Einstein, Nature, No. 2677, Feb 17, 1921.

From this it follows that, in respect of its role in the equations of physics, though not with regard to its physical significance, time is equivalent to space-coordinates (apart from the relations of reality.

From Relativity, Thermodynamics and Cosmology by Richard C. Tolman, page 29

In using this language it is important to gaurd against the fallacy of assming that all directions in the hyper-space are equivalent, and of assuming that extension in time is of the same nature as extention in space merely because it may be convenient to think of then plotted along perpendicular axes. ... That there must be a difference between the spatial and temporal axes in our hyper-space is made evident, by contrasting the physical possibility of rotating a metre stick from an orientation where it measures distances in the x-direction to one where it measures distances in the y-direction, with the impossibility of rotating a meter stick to a clock.

These points eloquently state my position on this subject.

Please don't think it's a conspiracy by them evil mods. I can assure you that we have better things to do than spy on people. We only do that when a situation calls for it - usually after something got reported. And even then, the rep is hardly worth our attention.

I would never have brought it up unless I didn't already get a PM from a moderator who questioned my use of the reputation system and then negatively judged me about who and why I +repped someone. They claimed I was abusing the system. I won't have that kind of crap in my life. I consider if to be very offensive. In fact the same moderator called me immature for reporting someones insults because I'm "too sensitive" and they don't even know me.

I'll let you in on something personal. Life has pounded the crap out of me. Aftrer getting Leukemia I damaged my back so I'll have to live on constant pain for the rest of my life and I can't work. My career is down the tubes. There's no rewards for me for a job well done. There's no sense of achievement in my life now. When I became disabled all my so-called friends abandoned me. So yeah! When people insult me I get irritated. Who wouldn't under identical conditions? So I've been deleting all PMs from that moderator and will forever do so. I won't be judged.

So forgive me if I take one last excuse out of my life that someone could use to sit in judgement of me.

I actually suspected this before, but isn't it interesting to note that the moderators are completely aware of who reps who. Why keep it a secret to us but then let be known to you guys?

Yes. That hasn't been mentioned in this thread yet so I'm glad that you brought it up/ Moderators not only know who's repping who but the also appear to be sitting injudgement of us when we use the rep system.

Let it be known that I will never rep anybody again for this reason. I don't like being spyed on and then judged from the results.

Of course time is a spatial dimension, this is why in relativity it was given a special name, called the imaginary space dimension.

Space refers to where things are. A time parameter doesn't tell you anything about where something is. That's why its not a spatial dimension. Be careful not to confuse "space" in the mathematical space from "space" in the physical sense. People have a tendancy to confuse these two usages

If time is change and a system reaches equilibrium, would it be reasonable to say that time has stopped in the frame of that system so time only actually exists within systems that are in disequilibrium?

No. Time is not simply that which pertains to a particular system. Time pertains to the universe in its entirety. As Aethelwulf pointed out a system can be static but that doesn't mean that time has stopped in that frame. Frames are infinite in size. Just because a box in intergalactic space is static and thus unchaning in time it doesn't mean that time has stopped. There's an entire universe of change going on around it.

... in the sense that time is often treated as a degree of freedom, just another space dimension.

I disagree. Time is not a spatial dimension. Its a dimension in spacetime. Spacetime is a space in the mathematical sense of the term but time is not a spatial dimension.

But setting time directly equal with change is problematic because obviously a system does not need to change while time trucks on.

This would be so much easier if people just agreed with everything I said.

You keep saying that but I consider that to be a straw argument since time is about change in the entire universe. It doesn't just refer to whether a particular system is static or not. Even for a static system one can place a clock near the system and it would tick thus measureing the passage of time. That's like saying that an electric field is the force that would be exerted per unit charge if a charged were placed in the field. But with the charge gone we still consider the field to be present. Same with time. Just because a clock isn't in the room its still said that time passes in the room because if one places a clock in the room it would tick thus noting the passage of time.

Of course it doesn't, but I didn't say time didn't apply to the system. I am giving you a perfect example of how a quantum system does not change even when time does.

True, but that doesn't mean that time doesn't pertain to changes, You can only speak of a stationary state when you have a clock to compare it to.

A.P. French speaks about time in his text Newtonian Mechanics[/i]. On page 61-62 he writes

The sense of the pssage of time is deeply embedded in every one of us. We know, in some elemental sense, what time is. But can we say what it is. The distinguished Dutch physicist H.A. Kramers once remarked: "My own pet notion is that in the world of human thought generally, and in physical science particularly, the most important and most fruitful concepts are those which it is impossible to attach a well defined meaning." To nothing, perhaps, doe this apply more cogently than to time. Nevertheless, if one tries to analyze the problem, one can perhaps begin to see that it is not entirely elusive. Even though a definition of time may be hard to com by, one can recognize that our concept of the psage of time is tied very directly to the fact that things change. In particular we are aware of certain recure events or situations-the beat of our pulse, the daily passage of of the sun, the seasons, and so on.

On another note, systems which are measurable are physical. Time is not physical, it's not even an observable; the kind of things we can measure by observation.

Of course that depends on how the term physical is defined. Different people have different ideas of what it means to be physical. When I use the term it means that its something that is directly related to something in nature that has an existance. In this case the chaning of the universe as a whole. If i was talking about velocity then that's a mathematical construct which cannot be measured directly but can only be calculated from other measurements such as the change in positioin of an object when compared to a clock. I think of velocity asbeintg physical. Energy pertains to a sum of terms for which the sum is constant of motion. Only the individual portions can be measured. E.g. we can't measure kinetic energy directly. What we can do is to measure its velocity and then calculate it from that an the body's mass. Or you cn let it do work on a system and then measure the variables which define the system. E.g. let the body hit a paddel which is emersed in water and let it stir it. The water will then heat up and you can measure that with observing the level of mrcury in a thermometer which is submerged in the water. Same with potential energy. It can't be measured directly. You can only measure the body's position in a field and then calculate its energy from that and the formula for potential energy. Then its the mathematical sum that is constant and I think of that as a physical quantity.

That would be a global time and that doesn't exist in GR. Global time vanishes when you quantize the EFE equations.

That doesn't mean that time doesn't pass around the universe. It just means that you have to be careful when you assign a number to it.

I can give you a perfect example of time not equaling change.

 

Make momentary observations on a system ready to up its energy in the form of radiation, then you will effectively freeze the quantum evolution of that system (the zeno effect). Does time stop because your system no longer changes?

 

Time does not mean change at all... time can truck on without there needing to be any change in your system.

Time does not refer to a particular system but to the universe as a whole. That means that somewhere in the universe something is changing. The sun is giving off energy, galaxies a moving away frmo each other, water pours over waterfalls, hearts are beating, cars race down the highway, the lab clock ticks away, radioactive material is decaying, paint is oxidizing, people fall in love, they work, pay bills, go food shopping, watch tv etc. The list goes on ad infinitum.

When a quantum system is stationary it means that when you compare it to the ticking of a clock the quantum state is independant of time. That doesn't mean that time dosn't apply to the system. And it also doesn't mean that the particle which the system my be describing isn't moving. The truth is that you can't even speak about what the system is doing unless you make a measurement.

Bit confused. Is time a scalar or vector quantity?

Time is a number, not a vector. The term scalar refers to a number which remains unchanged by a change in cordinates. A 4-scalar in relativity refers to a number which is independant on the choice of spacetime coordinates. A 3-scalar is a number which remains unchanged by a change in spatial coordinates. Time is a 3-scalar.

You put a period at the end of your link so it gives a "Page not found error". This is it I think;

 

http://www.wfu.edu/~brehme/time.htm

 

My attempt at a definition: a book-keeping or counting system used for sequencing and measuring the period between events.

I agree. In fact that is the essence of what appears in that link.

Rubbish. I have stated, not that his writing style is immature, but that his writing style could be interpreted to indicate that he is immature. I am advising him,

The moderator is trying to tell you that your opinion on my writing style is your own and he doesn't share it.

Have you ever heard of the term Doublespeak? Its defined as follows

Doublespeak is language that presends to communicate but really doesn't. It is language that makes the bad seem good, the negative appear positive, the unpleasant appear attractive or at least tolerable. Doublespeak is languge that avoids or shifts responsibility, language that is at variance with its real or purported meaning. It is language that conceals or prevents thought: rather than extending thought, doublespeak limits it.

When you write

...have you considered just taking a step back and appearing to behave like a mature human being?

This is very close to being doublespeak. It can only be read as meaning that without taking a step back, i.e. continuing as is, that I'm being an immature human being. I.e. its a veiled attempt at calling me immature.

Besides, nobody asked for your opinion and it'd be unwise to think that kind of "advice" would be desired by any reasonable person. That's most likely why it got a neg rep.

I can tell you, that time does not mean change. Things can be unchanging while time trucks on, so they are not synonymous.

I disagree. The very essense of time is directly related to change or "happenings".

A friend of mine wrote an article on this topic. See http://www.wfu.edu/~brehme/time.htm. I agree with everything in that page.

If there were a universe in which nothing happened and nothing changed then time would have no meaning.

How can the core of Earth ever lose all its' heat. Doesn't the pressure of gravity constantly create heat?

Note: The term you're looking for is thermal energy, not heat.

The thermal energy due to pressure would eventualy dissipate. The thermal energy due to pressure is from the process of compression. That's a finite process.

Eh. I have a dark sense of humor, I suppose. It clearly doesn't appeal to everyone. I'm also in no rush to treat this guy as anything more than an annoyance.

And what about everyone here who gets a sick feeling in our stomach when you won't cease talking about someones dead mother, even after comments by the moderators? Just because you don't like someone it doesn't mean you have to make your beef with him public. That's not what forums like this are for. Please show a little decorum.

studiot - It's not just EM waves that are quantized. The electromagnetic field itself is quantized, even when the field is static.That's what Quantum Field Theory (QFT) is all about. See http://en.wikipedia.org/wiki/Quantum_field_theory

Also, while its quite true that electrons are called particles it doesn't mean that they behave like a particles.

I think you should delete the term "dimension" from your vocabulary and re-learn it with a proper definition (e.g. the above-mentioned "number of independent degrees of freedom").

Well said. Let's start from scratch.

We call a set of values x¹, x², ... , x^N a point. The variables x¹, x², ... , x^N are called coordinates. The totality of points corresponding to all values of the coordinate with certain ranges constitute a space of N dimensions.

I was using personal attack as written, not in terms of the definition included in fallacy descriptions; it's clearer, IMO to simply used ad hominem because that term is typically used only when discussing the fallacy, while the phrase personal attack is, in this light, ambiguous if you don't state that it's the fallacy. But I think that clears up my confusion on this.

I'm glad we could discuss all this in a polite fashion and come to the resolution. Thanks for the conversation!

Ok so the electromagnetic field is a field, what is the relation(if any) to the spatial dimension(could they be described as fields?) and what about time?

To evaluate the field one needs to specialize the location in space r = (x, y, z) which to evaluate the field and the time t which it is evaluated. That mean we need to know the position vector of the location and that requires three numbers to uniquely specify it. The field is then expressed as

E = E(r, t)

This is what it means to speak of three spatial dimensions. This can be expressed as

E = E(x, y, z, t)

The element [v]X[/b] = (ct, x, y, z) is called a point in spacetime. Its also a position 4-vector. It requires 4 numbers to specify a point in spacetime. In relativity one uses the Faraday Tensor tensor to specify the electromagnetic field. Such a tensor is called a second rank 4-tensor.

Is the Higgs field the proposed idea about the spatial dimensions with the Higgs boson working as the photon? And is that QFT?

I don't know about all that Higgs stuff. I do know that QFT refers to Quantum Field Theory.

Is frustration necessarily a sign of impatience?

Please reread post #54

http://www.scienceforums.net/topic/67396-ad-hominem/page__view__findpost__p__687947

Btw, I made a mistake. Oh, for crying out loud is not an attack, its meant to show the emotion of either frustration, exasperation, or annoyance.

I think I see the source of our disagreement. You use the term personal attack to mean attack on a person. This is not what how the text, and several online sources, defines it. My text reads

Whenever we attack a person instead of his or her argument, we commit the fallacy known as personal attack.

Note that it doesn't call the fallacy the "personal attack fallacy" but merey calls it a personal attack.

By the way, you keep saying that this is my definition. Its not. Its how its defined in this text and elsewhere on the internet. Its the text that I use as an authoritative source though.

The following web site defines personal attack as follows

http://www.nizkor.org/features/fallacies/personal-attack.html

A personal attack is committed when a person substitutes abusive remarks for evidence when attacking another person's claim or claims.

Wikipedia defines personal attack as follows

http://en.wiktionary.org/wiki/personal_attack

personal attack (plural personal attacks)

1.Making of an abusive remark instead of providing evidence when examining another person's claims or comments

For these reaons its clear to me that a personal attack is not merely an attack on a person. You seem to believe that's how its defined. Is that correct? If so then why?