[jeffreyH (OP)]

That is inverted so shouldn't it be considered wrong? I do understand that it is a matter of convention. Does that by default make it right?

[PmbPhy]

That is inverted so shouldn't it be considered wrong? I do understand that it is a matter of convention. Does that by default make it right?

spacetime diagrams don't have magnitudes. The axes are labeled in terms of particular units, typically meters.

[jeffreyH (OP)]

You can derive a gradient and therefore by definition a spacetime magnitude.

[PmbPhy]

You can derive a gradient and therefore by definition a spacetime magnitude.

Gradients aren't derived. They are either defined or calculated. The gradient operator doesn't operate on objects in spacetime. They only operate on objects in space only then on 3-scalar fields. There is a similar object which operates in spacetime called the d'ALembertian operator. See: https://en.wikipedia.org/wiki/D%27Alembert_operator
It operates on 4-scalars. You can take the d'ALembertian of a 4-scalar and then contract it to get a magnitude. However that in no way is the magnitude of spacetime.

Consider the analogy of speaking of the magnitude of space. Do you think that makes sense? If you have a 3-scalar such as the electric potential then you can take the gradient to get the negative of the electric field. The magnitude of that is the magnitude of the electric field at the spatial point (x, y, z). But you cannot speak of the magnitude of such a spatial point . What you can speak of is the magnitude of the position vector r = (x, y, z)

Do you see the subtleties here?

[jeffreyH (OP)]

I see subtleties but space contracts and time dilates. Therefore a magnitude would make sense. If measures of space and time were constant this would be different.

[PmbPhy]

I see subtleties but space contracts and time dilates. Therefore a magnitude would make sense. If measures of space and time were constant this would be different.

You're referring to the contractions and dilations between spatial points and time intervals. There are magnitudes associated with those. There is even a magnitude associated with the spacetime interval. But, once again, you cannot associate a magnitude with spacetime itself.

Jeff - It's not enough to suggest that such a magnitude exists. You need to state that that magnitude is and what the meaning of that magnitude is. For example: What do you propose to associate the magnitude of spacetime with? I.e. spacetime is defined as the manifold (collection) of all events (x, y, z, t). What do you hold is the magnitude of that? Likewise, what do you think that the magnitude of space itself might be?

Before you respond I'd like to point something out. I'll use Cartesian space as an example. One might think that it'd be easy to assign a magnitude of a point in space since many associate (x, y, z) with the value r = sqrt(x^2 y^2, z^2). However x, y and z are the distances between lines in space and an arbitrarily chose set of coordinate axes. Even then you'd be associating a single point in space with a magnitude and not space itself so you're not really associating a magnitude with space.

[timey]

This is because the dimensions of spacetime are background-independent and emerge dynamically as a result of general relativity.  Therefore the magnitude of any one position in space changes over time.

[PmbPhy]

This is because the dimensions of spacetime are background-independent and emerge dynamically as a result of general relativity.  Therefore the magnitude of any one position in space changes over time.

Incorrect. Nothing in that statement is correct. In fact its all meaningless.

Tell me. What is it that you claim that the magnitude of a position in spacetime as a function of time is? Also, why didn't you post your explanation of why what I explained above is wrong and why what you just claimed is correct? Merely posting an assertion in a physics discussion forum is of no use to anybody.

Butt, okay. I'll bite. Please state what it is it for us. Give us an example of it. Write down the expression for the magnitude of the position of the point in spacetime associated with the following event, A, in spacetime

A: The center of the lobby of the Hancock tower (which is in Boston) exactly on next New years.

[timey]

Meaningless you say?

The calculation for the magnitude (presuming that magnitude is a description of the dynamics of spacetime) of the position of Hancock tower in spacetime will, unless some drastic changes occur in the planetary motions, remain approximately the same from one moment to the next, but the calculation for the positions in space that Hancock tower moves through will change drastically over time.
The positions of space that the Hancock tower moves into will be dynamically changed by the arrival of Hancock tower, and dynamically changed by the departure of the Hancock tower.

That is what the background-independent remit of general relativity is.  Mass tells spacetime how to bend, and spacetime tells mass how to move.

Therefore spacetime calculations for a given position in 'space' will change over time with the changing positions of mass, as opposed to the positions of mass in space which are dynamically changing the properties of the 'space' they move through.
Anyone who is wanting to understand what the magnitude of any given position in 'space' is must take on board that the background is not fixed.

This is not incorrect, nor is it meaningless.  In fact this consideration forms part of the two body problem.

[PmbPhy]

Meaningless you say?

And your response to my question showed two things (1) you don't know the subject matter and (2) you were unable or unwilling to state the magnitude of the event A.

Sometimes I wish I knew where people got such strange ideas like the ones you post so often. But those wishes don't last long because its like wondering where dreams come from.

The calculation for the magnitude (presuming that magnitude is a description of the dynamics of spacetime) of the position of Hancock tower in spacetime will, unless some drastic changes occur in the planetary motions, remain approximately the same from one moment to the next, but the calculation for the positions in space that Hancock tower moves through will change drastically over time.

Wrong. I gave you a specific question because I know you'd be confused over answering a simple question such as what's the magnitude of the event (x, y, z, t) in flat spacetime. That's because I'm 100% certain that you're going to confuse that with position 4-vector (x, y, z, ct) and confuse it with the magnitude of that 4-vector.

timey - Please give up while your this far behind. You simply don't understand what you've been posting. E.g. that nonsense about mass in your response when there's no mention of mass in my question. Its quite normal to speak of a position in spacetime with no need of speaking of mass or a planet in motion. You showed me that you don't understand that fact in your response.

This is not incorrect, nor is it meaningless.  In fact this consideration forms part of the two body problem.

I'm the king of Canada. Wow! I guess that if I write down a claim in a post then it must be true and that I really am the king of Canada! Very cool.

timey - When exactly are you going to learn that when you merely make a claim that nobody cares or pays attention to it unless you prove it! Don't you get it?

[timey]

Asking a non-mathematician to provide a mathematical answer and then complaining when the response is non-mathematical is a deliberate case you of setting the scene for ridicule.
My answer to your question is correct.
The calculations of the  spacetime dimensions of the Hancock Tower will be approximately the same next new years day as they are now, given that no drastic changes occur to the moons motion around the earth, the earth's motion around the sun, etc, or to the tower itself.
The spacetime calculations for a specific location of 'space' that the Hancock Tower moves into and then departs from will change dynamically from one moment to the next.

General relativity is a background independent theory.  Yes it is quite normal to calculate spacetime from the background dependent remit of special relativity.  A fact that theoretical physicists who work on background independent interpretations are well aware of.  A fact that any string theorist or quantum-gravity theorist will be happy to confirm to you forms a significant part of any considerations they make.

I certainly don't for a minute see why my lacking in ability to put my words into mathematical format should exempt me from a conversation.  Nor do I see any logic involved in requiring that a mathematical proof to a question is necessary to a continued conversation.

I came to this forum seeking mathematical help to formulate my own 10 year in the making theory into mathematical structure.  When are you going to 'get' this simple enough status quo and stop requiring that I provide mathematical proofs and just talk to me in English?

It's a known fact of the human condition that some people are better at some things than others.  Just because I cannot write mathematical format does not mean that I do not understand structures.
Instead of asking me mathematical questions that you know that I will not be able to answer in mathematical form and then ridiculing me for it, would it be such a problem for you to simply engage with the content?

I'm very disappointed in your attitude here Pete.  It stinks of the type of attitude prevalent in physics where people make any excuse not to listen to each other. Quite clearly I have been hoping to meet a mathematician who is knowledgeable in the physics quest for unification, understands the remits of the various unification theories that current theoretical physicists are working on, and can listen to and then calculate the remit of my theory as I describe it in words as to how it corresponds with what other theorists have been working on.
Yes I might as well dream on.  I can't even raise a conversation about time dilation without the response being 'from the observers point of view' when clearly the structure of general relativity and special relativity allow one to converse in term of structure.
And as to you - you don't seem able to conduct a conversation concerning the 'axis of evil' observations of preferred direction when it comes to discussing inflation.
(Edit: Just seen tour response to that.  Another display of misplaced self grandeur.  You clearly didn't read the New Scientist link.  How can you pose as an authority to make such disparaging remarks about something you clearly have not studied, but clearly need to.)

I can tell you now that this latest display of misplaced self appointed superiority and blatant rudeness has made me realise that I've been barking up the wrong tree here.
I want to discuss theoretical physics, MOND, DSR, quantum gravity, the axis of evil and the R scale, the acceleration of gravity and a theory of unification.
You want to discuss flat spacetime diagrams in terms of your mathematical knowledge and answer questions to the intellectual degree of A-level physics.

I don't see the point of posting here at the forum anymore.  I'm certain not going to get the help I seek, nor even an interesting conversation.

Cheers Pete for clearing that up for me.  I won't waste my time any further.

[PmbPhy]

Never mind timey. I gave up trying to reason with you.

[timey]

In fact Pete, you are being perfectly ridiculous...
I described the postulates of general relativity in response to a question about the magnitude of space, given that the magnitude of space is dynamical.
You demanding that I must provide proof of my statement is in as much as asking me to provide proof of the postulates of GR.
This is the equivalent of my saying that Elizabeth the second is the queen of England and you demanding that I prove it.

[alancalverd]

I think Jeffrey confused "dimensions" with "magnitude". Not the same thing in physics. 

[timey]

Unless he was talking about the magnitude of the force causing the dimensions, which is what I took him to mean, and why I mentioned dynamical background independence.  But my own use of physics terminology is far from conventional, despite trying hard, so perhaps I am not so fussed... I certainly wouldn't make an issue over it.  Issues are usually incredibly boring and time consuming, and to my mind unecessary when raised by people who are reputably intelligent, where a simply case of saying "don't you mean dimensions" would suffice, or "gravity is ignored in special relativity', and the conversation is then forwarded, which is the pupose of a thread isn't it?

[timey]

In any case I am interested in what the answer to the question is, the question being why are the dimensions of a spacetime diagram in units of T/L, because usually one sees L/T for a speed, and I don't seem to be finding any literature on T/L.

[alancalverd]

Most ST diagrams on the internet seem to show space as the horizontal axis and time as the vertical axis. No particular reason AFAIK but a useful reminder that the classical notions of velocity etc may not be applicable over the whole area.

Problem is that dimension and magnitude are somewhat interchangeable in everyday English, as are "force, power, strength, energy....." which people use interchangeably to make their prose less boring. It's a pity, because anyone who took the trouble to study both science and journalism could end up writing as precisely, entertainingly and powerfully as Steinbeck, Moore, Hoyle... and not confuse the public. 

[timey]

Most ST diagrams on the internet seem to show space as the horizontal axis and time as the vertical axis.

Which suggests to me that any variability in length or space is the depiction of the time dilation factor - as the time axis will be being held relative to the same length units of period of time that the speed of light is.

No particular reason AFAIK but a useful reminder that the classical notions of velocity etc may not be applicable over the whole area.

Which is what MOND is all about.

Problem is that dimension and magnitude are somewhat interchangeable in everyday English, as are "force, power, strength, energy.....

Yes - I had a quick investigative  foray onto the net, and found scientists from all disciplines discussing the phenomenon. It's not as uncommon as one might think.
And then to make matters more confusing, people such as Einstein show that things one once thought of separately, such as gravity and acceleration, are actually the same thing.

which people use interchangeably to make their prose less boring. It's a pity, because anyone who took the trouble to study both science and journalism could end up writing as precisely, entertainingly and powerfully as Steinbeck, Moore, Hoyle... and not confuse the public.

Ach Weel!  We canny all be perfect laddy... and hey, thanks for the reply.

[guest4091]

Someone here should know
Minkowski, in generalizing the time coordinate from t to ict, a 4th dimension, produced a new format for the space-time diagram. Horizontal x, vertical ct. A straight line represents object speed over light speed, vt/ct = v/c = a speed plot. Without the scaling of time by c, a graph would be useless for analyzing motion at fractions of c. Another gain, the issue of the essence of 'time' is eliminated.

[jeffreyH (OP)]

I think Jeffrey confused "dimensions" with "magnitude". Not the same thing in physics. 

He didn't.