# Dimensions

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There are three dimensions of space. Four dimensions of space time.

Isn't the fifth dimension e (as in E=MC²)  ?

There seems to be five properties of an event, not four. Space time without the involvement of energy doesn't do anything. It might as well not exist. And does time actually exist, without changes in the location of energy? So energy is more of a dimension than time.

So I'm proposing that events occur in five dimensions.

Whether you could work out a system of maths for that is beyond me though.

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That's an interesting idea.  If we are trying to identify the "properties of an event" it seems to me we are heading toward identifying all the characteristics that make the event unique, which is somewhat beyond dimensions.  It brings to mind thermodynamics where we can define an event in terms of equations of state.  This introduces other variables such as pressure, temperature, volume, mass, etc.  I think I'm drifting away from your initial intent and will  have to think some more about it.

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1 hour ago, mistermack said:

So I'm proposing that events occur in five dimensions.

What is an "event"? By what criteria do we differentiate discrete events from the event before, the event after, and all the simultaneous events that are taking place at the same time?

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5 minutes ago, Peterkin said:

What is an "event"? By what criteria do we differentiate discrete events from the event before, the event after, and all the simultaneous events that are taking place at the same time?

Well the history of the Universe is the real event, and you have to make arbitrary cut-off points, in time and space, to isolate the part of that event that you are interested in.

32 minutes ago, OldChemE said:

This introduces other variables such as pressure, temperature, volume, mass, etc.

Pressure and temperature are the result in the change in location of e over time. Volume is just the 3 dimensions of space, and mass is e/C²  so nothing new is needed there.

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24 minutes ago, mistermack said:

and you have to make arbitrary cut-off points, in time and space, to isolate the part of that event that you are interested in.

That works. It also you means you can arbitrarily - or, rather, selectively, according to the purpose of the exercise - limit or extend which factors, properties or dimensions that you take into consideration.

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Energy is frame dependent.
IOW, it depends on spatial-temporal co-ordinates, or dimensions.

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9 hours ago, mistermack said:

So I'm proposing that events occur in five dimensions.

Whether you could work out a system of maths for that is beyond me though.

There is an existing framework within Theoretical Physics for this.

This is because the concept of 'dimension' appears in several different forms, each with its own characteristics.

You are proposing a different mix of traditional continuous dimensions as used in traditional geometry to descibe shapes.

Such mixes have been studied, and when Relativity came along, Eddington discussed in some detail the possibility of employing  1,2,3,4, ... n spatial dimensions and 1,2,3, ...m temporal dimensions early in his treatise "The Mathematical Theory of Relativity".

Minkowski added the possibility of 'imaginary' dimensions by using complex numbers instead of real numbers.

The possibility that the Universe is not continuous in the traditional sense was also studied and that fractional dimensions (fractal) may be required

Quote

Wikipedia

In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff.[2] For instance, the Hausdorff dimension of a single point is zero, of a line segment is 1, of a square is 2, and of a cube is 3. That is, for sets of points that define a smooth shape or a shape that has a small number of corners—the shapes of traditional geometry and science—the Hausdorff dimension is an integer agreeing with the usual sense of dimension, also known as the topological dimension. However, formulas have also been developed that allow calculation of the dimension of other less simple objects, where, solely on the basis of their properties of scaling and self-similarity, one is led to the conclusion that particular objects—including fractals—have non-integer Hausdorff dimensions. Because of the significant technical advances made by Abram Samoilovitch Besicovitch allowing computation of dimensions for highly irregular or "rough" sets, this dimension is also commonly referred to as the Hausdorff–Besicovitch dimension.

This was demonstrated most vividly by Mandelbrot with his question "how long is the coastline"

In a different line of attack, it was realised that there is a tie up between the number of variables needed to completely specify the condition of a system and the concept of dimensions, since these variables can be plotted on a multidimensional 'graph'.

So in Thermodynamics we have state variables ( +1 to @OldChemE ), in Mechanics we have phase variables and so on.

The physics of the particular system gives us a new relationship. That of constraints and degrees of freedom.
The Physics of the system gives us a set of relationships (usually equations) between the variables and all these quantities are called 'dimensions' in some system of analysis or another.
The new thing is that we can use these relationships to trade off between the total number of degrees of freedom, variables and constraints.
So in thermodynamics we need one less state dimension than the 3  -  P,  V,  T as knowing 2 will always allow calculation of the third.

This brief survey hopefully shows that there is much more to this question than at first meets the eye.

Good topic, +1

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10 hours ago, mistermack said:

There are three dimensions of space. Four dimensions of space time.

Isn't the fifth dimension e (as in E=MC²)  ?

There seems to be five properties of an event, not four. Space time without the involvement of energy doesn't do anything. It might as well not exist. And does time actually exist, without changes in the location of energy? So energy is more of a dimension than time.

So I'm proposing that events occur in five dimensions.

Whether you could work out a system of maths for that is beyond me though.

Must admit I can't follow this. Why would a single, seemingly arbitrarily chosen, property of a physical system qualify as a dimension? An event is not a physical system, surely?  Distance and time are not properties of physical systems either. And why energy, rather than, say, momentum, or other properties of physical systems?

I can't help thinking there is a category mistake here.

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Posted (edited)
1 hour ago, exchemist said:

Must admit I can't follow this. Why would a single, seemingly arbitrarily chosen, property of a physical system qualify as a dimension? An event is not a physical system, surely?  Distance and time are not properties of physical systems either. And why energy, rather than, say, momentum, or other properties of physical systems?

I can't help thinking there is a category mistake here.

Not really.

mistermack is hinting at what developed in classical mechanics and and is now also used in quantum mechancis and fractal mechanics (in computing)

This is the system of Generalised Coordinates, of Dimension n.

Definition

If the configuration of a system S is determined by the values of a set of independent variables q1...qn then   {q1.....qn} is said to be a set of generalised coordinates for S, of dimension n.

The qn are often momenta in classical mechanics.

The set, S, is called the phase space.

Generalised dimensions are more modern and there are many modern texts on the subject

Edited by studiot
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13 minutes ago, studiot said:

Not really.

mistermack is hinting at what developed in classical mechanics and and is now also used in quantum mechancis and fractal mechanics (in computing)

This is the system of Generalised Coordinates, of Dimension n.

Definition

If the configuration of a system S is determined by the values of a set of independent variables q1...qn then   {q1.....qn} is said to be a set of generalised coordinates for S, of dimension n.

The qn are often momenta in classical mechanics.

The set, S, is called the phase space.

Generalised dimensions are more modern and there are many modern texts on the subject

But these have to be independent variables, right? Whereas energy is in general a function of space and time, is it not?

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3 minutes ago, exchemist said:

But these have to be independent variables, right? Whereas energy is in general a function of space and time, is it not?

But energy isn't a function of just the 3 dimensions of space. You can't describe energy just with the 3 spatial dimensions and time. But energy, in motion in the 3 dimensions, causes time, and pretty much covers everything that exists.

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1 hour ago, mistermack said:

But energy isn't a function of just the 3 dimensions of space. You can't describe energy just with the 3 spatial dimensions and time. But energy, in motion in the 3 dimensions, causes time, and pretty much covers everything that exists.

Energy being a dimension implies that it is somehow orthogonal to the spacetime dimensions. How does that work? How do you reconcile the units?

How do you have “energy in motion” if it’s a dimension?

What is the evidence that energy causes time? What is that relation? How much time does an energy E0 cause?

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space and time are the independent variables.
Energy is not independent.

4 hours ago, studiot said:

If the configuration of a system S is determined by the values of a set of independent variables q1...qn then   {q1.....qn} is said to be a set of generalised coordinates for S, of dimension n.

The 'configuration of a system' is the very definition of energy.

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Posted (edited)
2 hours ago, swansont said:

Energy being a dimension implies that it is somehow orthogonal to the spacetime dimensions. How does that work? How do you reconcile the units?

How do you have “energy in motion” if it’s a dimension?

What is the evidence that energy causes time? What is that relation? How much time does an energy E0 cause?

Yes, that's partly what I was getting at: how can energy be orthogonal to space and time?

But also, one can speak of two points separated in space or in time, but what can two  points separated in energy mean, without reference to the presence of a specified system, for the energy to be a property of? Energy is not free standing: it only exists as an attribute of a physical system.

Edited by exchemist
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On 7/29/2022 at 5:57 PM, mistermack said:

Pressure and temperature are the result in the change in location of e over time. Volume is just the 3 dimensions of space, and mass is e/C²  so nothing new is needed there.

Two events at the same location could have different combinations of pressure temperature and volume, but have the same total energy.  Energy alone is not sufficient to uniquely define an event.  For example, an adiabatic process would go through many different states without exchanging energy with the environment.

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7 hours ago, OldChemE said:

Two events at the same location could have different combinations of pressure temperature and volume, but have the same total energy.  Energy alone is not sufficient to uniquely define an event.  For example, an adiabatic process would go through many different states without exchanging energy with the environment.

+1

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On 7/30/2022 at 2:13 PM, swansont said:

What is the evidence that energy causes time? What is that relation? How much time does an energy E0 cause?

I'm really not the man to answer, I think you can tell by now I'm not a physicist. My OP was just me musing.

However, from that perspective, if no energy moved in your body, would you age or stay exactly the same? If no energy moved in a pendulum system, would the clock show any time? If a photon didn't move, the speed of light would be zero. That could only happen if time didn't happen.

As far as my imagination takes me, if no energy moved in the universe, there would be no time expended. (unless you were looking in from another universe)

9 hours ago, OldChemE said:

Two events at the same location could have different combinations of pressure temperature and volume, but have the same total energy.  Energy alone is not sufficient to uniquely define an event.  For example, an adiabatic process would go through many different states without exchanging energy with the environment.

But the four dimensions of space and time, are they sufficient to define an event ? We bring in mass and momentum and energy to fill in the picture, but don't they boil down to energy in motion?

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27 minutes ago, mistermack said:

I'm really not the man to answer, I think you can tell by now I'm not a physicist. My OP was just me musing.

You shouldn't make claims you can't support

27 minutes ago, mistermack said:

However, from that perspective, if no energy moved in your body, would you age or stay exactly the same? If no energy moved in a pendulum system, would the clock show any time? If a photon didn't move, the speed of light would be zero. That could only happen if time didn't happen.

I'm not sure what "energy moving" means. Energy is a property of a system, not a substance or particle. An object moves and it has kinetic energy. You toss a ball in the air and its kinetic energy decreases as its potential energy increases; the sum remains constant. Is energy moving?

A block of a radioactive material just sits there. Half of its atoms decay in one half-life. Or just one atom sits there, and decays after some time.  Where is the "moving energy"?

27 minutes ago, mistermack said:

But the four dimensions of space and time, are they sufficient to define an event ? We bring in mass and momentum and energy to fill in the picture, but don't they boil down to energy in motion?

This additional information that's required does not make the information a dimension. Color could then be a dimension. It fits some of the parameters - it's orthogonal, for one, but suffers from some of the other shortcomings I pointed out.

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18 minutes ago, swansont said:

You shouldn't make claims you can't support

That's why my OP was a question, an invitation to debate.

19 minutes ago, swansont said:

I'm not sure what "energy moving" means. Energy is a property of a system, not a substance or particle. An object moves and it has kinetic energy. You toss a ball in the air and its kinetic energy decreases as its potential energy increases; the sum remains constant. Is energy moving?

A photon is decribed as a "packet of energy".  And it moves at the speed of light in a vacuum. Surely that means moving energy? The ball is composed of energy, if E=MC2    , so you are tossing a lump of energy in the air.

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28 minutes ago, swansont said:

A block of a radioactive material just sits there. Half of its atoms decay in one half-life. Or just one atom sits there, and decays after some time.  Where is the "moving energy"?

Are protons and neutrons in the nucleus of an atom stationary relative to each other? And quarks in protons and neutrons can't move relative to each other?

9 minutes ago, mistermack said:

A photon is decribed as a "packet of energy".  And it moves at the speed of light in a vacuum. Surely that means moving energy?

Rather than moving, it jumps over. A photon has no trajectory in the classical sense, a photon has only a point of birth and a point of its absorption. We cannot trace the trajectory of a photon between these two points in principle, since it is possible to see a photon only by destroying it (absorbing it).

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9 minutes ago, SergUpstart said:

Are protons and neutrons in the nucleus of an atom stationary relative to each other? And quarks in protons and neutrons can't move relative to each other?

Doesn't vibration count as movement anyway? And don't particles also have wave properties, which involves movement of energy? Electrons are described as having an orbit, which implies movement, even when the lump of matter is at rest.

23 minutes ago, SergUpstart said:

Rather than moving, it jumps over. A photon has no trajectory in the classical sense, a photon has only a point of birth and a point of its absorption. We cannot trace the trajectory of a photon between these two points in principle, since it is possible to see a photon only by destroying it (absorbing it).

Maybe so, but you can demonstrate the trajectory, by issuing a stream of photons, and intercepting them at various points.

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34 minutes ago, mistermack said:

That's why my OP was a question, an invitation to debate.

The claim was made subsequent to the OP, and was not phrased as a question.

34 minutes ago, mistermack said:

A photon is decribed as a "packet of energy".  And it moves at the speed of light in a vacuum. Surely that means moving energy?

Such is the problem of relying on pop-science as your source of information. A photon has energy, and the photon is moving. But if I throw you a red ball, does "the red is moving" make much sense? Or if we agree the ball is small, does "the small is moving" make sense?

34 minutes ago, mistermack said:

The ball is composed of energy, if E=MC2    , so you are tossing a lump of energy in the air.

It is not "composed" of energy, as energy is not a substance.

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4 minutes ago, swansont said:

It is not "composed" of energy, as energy is not a substance.

What is a substance?

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38 minutes ago, SergUpstart said:

Are protons and neutrons in the nucleus of an atom stationary relative to each other? And quarks in protons and neutrons can't move relative to each other?

16 minutes ago, mistermack said:

Doesn't vibration count as movement anyway? And don't particles also have wave properties, which involves movement of energy?

You would have to demonstrate that this is relevant to the broader question, that energy causes time. What is the nature of that relationship? I'm pretty sure I can rebut the claim, but I have to know exactly what the claim is. But I have no interest in vague descriptions where the game is to try and find loopholes.

16 minutes ago, mistermack said:

Electrons are described as having an orbit, which implies movement, even when the lump of matter is at rest.

People who don't really know what they are talking about might describe electrons as having an orbit; that model went out of fashion ~100 years ago.

And we have gone from "energy" to "movement" which was not the claim. At rest means no center-of-mass kinetic energy.

If you want to invoke vibration as the energy, I need a more precise model in order to show that it's wrong. this is physics. We quantify things.

3 minutes ago, mistermack said:

What is a substance?

If you need these definitions then you are obviously not prepared to defend any of these WAG claims.

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41 minutes ago, swansont said:

People who don't really know what they are talking about might describe electrons as having an orbit; that model went out of fashion ~100 years ago.

I didn't say planetary orbit. This is the usual attempt at nit-picking.

Wikpedia said "Thus, the planetary model of the atom was discarded in favor of one that described atomic orbital zones around the nucleus where a given electron is most likely to be observed ".[31][32]

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