# Is Time The Imaginary Number?

Discussion in 'Physics & Math' started by ghost7584, Dec 21, 2005.

1. ### ghost7584Registered Senior Member

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374
In several scientific disciplines that involve mathematics an imaginary number is used in the calculations to make the numbers come out right. That should mean that there really is something acting on the physical world that is represented by that imaginary number, since it makes the math come out correctly in real world calculations.
An example of this is voltage = current x impedance
The number used for impedance is a complex number composed of a real number plus an imaginary number.
V=I*(R+J) voltage =current times impedance J is an imaginary number to make the math come out right.
Current is plotted horizontally on a graph and an imaginary vertical axis is used for j; a2 +b2 = c2 pythagorean theorem is used to calculate a value for the current. Showing that the imaginary number represents another dimension acting on the current. This imaginary axis, for the imaginary number, on the graph, is at a right angle to the real axis for the current. So the imaginary number is acting, mathematically, as another dimension.
Einstein's general relativity theory, to explain gravity, (which has been proven experimentally correct) uses time as a 4th dimension. In the real world the 3 dimensions, length, width, and depth are each one at a right angle to the other two dimensions. Time, being a 4th dimension, should be at a right angle to the 3 physical dimensions, to qualify as a 4th dimension. The imaginary number, used in calculating current and other things, has an imaginary axis on a graph that is at a right angle to the real axis, and it is therfore acting as a 4th dimension. Since the only proven 4th dimension is time:
I recommend that time should be substituted for the imaginary number in all calculations, in scientific disciplines, that use an imaginary number to make the math come out correctly.
This could lead to all sorts of new equations in all of these fields, and show how time itself is entering into the function of the real world in these scientific disciplines.
Could lead to seeing how time influences every science that uses imaginary numbers. Could (maybe) give a mathematical link between general relativity, [gravity] and electromagnetism, through substituting time symbols that represent time in each discipline into the other discipline. - Perhaps leading to a way of using electromagnetism to influence gravity.
Might even lead to a unified field theory that works.
Complex imaginary number applications
http://en.wikipedia.org/wiki/Complex_number
This substitution for the imaginary number being time is already done in relativity theory:
Relativity
In special and general relativity, some formulas for the metric on spacetime become simpler if one takes the time variable to be imaginary.
Since the universe is uniform I recommend:
SUBSTITUTE TIME FOR THE IMAGINARY NUMBER, IN EVERY SCIENTIFIC DISCIPLINE THAT USES AN IMAGINARY NUMBER TO MAKE THE MATH COME OUT CORRECTLY.
See what new equations that it leads to and do experiments to verify if those equations accurately show what happens in the real world.

Website showing example of use of imaginary or complex numbers:
http://regentsprep.org/Regents/mathb/2C3/electricalresouce.htm

Since complex numbers provide a system for finding the roots of polynomials, and polynomials are used as theoretical models in various fields, complex numbers enjoy prominence in several specialized areas. Among these specialized areas are engineering, electrical engineering and quantum mechanics. Topics utilizing complex numbers include the investigation of electrical current, wavelength, liquid flow in relation to obstacles, analysis of stress on beams, the movement of shock absorbers in cars, the study of resonance of structures, the design of dynamos and electric motors, and the manipulation of large matrices used in modeling. While many of these applications are beyond the scope of the Math B curriculum, an introductory glimpse of the application of complex numbers to electrical circuits can be easily understood and manipulated by students.
Application to Electrical Engineering:
 First, set the stage for the discussion and clarify some vocabulary. Information that expresses a single dimension, such as linear distance, is called a scalar quantity in mathematics. Scalar numbers are the kind of numbers students use most often. In relation to science, the voltage produced by a battery, the resistance of a piece of wire (ohms), and current through a wire (amps) are scalar quantities.
 When electrical engineers analyzed alternating current circuits, they found that quantities of voltage, current and resistance (called impedance in AC) were not the familiar one-dimensional scalar quantities that are used when measuring DC circuits. These quantities which now alternate in direction and amplitude possess other dimensions (frequency and phase shift) that must be taken into account.
 In order to analyze AC circuits, it became necessary to represent multi-dimensional quantities. In order to accomplish this task, scalar numbers were abandoned and complex numbers were used to express the two dimensions of frequency and phase shift at one time.
 In mathematics, i is used to represent imaginary numbers. In the study of electricity and electronics, j is used to represent imaginary numbers so that there is no confusion with i, which in electronics represents current. It is also customary for scientists to write the complex number in the form a + jb.
 Introduce the formula E = I • Z where E is voltage, I is current, and Z is impedance.
Possible Student Questions:
 The impedance in one part of a series circuit is 2 + j8 ohms, and the impedance in another part of the circuit is 4 - j6 ohms. Find the total impedance in the circuit. Answer: 6 + j2 ohms

 The voltage in a circuit is 45 + j10 volts and the impedance is 3 + j4 ohms. What is the current?

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3. ### chrootCrackpot killerRegistered Senior Member

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Well, you might want to actually finish that circuits course before you start congratulating yourself for redefining science as we know it.

Complex numbers are not used in disciplines like electrical engineering "to make math come out right," whatever that means. It happens that impedance is a vector quantity, having both a resistive and a reactive component. Some clever engineers decided to use complex numbers to represent this vector quantity, since most young students have explored complex numbers in more detail than generalized vector geometry, and most cheap pocket calculators include complex arithmetic.

Complex arithmetic is, of course, nothing but vector geometry on a 2-D Euclidean plane.

It also helps that complex numbers are intimately associated with circles, though not uniquely (there's a unit circle in any R^2 vector space). Circles and their associated sine and cosine functions are an electrical engineer's best friends, since a great deal of circuit analysis deals with a circuit's response to such sinusoids. Circuits are all just plain ol' linear algebra, and unforunately don't have any deep connections to Life, the Universe, and Everything.

I honestly have no idea why you think replacing half of the complex plane with "time" makes any sense, or why you think it would lead to any new conclusions. Keep in mind that most circuits are time-invariant: their response to a sine wave, for example, is the same at 1 pm as at 5 pm.

Most of your ideas about general relativity are also faulty: time is not "proven" to be the "4th dimension," it's simply used as one in a mathematical model. It's no deeper than that.

Keep studying.

- Warren

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5. ### ghost7584Registered Senior Member

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374
The idea is this. If the calculations produce accurate answers in the real world, then something is really acting on the real world that represents that imaginary number. [When dealing with real measurable values for circuitry it is not just a mathematical game. Something is acting on the real circuit to make the math correct. THE IMAGINARY NUMBER IS REPRESENTING SOMETHING REAL.] This real thing that it represents behaves like another dimension, which time is the only fourth dimension proven to act on the real world so far in general relativity.
Scalar quantities work for impedance for direct current. The imaginary number is added for alternating current, when frequency and phase shift force the math to be different.

v=i x (r+j) voltage = current times impedance
Suppose the imaginary number does represent time. Why would impedence be r + J for ac current. Let's call it r+ t, substituting time.
In AC the current is cycling from maximum to 0 to maximum in the opposite direction. Time has now become important. From r + t it looks like impedance changes value with time. v= charge/t x (r +t); v = (charge x r)/t + charge; the t's cancel each other. v = i x r + charge. Does that make any sense in the real world for alternating current? Could it be interpreted to make sense?
Could the equation be manipulated another way with t substituting for j.

That is the sort of inquiry I'm trying to start. Making the imaginary number t would allow algebraic manipulation in a different direction yielding new equations. Since the imaginary number acts like another dimension, and time does also, you can make the substitution. (They already do it in relativity using the time variable as an imaginary number.) I say try it and see what you come out with. And you need to yeild equations that can be tested with measuring instruments in the real world to verify if the equations are showing real relationships in real experiments.
I was suggesting doing this in every scientific discipline that uses such imaginary numbers, like it is already done in relativity.

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7. ### ghost7584Registered Senior Member

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374
Chroot-- You call yourself crack pot killer. You seem to have an overly skeptical mind set from the start and might oppose anything new whether it is right or wrong.
Whenever anything new is proposed these overly skeptical types seem to crawl out of the woodwork like bugs.

Science does not advance because of skeptics. It advances in spite of them.

"It is the responsibility of scientists never to suppress knowledge, no matter how awkward that knowledge is, no matter how much it may bother those in power. We are not smart enough to decide which pieces of knowledge are permissible and which are not."
--Carl Sagan, in a 1991 commencement address at UCLA

"Condemnation without investigation is the height of ignorance!"
--Albert Einstein

"The world is a dangerous place. Not because of the people who are evil; but because of the people who don't do anything about it."
--Albert Einstein

"There is something fascinating about science. One gets such wholesale returns of conjecture out of such trifling investments of fact."
--Mark Twain

"Man will occasionally stumble over the truth, but usually manages to pick himself up, walk over or around it, and carry on."
--Winston Churchill

"There is a principle which is a bar against all information, which is proof against all arguments, and which cannot fail to keep a man in everlasting ignorance--that principle is contempt prior to investigation."
--Herbert Spencer

"If you are going to tell people the truth, you had better make them laugh or they will kill you."
--Oscar Wilde

Truth will first be ridiculed, then violently opposed, and finally accepted as self-evident; A. Schopenhauer 1788-1860

8. ### URIIMURegistered Senior Member

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729
I am sure you are right

'i' is basically a "dimensional direction", IMO

9. ### Mosheh ThezionRegistered Senior Member

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2,650
yes... these are exactly the issues which stand in my way...

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Complex imaginary dimensional numbers.. which themselves transcend predictably along timing lines based on resonant properties.

-MT

10. ### chrootCrackpot killerRegistered Senior Member

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2,350
You appear to have just repeated what you said in your first post, in some cases verbatim, and then threw some tired old quotations at me. I suspect this qualifies as a scathing rebuttal in your universe, but, in mine, it's horse shit. Somehow, you've gone from being curious about Ohm's law in reactive circuits to thinking you've redefined the very groundwork of science, and apparently it's my "skeptical mind" that's keeping me from seeing "the truth."

I explained quite carefully why complex numbers are used in circuit theory, and why 'time' makes no sense in place of reactance in such equations. Most of your 'equations' aren't even dimensionally correct. And if you're going to replace the reactive component of impedance with 'time,' then where else does a capacitor's capacitance enter into such equations?

The sophomoric level of your musings indicate you have quite a few electronics and mathematics courses still ahead of you just to finish an undergrad EE degree. The truth is that this entire 'replace j with t' concept of yours is really nothing but the result of mathematical misconceptions coupled with terrible delusions of grandeur. Take it from those who understand the material better than you: you don't know what you're talking about yet.

- Warren

11. ### ghost7584Registered Senior Member

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374
Just like I said in my post, I expect this sort of thing from you and your type.
reposting:
Chroot-- You call yourself crack pot killer. You seem to have an overly skeptical mind set from the start and might oppose anything new whether it is right or wrong.
Whenever anything new is proposed these overly skeptical types seem to crawl out of the woodwork like bugs.

Science does not advance because of skeptics. It advances in spite of them.

That equation that I derived from substituting j with t makes sense after considering it.
v = i x r + charge [substitution was made for i = charge/time (or coulombs/t)
That equation makes sense for alternating current.
Current goes from max to 0 then back to max in the opposite direction and then to 0. When the current is at 0 and ready to change direction the charge (built up at both ends of the wire) is at a maximum, so the potential difference has reversed and ready to push the current back in the opposite direction. So, the value of the voltage (potential difference stays constant) throughout the cycle. As I x r increases the charge moves away from the ends of the wire, in current, and charge at ends of wire goes down while current goes up, still keeping voltage value v, constant. That equation does describe what is happening with alternating current. The substitution of j for time worked.
Also, v - (i x r) = charge is valid. When v = i x r then the charge built up at the end of the wires is 0. V = i x r in direct current, and with direct current there is never a charge built up at the end of the wire because the charge is flowing constanly in one direction through the wire.

I am typing this for others to read. Overly skeptical types like you seem to oppose everything whether it is right or wrong. They also seldom contribute anything new themselves. Criticize others and contribute nothing; I know the type.

12. ### chrootCrackpot killerRegistered Senior Member

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2,350
No, it doesn't make sense, retard. It's not even dimensionally correct. If you want the entire equation to be in volts, then every term in the equation must also be volts. (I*R) is volts, but charge is not! You can't add volts to coulombs and get anything meaningful. It's bogus.
Charge doesn't build up on opposite ends of an (ideal) wire, because wires are conductors. They have the same potential everywhere.
Current changing in one part of a wire without changing in the rest? Garbage.
It's not valid. Volts - volts does not equal coulombs.
More garbage about charge building up in wires. You apparently have no clue how stupid you are.
Why would I oppose something that's right? And I don't contribute anything? I have two patents, and am a senior IC designer at a semiconductor corporation on the Nasdaq-100. There's a 95% chance that the PC you're using right now contains at least one of the parts I have helped develop. Give me a break, shit-for-brains.

- Warren

13. ### DaleSpamTANSTAAFLRegistered Senior Member

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You are absolutely correct about that. However, what you are incorrect about is the idea that it is always used for the same thing or that it is ever unknown what it is. For example, with your ohm's law example, the imaginary number is simply there to conveniently handle capacitance and inductance in the same simple mathematical framework as resistance. No mystery, and it is not time.

This is, in general, the biggest problem for your idea. The imaginary number is unitless. Trying to replace it with time will generally make the equations dimensionally inconsistent. You can't just go around giving units to i any more than you could give units to pi.

-Dale

14. ### catoless hate, more scienceRegistered Senior Member

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2,959
*high 5's chroot*

man, thats what I call a burn.

why is it that people think they can change the world with little education in the field in which the make claims? I sometimes post little ideas I have, but I understand that they have little real substance.

15. ### chrootCrackpot killerRegistered Senior Member

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2,350
cato,

I think most precocious kids naturally go through a self-congratulatory phase where they think they might be The Next Big Thing. Kids who spend their time out on the blacktop want to believe their three-point skills are better than Michael Jordan's were at the same age. Kids who spend their time learning physics want to believe they are the next Einstein.

As a child, I personally remember feeling very "exceptional" after figuring something out, only to realize later that it was really common knowledge among adults.

This self-congratulation is usually stifled sometime during adolescence, and I'm sure many such kids really do go on to do great things.

- Warren

16. ### DaleSpamTANSTAAFLRegistered Senior Member

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I got about halfway through grad school before it really hit me on a visceral level that almost all of my great new ideas had already been published 10 or more years earlier.

-Dale

17. ### ghost7584Registered Senior Member

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374
volts is used with amps. An amp is one coulomb/sec; coulomb is a charge unit representing a certain number of electrons.
Amp is consistent with volt. amp is one coulomb per second. Using coulomb for charge is consistant with volt.

Charge builds up on wires connected to generator. I am talking about the real world here.

Nobody said anything about current changing in one part and not the rest. I was talking about the charge difference across the ends of the wires changing.

I repeat. volt is consistent with amp and amp is one coulomb per second.
therefor, volt is consistent with coulomb. Potential is another word for charge. voltage is potential difference across wire ends; charge difference.

The imaginary number is j in electical engineering. [i is used in math.]
Investigating the equation v = i x (r + j)
v = voltage or potential difference (charge difference); i = current, r = resistance, J = imaginary number
Trying to be more detailed [The units agree. amp = 1 coulomb/sec.]
time in seconds, the x is used as a multiplication symbol
Well let's do the substitution and see:
v = i x (r + j) substituting t (time) for j (the imaginary number)
v = i x (r+t); substituting i for charge/time [coulombs/time]
v = charge/t x (r + t); v = charge/t x r + charge/t x t; t's cancel
v = i x r + charge. For alternating current.
[I changed charge/time to i for current in last step; i is charge/time.]
That equation that I derived from substituting j with t makes sense after considering it.
v = i x r + charge [substitution was made for i = charge/time (or coulombs/t)
That equation makes sense for alternating current.
Current goes from max to 0 then back to max in the opposite direction and then to 0. When the current is at 0 and ready to change direction the charge (built up at both ends of the wire) is at a maximum, so the potential difference has reversed and ready to push the current back in the opposite direction. So, the value of the voltage (potential difference stays constant) throughout the cycle. As I x r increases the charge moves away from the ends of the wire, in current, and charge at ends of wire goes down while current goes up, still keeping voltage value v, constant. That equation does describe what is happening with alternating current. The substitution of j for time worked.
Also, v - (i x r) = charge is valid. When v = i x r then the charge built up at the end of the wires is 0. V = i x r in direct current, and with direct current there is never a charge built up at the end of the wire because the charge is flowing constanly in one direction through the wire.

This is easy to do as you see. Go to any scientific discipline that uses an imaginary number (as another dimension) to make the math come out correctly and substitute t (time) for the imaginary number and then derive your own equations. My argument for why this is a valid substitution is in the original post.
You could be the first man to see a new mathematical relationship in nature.

I tried to make you think about what is happening with alternating current and related that to my equation.
Charge build up when current is stopped and ready to change direction.
It is the charge build up that pushes the current to start it moving again.
Charge moving from the ends of the wire (attached to generator) as current rises charge goes down; voltage stays constant: As i x r goes up, charge (at ends of wire) goes down and vica versa keeping the value for v constant. v = (i x r) + charge.
Visualize current going back and forth in a wire, and charge built up at the ends alternating with the current motion. It is the charge build up at the ends that is the potential difference that pushes the current. Charge goes down as current increases; then charge builds up at the opposite end slowing current down till it stops; then charge pushes current in the opposite direction and the cycle repeats itself.
voltage pushes current. Voltage is potential difference. potential is another word for charge. Charge difference across the ends of a wire is voltage. Current is charge moving through the wire.
Looks easy to understand to me. Remember this is alternating current; current back and forth.

18. ### ghost7584Registered Senior Member

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374
It may be simply there to handle capacitance and inductance, but the important thing is that to use it to calculate current it is plotted on a graph using the imaginary number on a vertical imaginary axis at a right angle to the real axis for current. That means the imaginary number is acting like a fourth dimension. That means t for time can be substituted for it. Time is the only thing proven in general relativity theory to act like a fourth dimension and act on the physical world producing a warped space-time metric which is used to explain gravity. (General relativity theory was proven experimentally correct accurately predicting the angle a star passing near a solar eclipse would appear to move as light passed by the sun, and was bent by the sun's gravity.) So time is proven to act as a fourth dimension. The imaginary number with its imaginary axis acts as a fourth dimension. The time substitution for the imaginary number is therefore valid. There is no dimensional inconsistency. The imaginary axis is at a right angle to the real axis for current, and the pythagorean theorem is used to calculate current. Another dimension is at a right angle to the other three dimensions, length, width and height, which are each one at a right angle to the other two. The imaginary axis qualifies as another dimension, and so does the imaginary number plotted along it.
Summary: You may substitute that particular imaginary number for time.

19. ### ghost7584Registered Senior Member

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374
Oh, pardon me, you did contribute something. The problem seems to have been that you were commenting on something outside of your field of expertise.
I have a Bachelor's degree in physics, with emphasis on theory.
The physicists are the theory guys that invent the equations you people use.

20. ### DaleSpamTANSTAAFLRegistered Senior Member

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1,723
No. In the impedance example it is only acting as a second dimension. The first dimension is resistance; it has nothing to do with the three spatial dimensions. By using complex numbers for impedance you are simply able to handle resistance on the real axis and capacitance and inductance on the imaginary axis, all in one simple framework. I don't know why you would look at this and come to the ridiculous conclusion that it has anything to do with spacetime.

Again, no. Your units will be wrong. E.g. (3 ohm + 4 I ohm) makes sense whereas (3 ohm + 4 s ohm) does not. You are trying to add apples and oranges.

You do realize that the imaginary number is not "at right angles" to 1, don't you? They are orthogonal in a mathematical sense, not in a spatial sense. Take our favorite example here of complex impedance. Capacitance and inductance are not "at right angles" to resistance. They are orthogonal in the same mathematical sense that a function and its derivatives and integrals are orthogonal.

Summary: you are wrong because you didn't count dimensions, you made the units inconsistent, and you don't understand orthogonality.

-Dale

21. ### Euler is my HeroMath AddictRegistered Senior Member

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37
I admittedly don't know very much about electrical engineering, but I read all of these posts by ghost, dale, and chroot and it seems that dale and chroot know a hell of a lot more than ghost. They were able to explain their ideas better and show where ghost's ideas break down whereas ghost's theories were poorly supported. Ghost, you just kept saying the same damn thing over and over and continually got your ass shot down. And damn you're cocky. It seems incredibly far-fetched to think that just substituting time for an imaginary variable "might even lead to a unified field theory that works." Once again, I am not claiming to be anywhere near an expert in this field, but that claim seems beyond laughable. Best of luck to you in solving one of the most challenging problems in science and physics, but it'll probably take a little more than a substitution of variables. But what do I know?

22. ### melodicbardRegistered Senior Member

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208
Ghost,

Your theory is hardly correct. A signal can be analysed more easily by resolving its frequency components and by applying e^(jwt) = cos wt + j sin wt. You may want to link j with phase (a dimenionless quantity). j is a 90 degree phase shift. Try looking up "phasor" from the web.

23. ### DaleSpamTANSTAAFLRegistered Senior Member

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1,723
Thanks for the kind words Euler!

-Merry Christmas everyone!
Dale