Theory Of Everything (ToE)

[Agent Smith]

Inviting comments as well

 

[pines-demon]

Probably more than a single equation.

 

[Agent Smith]

String theory? One (master) equation?

 

[fresh_42]

String theory? One (master) equation?

What are the master equations of QED and QCD? TOE has to include both of them and therewith all equations of both. How could this be reduced to one equation if the parts don't already have one?

 

[pines-demon]

What are the master equations of QED and QCD? TOE has to include both of them and therewith all equations of both. How could this be reduced to one equation if the parts don't already have one?

Put all the equations that you need into an action and call it for the day. You know what, let us write all equations known to humans as
$$\Phi(\mathbf S)=0$$
where $\Phi$ is the operator that sends all variables $\mathbf S=(S_1,S_2,\cdots)$ to its corresponding equation. Theory of everything done.

 

[Ibix]

Theory of everything done.

Determining the exact form of $\Phi$ is left as an exercise for the reader.

 

[fresh_42]

Put all the equations that you need into an action and call it for the day. You know what, let us write all equations known to humans as
$$\Phi(\mathbf S)=0$$
where $\Phi$ is the operator that sends all variables $\mathbf S=(S_1,S_2,\cdots)$ to its corresponding equation. Theory of everything done.

Will be difficult to press Heisenberg's uncertainty principle into that scheme, or the concept of dimensions.

You could also say that TOE is a valid sentence over the alphabet of alphanumeric letters, using first-order (predicate) logic as grammar.

 

[PeroK]

What are the master equations of QED and QCD? TOE has to include both of them and therewith all equations of both. How could this be reduced to one equation if the parts don't already have one?

You should put this tee-shirt on your Christmas wish list:

 

[pines-demon]

Will be difficult to press Heisenberg's uncertainty principle into that scheme, or the concept of dimensions.

I never said that $\Phi$ had to be linear or that the $S_i$ had to be independent variables. I can accommodate as many equations and dimensions as you wish.

 

[Hornbein]

This facetious idea is in one of Richard. Feynman's book.

 

[pines-demon]

This facetious idea is in one of Richard. Feynman's book.

Do you know which one?

 

[Hornbein]

Do you know which one?

I read them about 30 years ago so I don't recall which.

 

[Agent Smith]

What are the master equations of QED and QCD? TOE has to include both of them and therewith all equations of both. How could this be reduced to one equation if the parts don't already have one?

$x^2 + y^2 + k_1 a + k_2 b = k_3$

 

[Agent Smith]

Is it true that Maxwell "united" electricity and magnetism into electromagnetism using the concept of fields? Did Rowan Hamilton have a role in this?

 

[pines-demon]

Is it true that Maxwell "united" electricity and magnetism into electromagnetism using the concept of fields?

Electricity and magnetism were unified by a series of experimental discoveries by Ørsted, Faraday and Ampère. Maxwell took hundreds of equations of electromagnetism and compiled them into 20 or so (Heaviside reduced them into 4). Maxwell using his equations unified electromagnetism with light waves (and EM radiation in general).

Did Rowan Hamilton have a role in this?

Barely, Hamilton did work on optics. Maxwell used a bit of Hamilton's quaternion algebra but not much.

 

[ergospherical]

I read them about 30 years ago so I don't recall which.

Volume II, Chapter 25 (Electrodynamics in Relativistic Notation), Section 25-6

Let us show you something interesting that we have recently discovered: all of the laws of physics can be contained in one equation. That equation is\begin{equation}
U = 0 \tag{25.30}
\end{equation}What a simple equation! Of course, it is necessary to know what the symbol means. $U$ is a physical quantity which we will call the “unworldliness” of the situation. And we have a formula for it. Here is how you calculate the unworldliness. You take all of the known physical laws and write them in a special form. For example, suppose you take the law of mechanics, $F = ma$, and rewrite it as $F - ma = 0$. Then you can call $(F - ma)$—which should, of course, be zero—the “mismatch” of mechanics. Next, you take the square of this mismatch and call it $U_1$, which can be called the “unworldliness of mechanical effects.” In other words, you take\begin{equation}
U_1 = (F - ma)^2 \tag{25.31}
\end{equation}Now you write another physical law, say, $\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$, and define\begin{equation*}
U_2 = \left( \nabla \cdot \mathbf{E} - \frac{\rho}{\varepsilon_0} \right)^2
\end{equation*}which you might call “the Gaussian unworldliness of electricity.” You continue to write $U_3$, $U_4$, and so on—one for every physical law there is. Finally, you call the total unworldliness $U$ of the world the sum of the various unworldlinesses $U_i$ from all the subphenomena that are involved; that is, $U = \sum U_i$. Then the great “law of nature” is\begin{equation}
U = 0 \tag{25.32}
\end{equation}This “law” means, of course, that the sum of the squares of all the individual mismatches is zero, and the only way the sum of a lot of squares can be zero is for each one of the terms to be zero.

So the “beautifully simple” law in Eq. (25.32) is equivalent to the whole series of equations that you originally wrote down. It is therefore absolutely obvious that a simple notation that just hides the complexity in the definitions of symbols is not real simplicity. It is just a trick. The beauty that appears in Eq. (25.32)—just from the fact that several equations are hidden within it—is no more than a trick. When you unwrap the whole thing, you get back where you were before.

 

[Agent Smith]

Electricity and magnetism were unified by a series of experimental discoveries by Ørsted, Faraday and Ampère. Maxwell took hundreds of equations of electromagnetism and compiled them into 20 or so (Heaviside reduced them into 4). Maxwell using his equations unified electromagnetism with light waves (and EM radiation in general).

Barely, Hamilton did work on optics. Maxwell used a bit of Hamilton's quaternion algebra but not much.

I've been watching a video on Rowan Hamilton(ian) and Action - "a new way of looking at physics" (?).

Maybe gravity waves?

 

[Agent Smith]

The best candidate for a ToE is allegedly String Theory i.e. there is an equation for ToE in that theory. I wonder what it looks like.

 

[DrGreg]

By the way, once you have formulated your theory of Everything in the form$$ U = 0, $$to convince everyone that it really is a theory of Everything, you should re-express it in terms of $V = U + 42$.

 

[Agent Smith]

I wonder why we need more dimensions to put it all together, as in string theory?
According to some learned physicists, gravity won't behave.

 

[pines-demon]

I've been watching a video on Rowan Hamilton(ian) and Action - "a new way of looking at physics" (?).

Can you link the video?

Maybe gravity waves?

Gravity waves were studied at the time of Newton, and the mathematics were simplified by Lagrange, Poisson and Laplace much before Hamilton. However you are probably referring to gravitational waves (gravity waves refers to surface waves in water). Gravitational waves were not considered until the 20th century.

 

[Agent Smith]

Can you link the video?

Gravity waves were studied at the time of Newton, and the mathematics were simplified by Lagrange, Poisson and Laplace much before Hamilton. However you are probably referring to gravitational waves (gravity waves refers to surface waves in water). Gravitational waves were not considered until the 20th century.

I see. Thanks. Yes I think I meant gravitational waves (LIGO).

 

[Hornbein]

In geometric algebra it's possible to write Maxwell's Equations as a single equation. But I always had to split it back into four to use it so it seemed kind of useless. But who knows, maybe I just didn't understand.

 

[Agent Smith]

I wonder why Einstein was trying to find the ToE? His disciples are too.

 

[Hornbein]

I wonder why Einstein was trying to find the ToE? His disciples are too.

They felt like doing it.

 

[pines-demon]

I wonder why Einstein was trying to find the ToE? His disciples are too.

When you think you are so smart that you revolutionize our perspective of space-time twice you may think that the next problem might be just of the same difficulty.

 

[pinball1970]

When you think you are so smart that you revolutionize our perspective of space-time twice you may think that the next problem might be just of the same difficulty.

They all did to some extent?

Feynman said that if they uncover one thing, there might be another unknown underneath. Like layers in an onion. In the 1980s I think in one of his interviews about the joy of knowing.

If they crack, DM, Dark Energy and harmonize QM with GR then that would be a decent wish list (reading the articles pop science)


Following this stuff tells me that every next question gets tougher experimentally.
Theoretically? Either it's there waiting to be confirmed or something new is needed.

Is this different to 1905? Yes, lots more big international collaborations, money and PhD physicists!