What Do Hamiltonians and Hamilton's Equations Tell Us About Dimensions?

[BadBrain]

One more question:

Why are you working so hard to pound me down when you know I'm soon to be permanently banned from this forum for my having challenged a Mentor?

 

[Max™]

Why do you think challenging a mentor gets you banned?

I haven't seen that rule anywhere, as far as I can tell they've just got moderator privileges on the board software, they're not sanctified or anything. Don't be a jerk and you probably won't get banned.Note, a particle can not be completely described with 3+1 dimensions.

You can say where it is, where it is going, but not what kind of particle it is, it's mass, it's spin, it's charge, all are dimensions in themselves.

 

[BadBrain]

Why do you think challenging a mentor gets you banned?

I haven't seen that rule anywhere, as far as I can tell they've just got moderator privileges on the board software, they're not sanctified or anything. Don't be a jerk and you probably won't get banned.

Note, a particle can not be completely described with 3+1 dimensions.

You can say where it is, where it is going, but not what kind of particle it is, it's mass, it's spin, it's charge, all are dimensions in themselves.

Aaauw, man!

Why don't you read what I wrote?

What I write above was: "Each particle with a given energy state within phase space is not a dimension; it is a particle moving within our observed dimensions, and, possibly (but not necessarily) others."

Jeeze, you're pounding me now to the point of attributing arguments to me which I did not make.

And, I probably won't get banned? I challenged a Mentor, so bye bye Charley!

 

[Neandethal00]

I wanted to know what is the definition and what actually is a dimension. I mean I get that length, width and height story, but how does time fit in as a dimension. Then what about higher dimensions. Like if a certain system was defined in 7 dimensions what exactly would those dimensions be? 4 could be time, length width and height but what about the other 3?

When everyone is explaining dimension using Math, particles, motion. etc, let's try another way to interpret dimension.

Dimensions prove existence. Zero dimension means true nothingness.
If anything exists, it has a dimension and vice versa.
Interesting, this also proves empty space is not nothingness as some people think.

 

[BadBrain]

OK, OK, I give up!

Each particle, together with its motion, is a dimension unto itself.

That means that, as gravitation affects the paths of photons, that photons are, in fact, massive particles, capable of response to immediate influence from gravitation.

That, in turn, means that, as each particle in the universe is a dimension unto itself, that the expansion of the observed spaciotemporal dimensions of the universe proceeds at precisely the speed of light in a vacuum.

And, in particular, that means that General Relativity is **** all.

***

Maybe you're right. Maybe I won't get banned after all, now that I've confessed myself back into the mould.

 

[Nabeshin]

Hamiltonians, and in general Hamilton's equations, make no reference to dimensionality at all. You can apply them to an arbitrary system.

What we're trying to say is as simple as this: When calculating integrals in a phase space, for example of one particle with momentum, you integrate over three spatial coordinates and three momenta to perform the integral over all of phase space. This is a six-dimensional integral, everyone calls it that, and these are the 'Dimensions' that we're familiar with. They might not share the same status as the 3+1 that we know about, but they certainly serve a similar mathematical function, and that's why we use the same word for both.

Your final comment about space expanding and gravitation makes little sense, everyone (who understands GR) knows that spacetime is warped by stress/energy/momentum, not simply mass. And the phrase 'each particle is a dimension' was never uttered anywhere except for in your post, and I can not make anything of it.

Finally, indeed challenging a mentor is not grounds for immediate banning, as you seem to think. Being obnoxious and adversarial, however, is not going to contribute any brownie points. I suggest you spend less time complaining about your imminent ban and more time trying to understand.

 

[Max™]

^Trufax.

 

[BadBrain]

Hamiltonians, and in general Hamilton's equations, make no reference to dimensionality at all. You can apply them to an arbitrary system.

What we're trying to say is as simple as this: When calculating integrals in a phase space, for example of one particle with momentum, you integrate over three spatial coordinates and three momenta to perform the integral over all of phase space. This is a six-dimensional integral, everyone calls it that, and these are the 'Dimensions' that we're familiar with. They might not share the same status as the 3+1 that we know about, but they certainly serve a similar mathematical function, and that's why we use the same word for both.

Your final comment about space expanding and gravitation makes little sense, everyone (who understands GR) knows that spacetime is warped by stress/energy/momentum, not simply mass. And the phrase 'each particle is a dimension' was never uttered anywhere except for in your post, and I can not make anything of it.

Finally, indeed challenging a mentor is not grounds for immediate banning, as you seem to think. Being obnoxious and adversarial, however, is not going to contribute any brownie points. I suggest you spend less time complaining about your imminent ban and more time trying to understand.

What I'm saying is that Hamilton was definitely ahead of his time, and that he suspected that something else was out there beyond the physics of his own understanding.

The three spatial dimensions are obvious. The three moments I see as functions of the three spatial dimensions with respect to time. In other words, his calculations respected time as a dimension which interacts with space, even though he never phrased it in that manner. Moments necessarily imply motion, and, in the absence of time, there is no motion, only a dead stasis which makes nonsense of the Hamiltonians, as kinetic energy is impossible and potential energy is irrelevant. He was, in fact, describing space-time eighty years before Einstein, having access to more advanced knowledge than that available to Hamilton, formalized the concept.