Individual Particles and General Relativity

[metacogitans]

From light's frame of reference, let d be the distance light travels during an increment of time in

the direction of a massive particle:

 

 

d_n+1 = d_n • w

 

 

 

Where w is the 'warp constant' of a particle, and w > 1

 

 

For massive non-boson particles:

 

d_n-1 = d_n • (1/w)

 

For massive non-boson particles, d_n-1 > 0

What this means is that two massive particles can not 'collide', and there will always be spacetime between them.

Edited January 5, 2016 by metacogitans

[Strange]

From light's frame of reference

 

There is no such thing.

 

 

d_n+1 = d_n • w

 

How did you derive this?

 

 

Where w is the 'warp constant' of a particle.

 

How is that defined?

And which particle?

 

 

For massive non-boson particles:

 

d_n-1 = d_n • (1/w)

 

How did you derive this?

Why does it only apply to fermions (i.e. "non-bosons")?

Edited January 5, 2016 by Strange

[metacogitans]

Going to draw pictures.. One minute please.

There is no such thing.

Light's local reference frame.

 

 

 

How did you derive this?

The dilation of spacetime described by general relativity

 

 

 

How is that defined?

And which particle?

It varies depending on the particle. Different particles have different warp constants, especially composite particles which could only be properly described with tensor calculus and not a simple constant.

 

 

 

How did you derive this?

Why does it only apply to fermions (i.e. "non-bosons")?

Bosons are the only particle capable of 'meeting' another particle, thereby accelerating them. As bosons mediate all interactions, fermions themselves must be intrinsically 'separated' from other fermions. Edited January 5, 2016 by metacogitans

[swansont]

Light's local reference frame.

There is no such thing. We don't have any physics to describe what's going on from the point of view of a photon. Our equations tend to diverge for v=c.

 

The dilation of spacetime described by general relativity

AFAICT that was a request for the math, not a description of the process.

[metacogitans]

The basis for d_n-1 = d_n • (1/w) is Special Relativity and also the Pauli Exclusion Principle.

With the Pauli Exclusion Principle, it could roughly be said that 'two fermions can not simultaneously occupy the same exact location'.

With special relativity, an object can not travel faster than the 'light' (or in a broader sense, any radiation or force-carrying boson) emitted by the object - as if an object were to 'collide' with another object, the 'collision' would have to be mediated by a force-carrying boson; no matter how close together two particles are, radiation traveling between them will still be observed as traveling at the speed of light.

There is no such thing. We don't have any physics to describe what's going on from the point of view of a photon. Our equations tend to diverge for v=c.

AFAICT that was a request for the math, not a description of the process.

If the speed of light is always locally constant, 'locally' would be a frame of reference wouldn't it?

The speed of light is not objectively constant according to general relativity. A ray of light that passes through the center of a gravity-well would seem to have traveled a shorter distance than a ray of light passing alongside the gravity well for the same amount of time. If we clocked a ray of light traveling through the center of a massive body's gravity well to find the body's diameter, the circumference of the massive body would be shorter than what we would expect when taking the measured diameter multiplied by pi.

 

AFAICT that was a request for the math, not a description of the process.

Well, it was derived philosophically from the mathematical concepts of special relativity. Deriving it strictly mathematically will take me a while, but I can certainly try.

Edited January 5, 2016 by metacogitans

[swansont]

If the speed of light is always locally constant, 'locally' would be a frame of reference wouldn't it?

Locally is an inertial frame, not that of a photon.

 

I can do a transform between inertial frames. How would I transform into the frame of a photon?

 

The speed of light is not objectively constant according to general relativity. A ray of light that passes through the center of a gravity-well would seem to have traveled a shorter distance than a ray of light passing alongside the gravity well for the same amount of time. If we clocked a ray of light traveling through the center of a massive body's gravity well to find the body's diameter, the circumference of the massive body would be shorter than what we would expect when taking the measured diameter multiplied by pi.

You are making that measurement in your frame. Irrelevant to the discussion, from what I see.

[metacogitans]

Locally is an inertial frame, not that of a photon.

 

I can do a transform between inertial frames. How would I transform into the frame of a photon?

The velocity of the photon remains constant while the grid plotting its trajectory is warped due to gravity.

 

 

You are making that measurement in your frame. Irrelevant to the discussion, from what I see.

(posted by user James S Saint on ilovephilosophy.com)

[swansont]

The velocity of the photon remains constant while the grid plotting its trajectory is warped due to gravity.

 

 

"the grid plotting its trajectory" is not the photon's frame of reference. Once again, you have sidestepped the issue.

[metacogitans]

 

"the grid plotting its trajectory" is not the photon's frame of reference. Once again, you have sidestepped the issue.

Well, whatever that grid would be called is what I meant. I guess I used the wrong terminology.

What should I say then? 'Where the speed of light is measured as a constant locally'?

Edited January 6, 2016 by metacogitans

[swansont]

Well, whatever that grid would be called is what I meant. I guess I used the wrong terminology.

What should I say then? 'Where the speed of light is measured as a constant locally'?

 

That would be some local frame of reference. Which, as I have already stated, is not the frame of a photon. You have presented exactly zero physics regarding being in a photon's frame, and yet that's how you lead off the discussion.

[metacogitans]

I'll have to correct my post then. I was trying to give a simple geometrical description of spacetime dilation for individual particles is all. What are your thoughts on the math?

[swansont]

I'll have to correct my post then. I was trying to give a simple geometrical description of spacetime dilation for individual particles is all. What are your thoughts on the math?

 

Still waiting on the important math: the derivation of your equations. It will be interesting to see that, plus see how a massive change in premise might affect it. I don't see how that could remain unchanged. Unless the equations were meaningless to begin with.

[metacogitans]

Alright. We know that gravity follows the inverse-square law; the intensity of the force falls off exponentially with distance, with the intensity approaching infinity as the distance between two massive objects decreases.

In General Relativity however, this must be expressed in terms of warped spacetime. As the distance between two massive objects decreases, spacetime dilation approaches infinity - meaning there will always be 'more space' between two massive objects when traveling towards each other.

 

Hence,

 

d_n-1 = d_n • (1/w)

 

Where d is the distance traveled by an object in an increment of time when traveling in the direction of another massive object.

 

For bosons however, which are emitted from particles, the distance between the boson and the particle emitting the boson starts as infinitesimal, or what we could practically consider to be 0. The distance d which the boson travels away from its source particle during an increment of time could be expressed by:

 

d_n+1 = d_n • w

 

Since the speed which a photon travels is the same in all reference frames, the distance traveled would be the same whether traveling towards or away from a massive particle; so bosons are thereby able to 'close the distance' between particles and be absorbed, accelerating the particle.

 

That was my 'correction' of the original post (please let me know what you think of it ); I'm still going to try showing how to derive it mathematically from other equations - it's going to take me a while though; I'm working on it.

Edited January 6, 2016 by metacogitans

[ajb]

What are your thoughts on the math?

I suggest you start with the lecture notes of Carroll.

http://arxiv.org/abs/gr-qc/9712019

[Mordred]

One of my favourite articles in my collection. Good pick AJB

[ajb]

 

From light's frame of reference...

As already pointed out, you need to be much clearer with this. There is no inertial frame for which a photon can be considered at rest. But then you may not be talking about inertial frames anyway. The closest thing I can think of, that are used in physics, are light-cone coordinates and the 'light-cone velocity'.

[swansont]

Alright. We know that gravity follows the inverse-square law; the intensity of the force falls off exponentially with distance, with the intensity approaching infinity as the distance between two massive objects decreases.

In General Relativity however, this must be expressed in terms of warped spacetime. As the distance between two massive objects decreases, spacetime dilation approaches infinity - meaning there will always be 'more space' between two massive objects when traveling towards each other.

No, I don't see how that follows.

 

Hence,

That's what you write just after all the math has been done, just before the final equation. We want to see this math.