/sci/ - Science & Math

You can easily send a finite (precise) number of photons through space.

http://iopscience.iop.org/0034-4885/68/5/R04

Using a precise number of photons (in an experimental setting) you can arrange the experiment as explained. Also there are not an infinite number of photons or there would be an infinite amount of heat generated upon every material surface.

If you skip the photons between you and a distant point you do not have to travel the distance. Paradox solved (if I understand it correctly).

Distance exists so long as events exist. If you can avoid the events, you can go straight to Alpha Centari. In an instant.

If there are no photons between Earth and Alpha Centari how can an observer experience distance?

If the spacecraft are very far apart, and they wait a long time until they can both see each other (start getting photons from each others ships) then we can define a span of space equal to teh number of photons of a given frequency that can populate a space.

So, we have a distance that is "filled" with a given number of photons of a given frequency (and wavelength). When the ships start to accelerate toward each other, it will take ***some time*** for the new signal (the blueshifted photon) to reach the distant ship.

Distance is the number of photon events between you and a point source. Alpha Centari is 4 light years away. But is that measured in miles or photon events?

It is measured in photon events. There is no distance without an event.

You define a local energy. IF you have an opportunity to compare results, you will notice that one result indicates light of a higher frequency then the other recorded result.

So I am saying that in the frame of the observer you cannot determine whether the sequence of photons is red or blue shifted unless there is a change from one photon event to the next. Or,

h*1 @t1 , h*2 @t2, h*3 @t3 .... etc indicates that the point source for the photons is accelerating.

The same is true in reverse. But, when you have,

h*1 @t1, h*1 @t2, h*1 @t3....... etc., you cannot say if the point source has a velocity. Or, you can say that if the point source has a velocity is has no acceleration.

The "two different observations" are equal to "two observers detecting separate photon(s)." So they are different events because they involve different information.

While one observer registers a redshifted photon series another registers a blue shifted photon series. The blue shifted photons are more frequent (more per unit local time) than the redshifted photons. Thus the idea of distance traveled is different for different observers. But there is no coordinate system, or if there is it is comprised only of photons separating observers.

There are no coordinate systems, there are only events.

That sounds argumentative but bear with me....

When you mention time, you are talking about a series of events. At time t an event takes place. At time t+1 another event happens. This is not the correct way of looking at the situations.

The object being observed is emitting photons. You will observe that these photons are red or blue shifted or remain constant. Velocity (relativistic sense) is the registration of these differences. It does not matter if you are moving or the observed object is moving the only detectable event is a photon, and this photon has a red or blue shift.

http://books.google.com/books?id=sdVrBM2w0OwC&pg=PA206&lpg=PA206&dq=relativistic+velocit
y+operator&source=bl&ots=MYFkasVkqy&sig=NC7VCy6_q3Px901znpO2YOmv7vI&hl=en#v=onepage&
amp;q=relativistic%20velocity%20operator&f=false

I am stating that you cannot observe a velocity without registering an event. The event is encoded as a change in energy. The chane in energy is quantized in units h. I am not speaking about determining the location (or, spread of possible locations) for a particle having a given energy (or momentum) I am specifying that the observation of velocity requires an event and that such an event is measured in units hf=E.

So a specific observation that transmits information regarding velocity is quantized in units of hf.

I am not sure I understand how you are deriving that relativistic velocity is quantized. It (the velocity operator in QM) is p/m and this is the definition of a classical relation, not a quantum one.

Yes but rather than using the standard notion of classical velocity you want to quantize velocity in units of photon energy. You can replace velocity altogether if you simply say that the ***observable difference*** in energy for an object in motion is calculated in units hf.

the rate of change is simply the difference in absorbed energy.

So if you want to measure the change imparted by having a velocity, you must measure the velocity. And so what units do you think velocity is transmitted in when it is observed?

States are rays in a Hilbert space, true. Mutually orthogonal states can have the same energy, true.

I should say that you cannot observe an event without observing a photon or a change in energy. And so a change in state is a change in energy inasmuch as you cannot encode that an event has actually occurred until you have absorbed a photon. Or, until you have absorbed energy quantized in photon units.

Velocity is an observable, not an operator, in QM. That is an argument, not a statement of fact. I am arguing that you cannot operate upon a mass to provide acceleration if you cannot observe the energy added during acceleration. The observation of the energy is the observation of a frequency differential over some period of time (time being a tricky subject here).

So velocity is an operator inasmuch as it is quantized in units hf.

There is of course the situation where a material objects has no position (or it is distributed to Unity) when it has no velocity.

This is a problem that crops up using Schrodinger's Equation. The probability that an electron has a location is zero when the electron has zero velocity. Or, I should say, the electron can appear at any photon in the universe.

This is quite obviously wrong. But it persists as a result of using Time as an independent parameter, rather than tying time to something like "number of photon events".

Yes he did. While I will not claim to have read it I will say that Brownian-scale forces can be calculated as changes in photon energy (at the level of electron valence and at the level of simple momentum or temperature).

An object in motion tends to stay in motion until acted upon by an opposing (or additive) force - this force is quantified in units hf.

And so it goes that every collision transmits energy in units hf.

All changes in state are accompanied by a change in energy measured in units hf. So a jerk can be quantified as some change (be it positive or negative) in photon energy for a given material object.

This is not relate f=ma to e=hf (yet).

You only need a measured difference in momentum and this is always transmitted in units of hf (plancks constant times some frequency) and hence the observation of velocity is relative to a local frame and is observable only via a photon absorption.

Velocity is an observable, not an operator. A change in velocity is measured as a change in momentum and can be calculated as a change in the frequency for some constant.

Velocity is equivalent to the absorption of a photon.

A decent book.

http://www.amazon.com/Maxwell-Pragmatic-Quantum-Relativity-ebook/dp/B002WPZVFA