How do space and time relate to momentum?

[geordief]

I have read an article that proposes that the space-time frame framework could be supplemented with a momentum -time framework.

Link:http://www.newscientist.com/article/mg21128241.700-beyond-spacetime-welcome-to-phase-space.html

Quoting from the article, they maintain

*When you look at your watch, for example, photons bounce off a surface and land on your retina. By detecting the energy and momentum of the photons, your brain reconstructs events in space and time *

Does that make sense to anyone and ,if so , could they please try to explain it to me (preferably in baby steps) ?

thanks

 

[Drakkith]

I don't really understand everything, but I think the statement you quoted means that by detecting the momentum and energy of things over time your brain "constructs" 3d space. This doesn't mean that we don't live in spacetime, it just means that you can also mathematically explain things using energy and momentum instead of space and time I believe.

 

[geordief]

yes that is what I thought it meant too.
But what would be the mechanism that would enable the brain to construct a 3D or 4D world from an interaction with a particle which has been measured for momentum and energy only?

 

[Drakkith]

What do you mean? Our eyes only detect a photon's momentum. The fact that we can "see" 3d space is due to the layout of the eye and how everything works. Only light from a particular direction can enter, then that light is focused, and finally the layout of your retina determines the patterns of signals your brain receives and uses to construct an image.

 

[BruceW]

The article is proposing a radical departure from Einstein's relativity. If you go to the 3rd page, it gives a link to a paper which explains it more directly.

I think the basic idea is that Einstein's relativity says that time and space depend on the observer (i.e. are relative), but 4-d spacetime is absolute (i.e. if two particles collide, then they will collide as viewed by all observers).

What the article suggests is that distant observers will not agree on whether the two particles collide. In other words, locality is relative. In the proposed theory, the observed spacetimes are energy and momentum dependent. That's why an 8-d (spacetime, energy,momentum) phase space is required. In other words, it is a further generalisation of relativity.

They also talk about how this may help with a theory of quantum gravity. Pretty interesting.

 

[Neandethal00]

I have read an article that proposes that the space-time frame framework could be supplemented with a momentum -time framework.

Link:http://www.newscientist.com/article/mg21128241.700-beyond-spacetime-welcome-to-phase-space.html

Quoting from the article, they maintain

*When you look at your watch, for example, photons bounce off a surface and land on your retina. By detecting the energy and momentum of the photons, your brain reconstructs events in space and time *

Does that make sense to anyone and ,if so , could they please try to explain it to me (preferably in baby steps) ?

thanks

In my opinion, I do not think this energy-momentum space will lead to anything new. We need a phase space in which all events are 'observer independent', all observers regardless of their location and speed will make an identical record of an event. Measurements in energy-momentum space are still relativity dependent.

 

[geordief]

In my opinion, I do not think this energy-momentum space will lead to anything new. We need a phase space in which all events are 'observer independent', all observers regardless of their location and speed will make an identical record of an event. Measurements in energy-momentum space are still relativity dependent.

in my opinion ,an *observer independent" understanding of the universe is at best wishful thing and at worst a tautology.
Maybe the reliance on observer dependence is a blessing in disguise -a bit like the bit of grit in the oyster- and that is what seems to keep changing the goalposts and prevent us from ever thinking we can know it all ..

 

[geordief]

What do you mean? Our eyes only detect a photon's momentum. The fact that we can "see" 3d space is due to the layout of the eye and how everything works. Only light from a particular direction can enter, then that light is focused, and finally the layout of your retina determines the patterns of signals your brain receives and uses to construct an image.

well , as I see it , the brain perceives the interaction (event?) between the body and the photon (already 2 dimensions there as it takes 2 to tango) .So doesn't that introduce space into the equation from the point of view of the retina's side to the reaction?
Or do you have to go back further and wonder how the body would understand (create?) its own spatial architecture irrespective of photon's striking the retina?
I mean ,does the mind have to implicitly have an awareness of space in order to function (internally) in the first place?

 

[Drakkith]

I don't know nearly enough about a lot of subjects to answer that geordief.

 

[cmos]

I think you might be confused with some of the terminology in the article, so with my two cents I'll just mention some basic stuff.

In the article, when he says "space-time," what he means is "position-space"-time. So then when he says "momentum space," he simply means a coordinate system where the axes are not position coordinates but rather momentum coordinates. So, for example, the Cartesian coordinate systems you see in high-school physics is usually in terms of "position space" (units of meters). That is the "space" that goes with the term "space-time." But now, if you replace the coordinate system with momentum (units of kg-m/s), then you are in a momentum domain or, more commonly, momentum space.

I hope that wasn't too confusing, what it comes down to is that he uses the word "space" in several different contexts and assumes you are able to figure out what he is saying.

Now, you may ask, if in relativity we speak of a "(position)-space-time," then can we speak of a "momentum-time?" The answer is no. In relativity, space and time get lumped together as the same quantity (i.e. the three-element position/space vector of non-relativistic mechanics becomes a four-element space-time vector in relativistic mechanics). Similarly, it is actually momentum and energy that get lumped together into the same quantity (i.e. the three-element momentum vector of non-relativistic mechanics becomes a four-element energy-momentum vector in relativistic mechanics).

Hope that helps...

 

[geordief]

I think you might be confused with some of the terminology in the article, so with my two cents I'll just mention some basic stuff.

In the article, when he says "space-time," what he means is "position-space"-time. So then when he says "momentum space," he simply means a coordinate system where the axes are not position coordinates but rather momentum coordinates. So, for example, the Cartesian coordinate systems you see in high-school physics is usually in terms of "position space" (units of meters). That is the "space" that goes with the term "space-time." But now, if you replace the coordinate system with momentum (units of kg-m/s), then you are in a momentum domain or, more commonly, momentum space.

I hope that wasn't too confusing, what it comes down to is that he uses the word "space" in several different contexts and assumes you are able to figure out what he is saying.

Now, you may ask, if in relativity we speak of a "(position)-space-time," then can we speak of a "momentum-time?" The answer is no. In relativity, space and time get lumped together as the same quantity (i.e. the three-element position/space vector of non-relativistic mechanics becomes a four-element space-time vector in relativistic mechanics). Similarly, it is actually momentum and energy that get lumped together into the same quantity (i.e. the three-element momentum vector of non-relativistic mechanics becomes a four-element energy-momentum vector in relativistic mechanics).

Hope that helps...

thanks
yes the more basic for me the better!
I do think I may have understood the notion of what a momentum-time might be but I am still a little unclear as to what the dimensions involved would be.

In the article it seems to imply that an extra 4 dimensions (in addition to the 4 in space-time) are used (so 8 in all in a framework that includes both momentum-time and space-time)
So what would they be precisely?

One of them ,surely , can't be time because that is already being used in space-time (or is that just nit-picking?)
Just to reduce it to the proposed momentum-time what would be the (4?) dimensions involved there
1)time
2) mass
3) distance
I can't find the 4th...

Shouldn't there be 4 axes in the proposed momentum-time?

apologies in advance for the elementary misunderstanding I must be making and if anyone can clear in up at all...

 

[BruceW]

in spacetime there is time, and the 3 space - so that's 4.
In momentum there is energy, and the 3 normal momentum - another 4.
So yes, there are 8 in total.

The reason energy is one component of the 4-momentum is because in relativity, energy cannot be treated as separate from the normal momentum (similar to how time and space are intimately connected).

 

[geordief]

in spacetime there is time, and the 3 space - so that's 4.
In momentum there is energy, and the 3 normal momentum - another 4.
So yes, there are 8 in total.

The reason energy is one component of the 4-momentum is because in relativity, energy cannot be treated as separate from the normal momentum (similar to how time and space are intimately connected).

What are those 3 dimensions to momentum in addition to energy which seems to be the first?

I am guessing they must be ones that I am familiar with and so would they be duplicates of the dimensions that make up relatavistic spacetime?

Apologies for plumbing further the depths of my ignorance!

 

[BruceW]

Yeah, the 3 momentum is the momentum you are familiar with. (Although it also includes the factor gamma). So if the particle was moving in the x direction, then the 3-momentum would be: $p = m_0 \gamma v$ In the x-direction.

In relativity, the 4-momentum is given by taking derivatives along the path through spacetime.
So essentially, in relativity, the spacetime contains all the important physics, and we can then get 4-momentum from the path through spacetime.
But in the article you've read, they suggest that the relevant physics is contained by the combination of both spacetime and the 4-momentum.

Edit: Also, I think the reason you have heard the 4-momentum being called 'momentum-time' is because the 3-momentum is given by taking the derivative of the path through spacetime with respect to space and the energy is given by taking the derivative of the path through spacetime with respect to time.
In other words, energy corresponds to the time coordinate and 3-momentum corresponds to space.

 

[geordief]

Yeah, the 3 momentum is the momentum you are familiar with. (Although it also includes the factor gamma). So if the particle was moving in the x direction, then the 3-momentum would be: $p = m_0 \gamma v$ In the x-direction.

In relativity, the 4-momentum is given by taking derivatives along the path through spacetime.
So essentially, in relativity, the spacetime contains all the important physics, and we can then get 4-momentum from the path through spacetime.
But in the article you've read, they suggest that the relevant physics is contained by the combination of both spacetime and the 4-momentum.

Edit: Also, I think the reason you have heard the 4-momentum being called 'momentum-time' is because the 3-momentum is given by taking the derivative of the path through spacetime with respect to space and the energy is given by taking the derivative of the path through spacetime with respect to time.
In other words, energy corresponds to the time coordinate and 3-momentum corresponds to space.

thanks
I have had a glance back through that article and I think that my confusion in terminology is on account of the reference to *space-time* being quickly followed by a reference to *momentum-space* .
This was later scrambled in my sensory network to * momentum-time*.

Apologies again - for that lack of attention to simple detail and thanks for helping me through that.