Iggy

I think you’re right. The gun must be traceable to gang related crimes and maybe even a murder. Here’s how I see the situation playing out: I close the case and take it. The following day I look in the paper and find out that two gang members were shot and killed in a drug deal gone bad. Police arrived on the scene and chased a fleeing vehicle. They arrested the two occupants following a short pursuit and are holding them on suspicion of murder. I realize that since the gang members dumped the case with all the incriminating evidence there will be nothing to tie them to the murders. They are going to get away with it. This is good news. I formulate a plan that requires all three items in the case. Step one--I use the money. I pay a bail bondsman a couple grand for the names of the individuals under arrest. I also buy a wireless portable security camera with portable monitor and a 2 way radio set. Step two--I use the drugs (not like that). I find a homeless druggy who will do anything for a big bag of marijuana--give him a message and send him into county lockup where he delivers the message to the gang members. The message is along the lines of “I have your case. You have one week to buy it back from me for $100,000. Otherwise, I take it to the police and they will be able to tie you to the murders. When you get out of jail you can contact me at sucks_to_be_blackmailed@yahoo.com” A couple days later the gang members are charged with fleeing a police officer and a couple days after that they make bail and they’re out on the street. Step three--I arrange for a straight swap in some shady back alley. When the gang members arrive they find a camera with a note saying “show me the money” and the two-way radio. They end up not having the money (big surprise), but they do have lots of fellow gang members waving guns around looking for someone to shoot. With the radio I tell them that the deal is off and the case is going to the police. I purposefully make myself sound like a nerdy weakling (no big stretch). They ask for another chance--another meeting with just the two of them and they will bring the cash. I say “OK, but it’s 150 grand now.” They agree, but of course they are still planning on killing me as soon as they see the case. At the second meeting I verify that they brought the money and that they’re alone. I show up (in a stolen car), shoot the overconfident gang members with their own gun, and take the money. I put the money and the gun in the suitcase and congratulate myself on my most productive and most interesting week ever. Smash cut to me fleeing from the cops throwing the suitcase off an overpass landing in front of a passerby who now has an ethical dilemma

Thank you. I agree, though I think it might be most accurate to say that the diagram is relative to an observer's reference frame or an observer's velocity--or, the velocity of an observer's reference frame, I suppose. Right. The event "sun emits photon" (the photon which Cleopatra observes) is in the same position relative to Cleopatra as "sun emits photon" (the one which we observe) is relative to us. But, also, a spacetime diagram shows more than one time. You might say that it shows more than one present, or more than one hypersurface of an observer's present. So, on a single diagram you can represent both Cleopatra's present and our present. You can show the past light cone of both Cleopatra and us--on the same diagram. On such a diagram the sun and the earth and any other object must intersect both light cones to be consistent with observation. We can prove that the sun was here yesterday and in the distant past with conservation of energy or Noether's theorem or we can prove it through direct evidence. Blue-green algae was using photosynthesis billions of years ago. But, regardless, either an object's path through spacetime is a curve or a moving dot. I don't know if the universe is really four dimensional in a philosophical sense, but I know that when it is represented that way with a spacetime diagram an object's path cannot be a moving dot. It must be a line or a curve. The two different representations have different observational consequences. In other words, I don't need to argue that "an object is a line", only that it must be represented that way in 4 dimensional spacetime. In your diagram in post 73 there are two moving dots--a black one and a red one. I don't believe I have misinterpreted your meaning. I believe my diagram follows logically from yours. Again, there is a moving dot behind the black one in your diagram, both representing objects and both moving. You said the difference between the red object and the black object is that the red object was a million years before the black object. Cleopatra was 2,000 years before us, so I think she would belong where I have put her. But, this does reveal the problem. Your diagram has two different kinds of 'before'. The problem is that time is twice represented in the moving dot diagram. The difference from one frame to the next is the advancement of time. The difference from one point along the vertical axis to the next is also the advancement of time. But, time is not a two dimensional construct and can't properly be represented that way to be consistent with observation. If you show an object's trajectory over time as an animation with multiple frames like wikipedia's image here, then there is no time axis and there shouldn't be one. On the other hand, if you have a time axis like wikipedia's image here, then there is no animated movement of an 'object' or multiple frames showing the movement of an object. The passage of time is shown with the vertical axis. It is a problem to have both the time axis and the animated, moving, object--not simply redundant, but a misrepresentation. I think it's fine to think of a particle as a moving dot, it's fine to diagram it that way, but not on a spacetime diagram. I think it's also fine to make an animated spacetime diagram like I drew here, But, we must recognize that the moving dot is an event, not an object. The path of an object (ie particle or material point) through spacetime still must be represented with a line.

Excellent questions Joshua. On the human retina there are two types of light-sensing cells--rods and cones. They detect light and send signals to the brain where an image is interpreted. Rods are more sensitive than cones which means if you are in a dark environment observing something that is scarcely lit then you see it almost entirely with rods. Rods cannot distinguish or perceive color like cones can--they can only distinguish the intensity of light. This means that people see things more and more desaturated of color in a darker and darker environment. In a sufficiently dark environment people see things in monochrome or what you might call black and white.

1. an 'object' as it is typically defined is represented as a world-line on a spacetime diagram. 2. a world-line is a line. 3. the physics community is quite convinced of 1 and 2. They say it explicitly. In physics, a world line of an object (approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresponding to the history of the object. A world line is a special type of curve in spacetime. Below an equivalent definition will be explained: A world line is a time-like curve in spacetime. Each point of a world line is an event that can be labeled with the time and the spatial position of the object at that time. For example, the orbit of the Earth in space is approximately a circle, a three-dimensional (closed) curve in space: the Earth returns every year to the same point in space. However, it arrives there at a different (later) time. The world line of the Earth is helical in spacetime (a curve in a four-dimensional space) and does not return to the same point. http://en.wikipedia.org/wiki/World_line That is incorrect. I have not said and not implied that past events exist somewhere (by which I assume you mean some place). I have refuted the idea that world-lines don't exist--that objects can be coherently represented as 'moving dots' on a space time diagram. I agree with that.

You would think that traveling back in time to see if there is a sun and earth would reveal the truth of this. So, I might go back a couple thousand years and stand next to Cleopatra and find out if the sun and earth are there. That would settle the issue for you. But, how is that different from what Cleopatra saw? Can I not take her word on this? The sun was here yesterday and two thousand years ago and we don't need a time machine to prove it. The consequences of this moving dot idea are shown very clearly in the diagram in my last post. The consequences are incompatible with observation. The entire physics community is convinced of that. It is explained in the links I've given through the thread. There is a reason a world line is a line. There is a reason Minkowski made it so. Conservation of energy and all of our human observations demand it.

That is essentially correct. You got your tenses mixed up, but it's essentially correct. It is equivalent to saying: "I occupied the center of central park on December 31, 1999 and no other object can occupy the center of central park on December 31, 1999 without having touched me." In other words, if something occupies (0,0,0,1) then that specific place and time is taken. I've depicted as clearly as I think I can the consequences of having an object be represented as a moving dot along a time axis, If the sun were a moving dot as you advocate then we would be very lucky to live in the one time with its light. A more immediate problem for our ancestors would be the missing earth. I'm sorry, Michel. I wish I could say your idea worked.

That seems possible. I can explain how a space time diagram works. A normal image shows no motion. In a flip book sort of way, motion can be shown by advancing the position of an object in each frame. In the following animation a ball is thrown into the air. The vertical axis measures height while each frame shows a change in position by advancing the time 1/2 seconds. To find the time when the ball is at its peak height you would look at the fifth frame and find T=2. Two seconds after the ball was thrown directly upward into the air it reached its maximum height. A different method of keeping track of time, and one which is very useful when considering relativity, is the space time diagram. Time is treated like another dimension so that an object's position can be shown in both space and time. The above animation could be equivalently diagramed like so: The horizontal axis now represents time. A single position on the diagram shows a specific place and time--called an event. The ball is the curve and we can find the time that it reached it's maximum height by following that event down to the time axis. A similar description is given half way down this text: http://www.physicsguy.com/ftl/html/FTL_part1.html. Your moving dot diagram doesn't translate to reality the way the above diagram does. The black dot in your diagram is missing to the red dot. If the black dot were the sun and the red dot a spaceship then the spaceship could literally travel to the center of the sun (or where the sun would be) never finding it or touching it, Your diagram depicts the idea that being one day before or after a specific time means that the sun is missing--gone--impossible to touch. Cleopatra, having lived before the black dot, must have had no sun. But, that is clearly not right--we know objects persist thorough time, so it just doesn't make sense.

Yes, we know the sun was there yesterday. The sun's mass is a conserved quantity over time. It is provable by conservation of energy or Noether's theorem. But, honestly, if you've convinced yourself that the sun was missing yesterday then I suppose conservation of energy won't change your mind.

You need to turn your diagram (the one with the moving red dot) into a thought experiment. The black dot is always in the same place in space. You can call it x=0, y=0, z=0. It is, according to your diagram, never anywhere else in space. It does not move in space. Your diagram would have us believe that another object can occupy that same space (x=0, y=0, z=0), but at some special time where it won't touch the first object, yet the first object is never anywhere but (x=0, y=0, z=0). That is simply not how reality works. If an object, let's say the sun, is always in the same place in space in our coordinate system then no other object can occupy that space (past present or future) without touching it. Your diagram tells us that a meteor could occupy the space at the center of the sun yet not touch the sun simply because it happened yesterday. It makes no reasonable sense. If time is represented by the vertical axis then the object should be a world line.

Yes. The earth had mass yesterday, and the many days before. No, it's the same mass. The earth's mass yesterday is the same mass we see from the earth today. This should be intuitive if you don't obfuscate it. Your diagram makes no sense to me. Space is for some reason not orthogonal to time, and you've marked off a space-like curve and called it mass, but mass is not proportional to volume so that doesn't work. I really don't understand what that diagram is supposed to show. It is, at the very least, moving faster than light which is a problem. You need to turn your diagram (the one with the moving red dot) into a thought experiment. The red dot is the comet that hit the earth 65 million years ago killing the dinosaurs. Presumably, the earth and the comet would be in the same place on any spacetime diagram 65 million years ago. According to your diagram, the comet would have missed the earth. Is that what happened? Does your diagram translate to reality? For a short description of how a spacetime diagram works: http://www.astro.ucla.edu/~wright/st_diags.htm For a more accurate, but more involved description: http://en.wikipedia.org/wiki/Minkowski_diagram

No, B and E are not objects--they are events. We've been over this. Objects are lines on a spacetime diagram. It's not "life-line" it's "world-line". The world line of the object accompanying D exists in the past, present, and the future. Noether's theorem demands it. An object is not a dot--moving or otherwise. An object is a line. An event is a dot. An object persists in space, an event does not. Correct. If ever two objects share the same space they will be touching. Your diagram only has one spatial dimension which means any time two lines cross the objects have essentially crashed into each other (assuming the both objects are in the same place in the other two spatial dimensions). If you were to add another spatial dimension it would make more sense: http://evankeane.files.wordpress.com/2007/04/world_line.png In this case two objects that share the same X and Y coordinate (regardless of what time it happens) will be touching (again, assuming they share the same Z coordinate). That is not correct. The meteor that hit earth and wiped out the dinosaurs shared the same x, y, and z spatial position as earth--that it happened some time ago doesn't mean the objects missed one another. As I said very early on in this thread--all of your confusion is stemming from your tendency to think of objects as dots on a space time diagram. That is not correct.

Right. You can also think of the observer (yourself) as always existing here and now which means the events are the moving dots. As the observer moves through time their view of the events of the universe changes. An example--an event on the moon is about a second old when we see it. The event moves from the observer's present to their past and intersects the past light cone of the observer when it is about a second old. The moon is always visible in the observer's here and now (the moon's world line always intersects the observer's past light cone), but this single event is only visible when it intersects (when it is a second old from this observer's perspective). I'll try to show. I know what you mean. If there are two observers with relative velocity then the location of events in space time is different between them, or you could think of a single observer accelerating. The location of events in space time and even the order that they happen will change for the observer. A wikipedia diagram shows (http://en.wikipedia.org/wiki/File:Lorentz_transform_of_world_line.gif) The diagram is like the one I just drew where the observer's here and now stays in the same place on the image as time moves along (the center). In this animation, the vertical direction indicates time and the horizontal direction indicates distance, the dashed line is the spacetime trajectory ("world line") of an accelerating observer. The small dots are arbitrary events in spacetime that are stationary relative to each other. The events passing the two diagonal lines in the lower half of the picture (the past light cone of the observer) are those that are visible to the observer. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the view of spacetime changes when the observer accelerates. In particular, absolute time is a concept not applicable in Lorentzian spacetime: events move up-and-down in the figure depending on the acceleration of the observer. Compare this to the absolute time apparent in Image:Galilean transform of world line.gif. http://en.wikipedia.org/wiki/File:Lorentz_transform_of_world_line.gif I hope this is insightful rather than confusing things.

Indeed they are. Lines don't hide inside past light cones and mass must be represented with lines. Yes, only a tiny fraction of past events are currently observable. No, it does not follow that a tiny fraction of the mass responsible for those events is currently observable. The reason it does not follow is because an event is not an object. The mass is what you call "directly observable" because its world line intersects the past light cone of the observer. We are not seeing the mass as it exists today, but we can see it.

A material object is a line. Noether's theorem would demand it. An event is a dot.

Earth's inner core?

Michel, you need to go back and draw world lines for every event on every diagram you've made. If you do, you'll figure out real quick what's wrong with this: That is unless you're really thinking that stars randomly pop into existence, emit some light, and quickly disappear.

I'd agree. That's a good diagram. I would just be careful in that you've labeled A, B, C, D, and E as events but you're talking about them as objects. The way you've drawn them they happened in the past so you would say "A, B, C, D, and E are in the past." But, your point is correct. Whatever matter accompanied those events are currently in the present--definitely a tautology. X and Y would go a lot further toward existing if you drew world lines for them. I don't believe cosmologists would say that they don't exist. It's just that their light isn't reaching earth right now. Here is a website: http://www.astro.virginia.edu/class/whittle/astr553/Topic16/t16_light_cones.html with a similar diagram, and I'll quote some. Solid red line shows, on both sides, the trajectory of a light ray which starts at the big bang from our current particle horizon. It is also the event-line which we witness now as light comes to us, ie we see only those events lying on the red line (light rays starting at other space-time events have either already arrived or will arrive in the future) -- the light cone is for light arriving now.

I understand completely now. You are confusing events with objects. An event happens at a single place and time. On the previous diagram the events were A, B, C, and D. Objects are represented as world lines. On the diagram they were the lines extended from the bottom to the top (earth, planet X, and star): I didn't draw the whole world line for the exploding star because it would have fanned out into a supernova remnant and been complicated to draw. The point is that mass cannot be hidden inside a past light cone the way you are thinking of an event hiding because mass doesn't last for an instant the way an event does. For example, Neil Armstrong walking on the moon was an event. We are currently inside the future light cone of that event so we cannot directly observe it today. In your words, it is hidden inside our past light cone. But, this does not mean the mass of the moon or the mass of Neil Armstrong is missing to us. It is directly observable today, we are just seeing it at a different time. Reading this page might be helpful: http://en.wikipedia.org/wiki/World_line

That's an interesting way of looking at things, I suppose. It would usually be said that any event in A's future light cone can be causally connected to A. That is to say, A could affect any of the events in the graph I posted. But, you are focused narrowly on the idea of "seeing" A--that only an event at distance ct can "directly observe" A. That may be true in your thought experiment, and it's usually true in astronomy, but it is not always true--it doesn't have to be true. We can observe some astronomical bodies like Einstein's cross where the light has not made a straight path to us. The light was bent and slowed even though it didn't technically interact with any other particles. Also, why do you think something being "directly observable" is important? All of the objects in your thought experiment are separated by some distance so none of them can directly interact. In order for one to communicate with another (or to observe another) means that some signal or some particles need to be sent between them. By only considering the one kind of path and one kind of particle (light) you neglect other methods of observation or communication. Also, where are you going with this?

I'm having some trouble with your wording, but the concept is correct. If you graph space and time it could be easier to understand what is happening. The star explodes at A. The light first reaches Planet X at B 1.5 million years ago then reaches Earth at C 1 million years ago. Event B is then seen by Earth at D--the here and now. Rather than saying "they don't look at me" and "they are observing an exploding star" you would avoid confusion if you said "they weren't looking at me" and "they were observing an exploding star". It would be in the past tense because it happened in the past. If there were a mirror on Planet X then you would see the exploding star--the same one they were looking at through their telescope--so it is misleading to say that you cannot see it. It is an event that you do not see when looking directly at the position where the star was. It takes light longer to travel ABD than it does to travel AC.

Then you could avoid all that by explaining in your thought experiment that by “seeing” you mean only the observation of unimpeded light traveling the shortest available distance between the two. Otherwise, “you cannot see the past event of the pencil falling down.” sounds like you’re saying it is impossible. You’re saying “cannot” rather than “won’t”. Figuring out how long ago an event happened involves the path length of the mediating particles and their speed. Where you say “distance tells exactly what your friend is able to see” I think you would do much better to either say “distance tells exactly what your friend sees” or if you really do want to imply that the observation is impossible then you could say “the distance, path, and speed of the signal tells exactly what your friend is able to see”--if you establish in your thought experiment that you're only talking about one kind of path and one kind of speed then that would be 100% correct.

Nature does not follow your approximations. If you put an aperture on a distant star cutting its radius in half then a person on earth would find the star one quarter as bright by the action of the aperture--whether or not you consider it a point source at that distance. Your idea that nature gives up following physics once you approximate something as a point souse is not right. It is precisely right. r is the radius of the Lambertian radiating body, d is the distance to that body and (r/d)2 is the factor by which brightness is reduced for the person viewing the object at distance d. Yes, but 1/d2 gives only the factor by which flux per unit surface area gets smaller. The formula I gave accounts for the radius of the radiating body. John was precisely correct.

I'd just like to agree with John's arithmetic here: The factor that flux is reduced is (r/d)^2 where r is the radius of the shiny object (shiny ) and d is the distance to said shininess. Like John says, if you make r 10 times smaller then the flux will be dimmer by a factor of 100. Making the object 100 times brighter will compensate. Distance also can be compensated for by a brighter object as he says: 10 times more distant and 100 times brighter = the same apparent brightness.

If you want to double or triple a physical quantity then you multiply it by the number 2 or 3. Numbers are dimensionless. You don't square or cube them. The units of velocity are squared in KE=1/2mv^2, like I said, m^2/s^2. The gravitational constant is dimensionful, with dimensions of: The dimensions assigned to the gravitational constant in the equation above — length cubed, divided by mass and by time squared (in SI units, metres cubed per kilogram per second squared) — are those needed to balance the units of measurements in gravitational equations. However, these dimensions have fundamental significance in terms of Planck units: when expressed in SI units, the gravitational constant is dimensionally and numerically equal to the cube of the Planck length divided by the Planck mass and by the square of Planck time. http://en.wikipedia.org/wiki/Gravitational_constant#Dimensions.2C_units_and_magnitude Looking at the last few posts again, it looks like I may have missed that Mr Skeptic and Swansont may have been talking about geometric units. In that case I agree that the speed of light is dimensionless since time is measured in the same units as length. I think we're off topic, in any case.

Thank you for the compliment. I admire your approach, and agree--you can't go wrong when you're willing to be proven so Not sure about game shows, but certainly my favorite game of mathematical probabilities is poker