Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 21/07/2019 22:32:48
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Here’s another one from the past.
https://www.thenakedscientists.com/forum/index.php?topic=52973.msg444979#msg444979
A spacetime event must be unique and immutable; so, how can something that is unique and immutable appear to be so different in different frames of reference?
The event has a specific set of spacetime coordinates, that's true. However its relationship between other events depends on the observer. That's what relativity is all about.
For clarity; I'm not disagreeing with Pete; just trying to clarify my thoughts.
The glib answer to the question: “…how can something that is unique and immutable appear to be so different in different frames of reference?” is that an event has a specific set of spacetime coordinates, which are unique, but its relationship to other events depends on the observer. “That's what relativity is all about”.
For most practical purposes, this answer is all we need. Never-the-less, the fact that discussions about what one might observe in relation to a person, or object, approaching, or crossing, an event horizon are so commonplace, does suggest that it leaves some aspects unclarified in the minds of hitch-hikers and, to some extent, experts.
One question might be. If a spacetime event is unique, but its relationship to other events is observer dependent, does this mean that it is unique only in its own reference frame? If so; is “uniqueness” relative, and what on Earth might that mean?
Consider a scenario in which a specific spacetime event (X) occurs in RF1. Observer A is in the same RF and is, therefore, stationary relative to X. Observer B is in RF2 which is in motion, relative to RF1.
Observer A sees X occurring at location L and at time t. These coordinates are unique and immutable.
Observer B sees X occurring at location Lʹ and at tʹ. These coordinates are unique and immutable. Under SR, both are to be considered valid. L ≠ Lʹ and t ≠ tʹ, but there is only one original event, which is “unique”. Observer B’s “reality” is valid, and also unique.
Should we conclude that place, time and uniqueness are all observer dependent, and therefor relative, and that “in translation”, uniqueness is conserved?
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Consider this. A particle follows a portion of its worldline through coordinate (x, y, z) at time t. At a later time t1 another particle follows a portion of its worldline through coordinate (x, y, z). The particles are of the same type and the coordinate position are the same.
The only things that make them distinct are the time separation and any differences between the two portions of their worldlines.
So uniqueness has to do with relative position and motion. If the two worldline portions were identical then they would only be distinct due to a separation in time.
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The confusion arises from the assertion of "specific coordinates". The relationship between any two events is a unique vector in spacetime, but that vector can be mapped onto any coordinate system you choose, including the possiblity of degeneracy if the extended vector passes through the origin of that system.
To give an example, suppose galaxy A explodes and emits a pulse of gamma radiation. After a thousand years, that pulse triggers the explosion of galaxy B which just happens to have moved into such a position that its gamma burst is indistinguishable from that of A at the time they both reach Earth. Having no other information, our observer can only conclude that there has been at least one explosion, somewhere in the direction of B, whereas an observer on Pluto would know that there were at least two explosions 1000 light years apart.
Time to resurrect the abbreviated version of the Patagonian Cows. Three blokes in a train see two cows in a field.
Politician: "The vast majority of Patagonian cows are black"
Statistician: "On a possibly insufficient sample, the Bayesian postulate is that half the cows in Patagonia are black"
Physicist: "I saw two bovine quadrupeds, at least one side of one of which was black."
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Consider this. A particle follows a portion of its worldline through coordinate (x, y, z) at time t.
What can we say about the spacial coordinate (x, y, z)? Is it, in any sense, unique? Is it an event?
In answer to the question: What is an event. https://www.thenakedscientists.com/forum/index.php?topic=76471.0
It [an event] is something which has a spatial point location at an instant of time.
I would use the word to indicate the boundary in spacetime where a change occurs between "before" and "after"….
We define what an event is. Usually it is when something happens and we can define the point at which it happens as a spacetime coordinate. The happening can be anything, an object passing a point, changing speed, hitting something, emitting a photon, etc. You name it
It would seem that spatial coordinates (x,y,z) alone cannot be an event. Something else is needed. Can that “something” be time? At least two of the above quotes suggest that it can.
Can (x,y,z,t) be considered as an event, without intervention by anything else?
BTW; like the cows!
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An event is the boundary between "before" and "after", as in "event horizon". Or it can be the process that develops "after" from "before", as in "3 day event". So it may have a transient or permanent location in space or time.
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Let's try this another way. To be unique is to be one of a kind. A set of one. How can you conserve uniqueness? Each unique thing has no equal by definition.
Energy can be conserved but is there anything unique about it? Any proton or electron or other particle can have identical kinetic or potential energy to any other. Can conserved properties be unique?
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Since today's "before" is yesterday's "after", any event is unique by definition.
The original question seems to confuse "unique" with "universally symmetric". And there's no reason why any event should be universally symmetric. Viewed from the side, a rocket launch is a vertical line. Viewed from above, it is a dot. But globally, ther is a lot more entropy after the launch.
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A spacetime event must be unique and immutable; so, how can something that is unique and immutable appear to be so different in different frames of reference?
The event has a specific set of spacetime coordinates, that's true. However its relationship between other events depends on the observer. That's what relativity is all about.
For clarity; I'm not disagreeing with Pete; just trying to clarify my thoughts.
The glib answer to the question: “…how can something that is unique and immutable appear to be so different in different frames of reference?” is that an event has a specific set of spacetime coordinates, which are unique, but its relationship to other events depends on the observer. “That's what relativity is all about”.
The relations might indeed be an objective vector as alancalverd points out, but some relations are dependent on the coordinate system chosen, and we don't directly observe those relations. Given events A and B, A is observable from event B or it isn't, and that fact does not change from one frame to the other. That's the observable. The computation that A is before or after B is an abstract one concerning reference frames (coordinate systems, not observers), and is thus not a real relation, but yes, that's what relativity is about.
Observer A sees X occurring at location L and at time t. These coordinates are unique and immutable.
Observer B sees X occurring at location Lʹ and at tʹ. These coordinates are unique and immutable. Under SR, both are to be considered valid. L ≠ Lʹ and t ≠ tʹ, but there is only one original event, which is “unique”. Observer B’s “reality” is valid, and also unique.
They're the same event. The two observers have simply overlayed different coordinate systems with different origins, different orientations of the axes, or both, all arbitrary. There is no actual coordinates of any event, which is why the location of Earth/now cannot be given by a set of 4 numbers since there is no objective origin for a coordinate system.
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A ball is dropped and hits the ground just before a super nova appears in the sky. Which occured first? Is this abstract?
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What can we say about the spacial coordinate (x, y, z)? Is it, in any sense, unique? Is it an event?
An event is a point in 4D spacetime. No, 3 fixed coordinates in 4D geometry defines a line, not a point.
We define what an event is. Usually it is when something happens and we can define the point at which it happens as a spacetime coordinate. The happening can be anything, an object passing a point, changing speed, hitting something, emitting a photon, etc. You name it
I like this description best, but would like to add that nothing needs to occur at a particular point for it to be an event. Given a coordinate system, any value for x,y,z,t defines an event, no matter how boring that particular event is.
Can (x,y,z,t) be considered as an event, without intervention by anything else?
One needs a defined coordinate system to give meaning to all 4 of those numbers. In other words, it needs to be relative to some other event where the origin 0,0,0,0 is assigned, and also needs a definition of which way each of the 4 axes goes. What direction is the x axis? It's totally arbitrary, and without picking one, event 1,0,0,0 is undefined even if an origin is specified.
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A ball is dropped and hits the ground just before a super nova appears in the sky. Which occured first? Is this abstract?
Yes, it is abstract. There are coordinate systems (inertial reference frames) which put the ball event before the supernova event, so the relation of before/after is not demonstrably real.
The photon hitting my eye is real. The event that caused it is abstract. It is only information about the event and not the event itself. This is the real problem with interpretations of relativity. The relativity of simultaneity is an information based interpretation. Which is all we can ever experience.
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The photon hitting my eye is real. The event that caused it is abstract.
No, a real ball hit the ground and was illuminated by ambient light, so the event causing your observation is quite real, unless you're some kind of idealist, but they deny even the photon hitting your eye.
The photon I was talking about was from the supernova. How can one photon be abstract and another real?
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Here is the point. I observe the information about the ball before the information about the supernova. I assume the ball is nearer in distance and it hits the ground before the supernova explodes. This is a reasonable assumption. However, the information is not giving me the true picture.
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Let's try this another way. To be unique is to be one of a kind. A set of one. How can you conserve uniqueness? Each unique thing has no equal by definition.
This may be rubbish, but consider that X is something, the characteristics of which make it unique, when viewed by an observer in the same RF. If, when viewed by on observer in another RF, the perceived characteristics change, such that it appears identical to some other entity; its original “uniqueness” has not been conserved. Alternatively, if its perceived characteristics, in the second RF, are still different from everything else, then “uniqueness” has been conserved.
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Since today's "before" is yesterday's "after", any event is unique by definition.
True; as long as no one argues that a spacial coordinate (x,y,z) is an event.
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I'm trying to read/respond to this thread while doing several other things; so forgive me if I fail to take into account some relevant posts, later in the thread.
The computation that A is before or after B is an abstract one concerning reference frames (coordinate systems, not observers), and is thus not a real relation,
That’s one of those things that I read and think “Got that”. Then I try to “explain” it, and I’m not so sure. (May be linked to being mildly dyslexic).
Why is it “not a real relation”?
There is no actual coordinates of any event, which is why the location of Earth/now cannot be given by a set of 4 numbers since there is no objective origin for a coordinate system.
There is no spacial coordinate (x,y,z), or even (x,y,z,t), unless one is designated by a (potential) observer. (??)
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Here is the point.
1) I observe the information about the ball before the information about the supernova.
2) I assume the ball is nearer in distance and
3) it hits the ground before the supernova explodes.This is a reasonable assumption.
However, the information is not giving me the true picture.
I numbered your assumptions for reference. I call the ball hitting the ground event B and the supernova event S. The observation events by you are events oB and oS respectively.
#1 is an empirical fact. oB occurred, and a short time later (a minute let's say), oS occurred. Nobody in any frame can disagree with that ordering, even if they disagree with the minute duration between them.
#2 is more difficult because neither you nor the ball are events, but rather worldlines, and worldlines don't have a defined distance from events or each other (especially since the worldlines have not been described in full). What I can agree with is that a line drawn through events S through B and on to where it intersects your worldline does indeed put the distance between that intersection point and event B much closer than that point and event S.
That leaves point 3: You assume B occurs before S. How do you figure this?? Even in the typical assumed frame, the supernova (Let's say Betelgeuse) happened 642 years ago and the ball event B just a minute ago, 642 years after (not before) the supernova event S.
My contention what that it was quite possible for either to occur before the other, but not definite, and thus any assertion one way or another is an abstract one.
The computation that A is before or after B is an abstract one concerning reference frames (coordinate systems, not observers), and is thus not a real relation,
That’s one of those things that I read and think “Got that”. Then I try to “explain” it, and I’m not so sure. (May be linked to being mildly dyslexic).
Why is it “not a real relation”?
There is no way to objectively test for A being before B if they're separated in a space-like manner. If they're separated in a time-like manner, then yes, A and B happen in that order, in any frame. For space like separation of events, the choice of an abstract coordinate system determines which occurs first. That makes the ordering an abstract choice, not an objective fact.
My example has always been a pair of dots drawn on a paper plate, and then the plate pasted to the wall. Your choice of orientation of the plate makes dot A or B the higher of the two, but there's no objectively correct way to orient the plate. So one dot on the plate (not yet pasted to the wall) being higher than the other is not a real relation between the dots.
There is no spacial coordinate (x,y,z), or even (x,y,z,t), unless one is designated by a (potential) observer. (??)
No, of course not. Have you ever seen the coordinates of Earth (or say the galaxy) published without specification of some origin, which almost always comes down to geocentrism? Earth is here. That's the origin. But that statement doesn't inform me one bit where Earth is in the universe if I don't already know where it is. I can say where it is in the galaxy, but that assumes I know the coordinates for the location of the galaxy.
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So the order of observation is not necessarily the order of occurrence. The great thing about relativity is that it doesn't actually matter. Two events may be simultaneous to an equispaced observer, and sequential to another, but the uniqueness of each event, that is the change of entropy that defined before and after in each case, is incontrovertible to both.
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Here is the point. I observe the information about the ball before the information about the supernova. I assume the ball is nearer in distance and it hits the ground before the supernova explodes. This is a reasonable assumption. However, the information is not giving me the true picture.
Surely, it is a reasonable assumption only if you ignore physical distances and the speed of light. (?)
This causes me to struggle with:
My contention what that it was quite possible for either to occur before the other, but not definite, and thus any assertion one way or another is an abstract one.
Presumably, there could be RFs, somewhere, in which either event could be seen as preceding the other, because there is no causative relationship between either, and these observations would both be valid under SR. Is that what you are saying?
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OK, so I know the ball is close to me. I can easily move position so that something in the near distance blocks the light from the supernova. If I am lucky and the supernova is in the path of the moon it will also block the supernova. This way I can determine how long the light from the ball took to get to my eye compared to a reasonable guesstimate of the distance to the supernova and how long that light should have taken.
So in this case my frame has nothing to do with it. The speed of light has everything to do with it. You could argue this about any frame. The distance is the crucial factor. If we take L as a light second, then for every multiple of L, which we label n, then in an ideal vacuum it will take light n seconds to reach us.
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I look forward to a viable definition of uniquity.
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So in this case my frame has nothing to do with it. The speed of light has everything to do with it. You could argue this about any frame. The distance is the crucial factor. If we take L as a light second, then for every multiple of L, which we label n, then in an ideal vacuum it will take light n seconds to reach us.
Except the spatial distance between events is frame dependent, so the amount of time it takes light to go that distance is also frame dependent.
In a frame where the ball event occurs first, the supernova event S needs to be close enough to be oberved within a minute (your time) of when B occurs. In the (arbitrary) frame of Earth, sure, the supernova event occurs first, despite your post assuming otherwise.
My contention what that it was quite possible for either to occur before the other, but not definite, and thus any assertion one way or another is an abstract one.
Presumably, there could be RFs, somewhere, in which either event could be seen as preceding the other
There is a RF somewhere where either event actually does precede the other. It isn't about seeing/observing. Select an orientation of the 4 axes for your coordinate system so the coordinates of event S has a lower value for the t coordinate than does the B event.
because there is no causative relationship between either
The causal relationship is impossible because the two events are not in each other's light cones. If they are in each other's light cones, they may or may not have a meaningful causal relationship, but the ordering is nevertheless one, then the other: objective, not abstract.
Jeffrey gave an example of a pair of events that are not in each other's light cones, which means the determination of the ordering of those events is frame dependent.
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Show me where I said the supernova explosion happened before the ball hit the ground. The information ABOUT the supernova was detected first. Please do not attribute ideas to me that I did not express. That is downright dishonest.
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@Halc you said "Except the spatial distance between events is frame dependent, so the amount of time it takes light to go that distance is also frame dependent."
So what you are saying is the speed of light differs in different frames of reference. What?
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I look forward to a viable definition of uniquity.
Since anything that might be labelled as an event necessarily involves an increase in entropy, "unique" and "event" may be considered sort of tautologous, like "orange" (adjective) and "orange" (noun).
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Show me where I said the supernova explosion happened before the ball hit the ground.
You never said that, and I didn't say you did.
The information ABOUT the supernova was detected first.
You 'expressed' otherwise, my bold:
A ball is dropped and hits the ground just before a super nova appears in the sky.
Trying to get the topic back on track.
This may be rubbish, but consider that X is something, the characteristics of which make it unique, when viewed by an observer in the same RF.
I would say an event X is unique because it is identical to itself and is not a different event. Any different event Y is going to have some kind of separation with X, but X is always X. All this is true in any frame, so the RF really doesn't matter in any of this.
So for instance, if event X is where the Titanic first touches the iceberg, that event is that event in any reference frame. It doesn't mean that the event has the same coordinates x,y,z,t since no coordinate system has been assigned, and if it is, any value for x,y,z,t might specify X. It has nothing to do with an observer since one observer might be able to see the event and another (in the same frame even) cannot see it, or see it from a different angle.
That event is <1000 km east, -108 years> relative to my event today, but <3000 km west, +5 days> to somebody just getting on the ship. That's pretty different coordinates from two observers using the same (rotating, not inertial) reference frame.
If, when viewed by on observer in another RF, the perceived characteristics change, such that it appears identical to some other entity; its original “uniqueness” has not been conserved. Alternatively, if its perceived characteristics, in the second RF, are still different from everything else, then “uniqueness” has been conserved
The uniqueness of my Titanic example event does not change for some other entity. It still has the one characteristic of the Titanic making contact with that ice.
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Show me where I said the supernova explosion happened before the ball hit the ground.
You never said that, and I didn't say you did.
The information ABOUT the supernova was detected first.
You 'expressed' otherwise, my bold:
A ball is dropped and hits the ground just before a super nova appears in the sky.
And what alerts us to the supernova appearing in the sky? ESP? Or maybe photons? Do you always feel the need to be vindicated?
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Since anything that might be labelled as an event necessarily involves an increase in entropy,
How can an event involve an increase of entropy? Entropy increases over a duration of time, and and event has not duration.
An event is what occurs between "before" and "after". Entropy after is always greater than entropy before. Therefore no entropy increase <=> no event.
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An event is what occurs between "before" and "after".
OK, you're working with a completely different definition than the physics one. I'll interpret your answers in light of this private definition.
And there you go again. I know what Alan means.
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I'd be interested to know what the physics definition of an event might be. I've only been studying physics for the last 65 years, and clearing up after events for the last 60. Seems that I have been wasting my time!
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Seems that I have been wasting my time!
That depends a lot on how thorough your clearing up has been. How far our would a guess at, "bordering on obsessive" be? :)
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Except the spatial distance between events is frame dependent, so the amount of time it takes light to go that distance is also frame dependent.
I interpreted this as saying, not that the speed of light was frame dependent, but that if distances varied from RF to RF, the time taken by light to travel these different distances would have to vary, as light would travel at c in each/every case. Is that right?
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I'd be interested to know what the physics definition of an event might be.
https://en.wikipedia.org/wiki/Event_(relativity):
In physics, and in particular relativity, an event is the instantaneous physical situation or occurrence associated with a point in spacetime (that is, a specific place and time).
On the particle physics end of things, (also wiki): "In particle physics, an event refers to the results just after a fundamental interaction took place between subatomic particles", but the OP is talking about the relativistic spacetime definition (the upper one), not the particle physics one.
I've never seen the wording you gave, and am not sure what it means, so clearly I'm not as clever as jeffrey. Your definition seems to completely discard a localized region of space, so an event could involve 20 galaxies or more.
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so an event could involve 20 galaxies or more.
We physicists are used to thinking big as well as small. What both of your quoted definitions have in common is the different states of the universe before and after the event. An event involving 20 galaxies would be small beer (almost a local brew) compared with the Big Bang, and whilst we don't have much idea of before, everything we now observe is pretty obviously after something like an event.
Since the universe is by definition never the same after any event, the occurrence of other events guarantees the uniqueness of each.
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Seems that I have been wasting my time!
That depends a lot on how thorough your clearing up has been. How far our would a guess at, "bordering on obsessive" be? :)
Way out! I live by "good enough", "engineering tolerance", "acceptable defects", "anywhere on the runway" and "life is too short...." I don't remember ever sailing a boat with a fully working toilet, but we never missed a tide.
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Just for the record and in support of Alan's point here is part of a reply to a question on another forum. Enjoy!
https://physics.stackexchange.com/questions/389488/what-is-an-event-in-special-relativity (https://physics.stackexchange.com/questions/389488/what-is-an-event-in-special-relativity)
In the original usage, as Einstein used it, an "event" is just something that happens, like a detector clicking. It's just the same as the colloquial meaning.
In the early 20th century, various thought experiments involving hypothetical events, and actual experiments involving physical events, were used to show that general relativity is an excellent model for our universe. In the context of general relativity, spacetime is modeled as a Lorentzian manifold, and physical events are modeled as points in this manifold.
Now, some mathematically minded people choose to forget all this history. They instead say the word "event" is defined as a point in a Lorentzian manifold. This is a clean and consistent definition, but as usual in mathematical physics, it misses the point. The only reason we care about these mathematical "events" is because they form part of a theory that does an excellent job of describing real events. By conflating the two, one glosses over the mountains of experimental work needed to link the two together."