# Observing our own past?

#### SW VandeCarr

It would seem that, in principle, we could observe our own past by means of reflected light. If gravitational mirrors could exist and the reflected light be processed to a high degree of resolution, we might be able to observe the earth as it existed in the past.

Light might be reflected 180 degrees at some distance from a black hole for example. Since, according to GR, simultaneous events are those linked by a light beam, does this mean that past events on earth could be in some sense simultaneous to "present" events on earth?

In fact, this occurs all the time on nanoscales. Just by looking in an ordinary mirror, you are in looking your past (maybe six nanoseconds ago).

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#### Fredrik

Staff Emeritus
Gold Member
It would seem that, in principle, we could observe our own past by means of reflected light.
There would of course have to be mirrors out there. If we send some mirrors out in space now, people in the future can use them observe the earth as it appeared at some time in their past (but not our past, since no mirrors have been sent into space yet).

Since, according to GR, simultaneous events are those linked by a light beam, does this mean that past events on earth could be in some sense simultaneous to "present" events on earth?
No. GR doesn't have one specific definition of simultaneity, and if it did, it wouldn't be that one. It doesn't make much sense except in a theory in which the speed of light is infinite.

This one can be somewhat useful though: If a radar device equipped with a clock emits a signal when the clock displays -T and detects the reflected signal when the clock displays T, then the reflection event is simultaneous with the event where the clock displays 0.

#### SW VandeCarr

There would of course have to be mirrors out there. If we send some mirrors out in space now, people in the future can use them observe the earth as it appeared at some time in their past (but not our past, since no mirrors have been sent into space yet).
As I said, gravitational mirrors may already exist near black holes. At some critical distance from the event horizon, one might expect light to be deflected by 180 degrees. The point, however, is more theoretical. Reflected light would seem to allow an observer to observe (in real time?) the local "past" or world line.

No. GR doesn't have one specific definition of simultaneity, and if it did, it wouldn't be that one. It doesn't make much sense except in a theory in which the speed of light is infinite.

This one can be somewhat useful though: If a radar device equipped with a clock emits a signal when the clock displays -T and detects the reflected signal when the clock displays T, then the reflection event is simultaneous with the event where the clock displays 0.
I like this definition, but it's far more radical than my speculation. It suggests that past events can 'simultaneously' affect events in the present.

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#### lightarrow

I like this definition, but it's far more radical than my speculation. It suggests that past events can 'simultaneously' affect events in the present.
But you can't create your own laws of physics, either it's in that way or it's not, and the answer is not.

#### SW VandeCarr

But you can't create your own laws of physics, either it's in that way or it's not, and the answer is not.
In what way is it not? The issue is the definition of 'simultaneous' as it applies to GR. My understanding is that any event occuring at some distance is 'simultaneous' with our observing it. Fredrik gave a diifferent definition which I found interesting. How do you define 'simultaneous' as it applies to GR?

Light reflected by an ordinary mirror would not be following a spacetime geodesic, but light reflected by a gravitiational mirror would, according my understanding; just as light focused by a gravitational lens follows a spacetime geodesic. If so, why aren't events in our own past 'simultaneous' with our observing them when connected by a light beam following a geodesic?

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#### JesseM

Fredrik said:
No. GR doesn't have one specific definition of simultaneity, and if it did, it wouldn't be that one. It doesn't make much sense except in a theory in which the speed of light is infinite.

This one can be somewhat useful though: If a radar device equipped with a clock emits a signal when the clock displays -T and detects the reflected signal when the clock displays T, then the reflection event is simultaneous with the event where the clock displays 0.
I like this definition, but it's far more radical than my speculation. It suggests that past events can 'simultaneously' affect events in the present.
What do you mean by that? This is a definition that would work for inertial frames in SR too--if you are one light-year away from me, and I send you a signal when my clock reads Jan. 1 2009 which you bounce back to me, and I receive your response when my clock reads Jan. 1 2011, then of course it should be true in my frame that the event of your receiving my signal and bouncing back a response was simultaneous with the event of my clock reading Jan. 1 2010. Do you think it makes sense to say that for inertial frames in SR, "past events can simultaneously affect events in the present"? If so, can you elaborate on the meaning of this phrase?

#### JesseM

In what way is it not? The issue is the definition of 'simultaneous' as it applies to GR. My understanding is that any event occuring at some distance is 'simultaneous' with our observing it.
No, that is certainly not true in SR. If I observe the light from an event 100 light-years away when clocks on Earth read a date of 2009 (as measured in my rest frame), then in my frame this event is actually simultaneous with the event of clocks on Earth reading 1809. If it worked the way you imagine, light would have an infinite coordinate velocity, since the light would be departing a distant event "simultaneously" with the event of my receiving that same light.

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#### SW VandeCarr

No, that is certainly not true in SR. If I observe the light from an event 100 light-years away when clocks on Earth read a date of 2009 (as measured in my rest frame), then in my frame this event is actually simultaneous with the event of clocks on Earth reading 1809. If it worked the way you imagine, light would have an infinite coordinate velocity, since the light would be departing a distant event "simultaneously" with the event of my receiving that same light.
Either the word 'simultaneous' is meaningful or is not. Two events occurring at any distance from each other are not simultaneous by this definition. Therefore the word has no physical meaning. Einstein himself defined events as simultaneous at the moment they are connected by a light beam. He also allowed that simultaneity is relative and that two events could be seen in opposite orders (AB and BA) according to the position of the observers. This is the only definition that gives the word any meaning. By your definition, no two distinct events can be simultaneous. There is no absolute time reference.

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#### Dmitry67

You can observe your own past (even even say hello to your past copy) in the closed time-like loops. Such weird geometry exists around super-extreme kerr black holes (even there is no proof that they really exist, but at least they are much more probable then famous wormholes, because they dont require any exotic matter). Also (I am not sure) the same happens inside horizons of the normal kerr black holes.

#### SW VandeCarr

You can observe your own past (even even say hello to your past copy) in the closed time-like loops. Such weird geometry exists around super-extreme kerr black holes (even there is no proof that they really exist, but at least they are much more probable then famous wormholes, because they dont require any exotic matter). Also (I am not sure) the same happens inside horizons of the normal kerr black holes.
I've heard of closed time-like loops. I don't know if what I'm describing is the same thing. If a black hole could act as gravitational mirror, reflecting light 180 degrees, we could be connected to our local past by means of this light but couldn't interact with it.

#### Dmitry67

No, you can place mirror far enough and look at your old reflection.
You even dont need black hole to do it. Just a big mirror.

In a close timelike loop you can TOUCH past or future copy of you.

#### Fredrik

Staff Emeritus
Gold Member
Einstein himself defined events as simultaneous at the moment they are connected by a light beam.
This is wrong. He defined it the way I did in #2 (and Jesse in #6).

You also seem to have overlooked what Jesse said in #7. If we use your definition to construct a coordinate system in which a physical observer is stationary at the origin, then the speed of light is infinite in this coordinate system, since the event where the light is emitted has the same time coordinate as the event where the light is detected. Light travels any distance in zero time.

Another problem with your definition: When I switch on the lights in my apartment, that event is connected by light rays to events one light-year away (say in the "straight up" direction), both one year into the future and one year into the past. Do you consider those two events to be simultaneous, even though the occur at the same location two years apart?

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#### Mentz114

Gold Member
If you want to watch yourself in the past, videotape yourself now. Or use a sheet of slow glass. If you stand in front of it for an hour, you can go around to the other side and watch yourself standing there. Then you go back to the original side and watch again etc. Hours of fun.

#### SW VandeCarr

This is wrong. He defined it the way I did in #2 (and Jesse in #6).

You also seem to have overlooked what Jesse said in #7. If we use your definition to construct a coordinate system in which a physical observer is stationary at the origin, then the speed of light is infinite in this coordinate system, since the event where the light is emitted has the same time coordinate as the event where the light is detected. Light travels any distance in zero time.

Another problem with your definition: When I switch on the lights in my apartment, that event is connected by light rays to events one light-year away (say in the "straight up" direction), both one year into the future and one year into the past. Do you consider those two events to be simultaneous, even though the occur at the same location two years apart?
The speed of light is obviously not infinite. Simultaneity is relative. When you turn on a light at A, equidistant observers at B and C (not necessarily in line with A) l both will observe the light at the same moment.

I'm not sure what you mean by sending light back into the past. My argument is that a gravitational mirror may reflect light so that the local past is directly observable. Whether this connection is 'simultaneous' or not is a matter of definition. I don't see how you can say that two events are simultaneous unless you observe them from a preferred third point in space.

By the way, I said I like your definition.

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#### JesseM

Either the word 'simultaneous' is meaningful or is not.
It's meaningful in the context of a particular coordinate system like the inertial coordinate systems of SR, it's not meaningful in any absolute sense according to modern physics.
SW VandeCarr said:
Two events occurring at any distance from each other are not simultaneous by this definition.
By what definition? The standard one in SR which Fredrik gave? Of course events at different locations can be simultaneous by that definition, if you're at rest relative to me and I send a signal to you when my clock reads t-T, then as soon as you receive the signal you bounce it back and I receive your reply when my clock reads t+T, then according to this definition, the event of your receiving the signal and bouncing it back is simultaneous with the event of my clock reading t. I gave an example of this in my first response to you:
This is a definition that would work for inertial frames in SR too--if you are one light-year away from me, and I send you a signal when my clock reads Jan. 1 2009 which you bounce back to me, and I receive your response when my clock reads Jan. 1 2011, then of course it should be true in my frame that the event of your receiving my signal and bouncing back a response was simultaneous with the event of my clock reading Jan. 1 2010.
SW VandeCarr said:
Einstein himself defined events as simultaneous at the moment they are connected by a light beam.
Here you are simply misinformed, the definition Fredrik gave is equivalent to the one Einstein gave in his 1905 paper, and also equivalent to the one you'd find in any SR textbook. In section 1 of the paper Einstein writes:
We have so far defined only an "A time" and a "B time." We have not defined a common "time" for A and B, for the latter cannot be defined at all unless we establish by definition that the "time" required by light to travel from A to B equals the "time" it requires to travel from B to A. Let a ray of light start at the "A time" $$t_A$$ from A towards B, let it at the "B time" $$t_B$$ be reflected at B in the direction of A, and arrive again at A at the "A time" $$t'_A$$.

In accordance with definition the two clocks synchronize if

$$t_B - t_A = t'_A - t_B$$
In the example from the earlier post I quoted above, I mentioned that the event of your sending back the signal would be simultaneous with the event of my clock reading Jan. 1 2010; therefore, if your clock is synchronized with mine according to Einstein's definition, your clock should also read a "B time" of $$t_B$$ = Jan. 1 2010 at the moment you reflect the signal back to me. And since I send the signal when my clock read $$t_A$$ = Jan. 1 2009 and received your reflected signal when my clock read $$t'_A$$ = Jan. 1 2011, Einstein's equation above is satisfied, since:

(Jan. 1 2010) - (Jan. 1 2009) = (Jan. 1 2011) - (Jan. 1 2010)

#### Fredrik

Staff Emeritus
Gold Member
The speed of light is obviously not infinite.
How do you define the speed of light in a coordinate system if not as the distance traveled divided by the time it took? To define the emission event to be simultaneous with the detection event is to assign the same time coordinate to both events, and "the time it took" is the difference between the time coordinates of the events. Since t-t=0 for all t, the definition of the speed of light contains a division by zero.

Simultaneity is relative.
Not when we use your definition. Different observers will not disagree about whether two given events can be connected by a light ray.

I'm not sure what you mean by sending light back into the past.
Not sending to. Receiving from.

#### SW VandeCarr

Not when we use your definition. Different observers will not disagree about whether two given events can be connected by a light ray.
I think the main point of disagreement concerns relative vs absolute frames of reference. I've been talking about simultaneity in terms of accelerating frames. A light beam bent by 180 degrees near a black hole obviously undergoes (angular) acceleration. In this case, the issue of synchronizing clocks as you would within a given frame isn't relevant. While there is no true definition of absolute simultaneity, it is true that, as you say, different observers will not disagree about whether two events can be connected by a light beam.

There is a good discussion of this at www.physicsforums.com/archive/index.php/t-219891.html

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#### Dmitry67

Yes, but if the simultaneity is defined based on the fact that events are connected by the light beam then it is not transitive: based on that definition if

A simulataneous B and B sim C --> does not mean that A sim C

and this is quite contreintuitive.

#### Fredrik

Staff Emeritus
Gold Member
I think the main point of disagreement concerns relative vs absolute frames of reference. I've been talking about simultaneity in terms of accelerating frames. A light beam bent by 180 degrees near a black hole obviously undergoes (angular) acceleration.
I don't think that's the issue here. You don't seem to see how strange your definition of simultaneity is. We have tried to explain it, but you seem to have ignored most of our comments.

What does "simultaneous" mean to you if not "occurring at the same time", i.e. "having the same time coordinate"? If that's what it means, then your definition makes the speed of light infinite, as Jesse and I have explained.

As Dmitry pointed out, if you define "simultaneous" as "can be connected by light signals", then your simultaneity isn't transitive. Let ~ mean "is simultaneous with". If (A~B and B~C) doesn't imply A~C, then "simultaneity" clearly can't have anything to do with the idea of two events "occurring at the same time".

Do you consider "right here, right now" to be simultaneous with one or two events one light-year away in the "straight up" direction? (Both at the same position, but two years apart). If the answer is "one", then your simultaneity isn't even reflexive, i.e. A~B doesn't imply B~A.

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#### lightarrow

I think the main point of disagreement concerns relative vs absolute frames of reference. I've been talking about simultaneity in terms of accelerating frames. A light beam bent by 180 degrees near a black hole obviously undergoes (angular) acceleration.
...if spacetime were euclidean, but it's not, it's warped.

#### SW VandeCarr

I don't think that's the issue here. You don't seem to see how strange your definition of simultaneity is. We have tried to explain it, but you seem to have ignored most of our comments.

What does "simultaneous" mean to you if not "occurring at the same time", i.e. "having the same time coordinate"? If that's what it means, then your definition makes the speed of light infinite, as Jesse and I have explained.

As Dmitry pointed out, if you define "simultaneous" as "can be connected by light signals", then your simultaneity isn't transitive. Let ~ mean "is simultaneous with". If (A~B and B~C) doesn't imply A~C, then "simultaneity" clearly can't have anything to do with the idea of two events "occurring at the same time". Do you consider "right here, right now" to be simultaneous with one or two events one light-year away in the "straight up" direction? (Both at the same position, but two years apart). If the answer is "one", then your simultaneity isn't even reflexive, i.e. A~B doesn't imply B~A.
OK. First, I'm not ignoring what you've all said. Correct me if I'm wrong, but what you're talking about is simultaneous events within a single frame of reference. I totally agree with the definition of synchronized clocks, say on a moving train. Who am I to disagree with Einstein?! However, I think we all agree there is no generally accepted definition of simultaneity across reference frames moving with respect to each other.

Regarding the idea of an absolute reference frame, the question seems to be open. I remember reading simultaneity being best defined as the moment a local connection is established in this case, but I can't locate the source. It seems reasonable to me, not weird at all. There is no defined absolute frame of reference . What is absolute is the speed of light which is the speed limit for information transfer. For light, there is no time; therefore no time passes in this 'absolute frame' between emitter and absorber. I'm not sure how the concept of transitivity would apply in this situation, but I would guess that transitivity is also a feature of a specific frame of reference.

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#### SW VandeCarr

...if spacetime were euclidean, but it's not, it's warped.
I guess you've lost me here. In GR the warping of space around a massive object is how gravity is defined. A gravitational field induces accelerating forces. Light is subject to this force. Why isn't a light beam which is bent 180 degrees near a black hole not undergoing acceleration?

#### lightarrow

I guess you've lost me here. In GR the warping of space around a massive object is how gravity is defined. A gravitational field induces accelerating forces. Light is subject to this force. Why isn't a light beam which is bent 180 degrees near a black hole not undergoing acceleration?
Because in GR there isn't any gravitational field.

#### JesseM

Regarding the idea of an absolute reference frame, the question seems to be open.
It's only "open" in the sense that it's always possible relativity will be falsified someday. But within the context of relativity, it's an explicit postulate of relativity that all the laws of physics are completely symmetrical between different inertial frames (and this is still true for local inertial frames at every point in spacetime in GR), so there can be no physical basis for preferring one frame's judgments over another's.

#### matheinste

Quote:-
--- I think we all agree there is no generally accepted definition of simultaneity across reference frames moving with respect to each other. ---

I don't think the phrase has any meaning.

Events have no extension in time or space, they are just "points" in space. They are not a property of any one frame in the sense that they can be defined to be at rest in that frame and they cannot have motion relative to each other. There will be frames in which they are judged to be simultaneous, and others where they are not.

Matheinste.
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