Causality in Relativity: Examining the Illusion of Simultaneous Cause and Effect

[palmer eldtrich]

I have heard some philosophers state that cause and effect can be simultaneous with each other.
Kant for example apparently claimed that when a bowling ball rests on a pillow creating a depression that the cause and the effect are simultaneous.
It seems to me this is forbidden in relativity. All causal relations must be transmitted at a speed no greater than c hence whilst a cause and effect might seem simultaneous that is just an illusion. Am I right?

 

[Khashishi]

Changes in the state will be transmitted at no greater than c. If nothing is changing, and you are talking about some static equilibrium, there is no cause and effect to talk about.

Drop the bowling ball on the pillow, and the depression will form at a speed less than c.

 

[palmer eldtrich]

Thanks for the reply. So you agree simultaneous causality is forbidden in relativity ? If it were allowed would it possible to send a signal back in time ?

 

[PeroK]

Thanks for the reply. So you agree simultaneous causality is forbidden in relativity ? If it were allowed would it possible to send a signal back in time ?

Then you could ask Emmanuel Kant directly!

 

[Ibix]

My understanding is that philosophers (in this context at least) aren't using "cause" in quite the same way as physicists do when talking about general relativity. Philosophy is off-topic here, and I'm hardly what you would call an expert, so I'll leave it at that.

As to what the consequences would be if simultaneous causation were possible, there isn't a way to reply to that. You aren't proposing a small change to relativity; you are throwing the whole thing out and putting an unspecified something else in its place. The properties of an unspecified something could be anything.

 

[Matterwave]

I'd like to add though that two events A and B which are null separated can, with an appropriate Lorentz transformation, be made to occur arbitrarily close to simultaneously with each other. If, for example, A occurred 10 seconds before B in one frame, there are frames of reference in which A occurred only .001s before B or .000001s before B. They can not be made to actually be simultaneous with each other; however, nor can you reverse the order in which they occurred. This is how causality is preserved in SR. Since space-like separated points can be made, with an appropriate Lorentz transformation, to occur in either temporal order, they can not have a cause and effect relationship in SR or else there would be some frames in which an effect came before the cause.

 

[nitsuj]

Thanks for the reply. So you agree simultaneous causality is forbidden in relativity ?

Implicit in "causality" is spacetime inbetween "happenings" until they happen. Your questions spoils causality defined.

Matterwave said it well with "causality is preserved in SR."

I deleted the second question because it's very confused.

 

[wabbit]

My understanding is that philosophers (in this context at least) aren't using "cause" in quite the same way as physicists do when talking about general relativity.

Also, remember Kant was writing more than a century before Einstein, at a time when Newtonian ideas of absolute simultaneity and absolute spacetime where the gold standard in physics, so you can't really expect him to give you insights into relativity. Some earlier philosophers would actually be much more relevant but as Ibix said that's off-topic here.

 

[palmer eldtrich]

I understand that but I have seen philosophers use this argument even today.

 

[wabbit]

I understand that but I have seen philosophers use this argument even today.

Ah I wish we could discuss that, but unfortunately if there was a philosophy section in the forum, it would probably swiftly descend into chaos so we have to do without : )

 

[Ibix]

As I noted earlier, those philosophers are using a different definition of "cause" to the one being used by the people responding to this thread. By the relativistic definition of causality, Kant's argument is wrong. But Kant wasn't using that definition (he couldn't - as wabbit noted, he predated Einstein by a way). Why people still buy into Kant's definition of "cause" is not a topic that we can address here - you'll have to ask in a philosophy forum.

 

[Dale]

Given the philosophical focus of this topic, the thread is in danger of being closed. Let's stick with physics here. There are good physics concepts that can be discussed here. If we can't stick to those then I will have to close the thread.

 

[wabbit]

Actually, there is a sense in which "simultaneous causality" is possible in relativity : remember that a photon "doesn't experience time" in the sense that it's proper time interval is zero - say, from emission to absorption, the two events being clearly causally related.
So you could say that emission and and absorption are simultaneous "from the point of view of the photon" as far as that makes sense.

 

[PeterDonis]

a photon "doesn't experience time" in the sense that it's proper time interval is zero

No, this is not correct. What is correct is that the concept of "proper time" does not make sense for a photon. It only makes sense for objects that travel on timelike worldlines. A photon's worldline is null, not timelike.

you could say that emission and and absorption are simultaneous "from the point of view of the photon" as far as that makes sense.

Which is to say, not at all. The concept of "simultaneous" only makes sense for events which are spacelike separated. The emission and absorption events for a photon are null separated.

 

[wabbit]

No, this is not correct. What is correct is that the concept of "proper time" does not make sense for a photon. It only makes sense for objects that travel on timelike worldlines. A photon's worldline is null, not timelike.

I see. The mathematical definition of proper time as the integral of the line element along the worldline does give a well-defined result of zero though, so I can't say I understand why it is incorrect to talk of "zero proper time along a null worldline".

Of course it is incorrect is to ascribe a "viewpoint" to the photon as this would be meaningful only if there was an inertial frame to represent that "viewpoint" - hence my "as far as that makes sense" - I would have said "not much" but I won't argue with "not at all".

 

[PeterDonis]

The mathematical definition of proper time as the integral of the line element along the worldline

That's part of the definition, but not all of it. The other part is that proper time must be an affine parameter along the worldline. Basically, that means each point on the worldline must be labeled with a different value of proper time. (There are also other technical conditions that aren't relevant here.) Arc length (the integral of the line element along the worldline) has this property for timelike worldlines, but not for null worldlines. So a null worldline can be said to have zero arc length, but not zero proper time, because arc length doesn't uniquely label points on the null worldline.

 

[palmer eldtrich]

Can you explain the difference between different notions of time, proper time, conformal time etc?

 

[PeterDonis]

Can you explain the difference between different notions of time, proper time, conformal time etc?

Physically, proper time is the time that is recorded on an (ideal) clock that follows a particular timelike worldline. Geometrically, it is just arc length along that worldline. It is invariant, i.e., it does not depend on the choice of coordinates.

Conformal time is a particular type of coordinate time. Coordinate time in general is just the value of the "time" coordinate in a particular coordinate chart. (Some charts actually do not have a "time" coordinate; we're restricting discussion here to those that do.) Ob viously, coordinate time depends on the choice of coordinates.

 

[doaaron]

It seems to me this is forbidden in relativity. All causal relations must be transmitted at a speed no greater than c hence whilst a cause and effect might seem simultaneous that is just an illusion. Am I right?

I have read before that gravity must be propagating many orders of magnitude faster than EM waves (nearly instantaneously). The argument was that if it didn't, then our solar system would not work. I don't know much about it but I think there are some experts on this forum who could explain it. Also, there are numerous posts on this forum related to the "speed of gravity".

Aaron

 

[Dale]

I have read before that gravity must be propagating many orders of magnitude faster than EM waves (nearly instantaneously). The argument was that if it didn't, then our solar system would not work.

Reference please.

For the most part, gravity doesn't propagate in our solar system, it is essentially a static field. For the minute part of gravity that does propagate our solar system would work fine with it propagating at c.

Please provide the reference. Either the reference is wrong or you misunderstood their point.

 

[doaaron]

Either the reference is wrong or you misunderstood their point.

Perhaps...
Or their point isn't considered mainstream but is in fact right...in which case I wouldn't be allowed to post it anyway.

If I find the link I will consider posting it.Aaronedit: I found the link. Not being a physicist, I only really understood the gist of it, and I don't know how mainstream or not it is considered to be.

<<deleted link>>

 

[Dale]

Not being a physicist, I only really understood the gist of it, and I don't know how mainstream or not it is considered to be.

<<deleted link>>

Hi doaaron,

You understood the link correctly, the link itself is flat out wrong. This is van Flandern who is a well-known crackpot, essentially anything you read from him is going to be wrong.

In this case, his basic mistake is in equating the observed lack of aberration with a very high propagation speed. The (obvious) other reason for there to be no aberration is for there to not be anything propagating. A static field does not propagate, by definition, so the lack of aberration for a static field gives no information at all about what speed the field would propagate at if it were propagating.

 

[doaaron]

This is van Flandern who is a well-known crackpot

I see...I hadn't heard of him until today, but either way, that sounds a bit harsh considering the paper showed an obviously high level of intelligence. Perhaps his theories are just not scientifically rigorous?

Anyway thanks for the correction.Aaron

 

[doaaron]

A static field does not propagate, by definition, so the lack of aberration for a static field gives no information at all about what speed the field would propagate at if it were propagating.

This is something I'm having a lot of trouble understanding actually. Its not really what this thread is about, so I may post a new thread once I can gather my thoughts...Aaron

 

[Dale]

that sounds a bit harsh

Perhaps it is a bit harsh. His Wikipedia page uses less harsh terms like "non-mainstream", "fringe-science", and "pseudo-science". If you prefer those terms over "crackpot", that is fine by me, but he is the first "pseudo-scientist" that I ever encountered and so to me he will always be the "standard crackpot" against which all others are measured.

Its not really what this thread is about, so I may post a new thread once I can gather my thoughts.

Sounds good.

 

[PeterDonis]

I have read before that gravity must be propagating many orders of magnitude faster than EM waves (nearly instantaneously).

If the name "Tom Van Flandern" occurs in any of what you have read, then it's wrong. [Edit: I see that it is--didn't see the most recent posts before. Another correct guess on my part. ] (Btw, whenever you find yourself saying "I have read before", that's a red flag that you should be providing a reference. There's lots of stuff out on the Internet; for discussion here we need something more solid.) The best treatment of this that I know of is Steve Carlip's classic paper:

http://arxiv.org/abs/gr-qc/9909087

He shows in some detail why the argument advanced by Van Flandern (and others) that purports to show that the solar system "would not work" if gravity propagates at $c$ is wrong.

Also, there are numerous posts on this forum related to the "speed of gravity".

Yes, and if you look them up, you will find that plenty of them reference the above paper.

 

[PeterDonis]

his basic mistake is in equating the observed lack of aberration with a very high propagation speed. The (obvious) other reason for there to be no aberration is for there to not be anything propagating. A static field does not propagate, by definition, so the lack of aberration for a static field gives no information at all about what speed the field would propagate at if it were propagating.

This is all correct, but it's worth noting that this is only the first-order answer, valid when the field is exactly static--i.e., the central object is the only significant mass in the system, so the system center of mass is the same as that object's center of mass. But there's also a second-order answer, which takes into account that the solar system is not exactly static--the planets, particularly Jupiter, have non-negligible masses, so the center of mass of the solar system is not the same as the Sun's center of mass, and we can't view the Earth's interaction with the Sun as the Earth being just a test object moving in the Sun's static field. Carlip shows that, even for a non-static system (he uses the Kinnersley photon rocket as his example, but his conclusions apply to the solar system with the non-static effects included), the lack of observed aberration of gravity is consistent with gravity propagating at $c$.

 

[doaaron]

Btw, whenever you find yourself saying "I have read before", that's a red flag that you should be providing a reference.

I know. I get lazy sometimes...

thanks for the reference,Aaron
.