Relativity Paradox

Hellas
reply to post by ChaoticOrder

 

So according to this 'paradox', both versions are right. But what if you would have a person right in front of the train, let's say the driver. When he comes out of the tunnel, he should be able to see the trainspotter, when for the trainspotter the train is still in the tunnel, thus he can't be seen by the driver.

Which is kind of odd...

Incorrect. When he is out of the tunnel, he is out, he will see the spotter and the spotter will see him.

The difference is that the spotter will think the BACK of the train is in the tunnel, and the conductor will think the back of the train has not entered the tunnel yet.

Arbitrageur
reply to post by ChaoticOrder

 

The space time diagrams show there is one reality, so that much is true, but they also show how that reality is perceived differently by different observers. The space-time diagrams are how physicists make sense out of the relativity of simultaneity (this issue).

Here is the same reality as seen by three different observers, which shows the three observers see three different things:

Relativity of simultaneity

Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.

So is the reality sequence A, B, C, or sequence C, B, A, or did all three happen simultaneously? The single reality is that all three are mathematically equivalent in relativity so it's a single reality, just seen differently by different observers.

edit on 18-12-2013 by Arbitrageur because: clarification

This is actually a beautiful example of perspective and how it can kind of layer contrasting realities into one cohesive environment. The reality of the measurement requires or hinges on a limited static perspective...otherwise the values or measurements fluctuate between the three different perspectives and associated values measured. Paradoxes aren't inherently wrong they are kind of like illusions.

I posted a thread about this called Perspectology that goes a little more in depth into what I'm talking about here.

The overtones in my thread were more psychological but have physical illustrations as well.

I really like this illustration though!

Arbitrageur, Bob Sholtz and mbkennel have all made valuable (and I believe, correct) contributions in an attempt to resolve the train and tunnel paradox. But perhaps an additional comment might add some clarity to this interesting thread.

If you have a train traveling at nearly the speed of light with respect to a tunnel, relativity tells us that observers standing still with the tunnel (tunnel-folk) will measure the train length to be shorter than measurements made by observers riding in the train (train-folk). So there can be a situation where tunnel-folk say the whole train is inside the tunnel, but the train-folk will say that the train can never be completely inside the tunnel. So who is right? And if a guillotine falls at the end of the tunnel when the back of the train hits the front of the tunnel, will the train hit the guillotine? Or will the guillotine cut the train in two?

The issue is that more than one "event" is occurring in the above scenario. In fact, there are at least three. Event one is when the back of the train hits the front of the tunnel. Event two is where the front of the train is when event one occurs as determined by tunnel-folk. Event three is where the front of the train is when event one occurs as determined by train-folk. Event two occurs with the front of the train still inside the tunnel, while event three occurs after the front of the train has emerged from the tunnel. All three events could "really" occur. But the tunnel-folk will disagree with the train-folk on when the events occurred, and what the distance is between the latter events and the front of the tunnel.

The tunnel-folk will say that event two occurs exactly at the same time as event one. And hence the whole train is in the tunnel.

The train-folk will say that event three occurs exactly at the same time as event one. And hence the train is longer than the tunnel.

The train-folk will agree that the tunnel-folk clocks read the same for events two and one, but they will say that the problem is that the tunnel-folk have incorrectly synchronized their clocks, and that really event two is happening before event one.

The tunnel-folk will agree that the train-folk clocks read the same for events three and one, but they will say that the problem is that the train-folk have incorrectly synchronized their clocks, and that really event three is happening after event one.

The issue is the relativity of simultaneity, which is the third thing that changes as we go from one reference frame to the other. (The other two being length contraction and time dilation.) Not only do moving clocks run slow, but observers in moving systems also synchronize them incorrectly (as determined by "non-moving" observers). And these discrepancies occur in just the right way so that each observer thinks it is the other one whose clocks are running slow and are mis-synchronized. The famous issue is that we can't (at least not yet) really say which group of observers are "right".

But back to your original question concerning a guillotine. The answer to whether the front of the train hits it or if the train is sliced in two revolves around the question: when does the guillotine fall? After or before the train gets to the end of the tunnel? And since this question is about an event at a single place, there is no paradox. Either the front of the train has passed or it has not when the guillotine falls. And both the train-folk and the tunnel-folk will agree that the event occurred, whichever event it was. What they will not agree on is the time interval and length between that event and event one. (Event one is the end of the train coinciding with the beginning of the tunnel.)

All of this emphasizes the point-like nature of relativity. Any event that occurs at a single point and a single time will be witnessed by observers in all frames. The event just happens. The disagreements arise when there are multiple events, as then the answers to questions of when and where become relative.

So in the end, there is no need for a superposition. The events just occur, and different observers just have different interpretations about the spatial and temporal intervals between those events. Also - through relativity, the train-folk observers can also understand why the tunnel-folk get the results they do, and vice versa. They can just apply the Lorentz transformation equations. So there is no paradox and relativity holds good.

Well, relativity holds good as far as the train/tunnel thing...

But there is another issue. And that is quantum collapse. If we have a quantum system that exists over a long distance, results can be clearly understood if we adopt calculations wherein the wave-function instantaneously collapses. But as we've just seen, "instantaneous" cannot be defined within relativity. Einstein, Podolski and Rosen raised this issue to then argue that quantum mechanics cannot be complete, and Bell then refined the EPR arguments so that tests could be done. Aspect, Dalibard and Roger did the tests - and quantum mechanics was proven right. In light of this experimental reality, it might therefore be considered that we should set relativity aside. We can do so by returning to the precursor theory of Lorentz, which produces the same equations as relativity and yet assumes a preferred frame of reference. Doing so could also resurrect the aether as an explanation for light waves, and all of this could greatly simplify the philosophical underpinning of physics. Physics could agree with common sense once again.

But to do so requires setting relativity aside.

a reply to: delbertlarson

But back to your original question concerning a guillotine. The answer to whether the front of the train hits it or if the train is sliced in two revolves around the question: when does the guillotine fall? After or before the train gets to the end of the tunnel? And since this question is about an event at a single place, there is no paradox.

My question is about what would happen if we attached a circuit to the setup, so we used metal blades which would connect together two points in the circuit when lowered, and only when both blades were lowered would the circuit be fully closed, allowing a current to flow. We also place a light bulb in the circuit so when both blades are lowered at the same time it lights up.

I understand how people will see different things from a different frame of reference, people watching the train from a distance will see the blades lower at different times compared to the people on the train. The people on the train observe the train to be longer than the tunnel and so the blades must lower and raise at different times as to never collide with the train, but the people outside the train see the train go inside the tunnel and the blades close at the same train, fully containing the train.

So as he says, the train will either be cut by the blades or wont, there's nothing relative about it, we have to agree on that one point, and it seems to make sense if we just say the people on the train never saw the blades shut at the same time because the train couldn't fit in the tunnel from their their perspective... but what does the light bulb actually do, it can only light up when the circuit is closed, and that can only happen if both blades are lowered at the same time, allowing electrons to flow through the metal wires. And if we record the bulb what do we see?

originally posted by: ChaoticOrder
a reply to: delbertlarson

But back to your original question concerning a guillotine. The answer to whether the front of the train hits it or if the train is sliced in two revolves around the question: when does the guillotine fall? After or before the train gets to the end of the tunnel? And since this question is about an event at a single place, there is no paradox.

My question is about what would happen if we attached a circuit to the setup, so we used metal blades which would connect together two points in the circuit when lowered, and only when both blades were lowered would the circuit be fully closed, allowing a current to flow. We also place a light bulb in the circuit so when both blades are lowered at the same time it lights up.

I understand how people will see different things from a different frame of reference, people watching the train from a distance will see the blades lower at different times compared to the people on the train. The people on the train observe the train to be longer than the tunnel and so the blades must lower and raise at different times as to never collide with the train, but the people outside the train see the train go inside the tunnel and the blades close at the same train, fully containing the train.

So as he says, the train will either be cut by the blades or wont, there's nothing relative about it, we have to agree on that one point, and it seems to make sense if we just say the people on the train never saw the blades shut at the same time because the train couldn't fit in the tunnel from their their perspective... but what does the light bulb actually do, it can only light up when the circuit is closed, and that can only happen if both blades are lowered at the same time, allowing electrons to flow through the metal wires. And if we record the bulb what do we see?

The people inside the train would never see the light. Remember they themselves are travelling at the speed of light. So by the time the circuit completes at the speed of light there through the tunnel. So to them upon exiting the light would be seen if the light could reach them which it can't until they slow down. So the light to them could in theory go off days later for example.

Relativity doesn't change what events occur it changes when they occur. Relativity everything past, present and future is occurring right now. The order things happen in depends on what frame of refrence is being used to observe the events.

I see the biggest problem is many are confusing relativity and physics. Observers all ways see the same events just the order things occur changes depending on the observer.

a reply to: dragonridr

Relativity doesn't change what events occur it changes when they occur. Relativity everything past, present and future is occurring right now. The order things happen in depends on what frame of refrence is being used to observe the events.

Ok well if the recording does show the bulb lighting up then we know in some absolutely sense that both blades must have lowered at the same time to close the circuit. So even though the people on the train didn't see that happen there was still some set of events which truly took place regardless of what anyone reports seeing, and that was my main point in this thread. But if at some point the tunnel was full enclosed can we say the train was physically contained in it despite being longer than the tunnel? Also my main issue with relativity is not so much issues of simultaneity, but with what you just said, that the past and future already exist in some sort of space-time continuum. It destroys any sense of free will and I find it very difficult to believe when quantum mechanics strongly indicates truly random events can occur. However that issue could possibly be solved with the many worlds interpretation of QM, although I don't really like that idea either because it suggests not only one predetermined time line exists, but an infinite number of predetermined times lines exist in which anything that could possibly happen does happen, making my choices seem absolutely irrelevant.

There once was a lady in Wight, Who's speed was as fast as light.
She left one day, in a relative way, to return the previous night.

Sorry, couldn't resist

a reply to: 2Faced

I like it.

a reply to: ChaoticOrder

Relativity is not predeterminism in any way. What it says is an event can occur and when you perceive it to have occurred is dependent on where you observe it from. What relativity does is show that when dealing with time Now can vary alot. What's Now for you could be the past for someone else.

a reply to: dragonridr

It is predetermined, the entire space-time continuum already exists according to the theory of relativity, the past and future are both just as real as the moment right now.



Tyson often also talks about this point, and even describes the concept of determinism as a "comforting" idea:

I am far from knowledgeable in this field, and from that perspective, I think/reason, that we as a species have to evolve to another level of thinking before we can fully grasp the way the universe exactly works, or if the smallest part of an atom really exists out of strings or something else. The same goes for the beginning of it all. We are to believe that the universe just came into existence out of nothing, into nothing. Even though our logic says that, if "something" has to exist, it has to exist in, and be contained by, a space, and that space should be contained by something, something that resides in another space, for it too has to be contained by a space, and so forth. Same goes for a creator, surely he/it did not appear out of nothingness, according to the way our logic works, there has to be a beginning, and so there has to be some- one/-thing that created the god. So where does it all begin? As long as we aren't able to answer that question satisfactorily, we will probably, if not most certainly, have a very hard time understanding the mechanics that make us be.

Maybe AI powered by quantum computing (at room temperature so it seems, as of late) will be able to answer and explain that question to us in a manner that we can comprehend, in about 10 yrs?

My two cents...

originally posted by: dragonridr
a reply to: ChaoticOrder

Relativity is not predeterminism in any way. What it says is an event can occur and when you perceive it to have occurred is dependent on where you observe it from. What relativity does is show that when dealing with time Now can vary alot. What's Now for you could be the past for someone else.

I agree that relativity is not predeterminism, but Briane greene's video presentation and the block universe seem to imply some kind of predeterminism.

originally posted by: ChaoticOrder
a reply to: dragonridr

It is predetermined, the entire space-time continuum already exists according to the theory of relativity, the past and future are both just as real as the moment right now.

In the first video, Brian Greene takes it a little too far. Ellis has written some papers describing how relativity can exist without predeterminism.

Is the Future Already Written?

Ellis’ new model is a modification, rather than a radical upheaval, of the block universe. In his framework, set out in a series of highly regarded papers published from 2006 onward, Ellis retains four-dimensional space-time, in line with relativity’s predictions. However, he argues that Einstein took that concept too far. There’s no need to assume that the fourth dimension must already exist out into infinity. Thus Ellis’ model has one crucial difference from Einstein’s: The future boundary does not encompass all that will ever happen.

Instead, the leading edge of space-time marks the “present” crawling outward, moment by moment, transforming tomorrow’s maybes into yesterday’s fixed happenings. “Tomorrow there will be one more day in the universe than there was today,” says Ellis. “The past is real and can have had an effect on us today, but the future cannot influence us because it does not yet exist.”

I'm not even sure Einstein said the future boundary encompasses all that will ever happen, but Ellis's interpretation clearly says the future doesn't exist yet, and to the extent Brian Greene implies the future already exists, I think he is wrong and Ellis is right.

The second video you posted was like watching two men in a pub drinking beers speculating about complete unknowns which they know nothing about. It was mostly complete speculation and not that good either. I like the terminator movies as much as the next guy, but I don't try to use science fact to explain backward time travel in that movie because there really isn't any. About the only thing that made any sense to me in that discussion was Tyson's statement that a future law of physics may be discovered which explains how backward time travel is impossible. Since that law hasn't been discovered yet, I guess he can make all the speculations he wants, but they are useless according to Newton's flaming laser sword since nobody can travel backward in time to kill their own grandfather to see what really happens. Now if someone ever figures out how to do that, then the "grandfather paradox" may be resolved, but I doubt they will because Tyson is probably right about there being something in physics which prevents backward time travel which we haven't fully grasped yet.

a reply to: Arbitrageur

I'm not even sure Einstein said the future boundary encompasses all that will ever happen, but Ellis's interpretation clearly says the future doesn't exist yet, and to the extent Brian Greene implies the future already exists, I think he is wrong and Ellis is right.

Well Greene does give a very strong reason for why both the past and future must be equally real when he shows how the "now slice" changes depending on motion. He sums it up by saying "Once we know that your now can be what I consider the past or your now can be what I consider the future, and your now is every bit as valid as my now, then we learn that the past must be real, the future must be real, they could be your now. That means past, present, future, all equally real, they all exist."

This confusion is simply indicative of the deficiencies of using standard mathematics and Euclidean geometry to try to explain what is happening in actual reality, in which we're dealing with complex interactions between dimensional realities that run on a spectrum from "unimagined" through "imagined" through "real," and where a real live person never, ever steps out of their own point of view.

originally posted by: ChaoticOrder
a reply to: delbertlarson

But back to your original question concerning a guillotine. The answer to whether the front of the train hits it or if the train is sliced in two revolves around the question: when does the guillotine fall? After or before the train gets to the end of the tunnel? And since this question is about an event at a single place, there is no paradox.

My question is about what would happen if we attached a circuit to the setup, so we used metal blades which would connect together two points in the circuit when lowered, and only when both blades were lowered would the circuit be fully closed, allowing a current to flow. We also place a light bulb in the circuit so when both blades are lowered at the same time it lights up.

I understand how people will see different things from a different frame of reference, people watching the train from a distance will see the blades lower at different times compared to the people on the train. The people on the train observe the train to be longer than the tunnel and so the blades must lower and raise at different times as to never collide with the train, but the people outside the train see the train go inside the tunnel and the blades close at the same train, fully containing the train.

So as he says, the train will either be cut by the blades or wont, there's nothing relative about it, we have to agree on that one point, and it seems to make sense if we just say the people on the train never saw the blades shut at the same time because the train couldn't fit in the tunnel from their their perspective... but what does the light bulb actually do, it can only light up when the circuit is closed, and that can only happen if both blades are lowered at the same time, allowing electrons to flow through the metal wires. And if we record the bulb what do we see?

Adding the light bulb makes this thought experiment less clear, not more clear. If we have two guillotines fall, one at each end of the tunnel, and connect them via wires to a light bulb and power supply, current will begin to flow as seen by tunnel-folk. But then the front of the train will hit the front guillotine, and the circuit will be smashed open. If the tunnel is 3 km long, the time it takes light to go from one end of the tunnel to the other is (3e3 m)/(3e8 m/s) = 10 microseconds so that gives some rough idea of how long the circuit will remain closed. But to get the exact answer we need to know what the specific lengths of the tunnel and train are. We need to know the specific relative velocity between the train and tunnel. And then we need to know if the length of the pulse is enough to heat the filament to the point that light is emitted. (We might also need relativistically moving gillotines to fall within the 10 microseconds, however, to explore the relativity question we can set that issue aside for now.) All of those details get us "off track" from our central "train of thought" - the relativity issue.

If the question is rephrased however to "will a signal be detectable?" the answer then is a qualified "yes", the qualification being that you still need to specify the details. Over a wide range of details however a pulse of electrons will begin to flow, the train will smash the front guillotine and terminate the pulse. That pulse could be picked up by sensors provided the sensors are sensitive enough, there was enough voltage, the resistance in the circuit had the right conditions, and the front of the train had enough distance from the front guillotine to allow the circuit to close for enough time to get a reasonable signal.

But the relativity issue is still the one I outlined in detail in a previous response. There is no paradox. You will always need at least three events to determine the two lengths involved here. You always need two events to measure a length, and you can superimpose one event from each frame, and that leads to three required events to do the analysis.

Back to your example - the guillotines close at the same time as observed by the tunnel-folk leading to a pulse as described above. The train-folk see the guillotines close as well, but they say that the one at the back of the tunnel closed well after the one at the front, since the train is longer than the tunnel for them. When the front guillotine falls, even though the back is still open, current begins to flow. This is because one side is at a potential that is different from the other. Then the front guillotine gets smashed, the back guillotine closes, and the pulse oscilates back and forth. Again, as before, there is a disagreement about when these events occured (and the distances between them) but there is no paradox concerning whether the events happenned or not.

A bit more on special relativity.

A moving observer will not say you are in the future nor in the past if you are at the same longitudinal coordinate. (Here, longitudinal is in the direction of relative motion.) That is, as a rocket ship goes by you, that moving observer will say you are in the present. After all, rocket-man sees you there! It is only before rocket-man gets there, or after he has passed, that rocket-man infers you are in the future or in the past with respect to what you think you are.

So to say an observer sees you far in the future or far in the past implies that the observer is far away spatially when making that assessment.

Now if we assign a separate time to each observer, then, yes, once rocket-man is far away you will be in the past or future (with respect to your time) according to his time. That is what relativity says. And according to relativity, each observer's time is equally good. But it also says that if rocket-man is very, very distant, and he reverse course, or changes directions, he sees your time vastly change. Thousands of years in the future can nearly instantly become thousands of years in the past, just because he makes a u-turn in a space ship far away. This comes about because of the adjustment needed in the simultaneity term of the Lorentz time relation as the u-turn is done. But again, conveniently for the special theory, none of these effects ever occur locally where they can actually be observed up close.

If we instead just say that clocks run slow when moving through an aether, then time itself is not changing, we just have clocks running slow, and none of this wild hocus pocus is needed. If I have a clock running slow in my living room, it is just running slow. I don't think I've entered some kind of fantasy world, or think I've stumbled upon some miraculous new scientific discovery - I just throw the clock away, it is broken.

Yeah, I know. Relativity conforms with almost all experiments. Once proper analysis is done, it survives all apparent theoretical paradoxes. And it is way cooler to think about than an old boring absolute theory that gives almost all the same results and where everything makes sense. We've moved on to a radically advanced way of thinking!

Yet as scientists the way to decide is tests. And the critical tests are the Einstein Podolski Rosen tests, which pit quantum mechanics against relativity. Quantum mechanics won. Relativity lost. Scientifically, we should set relativity aside and return to absolute theory.

But relativity is so cool!

originally posted by: 2Faced
There once was a lady in Wight, Who's speed was as fast as light.
She left one day, in a relative way, to return the previous night.

Sorry, couldn't resist

As we on Earth watch the illusion of a spacecraft traveling away from earth at near the speed of light "frozen in time" like a billboard.

a reply to: ChaoticOrder

Fascinating thread. Thank you for posting!

I’m a physics light weight and have never heard of the Lorentz contraction. I’m confused about something. Does it apply to all objects? So when a photon leaves the sun and is headed straight to earth it won’t actually need to cross the vast distance between the sun and earth as measured here from earth? Due to the Lorentz contraction the distance it needs to travel from its perspective is much smaller?

I always thought it roughly takes a photon 8 minutes from the sun to earth, but when factoring in the Lorentz contraction it should take less time...?

a reply to: Arbitrageur

Does your diagram show that entangled objects in QM don’t interact simultaneously when looked at from a different perspective? Never understood how they can pull that off.

Maybe there's a computer program out there that does this, but I was thinking the other day about what our night sky would look like if we saw it all "now." That is, there's a time lag between the time a stat shoots out its photons and the time we see it, but what if we were able to see the stars where they are now. Right now. So that star we're seeing that's 150 light years away probably isn't actually in that spot now, but that's where it used to be.

Then I got thinking about the concept of NOW, and determined that once again, the most important thing is what we currently perceive from our own points of view. There is no real "stepping outside" of time or space to observe something, so I can't step back away from the universe and see where are the stars really are right now. It's all a hypothetical fantasy.