Relativity Paradox

I just stumbled across a video titled "relativity paradox" made by Sixty Symbols (a popular science video channel) and I just cannot wrap my brain around this thought experiment that they explain in the video. I recommend watching the full video but if you're strapped for time then start at 3:30 to skip to an explanation of the thought experiment I am referring to.

At one point in the video the professor is asked "But what is the fact? Did the train dissapear in the tunnel or did it fall out the ends? What actually happened?" and the professor replies "Both! It just depends on whose reference frame you're in". Now this is the point at which I have great trouble comprehending how both situations can actually be true.

If both situations are indeed true then I would argue there is some type of really weird superposition happening here. The same type of effects you observe in quantum mechanics, where two different states can be occurring simultaneously, for example when a particle is in two places at the same time or has two different spin states at the same time.

Near the end of the video the professor says: "usually in physics, if you get something that looks like a stupid answer at the end you've probably don't something wrong, so go back and check and make sure that you haven't messed up. This is one of the cases where if you get something which looks like a stupid answer at the end you've probably done it right".

This is just completely absurd in my opinion. Did they ever actually think that maybe there is something wrong with the theory of relativity and that's why they are getting stupid answers? Can two different measurements from different frames of reference be equally true? Or put another way: can macroscopic objects like a train actually be in superposition?

Let me extend this thought experiment one step further: assume we now build an electric circuit which is only closed when both blades are completely lowered, and attached to this circuit is a light bulb. If both frames of reference are true, then does one frame of reference report the bulb lighting up and the other doesn't? What if we record the bulb?

Clearly only one of these can be true, the bulb will either light up or it wont light up, it cannot simultaneously do both because the recording must show one or the other. In my mind this proves there is something very wrong with the theory of relativity. Both frames of reference are not equally true, something definite happened regardless of the frame of reference.

Here's the embedded video:

reply to post by ChaoticOrder


I understand what you are saying and I agree to a large extent. It's like the analogy of the spinning platform and throwing the baseball from a pitcher in the middle to a catcher on the perimeter. The ball appears to curve, but that is only from one frame of reference. I have a problem with the mentality that a thing can be in two different states in absolute terms. Many times it is only used to describe some kind of phenomena that we can't understand any other way.


And as far as that train analogy goes, I care nothing about how someone perceives it, every part of the train is still in exactly the same place with reference to the tunnel as it would be no matter who sees it from where. I hate this kind of useless mental exercise. Our perception does not create reality.

reply to post by wtbengineer

The ball appears to curve, but that is only from one frame of reference. I have a problem with the mentality that a thing can be in two different states in absolute terms.

Exactly, just because one frame of reference reports that the ball did curve and the other reports that it didn't curve doesn't mean it did both things at the same time. But that is exactly what the theory of relativity is trying to say, that two different things can occur simultaneously and both are equally true in absolute terms. It's just insane imo.

reply to post by ChaoticOrder


I agree. But the problem is, when we are trying to understand things on a really, really small level, like atomically, then that kind of thinking seems to help explain observation. You know, an electron being in every possible position at any time, etc. I don't buy that either, I just think we don't know what's happening yet.

reply to post by wtbengineer


I thin quantum mechanics is a whole other ball game, and I do think that particles can be in more than one place at the same time and they can be in states of superposition. The experimental evidence makes that pretty clear. But when it comes to relativity and thought experiments like this, it makes no sense what so ever to say that the train can be in two different states at the same time... and personally I think my light bulb example makes it extremely clear that something definitive must happen.

reply to post by ChaoticOrder

with relativity it is different, it isn't like superposition.

the actual reality of the situation is completely relative to the observer. two different things didn't happen, only one happened; depending on whether you were observing from the train or observing as stationary relative to the tunnel.

reply to post by ChaoticOrder

two different things can occur simultaneously and both are equally true in absolute terms.

they are true only in relative terms. it has been experimentally verified with muons.

reply to post by Bob Sholtz

two different things didn't happen, only one happened; depending on whether you were observing from the train or observing as stationary relative to the tunnel.

Yes, but according to the theory of relativity both those frames of reference are EQUALLY VALID. Neither frame of reference is more true than the other, so therefore the events in both frames of references must have happened. The theory inherently prevents you from saying that one of those frames of reference is more true than the other.

reply to post by Bob Sholtz

the actual reality of the situation is completely relative to the observer.

And if you have two different observers in different frames of reference and they report different things then you must have two actual realities. Do you not see the problem here?

reply to post by ChaoticOrder

there isn't a problem.

what the observers report is what happened relative to them. the observers are NOT equal. their perspectives are not comparable.

i think the problem you're having is viewing it from a third, overarching perspective. a perspective that doesn't exist in reality.

research muons more and you may get a better idea. i assure you, this phenomena has been experimentally verified.

And if you have two different observers in different frames of reference and they report different things then you must have two actual realities. Do you not see the problem here?

two relative realities. frames of reference are not equal. did the train pass through the tunnel, or the tunnel over the train? one reality per reference frame.

reply to post by Bob Sholtz

did the train pass through the tunnel, or the tunnel over the train? one reality per reference frame.

The difference with that example is that both situations are qualitatively the same. Where as the two different situations which occur in the train though experiment are not qualitatively similar, they are completely different. In one frame of reference the blades close at the same time and in another they close at different times. Two very different things occurring from two different frames of reference. They both cannot be equally true unless you accept that two different things are occurring simultaneously.

reply to post by Bob Sholtz

research muons more and you may get a better idea. i assure you, this phenomena has been experimentally verified.

The first part of the video I embedded is all about muons. What has been experimentally verified is time dilation and length contraction. That does not mean the entire theory of relatively which has been built around those observations is also true.

Bob Sholtz
there isn't a problem.

what the observers report is what happened relative to them. the observers are NOT equal. their perspectives are not comparable.

i think the problem you're having is viewing it from a third, overarching perspective. a perspective that doesn't exist in reality.

I would have written similar replies to yours, but you beat me to it. This is really the answer.

ChaoticOrder, keep in mind that there's a reason it took centuries after Newton to discover relativity, partly because it's not intuitive, so, I don't think questioning relativity because it may disagree with our intuition is logical. If you stand on a train going 10kph and throw a baseball going 10kph in the same direction, you'd expect an outside observer to see the baseball going 20kph, which agrees with our intuition.

However if you stand on a train going half the speed of light and shine a flashlight emitting photons at the speed of light, you could apply the same logic to conclude that the outside observer should again see the sum of the two velocities, so the light beam would travel at 1.5 times the speed of light, but of course that's not what is observed.

So, don't throw all logic out the window, but we do have to rely on observation and experiment where intuition fails us, and that's what relativity requires us to do, and as Bob said there is lots of observation and experiment to support it.

Relativity may need some tweaking to bridge the gap with quantum mechanics but that's more along the lines of quantum gravity theory, which probably doesn't affect these macro examples being discussed in this thread.

reply to post by Arbitrageur

However if you stand on a train going half the speed of light and shine a flashlight emitting photons at the speed of light, you could apply the same logic to conclude that the outside observer should again see the sum of the two velocities, so the light beam would travel at 1.5 times the speed of light, but of course that's not what is observed.

That is special relativity, which I am not disputing in this thread. If you can explain to me how two different frames of reference which both report two clearly different things can both be equally valid and yet at the same time explain to me how something definitive did indeed happen regardless of their conflicting observations then I will be satisfied.

ChaoticOrder
That is special relativity, which I am not disputing in this thread. If you can explain to me how two different frames of reference which both report two clearly different things can both be equally valid and yet at the same time explain to me how something definitive did indeed happen regardless of their conflicting observations then I will be satisfied.

I don't think I can explain it any better than Bob did. He nailed the answer I would have given.

But to repeat what he said, you seem to be looking for "what really happened" independent of the two observers point of view, and in the theory of relativity you are searching for something that doesn't exist. You can add a third observer, but this will still not be "what really happened", you then have three different versions of events instead of two.

Where it really defies our intuition is that even the sequence in which events occur is not absolute. Observer A can see sequence 1-2-3 and observer B can see sequence 1-3-2. The only resolution to that apparent paradox is that there is no absolute version of events. Neither is "what really happened".

However if this really bothers you, you can do something outside the theory of relativity, which is to assign an arbitrary frame of reference which is stationary relative to the cosmic microwave background. Relativity says there is no preferred reference frame, so you can't support this idea with relativity, but you could just arbitrarily say what really happened is what was observed in that "stationary" reference frame (that wouldn't make it true, but if you don't want to accept relativity I don't know what other approach you can take).

reply to post by Arbitrageur

You can add a third observer, but this will still not be "what really happened", you then have three different versions of events instead of two.

Where it really defies our intuition is that even the sequence in which events occur is not absolute. Observer A can see sequence 1-2-3 and observer B can see sequence 1-3-2. The only resolution to that apparent paradox is that there is no absolute version of events. Neither is "what really happened".

EXACTLY. That is my whole point, the theory of relativity is saying one of two things (1 that neither of the observations were what really happened or 2) that both actually happened even though they are different (superposition).

Assuming the theory of relativity is entirely true, then the 1st option is the only reasonable option imo. Meaning something definitive must have occurred, but both observers did not see the true event as it really happened.

The last part of your post attempts to explain how this could be possible, but like you said there really is no preferred frame of reference according to the theory of relativity, and even if there was I would question the validity of using the CMB as that reference point.

reply to post by ChaoticOrder

What has been experimentally verified is time dilation and length contraction.

if you're accepting this as true, i don't understand what you're having trouble with.

the muons are the train, and earth is the tunnel. they are analogous examples.

ok: same example with the muons and frames of reference, but dealing with something different: force.

the observer on the muon sees earth coming at them very quickly with a large amount of momentum while the muon is at rest relative to them. the observer on earth sees the muon with a proportionately large amount of momentum, but their momentum is zero relative to them.

which is true? it depends on which observer you are.

putting it yet another way: one observer cannot watch both reference frames at the same time. now THAT would be a paradox.

if you've researched muons, try looking at the lorentz transformation.

reply to post by Bob Sholtz

if you're accepting this as true, i don't understand what you're having trouble with.

I am having trouble accepting the idea that both frames of reference are equally true. Obviously that cannot be the case, something definitive must have happened, and if you say otherwise than you must accept that both things happened even though they are clearly two different sequences of events, and that is where the real problem exists. I cannot accept the idea that both frames of reference are equally valid, there must be some definite frame of reference which dictates what really happened, otherwise there is no escaping the conclusion that some type of weird superposition is occurring.

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...

i'm not the best at normal math, but i can attempt to break down what you're doing mathematically with variables i invent.

observer 1 at position x is on the train, observer 2 is at position y watching the train. x=/=y (separate locations in spacetime) the event happens:

observer 1 at x sees "a" happen

observer 2 at y sees "b" happen where a=/=b

observer 3 at location z occurs AFTER both things have happened. observer 1 and observer 2 are brought to observer 3 z. moving observer 1 and observer 2 changes their locations to "z".
(ob=observer)
ob1x=a
ob2y=b
and this is completely fine. what isn't fine:
ob3z=(ob1z=a,ob2z=b)

you've changed the observer's locations without changing what they would have observed.