Do train gaps appear smaller in motion?

[JesseM]

Yes, I do very well. The point that you still fail to understand is that no matter how high the speed

So do you acknowledge that with 1 mm gaps and a normal-sized train, the speed would have to be very "high" (just slightly less than light speed) in order to meet the conditions of the OP, and thus that your comments about maglev trains and trains moving at 50 km/hour in post #31 were not relevant to the OP?

if the gap is smaller than the diameter of the wheels, the train will never fall through the gaps.

But if the speed is high enough that the length of the gap is greater than the length of the train in the platform frame, then obviously the length of the gap is greater than the diameter of each wheel in this frame too, so in this frame each wheel will spend some time totally out of contact with any part of the track (whereas if the gap is smaller than the diameter of the wheel in the train frame, then in the train frame each wheel will always be in contact with part of the track--this isn't an inconsistency though, it can be understood in terms of the relativity of simultaneity, in the train frame the event of the wheel making first contact with the track at the front of the gap happens before the event of the wheel losing contact with the track at the back of the gap, whereas in the platform frame the order of these events is reversed). Do you disagree?

 

[starthaus]

So do you acknowledge that with 1 mm gaps and a normal-sized train, the speed would have to be very "high" (just slightly less than light speed) in order to meet the conditions of the OP,

I don't think you are reading it right, what I've been telling you is that if the wheel diameter is oonly slightly larger than the gap (for example 60cm vs 650 cm to pick a realistic case) the train will never fall through the gap.

and thus that your comments about maglev trains and trains moving at 50 km/hour in post #31 were not relevant to the OP?

Sure they are relevant. Whatever happens in the frame of the train must also happen in the frame of the track regardless of the combination between the size of the train/wheels and the size of the gap and the speed of the train wrt track.

But if the speed is high enough that the length of the gap is greater than the length of the train in the platform frame, then obviously the length of the gap is greater than the diameter of each wheel in this frame too,

Correct, and this is the trivial problem solved in Taylor and Wheeler. It makes sense for a manhole and its cver but it doesn't make sense for a train.

 

[JesseM]

I don't think you are reading it right, what I've been telling you is that if the wheel diameter is oonly slightly larger than the gap (for example 60cm vs 650 cm to pick a realistic case) the train will never fall through the gap.

So when you said "no matter how high the speed", that wasn't an implicit acknowledgment that the speed must be a very large fraction of light speed in order to match the condition in the OP which says the train is shorter than the gap in the station frame?

and thus that your comments about maglev trains and trains moving at 50 km/hour in post #31 were not relevant to the OP?

Sure they are relevant.

Do you deny the OP was only talking about scenarios where the length of the train in the platform frame is shorter than the length of the gap in the platform frame, due to length contraction? Do you deny that a real maglev train cannot travel fast enough so that its length is shorter than the length of ordinary gaps in the track, in the rest frame of the tracks? Please tell me, yes or no, whether you deny either of these. If you don't deny either of them, it seems that talking about maglev trains and trains moving at 50 km/hour was not relevant to the type of scenario in the OP.

But if the speed is high enough that the length of the gap is greater than the length of the train in the platform frame, then obviously the length of the gap is greater than the diameter of each wheel in this frame too

Correct, and this is the trivial problem solved in Taylor and Wheeler. It makes sense for a manhole and its cver but it doesn't make sense for a train.

What do you mean "doesn't make sense"? Do you deny that it's possible in theory (though not in practice) for a train to move at a high fraction of light speed relative to its tracks? Do you deny that according to relativity, even if the length of the gap is 1 mm in the platform frame and the train's length is many meters in the train's rest frame, the train could have a length smaller than 1 mm in the platform frame if it was moving at a sufficiently large speed in this frame?

And if you don't deny either of these, please answer my question about whether you disagree that if the train's length is shorter than the length of the gap in the platform frame, in this frame each wheel will spend some time totally out of contact with any part of the track in this frame.

 

[starthaus]

So when you said "no matter how high the speed", that wasn't an implicit acknowledgment that the speed must be a very large fraction of light speed in order to match the condition in the OP which says the train is shorter than the gap in the station frame?

No, it means precisely what I have been showing you all along, that the train will never fall through the gap.

Do you deny the OP was only talking about scenarios where the length of the train in the platform frame is shorter than the length of the gap in the platform frame, due to length contraction?

Whatever he's talking about does not make physical sense for a train. What I am talking about makes sense.

Do you deny that a real maglev train cannot travel fast enough so that its length is shorter than the length of ordinary gaps in the track, in the rest frame of the tracks? Please tell me, yes or no, whether you deny either of these. If you don't deny either of them, it seems that talking about maglev trains and trains moving at 50 km/hour was not relevant to the type of scenario in the OP.

It is much more realistic to up the speed on the maglev than to have gap jumping trains. Your "interogatory" approach gets really boorish, you may want to tone it down.

even if the length of the gap is 1 mm in the platform frame and the train's length is many meters in the train's rest frame, the train could have a length smaller than 1 mm in the platform frame if it was moving at a sufficiently large speed in this frame?

You are asking the wrong question, the point is that the train can't fall through the gap at any speed under the above conditions. This is due to the fact that you are trying toapply a kinematic solution to a problem that is about normal forces and statics.

And if you don't deny either of these, please answer my question about whether you disagree that if the train's length is shorter than the length of the gap in the platform frame,

The point is that it isn't. Look, I understand perfectly your scenario, it is the one from "Spacetime Physics" and it is perfectly ok for manholes, it isn't that good for trains. Why don't you put some of your effort in understanding my scenario. I answered all your questions , so I would want you to answer one (and only one) from me: plaese describe my scenario and my solution.

 

[JesseM]

Whatever he's talking about does not make physical sense for a train. What I am talking about makes sense.

So you admit you are not talking about the scenario described in the OP? (a scenario which is theoretically possible in relativity as it does not violate any physical laws, even if it would be too difficult to realize in practice--do you disagree?)

Look, I understand perfectly your scenario, it is the one from "Spacetime Physics" and it is perfectly ok for manholes, it isn't that good for trains. Why don't you put some of your effort in understanding my scenario. I answered all your questions , so I would want you to answer one (and only one) from me: plaese describe my scenario and my solution.

Your scenario is off-topic for this thread, not to mention for the whole relativity forum since your train isn't moving at a relativistic velocity. If you want to start a new thread about your scenario in the classical physics forum, go for it and I'll answer your questions. But derailing someone else's thread to talk about an off-topic scenario is either completely oblivious to normal forum etiquette or deliberately trollish.

 

[Nabeshin]

Why don't you ask the OP what he's talking about?

As in most thought experiments, I am relying on a currently unrealizable train able to travel arbitrarily close to the speed of light. Ignore friction, and posit the train simply as a rectangular block moving horizontally on the track (or, if you like, infinitely many infinitely small wheels to create the same effect). Please, this is a thought experiment. If you wish to discuss how small gaps in railway tracks are or the physical size of most train wheels, I believe these forms would be better suited to that:
https://www.physicsforums.com/forumdisplay.php?f=101

Back to my original question... I can discern one, at most two, legitimate responses. I will ask vanadium about his:

Train frame order of events:

1. Front wheels enter gap
2. Front end of train begins to dip
3. Front wheels catch the tracks on the far side
4. Front end of train straightens out
5. Rear wheels enter gap
6. Rear end of train begins to dip
7. Rear wheels catch the tracks on the far side
8. Rear end of train straightens out


Station frame order of events:

1. Front wheels enter gap
2. Front end of train begins to dip
3. Rear wheels enter gap
4. Rear end of train begins to dip
5. Front wheels catch the tracks on the far side
6. Front end of train straightens out
7. Rear wheels catch the tracks on the far side
8. Rear end of train straightens out

It seems that the center of mass in the train frame never moves vertically (it merely rotates about the contact point), whereas in the station frame one cannot deny that the entire center of mass will fall vertically (between 4 and 5).

Vanadium, are you supposing the train to be infinitely rigid or not? I'm not sure about your use of the terminology "dip", whether you mean torque about the point of contact (the edge of the gap), or sag under the weight of gravity (like trying to hold a paper horizontally)? I would ideally like to be able to resolve the paradox with the rigid body assumption, but acknowledge that not all relativity paradoxes can deal with it (infinitely rigid poles, for example).

 

[starthaus]

Your scenario is off-topic for this thread, not to mention for the whole relativity forum since your train isn't moving at a relativistic velocity.

False. It is moving at relativistic speed. Please try reading and understanding before you answer again. So, once again, try explaining my solution.

 

[JesseM]

False. It is moving at relativistic speed.

You said in post #31 it could be a maglev train, which is not capable of moving at relativistic speed, or a train moving at 50 km/hour, which is not a relativistic speed. In any case, if it's moving at relativistic speed but not moving so fast that its length in the platform frame is shorter than the length of the gap in that frame, then it's off-topic for this thread. If you do mean for it to be traveling so fast its length is shorter than the length of the gap, then specify that that's what you're talking about. If you don't say one way or another whether the train's length is shorter than that of the gap in the platform frame, you're just being evasive.

 

[starthaus]

You said in post #31 it could be a maglev train, which is not capable of moving at relativistic speed,

I said that the train is moving at relativistic speeds starting from post 2. I said textually that
"the train will not fall through the cracks for any $$v<c$$"

Look,

If you are unwilling or unable to reproduce my explanation, this is fine. I will do it for you:

Solution 1: In the train frame, since the wheels are larger than the gap, the train can never go through the gap. In any other frame , POR says that the result must be the same, so the train cannot go through the gap in the track frame no matter how close v gets to c and no matter how much the train gets "contracted"

Solution 2. In the train frame the wheels are always in contact with the rails (because the gap is smaller than the diameter of the wheels). So, the reaction of the tracks , normal to the tracks is always non null.
In the track frame, the reaction of the tracks is

$$N'=\frac{N}{\gamma(v)}$$

, i.e. it is also non-null for all $$v<c$$. This means that the train can't slip through the gap.

You need to really understand what length contraction is: it is an artifact of the methods of measuring the dimensions of moving objects by attempting to mark their endpoints simultaneously. It doesn't mean that you can force the train in the exercise above through a 1mm gap.

 

[DrGreg]

Ignore friction, and posit the train simply as a rectangular block moving horizontally on the track

Yes, think of it as a rectangular block of metal sliding over ice, with a hole in the ice.

Vanadium, are you supposing the train to be infinitely rigid or not? I'm not sure about your use of the terminology "dip", whether you mean torque about the point of contact (the edge of the gap), or sag under the weight of gravity (like trying to hold a paper horizontally)? I would ideally like to be able to resolve the paradox with the rigid body assumption, but acknowledge that not all relativity paradoxes can deal with it (infinitely rigid poles, for example).

I think we have to conclude that an infinitely rigid block is just impossible, otherwise we would have a contradiction, with the block falling in some frames and not falling in others. The only way out of this is for the unsupported parts of the block to fall in every frame. In some frames the whole block starts to fall into a larger hole (but only a little, due to the very high speeds). In other frames just a part of the block that is over a smaller hole sags slightly into the hole.

 

[starthaus]

Yes, think of it as a rectangular block of metal sliding over ice, with a hole in the ice.

I think we have to conclude that an infinitely rigid block is just impossible, otherwise we would have a contradiction, with the block falling in some frames and not falling in others. The only way out of this is for the unsupported parts of the block to fall in every frame. In some frames the whole block starts to fall into a larger hole (but only a little, due to the very high speeds). In other frames just a part of the block that is over a smaller hole sags slightly into the hole.

Yes, this is problem 54 , chapter 1 in Taylor-Wheeler "Spacetime Physics".

 

[Nabeshin]

Yes, think of it as a rectangular block of metal sliding over ice, with a hole in the ice.

I think we have to conclude that an infinitely rigid block is just impossible, otherwise we would have a contradiction, with the block falling in some frames and not falling in others. The only way out of this is for the unsupported parts of the block to fall in every frame. In some frames the whole block starts to fall into a larger hole (but only a little, due to the very high speeds). In other frames just a part of the block that is over a smaller hole sags slightly into the hole.

Yeah this was my intuition. I suppose a detailed calculation would reveal the effects to be equal in both frames, leading to agreement, but I don't think anyone really wants to consider this due to the lack of the rigid body assumption... I'm a bit unsatisfied, because most relativity paradoxes can be satisfied by appealing to simple principles, and it's unfortunate to say "Detailed calculations would show..." which is what most people say. But of course, as with all physics, not all of it can be explained in a few sentences of English!

 

[DrGreg]

By the way, I have just remembered another discussion of two years ago which considered a somewhat similar, but not identical, scenario.

Have a look at my post #77 and the diagram attached to it, in the old thread "Relativistic Rod and Hole".

 

[Vanadium 50]

It's a shame that this thread got "derailed" (sorry - couldn't resist) into the question of how big a gap there is. Yes, real gaps are about a millimeter and not meters in size, but real trains don't go near the speed of light either. It's not relevant. Additionally, even for a tiny gap, there will be some speed at which the train is sufficiently Lorentz contracted to be shorter than the gap.

This is a red herring, unhelpful for the OP's question, and it's a pity that the person who did the derailing is injecting so much hostility into this thread: that's also unhelpful in answering the OP's question.

Onto the specifics. Even without relativity, if I support a locomotive from only the back wheels, it will tip down. The center of gravity will move down. If the geometry is right, the front wheels will eventually "catch" on the front tracks, and this will keep the locomotive from falling off the track. If the geometry isn't right, the train will fall, but from the context of the question, this wasn't the OP's intention.

So given that the train successfully navigates the gap in one frame, we can ask what observers in another frame see. That was the basis of my message.

 

[starthaus]

It's a shame that this thread got "derailed" (sorry - couldn't resist) into the question of how big a gap there is. Yes, real gaps are about a millimeter and not meters in size, but real trains don't go near the speed of light either. It's not relevant. Additionally, even for a tiny gap, there will be some speed at which the train is sufficiently Lorentz contracted to be shorter than the gap.

True but irrelevant. It is interesting to notice that in this case, the train will not fall through the gap. See post 44 for a detailed explanation.

This is a red herring, unhelpful for the OP's question, and it's a pity that the person who did the derailing is injecting so much hostility into this thread: that's also unhelpful in answering the OP's question.

I did not inject hostility, I simply solved a problem that has a surprising answer.

 

[Vanadium 50]

I have deleted a number of messages that were overly argumentative and were not addressing the OP's question. Let's try and focus on the question asked.

 

[macrylinda1]

Rest assured that no matter how high the speed $v<c$, the train will not "fall through the cracks" .

The mistake is to assume that you can apply then Lorentz contraction in one dimension(x) whilst ignoring it in the perpendicular (y).
Of course that is going to lead to paradox.
A proper analysis of the movement of the train in both directions eliminates the problem.
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[starthaus]

The mistake is to assume that you can apply then Lorentz contraction in one dimension(x) whilst ignoring it in the perpendicular (y).
Of course that is going to lead to paradox.
A proper analysis of the movement of the train in both directions eliminates the problem.
___________________
watch free movies online

There is no Lorentz contraction in the direction perpendicular to the direction of motion.

 

[JesseM]

The mistake is to assume that you can apply then Lorentz contraction in one dimension(x) whilst ignoring it in the perpendicular (y).

Lorentz contraction only happens along the axis of motion, so if the train is moving parallel to the x-axis in the platform frame, it will be contracted in the x-direction but not in the y-direction.