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In fact the distance between the marks from the platform perspective will be even longer than the “rest length” of the train because when the sprays are fired the railway passing by under the train is length contracted so the distance will be “amplified” when measured from the railway (platform) frame of reference
// Roelof said: “From George’s perspective Gracie seconds are longer so Gracies meters are longer” //
From George’s perspective Gracie seconds are longer than George’s clock seconds, that’s true, but that not make Gracie meters longer. Gracies meters are shorter from George perpective. Both measure the same time dilation and length contraction in the other frame of reference.
// Roelof said:”f the time unit changes (in this case a second becomes longer) light will cover more physical distance in that time unit and so the metre becomes longer” //
You are giving a strange definition of a meter, the distance traveled by light in Geroge reference frame each second of Gracies reference frame, that has no sense.
There is a mistake in the animation at the end of the video because it is not taking into account the time dilation. The animation visualize the synchronization procedure of clocks in team train as seen from the team platform. The clocks at the origin of both frames of reference must coincide at instant T=0 when they are in front of each other, but from that moment on, the clock on the origin of team train should present delay with respect to the clock at the origin of team platform due to time dilation. Instead of that, both clocks remain synchronized, so the animation is not accurate.
Hi Brian. The explanation is great, crystal clear, but unfortunately both the animation and the diagram are completely wrong. The light particle velocity should be c in both directions but, in both visualizations of the horizontal light clock, the speed is being added in the newtonian way. The board diagram is specially wrong beacuse after the reflexion on the right mirror the light particle is still going to the right at less speed. It should be travel to the left at speed c!
Although the reasoning is impecable of course, the diagram is wrong and confusing. You should correct it. You can not measure a moving train attaching a measuring tape at the ends of the train when its front and its back are passing by you. In case you use that technique, the measuring tape will be moving with respect to you so, the tape itself will suffer lenght contraction as well as the train. It is true, the reading of the measuring tape in motion would be the same than the reading when you measure the train at rest because in both cases the tape is at rest with respect the train. With the moving train, the tape would be also moving with respect to you, so 1 cm of the moving tape will be shorter than 1 cm of a tape at rest. You would be measuring the rest lengh in both cases and this is not what the experiment is trying to do
In my opinion, Brian is not going sufficiently deep in the explanation. The fact that the human is on a bench and the alien is riding a bicycle, give us the feeling that the human is at rest and the alien is in motion but, as we have learned, we can consider that is the human who is in motion and the alien being at rest. From that point of view the “now-there” of the human would be also in the “past-there” of the alien. At the same time we can say that the “now-here” of the alien is in our “past-here”.
So the now slices are respectively tilted in a way that both can say that his “now in the remote distance” is in the past of the each respective local now
SPACE —->
His now here —- My now there
My now here —- His now there
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VFor comparing “now slices” and determine whether an event is in the future or in the past of another event, we have to specify the location of these events. This is the reason I am talking of my “now here or there” and his “now here or there”.
During this section should have been stressed much more that, the relativity of simultaneity refers to measuring the moment when the events take place, not the way these events are really seeing by the eye of the observer. Namely, we are not taking into account the time that, after the event has “locally happened”, light takes to travel from this event to the eye of the observer. In fact, one observer in the train located at one of the wagon ends wouldn’t actually see them to sign at the same time either because the light would take more time to travel from the opposite end of the wagon. Nevertheless, he would still agree that both leaders had signed the treat simultaneously because for “measuring” the real moment when both events took place, he should take into account the delay of light to reach his eye (and this is the difference between measuring and seeing).
Elisabeth, although it is difficult to accept, at the end of the video Brian stress the difference between measuring and seeing. The shrink of the taxicab lengh is not only what you see but also what you measure, so it is more than an optical illusion. In that example, the twisting of the cab would be an optical illusion but the shortened lenght would be real “from your perspective”. But of course, if you think that the only “true lenght” is the lenghh measured at rest, this “true lengh” or “proper lenght” does not change, and you could calculate it from the lengh that you measure using the ecuations of relativity.
Yes, in fact it is considered that all of us are moving at the speed of light in the space-time.We mainly use that speed to travel through time but when we divert some of the speed in the space dimension we loose speed in the time dimension. Only light and massless particles are the one allowed to divert all of its speed in the space dimension.