High School Thought Experiment: Behavior of shadow of object moving at speed c

[Mohiaz]

I thought about the behavior of shadow when objects are moving at speed of light. The body goes many relativistic concepts such as length contraction etc...

My main focus was that does the length of shadow also contracts as the length of object contracts as it moves at speed or light or near the speed of light.

My thoughts on this are that when a body moves at speed of light it undergo length contract. But when it goes under length contraction its physical length doesn't contracts. It's just a visual phenomenon. There is nothing with the physical body of the object.

It may be physical. If it is physical contraction, then I was assuming that what if the body got heat up at undergo elastic thermal contraction. This is just what I am assuming. But I know that it didn't make any sense. This is relativistic effect not that physical.

Okay, let's talk about the shadow experiment. The object is moving at very high speed nearly the speed of light. Let's assume it is blocking light and a shadow is formed of that object. So, the shadow will no contract because the body blocks the light physically not visually. I was assuming that shadow will not contract.

I may be wrong. This is just a thought experiment. If you have any thought, let me know

Edit: I didn't know that this thought Experiment will gain that much attention.
I was just imagining it randomly at middle at middle of my college.

 

[.Scott]

For the general case, this is a very interesting question.

But for simplicity, I will answer a much more limited case.
Let's say that the object is moving parallel to the projection screen and rather close to it.
And let's say that the light source is quite distant - so that all of the light is landing on the projection screen at roughly a right angle.
In that case, what will appear on the projection screen will be exactly what appears when observing the object - but with a slight delay that results from the time it takes light to travel from the objects path to the screen.
So, what is seen on the screen will show exactly what is observed of the object - including the Lorentz contraction.

The effect is more "physical" than you suggest. The central issue is how the start and end positions of the shadow are determined. If your projection screen is marked on with a 1-meter grid, then both you and anyone riding the object will agree that the leading edge of the shadow passes the (for example) 1000-meter mark. The issue is where the trailing edge of the shadow is at that instant. It's the notion of "at that instant" where Special Relativity needs to be considered. You may see the trailing edge crossing the 999-meter mark "at that instant" while someone on the object may see it crossing the 990-meter mark "at that instant". As soon as you move away from the leading edge of the shadow, "at that instant" becomes relative.

 

[Mohiaz]

Yes, under the simplified case you described, the shadow will show Lorentz contraction.

 

[Ibix]

Let's say that the object is moving parallel to the projection screen and rather close to it.
And let's say that the light source is quite distant - so that all of the light is landing on the projection screen at roughly a right angle.
In that case, what will appear on the projection screen will be exactly what appears when observing the object - but with a slight delay that results from the time it takes light to travel from the objects path to the screen.
So, what is seen on the screen will show exactly what is observed of the object - including the Lorentz contraction.

You need to be a little careful here, because how the shadow appears still depends on how you're looking at it. If you look directly, varying light speed delay from the shadow edges to your eye means that the observed length may not be length contracted. If you turn the screen into a CCD and take a snapshot, the length depends on your choice of simultaneity convention.

It is all rather messy. There's always a unique answer, of course, but there are multiple ways to interpret the question even with your restriction.

 

[PeterDonis]

If you look directly, varying light speed delay from the shadow edges to your eye means that the observed length may not be length contracted.

This also applies to looking at the object itself. The OP might want to look up Penrose-Terell rotation.

 

[Ibix]

I think how I would phrase it is that Lorentz contraction does have an effect on the shadow length. If one were to compare a pseudo-Newtonian calculation in the lab frame (Newton plus an assumption that light moves at $c$ in the lab frame and we don't talk about other frames) to the relativistic calculation in the lab frame, the predicted shadow length measurements would be different and we would attribute that difference to the length contraction present in the relativistic calculation.

Edit: I think I put enough caveats in that!

 

[Ibix]

I thought about the behavior of shadow when objects are moving at speed of light.

Note that massive objects cannot travel at $c$. You correctly consider something travelling at near-$c$ further down your post, and answers have been on that basis. Trying to reason about massive objects travelling at $c$ involves an assumption that $1=0$, and any conclusions drawn from that are meaningless.

 

[A.T.]

But when it goes under length contraction its physical length doesn't contracts. It's just a visual phenomenon

Length contraction is not a visual phenomenon. It is what remains, after you accounted for all the visual effects. Your shadow experiment will likely have both: length contraction and visual effects affecting the outcome. But as others wrote, you have to define how exactly you will measure the shadow.

This website has many visualizations of the combined effect of length contraction and visual effects:
https://www.spacetimetravel.org/

For example:
https://www.spacetimetravel.org/fussball
https://www.spacetimetravel.org/tompkins/1

 

[PAllen]

You need to be a little careful here, because how the shadow appears still depends on how you're looking at it. If you look directly, varying light speed delay from the shadow edges to your eye means that the observed length may not be length contracted. If you turn the screen into a CCD and take a snapshot, the length depends on your choice of simultaneity convention.

It is all rather messy. There's always a unique answer, of course, but there are multiple ways to interpret the question even with your restriction.

If you make the distant light source a flash bulb (at rest in screen frame), the fixes simultaneity. Then, you will definitely see a length contracted shadow (assuming you have a very fast eye). And if the screen is a flat piece of film, it will photograph the length contracted shadow.

 

[Ibix]

If you make the distant light source a flash bulb (at rest in screen frame), the fixes simultaneity. Then, you will definitely see a length contracted shadow (assuming you have a very fast eye). And if the screen is a flat piece of film, it will photograph the length contracted shadow.

I agree in the film case, but I think in the screen case you also need the eye to be far from the screen, so the variation in light flight time from different points on the shadow (or just outside it, I suppose) to the eye is negligible.

 

[PAllen]

I agree in the film case, but I think in the screen case you also need the eye to be far from the screen, so the variation in light flight time from different points on the shadow (or just outside it, I suppose) to the eye is negligible.

Consider the scenario for a slow moving object (close to a screen, far away flash bulb). What do you see? How is the fast moving object any different, given the notion of a flash bulb?

 

[jbriggs444]

I agree in the film case, but I think in the screen case you also need the eye to be far from the screen, so the variation in light flight time from different points on the shadow (or just outside it, I suppose) to the eye is negligible.

If the screen and eye are stationary then it should not matter. The shadow of a flash will obviously be ephemeral. The illumination from the flash may not all be visible back at the eye simultaneously. One might see one or more moving illuminated lines, for example. But the portion of the screen that is never illuminated due to the shadow will have a fixed spatial location regardless of the light travel time from screen to eye. So the eye will see the shadow exactly where it fell.

 

[A.T.]

Consider the scenario for a slow moving object (close to a screen, far away flash bulb). What do you see?

The illumination from the flash may not all be visible back at the eye simultaneously.

I guess @Ibix refers to that fact that, if the object is very long (even when contracted), then you don't see both ends of its shadow flash simultaneously on the screen (for some eye locations close to the screen), making it difficult to judge it's length.

You have to remember where the first end appeared, but then we can just as well use a photosensitive film / sensor that remembers.

 

[PAllen]

Let’s keep in mind that the shadow would have to be 300 meters for a one microsecond delay between front and back. I don’t think the eye/brain could discern this. Meanwhile, Penrose-Terrell rotation relies on the existence of steady illumination such that at all times you are seeing light from all visible parts of the body. The rotation effect is then a first order phenomenon.

 

[Ibix]

No, you're right. When it's illuminated by an instantaneous flash, what part of the screen you see lit up when does depend on where you are, but which parts were ever illuminated doesn't.