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I came up with a thought experiment and it has been on my mind for quite some time now. Would like to hear the thoughts of others as my wife has no clue what I'm talking about.

Given two points of great distance apart (think light years). Now, assume that a giant of enormous size were to step from one point to the next (obviously nothing exists of that size/magnitude but it's a thought experiment). Wouldn't the giant taking that step defeat the speed of light as it would only take a few seconds to achieve from the giants point-of-view?

Just imagine two pebbles on a sidewalk and stepping from point to point in a single bound. A great distance is achieved because of my size, while an ant would have to take many steps.

I have a couple theories, but please feel free to point the flaw in my thinking or provide a better explanation.

A.) Traveling faster than the speed of light is possible.

B.) An observer living on one of the points would see the giant stepping as extremely slow (stuck in time - taking years), while the time for the giant would appear as instant due to time dilation/relativity caused by the giants velocity thus protecting the speed of light from being breached. So light would speed up from the giants point-of-view?

C.) We are really living in a computer simulation and traveling faster than the speed of light is not possible because our computer overlords made faster than light speed computationally impossible. Joking, but seriously.

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closed as off-topic by John Rennie, Bill N, ZeroTheHero, user191954, Aaron Stevens Nov 28 '18 at 17:13

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The problem here is your example between a human and an ant. Yes, you need less steps than the ant but you will never break the light speed. In the giant's point of view, that step is smaller than him but to make the step his legs need to go faster than light and that isn't possible due to special relativity. The issue is that you are thinking as in your example with the ant. For you an step is "instant" but that thought is not extensible for the giant.

A weird thing: If that step is so small from his perspective, then it has to be taller than distance between those points that are so far from each other. And here there is a funny thing: he can't see his own feet in real time. The world is very different from his point of view, so you cannot just extend what you see to what he sees.

Moreover, because of his size he should be very, very, very, very massive so he would curve the spacetime around him like a black hole. You see, very different from us.

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The fundamental reason you can't go faster than the speed of light is that it would take an infinite amount of energy to do so. At speeds much less than light, kinetic energy is the familiar $\frac{mv^2}{2}$. But including the effects of special relativity:

$E_k = (\gamma - 1)mc^2 = ((1 - \beta^2)^{-1/2} - 1 )mc^2$

You can see when $v << c$ and therefore $\beta$ is very small, this reduces to familiar kinetic energy.

Anyway, if you plug in $v = c$ you get $\beta = 1$, i.e.

$E_k = \frac{1}{\sqrt{1 - 1^2}} mc^2 = \frac{1}{0}mc^2 = \infty$

The giant's leg is just a red herring because it doesn't nothing to get around this simple fact.

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I think there are many problems with the way you design your thought experiment, and the conclusions you draw form it.But it's ok, we can try to go through some of what I think is the most problematic points.

I will try to do so without any form of math because I might be wrong, but I don't think you are very comfortable with formal science (my apologies if I got it wrong)

1) The way you make assumptions. First you assume that a giant several light-years tall could exist. I'm not saying that it is a problem that there is no such thing. The problem is that it is likely that no such thing could physically exist. Scale effects might imply that such a huge living organism doesn't obey the laws of physics. If the system you are thinking about is not physical, then your conclusions will most likely not be either. So you should be aware of that first big assumption out of the blue. You should provide some arguments on the validity of imagining such a monstruous thing. Quite often, the devil is in the details (think about the famous example of a light-year long stick that you wiggle around. The transmission of information to the far end of the stick could apparently occur at arbitriraly high speeds. The solution lies in taking into account the compressibility of the stick, which implies that the "mechanical signal" itself along the shaft has a limited speed. Your example is actually similar, and same argument might be one way among other to correct your thinking. Pay attention to details, make sure what you imagine respects the laws of physics)

Second, you assume that the step would only take a bunch of seconds from the giant "point of view". Why ??? Not to mention that I think you have some confusion on the notion of "point of view", it seems quite obvious that the step of an elephant is much slower than the step of a mouse. Why would you assume that the step-time is size-independant ? this is a HUGE assumption, which seems completely wrong to me. Your giant might cover a long distance, but it will probably take him a very long time. Think about the "ents" in Lord of the Ring. Accelerating the huge mass of his legs with such great magnitude would require insane amounts of energy. It's heavier, so it's most likely gonna be much slower. Of all the supraluminal travel device I've heard about, this is probably the most far-fetched and one :)

2) Your comprehension of the subject you are tackling : I might be wrong, and I'm sorry if I am, but it seems clear to me that your understanding of physics in general, and relativity in particular is limited. It's ok. So is mine. But before trying to break some theory that has been around for a century, and extensively challenged by the greatest minds of mankind, you should at least do a thorough research on the subject :) I'm not sure you understand the actual arguments between the impossibility of speed-of-light travel for a massive particle (if not you should at least check out lorentz transformations, infinite energy problem, etc...) That is the first step you should take. Don't wonder "how can I make it possible" before you wonder "why do they all say it ain't ?"

3)The way you draw your conclusions. First, I would like to remind you that, strictly speaking, in physics, a thought experiment is never considered a proof of anything. Experiment always has the last word. Of course, for a chill discussion like this, it is still interesting, but never take the conclusions out of a thought experiment too seriously.

That being said, I didn't look too much at your conclusions because the thought experiment is not valid for me. But they make me think again that you are not comfortable with the basic notions of relativity("light would speed up from the giants point-of-view" = "Fuck you, Einstein"). Finally, a big problem is that you lack the potential conclusion : "my thought experiment is ill-designed, and nothing should be concluded from it". This is always an option to consider, even for the greatest geniuses :)

I hope you won't take my comment in a bad way, but I think it is important to talk about the potential flaws on the basics, which should prevent us from going any further

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I'll make just a simple comment, to amplify the previous answers.

Your giant may make a single step, but in order to do that he has to make his foot move faster than light. That would take infinite energy, and there is no way that even giant muscles can provide that amount of energy to his foot.

Another way of thinking about it it is to think of sweeping a searchlight through an arc. At a far enough distance, the "illuminated spot" of light will seem to move faster than the speed of light. Yet, no photons ever move that fast, they only travel from the searchlight to the illuminated spot, at lightspeed. This cannot happen to the giant's foot, as that is a physical thing, unlike the "illuminated spot" which is not physical in the way that photons are.

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Ok, here is the giant. Light-years-big giant.

He decides to make a step. His brain sends signals to his legs muscles to start moving. But wait, here is a first small problem you probably had not thought of: his muscles wouldn't know that it's time to do anything, because they are too far from the brain and no signal can travel faster than light!

But ok, let's wait several years. Instructions from the brain have propagated throughout the giant's body, all the muscles are doing their job.

In order for step to happen, the giant's leg must be moved from the initial position to a new position far-far-away. This huge leg must gain greater than light speed. What makes you think that giant's muscles can do it? One of the results of relativity theory is that it is not possible to accelerate anything to a speed faster than light. No matter if you try to use steam engines, rockets or muscles to do it.

The point of my explanations was not to prove impossibility to achieve speed greater than light. The point is to show that introducing a giant doesn't necessarily result in greater-than-light speed.

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I see this situation as similar to one in which we have a laser and shine it from earth to the moon (choose a rock much further away from ours if desired). At the flick of a wrist, someone could move the laser point from one edge of the moon to the other, and from the perspective of a person on the moon, the laser point would travel across the surface at superluminal speeds. However, due to travel time, all information flow is still restricted by the speed of light, and therefore causality is preserved.

Also note that special relativity disallows rigid bodies of finite extent, so this laser represents the most responsive leg your giant could have.

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