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Let's say that we have 2 tennis balls in space, one being in motion (say, pushed by an astronaut), and the other one still.

If we could take a snapshot of both tennis balls, would there be any evidence that could suggest that one is moving and the other one is still? Is there anything happening, at the atomic level or bigger, being responsible for the motion?

If there isn't, and both balls are absolutely identical, then how come one is still and the other one moving? Where does the difference of motion come from?

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    $\begingroup$ Current theories don’t support an absolute notion of motion at all. They support notions of relative motion and of absolute changes in motion. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Oct 13, 2019 at 21:15
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    $\begingroup$ @StudyStudy Your comment seems to suggest that if I see an object moving relative to me that a force must be acting on it. This is not the case. $\endgroup$
    – BioPhysicist
    Commented Oct 14, 2019 at 5:53
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    $\begingroup$ @StudyStudy No, force is a required for acceleration. If either ball is changing velocity, then detecting forces might work, but then you'll probably have better ways to determine that than looking at the heat created by material deformation as a consequence of an outside force. (for one, it might be gravity doing the acceleration - good luck detecting a local heat change from that) $\endgroup$
    – Gloweye
    Commented Oct 14, 2019 at 8:02
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    $\begingroup$ Your question contains an inherent contradiction. You're asking about motion, but with the constraint that there be no passage of time (i.e., all you have is a snapshot). The problem is that you can't define motion without the concept of time. If you could relax the constraint (say, with multiple snapshots taken at different times), then you could start to define motion. But as it is, you can't, and therefore the question can't really be answered. $\endgroup$
    – Richter65
    Commented Oct 14, 2019 at 17:55
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    $\begingroup$ @Richter65 I think it is valid to ask what is the evidence collected from a still snapshot that an object is moving, because in terms of latent properties, the masses have nonzero momentum with respect to each other. The inability to observe such a property from a projection down to a single point in time does not contradict the existence of such a property, which becomes evident as time progresses. What the OP is asking is whether there is any remnant or indication of the momentum effect that could be observed from a single instantaneous observation. $\endgroup$
    – pygosceles
    Commented Oct 15, 2019 at 18:54

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According to classical physics: no. It is impossible to tell how fast something is moving from a snapshot.

According to special relativity: yes. If we choose a frame of reference where one of the balls is at rest then only that ball will look normal. The other ball is moving in this frame so it will be length contracted. If its rest length is $L$ then its length will now be $L\sqrt{1-v^2/c^2}$. Since $1-v^2/c^2<1$ the ball will be shorter in the direction it is moving.

According to quantum mechanics: yes? In quantum mechanics particles are described by a wavefunction $\psi(x)$ which (handwavingly) says how much of the particle is present at a certain point. A tennis ball is also described by a wavefunction which you can get by combining all the wavefunctions of its atoms. The wavefunction actually contains all the information you can possibly know about an object, including its velocity. So if you could pause time and look at the wavefunction you would have enough information to know its (most likely) velocity. In real life you can't actually look at wavefunctions: you have to perform an experiment to extract information from the wavefunction. At this point you might wonder if that still counts as taking a snapshot.

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    $\begingroup$ "According to quantum mechanics: yes?" Had a good chuckle at that. The most quantum of answers. $\endgroup$
    – Smeato
    Commented Oct 14, 2019 at 12:40
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    $\begingroup$ With an ideally perfect camera and ideally identical tennis balls, with motion not perpendicular to the camera, could you not use doppler shift in the spectrum to tell at least one of them was moving relative to the camera, (And which one, if you had the tennis ball to compare the photos to?) $\endgroup$
    – notovny
    Commented Oct 14, 2019 at 12:49
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    $\begingroup$ You are ignoring the Penrose-Terrell effect. A photograph would not show the flattening that special relativity predicts. math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html $\endgroup$
    – D. Halsey
    Commented Oct 14, 2019 at 13:00
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    $\begingroup$ You should specify in the answer what you mean by "snapshot". You seem to have interpreted it not as a photo but as a slice of the universe at a fixed coordinate time. There's no way to actually freeze a slice of the universe, so your answers end up depending on arbitrary assumptions about the magical process by which this was done. There's no record of the motion in the Newtonian case not because of any property of Newtonian mechanics, but because your magical process saved only the positions and threw away the velocities. $\endgroup$
    – benrg
    Commented Oct 14, 2019 at 16:22
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    $\begingroup$ I don't quite understand the QM answer. Classically, a system's state is the position and velocity of each particle. If you're saying a quantum snapshot contains the full wavefunction information, then surely a comparable classical snapshot contains both position and velocity! Saying that this is somehow a feature of quantum physics is misleading. $\endgroup$
    – JiK
    Commented Oct 15, 2019 at 8:25
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If we could take a snapshot of both tennis balls, would there be any evidence that could suggest that one is moving and the other one is still?

We can't. Problem solved.

Well, almost problem solved. So in reality, we can take shorter and shorter exposures. I can take a 1 second exposure of the scene, where the moving tennis ball will be heavily blurred while the stationary one will be crisp. I can capture the same scene at 1/100th of a second, and moving ball will look more crisp like the stationary one. I can capture the same scene at 1/1000th of a second, and it will be very difficult for the human eye to discern which one is in motion. I can make these snapshots shorter and shorter. Indeed, we have looked at imaging scenes at such exacting shutter speeds that we can watch light propagate through the scene. But we never quite hit a perfect standstill. We never hit an infinitely fast shutter speed.

Now forgive me if I handwave a bit, but there is an unimaginably large body of evidence that motion exists. In particular, you'll fail to predict very much if you assume no motion occurs. So from that empirical point of view, we should find that motion exists. From a philosophical point of view, there's some interesting questions to be had regarding endurable versus perdurable views of the universe, but from a scientific perspective, we generally agree that motion exists.

So how do we resolve the conundrum you are considering? The answer is calculus. Roughly 400 years ago, Isaac Newton and Gottfried Leibniz independently developed a consistent way of dealing with infinitesimally small values. We generally accept this as the "correct" way of handling them. It does not permit us to consider a shutter speed which is truly infinite, letting us isolate a moment perfectly, to see if there is motion or not, but it does let us answer the question "what happens if we crank the shutter speed up? What if we go 1/100th of a second, 1/1000th, 1/100000th, 1/0000000000th of a second and just keep going?" What happens if we have an infinitesimally small exposure period in our camera?

Using that rigor, what we find is that modeling the world around us really requires two things. The first is the values you are familiar with, such as position. And the second is the derivatives of those familiar things, such as velocity. These are the results of applying the calculus to the former group.

We find that models such as Lagrangian and Hamiltonian models of systems work remarkably well for predicting virtually all systems. These systems explicitly include this concept of a derivative in them, this idea of an "instantaneous rate of change." So we say there is motion, because it seems unimaginably difficult to believe that these patterns work so well if there was not motion!

As a side note, you set up your experiment in space, so there's nothing much to interact with. However, had you set the experiment up in the water, you would find the chaotic flow behind the moving ball very interesting. It would be ripe with fascinating and beautiful twirls that are very hard to explain unless associated with some forward motion.

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    $\begingroup$ I'm not in the slightest suggesting that motion does not exist, it would be absurd. I completely get all the newtonian - and other - sciences around motion, I'm not a conspirationnist. I'm just saying that it baffles me that in true life, when you look at the balls, you can't see any difference at all between them, yet one ball is moving and the other one isn't. It truly is fascinating to me. It doesn't seem to make sense that 2 objects in the very exact same state can have different behaviours. How come? Where is the difference stored? $\endgroup$
    – GaelF
    Commented Oct 14, 2019 at 6:25
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    $\begingroup$ @Skeptron they don't have the same state though - they have different velocities. They only appear to have the same state when the means by which you choose to observe the state are contrived to limit perception of the aspect of their state you're interested in. There is no such thing as directly observing something's state; only inferring it from interacting with it. If your interaction somehow takes place in infinitesimal time then velocity is imperceptible, but I'd argue this is impossible in absolute terms. Even with infinitesimal shutter speed, red-shift will still differentiate them. $\endgroup$
    – Will
    Commented Oct 14, 2019 at 8:37
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    $\begingroup$ @Skeptron There would also not be the slightest difference between a green ball and a red ball if you decided to observe them only in the dark ... $\endgroup$
    – Hagen von Eitzen
    Commented Oct 14, 2019 at 9:38
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    $\begingroup$ @Skeptron they also "hold information" about their velocity, whether you observe them over a finite time interval or not. Indeed, even the different-colored balls would be differently-colored again if they had no thermal energy, so the distinction is at best one between ordered and disordered kinetic energy. $\endgroup$
    – Will
    Commented Oct 14, 2019 at 12:58
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    $\begingroup$ But I think some of the issue you're having is mentioned in the last sentence of your comment. "... 2 objects in the very exact same state can have different behaviors." The two balls are not in the same state. The position only captures part of the state, not all of it. It's akin to the clever projections of the Godel Escher Bach book. In the case of that cover, a 2-d projection does not fully capture the 3d state of an object. In your case, a 3d "snapshot" of its position does not fully capture... $\endgroup$
    – Cort Ammon
    Commented Oct 14, 2019 at 15:09
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Cylinders Don't Exist

If I show you a picture of two round objects and tell you that one is a sphere and the other is a cylinder you are looking at head-on, how can you tell whether I am telling the truth or lying? You can't, and therefore, I conclude that there is no difference between spheres and cylinders, because we lack the proper evidence for their existence.

Projection

The point here is that motion requires time, and a snapshot is a projection of a 4-D extended object into 3- or 2-D. The most naive such projections will necessarily destroy information about additional dimensions. If I remove one of the axes which would help you distinguish a cylinder from a sphere (ignoring light reflections, etc.), this is no different than you removing the time dimension to make it impossible to distinguish between a moving or a static object.

Conclusion

If you want to establish the separate existence of spheres and cylinders, you must examine them in all the dimensions which make them different. If you want to establish the existence of dynamic 4-D objects (objects which vary in the time dimension), you must examine them in all the dimensions which differentiate them from purely static objects (ones which are constant along the time dimension).

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  • $\begingroup$ Who said anything about cylinders? $\endgroup$
    – John Alexiou
    Commented Oct 14, 2019 at 20:24
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    $\begingroup$ @ja72 This answer introduces cylinders/spheres as an analogy for moving/not-moving. $\endgroup$
    – Stig Hemmer
    Commented Oct 15, 2019 at 7:42
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    $\begingroup$ I think this answer is underrated. None of the others even attempt address the perceived problem in the question. If you think about all 4 dimensions as having all their points being simultaneously present, and our perception of time as just hindered, then what you have is really the equivalent of a 4d, unchanging model, like a display piece. This feels off, as it precludes change on the model itself, but can't think of how you would disprove it. Zero information transmitted (directly, not via inference or prediction) between moments in time seems suspect, if all moments are already exist. $\endgroup$
    – Brandon D
    Commented Jan 21, 2021 at 23:56
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It is about the frame of reference, in the frame of reference of the tennis ball pushed by the astronaut, it could be considered as standing still and the other ball, the astronaut, and everything else as moving. For the frame of reference of the other ball it could be considered as standing still, and the first ball as moving. If you were with either one, in it's frame of reference, all of the physical laws of the universe would be the same and neither could be preferred as absolute. This is one of the basics of relativity.

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  • $\begingroup$ One realization which helps understand that motion is only relative to an arbitrary inertial system is that the common cases we refer to as "standing still" (e.g., my keyboard as I type appears to be motionless -- I can hit the keys pretty reliably!) are in reality hurtling through space at enormous speeds and on complicated trajectories composed of the rotation and orbits of the earth, sun, galaxy, local group and space expansion. One could make a cosmological case for using the microwave background as an absolute reference frame but that wouldn't change special relativity of motion. $\endgroup$
    – Peter - Reinstate Monica
    Commented Oct 14, 2019 at 10:04
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    $\begingroup$ To elaborate on "we are not standing still": Not only are we moving from most reasonable points of view; we are not even in an inertial system because of the rotational components. We are under permanent acceleration: We are not standing still relative to any inertial system. $\endgroup$
    – Peter - Reinstate Monica
    Commented Oct 14, 2019 at 10:07
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Your question assumes one ball is moving and the other is still. That assumption is meaningless without specifying a frame of reference. All motion is relative. To each of the balls it would appear that the other was moving. The 'evidence' that they are moving includes the fact that they would appear smaller to each other, and that their separation was changing.

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You are limiting your snapshot to a 3D picture.

If you took a 2D snapshot, it would be impossible to tell how deep your tennis "balls" are (in addition to being unable to tell their motion).

So, take a 4D "snapshot", and all'll be fine.

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    $\begingroup$ This answer could explain what a 4D snapshot means and why it would show motion. $\endgroup$
    – JiK
    Commented Oct 15, 2019 at 10:28
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If we could take a snapshot of both tennis balls, would there be any evidence that could suggest that one is moving and the other one is still? Is there anything happening, at the atomic level or bigger, being responsible for the motion?

If the balls are truly identical and you are at rest with respect to one of them, the light of the one moving will look more red or blue, depending on whether it is moving toward or away from you, by the Doppler shift. This would be most evident if you were positioned between the balls and on their axis, but you would always be able to do it as long as the moving ball is at least partially approaching or moving away from you.

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  • $\begingroup$ A friendly addendum: this only identifies a ball in motion relative to the observer, not that one of the balls has intrinsic motion that the other ball does not have. You can freely choose the frame of reference of the observer to make one ball, or the other, or both, be in motion. $\endgroup$
    – asgallant
    Commented Oct 15, 2019 at 17:10
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The photos would look identical, but you would have to take each photo from a different inertial frame of reference. You have to be moving in a different speed in a different direction to take the photo. This shows that there is inherent differences between objects in motion.

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If there isn't, and both balls are absolutely identical, then how come one is still and the other one moving? Where does the difference of motion come from?

I don't think this question is nearly as perplexing as you might think nor do I think it requires sophisticated physics like the best answer describes. Ask yourself, how do you show with a snapshot that a bowl of soup is at a cold 5 C vs a warm 45 C? Or how could you show that a radio is turned off or is blaring music? Intuitive solutions to these questions would be to take a picture with a thermometer or an oscilloscope attached to a microphone respectively in the same frame.

The easiest way to show with a snapshot that a tennis ball is moving, is by taking a picture with a speedometer reading in the same frame as the ball.

These examples are hard to show directly in a single snapshot in time because they all involve the collective motion of small particles (uniform velocity for motion, random for thermal, and periodic for sound). And motion is described as the change of movement with time, but a snapshot captures an instance in time not a change.

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It is perhaps interesting to think about Mach's paradox in this context. I'll get back to your question and the limits of the two-body way of discussing special relativity in the end. One form of the paradox is this: imagine a bucket of water standing on the floor. The surface is (almost) flat. Now start spinning it. The water's surface begins to form a paraboloid. How does the water know it's spinning? Why is the frame of reference in which the water's surface is flat the same frame in which the stars do not move relative to the bucket (which almost coïncides with the frame where the Earth is still)?

The answer is that the presence of the stars determines the global geometry of the universe, and thus the local free-falling frame in which the bucket finds itself up to small corrections due to Earth's gravity and rotation (which is in free fall around the sun which is in free fall through the galaxy which is in free fall through the universe).

Now how does all this relate to your question? Well, we can determine accelerations relative to a global frame given by the fixed stars with as simple a tool as the aforementioned bucket. But if we accept that global frame as special, then we can also detect motion relative to that global frame, which is in a sense absolute as it is given by the universe in its entirety. To do this, you'd need a long exposure and a clear night-sky. You would then compare the motion of your tennis balls to the motion of the stars and you could in a meaningful sense call the difference of the motion relative to the stars an absolute motion, as it is relative to the universe as a whole (well, to good approximation depending on how many stars you can actually photograph). Since this is literally the opposite of what you had asked, it doesn't literally answer your question, but I think it answers the same question in spirit, namely whether there is a physical difference between "moving" and "stationary."

NB It may seem that I'm upending all of special relativity by that line of thinking but that's not true. Special relativity is a good law of nature, one just has to be aware of other objects which are present when applying it, and whether they have any influence on the question studied -- and that statement is a trivial truth which certainly was on Einstein's mind when he wrote the time dilation law for the first time.

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It is possible to measure absolute motion relative to the cosmic microwave background.. A system in rest with the moving ball would measure a dipole in the background radiation.

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If we look past your example with snapshots we can just look into modern technology and find a little thing called videos. They can record motion pretty easily. "Is there any physical evidence for motion", videos?

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