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If I'm in outer space, initially at rest, and every single particle in my body accelerates at the same rate in the same direction, will I feel that? My brain is fried thinking about this. There are two possibilities:

  1. initially at rest and then accelerating with const acceleration w.r.t. some inertial frame, and
  2. initially at rest and then accelerating with const acceleration w.r.t. some non-inertial frame

So will I feel anything:

  1. while I'm in motion
  2. when I transition from a state of rest to a state in motion

My intuition is that I shouldn't feel anything in any of the scenarios (every single particle in my body accelerates at the same rate - so there's no source of tension- any kind of push or pull- between various parts of my body), but I could be very wrong.

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The physics answer is, an accelerometer will detect all accelerations relative to an inertial frame. If you're in free fall being accelerated by a gravitational field, the answer is actually no, because a frame in free fall is inertial, even though for most purposes it's more useful to treat it as an accelerating frame.

So to your questions in order,

1a Yes, but free fall counts as inertial.

2a Only if you are also accelerating w/r/t an inertial frame.

1b No, if by "while I'm in motion" you mean constant velocity.

2b Yes, subject to the above.

The engineering/biology answer is flat "No." You specified that every part of you is being identically accelerated, and if that's the case, there's no way for an accelerometer (biological or otherwise) to be designed such that it will detect any acceleration. An accelerometer works by measuring the difference in motion between a mostly-inertial frame (like a mass on a spring, or fluid in your inner ear) and the accelerating frame (the body of the accelerometer, or your skull). If every particle is identically accelerating, there's nothing to measure.

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    $\begingroup$ There's not really any such thing as an object of which all parts are being identically accelerated. Acceleration is force divided by mass, so the only force that can identically accelerate all parts of an object is a force that varies directly with mass. The only force that does that is gravity, and gravity doesn't count. So in reality we'll always be able to build an accelerometer that works. $\endgroup$
    – g s
    Jul 23, 2021 at 18:28
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    $\begingroup$ @Andrea Your chair is pushing on your pants and your pants alone. Your pants push on your butt, which you feel as pressure. Your butt pushes on your interconnected rigid structures of skeleton and tendons and cartilage etc. These accelerate, causing your fluids to pool in the direction opposite the acceleration by momentum. This pooling of fluids gives you your orientation/acceleration sense in your head. $\endgroup$
    – g s
    Jul 23, 2021 at 20:45
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    $\begingroup$ @Andrea I think it's not the case that "all" of your body is being accelerated at the same rate in the case of you sitting in a chair $\endgroup$
    – user9343456
    Jul 24, 2021 at 3:44
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    $\begingroup$ @user9343456 have you ever ridden a roller coaster or elevator and felt your stomach lurch? That's your stomach accelerating at a different rate than the rest of your body. $\endgroup$
    – RonJohn
    Jul 24, 2021 at 13:47
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    $\begingroup$ I don't think it makes much sense to define "uniformly accelerated" to mean "accelerated nonuniformity until internal forces result in uniform acceleration", but I'm not the definition boss, so I suppose you're right if that's the definition you want to use. $\endgroup$
    – g s
    Jul 25, 2021 at 23:57
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No. Since every particle in your body accelerates at the same rate, there are no forces between them and no compression or tension. This is identical to being in freefall in a gravitational field. An astronaut in orbit, for example, is affected by the force of gravity at all times, but doesn't "feel" anything because they are in free fall. Half an orbit later, the astronaut is accelerating in the exact opposite direction, but it doesn't feel any different. At no point can the astronaut determine that they're in one half of the orbit versus the other, or just floating in deep space far from any mass and not in orbit at all. In all cases, they're simply accelerated by the local gravitational field, which always feels the same - like no acceleration at all.

Humans only feel proper acceleration, which is acceleration that deviates from the local gravitational field. Humans do not feel coordinate acceleration, which is acceleration with respect to some fixed point (and will vary based on the fixed point). Your unseen force is acting on every particle in your body exactly the way a gravitational field would. Since you can't feel the acceleration due to a gravitational field when in freefall, you can't feel the acceleration due to this force that operates in the exact same way.

See also: Would an astronaut experience a force during a gravity assist maneuver?

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  • $\begingroup$ This assumes the OP was with regards to gravity. Say a person is in an iron space capsule and a force (e.g. a magnetic field) suddenly begins acting equally across the entire body, there is still fluid in the person's inner ear and other places that are subject to inertia and will detect the acceleration. $\endgroup$
    – trpt4him
    Jul 25, 2021 at 19:38
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    $\begingroup$ @trpt4him the fluid in the inner ear is part of the 'entire body'... so you will accelerate with the entire body and therefore not be distinguishable from a normal resting state. $\endgroup$
    – NPSF3000
    Jul 25, 2021 at 21:23
  • $\begingroup$ But the magnetism only affects the ship, and the ship pushes me forward in my seat; thus the fluid in my ear wouldn't be affected by the magnetism. In this situation, I would most definitely feel the acceleration. $\endgroup$
    – trpt4him
    Jul 26, 2021 at 22:36
  • $\begingroup$ @trpt4him You're describing the mundane case of firing thrusters in a rocket or braking/accelerating in a car - when only the vehicle itself accelerates, you feel the acceleration because the external force is only applied where you're actually in contact with the vehicle (typically your seat). You won't feel it if it indeed induces a uniform acceleration in every part of your body (including your fluids), which is exactly what the OP describes - it's basically a gravitational force. $\endgroup$
    – Nuclear Hoagie
    Jul 27, 2021 at 12:49
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Yes. Via the equivalence principle if you accelerate with respect to a locally inertial reference frame, then you will not be able to distinguish the effects of acceleration from a gravitational field. So you will effectively feel a gravitational force acting in the direction of acceleration, with a magnitude proportional to the magnitude of the acceleration.

Note added due to discussion in the comments.

There's a contradiction implicit in the question. If you are truly isolated in empty space, then you can't be accelerating (you must be in a locally inertial reference frame), because of Newton's first law. So there's two strategies to answer this question:

(a) point out the contradiction and leave it at that (which is kind of a boring answer), or

(b) assume that you are accelerating but then also assume there is something causing the acceleration.

I'm taking approach (b) in my answer (although by adding this note I have also addressed point (a)).

Another key point that came up in the comments, is that a locally inertial frame is also a freely falling frame. (Here I am working in the framework of General Relativity, which is the most accurate description of gravity we currently have). So a freely falling observer is not accelerating relative to a locally inertial frame, and does not experience a force.

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    $\begingroup$ @Andrew "you will not be able to distinguish the effects of acceleration from a gravitational field" yes, that is true, but for a person in free fall, i.e they wouldn't really feel anything $\endgroup$
    – John Hunter
    Jul 23, 2021 at 18:02
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    $\begingroup$ OK, what's an experiment that will tell me if I'm floating in free space or are in free-fall acceleration? $\endgroup$
    – Ryan Cavanaugh
    Jul 23, 2021 at 18:29
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    $\begingroup$ You won't be able to distinguish this force from a gravitational force, that is true. But you also can't "feel" a gravitational force when in freefall - astronauts in orbit don't feel the orientation of their acceleration vector changing constantly. You can't distinguish this force from gravity, and you can't feel gravity while in freefall, so you therefore can't feel this force either. $\endgroup$
    – Nuclear Hoagie
    Jul 23, 2021 at 18:34
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    $\begingroup$ @user9343456 There's a contradiction implicit in your question. If you are truly isolated in empty space, then you can't be accelerating (you must be in a locally inertial reference frame), because of Newton's first law. So there's two tacks to answer this question: (a) point out the contradiction and leave it at that (which is kind of a boring answer), or (b) assume that you are accelerating but then also assume there is something causing the acceleration. I'm taking tack (b). I'll add a note to the answer. $\endgroup$
    – Andrew
    Jul 23, 2021 at 19:01
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    $\begingroup$ @Andrew The external force is gravity, or at least something indistinguishable from it. The force described by the OP might as well be gravity - as you point out, there's no way to tell that this force isn't gravity. Gravity alone won't make it "feel as if you were standing on a planet", you need the planet to push back to experience weight. You will experience a gravitational force as if you were in orbit, which just feels like zero-G. $\endgroup$
    – Nuclear Hoagie
    Jul 23, 2021 at 19:12
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No. Let's consider the case where you're out floating in free space, and suddenly a large moon pops into existence in your vicinity, which you start accelerating toward due to gravity.

Before the moon appears, you're obviously in an inertial frame.

After the moon appears, you're in free-fall toward it, which is also an inertial frame. See the equivalence principle:

Objects in free-fall do not experience being accelerated downward (e.g. toward the earth or other massive body) but rather weightlessness and no acceleration

Any two inertial frames are experienced equivalently; you could not distinguish transitioning from one to the other.

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Just what exactly is "constant acceleration" in relativity is a bit more complicated that it might seem at first. If, relative to a fixed reference frame, your change in velocity per unit time is constant, that at some point you will exceed the speed of light. So that type of acceleration is physically impossible in the long term, but in the short term it would be possible. However, if you are accelerating at a constant rate relative to some fixed frame of reference, then since your time is slowing down relative to that frame of reference, your acceleration will be increasing in your frame of reference.

We can also consider an object experiencing constant proper acceleration; that is, the acceleration relative to its instantaneous frame of reference is constant. This can be characterized by Rindler coordinates, but in Rindler coordinates an object of finite length will have to have different accelerations at different points.

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  • $\begingroup$ That's a very interesting answer, though I'm afraid I don't have an advanced enough knowledge to understand most of it. "your acceleration will be increasing in your frame of reference" sounds counter intuitive. Also, why is the last sentence true? $\endgroup$
    – user9343456
    Jul 26, 2021 at 19:13
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You've stumbled upon the difference between body forces and surface forces. Body forces act directly on the entire body of an object, while surface forces act directly only on the surface of an object. When you sit in a chair, the direct force you feel is the chair pressing against your bottom. You don't feel the chair throughout your whole body, because it's only acting on the surface. Gravity, however, is a body force. In your everyday life, you can't really feel it directly because it acts almost* evenly on your entire body. You can feel the fluid in your inner ear flow around, or your feet pressing against the floor, but you can't actually feel gravity itself.

*There are tidal forces caused by gravity being weaker higher up, but on Earth these are many orders of magnitude too small to feel.

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