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First off, I'd like to confess, I'm not a physicist, but this question, the one I'm about to ask, has been bothering me for quite some time. I have some basic knowledge of science and I'm afraid I can't get technical/mathematical at this point. If the question fails to meet the standards of Physics SE, kindly do let me know and I'll delete it or edit it; the former is more likely.

Ok, so let me begin.

I know that gravity causes time dilation and so does motion, the effect being noticeable in only in the extreme (massive objects or relativistic speeds). How would time dilation manifest for a chemical reaction? The reaction would slow down i.e. assuming the reaction is taking place in a spaceship travelling at 0.9c, an observer at rest will notice that the chemical reaction on the moving spaceship is taking longer than the same reaction at rest.

Cold also slows down chemical reactions. The mechanism of the slowing is different but the effect is equivalent i.e. it seems possible let the chemical reaction under normal conditions occur in a spaceship travelling at an appropriate speed such that the lengthened duration of the reaction is caused by time dilation, this duration being equal to the duration of the reaction at a lower temperature.

So, is cold equivalent to speed or gravity (with respect to time dilation)?

To reiterate, if the question is substandard, please say so and I'll delete it.

Gracias.

Agent Smith
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    I would like to opine that this is a very intriguing conceptual question, and illuminated a few gaps in my own understanding and spurred further questions. I think there is a tendency by some to down vote questions that at first glance seem a bit "off the wall" or light on mathematical jargon, which is disappointing for a knowledge-sharing site. – RC_23 Jan 19 '23 at 02:34
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    @RC_23, I apologized in advance because I know those who are experts will find the question silly or even insulting to science. – Agent Smith Jan 19 '23 at 03:28
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    It is not silly or insulting to science. A question like this that people like Einstein and Mach refused to handwave away is what has provided the biggest advances in science. – RC_23 Jan 19 '23 at 06:33

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The difference is that temperature may slow down some reactions (usually by making some activation energy less available in the environment), cold can also speed up other reactions. Think of the transition of gelatin from liquid to colloid (solid-ish), which must happen in the refrigerator. Or consider that virus particles may replicate at body temperature, but die at slightly higher temperature, which is why we get fevers when sick.

Time dilation, on the other hand, affects all clocks in exactly the same way. In special relativity, there is no experiment either of us can do to decide whether you’re moving and I’m stationary, or vice-versa.

rob
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  • May I propose a simplification of the scenario? If a universe consisted of only peoples A and B, with one clock each, and the only other things, two setups for the same chemical reaction, then can A or B determine whether the slowing down of the reaction is due to cold or speed? Off the top of me head, I won't be able to – Agent Smith Jan 18 '23 at 16:30
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    If the chemical reaction proceeds at a known rate, then it counts as a "clock." Observer A will be able to determine B's temperature by comparing B's reaction rate to B's clock. – rob Jan 18 '23 at 23:31
  • So the chemical reaction is also a clock and it should slow down at relativistic speeds, but only for the observer at rest. Cold, on the other hand slows down the reaction for the person in the same frame of reference as the observer and that's not time dilation. Gracias. – Agent Smith Jan 19 '23 at 00:55
  • I have a related question: if the average thermal motion of the atoms is indeed time dilated, can the outside observer say the item in question has lower temperature and lower internal energy? I presume this is equally or more than compensated for by the increase in bulk kinetic energy $(\gamma-1)mc^2$ – RC_23 Jan 19 '23 at 02:31
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    @RC_23 A redshifted or blueshifted blackbody spectrum is still a blackbody spectrum, with a different temperature. But in terms of the "zeroth law of thermodynamics" definition of temperature, you have to get into the weeds about whether two systems with constant relative velocity are ever really in thermal equilibrium with each other. For example, meteoroids in space are cold, and the Earth's upper atmosphere is cold, but a meteor in motion relative to Earth's atmosphere stops being cold. – rob Jan 19 '23 at 03:13
  • That is a good point, and brings up something else: if an object is moving toward me, its blackbody radiation appears blueshifted, i.e. hotter. But the individual motion of its atoms (if I could somehow see them), seems like it would be slower, implying it should seem colder. – RC_23 Jan 19 '23 at 06:40
  • @RC_23 It's a common misconception that temperature measures atomic speeds, but that's only true in a few common systems, such as an ideal gas without a spin degree of freedom whose molecular speeds follow a particular distribution. Temperature is about the effect that changes to internal energy have on entropy. – rob Jan 19 '23 at 13:24
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The effects are not really equivalent.

You could speed up a reaction by heating it. Or perhaps with a catalyst. OK, the reaction takes place at the same speed in both cases, but other things are different. Thermometers would have different readings for example. Or perhaps the air conditioner would turn on in one case but not the other.

mmesser314
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  • If all I can know/allowed to know is the duration of the chemical reaction, can I tell whether it's time dilation or cold? – Agent Smith Jan 18 '23 at 16:33
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    If you don't look at things that are different, all you will see is things that are the same. That is different from not having any differences. – mmesser314 Jan 18 '23 at 16:40
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No, cold is not equivalent to speed or gravity in that sense. Cold will prolong some types of chemical reaction- ie it will increase the time interval between the start and end of the reaction as measured by a clock in the rest frame in which the reaction occurs. Speed will not affect the duration of the reaction in its own rest frame.

Marco Ocram
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  • Ok, good answer, but if the reaction were to occur on a spaceship travelling at high speed, to me (at rest) the reaction will slow down, right? In other words cold, in a sense, even if not in the right sense, does mimic speed/gravity. – Agent Smith Jan 18 '23 at 22:39
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    Suppose I walk from one end of a room to the other, taking five seconds to do so. In the frame of a spaceship passing at 0.95c my five-second walk lasts about sixteen seconds. If I simply choose to walk more slowly, so the walk takes my ten seconds, it will seem to take thirty-two seconds in the frame of the spaceship. Would you consider that to be mimicking the effects of speed and gravity? – Marco Ocram Jan 19 '23 at 06:48
  • Indeed, it would, but only if my information is limited to your rest walking speed. It's a thought experiment akin to Einstein's locked in an elevator (no information at all but what your own weight). – Agent Smith Jan 19 '23 at 08:23
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I shall stress on "temperature" and "speed", not particularly on "cold"; without going into Special Relativity. And I shall put some mathematical expression for completeness, though I saw your no-math request.

In Thermodynamics there is a fundamental area known as Kinetic Theory. Among several of its consequences there is this link between temperature of a substance, and speed/velocity of the particles constituting that substance.

Assume a container filled with some sort of gas. That is, there are a lot of gas particles within it, whether $O_2$, $CO_2$ you name it. Now all these particles are in a state of constant, spontaneous, random motion (which is called Brownian Motion). And during this crazy movements, the particles collide with each other. The more energetic a particle is, the higher the chance of making a collision. And we have this well know expression for kinetic energy of a moving body: $\frac{1}{2}mv^2$ (m: body's mass, v: its speed). So clearly, the higher its speed, more energy it carries.
Now, when collision occurs, heat is generated. This is the fundamental origin of heat/temperature. No movement $\implies$ no heat. Also, there is this Equipartition Theorem, which results into the following equation (with simplification considered): \begin{equation} \frac{1}{2}mv^2 \propto k_BT \end{equation} ($k_B:$ Boltzmann Constant)
That is - temperature is very much linked with velocity (of constituent particles).

Let me know if it helps.

QuestionTheAnswer
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  • Which is the explanandum variable here? Does the kinetic energy (i.e. velocity) of the particles determine the temperature or vice versa? Also, when cooling the velocity of particles fall and that seems to be the opposite of what should happen for time dilation. – Agent Smith Jan 18 '23 at 18:15
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    As per your question, mine is an attempt to show the equivalence between temperature and speed. An equation with temperature on one side and velocity on the other means one gives information about the other; if temperature is known velocity can be figured out and vice versa. Lastly, your last point is not clear. – QuestionTheAnswer Jan 18 '23 at 18:25
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Here's another way in which time dilation is not equivalent to cooling.

Let's put the chemical reaction on a spaceship inside a spherical shell of radius 10 light seconds with walls that are impenetrable to spaceships. Let's park the spaceship in the center of the shell.

If the physicist on the spaceship manipulates the rate of the chemical reaction by adjusting the temperature, the rocket ship need not move and will not hit the sides of the sphere.

If the physicist wants to use time dilation, then the physicist will need to accelerate the rocket ship in some direction to a good fraction of the speed of light.

First, note this will only change the reaction rate for an observer at rest with respect to the spaceship. The physicist on the ship will not see a change in reaction rate -- that's already a major difference with respect to adjusting the temperature.

Second, the spaceship will after of order 10 seconds run into the walls of the container. That clearly didn't happen in the situation where temperature was used to control the reaction rate, so this is yet another difference between these two separate concepts.

Andrew
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    I understand now. If it's time dilation then for the observer moving with the chemical reaction, the reaction proceeds at the normal rate. So I couldn't possibly be experiencing time dilation if I detect the chemical reaction has slowed down because I'm in the same frame of reference as the reaction. – Agent Smith Jan 19 '23 at 00:49
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    @AgentSmith Exactly. – Andrew Jan 19 '23 at 00:52
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While this particular analogy might not be the best one, gravity and temperature are somehow related. Check "Unruh effect" and "Hawking radiation".

John
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  • I'll check 'em out. – Agent Smith Jan 18 '23 at 19:48
  • These are both effects of acceleration, but the question seems to be about constant-velocity time dilation. – rob Jan 19 '23 at 13:16
  • Well, s/he said "or gravity". So I only responded to that second half. Temperature is mysterious beast in physics, and who knows what new unexpected connections will surface up in future. – John Jan 19 '23 at 14:56