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When spacetime stretches, does both space and time stretch proportionally. That is, if you stretch Planck-length doesn't Planck-time also stretch proportionally? I find this to be a conundrum.

Qmechanic
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Baird1939
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    What does "stretch" mean here? – WillO Mar 02 '20 at 01:48
  • As an interpreter, I fail to see how the OP's question would not naturally arise from the post-GR formulation of "spacetime" as one single word, in comparison to the distinction between its morphemes in the answer by G. Smith, whose answers have usually engendered my sincere admiration. – Edouard Nov 15 '20 at 17:23
  • There's a book by Sklar, titled "Space, Time, and Spacetime", that may be helpful in understanding the functionality of time in the scale factor of GR. Physicists like Nikodem J. Poplawski (who has many cosmological papers available on Arxiv) have speculated that the distinction between physics above and below the Planck length may be somewhat artificial, but, as pointed out by G. Smith, verification of that possibility is impossible and likely to remain so. (Poplawski, consequently, specifies other means for falsifying his cosmological model.) – Edouard Nov 15 '20 at 18:04

1 Answers1

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When space-time stretches, does both space and time stretch proportionally.

No. For example, in the usual form of the Friedman metric, space stretches and time doesn’t. But the question is basically meaningless because in another coordinate system you could have both stretching.

If you stretch Planck-length doesn't Planck-time also stretch proportionally?

This is also a meaningless question. The Planck length and the Planck time are constants. As far as we know, they don’t change, even in an expanding universe.

Added in response to comments:

The Planck length is a unit of length like the meter. The Planck time is a unit of time like the second.

When space expands, as we believe it is doing on a cosmological scale, neither the meter nor the Planck length stretches. Instead, more meters or Planck lengths fit between, say, two galaxies than they did earlier. There is more space, measured in fixed units of length. Similarly, neither the second nor the Planck time stretches. It simply takes more seconds or Planck times for light to travel between those galaxies, measured in fixed units of time.

G. Smith
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  • How can we define an invariant Planck length without reference to some metric? – Charlie Mar 02 '20 at 20:14
  • The speed of light appears in the metric. If it required a metric to define it, things would be circular. Similarly $G$ and $h$ are not metric-dependent. In fact, $c$ and $h$ are now assigned exact numerical values, and are not measured quantities at all. – G. Smith Mar 02 '20 at 22:43
  • Is the name Planck length misleading then? If it physically represents some distance in space does that not require a choice of frame? – Charlie Mar 02 '20 at 22:54
  • The meter is also a length. Does it require a choice of frame? In every frame a meter stick at rest is a meter long. In every frame a Planck length at rest is a Planck length. Something that is a meter long in one frame is not a meter long in a boosted frame. Something that is a Planck length long in one frame is not a Planck length long in a boosted frame. – G. Smith Mar 02 '20 at 23:01
  • However, Planck-length is a metric, which includes ...per meter and Planck-time is a metric, which includes ...per second. All quantum metrics apply to barometric matter and energy, which is the frame of reference for all Planck constants. Dark-matter and energy is another frame of reference for we do not yet have verifiable metrics. I think I used the wrong frame of reference for space-time in my original question. – Baird1939 Mar 04 '20 at 20:20
  • “Metric” has a specific meaning in physics (coming from SR and GR), and when you use it in other ways physicists get confused. I don’t know of any physicist who would agree that “Planck-length is a metric”. “Quantum metric” is vague and not something there is any agreement on, since we have no accepted theory of quantum gravity. Dark matter and dark energy are not “frames of reference”. To successfully communicate with physicists, you must use physics terminology the way physicists do. – G. Smith Mar 04 '20 at 20:24
  • Finally “barometric” relates to air pressure, not baryons. – G. Smith Mar 04 '20 at 20:31
  • This Wikipedia article explains what “metric” means to physicists. – G. Smith Mar 04 '20 at 20:35
  • The Planck length is simply a particular length, which explains why it is called what it is called. Similarly, a meter is a particular length, and the Bohr radius is a particular length. – G. Smith Mar 04 '20 at 20:37
  • You are clearly much more learned than me. But I think you miss my point. Planck -length is expressed in ...per meter. And Plank-time is expressed in ...per second. Secondly, all Planck constants do not apply to dark-matter and dark-energy. – Baird1939 Mar 04 '20 at 20:38
  • No, the SI unit for the Planck length is meters, not “per meter”. Similarly for the Planck time. – G. Smith Mar 04 '20 at 20:40
  • I agree. It was my cut and paste error. I should had said "Baryonic". – Baird1939 Mar 04 '20 at 20:40
  • When space expands (such as we believe it is doing on a cosmological scale), neither the meter nor the Planck length stretches. Instead, more meters or Planck lengths fit between, say, two galaxies than they did earlier. There is more space, measured in fixed units of length. Does that help you understand how physicists think about expanding space? – G. Smith Mar 04 '20 at 20:44
  • I still think that Planck constants do not apply to dark-matter and dark-energy. Space-time see to me a phenomenon of dark-matter and dark-energy. Perhaps I should drop out of this forum where I clearly do not meet your standards. Bye. – Baird1939 Mar 04 '20 at 20:53
  • If you want to ask questions to learn how physicists understand the world, you should stay, and I hope you will. If you expect to voice non-mainstream opinions about physics without getting any pushback from physicists, you should go. The site sets the standards, which are that questions must be about mainstream physics. – G. Smith Mar 04 '20 at 20:58
  • You asked a question, and before it got closed as duplicative, you got an answer and further clarification via comments. Do you feel that this treatment is unfair? We never try to push people away if they accept the site’s rules. – G. Smith Mar 04 '20 at 21:05
  • @G. Smith -What is the observational or experimental evidence for the Planck length being inherently indivisible? (If I remember correctly, I've usually heard something like, "magnification of anything smaller than the Planck length would require magnification energy so intense that its mass would collapse that object into a black hole", or, "magnification of anything smaller than the Planck length would require more energy than is available in our observable region", but, after reading your replies to Baird1939, I'm expecting some simpler response like, "No evidence is required.") – Edouard Nov 15 '20 at 16:47
  • What makes this hard for me to grasp is partly the well-known variations in the speed of light through a "medium" (whose own definition might vary with continued discoveries of new subatomic particles), and partly the fact that the analogy between the speed of light and slower rates of passage between objects in space has varied (-in other words, that analogy has varied historically, with "historically" being used here in the everyday sense). – Edouard Nov 15 '20 at 17:11
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    @Edouard What is the observational or experimental evidence for the Planck length being inherently indivisible? I am not aware of any such evidence. We have no technology that can probe what happens at length scales as small as the Planck length. Furthermore, any such evidence would win the Nobel Prize and this hasn’t happened. – G. Smith Nov 15 '20 at 17:41